NEW METHODS FOR EXTRACTING ULTRAFAST WATER …core and an interfacial water shell. Each region has...

NEW METHODS FOR EXTRACTING ULTRAFAST WATER DYNAMICS AT

INTERFACES

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF CHEMISTRY

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Emily Elizabeth Fenn

September 2011

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/rp704hn7168

© 2012 by Emily Elizabeth Fenn. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii



http://purl.stanford.edu/rp704hn7168

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Michael Fayer, Primary Adviser


Hongjie Dai


Robert Pecora

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

v

Abstract

Bulk water exists as an extended hydrogen bond network in which hydrogen

bonds readily break and exchange. When water interacts with interfaces or exists in a

confined environment, the concerted orientational motions of water molecules that are

necessary for hydrogen bond network rearrangement can be disrupted. Water motions

become restricted, and the hydrogen bond dynamics slow down. Measuring how

quickly the hydrogen bond network rearranges and randomizes provides structural

information about the confined system. Such considerations are important in many

chemical, biological, and industrial processes.

Important questions arise as to how sensitive water dynamics are to the size of

the confining environment and how much the chemical composition of the interface

influences the dynamics. To answer these questions, ultrafast infrared (IR) pump-

probe and 2D IR vibrational echo techniques are used to measure population

relaxation, orientational relaxation, and spectral diffusion dynamics of water

molecules in a variety of confined environments. Orientational relaxation describes

how quickly water molecules rotate and randomize positions, thereby promoting

hydrogen bond exchange. Spectral diffusion measures how quickly water molecules

sample different environments and is characterized by the frequency-frequency

correlation function (FFCF). Population relaxation depends on how quickly

vibrational energy dissipates in a system and is extremely sensitive to changes in local

environment. Together, these experimental observables provide an extensive picture

of how water molecules behave dynamically in confinement and at interfaces.

It is shown that a two component model for population and orientational

relaxation accurately describes the dynamics for systems comprised of two types of

hydrogen bonding ensembles: waters that are hydrogen bonded to other waters and

waters at an interfacial region. Through a combination of spectroscopic and data

analysis techniques, the dynamics of these two environments become separable. This

two component model is first successfully applied to binary mixtures of water and a

vi

polyether compound, tetraethylene glycol dimethyl ether, and is shown to accurately

describe other two component systems.

The effects of confinement on water dynamics are studied by examining water

inside of reverse micelles (microemulsions that consist of a water pool surrounded by

a shell of surfactant molecules suspended in an organic phase). The surfactant

Aerosol-OT (AOT) is terminated by a charged sulfonate head group and forms reverse

micelles that range in size from 1.7 nm to 28 nm in diameter. Large reverse micelles

(diameter ≥ 4.6 nm) can be decomposed into two separate environments: a bulk water

core and an interfacial water shell. Each region has distinct dynamics that can be

resolved experimentally using the two component model developed for the water-

polyether mixtures. The core follows bulk water dynamics while interfacial water

shows slower dynamics. For large reverse micelles, the interfacial dynamics remain

independent with size, but smaller sizes exhibit even slower dynamics as the diameter

decreases further. To explore how the chemical composition of the interface

influences dynamics, the dynamics of water in AOT reverse micelles are compared to

water dynamics in reverse micelles made from the neutral surfactant Igepal CO-520.

It is found that the presence of an interface plays the major role in determining

interfacial water dynamics and not the chemical composition.

A two component model is also developed for spectral diffusion. The two

component model for spectral diffusion is an extended version of the center line slope

(CLS) analysis procedure, originally developed for single ensemble systems. The two

component CLS method works well for systems in which there is a bulk water

component, whose CLS behavior is known, and an interfacial region for which the

CLS behavior is not known. Using known spectral parameters and bulk water CLS

data, the interfacial CLS may be back-calculated. From the back-calculated CLS, the

FFCF for interfacial water may be determined. The two component CLS method is

tested for various model cases and then applied to experimental data for large AOT

reverse micelles. It is found that, similar to orientational relaxation behavior in large

AOT reverse micelles, the interfacial FFCFs vary little with increasing size.

vii

Acknowledgements

Graduate school has been a challenging experience, but it has also been

rewarding. Solving problems, seeing experiments through to the end, and finally

understanding a small piece of the universe have made my time here at Stanford a

formative set of years that have not only encouraged me to be a better scientist but

also to grow as an individual. I would like to thank a wonderful group of family

members, friends, and colleagues who have helped me along the way with their

constant love and support.

I consider myself extremely fortunate to have had the privilege of working in

Prof. Michael Fayer’s research group. Mike is extremely devoted to his students and

is always willing to help you work through problems and discuss research. He has

been a wonderful advisor to me, and I cannot thank him enough for his dedicated

support. I have enjoyed working with all the members of the Fayer Group during my

time here, as they are a welcoming group and an invaluable resource for

troubleshooting problems and talking through ideas. David Moilanen was an excellent

mentor who thoroughly trained me on the laser system. Daryl Wong, my stalwart

companion in Room 124, has been the best co-worker one could ask for. Chiara

Giammanco is the newest addition to our ‘Team Agua,’ and it has been fun working

with her despite our short time together. Jean Chung has been a great friend and lab

mate from our very first year and helped edit my thesis. I also thank Megan Thielges,

Kendall Fruchey, Daniel Rosenfeld, Adam Sturlaugson and Zsolt Gengeliczki for all

of their help and friendship over the years. Prof. Nancy Levinger from Colorado State

University has been a caring and supportive mentor to me at various points in my

graduate career, and I am very happy to have had the pleasure of working with her

throughout the years.

I would also like to acknowledge former co-workers from Prof. Robert Field’s

research group at MIT who helped me find my niche in physical chemistry, especially

Jeff Kay, Hans and Kate Bechtel, and Vladimir Petrovic. Vladimir first introduced me

to optical systems and taught me many things about working in a laser lab. Bob Field

was very supportive of his undergraduate researchers and always happy to help us

learn more.

viii

My parents, Pamela and Alan Fenn, taught me at an early age to appreciate

both the arts and the sciences and to balance work and home life, a mentality that has

been indispensable throughout my entire life. They have cheered me on at everything

I do. My brother, Ben, has always been my sanity check, whether it’s by making me

laugh or taking his little sister to see a movie or a baseball game.

I have met many good friends throughout childhood, high school, college, and

graduate school, and I will forever cherish the friendships I have made. Know that I

appreciate everyone of you and that I could never have come so far without you.

Lastly, I am grateful to Adam Lesser for being a loving companion and a

faithful friend for my entire time at Stanford. Our projects, trips, and culinary

adventures will remain some of my happiest memories from graduate school, and I am

very happy to return with him to Massachusetts to start the next stage of our life

together.

ix

Table of Contents

Abstract ........................................................................................................................... v

Acknowledgements ...................................................................................................... vii

Table of Contents .......................................................................................................... ix

List of Figures ............................................................................................................... xii

List of Tables ............................................................................................................... xvi

Chapter 1 Probing Hydrogen Bond Dynamics on Ultrafast Time Scales ...................... 1

1.1 Bulk and Interfacial Water ................................................................................... 1

1.2 Ultrafast Infrared Spectroscopy ............................................................................ 2

1.3 References ............................................................................................................ 6

Chapter 2 Experimental Design .................................................................................... 11

2.1 Introduction ........................................................................................................ 11

2.2 Ti:Sapphire Oscillator ........................................................................................ 13

2.3 Pulse Stretcher .................................................................................................... 16

2.4 Regenerative Amplification Cavity .................................................................... 21

2.5 Pulse Compressor ............................................................................................... 23

2.6 Optical Parametric Amplifier ............................................................................. 25

2.7 Mid-Infrared Spectrometer ................................................................................. 29

2.7.1 Beam Paths in the Mid-Infrared Spectrometer ............................................ 29

2.7.2 2D IR Vibrational Echo Spectroscopy ........................................................ 31

2.7.3 Transient Absorption Pump-Probe Spectroscopy ....................................... 34

2.8 References .......................................................................................................... 37

Chapter 3 Theoretical Background ............................................................................... 39

3.1 Introduction ........................................................................................................ 39

3.2 The Absorption Line Shape and Broadening Mechanisms ................................ 40

3.3 Nonlinear Response Theory ............................................................................... 43

3.4 Diagrammatic Perturbation Theory .................................................................... 48

3.5 2D-IR Spectroscopy ........................................................................................... 50

3.5.1 The Dual Scan Method ................................................................................ 50

3.5.2 Phasing 2D IR Spectra ................................................................................. 51

3.6 Pump-Probe Spectroscopy .................................................................................. 53

3.7 The Orientational Correlation Function ............................................................. 54

3.7.1 Introduction to the Orientational Correlation Function ............................... 54

3.7.2 Debye Model ............................................................................................... 55

x

3.7.3 Ivanov and Anderson Models ...................................................................... 57

3.7.4 Laage & Hynes Extended Jump Model ....................................................... 59

3.8 References .......................................................................................................... 62

Chapter 4 Water Dynamics and Interactions in Water – Polyether Binary Mixtures .. 65

4.1 Introduction ........................................................................................................ 65

4.2 Experimental Procedures .................................................................................... 67

4.3 Results and Discussion ....................................................................................... 68

4.3.1 Absorption Spectroscopy ............................................................................. 68

4.3.2 Population Relaxation ................................................................................. 70

4.3.3 Analysis of the Spectra with the Two Component Model .......................... 76

4.3.4 Orientational Relaxation .............................................................................. 79

4.4 Concluding Remarks .......................................................................................... 90

4.5 References .......................................................................................................... 91

Chapter 5 Water Dynamics at Neutral and Ionic Interfaces ......................................... 95

5.1 Introduction ........................................................................................................ 95

5.2 Experimental Procedures .................................................................................... 98

5.3 Results and Discussion ....................................................................................... 99

5.3.1 Absorption Spectroscopy ............................................................................. 99

5.3.2 Population Relaxation and Orientational Relaxation ................................ 102

5.4 Concluding Remarks ........................................................................................ 110

5.5 References ........................................................................................................ 111

Chapter 6 Water Dynamics in Small Reverse Micelles in Two Solvents: Two-

Dimensional Infrared Vibrational Echoes with Two-Dimensional Background

Subtraction .................................................................................................................. 113

6.1 Introduction ...................................................................................................... 113

6.2 Experimental Procedures .................................................................................. 116

6.3 Results and Discussion ..................................................................................... 120

6.3.1 Infrared Absorption Spectroscopy and Pump-Probe Experiments ............ 120

6.3.2 2D IR Vibrational Echo Experiments ........................................................ 126


6.5 References ........................................................................................................ 139

Chapter 7 Extracting 2D IR Frequency-Frequency Correlation Functions from Two

Component Systems ................................................................................................... 143

7.1 Introduction ...................................................................................................... 143

7.2 Theoretical Development ................................................................................. 147

xi

7.2.1 CLS Method for a Single Component System .......................................... 147

7.2.2 Extension of the CLS Method to Two Components ................................. 150

7.2.3 Model Calculation Details ......................................................................... 158

7.3 Testing the Two Component CLS Method ...................................................... 159

7.3.1 Practical Application of the Two Component CLS Algorithm ................. 159

7.3.2 Non-Overlapping Bands ............................................................................ 162

7.3.3 Overlapping But Distinguishable Bands ................................................... 165

7.3.4 Unresolved Overlapping Bands ................................................................. 166

7.3.5 Degree of Error in the Two Component CLS Method .............................. 172


7.5 References ........................................................................................................ 174

Chapter 8 Spectral Diffusion of Water Molecules in Reverse Micelles .................... 179

8.1 Introduction ...................................................................................................... 179

8.2 Experimental Procedures .................................................................................. 182

8.3 Results and Discussion ..................................................................................... 186

8.3.1 Linear Absorption and Pump-Probe Spectroscopy ................................... 186

8.3.2 Spectral Diffusion in Large Reverse Micelles ........................................... 194

8.3.3 Spectral Diffusion in Igepal Reverse Micelles .......................................... 203

8.3.4 Spectral Diffusion in Small Reverse Micelles ........................................... 204


8.5 References ........................................................................................................ 208

Appendix A Derivation of the Homogeneous and Inhomogeneous Components of the

Line Shape Function ................................................................................................... 211

A.1 Homogeneous Component ............................................................................. 211

A.2 Intermediate Components ............................................................................... 212

A.3 Inhomogeneous Component ........................................................................... 212

Appendix B Derivation of the Anisotropy for a Two Component System ............... 213

B.1 Anisotropy for a Single Component System .................................................. 213

B.2 Anisotropy for a Two Component System ..................................................... 214

Appendix C Details for 2D IR Background Subtraction ........................................... 217

C. 1 Experimental Procedures ............................................................................... 217

C.2 MATLAB Routines ........................................................................................ 218

C.3 Notes ............................................................................................................... 219

xii

List of Figures

Figure 2.1 Flow chart describing the sequence of laser systems that produce ultrafast

mid-IR pulses for 2D IR and pump-probe experiments ............................................... 12

Figure 2.2 Schematic of the Ti:Sapphire oscillator and optics that prepare the

oscillator output for the stretcher.. ................................................................................ 14

Figure 2.3 Schematic of the pulse stretcher.. ............................................................... 17

Figure 2.4 Schematic of the regenerative amplification cavity. .................................. 21

Figure 2.5 Schematic of the pulse compressor. ........................................................... 24

Figure 2.6 Schematic of the OPA used to create near-IR signal and idler frequencies

and subsequent difference frequency mixing in AgGaS2 to produce 4 µm .................. 26

Figure 2.7 Schematic of the mid-IR spectrometer. ...................................................... 30

Figure 2.8 Pulse sequences for ultrafast 2D IR and pump-probe experiments. .......... 33

Figure 2.9 Polarization-selective pump-probe set-up .................................................. 35

Figure 3.1 Feynman diagrams for the nonlinear third order response functions ......... 48

Figure 3.2 Proposed mechanism for hydrogen bond switching. ................................. 60

Figure 4.1 Molecular structures of poly(ethylene oxide) (PEO) and TEGDE. ........... 65

Figure 4.2 FT IR absorption spectra of the OD stretch of HOD in H2O for eight

water/TEGDE mixtures and water ............................................................................... 69

Figure 4.3 Population relaxation data for the OD stretch of HOD in H2O in eight

water/TEGDE mixtures and water at the center wavelengths ...................................... 71

Figure 4.4 Viscosity data for mixtures of water and TEGDE ..................................... 75

Figure 4.5 Results of two component FT IR spectral fitting. ...................................... 76

Figure 4.6 Plot of the orientational relaxation of water, r(t), for the 50:1 solution and

bulk water ..................................................................................................................... 81

Figure 4.7 A calculated anisotropy curve using the two component model for

anisotropy ..................................................................................................................... 82

Figure 4.8 Simultaneous fits (solid curves) to R(t) and P(t) data (symbols) for the 50:1

and 7:1 solutions ........................................................................................................... 83

xiii

Figure 5.1 Molecular structures for the surfactants Igepal CO-520 (neutral head group

containing a hydroxyl) and AOT (ionic sulfonate head group with a sodium counter

ion). ............................................................................................................................... 96

Figure 5.2 IR absorption spectra of the OD stretch of 5% HOD in H2O for Igepal

w0=20, AOT w0=25, and bulk water. .......................................................................... 100

Figure 5.3 Vibrational population relaxation data ..................................................... 101

Figure 5.4 Anisotropy data for bulk water and Igepal w0=20 and AOT w0=25 which

both have water nanopool diameters of 9 nm. ............................................................ 105

Figure 5.5 Data analysis with three component model. ............................................ 106

Figure 6.1 Molecular structure of AOT. ..................................................................... 114

Figure 6.2 FT IR absorption spectra for bulk water and water in AOT/isooctane and

AOT/CCl4 reverse micelles ........................................................................................ 121

Figure 6.3 Population relaxation data for water in the three sizes of reverse micelles

showing the invariance with nonpolar phase. ............................................................. 124

Figure 6.4 Orientational relaxation data for water in the three sizes of reverse

micelles, again showing the invariance with the nonpolar phase. .............................. 125

Figure 6.5 2D IR correlation spectra for w0=2/CCl4 at a range of Tw values ............ 127

Figure 6.6 Experimental CLS data for AOT w0 = 2 .................................................. 128

Figure 6.7 Interferogram data comparing water in AOT reverse micelles in different

solvents ....................................................................................................................... 129

Figure 6.8 Interferogram data showing the beat subtraction procedure. ................... 130

Figure 6.9 FT IR spectra of the solvents and stock solutions relevant to the echo beat

subtraction study ......................................................................................................... 133

Figure 6.10 Cartoon illustrating how topography changes through movements of

individual sulfonate head groups (green circles) in the surfactant shell of the reverse

micelle can change the environment felt by the water molecules. ............................. 137

Figure 7.1 Calculated 2D IR spectra for bulk water at Tw = 0.2 ps and Tw = 2 ps .... 147

Figure 7.2 CLS decay curve for bulk water .............................................................. 148

Figure 7.3 Linear IR absorption spectra for water (5% HOD in H2O) inside the AOT

w0=12 reverse micelle (black line) ............................................................................. 153

xiv

Figure 7.4 Frequency and Tw-dependent fraction of bulk water for the AOT w0=12

reverse micelle system. ............................................................................................... 154

Figure 7.5 Flow chart illustrating the algorithm that calculates the center line data and

FFCF for a second component from known information ........................................... 161

Figure 7.6 Representative center line data used in the two component CLS algorithm.

.................................................................................................................................... 162

Figure 7.7 Calculated 2D IR spectra for non-overlapping bands at Tw = 0.2 ps (a) and

Tw = 5 ps (b). ............................................................................................................... 163

Figure 7.8 Model case 1 for non-overlapping bands ................................................. 164

Figure 7.9 Model case 1 for overlapped but distinguishable bands .......................... 165

Figure 7.10 Model case 1 for overlapping bands. ..................................................... 167

Figure 7.11 Model case 1 for overlapping bands ...................................................... 168

Figure 7.12 CLS results for the second model case of overlapping bands ................ 170

Figure 7.13 CLS decay, calculated around the 2D IR maxima, for the first model case

(Table 7.1 with component 2 center at 2550 cm-1

) without decomposing the data into

different components .................................................................................................. 171

Figure 7.14 CLS decay, calculated around the 2D IR maxima, for the second model

case (Table 7.3 with component 2 center at 2565 cm-1

) without decomposing the data

into different components ........................................................................................... 172

Figure 8.1 Molecular structures for AOT and Igepal CO-520 ................................... 180

Figure 8.2 Linear IR absorption studies. ................................................................... 189

Figure 8.3 Linear FT IR absorption spectra for Igepal w0=12 (blue) AOT w0= 16.5

(red). ........................................................................................................................... 190

Figure 8.4 Population relaxation decays for AOT w0=12 (green), AOT w0=16.5 (red),

and Igepal w0=12 (blue) at a detection wavelength of 2589 cm-1

. ............................. 190

Figure 8.5 Anisotropy (orientational relaxation) data for AOT w0=12 (green), AOT

w0=16.5 (red), and Igepal w0=12 (blue) at a detection wavelength of 2589 cm-1

...... 192

Figure 8.6 2D IR correlation plots for AOT w0=16.5 at Tw = 0.2, 1, and 4 ps. ......... 196

Figure 8.7 2D IR correlation plots for AOT w0=2 at Tw = 0.2, 3, and 15 ps. ............ 197

Figure 8.8 Representative center line data for the back-calculation of the interfacial

CLS ............................................................................................................................. 199

xv

Figure 8.9 Interfacial CLS data for AOT w0=16.5, 12, and 7.5. ............................... 200

Figure 8.10 CLS data for Igepal w0=12 (blue squares) and AOT w0=16.5 (red circles),

showing close agreement between the samples .......................................................... 204

Figure 8.11 CLS data for small reverse micelles: AOT w0=2, 4, and 7.5. ................ 205

xvi

List of Tables

Table 4.1 Water/TEGDE Population Relaxation Fitting Parameters. ......................... 72

Table 4.2 Fitting Parameters for Spectra in Figure 4.5. .............................................. 77

Table 4.3 Parameters from Simultaneous Fits to the R(t) and P(t) Data ..................... 87

Table 5.1 Parameters for Population and Orientational Relaxation for Water in w0=20

Igepal Reverse Micelles (2576 cm-1

). ai’s – fractional populations; T1’s – lifetimes;

r’s – orientational relaxation times. ........................................................................... 108

Table 6.1 Wavelength-dependent vibrational relaxation times for AOT reverse

micelles in CCl4 and isooctane. .................................................................................. 122

Table 6.2 Two component model vibrational lifetimes and orientational relaxation

parameters for w0=7.5 reverse micelles in CCl4 and isooctane. ................................. 126

Table 6.3 Biexponential fit parameters for CLS data for w0=2/CCl4. Ai – amplitudes;

ti – time constants; y0 – offset. .................................................................................... 127

Table 6.4 Frequency-frequency correlation function parameters for AOT w0 = 2. Γ –

homogeneous line width; Δi – amplitudes; ti – time constants. .................................. 134

Table 6.5 Biexponential fit parameters for beat subtracted w0=2/isooctane and

w0=2/isooctane without beat subtraction. ................................................................... 135

Table 7.1 First Model Case FFCF Parameters. ......................................................... 159

Table 7.2 Parameters Obtained for Component 2 Via Eq.7.34 and Simultaneous

Fitting. ........................................................................................................................ 169

Table 7.3 Second Model Case Parameters. ............................................................... 169

Table 8.1 Population and Orientational Relaxation Parameters for Large and

Intermediate Reverse Micelles. .................................................................................. 188

Table 8.2 Population Relaxation Parameters for Small Reverse Micelles. ............... 191

Table 8.3 Population and Orientational Relaxation Parameters for Igepal w0=12. ... 193

Table 8.4 Exponential Fit Parameters to Raw CLS Data for Large and Intermediate

Reverse Micelles. a0 – drop from 1; ai – amplitude; ti – time constant; y0 - offset .. 199

Table 8.5 Interfacial FFCF Parameters for Large and Intermediate Reverse Micelles.

.................................................................................................................................... 201

Table 8.6 FFCF Parameters for Small and Intermediate Reverse Micelles. ............. 206

1

Chapter 1 Probing Hydrogen Bond Dynamics on

Ultrafast Time Scales

1.1 Bulk and Interfacial Water

While water as a bulk liquid has many fascinating and useful properties, such

as a high heat capacity, high surface tension, and the ability to dissolve a wide range

of compounds, many applications require water molecules to be present in distinctly

non-bulk environments. In non-bulk environments, water molecules are found in

cramped spaces or closely associated with ions, organic molecules, biological

structures, and interfaces. Interfaces can be charged or neutral and hydrophilic or

hydrophobic. For example, in chemistry, water molecules can participate in

heterogeneous catalysis where reactions take place at the junction of two interfaces.1-3

In geology, interfacial water molecules affect ion adsorption,4,5

mineral dissolution,6-8

and the structural and chemical properties of zeolites.9-11

Industry abounds with

examples of interfacial water molecules such as water in ion exchange resins which

are used for purifying water and other compounds.12,13

Proton transport across

hydrated membranes, via hydrogen bond exchange of water molecules, is necessary

for completing the electrochemical circuits of fuel cells.14,15

In biology, water is

almost never found in its bulk form and instead is often found in crowded cellular

environments in constant contact with organelles, proteins, and other biological

structures and compounds.16

The presence of water is often responsible for proper

protein function and folding mechanisms17-21

and is also an important consideration in

designing pharmaceuticals.22-24

Water generally interacts with interfaces and solutes through hydrogen bonds.

In the bulk, water molecules only interact with other water molecules, forming an

extended network of hydrogen bonds that are continually rearranging and exchanging

with one another. The currently accepted theory of hydrogen bond exchange through

a mechanism called jump reorientation25,26

will be discussed in detail in Chapter 3, but

2

it should be noted here that a water molecule exchanges hydrogen bonds in a

concerted manner involving simultaneous motions of water molecules in its first and

second solvation shells.25,26

The water hydrogen bonding network remains intact

because of these concerted motions. In addition, hydrogen bond exchange requires the

water molecules to make large angular jumps that effectively allow water molecules to

swap hydrogen bonding partners. As a result, the jump reorientation mechanism

suggests that hydrogen bond exchange is not a diffusive process. Water molecules

typically undergo hydrogen bond rearrangement on a time scale of ~1.7 picoseconds

(ps).27

The presence of solutes and interfaces can disrupt the jump reorientation

mechanism, thus slowing down the process of hydrogen bond rearrangement and

exchange.16,27-46

A key question arises as to how much the hydrogen bond

rearrangement dynamics of water slow down in the presence of interfaces. In

addition, how does the chemical composition of an interface or solute affect the

dynamics? Does it matter whether an interface is hydrophilic or hydrophobic, charged

or neutral? In a confined environment, does the size of the confining cavity matter?

This thesis will address these questions in detail. In some systems there exist both

bulk and interfacial water environments, and it is often challenging to separate the

contributions from each species. The bulk environment dynamics are well understood,

but the interfacial dynamics are generally unknown. This thesis presents recent

experimental and data analysis techniques that successfully decouple interfacial water

dynamics from bulk dynamics.

1.2 Ultrafast Infrared Spectroscopy

Water dynamics, including hydrogen bond rearrangement, take place on the

picosecond time scale.47-51

The femtosecond time resolution required to measure these

processes can be achieved using ultrafast infrared spectroscopy. Ultrafast laser pulses

can be routinely made in the laboratory due to recent advances in solid state laser

technology, including Ti:Sapphire oscillators and regenerative amplifiers.52

In order

to use the ultrafast laser pulses to probe the hydrogen bonding dynamics of water, the

pulses must be converted to the mid-infrared (mid-IR) region of light which falls

3

between 3-8µm. Using nonlinear optical processes, the laser pulses are converted to

~4 µm light with a pulse duration of ~70 fs and ~230 cm-1

of bandwidth. The mid-IR

light is used to excite the hydroxyl stretch of the water molecules. Infrared

spectroscopy is an extremely useful experimental technique for studying equilibrium

dynamics in the condensed phase because molecular vibrations in the condensed phase

are extremely sensitive to local environments. Because infrared light excites

molecular vibrations, the sample is not chemically altered during the experiment.

In bulk water, the hydroxyl stretch shows a broad linear infrared (IR)

absorption spectrum because there is a large distribution in the lengths and strengths of

hydrogen bonds in the condensed phase. Strong hydrogen bonds to a hydroxyl will

effectively lengthen the hydroxyl bond length, thus shifting the vibrational frequency

to lower frequency (red shift). In contrast, weak hydrogen bonds will cause a blue

shift. The experiments in this thesis use water that consists of 5% HOD in H2O. The

OD stretch, which absorbs around 2509 cm-1

(~4 µm), is excited and observed in the

experiments. The OH stretch has overlapping symmetric and anti-symmetric

stretching modes while the OD stretch is an isolated mode. The dilute amount of OD

probe eliminates effects from vibrational excitation transfer.53,54

Molecular dynamics

(MD) simulations suggest that using a small amount of OD does not disrupt water’s

natural hydrogen bonding network and that the OD stretch is an accurate reporter of

water dynamics.55

When water is not in bulk form, the linear IR spectrum of the OD stretch can

change. A blue shift in the overall spectrum typically means that there exists an

ensemble of weakly hydrogen bonded water molecules. This type of shift can occur,

for instance, when water interacts with a weakly hydrogen bonding solute, such as the

bromide ion in solutions of water and sodium bromide.31,32

The blue shift has also

been attributed to the relative strength and directionality that the electric field of a

solute exerts on the water OD bond vector.56

For example, a bromide ion exerts a

more diffuse electric field due to its size than, for example, a smaller fluoride ion and

therefore causes a larger blue shift. With either interpretation, linear IR spectra can

provide much information concerning the types and relative populations of hydrogen

bonding species in an aqueous environment.33

4

Linear IR spectra cannot provide dynamic information, so ultrafast infrared

spectroscopy is used to fill this role.57

When an electric field interacts resonantly with

a vibrational transition in a sample, a coherent superposition of the ground and first

excited states can arise. The resulting non-equilibrium charge distribution creates a

time-dependent macroscopic polarization that emits an electric field.58,59

When an

ensemble of vibrational transitions is excited, structural evolution of the environment

will cause the phase relationships between the oscillators to decay, leading to a

process called dephasing. Nonlinear four wave mixing ultrafast infrared experiments

are used to manipulate the quantum pathways by which a system evolves and,

depending on the light-matter interactions induced in the sample, they can distinguish

between different time scales and processes that contribute to hydrogen bond

dynamics.

Transient absorption polarization-selective pump-probe spectroscopy is an

example of a four wave mixing experiment that can measure the population relaxation

and orientational relaxation dynamics of the water molecules. Population relaxation

describes how quickly vibrational energy dissipates in a system and is characterized

by a time constant called the vibrational lifetime. In more constrained systems, certain

pathways that promote vibrational relaxation that were once available in bulk water

may no longer be accessible, thereby slowing down population relaxation.

Orientational relaxation describes how quickly water molecules rotate in solution and

is obtained by measuring the anisotropy. Because water hydrogen bond

rearrangement requires large angular motions (rotations), measuring orientational

relaxation determines how quickly water hydrogen bond exchange can occur.25,26

Two-dimensional infrared (2D IR) experiments, also involving four wave

mixing, measure a process called spectral diffusion. Spectral diffusion is described by

the frequency-frequency correlation function (FFCF) which determines the likelihood

that a vibrational chromophore excited at a certain frequency will have the same

frequency after a given amount of time. The frequency can change because of

structural evolution of the hydrogen bond network. 2D IR spectroscopy has been used

to measure spectral diffusion in a wide range of systems from bulk water47,50,60-64

and

other hydrogen bonding systems31,65,66

to proteins and other biological systems.67-76

5

2D IR spectroscopy has also been used to characterize systems that undergo coherence

transfer,77

chemical exchange,78-81

and isomerization.82,83

In addition, 2D IR

spectroscopy can distinguish between homogeneous and inhomogeneous broadening

processes. Linear IR absorption spectroscopy is usually unable to do this because the

IR line shape is a convolution of the homogeneous and inhomogeneous line widths,

and it is often impossible to deconvolve the two contributions accurately.

Homogeneous broadening arises from extremely fast processes such as rapid motions

of the solvent or surroundings.84

Inhomogeneous broadening arises when processes

occur on a longer time scale than the 2D IR pulse sequence.58

The FFCF contains

both homogeneous and inhomogeneous components. Diagrammatic perturbation

theory can be used to calculate all linear and nonlinear optical experimental

observables from the FFCF parameters.59

The FFCF therefore provides valuable

chemical, structural, and spectroscopic pieces of information about a system.

Chapter 2 in this thesis provides more detail about the nonlinear response

theory that governs the pump-probe and 2D IR experiments and includes a discussion

on broadening effects and diagrammatic perturbation theory by way of Feynman

diagrams. Chapter 2 also discusses the historical treatment of the orientational

correlation function in the context of pump-probe experiments, leading up to the

theory of jump reorientation as presented by Laage and Hynes.25,26

Chapter 3 outlines

the laser system used for the experiments and also the experimental design of the

pump-probe and 2D IR spectrometer.

Chapter 4 discusses the development of a two component model used to

interpret pump-probe population and orientational relaxation data for water-polyether

binary mixtures.40

Chapter 5 extends the two component model to a system of three

components and also compares the effects of chemical composition of the interface on

the dynamics of confined water.41

The behavior of confined water, as explained in

Section 1.1, is a relevant topic in biology. Since biological systems are prone to

scattering, reverse micelles are useful systems for modeling confined water, as they

form optically clear solutions of water pools surrounded by surfactant molecules.

Chapter 5 compares the dynamics of water inside of reverse micelles made of Aerosol-

6

OT (AOT) with ionic head groups and Igepal CO-520 with neutral hydroxyl head

groups.

Chapter 6 examines spectral diffusion of water in small AOT reverse micelles

and presents a solvent-dependent study that determines whether the identity of the

nonpolar phase of the reverse micelle solutions affects the dynamics.42

In addition,

Chapter 6 discusses some anomalous findings obtained during the solvent-dependent

study and presents a data analysis procedure that corrects for such anomalous

behavior. Chapter 7 presents a new data analysis procedure for interpreting 2D IR

spectra with a two component model from which the spectral diffusion of water at the

interface may be explicitly separated from the spectral diffusion of bulk water.85

Lastly, Chapter 8 examines the dynamics of water for a full range of sizes of AOT

reverse micelles.86

A comparison between AOT and Igepal large reverse micelles is

also presented. Chapter 8 utilizes both the two and three component models of

population and orientational relaxation presented in Chapters 4, 5, and 6, in addition to

the two component spectral diffusion model of Chapter 7 to determine the interfacial

dynamics of water inside of large AOT reverse micelles.

1.3 References

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J. L.; Fayer, M. D. J. Chem. Phys. 2004, 121, 12431.

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Fayer, M. D. Chem. Phys. Lett. 2004, 386, 295.

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108, 10957.

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122, 054506.

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2011, ASAP, DOI:10.1021/jp206903k.

11

Chapter 2 Experimental Design

2.1 Introduction

The dynamics of water explored in this thesis occur on a picosecond time scale

and can be probed using ultrafast infrared laser pulses. The experimental set-up is

designed to meet several goals. Firstly, the laser system must generate short enough

laser pulses (on the order of tens of femtoseconds) to probe the picosecond dynamics.

Secondly, the laser pulses must be converted into the mid-infrared (mid-IR) region of

light at ~4 µm. Additionally, the laser pulses must be mechanically manipulated

through a system of beam splitters and delay stages so that the proper interactions with

the sample are produced. An appropriate detection system must also be available to

measure the infrared experimental signal. These four requirements are met with the

laser system outlined briefly in Figure 2.1. Each component will be described in more

detail subsequently, but first a brief introduction to the components is useful for

understanding the overall goals of the system.

The first part of the laser system is a home-built solid-state Titanium Sapphire

(Ti:Sapphire) oscillator. Ti:Sapphire oscillators can produce weak laser pulses of

short pulse duration (less than 10 femtoseconds if transform-limited1) and large

bandwidth (up to 70 nm). The oscillator produces these pulses at ~80 MHz repetition

rate, but the overall energy is only ~5 nJ/pulse. This weak pulse energy is inadequate

for producing infrared (IR) light. In order to achieve greater pulse energy, the

oscillator output is seeded into a commercial regenerative amplifier system which

selects individual pulses from the oscillator and amplifies them by a factor of 1000000

to achieve ~1.5 mJ/pulse at a 1 kHz repetition rate. The regenerative amplifier system

is composed of three compartments: the pulse stretcher, regenerative amplification

cavity, and the pulse compressor. Each compartment will be discussed in the

following sections. The regenerative amplifier output pumps a highly modified

commercial optical parametric amplifier (OPA) to produce near-IR light via nonlinear

optical processes. In order to produce mid-IR frequencies, the OPA output is

12

difference frequency mixed in a AgGaS2

crystal. The resulting mid-IR light is sent

into the mid-IR spectrometer which contains the necessary optics and detection system

for the nonlinear ultrafast spectroscopic experiments discussed in this section, namely

the polarization-selective pump probe and 2D IR experiments.

Figure 2.1 Flow chart describing the sequence of laser systems that produce ultrafast mid-IR pulses for 2D IR and pump-probe experiments.

In order for these nonlinear experiments to produce viable data, it is crucial

that each component in the laser system works at peak performance. A single error in

alignment or timing electronics can greatly degrade the performance of the laser

system. Fortunately, ultrafast laser spectroscopy has benefitted from recent advances

in solid state laser design, infrared detection, and motion control. Atmospheric

controls, such as temperature control and air filtration, as well as the damping of room

Ti:Sapphire Oscillator84 MHz; λc=800 nm;

~50 nm FWHM; ~20 fs pulses; 5 nJ/pulse; p-polarized

Pulse Stretcher84 MHz; λc=800 nm;

~50 nm FWHM; >100 ps pulses; p-polarized

Regenerative Amplifier1 kHz; λc=800 nm;

30 nm FWHM; >100 ps pulses; 1.4 mJ/pulse; s-polarized

Pulse Compressor1 kHz; λc=800 nm;

30 nm FWHM; ~ 40 fs pulses; 1 mJ/pulse; p-polarized

Optical Parametric Amplifier1 kHz; total energy ~ 130 µJSignal: ~1.3 µm; p-polarizedIdler: ~2.0 µm; s-polarized

Difference Frequency Mixing1 kHz; λc ~ 4 µm;

~230 cm-1 FWHM; ~70 fs pulses4 µJ/pulse; p-polarized

Mid-IR Spectrometer

13

vibrations through building and laser table design have also contributed to the

successes of ultrafast infrared spectroscopy.

2.2 Ti:Sapphire Oscillator

The Ti:Sapphire oscillator is a home-built device based on a design by

Kapteyn and Murnane.2

To achieve lasing, the Ti:Sapphire rod is pumped with 3.4 W of 532 nm light

produced by a Spectra-Physics Millennia VsJ CW diode laser. The Millennia output

enters the cavity through the back of the first curved mirror (CM1) and is focused into

the rod with a 10 cm focal length lens (L1). The resulting fluorescence from the rod is

then steered onto the centers of the OC and HR. A beam height of 9 cm must be

maintained throughout the cavity. The back reflection from the OC is then aligned

onto the fluorescence, a process best observed at a point in between prisms P1 and P2.

The back reflection from the HR is then aligned onto the incoming beam. Provided

that the cavity optics have been placed in their correct positions (or as close as

possible), small adjustments to the HR should allow the cavity to start lasing. After

this point, adjustments may be made to the HR, OC, curved mirror translations, prism

insertion, lens, and the rod translation to optimize the cavity output.

All of the optics in the oscillator cavity were purchased from

Kapteyn-Murnane. Figure 2.2 shows the optical layout of the oscillator. The

oscillator cavity is in a ‘Z’ configuration (an ‘X’ configuration is an alternative

layout). The middle section of the ‘Z’ consists of a set of curved mirrors (focal length

5 cm) separated by ~10 cm. In between these mirrors is a 5 mm-long Ti:Sapphire rod.

The right-most arm of the oscillator in Figure 2.2 is terminated by the output coupler

(OC), a mostly reflective optic which allows a small percentage of the laser cavity

energy to travel through. The other arm of the oscillator contains two prisms (P1 and

P2) for dispersion compensation and a high reflector (HR) at the end. The total cavity

length between the two end mirrors (OC and HR) is ~180 cm, yielding a round trip

time of ~12 ns.

14

Figure 2.2 Schematic of the Ti:Sapphire oscillator and optics that prepare the oscillator output for the stretcher. L1, L2, L3 – lenses; CM1, CM2 – curved mirrors; P1, P2 – prisms; HR – high reflector; OC – output coupler; PS – periscope; PD – photodiode.

When lasing is first achieved, the oscillator runs in continuous-wave (CW)

mode, but ultimately a pulsed output is desired and can be achieved by a process

called mode-locking. When the oscillator runs in CW mode, no pulses are produced.

After the cavity has been optimized, adjustments can be made to the second curved

mirror (CM2) position and the prisms that will facilitate mode-locking. The two

curved mirrors focus the cavity mode into the crystal so that it overlaps with the 532

nm pump beam that is focused into the rod with a lens (L1). To minimize reflection

losses, the Ti:Sapphire rod is cut at Brewster’s angle for 800 nm (60.4°), forcing the

cavity to run with p-polarization. The laser is actively mode-locked by gently joggling

the mount that holds prism P2. The cavity output (through the OC and the steering

mirror behind it) is monitored with several diagnostics. A CCD video camera

observes the spatial mode of the oscillator output while a fast photodiode (PD)

monitors the stability of the pulse train. When the oscillator is running in CW mode,

Millennia VsJ diode laserCW @ 532 nm

HR

OC

Ti:Sapphire rodL1P2

P1

CM2

CM1

L2

L3

PS

To Stretcher

To CCDand PD

15

the spatial mode is vertically elongated, but it will switch to a round mode upon mode-

locking. Very often the mode-locked spatial mode is accompanied by higher order

structure that can take the form of a sheath or sometimes several satellite spots. These

structures can generally be ignored because their focusing characteristics will make

them diverge from the main round mode by the time the output reaches the

regenerative amplifier. An Ocean Optics spectrometer is used to measure the

spectrum and bandwidth of the oscillator output. When mode-locked, the oscillator

typically produces a large bandwidth of ~50-60 nm or more, and the spectrum is

generally centered at 800 nm.

Mode-locking occurs when the cavity loss can be modulated at the round trip

time of the cavity.3 The oscillator is able to achieve mode-locking due to the Kerr lens

effect in the Ti:Sapphire rod.4-6 In the Kerr lens effect, a material experiences an

intensity-dependent change in index of refraction when a high intensity electric field

propagates through it.7

For transform-limited pulses, the pulse duration is determined by the time-

bandwidth product for Gaussian pulses,

In the Ti:Sapphire oscillator, the Kerr lens effect causes the

beam to self-focus. The self-focusing of the beam couples the many longitudinal

modes (spatial and temporal) that are normally produced in the lasing cavity,

effectively periodically modulating the cavity loss. The number of modes depends on

the length of the cavity and operating wavelength. In a mode-locked configuration,

the phase of the modes relative to each other is fixed. When the phases are locked in

this way, constructive and destructive interference between the modes leads to a

pulsed output. The number of modes that travel in phase will determine the pulse

duration and the bandwidth of the output. The prisms help correct for dispersion and

will increase the number of modes in the cavity. Generally, the mode-locked output is

made more stable than the CW beam by tuning the end mirrors and translation of the

curved mirrors such that the power discrimination between the CW and mode-locked

beam is ~120 mW. Normal mode-locked power is ~350 mW with a pulse energy of

~5 nJ at a repetition rate of ~80 MHz.

2

0.44 ,center

cλτ

λ∆ =

∆ (2.1)

16

where Δτ is the pulse duration, centerλ is the center wavelength, Δλ is the bandwidth,

and c is the speed of light. Ti:Sapphire oscillators have been known to create

transform limited pulses with pulse durations of less than 10 fs.1

2.3 Pulse Stretcher

Typically, the

Ti:Sapphire oscillator described in this section produces ~20 fs pulses. It is not a

problem that these pulses are not transform limited because they must be temporally

stretched (chirped) before amplification anyway. Without stretching the pulse

duration, the resulting high peak power would severely damage the optics in the

regenerative amplifier cavity. The induced chirping of the oscillator pulses is

accomplished with the pulse stretcher that precedes the amplification cavity. The seed

beam that enters the pulse stretcher must be well collimated. After the oscillator

output exits through the OC, collimation is accomplished with an expanding telescope

consisting of a 7.5 cm focal length lens and a 25 cm focal length lens (L2 and L3).

The telescope increases the seed beam diameter to ~5 mm. A large seed beam

diameter is desired because larger beams support longer Rayleigh ranges. The

diameter cannot be much larger than 5 mm because the seed must be able to fit

through a gap in a roof mirror assembly in the pulse stretcher without clipping.

The pulse stretcher, regenerative amplifier cavity, and pulse compressor

represent the three sequences of a chirped pulse amplification system. The overall

concept of chirped pulse amplification, developed several decades ago,8

After collimation by the telescope, a periscope (PS in Figure 2.2) flips the seed

beam to vertical (s) polarization. The beam is then steered into the stretcher

compartment. A layout of the stretcher is presented in Figure 2.3. The first mirror

involves

temporally stretching a low power seed pulse, amplifying the stretched seed pulse, and

then compressing the amplified output to achieve a short pulse duration. The seed

must be stretched out in time so that the peak power during amplification remains

below the damage threshold of the optics in the amplifier cavity. Chirped pulse

amplification is achieved in the laser system presented in this chapter via a Spectra-

Physics Spitfire Pro 40F Regenerative Amplifier.

17

inside the stretcher, M1, collects the seed and sends it through a Faraday isolator, FI,

which returns to the beam to horizontal (p) polarization. The Faraday isolator also

prevents amplified pulses from leaking back into the oscillator. Mirrors M2 and M3

then steer the beam between the gap in the mount of the vertical roof mirror assembly

(RM). The beam impinges on a 1200 line/mm diffraction grating (DG) that is rotated

at the near Littrow configuration that diffracts the first order towards the curved mirror

(CM). The incident beam hits the grating in the position marked as ‘1’ in Figure 2.3.

The diffracted beam arrives at CM in the form of a horizontal stripe. The curved

mirror is very wide in order to collect an optimal amount of the dispersed frequencies

from the diffraction grating. In reality, the oscillator produces enough bandwidth such

that some of the colors inevitably slough off the sides of CM. The stretcher

configuration produces positive dispersion in which low frequencies travel a shorter

spatial distance, and therefore faster, than blue frequencies. The compressor

introduces negative dispersion to the beam to reverse the positive dispersion from the

stretcher.

Figure 2.3 Schematic of the pulse stretcher. M1 through M5 – steering mirrors; FI – Faraday Isolator; RM – vertical roof mirror assembly; DG – diffraction grating, CM – curved mirror; FM – flat mirror; PS – periscope.

From oscillator

M1M2

M4

FI

RM

M5PS

CM

M3DG FM

To amplifier cavityPattern on diffraction grating

3

21

4

18

The CM is oriented such that it reflects the first diffraction stripe back towards

the DG but slightly upwards so that it clears the DG. The stripe strikes the flat mirror

(FM), which is also very wide to accept the dispersed frequencies in the beam. The

FM is located one focal length away from the CM. The flat mirror is tilted such that it

sends the beam back towards the CM at a lower level. The CM reflects the beam back

to the DG. The beam at this point is still a stripe and hits the grating at the position

marked as ‘2’ in Figure 2.3. The DG sends the beam towards the RM, but since the

height has been lowered, the RM is able to collect the beam and vertically translate it

such that the reflection off the top mirror of the RM assembly sends the stripe to

position ‘3.’ The beam travels once more through the stretcher via the path described

above and returns to the grating at position ‘4.’ The beam is now at the lowest

possible position, so as it travels back towards the RM, steering mirror M4 is able to

pick it off and send it into the regenerative amplifier cavity. The CM and the FM

create a 1:1 telescope so that the effective distance between the second incident spot

on the DG and the image of the first bounce is negative.9

Alignment errors in the stretcher can cause the seed beam to have spatial chirp

and higher order dispersion. These undesirable characteristics can cause problems in

pulse compression. In order to avoid these issues, it is necessary to take great care

while aligning the stretcher. To align the stretcher, it is first necessary to have the

oscillator operate in CW mode at 800 nm. A slit is inserted between prisms 1 and 2

(closer to prism 2). The slit is on a translation stage. The CW output is observed by

the Ocean Optics spectrometer so that the CW lasing wavelength may be measured.

There should be one extremely narrow band observed when the oscillator operates in

CW mode. Translating the slit tunes the CW wavelength. A CW wavelength of 800

nm is desired because that is the operating wavelength in the Spitfire system. The 800

nm CW beam is used to geometrically align the stretcher. It enters the stretcher via

the periscope and steering mirrors shown in Figure 2.2 and is first aligned through

irises that are set before and immediately after the FI in the stretcher cavity. If the

The compressor produces a

positive distance that leads to the negative dispersion that compensates for stretching.

Overall, the stretcher increases the seed pulse duration by four orders of magnitude,

yielding a pulse >100 ps in duration.

19

beam is not aligned onto these irises, then the two steering mirrors right before the

stretcher may be adjusted. Mirrors M2 and M3 are then adjusted to ensure that the

beam travels along the beam path outlined by hole ‘A’ in the blue alignment card

provided with the Spitfire system. This blue card is inserted right after the RM and

right before the DG. The beam is relatively large (about 5 mm in diameter) but should

pass cleanly through the gap in the mirrors of the RM assembly. This initial geometric

alignment has been streamlined by the addition of a long-path diagnostic before the

stretcher. Before looking at the stretcher alignment at all, a drop-in mirror is inserted

right before the stretcher that shunts the beam away from the stretcher entrance. The

location of the drop-in mirror is shown by the dotted square in Figure 2.2. The

oscillator beam then propagates a very long distance by bouncing off of two mirrors

(four times each) that are separated by about 6 feet. Using the two mirrors after the

periscope in Figure 2.2, the beam is steered through two irises. Putting the seed

through these two irises very reproducibly sends the seed along the correct beam path.

This diagnostic also allows the collimation of the seed beam to be monitored over a

long path length.

When the oscillator runs in CW mode, only one wavelength diffracts off of the

grating, producing a spot on the CM. At this point, it is necessary to put a beam block

right in front of the FM so that only one spot is observed. The grating is rotated such

that the spot hits the horizontal center of the CM. Then, the beam block in front of the

FM can be removed. The reflection from the CM should hit the horizontal center of

the FM. If it does not, then the CM steering can be adjusted. The blue alignment card

is then replaced in its first location near the RM. The spot should be centered on the

hole below hole ‘A’ in the blue alignment card. If the spot is not aligned on the

correct hole, then the FM can be adjusted. At this point, the stretcher should be

aligned. To check the quality of alignment, observe the pattern of spots on the

diffraction grating and the CM using an IR viewer. Each optic should show a vertical

column of four spots. If this pattern is achieved, then the oscillator can be re-mode-

locked. With a mode-locked beam, the DG should show the dot and stripe pattern

illustrated in Figure 2.3. On the CM, four horizontal stripes stacked vertically will be

observed.

20

If the spots (in CW mode) do not make a straight vertical line on both the DG

and CM, then the stretcher alignment should be checked again. Very often

misalignment of the spots can be fixed easily by merely double-checking the initial

alignment of the seed before it hits the DG. Because the beam is large, sometimes it is

difficult to see whether it is aligned properly on hole ‘A’ of the alignment card. If

spots 3 and 4 are offset from spots 1 and 2 on the DG, then a small adjustment in the

horizontal rotation of the RM assembly may be required, but do not adjust the knobs

of the individual RM mirrors. These mirrors are critically aligned and are not easily

re-adjusted to the correct settings. Adjustment of the RM assembly can be

accomplished by gently unscrewing the bolt that holds the RM assembly to the bread

board and gently tapping the assembly until the spots line up. This adjustment is

rarely required.

Once the stretcher is fully aligned and the oscillator is mode-locked, the spatial

chirp of the seed beam must be checked. Correcting for spatial chirp will ensure

optimal pulse compression of the regenerative amplifier output. Failure to eliminate

spatial chirp in the stretcher can prevent transform-limited pulses from being created.

To check the spatial chirp, a drop-in mirror is placed right after the periscope (PS in

Figure 2.3), and the beam is steered into an Ocean Optics spectrometer. It is necessary

to check the horizontal spatial chirp, but since the periscope rotates the seed to vertical

(s) polarization, the spatial chirp must be measured in the vertical direction. Using the

vertical adjustment knob of the drop-in mirror, the beam is scanned across the fiber of

the Ocean Optics spectrometer. Spectra for the top and bottom portions of the beam

are measured and compared. When there is no spatial chirp, the spectra should be

nearly identical. If spatial chirp is present, then the spectra will be shifted from one

another. If the shift is more than 2-3 nm, then the spatial chirp must be corrected.

Spatial chirp can arise when the distance between the CM and FM differs from one

focal length or when the collimation of the oscillator output is incorrect. If the

collimation of the seed is correct, spatial chirp can be corrected by adjusting the

translation of the FM closer to or further away from the CM. The translation can be

finely adjusted with the knob on the FM mount or coarsely by moving the entire

assembly on the bread board. After making an adjustment to the FM translation, the

21

spatial chirp of the beam should be checked again and the process iterated until the

spatial chirp is 2-3 nm or less. After the spatial chirp has been checked and corrected

if needed, the drop-in mirror can be removed, and the now vertically (s) polarized seed

beam enters the regenerative amplification cavity via mirror M5.

Figure 2.4 Schematic of the regenerative amplification cavity. TS – Ti:Sapphire rod; M1 through M3 – steering mirrors, PC1, PC2 – Pockels cells; λ/4 – quarter wave plate; CM1, CM2 – curved mirrors, TFP – thin film polarizer; L1, L2 – lenses; WP – half wave plate; Pol. – polarizer; PS – periscope.

2.4 Regenerative Amplification Cavity

The multipass regenerative amplifier, shown in Figure 2.4, selects single pulses

from the ~80 MHz seed pulse train and by trapping them in the cavity, amplifies the

pulses from nanojoules of power to millijoules.6

An individual seed pulse is selected and then ejected from the cavity using

Pockels cells. A Pockels cell contains a KD

The cavity traps a pulse such that it

passes multiple times through the Ti:Sapphire gain medium, picking up energy with

each pass. A 7 W beam from a diode-pumped intracavity doubled YLF laser

operating at 527 nm with a repetition rate of 1 kHz is focused into the Ti:Sapphire rod

gain medium (TS), creating a population inversion. As the seed repeatedly passes

through the rod, the pulse energy is amplified through stimulated emission. When the

pulse has acquired enough energy it is ejected from the cavity.

*P (potassium dideuterium phosphate)

dichroic crystal which, when applied with a quarter wave voltage (~3.5 kV), acts as a

quarter wave plate through the electro-optic effect.7

To CompressorFrom Stretcher

CM1

CM2

λ/4 PC1

PC2

L1 L2

PS

M1

M2

M3

TFPTS~7 W @ 527 nm

WP Pol.

The quarter wave voltage induces

22

a change in the crystal’s refractive indices along its two axes, resulting in a phase

delay of light polarized along one of the axes. The phase delay results in a rotation of

the polarization. Depending on which Pockels cells have been applied with the

quarter wave voltage, the seed may experience three types of trips in the cavity.

The first situation arises when none of the Pockels cells are activated with the

quarter wave voltage. The seed enters the cavity and, because it is vertically (s)

polarized, reflects off of the face of the Ti:Sapphire rod (TS). The fold mirror, M1,

reflects the beam towards curved mirror CM1. The seed passes through the first

Pockels cell (PC1) and a quarter-wave plate (λ/4). PC1, which is turned off, does not

rotate the polarization, but the quarter-wave plate does rotate the polarization. CM1

reflects the seed back through the quarter-wave plate. This double-pass through the

quarter-wave plate rotates the seed to horizontal (p) polarization. The beam can now

travel through the rod (TS) via reflection off of M1. M2 sends the seed through a thin-

film polarizer (TFP) and a second Pockels cell (PC2). PC2 remains off, so the seed

remains at horizontal (p) polarization. The seed reflects off of the second curved

mirror (CM2) and retraces its way back through the cavity. When it double passes the

quarter-wave plate (λ/4) again, the seed becomes s-polarized again and is ejected out

of the cavity by the surface of the TS rod. No amplification has taken place.

In the second situation, after the seed first double-passes the λ/4 and clears

PC1, PC1 is turned on. PC2 remains off. When the seed, now horizontally (p)

polarized, retraces its way through the cavity after reflecting off of CM2, a double-

pass through PC1 and λ/4 maintains the p-polarization. The seed pulse is now trapped

in the cavity. After about 20 roundtrips through TS, the third situation arises when

PC2 is turned on. A double pass through PC2 will rotate the seed back to vertical (s)

polarization. When the s-polarized seed hits the TFP, which is oriented to let p-

polarizations through, the seed is reflected and thus ejected out of the cavity. The

timing of PC1 is set by monitoring the repetition rate of the YLF and the oscillator

pulse train such that a single pulse is injected into the cavity. The timing of PC2 is set

by monitoring the build-up inside the cavity, which is measured by a photodiode that

measures a small amount of signal that bleeds through the back of CM2. Both the

23

PC1 and PC2 timings can be adjusted with the Spectra-Physics software that operates

the Spitfire.

Mirror M2 collects the amplified pulse and sends it through an expanding

telescope consisting of lenses L1 and L2, which have focal lengths of -5 cm and 40

cm, respectively. The beam diameter is roughly 6 mm before entering the compressor.

L2 is on a translation stage such that the collimation of the amplified pulse may be

finely tuned. After the telescope, the beam passes through a half-wave plate (WP) and

polarizer (Pol.) to variably attenuate the beam so that the compressor produces the

correct pump power for the optical parametric amplifier (OPA). The attenuators are

set such that a power of ~570 mW reaches the OPA. The beam is attenuated in this

location before the compressor because the use of attenuation optics on the full output

power after the compressor can spectrally distort beam. After attenuation, the

vertically (s) polarized beam is rotated back to horizontal (p) polarization by a

periscope (PS) before entering the pulse compressor.

2.5 Pulse Compressor

By introducing negative dispersion to the beam the compressor undoes the

stretching from the pulse stretcher. In this situation, the blue frequencies travel a

shorter spatial distance than the red frequencies. Figure 2.5 illustrates the layout of the

pulse compressor. The horizontally (p) polarized beam is reflected towards a 1500

line/mm diffraction grating (DG). The beam hits the location marked as ‘1’ in Figure

2.5. When the spot hits the DG, the colors are dispersed in a stripe towards the left

side of a horizontal roof mirror assemble (HRM). The HRM reflects the stripe back

towards the DG at position ‘2,’ reversing the orientation of the high and low

frequencies in the stripe. The DG reflects the stripe towards a vertical roof mirror

assembly (VRM) which lifts up the beam height and sends the stripe back towards the

DG. The stripe now hits the DG at position ‘3.’ Because the high and low frequencies

have switched places in the stripe, when the stripe at position ‘3’ diffracts back

towards the HRM, the frequencies start coming back together. The HRM reflects the

beam back towards the DG one last time. Now, the beam is a spot again and hits the

DG position 4. The beam is reflected out of the compressor, but since the beam height

24

has been increased by the VRM, the beam passes above M1. Outside the compressor,

another periscope rotates the beam to vertical (s) polarization to pump the OPA.

Figure 2.5 Schematic of the pulse compressor. M1 – steering mirror; DG – diffraction grating. HRM – horizontal roof mirror assembly; DL – delay line; VRM – vertical roof mirror assembly.

The compressor may be aligned geometrically by first rotating the DG out of

the way and using the red alignment card provided by Spectra-Physics to align the

beam on a straight path towards the DG. Generally the card is placed just after M1

and at a point past the rotated grating. The top mirror of the periscope and M1 are

adjusted so that the beam goes through the card at both locations. Next, it is extremely

important to attenuate the power of the beam even further using the wave plate (WP).

The red alignment card is placed just after M1, and the grating is rotated such that the

specular reflection spot crosses the alignment aperture on the card. If the height of the

specular reflection is not correct, then it may be adjusted with the vertical adjustment

knob on the DG. If the power is not attenuated during this process, the specular

reflection may damage the optics back in the regenerative amplification cavity. Once

the height is correct, the grating is rotated again such that the +1 and -1 diffraction

Pattern on diffraction grating

3

2 1

4

From regenerative amplifier

VRM

HRM

DL

DG

M1To OPA

L/2

25

orders are scanned across the alignment aperture of the red card. If the diffraction

orders are not at the same height (one is lower than the other), then the two screws on

the back of the DG may be gently loosened and the roll of the DG slightly changed so

that the diffraction orders have the same height. After this step, the compressor should

be aligned, and the DG may be rotated back to its initial angle. The power can also be

brought back to its proper operating value by adjusting the attenuator. The dots and

stripes should show the pattern illustrated in Figure 2.5. For general everyday

alignment, it is normally sufficient to just check the initial alignment of the beam

using the red card and then the grating pattern without having to rotate the DG to

observe the specular reflection and +/- 1 diffraction orders.

Proper pulse compression is achieved by adjusting the grating distance, L,

which determines the path length differences for the high and low frequencies. This

path length is varied by adjusting the translation of the delay line (DL) that supports

the HRM. The compression is set and the pulse duration measured by using a home-

built autocorrelation set-up. In brief, the output of the compressor is sent through a

beam splitter that sends one beam along a computer-controlled variable delay line.

The beams are focused by a 100 cm focal length lens and crossed into a KD*

2.6 Optical Parametric Amplifier

P crystal.

The resulting doubled light is selected with an iris and detected with a large area

photodiode. When the two beam paths of the autocorrelator are perfectly matched in

time, the signal intensity is highest. By scanning the delay line, the autocorrelation of

the pulse can be measured and the FWHM of the pulse determined. To achieve

optimal pulse durations, the compressor grating angle and the distance between the

DG and the HRM may be adjusted iteratively while monitoring the pulse duration with

the autocorrelator. Occasionally, small adjustments to the stretcher grating angle may

also be necessary.

The 800 nm output from the compressor pumps a modified Spectra-Physics

Optical Parametric Amplifier (OPA) which produces near infrared signals that can

eventually be used to generate ~4 µm light. Figure 2.6 shows a schematic of the OPA

layout. The OPA contains a beta barium borate (BBO) nonlinear crystal which is

26

birefringent, meaning that it has different indices of refraction for polarized light

propagating along different axes of the crystal. This birefringence allows nonlinear

second order frequency mixing processes to occur in the BBO, including sum

frequency generation, difference frequency mixing, and the generation of higher

harmonics of the input light.7

The OPA in Figure 2.6 utilizes a 2 mm-thick Type II

BBO in which the 800 nm light propagates along the extraordinary axis of the crystal.

The 800 nm light propagates collinearly through the crystal with a weak signal pulse

at ~1.3 µm that propagates along the ordinary axis. The two frequencies undergo

difference frequency mixing such that the resulting second order polarization creates

an idler pulse at ~2.0 µm. In the Type II crystal, the signal and idler have opposite

polarizations. It should be noted that the 800 nm light, as explained above, is rotated

to vertical (s) polarization before entering the OPA. However, the 800 nm is p-

polarized with respect to the BBO. The 1.3 µm is horizontally polarized but s-

polarized with respect to the BBO.

Figure 2.6 Schematic of the OPA used to create near-IR signal and idler frequencies and subsequent difference frequency mixing in AgGaS2

Difference Frequency Mixing

DL1

DL2

DL3BBO

AgGaS2

800 nm

1.3 µm2.0 µm

4.0 µm

OPA

BS1(99%R)

BS2(85%R)

S

TFP

DC2

DC1

λ/2

DC3

CM2

CM1

to produce 4 µm. BS1, BS2 – beam splitters, CM1, CM2 – curved mirrors; λ/2 – half wave plate; TFP – thin film polarizer; S – sapphire; BBO – beta barium borate nonlinear crystal; DC1 through DC3 – dichroic mirrors; DL1 through DL3 – delay lines.

27

The 800 nm, signal, and idler pulses each have characteristic sets of

frequencies and wavevectors, (ω1, k1), (ω2, k2), and (ω3, k3), respectively. A

nonlinear crystal can mix frequencies so long as energy and momentum are

conserved7 such that ±ω1 ± ω2 ± ω3 = 0 and ±k1 ± k2 ± k3 = 0. Difference frequency

mixing requires ω3 = ω1 – ω2 and k3 = k1 – k2. Normal materials have refractive

indices that increase monotonically with the frequency of light, a property which does

not allow the conservation of energy and momentum to be satisfied. This property can

be best understood using the relationship k = n(ω)ω where n(ω) is a frequency-

dependent index of refraction. If n(ω3)ω3 = n(ω1)ω1 – n(ω2)ω2 with ω1 > ω2 > ω3,

then n(ω1) > n(ω2) > n(ω3), and the conservation of energy (ω3 = ω1 – ω2) and

momentum (n(ω3)ω3 = n(ω1)ω1 – n(ω2)ω2) cannot be satisfied. In a nonlinear

crystal, the frequency-dependence of the index of refraction is different for ω1, ω2, and

ω3

The second order polarization produced in the BBO is given by

so that the conservation of energy and momentum can be satisfied.

[ ] [ ]

1 1 2 2

1 2 1 2 1 2 1 2

2 ( ) 2 ( )2 (2) 2 21 2

( ) ( ) ) ( ) ( ) )1 2 1 2

* *1 1 2 2

( ) [

2 2 . .

2( )].

i t k r i t k r

i t k k r i t k k r

P t E e E e

E E e E E e c cE E E E

ω ω

ω ω ω ω

χ − − − −

− + − + − − − −

= +

+ + +

+ +

(2.2)

The first two terms are the second harmonics of the pump (800 nm) and signal (1.3

µm). The third and fourth terms are sum and difference frequency terms. The last

term is a quasi-DC static electric field known as an optically rectified signal.7

The beam paths inside the OPA are outlined in Figure 2.6. This OPA has been

modified such that no high-intensity beams pass through any optical material besides

the BBO crystal. In the original commercially-bought system, the beam splitters were

low reflectance and high transmittance. It was found that the 800 nm beam became

distorted when passing through these high transmittance beam splitters and also

through lens materials. In the new OPA design shown in Figure 2.6, the 800 nm pump

impinges on the first beam splitter (BS1) which reflects 99% of the beam and

transmits 1%. The 99% portion is used to create two 800 nm pump beams for the first

and second passes of the OPA while the 1% portion is used to seed the first pass. The

1% portion passes through a half wave plate (λ/2) and a thin film polarizer (TFP)

which are used to control the intensity of the beam. The beam is focused into a

28

sapphire (S) that generates a white light continuum (WL). The WL is directed through

the BBO, passing through the back of a dichroic mirror, DC1. The WL serves as the

1.3 µm signal for the first pass.

The first pass pump beam originates from the 99% reflected portion of the 800

nm beam described above. This portion is directed to another beam splitter (BS2) that

reflects 85% and transmits 15%. The 15% travels through a telescope and is then sent

into the BBO collinearly with the WL using DC1, which is coated to reflect 800 nm

and transmit the WL signal. The delay line DL1 contains two of the steering optics for

the WL and is adjusted to temporally overlap the first pass 800 nm pump and the WL

signal. When the signal and 800 nm are overlapped both spatially and temporally the

2.0 idler is produced, and the 1.3 signal is amplified. The signal and idler pass

through a second dichroic mirror, DC2 that reflects the 800 nm away. The signal and

idler reach a third dichroic mirror, DC3, that lets the idler passes through but not the

signal. A mirror placed behind DC3 back-reflects the idler, but DC3 is oriented such

that when the idler passes back through it, it is shifted from the original beam path.

The idler reaches the BBO again, but horizontally displaced.

In order to amplify the idler and produce more signal, the second pass 800 nm

pump beam must propagate collinearly through the BBO with the back-reflected idler.

To do this, the 85% reflected 800 nm is sent through a telescope consisting of two

curved mirrors to avoid a large intensity beam passing through lens material. These

two mirrors are labeled CM1 and CM2 and have focal lengths of +15 cm and -7.5 cm,

respectively. The second pass 800 nm pump is sent into the BBO using the steering

optics on a second delay line (DL2) and then via DC2. The pump and idler mix in the

BBO to produce amplified idler and signal. Temporal overlap between the second

pass pump and idler is achieved by adjusting DL2. Before exiting the OPA, the signal

and idler are separated from the residual 800 nm pump.

The signal and idler are then difference frequency mixed in a 0.5 mm-thick

Type II AgGaS2 crystal. In this case, the 1.3 µm is horizontally polarized and travels

along the extraordinary axis of the AgGaS2 crystal (making it p-polarized relative to

the crystal). The opposite is true for the idler. A dichroic mirror separates the signal

and idler and sends them along two different beam paths. The signal travels along the

29

path that has the variable delay line, DL3. After recombining at a second dichroic, the

beams travel collinearly through the AgGaS2

The 4 µm wavelength is used in the experiments because it corresponds to the

OD stretch frequency of the HOD molecule (water with one hydrogen exchanged with

deuterium). In all water systems examined in the following chapters, the water

component consists of 5% HOD in H

crystal. Temporal overlap is achieved

by adjusting DL3. The resulting mid-infrared (mid-IR) light is centered around 4 µm

(horizontally and p-polarized) and detected on a Joule meter. Adjustments to the idler

steering and DL3 timing are made until the mid-IR signal on the Joule meter has been

optimized.

2O. The OD stretch is used because it provides

an isolated stretching mode to measure, thus simplifying the absorption spectrum.

Dilute HOD is used to eliminate problems from vibrational excitation transfer which

can cause the various correlation functions measured experimentally to artificially

decay.10,11 Molecular dynamics (MD) simulations have shown that using a small

amount of HOD does not disrupt water structure and that the OD stretch reports on the

dynamics of water.12

2.7 Mid-Infrared Spectrometer

2.7.1 Beam Paths in the Mid-Infrared Spectrometer

The mid-infrared (mid-IR) spectrometer is capable of performing both ultrafast

2D IR vibrational echo and transient absorption pump-probe experiments. The

schematic of the mid-IR spectrometer is shown in Figure 2.7. Optics on drop-in

mirror mounts (denoted as DI) allow rapid conversion between experiment types with

minimal realignment. Both experimental set-ups will be discussed in detail in this

section.

The 4 µm light that is generated in AgGaS2 is collimated with an expanding

telescope consisting of a -7.5 cm lens and +30 cm focal length lens. After the

telescope, the beam passes through a series of calcium fluoride (CaF2) plates which

are used to correct for linear chirp in the beam. The 4 µm light enters the mid-IR

spectrometer beam path after transmitting through a thin piece of germanium.

30

Germanium and CaF2 have opposite signs in their GVD (negative and positive

dispersion, respectively) and thus are a good pair to compensate for chirp.13,14

The

piece of germanium is also used to spatially overlap the 4 µm light with a HeNe laser

beam for co-alignment purposes.

Figure 2.7 Schematic of the mid-IR spectrometer. In the 2D IR experiments, delay lines 1 and 2 are scanned, while 3 remains fixed. The three excitation beams form a diamond pattern as shown. The echo signal, emitted in the phase matched direction ksig

The IR light then reaches a series of beam splitters which divides the beam into

four separate beam paths, 1 (blue), 2 (red), 3 (pink), and P (green). Each of these

paths send the beam along a variable delay line with a retro-reflecting corner cube.

Stages 1 and 2 are controlled electronically (ANT50L precision translations stages

from Aerotech) and are scanned during experiments. Stage 3 remains fixed. In an

echo experiment, beams 1, 2, and 3 are excitation beams, while P is only used for

alignment purposes. P is also known as the tracer beam. In the echo experiment, the

DI mount (shown by the dark grey dotted square) that intercepts the tracer beam is

removed so that the tracer becomes a local oscillator (LO) beam used for heterodyned

detection. The LO beam path is denoted in black. The LO also travels along another

, is overlapped with the LO for heterodyned detection. In the pump-probe experiment, delay line 1 becomes the pump, and P becomes the probe. Delay line 1 is scanned. LO is not used in pump-probe experiments. The 2D-IR experiment is readily converted to the pump-probe set-up by insertion of the drop-in mirrors (DI) outlined in dotted purple and dotted grey. Both heterodyned echo and pump-probe signals are frequency-dispersed by the monochromator and detected on the 32 element mercury cadmium telluride (MCT) detector.

ksig

2 1

P 3Monochromator

LO

Sample

OAP1 OAP2

k1

k2

k3

MCT arraydetector

DI

DI~4 µm

31

computer-controlled delay line (ANT50L) that is used to control the timing between

the LO and echo signals.

The three excitation beams are crossed and focused into the sample position

using a 6” parent focal length off-axis parabolic mirror (OAP1). When the beams are

overlapped both spatially and temporally, the echo signal is emitted in the phase

matched direction ksig = -k1 + k2 + k3

The pump-probe experiments utilize the same optics and detection systems as

the 2D IR set-up, but only beams 1 and P are required. P, in this instance, is the probe

beam, and beam 1 is the pump. The echo experiment is readily converted to pump-

probe geometry by insertion of two drop-in mirror mounts (DI), shown in dotted

purple squares, and the insertion of the third DI mirror mount in dotted dark grey.

These drop-in mirrors shunt the beam around two of the echo experiment beam

splitters and instead send the beam through a single 90/10 beam splitter to create an

intense pump and weak probe. The pump and probe are focused and crossed in the

sample by OAP1. The probe signal is selected out and sent into the monochromator as

before. There is no separate LO in the pump-probe experiment because the pump-

probe signal heterodynes with the probe. More experimental details concerning the

2D IR vibrational echo and pump-probe experiments will be presented in the next two

sections.

. The three excitation beams form a diamond

BOXCARS geometry, shown in Figure 2.7. The echo signal (pink) is selected out

from the other beams and re-collimated by OAP2. The echo signal is then combined

spatially and temporally with the LO (black dots). The combined beam is frequency-

dispersed by a Horiba Jobin Yvon iHR320 monochromator. The heterodyned signal is

detected by a 32 element mercury cadmium telluride (MCT) detector (Infrared

Associates).

2.7.2 2D IR Vibrational Echo Spectroscopy

In the 2D IR experiments, the IR beam is split into three excitation pulses and

a fourth beam, the local oscillator (LO). The three excitation pulses are precisely time

ordered,15-17 with pulses 1 and 2 traveling along variable delay stages. The pulse

sequence is outlined in Figure 2.8a. The first pulse creates a coherence consisting of a

32

superposition of the v = 0 and v = 1 vibrational levels. During the evolution period τ

the phase relationships between the oscillators decay. The second pulse reaches the

sample at time τ and creates a population state in either v = 0 or v = 1. A time Tw (the

waiting period) elapses before the third pulse arrives at the sample to create another

coherence that partially restores the phase relationships. Rephasing of the oscillators

causes the vibrational echo signal to be emitted at a time t ≤ τ after the third pulse.

During Tw, spectral diffusion occurs as the oscillators sample different environments

due to dynamic structural evolution of the system. The frequencies of the vibrational

oscillators evolve (spectral diffusion) as the structure of the environment changes.

The vibrational echo signal is spatially and temporally overlapped with the LO for

heterodyned detection. The heterodyned signal is frequency dispersed by a

monochromator and detected on a 32 element mercury cadmium telluride detector. At

a fixed Tw, τ is scanned to generate an interferogram at every detection frequency.

Then Tw is changed and another set of interferograms is collected. Double Fourier

transformation along each of the coherence time periods generates a 2D IR spectrum.

Each 2D IR spectrum has two axes. The vertical ωm (or ω3) axis corresponds to the

Fourier transform along the detection time period between the third pulse and the echo

(the second coherence period). This Fourier transform is performed experimentally by

the monochromator through frequency dispersal. The second (horizontal) axis of the

2D IR spectrum is known as the ωτ (or ω1

The correlation spectra are vulnerable to errors in delay stage timing as well as

linear chirp. The chirp in the IR pulses is measured by a frequency resolved optical

gating (FROG) technique

) axis and corresponds to the Fourier

transform along the evolution time period (first coherence period). This Fourier

transform is performed numerically during data processing after the experiment has

finished. The time evolution of the 2D spectra provides the information on spectral

diffusion.

18 in a non-resonant version of the experimental sample (no

OD chromophore) The chirp is corrected by changing the amount of calcium fluoride

through which the IR beam travels. The temporal overlaps between pulses 1, 2, and 3

are set through a three pulse cross-correlation experiment in the non-resonant sample.

An automatic computer-controlled program periodically resets the timing between

33

pulses 1, 2, and 3 to prevent temporal overlap drifts that are significant to the

experiment. In this process, data collection on the experimental sample is halted and a

computer controlled pneumatic translation stage moves the non-resonant sample into

the experimental position. The intensity level signal is then directed into a single

element IR detector using a computer controlled mirror. The temporal overlap of the

three stages is checked and corrected if necessary, after which the experimental

sample is moved back into position.

Figure 2.8 Pulse sequences for ultrafast 2D IR and pump-probe experiments. a) The heterodyned detected vibrational echo experiment is a three pulse, four wave mixing experiment. The time between pulses 1 and 2 is the coherence period, and the time period between pulses 2 and 3 (Tw

The timing between the signal and LO is also checked periodically. Before the

experiment, with pulses 1, 2, and 3 having zero delays, the signal from the resonant

experimental sample is combined with the local oscillator and directed into a single

) is the population period. The echo is emitted during the second coherence period after pulse 3 at a time t ≤ τ. b) The polarization-selective pump-probe experiment is a two pulse four wave mixing experiment. Two field-matter interactions occur during the intense pump pulse. The probe interrogates the sample after a population period of time t. The pump-probe signal emits at the same time as the probe interaction and travels along the same direction as the probe. Thus, the pump-probe signal heterodynes with the probe.

1 2τ ≤τ3Tw

τ – coherence periods; Tw – population period

vibrationalecho (combineswith localoscillator pulse)

a.

1,2 (pump) 3, probett – population period

pump-probe signal (heterodyne amplified by probe pulse)

b.

34

element detector. The LO is scanned to record a temporal interferogram which is used

as a reference during the experiment. After the zero of time of pulses 1, 2, and 3 is

reset and the resonant experimental sample is back in place, the signal combined with

the local oscillator is again directed into the single element detector using a computer

controlled mirror. The local oscillator is scanned, and the temporal interferogram is

compared to the one recorded at the beginning of the experiment. The local oscillator

delay stage position is then reset to match the measured interferogram to the initially

recorded interferogram. Because there are a very large number of oscillations, the

timing can be set accurately. The periodic retiming of pulses 1, 2, and 3 and the LO

relative to the signal eliminates drift which can be detrimental to data collection. The

signal to noise of the data is improved by averaging the interferograms from many

scans. The procedure outlined above enables data to be collected for days without

timing errors distorting the data. When a new sample is used, the initial measurements

must be repeated to account for differences in the properties of the samples.

2.7.3 Transient Absorption Pump-Probe Spectroscopy

The pump-probe experiment also requires three field-matter interactions, but

since the first two interactions occur nominally simultaneously with the intense pump

pulse, τ = 0. The pump-probe pulse sequences are shown in Figure 2.8b. After a

population period of length t, the weak probe interrogates the sample. The pump-

probe signal emits instantaneously in the direction of the probe. In this way, the

pump-probe signal heterodynes with the probe itself. The pump-probe signal is

related to the change in transmission of the probe with time. When the sample is

excited by the pump, the probe will have an increased transmission through the sample

because there is a decreased population of oscillators at the 0-1 transition frequency,

causing a positive-going signal. There will be an induced absorption at the 1-2

transition frequency, causing a negative-going signal.

Polarization-selective pump-probe spectroscopy is used to measure population

relaxation and orientational dynamics (anisotropy). In these experiments, the

polarization of the intense pump pulse is rotated at 45° relative to the probe.

Oscillators whose transition dipole moments are aligned with the pump will be

35

preferentially excited, but as the molecules tumble in solution, the anisotropy will

decay. To obtain the population relaxation and anisotropy, the parallel and

perpendicular signals relative to the pump are resolved after the sample.

Polarization-selective experiments require that the incident light is linearly

polarized and that the absolute signal intensities of the parallel and perpendicular

signals are detected. Keeping the polarizations purely linear can be difficult because

of limitations in optics and diffraction gratings. A metallic mirror will cause a phase

shift between the s and p components of incident light that is not linearly polarized.19

In addition, the diffraction grating in the monochromator will diffract one polarization

more effectively than the other. Furthermore, the diffraction efficiencies for both

components will also have different frequency-dependences. For ultrafast

experiments that use and detect signals with large bandwidths, these limitations can

seriously affect the quality of data measured in a pump-probe experiment.

Figure 2.9 Polarization-selective pump-probe set-up. To obtain a linearly polarized pump beam, a fixed polarizer, P1, set at 45° is placed just before the sample. The parallel and perpendicular components of the probe are resolved by polarizer P2, which is under computer control. A third polarizer, P3, adjusts the relative amplitudes of the parallel and perpendicular signals and provides a common polarization for the two signals to travel through the monochromator.

To correct for these issues, the polarization-selective pump-probe set-up shown

in Figure 2.9 was used in the experiments. It should be noted that the polarization of

the pump determines the parallel and perpendicular directions of the measured signals.

The pump does not have to be specifically s or p-polarized, but it must be linearly

polarized. In this set-up, the pump-pulse is polarized at 45°, and the probe is

horizontally polarized. The pump polarization is set to ~45° before reflecting off of

P3

P1

Sample

Probe Pump ~ 45°

P2

36

the first off-axis parabolic mirror (OAP). It is not a problem if the pump polarization

is not exactly at 45° because a fixed wire grid polarizer (Thorlabs, P1 in Figure 2.9)

set at 45° is placed just before the sample to ensure that the pump is linearly polarized.

The probe does not travel through P1 and remains horizontally polarized as it

transmits through the sample. The probe is polarized 45° relative to the pump, so it

therefore has components that are parallel and perpendicular to the pump. After the

sample, the probe is collected by the second OAP, and a CaF2

In practice, the parallel and perpendicular components are never perfectly at

±45° and therefore not perfectly 50/50 s/p polarized. To correct for this practical

concern, another polarizer, P3, is placed immediately after the resolving polarizer, P2,

which is used to adjust the relative intensities of the parallel and perpendicular probe

signals as well as to define a common polarization that travels through the

monochromator. P3 is generally set close to horizontal polarization (0°). P3 allows

the parallel and perpendicular signals to have the same spectra and same relative

intensities, which are critical in obtaining an absolute measurement of the parallel and

perpendicular polarizations.

wire grid polarizer

(Thorlabs, P2) resolves the parallel and perpendicular components of the probe

relative to the pump (±45°). P2 is held in a computer controlled rotation mount

(Newport model NSR1) to alternately resolve the components in the following

sequence: parallel, perpendicular, perpendicular, parallel, followed by perpendicular,

parallel, parallel, perpendicular. This sequence mitigates effects of laser drift on the

relative measurements of parallel and perpendicular as well as possible mechanical

drift in the polarizer position.

The parallel and perpendicular signals are defined as

2( ) ( )(1 0.8 ( )),I t P t C t= +

(2.3)

2( ) ( )(1 0.4 ( )),I t P t C t⊥ = − (2.4)

where P(t) is the population relaxation, and C2

(t) is the second Legendre polynomial

orientational correlation function for a dipole transition. Pure population relaxation

(no orientational terms) can be calculated from

3 ( ) ( ) 2 ( )P t I t I t⊥= +

. (2.5)

37

The anisotropy is calculated from

( ) ( )

( )( ) 2 ( )

I t I tr t

I t I t⊥

⊥

−=

+

. (2.6)

The analysis of population relaxation and anisotropy, including special considerations

concerning these observables, will be discussed in detail in Chapters 4, 5, 6, and 8.

2.8 References

(1) Zhou, J. P.; Taft, G.; Huang, C. P.; Murnane, M. M.; Kapteyn, H. C.; Christov, I. P. Opt. Lett. 1994, 19, 1149.

(2) Murnane, M. M.; Kapteyn, H. C.; Huang, C.-P.; Asaki, M. T.; Garvey, D. “Designs and Guidelines for Constructing a Mode-locked Ti:sapphire Laser,” Washington State University, 1992.

(3) Hargrove, L. E.; Fork, R. L.; Pollack, M. A. Appl. Phys. Lett. 1964, 5, 4. (4) Christov, I. P.; Kapteyn, H. C.; Murnane, M. M.; Huang, C. P.; Zhou, J. P.

Opt. Lett. 1995, 20, 309. (5) Spence, D. E.; Kean, P. N.; Sibbett, W. Opt. Lett. 1991, 16, 42. (6) Backus, S.; Durfee, C. G.; Murnane, M. M.; Kapteyn, H. C. Rev. Sci. Instrum.

1998, 69, 1207. (7) Boyd, R. W. Nonlinear Optics; Academic Press: San Diego, 2008. (8) Strickland, D.; Mourou, G. Opt. Commun. 1985, 56, 219. (9) Martinez, O. E. IEEE J. Quantum Electron. 1987, 23, 1385. (10) Gaffney, K. J.; Piletic, I. R.; Fayer, M. D. J. Chem. Phys. 2003, 118, 2270. (11) Woutersen, S.; Bakker, H. J. Nature (London) 1999, 402, 507. (12) Corcelli, S.; Lawrence, C. P.; Skinner, J. L. J. Chem. Phys. 2004, 120, 8107. (13) Gruetzmacher, J. A.; Scherer, N. F. Rev. Sci. Instrum. 2002, 73, 2227. (14) Demirdoven, N.; Khalil, M.; Golonzka, O.; Tokmakoff, A. Opt. Lett. 2002, 27,

433. (15) Asbury, J. B.; Steinel, T.; Kwak, K.; Corcelli, S. A.; Lawrence, C. P.; Skinner,

J. L.; Fayer, M. D. J. Chem. Phys. 2004, 121, 12431. (16) de Boeij, W. P.; Pshenichnikov, M. S.; Wiersma, D. A. Chem. Phys. 1998,

1998, 287. (17) Khalil, M.; Demirdoven, N.; Tokmakoff, A. J. Phys. Chem. A. 2003, 107,

5258. (18) Trebino, R.; DeLong, K. W.; Fittinghoff, D. N.; Sweetser, J. N.; Krumbugel,

M. A.; Richman, B. A.; Kane, D. J. Rev. Sci. Inst. 1997, 69, 3277. (19) Tan, H.-S.; Piletic, I. R.; Fayer, M. D. J. Opt. Soc. Am. B: Opt. Phys. 2005, 22,

2009.

39

Chapter 3 Theoretical Background

3.1 Introduction

Two-dimensional infrared (2D IR) vibrational echo spectroscopy is an

experimentally complex technique, but such complexity is rewarded by the wealth of

information gained concerning the dynamics of molecules. Like 2D NMR, 2D IR

experiments allow one to better understand complex systems and congested spectra.

The timescales involved in 2D IR spectroscopy are ~6-10 orders of magnitude faster

than those accessible by 2D NMR. 2D IR spectroscopy probes molecular vibrations

and yields time-dependent information about how systems evolve through quantum

pathways or how molecules respond to different chemical surroundings. Ultimately,

2D IR spectroscopy provides a dynamic way of interpreting the infrared absorption

line shape, which, by itself, can often yield ambiguous dynamic information.

This chapter discusses the theory of both 2D IR vibrational echo and pump-

probe spectroscopy. The nature of the 2D IR echo and pump-probe signals will be

described using third order response functions. The origin of these response functions

and their contributions to IR observables will be discussed. The formal derivation of

these functions has been treated in detail previously by various authors.1-5

The

molecular information embedded in the response functions will be illustrated using

diagrammatic perturbation theory. While specific models used to interpret 2D IR and

pump-probe experiments are included in their relevant chapters, Section 3.7 presents a

brief history of orientational relaxation models from which modern orientational

relaxation models are based. A good place to begin when describing the theory of

nonlinear ultrafast IR experiments is to first address the broadening mechanisms,

powers, and limitations of the linear absorption line shape. Later, it will be shown

how nonlinear experiments relate to this simpler observable.

40

3.2 The Absorption Line Shape and Broadening Mechanisms

Before using 2D IR experiments to study a system, it is often extremely

instructive and practical to first characterize the system using linear absorption

spectroscopy, such as Fourier Transform IR (FT IR) spectroscopy. The linear

absorption spectrum is given by the Fourier transform of the quantum dipole

correlation function,

1

( ) (0) ( ) ,2

i tI dte t

(3.1)

where is the dipole operator. For a 0-1 transition and for Gaussian frequency

fluctuations, Equation 3.1 in the semi-classical limit becomes6

10 10 10

0

1( ) (0) ( )exp ( ) ,

2

t

i tI dte t i d

(3.2)

where 10 is the 1-0 matrix element of the dipole operator, and 10( )t is the classical

time-dependent transition frequency. If the frequency is thought of in terms of a time-

dependent fluctuation from an average, then the substitution 10 10 10( )t yields

10( )

10 10 10

0

1( ) (0) ( )exp ( ) .

2

ti t

I dte t i d

(3.3)

Equation 3.3 is known as the non-Condon expression for the absorption line shape.

From this equation, we may introduce two important approximations that one may use

to simplify the expression. The non-Condon expression accounts for a varying

transition dipole across the line shape. In the Condon approximation, the transition

dipole is considered to be a constant across the line shape, yielding

102 ( )

10 10

0

1( ) exp ( ) .

2

ti t

I dt e i d

(3.4)

Further simplification is possible by doing a cumulant expansion4,6,7

of Equation 3.4

and truncating at 2nd

order to obtain

41

10 12 ( ) ( )

10

1( ) ,

2

i t g tI dt e e

(3.5)

where

2 2

1 2 1 1 1 2 1 10 10

0 0 0 0

( ) ( ) ( ) (0) .

t t

g t d d C d d t

(3.6)

Equation 3.6 is known as the line shape function and provides a link to the chemistry

occurring in a system and other molecular information. 1( )C t

is known as the

frequency-frequency correlation function (FFCF) and is a central point of discussion

in 2D IR spectroscopy. The FFCF ( 1( )C t ) describes the likelihood that an oscillator

vibrating at a certain frequency at an initial starting point will have the same frequency

at a later time, t,

1 10 10( ) ( ) (0) .C t t (3.7)

Equation 3.5 allows us to redefine the absorption spectrum as the Fourier Transform

of the linear response function, 1( )R t , where

10 12 ( )1

10( ) .i t ig t

R t e e

(3.8)

In Equation 3.8, contributions from dephasing, vibrational lifetime, and reorientation

of the dipole transition are not explicitly treated here, but they can be subsumed into

the line shape function if desired.

The practical form of the FFCF (Equation 3.7) is given by a generalized

version of a model originally developed by Kubo,8,9

/2

1 10 10

2

( )( ) ( ) (0) .it

i

i

tC t t e

T

(3.9)

The Δi‟s are frequency fluctuation amplitudes, and the i ‟s are their associated time

constants. These different parameters contain molecular information about the system

dynamics. The dephasing time, T2, is actually comprised of several processes,

*

2 2 1

1 1 1 1.

2 3 orT T T (3.10)

42

*

2T is known as the pure dephasing time and describes how quickly the phase

relationship of an ensemble of oscillators degrades, either by interactions with other

particles or solvent molecules. T1 is the vibrational lifetime, a parameter that describes

how quickly vibrational energy deposited in the system takes to dissipate. This

process is often referred to as population relaxation. The third component, or ,

represents the orientational lifetime of a dipole transition which describes how long it

takes a dipole to randomize its orientation. These three processes contained in the

dephasing time (Equation 3.10) represent homogenously broadened, or motionally

narrowed, contributions to the absorption line shape. They are extremely fast

processes and thus are considered to dynamically broaden the line shape. If the

product is much less than 1, then the line shape is homogeneously broadened.

The homogenous line width is given by

2

1,

T (3.11)

where T2 is the dephasing time, as given by Equation 3.10. Homogeneously

broadened processes give rise to a Lorentzian line shape of the form,

2

2 2 2

0

/( ) .

( ) ( )I

(3.12)

In the other extreme, >>1, the line shape becomes inhomogeneously

broadened. Inhomogeneous broadening occurs when there is a static distribution of

environments or resonance frequencies and thus reports on solute-solvent structure.10

The inhomogeneous line shape is Gaussian,

2 20( ) /(2 )

2

1( ) .

2I e

(3.13)

Integration of the line shape function (Equation 3.6) will yield two different

contributions in the limits of pure homogeneous and pure inhomogeneous broadening.

A motional narrowed (homogeneous, or dynamic) component yields a 2/t T

contribution to the line shape while an inhomogeneous (or static) component yields a

contribution of 2 2 / 2t . The derivation of these limits is presented in Appendix A.

43

Many molecular processes occur on intermediate timescales between the

homogenous and inhomogeneous limits. These processes allow the system to

experience spectral diffusion in which the oscillators in a system experience time-

dependent fluctuations as the system dynamically reorganizes. The time scales for

such intermediate processes are given by the i terms in Equation 3.9, and their

contributions to the line shape are given by their associated Δi terms.

It is difficult to separate and identify homogeneous and inhomogeneous

processes from the linear absorption line shape by itself because the actual absorption

line width is determined by the convolution of the homogeneous (Lorentzian) and

inhomogeneous (Gaussian) line shapes. One also loses information about the time

scales of spectral diffusion. Further ambiguity in interpreting spectra can occur, for

example, if there are two nearby resonance peaks. Are these peaks due to two separate

dipole oscillations, or are they due to chemical exchange between ensembles?

Fortunately, 2D IR vibrational echo spectroscopy has the power to distinguish

between these processes and separate out the homogeneous and inhomogeneous

contributions through a controlled time-ordered sequence of laser pulses.

3.3 Nonlinear Response Theory

The absorption spectroscopy described in the previous section is an example of

a linear spectroscopic technique, meaning that a single weak electric field interacts

with the sample. In nonlinear spectroscopy, more than one incident electric field

interacts with a sample to cause an ensemble of dipoles to oscillate. These oscillating

dipoles generate a macroscopic polarization that produces the signal electric field that

is detected in the experiment. The generated polarization links the experiment to the

underlying quantum mechanics and ultimately the chemical information concealed

within the detected electric field. It should be noted that the macroscopic polarization,

P(t), can have contributions from both resonant and non-resonant interactions,

( ) ( ) ( ).R NRt t t P P P (3.14)

In the infrared experiments considered here, the incident electric fields excite

specific vibrational transitions with characteristic frequencies, leading to a resonant

44

response. However, the electron clouds of the molecules can also produce an

instantaneous electrical response when driven by an electric field that is off-resonance,

or when several resonant fields are overlapped in time. These non-resonant

interactions are useful for setting the timing between the 2D IR vibrational echo

pulses, for example, but since the detected vibrational echo signal is produced by

resonant interactions, we will not consider non-resonant polarization effects further in

this chapter.

The polarization depends upon both the strength and number of input electric

fields. This relationship may be written in a power series expansion as,11

(1) (2) 2 (3) 3 ( )( ) ( ) ( ) ( ) ... ( ) .n nt t t t t P E E E E (3.15)

In this equation, the terms represent the susceptibility of the system, and ( )tE is

the input electric field. (1) is known as the linear susceptibility and is used in a linear

absorption experiment. The remaining terms are higher order terms. In systems

that have no material symmetry, such as isotropic liquids, the even order terms

vanish.11

In general, n input fields will create the nth

order polarization in an n + 1

wave mixing experiment. Equation 3.15 may also be written as

(1) (2) (3) ( )( ) ( ) ( ) ( ) ... ( ).nt t t t t P P P P P (3.16)

where n is the number of input electric fields. In a three pulse 2D IR vibrational echo

experiment the third order polarization, (3) ( )P t , generates the detected signal electric

field,

(3) /22

( ) ( )sinc( ) .( ) 2

sig i kl

sig

sig

i l klt t e

n c

E P (3.17)

In this equation, the signal electric field, ( )sig tE , depends upon its frequency, sig , the

wavelength-dependent index of refraction, ( )sign , the speed of light, c, the thickness

of the sample, l, and the wavevector mismatch, Δk, which occurs between the

wavevector of the polarization and the wavevector of the signal field.

There are still a few missing links that connect the third order polarization to

the underlying quantum mechanics and also the molecular information in the system.

45

The macroscopic polarization of a system may be obtained from the expectation value

of the dipole operator. In general, the expectation value of any operator A is given by

ˆ ( ),A Tr A (3.18)

where ρ is the density matrix, defined as12

( ) ( ) .t t (3.19)

In this case, the expectation value of the dipole operator may be obtained by

calculating the trace of the product of the transition dipole operator and the density

matrix,

(3) (3)ˆˆ( ) ( ( )),t Tr tP (3.20)

where is the transition dipole operator, and (3) ( )t is the third order perturbation

series expansion of the density matrix.4,7,13

. Equation 3.20 suggests that we can know

the third order polarization by monitoring the time dependence of the density matrix.

Diagrammatic perturbation theory (presented in Section 3.4) will expound upon this

point further.

Equation 3.15 related the polarization to the material susceptibility and the

input electric fields. In a simple absorption case, where there is only one input electric

field, the polarization may be expressed as the convolution of the electric field with

the material response function, which is related to the susceptibility,11

0

( ) ( ) ( ),t d t

P R E (3.21)

where R(τ) is the response function. In the case of a third order experiment, the

polarization is equal to the convolution of the third order response function,

(3)

3 2 1( , , )t t tR , and the three input electric fields,

(3) (3)

3 2 1 3 2 1

0 0 0

3 3 2 3 2 1

( , ) ( , , )

( , ) ( , ) ( , ).

r t dt dt dt t t t

r t t r t t t r t t t t

P R

E E E

(3.22)

Evaluation of Equation 3.20, using the third order expansion of the density matrix,

will yield a third order response function as follows,

46

3

(3)

3 2 1 1 2 3 1 2 1 0ˆˆ ˆ ˆ ˆ( , , ) ( ), ( ) , ( ) , (0) ( ) .

it t t t t t t t t t

R (3.23)

Evaluation of the nested commutators in Equation 3.23 will yield eight terms. Six of

these terms, which represent six response functions, contribute to the 2D IR signal and

may be expressed in terms of the line shape functions g1, g2, and g3,

10 3 10 143 3 1

1 3 2 1 2 3 2 1 10 1 2 3

1 1 1 2 1 3 1 2 1

1 3 2 1 3 2 1

( , , ) ( , , ) , ,

exp

i t i tR t t t R t t t e e t t t

g t g t g t g t t

g t t g t t t

(3.24)

10 3 10 12 23 2

3 3 2 1 10 21 1 2 3

1 1 2 2 3 3 2 2 1

2 3 2 2 3 2 1

( , , ) , ,

exp

i t i tR t t t e e t t t

g t g t g t g t t

g t t g t t t

(3.25)

10 3 10 143 3 1

4 3 2 1 5 3 2 1 10 1 2 3

1 1 1 2 1 3 1 2 1

1 3 2 1 3 2 1

( , , ) ( , , ) , ,

exp

i t i tR t t t R t t t e e t t t

g t g t g t g t t

g t t g t t t

(3.26)

10 3 10 12 23 2

6 3 2 1 10 21 1 2 3

1 1 2 2 3 3 2 2 1

2 3 2 2 3 2 1

( , , ) , ,

exp .

i t i tR t t t e e t t t

g t g t g t g t t

g t t g t t t

(3.27)

The time variables t1, t2, and t3 are the time intervals between electric fields 1 and 2, 2

and 3, and 3 and the echo signal, respectively. The time period t2 is often denoted as

Tw. The remaining two response functions arise when pulse 3 precedes pulses 1 and 2

(negative Tw).14

These response functions lead to “reverse echo” signals. Since these

pathways are not relevant to the 2D IR experiments in this thesis, they will not be

discussed further. 10 and 21 are the magnitudes of the transition dipole moments

for the transitions between the 0-1 and 1-2 vibrational states, respectively. Δ is the

vibrational anharmonicity between the 0-1 and 1-2 transitions. The 10 term is the

frequency of the transition between the 0 and 1 vibrational states. The Γi are damping

terms that account for the vibrational lifetime (T1) of a dipole transition,

1 2 3

1

( 2 )

21

1 2 3( , , ) ,

t t t

Tt t t e

(3.28)

47

1 2 3

1

( 2 3 )

22

1 2 3( , , ) .

t t t

Tt t t e

(3.29)

While not explicitly included, effects from reorientation may be included in the

response functions (Equations 3.24 through 3.27) as a multiplicative factor. The line

shape function g1 is given by Equation 3.6 while the remaining line shape functions

are given similarly by

2

2 2 1 21 10

0 0

( ) (0) ,

t

g d d t

(3.30)

2

3 2 1 21 21

0 0

( ) (0) .

t

g d d t

(3.31)

Equation 3.30 represents the cross-correlation of the 0-1 and 1-2 transition frequency,

while Equation 3.31 is the autocorrelation of the 1-2 transition frequency. It is

important to emphasize that the time ordering and direction of propagation of the input

electric fields determine the type of signal detected in the experiment. The first three

response functions (Equations 3.24 and 3.25) represent rephasing pathways in which

the electric fields reach the sample in the order of E1, E2, E3. The non-rephasing

pathways are represented by Equations 3.26 and 3.27 and occur when the order of

electric fields is E2, E1, E3. Changing the order of pulses 1 and 2 will flip the sign of

t1, as manifested in the change of sign in the exponential term 10 1te in the rephasing

response functions to 10 1te in the non-rephasing response functions.

If one assumes delta function input pulses, then Equation 3.22 becomes

3

(3)

3 2 1

1

( , ) ( , , ).n

n

t R t t t

P r (3.32)

In other words, the third order polarization for the rephasing signal is given by the sum

of the first three response functions, while the non-rephasing pathway is given by the

sum of the last three response functions. Substituting Equation 3.32 into Equation

3.17 with Δk=0 (perfect phase matching) yields

3

3 2 1

1

( , ) ( , , ).S n

n

E z t R t t t

(3.33)

Equation 3.32 shows how the signal electric field directly comes from the response

functions. The response functions contain all of the molecular and dynamic

48

information about a system. This is because the dipole operator evolves under the

system Hamiltonian Ho.15

The total Hamiltonian is H = Ho + Hint where Hint represents

the field-matter interactions. Each response function corresponds to a different

evolution pathway of the density matrix.

Figure 3.1 Feynman diagrams for the nonlinear third order response functions. The top set of

diagrams represents rephasing pathways while the bottom set represents non-rephasing pathways.

Time progresses bottom to top. The solid small arrows represent light-matter interactions with the three

input electric fields during the three time periods, t1, t2, and t3. The dotted arrow represents the signal

electric field. See text for additional conventions.

3.4 Diagrammatic Perturbation Theory

The importance of time ordering between the input electric fields is best

explained by diagrammatic perturbation theory through the use of double-sided

Feynman diagrams. Diagrammatic perturbation theory represents a way to concisely

express and keep track of the types of interactions that the input electric fields have

with the density matrix. Feynman diagrams clearly represent the time evolution of the

density matrix operator and also the resulting wavevector of the signal electric field.

Each response function corresponds to a specific Feynman diagram, thus linking the

0 00 10 01 00 0

0 00 11 11 00 0

t1

t2

t3

0 00 11 12 11 1

Rephasing Pathways: 1 2 3k k k

0 01 00 01 00 0

0 01 01 11 00 0

t1

t2

t3

0 01 01 12 11 1

Non-rephasing Pathways: 1 2 3k k k

49

chemical nature of the FFCF within the line shape functions (embedded in the

response functions) to the quantum mechanical origin of the generated nonlinear

polarization that is detected in the experiment.

Figure 3.1 shows the six double-sided Feynman diagrams for the six response

functions presented in Section 3.3 (Equations 3.24 through 3.27). The Feynman

diagrams follow a set of conventions:4,7

1. The vertical lines of the diagrams represent the ket and bra portion of the

density matrix operator, respectively. Population states occur when the ket

and bra have identical eigenstates. Coherence states occur when the ket

and bra have different eigenstates. The system always begins and ends in a

population state.

2. Time progresses in the vertical direction, bottom to top. The time periods

between the input electric fields (t1, t2, and t3) are delineated with the

horizontal dashed lines.

3. The light-matter interactions via the input electric fields are represented by

the small solid arrows interacting with the ket and bra. Arrows pointing

towards the vertical lines correspond to absorption, while arrows pointing

away from the vertical lines correspond to emission. The generated signal

electric field (the dashed line) is always an emission. The last interaction

(the generated signal field), which is given by Equation 3.17, is represented

by a dotted line instead of a solid line because its origin is different from

the other light-matter interactions. The first two fields effectively create a

population grating, and the emitted echo signal is caused by the diffraction

of the third pulse off of this grating.16

4. Each diagram carries a sign of (–1)n where n is equal to the number of

interactions from the right (the bra).

5. Arrows pointing to the right indicate an input electric field of i t ikre while

arrows pointing to the left indicate input an input electric field of i t ikre .

50

The frequency and wavevector of the output field will be equal to the sums

of the frequencies and wavevectors of the input fields.

The last convention explains how different time orderings lead to rephasing and non-

rephasing pathways. In the rephasing pathways, the first and last fields

(corresponding to coherence periods) have opposite signs in both frequency and

wavevector, meaning that the oscillators rephase at the opposite frequency at which

they dephased. In the non-rephasing pathways, the frequencies and the wavevectors

are the same for the first and last interactions, so the oscillators do not rephase. The

output field for the rephasing pathways therefore have 1 2 3sigk k k k while the

non-rephasing pathways have 1 2 3sigk k k k .

3.5 2D-IR Spectroscopy

3.5.1 The Dual Scan Method

In the 2D-IR experiment, the three time periods, t1, t2 (or Tw), and t3 are known

as the evolution, waiting, and detection periods, respectively. As explained above,

during periods t1 and t3 the oscillators carry a time-dependent characteristic phase. A

double Fourier transform of the signal electric field will yield the oscillator

frequencies during the evolution (t1) and detection (t3) time periods, denoted as 1

and 3 , respectively. Two-dimensional correlation spectra are plotted as 3 vs. 1 .

The second Fourier transform is performed by the monochromator during the

experiment, so the 3 axis is often referred to as m . The first Fourier transform

(yielding the 1 axis) is performed numerically during data processing.

Equation 3.33 indicated that the signal electric field is proportional to the sum

of the response functions. In order to extract the molecular information (the FFCF

presented in Section 3.2) from the two-dimensional correlation spectra, the purely

absorptive 2D line shape must be obtained. However, double Fourier transformation

of the response functions will yield both absorptive and dispersive features. The

double Fourier Transform of the rephasing pathways is

51

2 1 3 3 1 3 2 1

0 0

0 0 0 0

0 0 0 0

0 0 0 0

, , exp , ,

.

R m m R

m m

m m

m m

R t dt dt i t i t R t t t

A iD A iD

A A D D

i A D D A

(3.34)

A and D are the absorptive and dispersive components, respectively, and 0 is the

center of the absorption line. The real part of Equation 3.34 does not yield a purely

absorptive line shape. This problem may be eliminated by using a dual-scan

procedure17

in which the time-ordering of pulses 1 and 2 are reversed experimentally

using computer-controlled delay stages. In this way, the rephasing and non-rephasing

pathways are both measured. The double Fourier Transform of the non-rephasing

pathways is

2 1 3 3 1 3 2 1

0 0

0 0 0 0

0 0 0 0

0 0 0 0

, , exp , ,

.

NR m m NR

m m

m m

m m

R t dt dt i t i t R t t t

A iD A iD

A A D D

i A D D A

(3.35)

In Equation 3.35, the sign of the dispersive component is reversed. The real part of

the sum of the double Fourier Transforms of the rephasing and non-rephasing

response functions will therefore yield the purely absorptive line shape,

2 1 3 1 3 1 3( , , ) Re[ ( , , ) ( , , )].D w R w NR wS T R T R T (3.36)

3.5.2 Phasing 2D IR Spectra

Equation 3.36 holds only when the timing between the three input fields is

perfect. Experimentally, this is virtually never the case. Small errors in the timing

between pulses 1 and 2, as well as the output electric field (echo) and the local

oscillator, cause distortions in the 2D IR spectra. Chirp in any of the infrared beams

also cause distortions. It is therefore necessary to correct for these timing and chirp

errors by multiplying each term in Equation 3.36 by phase factors. If we call the

52

rephasing and non-rephasing signals , ,R m wS T and , ,NR m wS T , respectively,

then the corrected echo signal, , ,C m wS T , is given by

, , , , , ,

, , , , .

C m w R m w R m w

NR m w NR m w

S T S T T

S T T

(3.37)

The , ,m wT phase factors are given by18

3 12

3 12

, , exp ,

, , exp .

R m w m LO m m m

NR m w m LO m m m

T i Q C

T i Q C

(3.38)

The Δ3LO term accounts for the error in timing between the local oscillator (LO) and

pulse 3. The 12 term corresponds to the error in timing between the first and second

pulses. Q corrects for chirp differences between the echo and LO. C corrects the

chirp on the first and second pulses. The sign of the 12 term changes between the

rephasing and non-rephasing scans because of the difference in time-ordering between

pulses 1 and 2. Previous treatments of the phase factors used the same sign for C

(positive),19

but Moilanen has shown that this sign should change between the

rephasing and non-rephasing scans.18

Practically, the 2D IR spectra are phased using

several metrics: the projection slice theorem and the center of gravity.15

The

projection slice theorem states that the projection of the purely absorptive 2D IR

spectrum along the m axis at a certain Tw should be identical to the pump-probe

spectrum at the same Tw.16

The pump-probe spectrum is measured in a separate

experiment, generally right after the echo experiment is taken in order to preserve the

laser conditions (chirp, laser pulse duration, etc). The phase parameters can then be

adjusted to minimize differences between the pump-probe spectrum and the m

projection. While this procedure greatly aids in the proper phasing of spectra, an

additional constraint is required along the (or 1 ) axis. “Center of gravity” lines

may be determined for each spectrum by finding the peak positions of cuts through the

absolute value spectrum along for all m frequencies. The absolute value spectrum

is just the absolute sum of the rephasing and non-rephasing spectra. Plotting the

peak frequencies vs. m yields the center of gravity line. Center of gravity lines are

53

then calculated for the absolute value of the absorptive spectrum (Equation 3.37) and

compared to those for the absolute value spectrum. The phase parameters are adjusted

such that both the center of gravity lines and pump-probe projections match for each

Tw. It should be noted that the center of gravity may only be used in systems that have

a single 0-1 peak (and corresponding 1-2 peak) along the axis, such as bulk water.15

After proper phasing procedures have been completed, the full FFCF (Equation

3.9) may then be extracted from the 2D correlation plots in conjunction with the linear

absorption spectrum.14

The technique utilized in this thesis for FFCF determination is

the center line slope (CLS) method.14,15,20

In the CLS method, cuts through the spectra

parallel to the m axis are fit to Gaussian line shape functions to determine the peak

positions of the cuts. These peak positions are plotted vs. , and the slope through

the resulting line is calculated. This procedure is repeated for each Tw. The slopes vs.

Tw are plotted and then fit to either a single exponential or bi-exponential function,

depending on the system. The CLS method yields the Tw-dependent portion of the

FFCF (the exponential terms in Equation 3.9). To obtain the motionally narrowed

component (the first term in Equation 3.9), the IR spectrum is fit using the line shape

function (Equation 3.6) simultaneously with the CLS data. These methods will be

discussed in more detail in the subsequent chapters.

3.6 Pump-Probe Spectroscopy

Even though it is simpler in execution and analysis compared to 2D IR

experiments, pump-probe spectroscopy is an extremely useful experimental technique

for measuring population relaxation and orientational dynamics. Like 2D IR, the

pump-probe signal is due to the third order nonlinear polarization and arises from the

same set of response functions (Equations 3.24-3.27). One main difference between

the two techniques is that the first two light-matter interactions happen simultaneously

through the intense pump field, thereby making t1=0. Because t1=0, the signal electric

field emits simultaneously with the third input field (the probe), yielding t3=0. The

signal field is phase locked with the probe, so a purely absorptive signal is always

measured. Setting t1= t3=0 greatly simplifies the response functions.

54

Detection of the pump-probe signal parallel and perpendicular to the pump

field yield two signals,

2( ) ( )(1 0.8 ( )),I t P t C t (3.39)

2( ) ( )(1 0.4 ( )).I t P t C t (3.40)

In these equations, P(t) is the vibrational population relaxation (how long an oscillator

takes to dissipate vibrational energy) and C2(t) is the second Legendre polynomial

orientational correlation function for a dipole transition. Equations 3.39 and 3.40 may

be combined to give a pure vibrational signal (no effects from orientation),

( ) 2 ( ) 3 ( ).I t I t P t (3.41)

The orientational anisotropy may also be calculated from

2

( ) ( )( ) 0.4 ( ).

( ) 2 ( )

I t I tr t C t

I t I t

(3.42)

Equation 3.42 only holds for a single reorienting component. When more than one

rotating species is present in a system, Equation 3.42 adopts a more complicated

form.21-23

This subject will be discussed more thoroughly in context of the

experiments presented in the ensuing chapters.

3.7 The Orientational Correlation Function

3.7.1 Introduction to the Orientational Correlation Function

The rotational motions of molecules can provide much information about

internal structure, bulk properties, and the nature of surrounding environments. On the

quantum mechanical level, rotational infrared spectra can yield bond lengths and force

constants. On a macroscopic level, the molecular rotations of bulk liquids can factor

into viscosity and diffusion properties. On a nanoscopic scale, the rotations of small

molecules, such as water, can report upon dynamics at interfaces. For example,

consider water in a reverse micelle (a water core surrounded by surfactant molecules

with amphiphilic head groups). Water molecules up against the head group interface

will rotate more slowly than water molecules in the core.23

Spectroscopic methods,

such as transient absorption pump-probe techniques, can differentiate between these

55

different types of water molecules.23

Pump-probe methods obtain the orientational

correlation function which describes how molecules reorient in space. To describe the

orientational motions of molecules, the orientational correlation function must be fit to

an appropriate model. Many models for molecular reorientation exist, each with

numerous variations to fit either extremely specific or extremely general situations. It

is instructive to briefly discuss the derivations, main results, and limitations of four of

the most relevant models, namely those of Debye,24

Ivanov,25

Anderson,26

and Laage

& Hynes.27

One will readily observe that molecular reorientation models have

evolved quite significantly over the years. The model developed by Laage and Hynes

is the most modern in this list, and is consequently the model currently used to

interpret the pump-probe data presented in upcoming chapters.

Recall that the anisotropy is given by Equation 3.42 and that C2(t) is the second

Legendre polynomial orientational correlation function, generally written as

2 2 0( ) ( )tC t P . P2 denotes the second Legendre polynomial, and the i ‟s are

unit vectors along the direction of the transition dipoles at times 0 and t. C2(t)

measures the correlation that a molecule with a dipole with initial orientation Ω0 at t=0

has orientation Ω at time t. The anisotropy measures how quickly molecular

orientations randomize after excitation by the pump pulse. The molecules tumble in

solution, and the excited dipoles change direction, causing the anisotropy to decay

over time. To understand where the second Legendre polynomial comes from, let us

start with the Debye model for small angle rotational diffusion, which is the stepping

stone for many other models and to which many others reduce to in the limit of small

angular jumps.

3.7.2 Debye Model

In 1929 Debye formulated a model for rotational diffusion of spherical

molecules in the liquid phase.24

Picture a molecule whose dipole (represented by the

unit vector ) is oriented in a specific direction, Ω = (θ,φ), in spherical coordinates.

Debye assumes that a molecule can only rotate through a small angular distance

between collisions, which are frequent in a liquid. Over time, the molecule‟s

orientation will eventually diffuse through small-step (infinitesimal) rotations,

56

effectively mapping out the surface of a sphere defined by the vector .28

The

rotational motions, following Tokmakoff‟s notation,3 are described by the diffusion

equation,

2( , )( , ),

W tD W t

t

(3.43)

where W(Ω,t) can be interpreted as either the fraction or probability of molecules at

position Ω at time t.3,28

D is the orientational diffusion constant. A full derivation of

C2(t) is shown by Berne and Pecora;28

their derivation will be described here with the

main results displayed. Since we are dealing with spherical rotors, the Laplacian

operator may be written in spherical polar coordinates. The radius of the sphere is

fixed, so all derivatives with respect to r disappear. The remaining angular part of the

Laplacian equals 2I , where I is the quantum mechanical orbital angular momentum

operator. The eigenfunctions of 2I are the spherical harmonics, Ylm(Ω), and the

eigenvalue equation may be written as follows28

2ˆ ( ) ( 1) ( ), 0,1,2, ,lm lmI Y l l Y l (3.44)

W(Ω,t) can be thought of as a joint probability function,28

0 0( , ) ( ) ( , ),W t d W G t (3.45)

where

*

0 0

0

( , ) ( ) ( ) ( )l

m

i i l i lm lm i

l m l

G t C t Y Y

.3,28

(3.46)

0( , )i iG t is the Green‟s function that solves the diffusion equation and represents

the probability that a dipole with orientation Ω0 at t =0 has orientation Ω at time t. The

m

lC functions are called expansion coefficients, and are equal to

( ) exp( ( 1) ),m

lC t l l Dt (3.47)

because of the eigenvalue relation above. Since Equation 3.45 represents a

probability, the correlation functions *

' ' 0( ) ( , )l m lmY Y t may then be evaluated. It is

found that the functional form of the correlation functions is given by Equation 3.47,

and the spherical harmonics are reduced to Legendre polynomial form such that

( ) ( ( ) (0))l lC t P t .3,29

(3.48)

57

Typically, one-photon processes such as dielectric spectroscopy and infrared

absorption are described by C1(t).3 C2(t) is for two-photon processes such as Raman

spectroscopy and pump-probe experiments.3

The time constant, τl, is given by

1

.( 1)

ll l D

(3.49)

If both τ1 and τ2 can be measured for a system, then the theoretical ratio τ2/ τ1 should

be equal to 1/3. This is because τ1= 1/(2D) and τ2= 1/(6D). If the measured ratio does

not equal 1/3, then Debye‟s small-angle rotational diffusion model is not appropriate

for a system. In a gas where collisions induce large angular reorientations, the Debye

model would not be appropriate. It has also been postulated that while large

molecules may undergo small angular motions in solutions due to their bulky size, the

same is not necessarily true for smaller molecules.30

3.7.3 Ivanov and Anderson Models

As an alternative to the Debye model, Ivanov in 1964 produced a “jump

diffusion” model25

in which molecules reorient by jumps of finite angular size (as

opposed to infinitely small angular changes in the Debye model). In between the

jumps, which are instantaneous, the molecule remains frozen. As Berne and Pecora

point out, these assumptions reveal a flaw in the model, and that is the lack of inertial

motion in between jumps.28

A molecule should undergo free rotation when the

perturbation that caused a jump is removed. In recent years, Laage and Hynes

modified Ivanov‟s theory to formulate their ideas of jump reorientation of water

molecules, allowing certain diffusive motions between jumping events.27

The derivation and treatment of Ivanov‟s model has been discussed in detail in

the literature,25,28,31,32

so the full derivation will not be presented here. Besides the

basic assumptions of the model, one of the main differences from the Debye model is

that a Poisson distribution is used in calculating the joint probability function.32

The

important result is the equation for the time constant for jump reorientation,

corresponding to the decay of the associated ( ( ) (0))lP t correlation functions,

58

0 .1 sin( 1/ 2)

12 1 sin( / 2)

jump

l l

l

(3.50)

In this equation, τ0 represents the average time between rotations, θ is the angle

involved in the reorienting jump, and l is either equal to 1 or 2, as before. If θ

approaches zero, corresponding to infinitesimally small jumps, Equation 3.50 reduces

to Equation 3.48 for Debye‟s rotational diffusion. To see this “Debye limit,” the sine

functions must be Taylor expanded around θ = 0, as follows:

3

3( 1/ 2)sin( 1/ 2) ( 1/ 2) .

3!

ll l

(3.51)

To make a step simpler later on, Equation 3.51 can be rewritten as

2

3( 1/ 2)( 1/ 2)sin( 1/ 2) ( 1/ 2) .

6

l ll l

(3.52)

Also,

sin( / 2) / 2. (3.53)

Substituting Equation 3.51 and Equation 3.52 into Equation 3.49 yields

0

3

2

0

22

0 0

2 22

( 1/ 2) ( 1/ 2)( 1/ 2)1 61

12 1

2

11 (2 1 (2 1)( 1/ 2)

2 1 6

6,

( 1)1 1 ( 1/ 2)

6

jump

l

l l l

l

l l ll

l ll

(3.54)

assuming that (l + 1/2)2

= l2

+ l +1/4 ≈ l2

+ l = l(l + 1). If D = θ2/τ0, then the Debye

limit has been recovered. The ratio τ2/ τ1 equals 2

0

2

0

/ 1

3 / 3

, as it should. Another

interesting limit is that of very large jump angles. As it is unlikely that molecules

undergo extremely large jumps, the literature reports τ2/ τ1→ 1 for large angles.25,26,28

Since the rotational and jump diffusion limits are so different, experimentalists can test

the validity of each model for a certain system.

59

A few years after Ivanov, Anderson in 1972 developed a slightly different

jump model in which after each jump, the angles θ and φ are randomized.26

As a

result, the probability used to calculate the correlation function is slightly different,

and the time constants, τl , are

1

1,

(1 cos )R

(3.55)

22

1,

3(1 cos )

2

R

26 (3.56)

where R is a constant. Taylor expansions of the cosine functions around θ = 0 will

yield the Debye limit,

2 2

2 2 2 2 2

2

1 1cos cos(0) sin(0) cos(0) 1

2 2

1cos cos (0) 2cos(0)sin(0) 2( sin (0) cos (0))

2

1 .

(3.57)

These Taylor expansions yield τ1 = 2/(Rθ2) and τ2= 2/(3Rθ

2). The ratio τ2/ τ1 equals

1/3, as it should, for the small angle limit. For the large angle limit (θ → 180º), τ2/ τ1

→ ∞ because cos2(180º) =1 in the denominator of τ2. As Anderson shows in his

derivation, his model matches closely with Ivanov‟s model up to ~110º, which

constitutes a very large, and probably unlikely, jump in a liquid.26

3.7.4 Laage & Hynes Extended Jump Model

Water, unlike some other liquids, consists of a network of strong hydrogen

bonds, a property that is not necessarily included in rotational models. Water

molecules are continually exchanging hydrogen bonds. In order for exchange to

happen, the molecules must rotate. In 2006 Laage and Hynes developed an extended

jump diffusion model27

based upon the work of Ivanov.25,28,31,32

To test their model,

they performed molecular dynamics (MD) simulations which carefully monitored the

angular motions of hydrogen bonded water molecules. The simulations involved 256

water molecules, described by the simple point charge extended (SPC-E) model, and a

0.5 fs time step. Figure 3.2 shows the geometry of hydrogen bond exchange in the

60

simulation. At first, the water molecule labeled with O*H* donates a hydrogen bond

to oxygen „a.‟ The distances between O* (on the donor molecule) and Oa and O

b are

monitored (ROOa and ROO

b), as well as θ, the angle between the O*H* and ROO

vectors. The typical criteria for a hydrogen bond are ROO<3.5 Å and θ<30º. The

authors loosen this definition to ROO<4 Å and θ<50º for their simulations. As shown

in Figure 3.2a, Oa is at first over-coordinated, causing its water molecule to move

away from O*H*. At the same time, the water with Ob is under-coordinated, so it

moves towards O*H*. When ROOa = ROO

b, the donating water molecule can switch its

hydrogen bond over to Ob. Figure 3.2b shows that the donating water molecule

undergoes a five-coordinate transition state with a bifurcated hydrogen bond between

Oa and O

b. The molecules switch hydrogen bonds (Figure 3.2c) about 60% of the

time, and the donor water rotates through an average jump angle of 60º. This

mechanism refutes the idea that a water molecule first breaks a hydrogen bond

(leaving a dangling hydroxyl) and then reorients. Instead, this jump model asserts that

hydrogen bond switching is a concerted process involving the first and second

solvation shells of water molecules.

Figure 3.2 Proposed mechanism for hydrogen bond switching. According to Laage and Hynes,

water reorientation involves an extended jump diffusion mechanism, as discussed in the text. Dashed

lines denote hydrogen bonds. The blue dashed lines correspond to hydrogen bonds directly involved in

the jump reorientation mechanism, while the dashed green lines are hydrogen bonds to other water

molecules in the hydrogen bonding network.

Laage and Hynes‟ MD simulations generated the ( ( ) (0))lP t correlation

functions for l = 1, 2, and 3 (the latter being unattainable through experiments at this

time). The correlation functions were fit to exponentials to obtain decay times. The

authors then compared these times to fits with Ivanov‟s model, Equation 3.50, using θ

O* H*

Ob

OaO*

H*

H*

O*

Ob Ob

Oa Oa

a. b. c.

61

= 60º and τ0 = 1.8 ps, the time found for hydrogen bond switching in the simulation. It

should be noted that the water molecules here are treated as spherical rotors, even

though they are anisotropic. The MD simulations obtained a τ1/ τ2 ratio of 2.1, while

the Ivanov jump model obtained a ratio of 2.4, showing good agreement. Remember

that the diffusion model yields a ratio of 3. The Ivanov model assumes that the water

orientation remains frozen between jumps,25,27,28

but Laage and Hynes noticed that

there was a second, slower, exponentially decaying component to the calculated

correlation functions. They attributed this second component to motion of the OO

axis between jumps. Since the OO motion and OH reorientation are uncorrelated, the

new decay time is given by

1 1 1,

jump OO

l l l (3.58)

where jump

l is given by Equation 3.50 and 1OO

l= 15.5 ps and 5.2 ps for l = 1 and 2,

respectively (determined from fitting the correlation functions). Since the ratio

1 2/ 3OO OO , they conclude that it is a diffusive process. This “extended” jump

model, which includes the OO axis motions, yields τ1/ τ2 = 2.5, which is still

consistent with the ratio obtained by the simulations and suggests that overall water

reorientation is not a diffusive process.

Currently, the Laage and Hynes extended jump reorientation model is the most

accepted description of water reorientation. The development of the model followed a

typical pattern. Its roots began with a fundamental work (Ivanov‟s model) but then

necessary modifications were made according to the interesting behavior observed in

the simulations. The great number of diffusion and jump models exists because there

are many types of interactions involved in liquids, and each model must adapt to the

system in question. One prominent model that was not discussed is Gordon‟s

extended diffusion model which accounts for collisions in a system.30

Gordon

generalized the Debye model to allow diffusion through angular steps of arbitrarily

large size. His model was used to describe the orientations of both gas and liquid

systems. It should also be noted that the models presented in these sections only

describe isotropic rotations in which the diffusion coefficients along each molecular

62

axis are equal. Diezemann and Sillescu present the Ivanov and Anderson models in

terms of anisotropic rotations for use in studying the reorientation of viscous liquids.32

It is not surprising that the realm of anisotropic rotational motion is just as large as its

isotropic counterpart.

3.8 References

(1) Sung, J.; Silbey, R. J. J. Chem. Phys. 2001, 115, 9266.

(2) Golonzka, O.; Tokmakoff, A. J. Chem. Phys. 2001, 115, 297.

(3) Tokmakoff, A. J. Chem. Phys. 1996, 105, 1.



(5) Piletic, I. R. Dynamics of Nanoscopic Hydrogen Bonding Systems Probed

Using Ultrafast Nonlinear Infrared Spectroscopy; Stanford University, 2006.

(6) Schmidt, J. R.; Corcelli, S. A.; Skinner, J. L. J. Chem. Phys. 2005, 123,

044513(13).

(7) Hamm, P.; Zanni, M. T. Concepts and Methods of 2D Infrared Spectroscopy;

Cambridge University Press: Cambridge 2011.

(8) Kubo, R. Adv. Chem. Phys. 1969, 15, 101.

(9) Schmidt, J.; Sundlass, N.; Skinner, J. Chem. Phys. Lett. 2003, 378, 559.

(10) Saven, J. G.; Skinner, J. L. J. Chem. Phys. 1993, 99, 4391.

(11) Boyd, R. W. Nonlinear Optics; Academic Press: San Diego, 2008.

(12) Fayer, M. D. Elements of Quantum Mechanics; Oxford University Press: New

York, 2001.

(13) Tokmakoff, A. 5.74 Introductory Quantum Mechanics II, Spring 2009.

(Massachusetts Institute of Technology: MIT OpenCourseWare),

http://ocw.mit.edu (Accessed 17 May, 2011). License: Creative Commons BY-

NC-SA

(14) Kwak, K.; Park, S.; Finkelstein, I. J.; Fayer, M. D. J. Chem. Phys. 2007, 127,

124503.

(15) Park, S.; Kwak, K.; Fayer, M. D. Laser Phys. Lett. 2007, 4, 704.

(16) Faeder, S. M. G.; Jonas, D. M. J. Phys. Chem. A 1999, 103, 10489.

(17) Khalil, M.; Demirdoven, N.; Tokmakoff, A. Phys. Rev. Lett. 2003, 90,

047401(4).

(18) Moilanen, D. E. Water Dynamics Near Solutes and Surfaces; Stanford

University, 2009.


M. D. J. Chem. Phys. 2003, 119, 12981.

(20) Kwak, K.; Rosenfeld, D. E.; Fayer, M. D. J. Chem. Phys. 2008, 128.


Phys. Chem. A 2006, 110, 4985.


2009, 131, 5530.

63


113, 8560.

(24) Debye, P. J. W. Polar Molecules; Dover Publications: New York, 1928.

(25) Ivanov, E. N. Soviet Physics JETP 1964, 18, 1041.

(26) Anderson, J. E. Faraday Symp. Chem. Soc. 1972, 6, 82.


(28) Berne, B. J.; Pecora, R. Dynamic Light Scattering; J. Wiley: New York, 1976.

(29) Tao, T. Biopolymers 1969, 8, 609.

(30) Gordon, R. G. J. Chem. Phys. 1966, 44, 1830.

(31) O'Reilly, D. E. J. Chem. Phys. 1972, 57, 885.

(32) Diezemann, G.; Sillescu, H. J. Chem. Phys. 1999, 111, 1126.

65

Chapter 4 Water Dynamics and Interactions in

Water – Polyether Binary Mixtures

4.1 Introduction

The polymer poly(ethylene oxide) (PEO, Figure 4.1), a polyether compound

also known as poly(ethylene glycol) or poly(oxoethylene), is important in many

industrial, environmental, and biological applications because of its hydrophilic

properties. PEO is soluble in both water and non-polar solvents while similar

polymers, such as poly(methylene oxide) and poly(propylene oxide), exhibit different

behaviors.1 PEO-based membranes find utility in industrial applications to enhance

proton conduction in fuel cells,2,3

ion conduction in polymer electrolyte batteries,4 and

in other situations requiring ion-exchange membranes. In biological applications,

PEO aids in crystallizing macromolecules5 and, as a hydrated thin film, provides an

antifouling coating for metal surfaces and biomedical devices.6 Using PEO-based

surfactants is advantageous for the environment because they are more biodegradable

than alkylphenol-based surfactants.7

Figure 4.1 Molecular structures of poly(ethylene oxide) (PEO) and TEGDE. The n denotes the

number of repeat units.

The properties of PEO change with the extent of hydration, so it is important to

gain an understanding of the molecular processes governing the interactions between

the polymer and water molecules. PEO is terminated with hydroxyl groups, which

contribute to the compound’s hydrophilicity. However, the ether oxygens along the

polymer backbone as well as hydrophobic interactions with the ethylenes must also be

H

O

OH

n

H3C

O

OCH3

n = 4

PEO

TEGDE

H

O

OH

nH

O

OH

n

H3C

O

OCH3

n = 4H3C

O

OCH3

n = 4

PEO

TEGDE

66

considered to gain insights into polymer/water interactions. To explicate the role

played by the polyether backbone, we have studied tetraethylene glycol dimethyl ether

(TEGDE) (see Figure 4.1) over a range of water concentrations from almost pure

water to one water per TEGDE molecule (one water per five ether oxygens).

Orientational dynamics and vibrational population relaxation of the water were

explored for the TEGDE/water systems using ultrafast infrared (IR) polarization

selective pump-probe spectroscopy of water’s hydroxyl stretch.

Neutron-scattering,8-11

steady-state IR and Raman spectroscopy,12-23

thermodynamic measurements24-28

and simulations7,10,29-32

have produced a substantial

amount of important information about the static, and to some degree the dynamic,

nature of PEO-water systems. The studies indicate that PEO chains can form helical

structures in water that allow the ether oxygens to lie approximately the same distance

apart as oxygens in bulk water. Specifically, the waters stabilize a gauche

conformation of oxygens around the C-C bonds of the backbone, the preference for

which generally increases with higher water content.21,33

This structure can permit

water molecules to form bridging hydrogen bonds between the oxygens.21,33

The C-C

bonds can also adopt a trans conformation that will occur more frequently with less

water in the system.21,33

The proposed structure of TEGDE/water suggests that water

dynamics can be strongly influenced by hydrogen bonding to the ether oxygens, and

dynamical information can provide insights into TEGDE structure as a function of

water concentration. PEO generally has two alcohol (hydroxyl) end groups which

significantly affect the dynamics for low water content solutions and for solutions with

short polymer chains.31

With little water, the water molecules will mainly hydrogen

bond to the hydroxyls. In contrast, TEGDE has terminal methyl groups which makes

the molecule similar to long-chain PEO whose terminal hydroxyl groups are no longer

significant.31

By studying TEGDE it is possible to investigate the dynamics and

interactions of water with the polymeric ether chains without competition from water-

alcohol interactions. The number of hydrogen bonds that an ether oxygen can

accept32,34,35

and the ability of waters to cross-link separate ether molecules have been

studied.21,32

The results indicate that hydrophobic interactions of water with TEGDE

are also important.

67

Ultrafast IR polarization selective pump-probe experiments36

on the water

hydroxyl stretch enable us to measure the water dynamics in water/polyether systems

on the time scale on which the water molecules are moving, providing information

beyond the scope of steady-state measurements.37

The experiments yield both the

population relaxation (vibrational lifetime) and the orientational relaxation.

Vibrational population relaxation is sensitive to the local structural environment

experienced by the water molecules while anisotropy measurements provide

information on the hydrogen bond network rearrangement. Together, these

experiments provide significant insights into the dynamics and interactions of the

polyether/water solutions.

The polyether/water environment provides an instructive system for

understanding how to treat multi-component systems. We find that two types of

hydrogen bonds contribute to the pump-probe signals: waters hydrogen bonded to

other waters and waters hydrogen bonded to the oxygens of the polyether backbone. It

will be shown that traditional analysis of the pump-probe data, especially in regards to

orientational relaxation results, is insufficient and that more complicated data fitting

procedures must be implemented in order to obtain the correct dynamics. We present

a two component model that extracts the dynamics of water interacting with both

kinds of hydrogen bonding ensembles (water-water and water-polyether interactions).

The two component model presented here was first successfully tested with this

polyether/water system,38

and the following chapters will present more examples of its

utility and its extension to spectral diffusion processes in other hydrogen bonding

systems.

4.2 Experimental Procedures

The IR pump-probe experiments are made on the OD stretch of dilute HOD in

H2O. The use of dilute HOD, as opposed to pure H2O or D2O, is important to

eliminate vibrational excitation transfer.39-42

Vibrational excitation transfer causes the

decay of the transition dipole anisotropy induced by the pump pulse43

which interferes

with measurements of orientational relaxation. It also changes the location of the

excitation, impeding the use of the vibrational lifetime as a probe of the local

68

environment. Molecular dynamics (MD) simulations of pure water have shown that

dilute HOD in H2O does not change the behavior of water and that observations of the

OD hydroxyl stretch report on the dynamics and local environment of water.44

Tetraethylene glycol dimethyl ether (99+% from Acros) was used as received.

Mass spectral analysis verified the purity of the material. The mixtures of water and

TEGDE were prepared by mass with the following molar ratios of water:TEGDE:

200:1, 100:1, 50:1, 37:1, 25:1, 15:1, 10:1, 7:1, 2.7:1, and 1:1. The corresponding mole

fractions of water in these systems, in the above order, are: 0.995, 0.99, 0.98, 0.974,

0.962, 0.937, 0.89, 0.875, 0.73, and 0.50. The water portion consisted of 5% HOD in

H2O. Water content was verified for each of the solutions by Karl Fischer titration

(Mettler Toledo). Background-subtracted infrared spectra were taken with an FT IR

spectrometer. Samples for the experiment were prepared by sandwiching a portion of

the water/TEGDE mixture between two CaF2 windows separated by a Teflon spacer

of various thicknesses. The thickness was chosen so that the optical density at the OD

stretching frequency was between 0.3 and 0.5.

An optical parametric amplifier converts the output from a Ti:Sapphire

oscillator-regenerative amplifier into ~4μm, ~70 fs mid-IR pulses, which are then

beam-split into the probe and pump pulses. The pump is rotated 45° relative to the

probe and chopped. The two beams cross in the sample, and the parallel and

perpendicular components of the probe are selected by a polarizer on a computer-

controlled rotation mount. The probe signal is frequency-resolved by a

monochromator and detected by a 32-element mercury-cadmium-telluride array

detector.

4.3 Results and Discussion

4.3.1 Absorption Spectroscopy

Figure 4.2 shows FT IR spectra for the OD stretch of HOD in pure water and

in eight mixtures, 50:1 down to 1:1. The higher water content samples (200:1 and

100:1) have spectra that are indistinguishable from pure water. The spectrum of the

50:1 sample is almost identical to that of the OD stretch of HOD in pure H2O and

69

peaks at 2511 cm-1

. The peak positions of the absorption bands shift to the blue

(higher frequency) over an ~80 cm-1

range as the water content is decreased. The

largest blue shift occurs for the 1:1 mixture in which there is only one water molecule

per TEGDE molecule. The IR spectrum for the 1:1 mixture peaks at 2589 cm-1

. As

water content decreases, the spectra develop an increased asymmetry. Even for pure

water, the IR spectrum of the OD stretch displays a substantial tail on the red side of

the spectrum. The pronounced tail is most likely attributable to hydroxyls bound to

water oxygens even in the lowest water content sample in which the spectrum is

dominated by water associated with TEGDE. That the lowest water content solutions

contain a significant amount of ODs still hydrogen bonded to water oxygens is

supported by the analysis of the pump-probe data.

Figure 4.2 FT IR absorption spectra of the OD stretch of HOD in H2O for eight water/TEGDE

mixtures and water. An increasing blue shift can be seen as the water content decreases.

Recent theoretical studies with comparison to experiments of various salt/water

solutions attribute a blue shift to a reduction in the electric field along the hydroxyl

stretch of the water bound to a large anion compared to a hydroxyl bound to a water

oxygen.45

Even though the hydrogen bonding interactions in the polyether system are

2300 2400 2500 2600 2700

0.0

0.2

0.4

0.6

0.8

1.0

ab

sorb

an

ce (

no

rm.)

frequency (cm-1)

Water

50:1

37:1

25:1

15:1

10:1

7:1

2.7:1

1:1

70

nonionic in nature, a similar situation arises. The ether oxygens form hydrogen bonds

with water that are weaker than water-water hydrogen bonds. Weaker hydrogen bonds

cause a blue shift in the OD absorption spectrum. As the water content steadily

decreases, the amount of water-water interactions decreases, and more water-polyether

interactions occur. It should be noted that the blue shift does not mean that the

hydrogen bonds are getting weaker, only that there are a greater number of weak

hydrogen bonds. The OD absorption spectra blue shift as water content decreases

because of the greater number of weak hydrogen bonds contributing to the system.

The blue shift of the absorption spectra suggest that there are two distinct vibrating

ensembles in the water/polyether environment: waters hydrogen bonded to waters and

waters hydrogen bonded to the ether oxygens. MD simulations have also observed

different environments of bulk-like water (free) and bound water associated with the

polyether.10

If this two-component model is valid, then each of these ensembles will

contribute to the pump-probe signals. The absorption spectra will be addressed again

in Section 4.3.3 using the this two component model.

4.3.2 Population Relaxation

As discussed in the previous section and in Chapter 2, the polarization

selective IR pump-probe experiments are performed on the OD stretch of dilute HOD

in H2O/TEGDE systems. The measurements yield the signal parallel, ( )I t , and

perpendicular, ( )I t , to the pump polarization. With ( )I t and ( )I t , the vibrational

excited state population decay, P(t), is obtained using,36

( ) ( ) 2 ( )P t I t I t . (4.1)

Equation 4.1 holds whether there are one or several sub-ensembles in the system.

( )I t and ( )I t are also used to determine the orientational relaxation in Section 4.3.4,

where they are discussed further. The deposition of heat following vibrational

relaxation produces a constant offset in the data at long-time, an effect that has been

well documented.36,46-49

The P(t) data have been corrected for this heating

contribution using procedures developed previously.46,47

71

Figure 4.3 Population relaxation data for the OD stretch of HOD in H2O in eight water/TEGDE

mixtures and water at the center wavelengths. As water content decreases, the vibrational lifetimes

increase. Inset: Semilog plot of the 50:1 and 7:1 population relaxation decays. The 50:1 data are fit

well to a single exponential decay, while the 7:1 sample are not (red lines). The 7:1 data are fit well to

a biexponential decay (blue line).

Population relaxation data, P(t), are shown in Figure 4.3. The decay for pure

water is also shown for comparison. These data are collected at the wavelength

corresponding to the peak of the IR absorption for each sample (see Figure 4.2). Each

set of data was fit to either a single or biexponential decay. To obtain the wavelength-

dependence of population relaxation in this system, data were also analyzed at a

wavelength on the blue side of the absorption line corresponding to the quarter width

point. The wavelengths and the results of the fits are given in Table 4.1. A single

exponential decay would imply that there is a single vibrating ensemble while a

biexponential decay would indicate that there are two distinct species.

The OD stretch under observation has distinct structural environments that

depend on the nature of the hydrogen bonding interactions. The structure will affect

the process of vibrational relaxation.36,50,51

Water molecules can either interact with

other water hydroxyls (labeled as w waters), or they can interact with the polyether

0 5 10 15 20 25 30

0.0

0.2

0.4

0.6

0.8

1.0

P(t

) (n

orm

.)

t (ps)

Water

50:1

37:1

25:1

15:1

10:1

7:1

2.7:1

1:1

0 5 10 15

0.01

0.1

t (ps)

7:1

50:1

0 5 10 15 20 25 30

0.0

0.2

0.4

0.6

0.8

1.0

P(t

) (n

orm

.)

t (ps)

Water

50:1

37:1

25:1

15:1

10:1

7:1

2.7:1

1:1

0 5 10 15

0.01

0.1

t (ps)

7:1

50:1

0 5 10 15

0.01

0.1

t (ps)

7:1

50:1

72

molecule (labeled as e waters). Each of these environments will affect the process of

vibrational relaxation in different ways. In the ultrafast pump-probe experiments we

excite the 0→1 vibrational transition. This excitation will decay by pathways

involving other modes in the system. Energy must be conserved. The initially excited

OD stretch decays into a combination of lower frequency modes that have energies

that sum to the original OD vibrational energy.50

These pathways include high

frequency modes of the excited water molecule, such as bends, high frequency modes

of other molecules (water or TEGDE), and low-frequency bath modes (torsional and

translational).36,52

Because several discrete intramolecular modes are unlikely to

match the energy of the initially excited mode, creation or annihilation of one or more

modes of the continuum is necessary to conserve energy.50

The OD stretch in

different structural environments will have different coupled intramolecular modes

and will experience different density of states of the continuum. Therefore, the

lifetime is very sensitive to the local environment.36

Table 4.1 Water/TEGDE Population Relaxation Fitting Parameters.

afw is the amplitude of the T1w water-like component. The T1e ether associated component has amplitude

1 fw. Amplitude error bars: 0.02 for single exponentials and 0.04 for biexponentials. Time

constant error bars: 0.2 ps for single exponentials and 0.3 ps for biexponentials. bAs discussed in the

text, these are not purely water-like. Further discussion of these values is given in connection with

Table 4.3.

sample wavelengths (cm-1

) center blue

center blue fwa

T1w (ps) T1e (ps) fw T1w (ps) T1e (ps)

water 2507 1 1.7

50:1 2510 2549 1b

1.9b 1

b 2.1

b

37:1 2520 2559 1b 1.9

b 1

b 2.2

b

25:1 2520 2559 1b 2.0

b 1

b 2.4

b

15:1 2530 2559 0.61 1.7 3.4 0.60 2.0 3.4

10:1 2534 2565 0.50 1.8 3.7 0.46 2.1 4.2

7:1 2539 2568 0.42 1.7 3.8 0.38 2.0 4.5

2.7:1 2569 2589 0.31 2.0 5.5 0.26 2.3 6.2

1:1 2589 2610 0.25 2.3 7.7 0.18 2.8 9.3

73

In the current experiments, if the OD stretch is hydrogen bonded to a water

oxygen (w water) it will be coupled to a different set of intramolecular modes and a

different continuum than if the OD is hydrogen bonded to an ether oxygen (e water).

First consider the data for the center wavelengths (Table 4.1). The three water-rich

samples, 50:1, 37:1, and 25:1, fit very well to single exponential decays. The time

constants are a little longer than the time constant for OD relaxation of dilute HOD in

bulk water and get longer as the water content decreases. At these high water

concentrations, the sample will be composed of mostly w waters with e waters

saturating the polyether molecules. If the e waters decay with a somewhat longer

lifetime than the w waters, which should have a value essentially that of bulk water,

then the data will appear as single exponential decays within experimental error with a

lifetime that is a bit longer than that of found in bulk water. At the center wavelength,

most of the signal will come from water-like ODs (w) with a small contribution from

ODs bound to ether oxygens (e). As the water concentration decreases, the fraction of

e waters relative to w waters increases, and the vibrational relaxation will display a

slower single exponential decay, as is observed. The wavelength dependence supports

this interpretation (see Table 4.1). The data collected at the blue wavelengths for these

three high water concentrations still fit quite well to single exponential decays, but in

each case the decay is somewhat slower. At the blue wavelengths the fraction of the

pump-probe signal coming from e water will increase relative to w water. The slower

contribution to the decay increases, and the fit to the data yields a slower decay.

Therefore, the wavelength dependence supports the idea that the apparent single

exponential population decays for high water content samples arises from

contributions from both w water and e water.

When the water concentration is lowered to the point where w waters stop

dominating the system, ~15:1, the population relaxation data fit better to a

biexponential decay rather than a single exponential. The inset in Figure 4.3 shows

the 50:1 data (black) and the 7:1 data (magenta) both with single exponential fits (red).

The 50:1 data are fit well by a single exponential. The 7:1 data cannot be fit to a

single exponential but fit well to a biexponential, shown as the blue curve through the

7:1 data.

74

The 15:1 solution marks a point at which the e waters begin to be the dominant

water species. TEGDE, with five ether oxygens, can make up to ten hydrogen bonds

with water hydroxyls. A 15:1 solution has thirty hydroxyls per five ether oxygens. In

addition to actual hydrogen bonding, some water molecules will have hydrophobic

interactions with the methyl end groups and the ethylene segments. At 15:1 and lower

water concentrations, the system's preference for gauche conformations decreases,21,33

altering the structure of the polyether. As the water concentration is decreased further,

the number of w waters becomes very small and e waters should predominate.

The fractions (fw) in Table 4.1 show smaller relative populations of the w water

with decreasing overall water content. A surprising result occurs for the 1:1 sample

(one water per five ether oxygens). If the waters were distributed uniformly among

the ether oxygens, there would only be e waters, which should result in a single

exponential decay. At the center frequency for the 1:1 sample (Table 4.1), there is a

very slow component, 7.7 ps, with substantial amplitude (75%). Based on the results

for the high water concentration samples that yield single exponential decays, all of

which are ~2 ps, and the results for the intermediate biexponential decays, it is

reasonable to assign this slow component to e water. However, there is a 25%

component of the relaxation that occurs on a time scale consistent with w water. The

observation of the biexponential decay for the 1:1 sample strongly suggests that the

water molecules are not distributed uniformly among the ether oxygens. Even in the

very low water content samples, aggregation of water occurs, resulting in w water to

be present. Water cluster formation in concentrated TEGDE solutions has been

suggested by MD simulations and thermodynamic calculations.8,10,25,32

The

population decay results provide direct evidence for water clustering.

Considering only the center frequency (Table 4.1) as the water concentration is

increased to 2.7:1, 7:1, and 10:1, the fraction of the slow component decreases with a

corresponding increase in the fast component. This is consistent with the basic picture

that the number of e waters decreases while the number of w waters increases as the

water concentration increases. Note also that the decay time of the fast component (w)

is basically unchanged within experimental error and is close to the 1.7 ps decay time

of OD for dilute HOD in bulk water. In contrast, the decay time of the slow

75

component becomes significantly faster. There is a very large change in going from

the 1:1 sample to the 7:1 sample. The significant change in decay times with water

concentration indicates that the local environment experienced by e water changes as

the amount of water changes and that the e water should not be associated with a

single unique structure. For 7:1 and higher water contents, the change of the slow

component is less dramatic. The change in the decay times with wavelength at a given

water concentration demonstrates that there is an inhomogeneous distribution of

environments. Distinct environments that give rise to different lifetimes are correlated

with the absorption wavelength.49

Figure 4.4 Viscosity data for mixtures of water and TEGDE. The viscosity data comes from McGee

et al.28

The positions of the eight solutions studied in this work as well as pure water and TEGDE are

noted on the plot.

Figure 4.4 shows a plot of the viscosity as a function of the TEGDE mole

fraction taken from the literature28

with the specific water concentrations studied here

indicated. The slow component of the biexponential decays becomes longer as the

water concentration decreases from 15:1 to 1:1, but the viscosity first increases and

then decreases. The density of the water/TEGDE solution series peaks at the 10:1

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

vis

co

sity

(cP

)

mole fraction TEGDE

water

50:1

37:1

25:1

15:1

10:1

7:1

2.7:1

1:1

TEGDE

76

solution.26,28,53

The lack of correlation of the slow population decay component with

either the density or viscosity shows that local molecular structure is not directly

related to the bulk density or viscosity.

Figure 4.5 Results of two component FT IR spectral fitting. a) FT IR spectra (circles) of the OD

stretch of HOD in H2O and fits (red curves) using a linear combination of the bulk water and 1:1

spectra. The spectra are not fit well by this model at the lower concentrations. b) Fits (red curves) to

the FT IR spectra (circles) using bulk water and the 10:1 spectra for the water-rich samples and the 10:1

and 1:1 spectra for the water-poor samples. The fits are greatly improved but still deviate from the data

at the lower water concentrations.

4.3.3 Analysis of the Spectra with the Two Component Model

Because the pump-probe data can be rationalized well with a two component

model (w and e waters) that describes the water/polyether system, we investigated

whether this model works for the FT IR spectra. The results of a study of the OD

stretch of HOD in H2O in the AOT reverse micelle system36

show that the absorption

spectra of water inside different sizes of reverse micelles could be fit with a linear

combination of the pure water spectrum and the spectrum of water in the smallest

reverse micelle in which water primarily interacts with the ionic AOT head groups.36

These results are consistent with the recent theoretical work on salt/water solutions.45

2300 2500 27000

1

2.7

:1

0

1

7:1

0

1

10:1

0

1

15:1

0

1

25:1

0

1

37:1

0

1

50:1

2300 2500 27000

1

2.7

:1

0

1

7:1

0

1

0

1

15:1

0

1

25:1

0

1

37:1

0

1

50:1a b

frequency (cm-1) frequency (cm-1)

77

Hydroxyls associated with the negatively charged AOT sulfonates yield a blue shifted

spectrum and hydroxyls not associated with the sulfonates yield the spectrum of pure

water.

Based on the results for ions in water solutions45

and AOT reverse micelles,36

a

simple two component model was tried for fitting the FT IR spectra obtained for the

eight water/TEGDE mixtures to determine if the series of spectra could be reproduced

by combining the spectrum of pure water with the spectrum of the lowest

concentration of water in TEGDE. We fit the FT IR spectra of the 50:1, 37:1, 25:1,

15:1, 10:1, 7:1, and 2.7:1 mixtures with differing ratios of the pure water spectrum to

the 1:1 spectrum, which is the most water-poor of the series. The results of this

procedure are shown in Figure 4.5a and the fit parameters are listed in Table 4.2. The

dashed line is centered at the peak of the 50:1 spectrum and is an aid to the eye. The

fits are good for the highest water concentrations, but this is not surprising because the

spectra are dominated by hydroxyls that are not associated with the polyether. Note

that even in the 25:1 spectrum, the fit is somewhat low to the blue of the center of the

spectrum. As the water concentration decreases, the fits become increasingly poor.

There are substantial discrepancies in peak position, width, and overall shape.

Table 4.2 Fitting Parameters for Spectra in Figure 4.5.

Simulations have suggested that long PEO chains saturate with water around

0.5 weight percent.10,30

Using this idea that the backbone becomes saturated at a

certain water content, and that each ether oxygen can accept a maximum of two

hydrogen bonds from water, it is possible that a structural change occurs at an

intermediate concentration. The structural change could be an increasing

heterogeneity amongst the conformations of the backbone in intermediate solutions,

such as a greater mix of gauche and trans C-C bonds, as well as increased contact with

50:1 37:1 25:1 15:1 10:1 7:1 2.7:1

Bulk/1:1

(Figure 4.5a)

Fraction bulk 1.0 0.99 0.97 0.89 0.81 0.70 0.37

Fraction 1:1 0 0.01 0.03 0.11 0.19 0.30 0.63

Bulk/10:1/1:1

(Figure 4.5b)

Fraction bulk 0.99 0.92 0.75 0.38

Fraction 10:1 0.01 0.08 0.25 0.61 0.88 0.48

Fraction 1:1 0.12 0.52

78

hydrophobic groups. For PEO/water systems, it was established that both the pure

polymer melt and dilute solutions contain less structural heterogeneity than in

intermediate solutions of water and PEO.30

After the backbone has been saturated,

addition of more water will not induce further stabilization, making the environment

more homogeneous in dilute solutions.

To account for possible structural changes, a second fitting procedure was

used. The spectra for the samples with the higher water concentrations (50:1, 37:1,

25:1, and 15:1) were fit with a combination of the pure water spectrum and the 10:1

spectrum, and the spectra for the samples with the lower water concentrations (7:1 and

2.7:) were fit with a combination of the 10:1 and 1:1 spectra. Figure 4.5b shows the

results of this fitting procedure. Again, the dashed line is centered at the peak of the

50:1 spectrum and is an aid to the eye. The higher concentration samples are fit well.

The lower concentration samples are not fit as well, but there is substantial

improvement compared to the fits in Figure 4.5a.

The two component model used in attempting to fit the spectra in Figure 4.5a

works well for water in AOT reverse micelles because the local interactions that are

responsible for each component’s spectrum do not change with the amount of water.

As more water is added to the AOT reverse micelles system, the water nanopool

increases in size. The manner in which the water’s hydroxyl group interacts with the

AOT head group does not change, so the spectrum as a function of water content can

be reproduced by the sum of the two component spectra.

In the water/TEGDE system at high water concentrations, the polyether is

saturated with water. Additional water forms a water-water network that has a

spectrum like that of pure water. Hydroxyls associated with the saturated polyether

have another spectrum. That the pure water spectrum and the 10:1 spectrum do a

reasonable job of reproducing the higher water concentration spectra indicates that the

spectrum of water associated with the saturated polyether does not change

significantly when additional water is added. The 10:1 sample corresponds to two

water molecules (four hydroxyls) per ether oxygen. Even for this sample, it is quite

possible that not all ether oxygens accept hydrogen bonds from water hydroxyls.

Reducing the concentration should result in an increased number of ether oxygen sites

79

with either one or zero hydrogen bonded hydroxyls. The lowest concentration sample,

1:1, has one water molecule (two hydroxyls) for every five ether oxygens. If the only

thing that changed when the water concentration decreases below 10:1 was that sites

with originally two hydroxyls bound to each ether oxygen end up with one or no

hydroxyls per ether oxygen, then the fitting procedure used in Figure 4.5b should still

work to fit the low concentration spectra. Clearly the fitting procedure does not work

well. It is possible that structural changes occur that modify the nature of the

interaction between water hydroxyls and TEGDE. A similar structural reorganization

effect on the IR spectrum of water in heterogeneous systems has been observed in

studies of water in Nafion fuel cell membranes.54

The non-statistical mixing of the

lower water content solutions (as demonstrated by the population relaxation data)

could in part account for a structural change. However, recent NMR and heterodyned

optical Kerr effect studies have suggested that the TEGDE molecule does not undergo

a dramatic structural change as water content changes.55,56

The overall shape (or

aspect ratio) of the TEGDE molecule therefore may not change very much or at all,

but it could potentially form a heterogeneous mixture of conformers which could

make it impossible to define a specific water-polyether absorption spectrum that is

constant for all water contents.

4.3.4 Orientational Relaxation

In addition to the population relaxation, the orientational relaxation parameters

of a system are extracted from polarization selective pump-probe experiments using

the signals ( )I t and ( )I t . ( )I t , and ( )I t are given by

2( ) ( )(1 0.8 ( ))I t P t C t (4.2)

2( ) ( )(1 0.4 ( ))I t P t C t (4.3)

where P(t) is population relaxation and C2(t) is the second Legendre polynomial

orientational correlation function.57

For a single vibrating ensemble the population

relaxation follows a single exponential decay, 1/( ) t TP t e , with T1 being the

vibrational lifetime decay constant. For a single ensemble, the anisotropy decay, r(t),

is obtained from

80

2

( ) ( )( ) 0.4 ( )

( ) 2 ( )

I t I tr t C t

I t I t

(4.4)

The denominator in Equation 4.4 is the population relaxation (given in Equation 4.1).

In Equation 4.4 the denominator divides out population relaxation and gives the pure

orientational relaxation. As discussed in the previous section, the OD hydroxyls can

be divided into two sub-ensembles, those that are water-like (w), in which the OD is

hydrogen bonded to a water oxygen, and ether associated (e) with OD hydroxyls

hydrogen bonded to an ether oxygen or otherwise associated with a TEGDE molecule,

possibly through a hydrophobic interaction.58,59

If these two sub-ensembles, w and e,

have different lifetimes and, of most importance, different orientational correlation

functions, then r(t) is given by36

1 1

1 1

( / ) ( / )

2 2

( / ) ( / )

( ) ( )( ) 0.4

w e

w e

t T t Tw e

w e

t T t T

w e

f e C t f e C tr t

f e f e

, (4.5)

where the fi are the fractions of the signal coming from the two ensembles. The

derivation of Equation 4.5 is presented in Appendix B. The fi depend on both the

concentration of the two sub-ensembles and their transition dipoles. T1i are the

vibrational population decay time constants as discussed in connection with Table 4.1.

2 ( )iC t are the orientational correlation functions for the ith

species and may or may not

be the same for the two sub-ensembles. The numerator is ( ) ( )I t I t , and the

denominator is ( ) 2 ( )I t I t . In contrast to a system composed of a single ensemble,

the denominator no longer divides out the population relaxation. For a system with

two sub-ensembles, using r(t) to obtain the orientational correlation functions can be

difficult due to the large number of parameters.

In all samples containing water, r(t) has a very short time inertial component

that decays in less than 200 fs regardless of whether Equation 4.4 or 4.5 applies.60-63

Following this ultrafast component, the orientational relaxation in pure water and

other systems containing water decays much more slowly.36,46,47,49

For example, the

time constant for orientational relaxation of HOD in H2O is 2.6 ps.47

The inertial

component is obscured in these experiments by a large non-resonant signal that tracks

the IR pulse duration. Therefore, we do not obtain data for times less than 200 fs. The

81

inertial component is manifested as an initial value for the anisotropy in Equations 4.4

or 4.5 that is less than 0.4. This value is determined by extrapolating the data back

200 fs to t = 0.

Figure 4.6 Plot of the orientational relaxation of water, r(t), for the 50:1 solution and bulk water.

Bulk water decays to zero while the 50:1 solution displays a plateau starting at ~ 5ps.

For samples with very high water contents, 200:1 and 100:1, following the

inertial component, the r(t) decays appear to be single exponential within experimental

error with time constants of 2.8ps and 3.4ps, respectively. These decays times

(discussed further below) are somewhat longer than that of HOD in bulk water.

Beginning with the 50:1 sample and for all of the lower water concentration samples,

the anisotropy decays are not single exponential, and they differ dramatically from

pure water. Figure 4.6 displays the anisotropy decay (Equation 4.4) of HOD in bulk

water and in the 50:1 water/TEGDE solution. The 50:1 sample decays to what

appears to be a constant offset with a substantial fraction of the anisotropy in the

offset. Fitting the 50:1 data to a decay plus a constant offset or to a biexponential

decay yields a decay time constant of 1.7 ps and a constant that corresponds to an

t (ps)0 1 2 3 4 5 6 7

0.0

0.1

0.2

0.3

0.4

pure water

50:1 water/TEGDEr(t)

t (ps)0 1 2 3 4 5 6 7

0.0

0.1

0.2

0.3

0.4

pure water

50:1 water/TEGDEr(t)

82

effectively infinitely long decay. The water (HOD in H2O) data, in contrast, fit well to

a single exponential decay with a time constant of 2.6 ps. If the 50:1 is indeed

composed of two sub-ensembles of water molecules, those that are water-like and

those that are ether-associated, then the w and e sub-ensembles will have different

orientational correlations functions (Equation 4.5). NMR58,64-66

and MD

simulations67,68

support a two component picture of water orientational dynamics near

surfaces and solutes. These studies find that the water interacting directly with the

solute or surface has slower orientational dynamics than bulk water, but the rest of the

water has essentially bulk-like dynamics. Two sub-ensembles, each having single

exponential orientational relaxation, do not produce anisotropy data that is

biexponential. The anisotropy decay for two sub-ensembles, each with its own

vibrational lifetime and orientational correlation function, is given in Equation 4.5.

Figure 4.7 A calculated anisotropy curve using the two component model for anisotropy

(Equation 4.5). At long time, r(t) decays to zero. At short time, the curve appears to approach a

plateau. The inset has an expanded time axis and displays the experimentally accessible time range.

The inset has the same shape as the 50:1 data displayed in Figure 4.6.

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

t (ps)

r(t)

t (ps)

r(t)

0 1 2 3 4 5 6 70.0

0.1

0.2

0.3

0 5 10 15 20 25 30 35 40 45 500.0

0.1

0.2

0.3

0.4

t (ps)

r(t)

t (ps)

r(t)

0 1 2 3 4 5 6 70.0

0.1

0.2

0.3

83

Figure 4.7 shows the results of a calculation of r(t) using Equation 4.5. The

2

iC terms are taken to be single exponentials with orientation relaxation decay time

constants for the water-like and ether associated hydroxyls given by rw and re,

respectively. In this example, T1w = 1.6 ps, rw = 2.8 ps, fw = 0.83 and T1e = 2.6 ps, re

= 15 ps, and fe = 0.17. Here the Tw and rw values for the lifetime and the orientational

relaxation time constants for the water-like portion match the values for OD of HOD

in pure water within experimental error. The main portion of the figure shows the

calculated decay to 50 ps. The curve decays rapidly, plateaus, and then continues to

decay at a much slower rate. In the experiments, the vibrational lifetimes limit the

time range over which the data can be observed. This is particularly true for r(t),

where at long time, two small numbers are subtracted and then divided by a small

number. Therefore, it is not possible to measure the data past ~8 ps.

Figure 4.8 Simultaneous fits (solid curves) to R(t) and P(t) data (symbols) for the 50:1 and 7:1

solutions. The simultaneous fits yield the population relaxation and orientational relaxation parameters

(Table 4.3).

50:1

7:1

P(t)

P(t)

R(t)

R(t)

t (ps)

R(t

) an

d P

(t)

R(t

) an

d P

(t)

0 1 2 3 4 5 7 860.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

84

The inset in Figure 4.7 shows the first 8 ps of the curve in the main portion of

the figure. The calculated curve out to 8 ps is composed of a relatively fast decay to a

plateau like the 50:1 data shown in Figure 4.6. The inset in Figure 4.7 reproduces the

50:1 data in Figure 4.6. Thus a reasonable explanation for data like that shown in

Figure 4.6 is that the two sub-ensembles of water molecules, w and e, give rise to the

anisotropy decay like that shown in the main portion of Figure 4.7. Because the

measurements have a limited experimental time window, the data give the false

appearance of arising from a fast decay followed by an essentially infinitely slow

decay. The generated curves in Figure 4.7 use parameters that were obtained from

fitting the 50:1 data in the manner discussed next.

For two sub-ensembles, Equation 4.5 shows that the denominator does not

divide out the population relaxation. Therefore, it is better to simultaneously fit two

separate curves: P(t) given in Equation 4.1 and the numerator of Equation 4.5,

1 1

1 1

( / ) ( / )

2 2

( / ) ( / ) ( / ) ( / )

( ) ( ) ( ) ( ) ( )w e

w rw e re

t T t Tw e

w e

t T t t T t

w e

R t I t I t f e C t f e C t

f e e f e e

. (4.6)

The 2

iC functions are single exponentials with orientational relaxation decay time

constants rw and re for the water-like and ether interacting hydroxyls, respectively.

The fits need to be internally consistent, reproducing both R(t), which depends on the

orientational relaxation and the population decays, and P(t), which is determined only

by the vibrational lifetimes. The advantage of this method is that the two curves, R(t)

and P(t), have better signal-to-noise ratios than r(t), which is their ratio. Figure 4.8

shows two sets of R(t) and P(t) data (symbols) with the simultaneous fits (solid

curves) for the 50:1 and 7:1 samples’ data. With the sum of the fractions, fw + fe = 1,

the initial value of R(t) from Equations 4.2 and 4.3 is 1.2. However, in the figure, R(t)

has been normalized to 1. It is clear from Figure 4.8 that the simultaneous fits are very

good.

Before discussing the lower water content samples, we will return briefly to the

200:1 and 100:1 samples. These samples have anisotropy curves that can be fit to

single exponentials. To fit the anisotropy for these two samples, calculations were

performed using Equation 4.5 with the time constants used to produce the data for the

85

50:1 sample (see Figures 4.6 and 4.7 and Table 4.3). The fractions fw and fe, were

changed to reflect the additional water present in the 200:1 and 100:1 samples. The

50:1 sample has fw = 0.83 and fe = 0.17, which correspond to 83 and 17 hydroxyls in

the two fractions. We fixed the number of hydroxyls associated with the ethers

because they are saturated at 50:1 and for the 200:1 sample increased the number of

hydroxyls in the water fraction to 383 and in the 100:1 sample to 183. Increasing fw

causes the fast decay to drop further at short times. Within the experimental time

window, the observable portions of the calculated curves were fit extremely well as

single exponentials with decay constants of 2.9 ps and 3.4 ps for the 200:1 and 100:1

samples, respectively. These numbers are essentially identical to the measured decay

times given above. Therefore, the two component model reproduces the apparent

single exponential decays for high water content and yields the observed decay times.

Table 4.3 gives the results for simultaneous fits to R(t) and P(t) for the center

wavelengths and the higher frequency (blue) wavelengths for the various lower water

content samples. The wavelengths are given in Table 4.1. As discussed in Section

4.3.2, the high water content samples, 50:1, 37:1, and 25:1, have population decays

that were fit to single exponentials. We suggested that these decays actually contained

two components with similar enough lifetimes that the two components could not be

readily separated. The results of the simultaneous fits to R(t) and P(t) yield the two

lifetimes. The T1w values show little change with water content and for all but the

lowest two water content samples, the values are within experimental error of the 1.7

ps OD lifetime in bulk water. In contrast, T1e displays a concentration dependence that

is well outside the error bars, with the lowest two water content samples showing the

largest changes. The lifetime is very sensitive to local structure. Particularly at low

water concentration there are large changes in T1e with wavelength. These changes

demonstrate that there is considerable heterogeneity in the nature of the environments

experienced by ether-associated water.

The rotational time constant for the water-like component, rw, of the 50:1

sample is within experimental error the same as pure water (2.6 ps). For the center

wavelength rw increases as the water content is decreased and then decreases again.

The maximum for rw occurs at the 10:1 sample. The blue wavelength shows the same

86

trend although at this wavelength, the variation is virtually within the error bars except

at the lowest water concentrations. The net result is that the influence of TEGDE on

the water-like component is not great. Both the vibrational lifetime and the

orientational relaxation time are very similar to those of bulk water except for the

lowest water concentration samples, particularly the (1:1) sample. We will return to

the 1:1 sample below.

The rotational decay times, re, for the ether associated water differ

substantially from those of HOD in bulk water. The trend for the center wavelength

and the bluer wavelength are the same. The error bars for re are 3 ps. Given the

size of the error, the trend (Table 4.3) shows that the highest two water content

samples and lowest two water content samples have faster orientational relaxation than

the middle concentrations. The 7:1 sample seems to mark a transition point in the

series of solutions. The 1:1 sample is significantly faster than the rest. The error bars

for this sample are smaller than 3 ps because the lifetimes, particularly T1e, are

longer. The longer ether component lifetime and the faster reorientation make the

measurements subject to smaller error.

The amplitude of the water-like component, fw, decreases monotonically as the

water content decreases. The amplitude of the hydroxyls associated with the ether

increases as fe = 1 – fw. For the bluer wavelength, the fw values are all smaller than

they are at the center wavelengths. This is consistent with the hydroxyls bound to

ethers having spectra that are blue shifted from the water-like hydroxyls. The fis

cannot be directly associated with the concentrations of the species because they

depend on both the concentration and the transition dipole to the fourth power.36

As

discussed above, the ether-associated fraction can include both water bound to ether

oxygens and water molecules that have hydrophobic interactions with the methyl and

ethylene portions of TEGDE. The combination of these two effects can decrease the

water-like fraction fw. Although the fractions cannot necessarily be directly related to

the concentrations, the trend is significant. As the water concentration is decreased the

water-like component decreases. As discussed in Section 4.3.2, even at the lowest

water concentration, where statistically we might expect all the hydroxyls to be bound

with ether oxygens, the water-like fraction, arising from OD hydroxyls bound to water

87

oxygens, is significant. Therefore, the non-negligible fraction of water-like hydroxyls

at low water concentrations indicates the formation of water rich regions. There is

some clustering of waters such that even at very low water contents there are still

some w waters.

Table 4.3 Parameters from Simultaneous Fits to the R(t) and P(t) Data

afw is the amplitude of the water-like component. The ether associated component has amplitude fe =

1fw. Amplitude error bars: 0.04. Time constant error bars: 0.3 ps for T1w, T1e (ps) and rw; 3 ps for

re. bSee text for revised values using wobbling-in-a-cone mechanism.

Center Wavelengths

sample wavelength (cm-1

) fwa

T1w (ps) T1e (ps) rw (ps) re (ps)

50:1 2510 0.83 1.6 2.9 2.8 15

37:1 2520 0.80 1.6 3.0 3.7 17

25:1 2520 0.77 1.7 3.1 3.6 25

15:1 2530 0.61 1.7 3.4 3.4 20

10:1 2534 0.50 1.8 3.7 3.9 19

7:1 2539 0.42 1.7 3.8 2.9 23

2.7:1 2568 0.31 2.0 5.5 2.4 16

1:1 2589 0.25 2.3 7.7 1.0b 11

b

Blue Wavelengths

sample wavelength (cm-1

) fw T1w (ps) T1e (ps) rw (ps) re (ps)

50:1 2549 0.75 1.8 2.8 2.4 12

37:1 2560 0.70 1.8 3.0 2.9 14

25:1 2560 0.68 1.9 3.3 2.9 23

15:1 2560 0.60 2.0 3.4 3.4 21

10:1 2565 0.46 2.1 4.2 3.0 17

7:1 2568 0.38 2.0 4.5 2.8 20

2.7:1 2589 0.26 2.3 6.2 1.8 15

1:1 2610 0.18 2.8 9.3 0.9b 9

b

88

The two component model fits the data well with consistent and reasonable

values and trends except for the lowest water concentration sample, 1:1. That the

model may not be correct for the 1:1 sample is made particularly clear by the rw value

of ~1 ps, which is much faster than the values found for other samples including bulk

water. It is not reasonable to have orientational relaxation that is almost a factor of

three faster than pure water in a sample that has almost no water in it. Complete

orientational randomization requires a concerted swapping of hydrogen bonds that

takes the OD hydroxyls under observation to new orientations.61

The 1:1 sample

displays a biexponential anisotropy decay which suggests that a wobbling-in-a-cone

mechanism36,49,69,70

for orientational relaxation might be applicable for low water

content solutions. With wobbling-in-a-cone, orientational relaxation occurs on two

time scales. For water in restricted environments, there is a fast time scale (~1 ps),

corresponding to orientational diffusion that can only sample a limited cone of

angles.36,49,70

The fast wobbling component is associated with fluctuations of the

intact hydrogen bond network that cause the OD hydroxyl to sample a restricted range

of angles.71

Following the sampling of the cone of angles, orientational randomization

is completed on a longer time scale by jump orientational relaxation.49,61

The biexponential decay of the population relaxation, P(t), demonstrates that

there are indeed two sub-ensembles of water molecules in the 1:1 sample.

Nonetheless, when the two sub-ensembles are tightly coupled through the hydrogen

bond network, it has been observed in other systems that the orientational relaxation

can decay as a single ensemble even though the population decays as a

biexponential.36

Here, the basic idea is that in the 1:1 sample there are so few water

molecules that the concerted jumps necessary for complete orientational

randomization require participation of both hydroxyls bound to water oxygens and

hydroxyls bound to ether oxygens. The orientational relaxation of the two sub-

ensembles is not independent, and the result is a single orientational correlation

function. If we assume that the wobbling-in-a-cone mechanism accurately describes

the dynamics of the 1:1 sample, then we obtain a wobbling time constant of0.7 ps (w)

and a time constant for complete randomization of 15 ps (l ). The cone semi-angle is

25. The result is that the slower decay component is almost the same as the 2.7:1

89

sample’s slow decay. Details outlining the extraction of wobbling-in-a-cone

parameters from anisotropy data have been described in detail previously.36

All of the concentrations from 50:1 through 7:1 give either infinite or

extremely long l values with no consistent trend if the wobbling model is applied.

The rw and re values obtained from the two component model for the 2.7:1 data are

reasonable and consistent with the values for higher water content samples (see Table

4.3). A fit to the wobbling model yields time constants w = 1.3 ps and l = 24 ps,

which are also reasonable values. Therefore, we cannot be certain whether the two

component model or the wobbling model is more appropriate for this sample. The

significant differences between the T1e value for the 2.7:1 sample and the higher water

concentration samples suggest that there has been a substantial change in the hydroxyl

local environment, perhaps supporting the wobbling model. In either case, the 2.7:1

sample has a long orientational relaxation decay of ~20 ps.

NMR studies of PEO have suggested that water makes hydrogen bonds

between separate PEO molecules at low water contents, leading to restricted polymer

motion.35

It has been further proposed through simulations that single water

molecules could form cross-links between different polyether molecules, although the

cross-links would be most stable and abundant in long-chain hydroxyl-terminated

PEO.31

Even if only some of the TEGDE molecules in the 7:1 solution are cross-

linked, those molecules that are cross-linked could contribute to the observed high

viscosity (see Figure 4.4). The biexponential population decays, P(t), observed here

show that there are two types of water hydroxyls at all concentrations, those that are

hydrogen bonded to water oxygens and those that are bonded to ether oxygens. There

can be a small concentration of transitory unbound hydroxyls, but free hydroxyls are

energetically unfavorable. For a water molecule to undergo reorientation, its

hydroxyls will switch oxygen hydrogen bonding partners. The results shown in Table

4.3 demonstrate that the orientational relaxation has only a mild dependence on water

content. Even at the lowest water content, 1:1, for which the wobbling-in-a-cone

model was used, the orientational randomization time is very similar to the slow time

components measured at higher water concentrations. There is a tendency for both the

90

water-like and ether associated reorientation times to be slower in the region of higher

viscosity, but the trend is not pronounced.

4.4 Concluding Remarks

Polarization selective pump-probe experiments were used to study the

vibrational population relaxation and orientational relaxation of the OD hydroxyl of

dilute HOD in mixtures of H2O and TEGDE. The ratio of water to TEGDE was

varied from 200:1 to 1:1. Substantial differences from a sample of bulk water became

observable in the 50:1 sample. At higher water contents (200:1 and 100:1), the

population relaxation and orientational relaxation were similar to but somewhat slower

than those measured in bulk water, with the orientational relaxation exhibiting single

exponential decays. Even for these samples the small increases in the orientational

relaxation times relative to bulk water are consistent with the two component model.

Vibrational population relaxation (Tables 4.1 and 4.3) is very sensitive to the

local environment. Biexponential decays arise because there are two distinctly

different environments for the water hydroxyls. Differences in the local structure

change the coupling of the hydroxyl stretch oscillator to other modes and also change

the types and density of states of modes that accept the energy upon vibrational

relaxation. The water-like fraction, fw, decreases monotonically as the water content is

decreased. Of particular interest is that biexponential population relaxation is

observed at the lowest concentrations, and the water-like component has significant

amplitude. In the 1:1 sample, there are only two hydroxyls for five ether oxygens. If

the hydroxyls were hydrogen bonded uniformly among the ether oxygens, the

population decay would be single exponential. The significant amplitude in the water-

like vibrational relaxation component is a strong indication that water clusters such

that a fraction of the water hydroxyls are bound to water oxygens with the majority

bound to ether oxygens. Significant changes in the structure of the TEGDE hydroxyl

binding sites are indicated for the lowest two water content samples, 2.7:1 and 1:1, by

the substantial increase in the hydroxyl-ether population relaxation time, T1e (see

Table 4.3).

91

The most striking feature of the orientational relaxation is that the

concentration dependence is quite mild. With the exception of the 1:1 sample, the

water-like reorientation time, rw, is at most a factor of 1.5 slower than that found in

pure water (2.6 ps). This result indicates that for hydroxyls bound to water oxygens,

orientational relaxation is not greatly hindered by the presence of TEGDE even at high

TEGDE concentrations. The orientational relaxation of hydroxyls associated with the

polyether is considerably slower than that of pure water, but the dependence on water

content is not great. The orientational relaxation times are all ~20 ps, with the times

being somewhat slower in the intermediate concentration range where the bulk

viscosity is the highest. Water is not locked into quasi-static configurations even in

very low water content samples. Between the 50:1 sample and the 7:1 sample, the

bulk viscosity changes by over a factor of three (see Figure 4.4), but the water

orientational relaxation displays a much smaller variation. The water content has a

much more pronounced effect on the bulk viscosity than it does on the water

reorientation times.

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Chem. Chem. Phys. 2004, 6, 784.

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95

Chapter 5 Water Dynamics at Neutral and Ionic

Interfaces

5.1 Introduction

As seen in the previous chapter, when water interacts with an interface, its

hydrogen bonding properties are distinct from those of bulk water. Interactions with

an interface influence water’s ability to undergo hydrogen bond network

rearrangements, which is a concerted process that involves a water molecule and its

two water solvation shells.1,2

For a water molecule to switch hydrogen bonding

partners, other waters must also break and form new hydrogen bonds.1,2

Such

hydrogen bond rearrangements are necessary for both orientational and translational

motions. An interface eliminates many of the pathways for hydrogen bond

rearrangement that are available in bulk water. The behavior of water molecules near

interfaces is extremely important in many biological, chemical, geological, and

industrial processes. Roles of interfacial waters range from facilitating protein folding

mechanisms to mediating chemical reactions involving heterogeneous catalysis. A

fundamental question is whether the composition of or solely the presence of an

interface plays the dominant role in affecting the hydrogen bond dynamics of

interfacial water.

Ultrafast infrared (IR) spectroscopy is a valuable technique for probing the

dynamics of both bulk water and water at interfaces using the hydroxyl stretching

mode of water as a reporter.3-17

Because processes in water involving hydrogen bond

rearrangements occur on the picosecond timescale, the femtosecond time resolution of

the IR techniques makes it possible to resolve the motions of water molecules on the

timescale on which they are occurring. Examples of confined or restricted

environments that have been studied with ultrafast IR spectroscopy include salt water

solutions,7,18-21

zeolite cavities,22

channels of Nafion fuel cell membranes,9,10

polyether

systems,23

lipid bilayers,24

and the interiors of reverse micelles.3-5,8,16,17

It has been

96

shown by both theoretical and experimental studies that only water molecules in the

immediate vicinity of an interface or solute differ significantly from bulk water.3-5,20,25-

28 These water molecules undergo orientational relaxation that is slower than in bulk

water3-5,8,16,17

because they have a reduced number of neighbors with which they can

exchange hydrogen bonds.29

Large reverse micelles are useful for studying the behavior of water at

interfaces. In a reverse micelle, the polar head groups of the surfactant molecules

surround a pool of water, while the hydrophobic tails are suspended in an organic

phase. A commonly used surfactant that forms reverse micelles is Aerosol-OT, or

AOT, (sodium bis(2-ethylhexyl) sulfosuccinate) which has an aliphatic tail and

sulfonate head groups (Figure 5.1). AOT forms monodispersed spherical reverse

micelles in isooctane that have been well characterized.30

Depending upon the amount

of water added, AOT can form water pool sizes from 1 nm (~30 water molecules) to

14 nm (~400,000 water molecules).8 The number of water molecules per surfactant

molecule is w0 = [H2O]/[surfactant] and is used to denote the relative size of the

reverse micelle.

Figure 5.1 Molecular structures for the surfactants Igepal CO-520 (neutral head group

containing a hydroxyl) and AOT (ionic sulfonate head group with a sodium counter ion).

The water environment inside the AOT reverse micelles has been described

with a two component model.3-5,8,16,17

Water inside large reverse micelles exists in

two environments: a bulk-like water core and a shell of interfacial waters that hydrate

the AOT head groups.3-5

The infrared spectra of the OD stretch of dilute HOD in H2O

inside AOT reverse micelles can be reproduced by linear combinations of the bulk

Igepal CO-520

AOT

97

water absorption spectrum and the spectrum of a very small reverse micelle (w0 = 2) in

which virtually all of the waters interact with the head groups.8 In the experiments

presented below, the OD stretch of dilute HOD in H2O is also used. Studying dilute

HOD is important because its use eliminates vibrational excitation transfer that causes

artificial decay of the orientational correlation function in either pure H2O or D2O.31,32

Molecular dynamics (MD) simulations of bulk water have shown that dilute HOD in

H2O does not change the behavior of water and that observations of the OD hydroxyl

stretch report on the dynamics and local environment of water.33

Recently, Moilanen

et al. analyzed data for large AOT reverse micelles (w0 = 25, 37, and 46) in terms of

the two component model. 3-5

The diameters of these reverse micelles are 9 nm, 17

nm, and 20 nm, respectively. The water pools are so large that they contain a large

bulk water core. A shell of waters surrounds the core and hydrates the surfactant head

groups. The frequencies associated with water molecules hydrating the interface were

identified, and the experiments yielded the interfacial water vibrational lifetimes,

orientational relaxation times, and the fractional population of interfacial water

molecules in each micelle. In all of these large reverse micelles, the orientational

relaxation time constant for water at the interface is ~18 ps, and the interfacial

vibrational lifetime is ~4.3 ps.3

A fundamental question is the relative importance of the presence of an

interface as opposed to the chemical composition of the interface. To address the

question of the role of the chemical nature of the interface, we compare water

orientational relaxation at the AOT interface, containing ionic head groups, to

orientational relaxation at a neutral interface in reverse micelles of Igepal CO-520

(Igepal). The structure of Igepal is shown in Figure 5.1. Igepal, like AOT, forms well

characterized, monodispersed, spherical reverse micelles.34

Igepal is a non-ionic

surfactant with a head group terminated by an alcohol hydroxyl. Therefore, the

interactions of water with the AOT and Igepal interfaces will be very different.

The role of the chemical composition of the interface on water dynamics was

addressed previously by Moilanen et al. in relatively small AOT and Igepal reverse

micelles (4 nm diameters).11

The experiments showed that the orientational relaxation

anisotropy decay curves were qualitatively very similar. However, the analysis did

98

not separate the interfacial orientational relaxation times from the orientational

relaxation times of water in the core, nor did it account for the contribution to the

signal from the Igepal alcohol head groups. In addition, it was assumed that all of the

water in the reverse micelles comprised a signal ensemble with a single orientational

anisotropy decay. Recent experiments on 4 nm (w0 = 10) AOT reverse micelles have

demonstrated that reverse micelles of this size have both core and interfacial water

with distinct dynamics and that the core water molecules are not bulk-like.5

Therefore, in the earlier study of AOT and Igepal reverse micelles, the orientational

relaxation times of water at the interfaces of the two types reverse micelles were not

determined and compared.

To separate the interfacial dynamics from the core dynamics, it is necessary to

know the vibrational lifetime and orientational relaxation time of the core.3,5,23

For

large reverse micelles studied here, the core has bulk water dynamics; therefore, the

necessary dynamical parameters are known. The study is performed on w0 = 20 Igepal

reverse micelles with a water nanopool diameter of 9 nm, which is the same size as the

water nanopool in w0 = 25 AOT reverse micelles. The difference in w0 for the same

size water nanopool is caused by the different aggregation numbers of the two

surfactants. A water pool size of 9 nm is more than sufficient to have distinct

interfacial and bulk-like core sub-ensembles of water molecules.5 The method for

extracting the interfacial water dynamics from the data3 is modified to account for the

contribution to the signal from the Igepal head group alcohol hydroxyls. The results

show that the orientational relaxation time of water at the Igepal interface (13 ps) is

very similar but probably not identical to water at the AOT interface (18 ps). Thus,

the presence of an interface is the dominant factor in determining interfacial hydrogen

bond dynamics while the chemical composition of the interface plays a minor role.


Igepal CO-520, n-hexane, cyclohexane, H2O, and D2O (Sigma-Aldrich) were

used as received. A 0.3 M stock solution of Igepal CO-520 in a 50/50 weight percent

mixture of n-hexane and cyclohexane was prepared. Enough water (5% HOD in H2O)

was added to obtain w0 = 20 Igepal reverse micelles with a water pool diameter of 9

99

nm.34

The water content of the reverse micelles was verified by Karl Fischer titration.

The optical density of the sample was ~0.6.

The pump-probe measurements were made with a Ti:Sapphire

oscillator/regenerative amplifier operating at 1 kHz that pumped an optical parametric

amplifier to produce ~70 fs mid-IR pulses at ~4 μm (2500 cm-1

). The mid-IR light is

beam-split into weak probe and intense pump pulses with horizontal polarization. The

pump pulse is rotated by 45º immediately before the sample. After the beams cross in

the sample, the probe is resolved parallel and perpendicular to the pump by a polarizer

on a computer-controlled rotation stage before it is dispersed by a monochromator

onto a 32 element mercury cadmium telluride detector. The experimental system is

purged with CO2 and H2O-scrubbed air.


5.3.1 Absorption Spectroscopy

Figure 5.2 displays FT IR spectra of the OD stretch of dilute HOD in H2O in

three different environments: pure water, w0 = 20 Igepal reverse micelles, and w0 = 25

AOT reverse micelles. Both reverse micelle spectra are slightly blue-shifted from

bulk water, which peaks at 2509 cm-1

. The AOT and Igepal spectra peak at 2519 cm-1

and 2514 cm-1

, respectively.

The AOT spectrum for w0 = 25 and other sizes can be fit as a linear

combination of the bulk water spectrum and the spectrum of a w0 = 2 AOT reverse

micelle, which peaks at 2565 cm-1

.3,8

The w0 = 2 spectrum is akin to the interfacial

water spectrum because essentially all of the water molecules are associated with the

AOT sulfonate head groups.3,8

The equivalent analysis is not possible for the Igepal

reverse micelles. The sizes of smaller Igepal reverse micelles (under ~w0 = 10) are not

well characterized, so it is not possible to have a well defined small reverse micelle to

use as a model for the interfacial water spectrum.34

The Igepal surfactant has hydroxyl

head groups that will exchange deuterium atoms with the HOD molecules in the water

nanopool. The surfactant’s deuterated hydroxyls will contribute to the spectrum. For

a very small Igepal reverse micelle (with little water), the head group hydroxyls will

100

make a major contribution to the spectrum, preventing the spectrum from being used

to represent interfacial water.

The small blue shift and broadening on the blue side of the w0 = 20 Igepal

reverse micelle OD stretch spectrum and the fact that a blue shift has been observed in

many systems of confined or hydrating water,3,10,11,18,19,21,23

indicate that the

frequencies associated with interfacial water are on the blue side of the spectrum. As

in the AOT studies, it will be shown below that interfacial water population relaxation

and orientational relaxation for the Igepal reverse micelle system can be obtained from

measurements on the blue side of the spectrum.

Figure 5.2 IR absorption spectra of the OD stretch of 5% HOD in H2O for Igepal w0=20, AOT

w0=25, and bulk water.

2300 2400 2500 26000.0

0.2

0.4

0.6

0.8

1.0 bulk water

Igepal w0= 20

AOT w0= 25

frequency (cm-1)

abso

rban

ce (

no

rm.)

101

Figure 5.3 Vibrational population relaxation data. a) Data for the OD stretch of HOD in H2O in the

water nanopools of w0=20 Igepal reverse micelles at four detection frequencies and bulk water for

comparison. b) The vibrational population relaxation data for the 2576 cm-1

detection frequency and a

biexponential fit.

t (ps)

P(t

) (n

orm

.)

1 2 3 4 5 6 7 8 9 10 11

0.0

0.2

0.4

0.6

0.8

1.0

Data and fit - 2576 cm-1b

0.0

0.2

0.4

0.6

0.8

1.0

P

(t) (n

orm

.)

a

bulk water

2520 cm-1

2538 cm-1

2557 cm-1

2576 cm-1

102

5.3.2 Population Relaxation and Orientational Relaxation

Polarization selective pump-probe measurements yield both the population

relaxation (vibrational lifetimes) and decay of the anisotropy (orientational relaxation

parameters). Vibrational lifetimes are very sensitive to the details of the local

environment of the vibrational oscillator, which in this case is the OD stretching

mode.8,35,36

As discussed in Section 3.7.4, orientational relaxation of water occurs by

concerted hydrogen bond switching, referred to as jump reorientation.1,2

Orientational

relaxation is strongly influenced by the local details of the hydrogen bonding network.

Both the population relaxation and the anisotropy decay are obtained from

measurements of the pump-probe signals with the probe pulse polarization parallel and

perpendicular to the pump pulse, denoted as I and I , respectively. The population

relaxation, P(t), is

( ) 2P t I I . (5.1)

The anisotropy decay is

2( ) 0.4 ( ),2

I Ir t C t

I I

(5.2)

where C2(t) is the second Legendre polynomial orientational correlation function for

the OD stretch transition dipole.37

Figure 5.3a displays population relaxation data for four frequencies in the

Igepal w0 = 20 reverse micelle and bulk water. As the frequency is increased, the data

decay more slowly. The decays are not exponential. Figure 5.3b shows the data for

2576 cm-1

(circles) and a bi-exponential fit to the data (solid curve). In the fit, one

component has its lifetime fixed at 1.8 ps, the value measured for bulk water.3 The

amplitudes and the second decay time are allowed to float. However, if the core water

component is also allowed to vary, the fit again yields 1.8 ps for the major component

of the decay. To determine the other decay component, a number of decay curves for

a range of wavelengths on the blue side of the line were fit simultaneously. The

results of this fit yield an interfacial water vibrational lifetime of about 3.6 0.3 ps

and fractions ranging from 0.96 bulk water for 2520 cm-1

to 0.78 bulk water for 2595

103

cm-1

. The apparent slowing of the decays as the frequency is increased is caused by a

larger fraction of the decay coming from the slower decaying interfacial component.

In the recent study of large AOT reverse micelles, including w0 = 25, very

similar biexponential population decays were observed with the core (bulk water)

component having a vibrational lifetime of 1.8 ps.3 The second component is assigned

to the OD stretch of water molecules at the AOT interface. Here the situation is more

complicated. In the population decays for the Igepal reverse micelles (Figure 5.3), the

1.8 ps component is also the core (bulk water) component. The other component is

associated with interfacial ODs. Because the Igepal head group hydroxyls will

exchange deuterium atoms with the water HODs, 5% of the head group alcohol

hydroxyls will be ODs as well. Thus, there are two types of interfacial OD hydroxyls

that will contribute to the slow component of the population decay. As a result, the

population decay must be described with three components, a bulk water-like core (1.8

ps decay), an interfacial water shell, and the Igepal hydroxyls,

1 1 1/ / /( )

cw iw iat T t T t T

cw iw iaP t a e a e a e

, (5.3)

where the ai’s and 1

iT ’s are the amplitudes and vibrational lifetimes of the three

components, respectively. The subscript cw stands for core water; iw stands for

interfacial water; and ia stands for interfacial alcohol. As discussed below, the fact

that the population relaxation data fit so well to a biexponential decay arises because

aia << aiw, and 1

iwT and 1

iaT are similar in value.

In the AOT system, the orientational decay involved the core water with an

orientational relaxation time of 2.6 ps and interfacial water with one unknown

orientational relaxation time. Fitting the data gave ~18 ps for the interfacial water

orientational relaxation time. Here there are three orientational relaxation times. The

core value is that of bulk water, and the orientational relaxation time of the alcohol

head group can be taken to be infinitely long on the time scale of the experiments.

Therefore, there is one unknown orientational relaxation time. Nonetheless, the

presence of the third component, the head group alcohol hydroxyls, complicates the

data analysis and increases the error bars on the results. The anisotropy for the three

component system is,

104

1 1 1

1 1 1

/ / / / /

/ / /( ) ,

cw cw iw iw iar r

cw iw ia

t T t t T t t T

cw iw ia

t T t T t T

cw iw ia

a e e a e e a er t

a e a e a e

(5.4)

where the ai’s and Ti’s are the same as those in Equation 5.3, and the i

r ’s are the

orientational relaxation times. Because the alcohol hydroxyl will not reorient on the

time scale of the experiments, the third term in the numerator does not contain an

orientational relaxation exponential. We know most of the parameters in Equation

5.4. 1

cwT and cw

r are the bulk water values, 1.8 ps and 2.6 ps, respectively. At a

given wavelength, we know acw from fitting the population decay curve. We also

know that aiw + aia = 1 – acw. Furthermore, we know that at each wavelength

1 1/ /iw iat T t T

iw iaa e a e

must have the appearance of a single exponential decay, and the

two terms combine to give the time constant and amplitude of the slow component of

the population decay curve. To make additional progress, we need to address the issue

of the relative sizes of aiw and aia.

Without the interfacial alcohol terms, Equation 5.4 is the same equation that

was used to fit the AOT reverse micelle data.3-5

As has been discussed in detail

previously, r(t) does not necessarily decay monotonically for a two component

system.3,8,16

For systems that have a bulk water component and water interacting with

an interface or solutes, it has been measured that both the lifetime and the orientational

relaxation of water interacting with other species are slower than those of bulk

water.9,10,18,19,21,23,38,39

In these situations, a two component system will display an

anisotropy decay that is fast initially, then levels off to a plateau or even increases for

a time before finally decaying with the orientational relaxation time of the slow

component.3,6,23,39

Plots of this type were discussed in Chapter 4 and illustrated by

Figure 4.7. This is the situation for water in large AOT reverse micelles, such as w0 =

25, which is being used for comparison to the Igepal reverse micelles studied here.

Because of the limitation imposed by the vibrational lifetimes, it is not possible to

observe the full experimental r(t) curve. In the AOT systems, with the bulk water

parameters known and the interfacial water lifetime determined from the population

relaxation curve, the form of the anisotropy data around the plateau and the plateau

level are very sensitive to the interfacial orientational relaxation time.

105

Figure 5.4 Anisotropy data for bulk water and Igepal w0=20 and AOT w0=25 which both have

water nanopool diameters of 9 nm. The decays are quite similar but not identical.

The analysis of the Igepal data is similar to the method used for AOT except

that there are the additional terms in Equation 5.4 to account for the non-reorienting

alcohol hydroxyls. The term in the numerator contributes a time independent

anisotropy that decays with the Igepal surfactant hydroxyl lifetime. This constant

anisotropy term will contribute to the level of the plateau. Therefore, to fit the data we

need a reasonable estimate of the size of this term.

To illustrate the procedure for extracting the interfacial water dynamics, data at

the specific frequency 2576 cm-1

will be discussed. Figure 5.4 shows the anisotropy

data for the w0 = 20 Igepal system (solid curve) and the w0 = 25 AOT system (dashed

curve), and bulk water. For comparison to the Igepal curve, the AOT curve was shift

down by 0.03 because it has a smaller ultrafast (<200 fs) inertial drop.12

First it is

obvious that the Igepal and AOT data are quite similar in shape, but they are not

identical. The AOT data displays a plateau at long time while the Igepal data turns up

slightly. In addition, the analysis of the Igepal data needs to include the constant

0 1 2 3 4 5 6 7 80.0

0.1

0.2

0.3

0.4

t (ps)

r(t)

an

iso

tro

py

Igepal w0 = 20 2576 cm-1

AOT w0 = 25 2575 cm-1

bulk water

106

anisotropy and lifetime terms that come from the alcohol head groups. Fitting the

population relaxation for Igepal at 2576 cm-1

to a biexponential decay, gives a lifetime

of 1.8 ps and an amplitude of 0.74 for the core bulk water component, and an

amplitude and time constant of 0.26 and 3.2 ps for the second component. This

second time constant is essentially a weighted average of the lifetimes of the

interfacial water and Igepal hydroxyls and is consistent with the global fit described

previously. The 0.26 fraction is the sum of the amplitudes for the interfacial water

(iw) and alcohol head group (ia) components.

Figure 5.5 Data analysis with three component model. a) Fit to population relaxation data (2576

cm-1

). b) Fit to anisotropy data (2576 cm-1

).

0 1 2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

b

t (ps)

r(t)

an

iso

tro

py

Data (2576 cm-1)

Fit – three component model

0 2 4 6 8 10 12 14

0.0

0.2

0.4

0.6

0.8

1.0

a

t (ps)

P(t

) (n

orm

.)

Data (2576 cm-1)

Fit – three component model

107

The fractions aiw and aia (Equations 5.3 and 5.4) can be estimated from the

molar ratios of water and Igepal surfactant molecules and the physical geometry of the

water nanopool. The diameter of the water nanopool is 9 nm. Experimental and

theoretical results have shown that only the first hydration layer around an interface or

solute is substantially perturbed,20,25-28

so we can assume that the interfacial water is

located primarily within a shell of thickness 0.28 nm,3 which is the approximate

diameter of a water molecule. Calculating the volume of this shell and dividing it by

the total volume of the micelle interior yields a fraction of 0.18. In the w0 = 20 Igepal

reverse micelle, there are ~12800 water molecules. 18% of them will be at the

interface. There are two hydroxyls per water molecules, yielding ~4500 interfacial

water hydroxyls in total. We estimate that approximately six hundred Igepal

surfactant molecules form the w0 = 20 reverse micelles, and each surfactant has a

single alcohol hydroxyl in the head group. Therefore, there are ~4500/600 or ~7.5

water hydroxyls per Igepal hydroxyl head group. To reflect this ratio, we can assign a

fraction of 0.23 and 0.03 to the interfacial water hydroxyls and Igepal alcohol

hydroxyls, respectively. Their sum equals 0.26, the fraction of non-bulk hydroxyls.

We can now fix aiw and aia to these fractions. Because the contributions to the signal

depend on the transition dipoles as well as the population fractions, we assume that the

transition dipoles of the two species at the same frequency are the same. Recently it

was shown that the interfacial water and the core water in AOT reverse micelles have

the same transition dipoles at the same frequency within experimental error.3 These

transition dipoles also have the same frequency dependence. It is known for bulk

water that both the hydrogen bond strength and the transition dipole vary together with

frequency.40

Here the signals from the three types of hydroxyls are detected at the

same frequency, so the assumption that their transition dipoles are the same may be

reasonable. To account for error in our estimate of the fractions and possible

differences in the transition dipoles, we varied the fractions around the calculated

values in the data fits. There are three remaining parameters, the lifetimes 1

iwT and 1

iaT

and the interfacial water rotation time, iw

r . 1

iwT and 1

iaT are highly constrained

108

because they must yield the slow component of the population decay. For a given

choice of aiw and aia, the 1

iwT and 1

iaT values have little room to vary.

Figure 5.5 shows the population relaxation data and the anisotropy data at 2576

cm-1

along with the fits to the data. In the fits, the following parameters have fixed

input parameters: acw = 0.74, 1

cwT = 1.8, cw

r = 2.6, aiw = 0.23, and aia = 0.03. The fits

return the following values: 1

iwT = 3.0 ps, 1

iaT = 4.9 ps, and iw

r = 16 ps. As mentioned

above, the values obtained from the geometric considerations for the interfacial water

fraction and the interfacial alcohol fraction were varied. The value for aiw was varied

from 0.20 to 0.25 with aia varied correspondingly. Outside of this range, the fits were

clearly poor. For each pair of values, the data were fit. Any set of fit parameters that

could not reproduce both the population and anisotropy data was rejected. In the end,

ranges of acceptable values of the parameters were obtained. The ranges were used to

assign the error bars. The results are given in Table 5.1. Fractions for aiw between

0.21 and 0.23 gave the best fits. The 1

iwT varied over a range of 2.8 ps to 3.5 ps, and

1

iaT varied between 4.4 and 5 ps. The 1

iwT values are reasonable for the OD stretch of

HOD in water in confined or restricted environments.3,8,23

Table 5.1 Parameters for Population and Orientational Relaxation for Water in w0=20 Igepal

Reverse Micelles (2576 cm-1

). ai’s – fractional populations; T1’s – lifetimes; r’s – orientational

relaxation times.

The key parameter of interest is the interfacial water reorientation time. The

fits yield 13 4 ps.iw

r Moilanen et al. found the interfacial reorientation time in

large AOT reverse micelles, including w0 = 25, to be 18 3 ps.3 The error bars reflect

estimates of the maximum absolute errors which depend on the data analysis model.

Precision and reproducibility of the data are much better. The error bars for iw

r in

Igepal and AOT overlap to some extent. The orientational relaxation time of water at

bulk water interfacial water alcohol head group

acw 0.74a aiw 0.22 0.01 aia 0.04 0.01

1

cwT 1.8 psa

1

iwT 3.2 0.3 ps 1

iaT 4.7 0.3 ps

or

1 2.6 psa iw

r 13 4 ps

afixed parameters

109

the neutral interface of Igepal is at most modestly faster than it is at the ionic interface

of AOT.

A good deal is known about the AOT interface including the surface area per

head group and how it changes with reverse micelle size.41

Little is known about the

nature of the Igepal interface. The alcohol hydroxyls that terminate the Igepal

surfactant molecules do not have sufficient area to solely comprise the interface. It is

likely that there are also ether oxygens, which can make hydrogen bonds with water,

and possibly methylenes at the interface. Therefore, water molecules will have a

variety of types of interfacial interactions. While AOT in some sense has a more

chemically homogeneous interface, it will also be inhomogeneous in the details of the

water-head group interactions. Therefore, the interfacial orientational relaxation times

of water at the Igepal and AOT interfaces should be considered average values for the

interfacial water dynamics.

In the analysis, exchange of population between interfacial water and the core

water was not included, although possible exchange was considered in connection

with the previous experiments on AOT reverse micelles.3 For exchange to occur,

water must move away from the interface into the core and vice versa. Such

translational motion requires hydrogen bond rearrangements, which involve large

amplitude angular jumps from one hydrogen bond acceptor to another.1,2

Thus,

reorientation must occur for exchange to occur. The converse is not true. As

discussed briefly above, there are multiple water binding sites at the interfaces.

Reorientation may take place by forming a new hydrogen bond at a different

interfacial binding site without exchanging away from the interface. It would be

unphysical to imagine a water molecule diffusing away from the interface into the

bulk-like core without rotating. Furthermore, both the lifetime and orientational

relaxation time of water at the reverse micelle interfaces are slower than those of bulk

water. Exchange between interfacial water and the bulk-like core water would result

in apparent vibrational lifetimes and orientational relaxation times of the core water

being slower than those of bulk water.21

However, the data for all large AOT reverse

micelles3 and the w0 = 20 Igepal reverse micelles studied here were fit very well using

the bulk water lifetime and orientational relaxation time. Based on these

110

considerations and the experimental results of chemical exchange in concentrated salt

solutions,21

the orientational relaxation time of reverse micelle interfacial water can be

taken as a lower bound for the exchange time.


The results presented here demonstrate that water at the neutral Igepal interface

undergoes orientational relaxation (13 ps) that is much slower than that of bulk water

(2.6 ps) and possibly somewhat faster than water at the ionic AOT interface (18 ps).

Orientational relaxation of water requires concerted hydrogen bond rearrangement.1,2

The presence of an interface blocks many of the pathways that are needed for the

hydrogen bond rearrangements that gives rise to jump reorientation. The results show

that the main influence on interfacial hydrogen bond dynamics and orientational

relaxation is the presence of the interface rather than its chemical composition: ionic

head groups (AOT) vs. neutral head groups (Igepal).

The possibly faster orientational relaxation at the neutral interface compared to

the ionic interface seems reasonable in light of recent experiments on the exchange

time for a water hydroxyl hydrogen bonded to an anion to go to being hydrogen

bonded to another water molecule. Ultrafast 2D IR vibrational echo chemical

exchange experiments were used to directly measure the time for hydrogen bond

switching between waters bound to tetrafluoroborate anions and water hydrogen

bonded to other water molecules.21

The time for a water to go from being bound to an

anion to being bound to another water is 7 ps.21

The equivalent number for water is

~2 ps. Therefore, interaction with an ion slows hydrogen bond switching in a

concentrated salt solution, but not to a great extent. For water at the interfaces of ionic

and non-ionic reverse micelles, a similar trend is observed in the orientational

relaxations times, which depend on hydrogen bond switching. The difference in the

time for hydrogen bond switching from ion to water vs. water to water is similar to the

difference between the orientational relaxation times at the ionic interface vs. the non-

ionic hydrophilic interface in reverse micelles. While the orientational relaxation

times at the two types of interfaces are similar, the chemical compositions of the

interfaces may have some influence on the dynamics.

111

5.5 References




113, 8560.


131, 8318.


131, 014704.


(7) Park, S.; Moilanen, D. E.; Fayer, M. D. J. Phys. Chem. B 2008, 112, 5279.


Phys. Chem. A 2006, 110, 4985.

(9) Moilanen, D. E.; Piletic, I. R.; Fayer, M. D. J. Phys. Chem. C 2007, 111, 8884.

(10) Moilanen, D. E.; Piletic, I. R.; Fayer, M. D. J. Phys. Chem. A. 2006, 110, 9084.

(11) Moilanen, D. E.; Levinger, N.; Spry, D. B.; Fayer, M. D. J. Am. Chem. Soc.

2007, 129, 14311.

(12) Moilanen, D. E.; Fenn, E. E.; Lin, Y. S.; Skinner, J. L.; Bagchi, B.; Fayer, M.

D. Proc. Natl. Acad. Sci. USA 2008, 105, 5295.


122, 054506.



(15) Steinel, T.; Asbury, J. B.; Corcelli, S. A.; Lawrence, C. P.; Skinner, J. L.;

Fayer, M. D. Chem. Phys. Lett. 2004, 386, 295.

(16) Dokter, A. M.; Woutersen, S.; Bakker, H. J. Proc. Natl. Acad. Sci. USA 2006,

103, 15355.





C14.


13847.


Natl. Acad. Sci. USA 2009, 106, 375.

(22) Kubota, J.; Furuki, M.; Goto, Y.; Kondo, J.; Wada, A.; Domen, K.; Hirose, C.

Chem. Phys. Lett. 1993, 204, 273.


2009, 131, 5530.

(24) Zhao, W.; Moilanen, D. E.; Fenn, E. E.; Fayer, M. D. J. Am. Chem. Soc. 2008,

130, 13927.

(25) Bhide, S. Y.; Berkowitz, M. L. J. Chem. Phys. 2006, 125, 094713.

(26) Bagchi, B. Chem. Rev. 2005, 105, 3197.

112


(28) Halle, B.; Davidovic, M. Proc. Natl. Acad. Sci. USA 2003, 100, 12135.

(29) Laage, D.; Stirnemann, G.; Hynes, J. T. J. Phys. Chem. B 2009, 113, 2428.

(30) Zulauf, M.; Eicke, H. F. J. Phys. Chem. 1979, 83, 480.




(34) Lipgens, S.; Schubel, D.; Schlicht, L.; Spilgies, J.-H.; Ilgenfritz, G.; Eastoe, J.;

Heenan, R. K. Langmuir 1998, 14, 1041.




(38) Piletic, I. R.; Moilanen, D. E.; Levinger, N. E.; Fayer, M. D. J. Am. Chem. Soc.

2006, 128, 10366.

(39) Rezus, Y. L. A.; Bakker, H. J. Phys. Rev. Lett. 2007, 99, 148301.

(40) Corcelli, S.; Skinner, J. L. J. Phys. Chem. A. 2005, 109, 6154.

(41) Eicke, H.-F.; Rehak, J. Helv. Chim. Acta 1976, 59, 2883.

113

Chapter 6 Water Dynamics in Small Reverse

Micelles in Two Solvents: Two-Dimensional

Infrared Vibrational Echoes with Two-

Dimensional Background Subtraction

6.1 Introduction

Chemical, biological, geological, and industrial systems often involve water

molecules in nanoconfined environments mediating processes at interfaces. The

chemical composition of the interface can vary (neutral, charged, hydrophobic, etc.),

as well as the size of the confining space. In its bulk form, water exists in an extended

hydrogen bond network where water molecules readily make and break hydrogen

bonds. Hydrogen bond reformation is a concerted process involving water motions of

both the first and second solvation shells.1,2

Interfaces and nanoscopic confinement

can disrupt the rearrangement pathways and slow down hydrogen bond dynamics.3-5

Important questions involve how an interface influences water dynamics as a function

of the size of the system. Observables that report on these influences include the

orientational relaxation,6 vibrational lifetime,

7 and spectral diffusion of the water

hydroxyl stretch.8

To study confined water, it is useful to employ a system in which the size of

the water nanopool can be controlled. The ternary system of the surfactant Aerosol-

OT (AOT), water, and a nonpolar phase is often used for this purpose, as reverse

micelles of varying water pool diameters, ranging from 1 nm to tens of nanometers,

can be made by changing the relative amounts of the components of the mixture.9-11

The parameter w0=[H2O]/[AOT] determines the water pool size.11

AOT (Figure 6.1)

is a charged surfactant molecule with an anionic sulfonate head group and a sodium

counter ion. The head group region comes into direct contact with the water pool.

The branched, alkyl tails of AOT are immersed in a nonpolar solvent. In large reverse

micelles, most of the water resides in a bulk-like core while a smaller fraction is

114

influenced by the interface.12

In small reverse micelles, the interface can perturb the

entire water nanopool so that all water molecules deviate from bulk-like behavior.5,12

In addition to having a range of sizes, AOT reverse micelles are spherical,

monodispersed, and well-characterized, making them a useful system for study.

Furthermore, a variety of solvents, including isooctane, hexane, toluene, and carbon

tetrachloride, may be used as the nonpolar phase without significantly changing the

size or characteristics of the enclosed water pool.13,14

In this chapter, we will address

whether changing the identity of the nonpolar phase affects the dynamics of the water

pool even though the static properties, such as size, remain the same.

Figure 6.1 Molecular structure of AOT.

Techniques which have been employed to study the dynamics of water in AOT

reverse micelles include ultrafast infrared spectroscopy,3-5,12,15-22

nuclear magnetic

resonance,23,24

fluorescence,25-30

neutron scattering,31

, dielectric relaxation,32

and

simulations.33-35

These studies collectively agree that water hydrogen bond

rearrangement slows down as the reverse micelle size decreases. In particular,

ultrafast infrared (IR) spectroscopy is a potent technique, as it can probe water

dynamics on the relevant picosecond timescale by monitoring observables associated

with the water hydroxyl stretching mode.

Spectral diffusion and orientational relaxation in bulk water using dilute HOD

in either H2O or D2O have been studied with experiments36-45

and molecular dynamics

(MD) simulations.46-55

HOD is studied rather than pure H2O or D2O to eliminate

vibrational excitation transfer56,57

and to simplify the hydroxyl stretch spectrum. For

HOD in bulk H2O, 2D IR vibrational echo experiments show a homogeneous

component and spectral diffusion.38,41

The spectral diffusion occurs on multiple time

scales. There is a very fast time scale (<0.4 ps) that MD simulations show arises from

very local hydrogen bond fluctuations, mainly of the lengths of the hydrogen

115

bonds.51,53

The longest time scale for spectral diffusion (1.7 ps) is associated with

complete randomization of the hydrogen bond network structure.58

Pump-probe

orientational anisotropy measurements yield a 2.6 ps orientational relaxation time59

(second Legendre polynomial orientational correlation function decay6) following an

ultrafast inertial component.60

The 2.6 ps time arises from jump orientational

relaxation.1,2

The two times, 2.6 ps and 1.7 ps, are very similar, so it is concluded that

the jump reorientation mechanism for orientational relaxation is closely related to the

hydrogen bond network randomization that gives rise to the slowest component of the

spectral diffusion.

In this chapter polarization selective IR pump-probe experiments and ultrafast

2D IR vibrational echo experiments are used to monitor the water dynamics inside

reverse micelles. The IR pump-probe experiments measure the vibrational population

relaxation and orientational relaxation for three small sizes of micelles, w0=2, 4, and

7.5. Each w0 was prepared in isooctane and in carbon tetrachloride. We also present a

study of the spectral diffusion of water in the w0 = 2 reverse micelle using ultrafast 2D

IR vibrational echo experiments to monitor the structural evolution of the water

hydrogen bond network, also in the two different solvents. The w0 = 2 reverse

micelles have a water pool diameter of 1.7 nm and contain ~40 water molecules.12

In

w0 = 2, all of the water molecules are strongly influenced by the presence of the

interface, but not all hydroxyl groups are necessarily hydrogen bonded to a sulfonate.

Isooctane has been widely used as the nonpolar phase for AOT reverse micelle

systems in a variety of experiments ranging from viscosity and density

characterizations to X-ray scattering and ultrafast IR measurements.10,12,61,62

MD

simulations have also utilized isooctane as the nonpolar phase. It is therefore

important to know whether experiments carried out in different solvents may be

compared. This chapter compares results for the solvents isooctane and CCl4. It is

found that within experimental error the spectra, population relaxation, and

orientational relaxation remain constant for a given w0 regardless of the solvent.

Initially the spectral diffusion of the OD stretch of dilute HOD in H2O in w0 = 2

reverse micelles appears to be much faster when the solvent is isooctane vs. CCl4.

However, the interferograms that are Fourier transformed to obtain the 2D IR

116

vibrational echo spectra are distorted in the isooctane solvent system. In the absence

of HOD and in the absence of any water, two situations in which no signal should be

produced, the AOT/isooctane sample gives a signal in the vibrational echo experiment,

but the AOT/CCl4 sample does not. Isooctane by itself gives no signal. A method

was developed in which the interferogram signals from the AOT/isooctane/H2O

sample were recorded and subtracted from the interferogram signals obtained from the

AOT/isooctane/HOD/H2O sample. When this 2D background is removed, the spectral

diffusion from the samples with CCl4 and isooctane become similar. Because of the

distortions introduced by the isooctane solvent, CCl4 is a better solvent for the 2D IR

experiments. These results show that experimental and simulated results may be

directly compared even if different solvents are used as the nonpolar phase.


Isooctane, carbon tetrachloride, H2O, and D2O (Sigma-Aldrich) were used as

received. Aerosol-OT (AOT), which is sodium bis(2-ethylhexyl) sulfosuccinate, was

vacuum dried for at least a week before sample preparation. 0.5 M stock solutions of

AOT were prepared in isooctane and in carbon tetrachloride (CCl4). The residual

water content was determined by Karl Fischer titration to be w0 = 0.14 in the isooctane

stock solution and w0 = 0.2 in the carbon tetrachloride stock solution. Reverse micelle

samples were prepared by mass by adding appropriate amounts of a stock solution of

5% HOD in H2O to measured quantities of the AOT stock solutions to make the

desired w0.

The OD stretch of dilute HOD in H2O is studied because it prevents vibrational

excitation transfer processes from causing artificial decays of the orientational

correlation function and the frequency-frequency correlation function (spectral

diffusion).56,57

MD simulations have shown that a small percentage of HOD does not

change the structure and properties of H2O and that experiments on the OD stretch

yield the dynamics of water.52

The samples for IR absorption and ultrafast experiments

were contained in sample cells consisting of two calcium fluoride windows separated

with a Teflon spacer. The Teflon spacer thickness was chosen such that the optical

117

density in the OD stretch region was ~0.1 for 2D IR echo experiments and ~0.5 for

pump-probe experiments

In the laser system, a Ti:Sapphire oscillator seeds a regenerative amplifier

which pumps an optical parametric amplifier (OPA). The output of the OPA is

difference frequency mixed in a AgGaS2 crystal to generate ~70 fs pulses at ~4 µm

(2500cm-1

). The wavelength of IR light is tuned to the frequency of the peak

absorption of the OD stretch spectrum, which is 2565 cm-1

for w0 = 2. In the 2D IR

experiments, the IR beam is split into three excitation pulses and a local oscillator

(LO) beam that is used for heterodyne detection. The three excitation pulses are time

ordered, with pulses 1 and 2 traveling along variable delay stages. The first pulse

creates a coherence consisting of a superposition of the v = 0 and v = 1 vibrational

levels. During the evolution period τ the phase relationships between the oscillators

decay. The second pulse reaches the sample at time τ and creates a population state in

either v = 0 or v = 1. A time Tw (the waiting period) elapses before the third pulse

arrives at the sample to create another coherence that partially restores the phase

relationships. Rephasing of the oscillators causes the vibrational echo signal to be

emitted at a time t ≤ τ after the third pulse. During Tw, spectral diffusion occurs as the

water molecules sample different environments due to dynamic structural evolution of

the system. The frequencies of the OD vibrational oscillators evolve (spectral

diffusion) as the water network structure changes. The vibrational echo signal is

spatially and temporally overlapped with the LO for heterodyned detection. The

heterodyned signal is frequency dispersed by a monochromator and detected on a 32

element mercury cadmium telluride detector. At a fixed Tw, τ is scanned to generate a

2D IR vibrational echo spectrum. Then Tw is changed and another 2D spectrum is

recorded. The time evolution of the 2D spectra provides the information on spectral

diffusion.

Center line slope (CLS) analysis63-65

of the 2D IR vibrational echo spectra is

used to analyze the data. In the CLS technique, slices are cut through the 2D spectra

parallel to the ωm (detection) axis and fit to Gaussian line shapes to obtain the peak

positions for each slice. The peak positions are plotted versus ωτ (the excitation axis

frequency intercepted by each slice) over a range of frequencies about the center of the

118

spectrum and fit with a linear regression to find the slope of the line. These slopes are

obtained for each Tw and plotted vs. Tw. The CLS method of data analysis is a useful

method for extracting information from the 2D data. It is independent of a specific

model of the spectral diffusion dynamics. A fit to the CLS data using, for example, a

multi-exponential model yields time constants that can be compared for different

systems. MD simulations can be used to calculate the 2D IR vibrational echo spectra,

and then the CLS can be obtained from the simulated 2D spectra and compared to

data.

It has been shown theoretically that the CLS method can be used to determine

the frequency-frequency correlation function (FFCF) under the assumption of

Gaussian fluctuations.63,65

The FFCF is a key to understanding the structural evolution

of molecular systems in terms of amplitudes and time scales of the dynamics. The

FFCF is the joint probability distribution that a frequency has a certain initial value at t

= 0 and another value at a later time t. The FFCF connects the experimental

observables to the underlying dynamics. Once the FFCF is known, all linear and

nonlinear optical experimental observables can be calculated by time-dependent

diagrammatic perturbation theory.66

However in bulk water, non-Condon effects and

deviation from Gaussian fluctuations play a role in the nature of the 2D IR vibrational

echo spectra and other observables.67,68

Non-Condon effects account for a varying

transition dipole with absorption frequency.67,68

The FFCF is based on a theoretical

methodology that does not include non-Condon effects. Simulations of bulk water

using the Gaussian approximation or simulations without the Gaussian approximation

that include non-Condon effects, and other details, show that variations in the

simulations of the experimental observables using different water models are as large

as differences that arise from making or not making the Gaussian

approximation.38,41,53,67

For water nanopools in reverse micelles, which are even more

complex than bulk water, the difficulties of trying to extract useful information from

2D IR spectra using full simulations are monumental. Therefore, employing the CLS

to determine the FFCF, in spite of its approximate character, is a very useful approach

for determining the time scales of structural fluctuations and for comparing one

system to another.

119

The FFCF can be described with the form

2

1 1,0 1 1,0

2

( )( ) ( ) (0) exp( / )i i

i

tC t t

T

. (6.1)

The Δi are the frequency fluctuation amplitudes of each component, and the τi are their

associated time constants. If 1 for one component of the FFCF, then Δ and τ

cannot be determined separately and instead give rise to a motionally narrowed

homogeneous contribution to the absorption spectrum with a pure dephasing width

given by * 2 *21/ T , where *

2T is the pure dephasing time, and Γ* is the pure

dephasing line width. The total homogeneous dephasing time, T2, also has

contributions from the vibrational lifetime and orientational relaxation. T2 is given by

*

2 2 1 or

1 1 1 1

2 3T T T T , (6.2)

where *

2T , T1, and Tor are the pure dephasing time, vibrational lifetime, and

orientational relaxation times, respectively. The total homogeneous line width is

21/ T . The homogeneous line width is dominated by pure dephasing. The CLS

decay yields the normalized FFCF. Detailed procedures for converting the CLS

measurement into the FFCF have been described previously.65

By combining the CLS

with the linear absorption spectrum, the full FFCF is obtained including the

homogeneous component.

In the polarization and wavelength selective pump-probe experiments, the IR

beam is split into two pulses, a weak probe and intense pump. The pump is polarized

at 45° relative to the horizontally polarized probe pulse. The pump and probe impinge

on the sample, after which the polarization of the probe is resolved parallel and

perpendicular (±45°, respectively) to the pump using a polarizer on a computer

controlled rotation stage. The polarization is again set to horizontal before entering

the monochromator in order to eliminate problems from polarization-dependent

diffraction and reflection efficiencies of the monochromator. The frequency-dispersed

signal is detected by the 32 element mercury cadmium telluride detector. The

measured parallel and perpendicular signals contain information about the population

relaxation and orientational dynamics of the water molecules (HOD),

120

2( )(1 0.8 ( )),I P t C t (6.3)

2( )(1 0.4 ( ))I P t C t , (6.4)

where P(t) is the vibrational population relaxation and C2(t) is the second Legendre

polynomial orientation correlation function for a dipole transition. The parallel and

perpendicular signals are combined to give the pure population relaxation,

( ) 2P t I I . (6.5)

The signals may also be combined to give the anisotropy r(t), from which C2(t) can be

extracted,

2( ) 0.4 ( ).2

I Ir t C t

I I

(6.6)


6.3.1 Infrared Absorption Spectroscopy and Pump-Probe Experiments

Figure 6.2 shows the linear absorption spectra of the OD stretch in H2O in

three small reverse micelles in carbon tetrachloride and isooctane solvents, in addition

to the spectrum of bulk water for comparison. The spectra for a given w0 for the two

solvents are identical within experimental error, which supports previous experimental

results that concluded that the micelle size varies little with the identity of the

nonpolar solvent.13

As has been discussed extensively previously,12

the spectra exhibit

a systematic blue shift as the size of the micelle decreases. Compared to the peak

absorption of the OD stretch of HOD in bulk water that falls at 2509 cm-1

, the OD

spectrum in water in the w0 = 2 micelle has its peak absorption at 2565 cm-1

. When

OD is bound to sulfonate moieties the stretching spectrum is blue shifted relative to

OD bound to a water oxygen. The spectra with high proportions of interfacial waters

have greater blue shifts.3,5,12

Moilanen et al. recently studied the orientational dynamics of water molecules

at the interface in AOT reverse micelles in isooctane, showing that in large reverse

micelles, the dynamics of water molecules at the interface and in the core (bulk-like

water in the center of large water nanopools) may be separated.3,5

Each region has

121

dynamics with its own characteristic decay constants. The water dynamics for small

reverse micelles (w0 ≤ 5) exhibit reorientation dynamics that are no longer separable

into core and shell values.5 The orientational relaxation of the OD stretch of HOD in

H2O in w0 = 2 reverse micelles has an ultrafast inertial component (<200 fs), a fast

component (~1 ps), which has been attributed to a wobbling-in-a-cone

mechanism,5,19,69

and a very slow component of 110 ± 40 ps.5 Because of limitations

in the longest time that can be measured caused by the vibrational lifetime, even

slower relaxation may occur.

Figure 6.2 FT IR absorption spectra for bulk water and water in AOT/isooctane and AOT/CCl4

reverse micelles. The spectra of water inside reverse micelles of the same size in different solvents are

identical. As the reverse micelle size decreases, the spectra systematically shift to the blue.

Besides orientational relaxation, population relaxation (vibrational lifetime)

behavior also provides insight into the structure and environment of water molecules

in heterogeneous environments such as reverse micelles. When an oscillator becomes

excited, its vibrational energy will dissipate into a combination of low frequency

modes, such as bending modes, torsions and bath modes, which sums to the original

energy.7,70

In unrestricted environments such as bulk water, vibrational energy readily

dissipates via these modes. When a solute or interface disrupts the hydrogen bonding

2400 2500 2600 27000.0

0.2

0.4

0.6

0.8

1.0

w0=7.5/CCl

4

w0=4/CCl

4

w0=2/CCl

4

w0=7.5/isooct.

w0=4/isooct.

w0=2/isooct.

bulk water

frequency (cm-1)

abso

rban

ce (n

orm

.)

122

network, pathways that were available in the bulk may no longer be accessible by the

water molecules. Consequently, vibrational lifetimes are very sensitive to local

environments. For instance, the two vibrational lifetimes observed in large AOT

reverse micelles reflect a population of water molecules hydrogen bonded to other

waters and a second population of waters hydrogen bonded to the sulfonate head

groups. The lifetimes associated with these populations are 1.8 ps and 4.3 ps,

respectively.3 Previous experiments reported single exponential vibrational lifetime

behavior in very small AOT reverse micelles (w0=2 and 5) at all wavelengths,12

but

upon more rigorous analysis, we find that there is a slight wavelength dependence to

the vibrational lifetime. Well to the blue side of the OD stretch vibrational spectrum,

starting at ~2620 cm-1

, the vibrational lifetime for water in the AOT w0=2/CCl4 system

is single exponential, but the single lifetime varies somewhat with wavelength. For

instance, at 2620cm-1

, the lifetime is 7.4 ps, while at 2640 cm-1

it is 8.1 ps. At lower

frequencies in the absorption spectrum, the vibrational lifetime displays biexponential

behavior. For the w0=2/CCl4 sample, there is a relatively fast lifetime component of

2.0 ps with a small amplitude (13% and 8% at 2590 cm-1

and 2610 cm-1

, respectively)

while a second slower component of ~7.5ps makes up the rest of the amplitude.

Again, there is a slight wavelength dependence to the value of this second time

constant (see Table 6.1).

Table 6.1 Wavelength-dependent Vibrational Relaxation Times for AOT Reverse Micelles in

CCl4 and Isooctane.

Sample Parameter 2590 cm-1

2610 cm-1

2620 cm-1

2640 cm-1

w0 = 2/CCl4 A1 0.13 0.08 1.0 1.0

τvib1 (ps) 2.0 2.0 7.4 8.1

τvib2 (ps) 7.3 7.5 - -

w0 = 2/isooctane A1 0.10 0.05 1.0 1.0

τvib1 (ps) 1.9 1.9 7.2 7.9

τvib2 (ps) 6.7 7.1 - -

w0 = 4/CCl4 A1 0.22 0.15 0.13 0.10

τvib1 (ps) 2.0 2.0 2.0 2.0

τvib2 (ps) 6.4 6.6 6.9 7.4

w0 = 4/isooctane A1 0.27 0.19 0.14 0.17

τvib1 (ps) 2.0 2.0 2.0 2.0

τvib2 (ps) 6.2 6.4 6.5 6.7 Error bars are ±0.2 ps for time constants, ±0.04 for amplitudes

123

The existence of two separate lifetimes does not necessarily mean that there

are two distinct ensembles of water molecules as there are in larger reverse micelles.

In larger reverse micelles (w0 ≥ 7.5), there are distinct core and interfacial regions of

water molecules, each with associated vibrational lifetimes. In w0 = 2, the water pool

is too small to have a distinct core region. A distinct core exists if there are at least

some water molecules with first and second solvation shells that do not directly

interact with the interface. In the very small reverse micelles, the majority of water

molecules interact with the interface. However, some of the hydroxyls will be

hydrogen bonded to oxygens of other water molecules rather than to sulfonate head

groups. Thus there are two types of local environments for the OD stretch vibrational

relaxation. As vibrational lifetimes are extremely sensitive to local environment, these

two environments give rise to two lifetimes. As the short lifetime, ~2 ps, is very

similar to the lifetime found in bulk water, we assign this to ODs bound to water

oxygens. This assignment is further supported by the lack of this lifetime component

on the blue side of the spectrum which arises from water molecules bound to

sulfonates. These ODs display only the long lifetime. The water molecules are not

segregated into two regions with distinct lifetimes as they are in large reverse micelles.

In contrast, orientational dynamics rely on concerted motions involving many water

molecules.1,2

Therefore, in very small reverse micelles orientational relaxation

involves a single collective ensemble of water molecules while vibrational relaxation

is sensitive to the differences in the immediate environment of the a hydroxyl.

The w0=4/CCl4 reverse micelle system also shows two component vibrational

lifetime behavior with one time constant equal to 2.0 ps and the second time constant

ranging from 6.4 to 7.4 ps depending on the wavelength (Table 6.1). Again, local

heterogeneities in hydrogen bonding inside the reverse micelle yield separate lifetimes

even if the orientation dynamics do not yield separate orientation times. The

vibrational lifetimes were measured for both the CCl4 and isooctane systems (Table

6.1). Within experimental error, the observed lifetimes and associated amplitudes do

not vary with solvent, further supporting the idea that the water nanopools remain

constant regardless of the nonpolar phase’s identity. Figures 6.3 and 6.4 display

population and orientational relaxation data, respectively, for the three micelles in both

124

solvents at a common wavelength. Within experimental error, the data are invariant

with solvent.

Figure 6.3 Population relaxation data for water in the three sizes of reverse micelles showing the

invariance with nonpolar phase.

0.0

0.2

0.4

0.6

0.8

1.0

w0=2/CCl4, 2589 cm-1

w0=2/isooctane, 2589 cm-1

0 5 10 15 200.0

0.2

0.4

0.6

0.8

1.0

w0=7.5/CCl4, 2589 cm-1

w0=7.5/isooctane, 2589 cm-1

0.0

0.2

0.4

0.6

0.8

1.0

w0=4/CCl4, 2589 cm-1


t (ps)

P(t

) –

(no

rm.)

P(t

) –

(no

rm.)

P(t

) –

(no

rm.)

125

Figure 6.4 Orientational relaxation data for water in the three sizes of reverse micelles, again

showing the invariance with the nonpolar phase.

Vibrational and orientational relaxation parameters were also measured for the

w0=7.5/CCl4 reverse micelle system, listed in Table 6.2. Unlike the two smaller

reverse micelle sizes, w0=7.5 shows two component behavior in both vibrational

lifetime and orientational relaxation. The functional form and implementation of the

two component model has been addressed in depth in previous publications3-5,71

. The

w0 = 7.5 reverse micelles behave the same as the w0 = 10 reverse micelles studied

0.0

0.1

0.2

0.3

0.4

w0=2/CCl4, 2589 cm-1


0.0

0.1

0.2

0.3

0.4

w0=4/CCl4, 2589 cm-1


0 1 2 3 4 5 6 7 80.0

0.1

0.2

0.3

0.4

w0=7.5/CCl4, 2589 cm-1

w0=7.5/isooctane, 2589 cm-1

t (ps)

r(t)

–an

iso

tro

py

r(t)

–an

iso

tro

py

r(t)

–an

iso

tro

py

126

previously.5 Distinct core and interfacial regions exist for w0=7.5, but unlike the larger

reverse micelles (w0 ≥ 16.5), the core region is not purely bulk-like. Instead, its

parameters are 2.1 ps for vibrational lifetime and 4.4 ps for orientation, which are

slower than the bulk water values of 1.8 ps for vibrational lifetime and 2.6 ps for

orientational relaxation. The interfacial values are 5.5 ps for vibrational lifetime and

30 ps for orientational relaxation. The corresponding values are also listed for the

reverse micelles in isooctane, and they further show the insensitivity of the dynamics

to solvent. Therefore, the spectra, lifetimes, and orientational relaxation times are the

same within experimental error whether the solvent is isooctane or CCl4.

Table 6.2 Two Component Model Vibrational Lifetimes and Orientational Relaxation

Parameters for w0=7.5 Reverse Micelles in CCl4 and Isooctane.

6.3.2 2D IR Vibrational Echo Experiments

Figure 6.5 displays 2D IR vibrational echo spectra for w0 = 2 in CCl4 at a

series of Tws. The ωτ axis is the frequency axis for the first radiation field interaction

(first pulse) and the ωm axis is the frequency of the vibrational echo emission, which

corresponds to the frequency of the third radiation field interaction (third pulse). The

positive peak along the diagonal is from the 0-1 vibrational transition while the

negative-going peak below it arises from vibrational echo emission at the 1-2

transition frequency. The 1-2 peak is shifted along the ωm axis by the vibrational

anharmonicity. The spectrum is very elongated along the diagonal at early Tw,

meaning that there is a high probability that an oscillator excited at one frequency will

be detected at the same frequency. As time progresses the elongated peak becomes

more symmetric as the oscillators sample different environments, causing changes in

frequency (spectral diffusion). At the longest Tw’s for w0 = 2, spectral diffusion is not

complete. There is still significant elongation along the diagonal.

The 2D IR spectra can be analyzed with the CLS method63-65

described in the

experimental section. The CLS data for w0 = 2 in CCl4 are shown in Figure 6.6a. The

w0 τvib1 (ps) τvib2 (ps) τor1 (ps) τor2 (ps)

7.5/CCl4 2.1 5.5 4.4 30

7.5/isooctane 2.1 5.6 4.4 21 Error bars are ±0.2 ps for time constants, ±0.5 ps for τor1, and ±5 ps for τor2

127

vibrational lifetime prevents the acquisition of data at longer times. For the physical

reasons discussed below, we assume that there is a very slow component to the

spectral diffusion that is beyond the experimental time window. In fitting the CLS,

the very slow component is modeled as being infinitely slow, so the fit involves a sum

of exponentials plus a constant (Table 6.3). In addition to the homogeneous

component there is a fast time constant of 0.9 ps, an intermediate time constant of 10

ps, and an offset reflecting the very slow dynamics. Using the CLS data and the linear

absorption line shape, the FFCF was determined.65

The results are presented in Table

6.4. Previously, echo peak shift measurements and diagrammatic perturbation theory

were used to obtain the FFCF parameters for w0 = 2 AOT.12,14,20

However, these

experiments only made measurements out to 2 ps. Here, measurements were made to

20 ps, and many more Tw time points were measured.

Figure 6.5 2D IR correlation spectra for w0=2/CCl4 at a range of Tw values. The ωm and ωτ axes

are both in units of wavenumbers (cm-1

).

Table 6.3 Biexponential Fit Parameters for CLS Data for w0=2/CCl4. Ai – amplitudes; ti – time

constants; y0 – offset.

The initial echo experiments used isooctane as the organic phase because the

AOT/water/isooctane microemulsion system has been well characterized, both in

terms of steady-state characteristics and water hydrogen bonding dynamics. In

addition, reverse micelles may be made up to very large diameters in isooctane

whereas those in CCl4 are only stable up to w0 ~10.12,72

The bottom curve in Figure

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650 Tw = 0.2 ps Tw = 3 ps Tw = 15 ps

ωm

ωτ ωτ ωτ

A1 t1 (ps) A2 t2 (ps) y0

0.10 0.9 ± 0.1 0.35 10 ± 1 0.36 Error bars on amplitudes and offset are ±0.01

128

6.6b displays the CLS for w0 = 2 with isooctane as the solvent. The top curve is the

same data as Figure 6.6a; the solvent is CCl4. We will return to the middle curve

below. In spite of the fact that the spectra, vibrational lifetimes, and orientational

relaxation were identical in the two solvents, initially it appeared that the spectral

diffusion was very different.

Figure 6.6 Experimental CLS data for AOT w0 = 2. a) CLS data for w0=2/CCl4 reverse micelles.

The line through the data is the normalized FFCF for w0=2. b) Experimental CLS results: w0=2/CCl4

(solid dots), w0=2/isooctane beat subtracted data showing decent agreement with results in CCl4 (hollow

dots), and non-beat subtracted w0=2/isooctane CLS data showing extremely fast decay (triangles). The

line through the top curve is the normalized FFCF for that sample while the bottom tow lines are the

biexponential fits from Table 6.5.

0.0

0.2

0.4

0.6

0.8

1.0

w0=2/CCl4 CLS

w0=2/CCl4 FFCF

Tw(ps)

CL

S

A.

0 2 4 6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

w0=2/CCl4

w0=2/Isooctane, beat-subtracted

w0=2/Isooctane, no beat-subtraction

B.

CL

S

129

Figure 6.7 Interferogram data comparing water in AOT reverse micelles in different solvents. a)

Resonant interferogram in AOT/isooctane for w0=2 at Tw = 1 ps and 2580 cm-1

, showing the strange

beat behavior. b) AOT/CCl4 interferogram for w0=2 at Tw = 1 ps and 2580 cm-1

, showing normal echo

behavior.

A

B

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8-6

-4

-2

0

2

4

6

w0=2/CCl4

Tw=1 ps, 2580 cm-1

Resonant interferogram-6

-4

-2

0

2

4

6

Resonant Interferogram

w0=2/isooctane

Tw=1ps, 2580 cm-1

t (ps)

ech

o in

ten

sity

ech

o in

ten

sity

130

Figure 6.8 Interferogram data showing the beat subtraction procedure. a) Nonresonant pure H2O

in w0=2 AOT/isooctane, showing strange beat behavior. b) The red and blue interferograms

respectively show the resonant and nonresonant w0=2 interferograms at Tw = 1 ps and 2580 cm-1

used

for beat subtraction. c) Results of the beat subtraction method in isooctane. The interferogram looks a

lot cleaner and similar to the interferogram in Figure 6.7b.

-6

-4

-2

0

2

4

6w

0=2/isooctane

Tw=1 ps, 2580 cm-1

Non-resonant

interferogram

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8-6

-4

-2

0

2

4

6 w

0=2/isooctane

Tw=1 ps, 2580 cm-1

Beat-subtracted

Interferogram

-6

-4

-2

0

2

4

6

w0=2/isooctane

Tw=1 ps, 2580 cm-1

Resonant

Nonresonant

t (ps)

ech

o in

ten

sity

A

B

C

echo inte

nsi

tyech

o in

ten

sity

131

Examination of the raw interferogram data for the isooctane solvent showed

strange behavior. Figure 6.7a displays an echo interferogram (raw data) of w0=2

AOT/isooctane at 2580 cm-1

at Tw = 1 ps. There are several peculiar features in this

interferogram. First, there is a small beat around -0.3 ps. In addition, the amplitude

rises very sharply as zero is approached from negative time with the peak of the

intensity at ~0 ps. The rising edge should be determined by the free induction decay,

which is the Fourier transform of the absorption spectrum. The observed rising side is

too fast. There is little to no peak shift, and the rephasing (positive time) region has a

strange, concave shape. The beat pattern and strange shapes were reproducible and

found at nearly all detection wavelengths and Tw’s, with some exceptions at

wavelengths far to the red. Similar patterns were observed for other w0’s in isooctane

as well. Figure 6.7b displays an interferogram from an AOT reverse micelle of the

same w0, Tw, and detection wavelength, but the nonpolar phase is CCl4. This

interferogram looks completely normal. There are no beats and the rising edge is

slower, in accord with the free induction decay.

To determine the reason for the unusual nature of the interferograms in the

isooctane solvent and the possible influence on the CLS (the bottom curve in Figure

6.6b), we ran a series of vibrational echo experiments on samples which should have

yielded no echo signal. One experiment was to see if pure isooctane generated an

echo signal. It did not, and nor did pure carbon tetrachloride. We also ran the

AOT/water/isooctane w0=2 reverse micelle without any OD probe (just pure water in

the micelle core) and obtained the interferogram shown in Figure 6.8a. In addition to

the large component centered on τ = 0, the negative time beat seen in Figure 6.7a is

present and a positive beat can also be seen. This second beat was obscured in Figure

6.7a by the much larger signal produced by the OD stretch. We also obtained

interferogram data on a sample of 0.5 M AOT solution in isooctane from which the

reverse micelles were made. This sample had virtually no water (w0 = 0.14). The

stock solution yielded essentially identical data to the w0 = 2 sample without HOD

(Figure 6.8a), demonstrating that the addition of H2O does not affect the beat patterns.

In addition we made measurements on the CCl4 stock solution (0.5 M AOT in CCl4).

132

This sample gave no signal. We only found the beating interferograms for samples

that contained both isooctane and AOT.

In a very different context, multicolor stimulated Raman experiments by John

Wright and co-workers studying AOT/D2O reverse micelles in octane in the same IR

spectral range found anomalous components in the 2D spectrum.73

Following

discussions about the experiments presented here, they found that the anomalous band

was even larger when they used isooctane as the solvent. Chapter 8 discusses

experiments that use cyclohexane as the solvent for AOT reverse micelles. The

combination of cyclohexane and AOT does not produce beat patterns.

The exact origin of the beats in the 2D IR vibrational echo signal in the

AOT/isooctane reverse micelle system is not understood, but inspection of the FT IR

spectra of the solvents and stock solutions (Figure 6.9) allows one to determine

whether an absorption in the experimental spectral region could potentially be the

cause. Figure 6.9 shows the FT IR spectra of cyclohexane, carbon tetrachloride

(CCl4), isooctane, and the 0.5 M AOT stock solutions prepared in each of the solvents.

The spectra of CCl4 and its stock solution show little absorption within the

experimental window, suggesting that an absorption due to the solvent or AOT might

cause the beats, since the CCl4 system is clean and does not give rise to beats. Figure

6.9 also shows that the spectra for isooctane and cyclohexane are very similar to their

respective AOT stock solutions. Unlike CCl4, these hydrocarbon solvents show

numerous absorptions. Even though cyclohexane actually has more and stronger

absorptions than isooctane, the cyclohexane system does not give rise to beats. Thus

having absorptions in the experimental spectral window is not sufficient to produce

the beats. Also remember that isooctane does not generate beats by itself and that the

combination of AOT and isooctane is required for beat generation. The one difference

between cyclohexane and isooctane is that cyclohexane does not contain any methyl

groups. It is possible that the presence of methyl groups produces interactions

between AOT and isooctane that are not possible with cyclohexane or CCl4.

133

Figure 6.9 FT IR spectra of the solvents and stock solutions relevant to the echo beat subtraction

study. A single absorption in the experimentally detected frequency region cannot be linked to the beat

behavior in the interferograms.

In an attempt to remove distortions from the isooctane data, we ran two sets of

vibrational echo experiments back-to-back, with one sample being the normal resonant

w0 = 2 AOT/isooctane reverse micelle with 5% HOD/H2O and the other being the w0

= 2 AOT/isooctane sample with pure H2O. Running the samples right after one

another preserved the laser conditions between the experiments as much as possible to

make the data processing more reliable. Using the two sets of data, “beat-subtracted”

sets of interferograms were obtained. Figure 6.8b shows the pure H2O interferogram

(blue) superimposed on the interferogram taken with HOD (red) for w0 = 2 at 1 ps and

2580 cm-1

. Using the region of the negative time beat, the pure H2O data were

multiplied by a constant so that its amplitude matched the amplitude of the beat from

the HOD data. In addition, a small < 2 fs adjustment in time was made to match the

phases of the two sets of oscillations in the negative time beat region. The pure H2O

interferogram (blue) was then subtracted from the HOD interferogram (red). The

result of the subtraction is shown in Figure 6.8c. This interferogram has been scaled

for clarity. The interferogram after subtraction is virtually identical to the one shown

2300 2400 2500 2600 2700

0.0

0.2

0.4

0.6

0.8

1.0

abso

rban

ce

frequency (cm-1)

cyclohexane

0.5 M AOT/cyclohexane

isooctane

0.5 M AOT/isooctane

CCl4

0.5 M AOT/CCl4

134

in Figure 6.7b. The negative time beat is gone. The rising edge has the correct shape

as does the positive time decay.

Table 6.4 Frequency-frequency Correlation Function Parameters for AOT w0 = 2. Γ –

homogeneous line width; Δi – amplitudes; ti – time constants.

This subtraction procedure was done at every wavelength for every Tw

(automated by a MATLAB fitting routine). Appendix C outlines a procedure for

using the custom-written MATLAB routines to perform beat subtraction. It is

important to state that this procedure is fraught with difficulties. Two completely

separate sets of vibrational echo experiments need to be conducted on two samples.

Just switching the samples, which are in different sample cells, can introduce error.

After the subtraction procedure was applied to all of the interferograms from the

isooctane sample, 2D IR vibrational echo spectra were constructed in the normal

manner by Fourier transformation. From these spectra the Tw dependent CLS was

obtained. The plot of this CLS curve is the middle curve in Figure 6.6b. While the

middle curve in Figure 6.6b (beat subtracted isooctane) is not identical to the top curve

(CCl4), they are very similar. From the CLS plots the frequency-frequency correlation

functions were calculated and compared. We found little difference between the

isooctane and CCl4 data. The FFCF for the w0=2 reverse micelles in CCl4 is given in

Table 6.4. However, due to the inherent noise generated by so many data processing

steps in the beat subtraction, especially at long Tw’s, we feel more confident in our

ability to fit and interpret the CCl4 data. Both the CCl4 and isooctane CLS data sets

can be fit with the same time constants shown in Table 6.3 with differences only in the

amplitudes. The biexponential fit parameters for the middle and bottom curves in

Figure 6.6b are listed in Table 6.5. Without beat subtraction, the data from the reverse

micelles in isooctane decay very quickly (bottom curve, Figure 6.6b) and bear no

resemblance to the CCl4 data (top curve, Figure 6.6b). After beat subtraction, the time

constants of the CLS (Table 6.5) are the same as those found for the system with CCl4

(Table 6.3) as the solvent.

Γ (cm-1

) Δ1 (cm

-1) t

1 (ps) Δ2 (cm

-1) t

2 (ps) Δ3 (cm

-1)

33 ± 5 19 ± 2 0.9 ± 0.1 36 ± 1 10 ± 1 37 ± 1

135

Our main purpose in pursuing the isooctane 2D IR spectrum background

subtraction experiments was to show that there is little difference in dynamics with

different solvents, allowing us to compare our experimental CCl4 data with other

experiments and simulations conducted with isooctane as the solvent. The lack of

difference in the spectral diffusion between solvents is perhaps not too surprising, as

the infrared spectra and pump-probe experiments show perfect agreement in

absorption line shapes (Figure 6.2), vibrational relaxation (Figure 6.3), and

reorientation dynamics (Figure 6.4) between the two solvents. We conclude that water

nanopools in small reverse micelles of the same size prepared in CCl4 and in isooctane

have identical characteristics.

Table 6.5 Biexponential Fit Parameters for Beat Subtracted w0=2/isooctane and w0=2/isooctane

without Beat Subtraction.

We can now discuss the FFCF parameters given in Table 6.4. In bulk water

the FFCF is characterized with two time constants of ~400 fs and 1.7 ps and a

motionally narrowed homogeneous component.58

The homogeneous component and

the 400 fs component have been attributed to fast, local fluctuations in the hydrogen

bonding network, while the 1.7 ps time constant is associated with complete structural

randomization through global hydrogen bond rearrangement. As discussed in Section

6.1, bulk water orientational relaxation has a time constant of 2.6 ps, which is

attributed to jump reorientation.1,2

The two time constants for spectral diffusion and

orientational relaxation are very similar because the mechanisms that give rise to them

are very similar. However, in the w0 = 2 reverse micelle water nanopools, there are at

least three decay times in addition to a homogeneous component. In analogy to bulk

water, the 0.9 ps decay may be the result of local hydrogen bond fluctuations that are

slowed compared to bulk water because of the constraints placed on the hydrogen

bond network by the interactions with the interface. The offset in the FFCF

sample A1 t1 (ps) A1 t2 (ps) y0

w0=2/isooctane

with beat

subtraction

0.01 0.9 0.47 10 0.21

w0=2/isooctane

without beat

subtraction

0.16 0.44 0.52 5.7 0.02

136

parameters reflects dynamics that are so slow that they are outside the experimental

time window, which is limited by the vibrational lifetime. Simulations show that there

are very slow dynamics that contribute at long time to the FFCF.35

For example, water

molecules that are surrounded by other water molecules will have a different

distribution of vibrational frequencies than water molecules directly interacting with

the interfacial sulfonate head groups. For complete spectral diffusion to occur, all

water molecules must sample all frequencies, which means that they must experience

all structures. A water molecule surrounded by other water molecules will have to

diffuse to the interface before spectral diffusion can be completed. Diffusion to the

interface, or perhaps exchange between populations, will be very slow in the

extremely crowded and constrained environment of a very small reverse micelle water

nanopool.

What might give rise to the 10 ps intermediate component that is not present in

bulk water? The key difference between bulk water and water in the small reverse

micelle is the strong influence of the interface on all of the water molecules. Water

hydroxyls are either directly interacting with the interface or bound to a water that is

directly interacting with the interface. Even though on average AOT reverse micelles

are spherical, the interface is far from a smooth sphere. The interface has a rough

topography, and studies have shown the necessity of including surface roughness in

MD simulations in order to capture accurate line shapes.35

Water at the rough interface

is shown schematically in the cartoon in Figure 6.10. This rough topography will

contribute to inhomogeneous broadening as the water molecules must accommodate

this topography. The hydrogen bonding network will be forced out of the ideal

structure it can assume in bulk water. Individual sulfonate head groups can move

relatively rapidly. Such motions will change the local hydroxyl environment, and

produce some spectral diffusion. One possibility is that fluctuations in the interfacial

topography could be responsible for the 10 ps component of the spectral diffusion.

According to the beat subtraction study, it does not appear that the identity of the

solvent would affect the degree of surface roughness or fluctuations, given that the

time constants remain the same both systems.

137

Figure 6.10 Cartoon illustrating how topography changes through movements of individual

sulfonate head groups (green circles) in the surfactant shell of the reverse micelle can change the

environment felt by the water molecules.

Returning to Table 6.4, the FFCF has a homogeneous (motionally narrowed)

component. The homogeneous component can be quantified by the homogeneous line

width, Γ. The time constant t1 has been attributed to fluctuations in the hydrogen bond

network, and t2 describes possible topography fluctuations or other dynamics induced

by the presence of the interface. Each time constant has an associated frequency

amplitude (Δi) which describes how much each component contributes to the line

width. The intermediate component (t2) adds a significant amount of inhomogeneous

broadening, more than Δ1. The parameter Δ3 corresponds to the component described

by an offset in the biexponential fit and reflects very slow dynamics outside of the

experimental time window. This component is also large.


Here we have compared four experimental observables that describe the nature

of the water nanopool in small AOT reverse micelles in two solvents, isooctane and

CCl4. The OD stretch of dilute HOD was studied. It was found that the linear

absorption spectra were identical for reverse micelles in the two solvents. Polarization

and wavelength selective pump-probe experiments showed that the vibrational

lifetimes and orientational relaxation were independent of the solvent. Both of these

time dependent observables are quite sensitive to the local environment of the HOD.

Ultrafast 2D IR vibrational echo spectroscopy, which measures spectral diffusion,

provides detailed information on structural dynamics of the water hydrogen bonded

138

network that is not accessible by other techniques. The initial studies of the AOT

reverse micelles with isooctane as the solvent produced results that were inconsistent

with expectations based on a large number of previous experiments on aqueous

systems.38,41,58,74

In particular, the individual interferograms had features that were

inconsistent with water signals (see Figures 6.7 and 6.8). Although isooctane is often

used to form AOT reverse micelles, the problems with the interferograms led to

performing the 2D IR vibrational echo measurements with CCl4 as the solvent. The

experiments with CCl4 did not have the problematic interferograms observed with

using isooctane. The efficacy of using CCl4 led to the necessity of demonstrating that

the choice of solvent did not significantly change the properties of the water

nanopools. As shown above, the nature of the water in reverse micelle nanopools is

independent of whether CCl4 or isooctane is used as the solvent.

Examination of the AOT/isooctane system without the HOD in the water and

without any water at all showed that the combination of AOT and isooctane gives rise

to a signal with beats that do not occur under the same conditions with AOT in CCl4.

The beat pattern observed in the interferograms of the AOT/isooctane system (Figures

6.7 and 6.8) prompted the development of a 2D background subtraction procedure

which was relatively successful in removing the solvent background from the true

vibrational echo signal from the OD stretch. The observation of the solvent

contribution to the desired signal is an important warning to other workers using 2D

IR spectroscopy. It is generally assumed that the solvent will not give a well defined

signal that can influence the signal from a resonant vibrational chromophore. Clearly

this is not always the case. 2D background subtraction may be useful in other systems

that give rise to a solvent contribution to the 2D spectra.

It is interesting to note that neither of the AOT stock solutions in isooctane and

CCl4 produce a background signal, nor does isooctane by itself. We also found that

AOT/cyclohexane does not produce a signal. It was observed in a different type of 2D

experiment that AOT/octane did produce a background signal, but it is smaller than

that with AOT/isooctane.73

From these observations, the methyl groups are implicated

as interacting with AOT in some manner to permit the background signal to occur.

139

The 2D IR vibrational echo experiments on the water nanopools of w0 = 2

AOT/CCl4 reverse micelles displayed dynamics on several time scales. In addition to

a substantial motionally narrowed homogeneous component, relatively fast

fluctuations on an ~1 ps timescale contribute to spectral diffusion. These fluctuations

are likely due to very local length fluctuations of hydrogen bonds. This timescale is

somewhat longer than that found in bulk water for the same process. An intermediate

timescale (~10 ps) does not have an analog in bulk water. This component probably

arises from the influence of the interface on hydrogen bond dynamics. There are

longer time scale fluctuations that are outside of the experimental time window, such

as diffusion and exchange which are limited by the vibrational lifetime of the OD

hydroxyl stretch. Chapter 8 explores the spectral diffusion dynamics for a larger range

of reverse micelles, w0 = 2, 4, 7.5, 12, and 16.5. Appropriate solvents were chosen for

these experiments (CCl4 and cyclohexane) such that beat subtraction is not required

during data analysis.

6.5 References




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Phys. Chem. A 2006, 110, 4985.

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T. Chem. Phys. Lett. 2002, 354, 256.

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Chem. A. 2002, 106, 2341.

(44) Fecko, C. J.; Eaves, J. D.; Loparo, J. J.; Tokmakoff, A.; Geissler, P. L. Science

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(50) Lawrence, C. P.; Skinner, J. L. Chem. Phys. Lett. 2003, 369, 472.



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Skinner, J. L. J. Chem. Phys. 2004, 121, 8897.

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(60) Moilanen, D. E.; Fenn, E. E.; Lin, Y. S.; Skinner, J. L.; Bagchi, B.; Fayer, M.

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143

Chapter 7 Extracting 2D IR Frequency-

Frequency Correlation Functions from Two

Component Systems

7.1 Introduction

2D IR vibrational spectroscopy has proven to be an extremely powerful

technique for elucidating molecular dynamics and understanding congested spectra of

condensed matter systems.1,2

Through analysis of the 2D spectral line shapes and

other experimental observables, the frequency-frequency correlation function (FFCF)

can be determined.3-10

The frequency-frequency correlation function describes the

likelihood that an oscillator of a certain frequency will have the same frequency after a

given period of time. The frequency of an oscillator will change with time because of

structural fluctuations in the system, a process known as spectral diffusion. The FFCF

is often sensitive to the different structural environments that a species interacts with

over time, giving insight into the time scales of processes involved in spectral

diffusion. For instance, bulk water undergoes fast local hydrogen bond fluctuations on

a relatively fast, ~0.4 ps, time scale and a set of slower processes on ~1.7 ps time scale

caused by complete randomization of the hydrogen bonding network.11

In addition to

extracting these time scales in the FFCF, 2D IR spectroscopy can also separate

contributions of homogeneous (motionally narrowed) and inhomogeneous broadening

to the line shape. Homogeneous broadening occurs when very fast fluctuations cause

motional narrowing while inhomogeneous broadening arises from slower processes.

Water has a relatively large homogeneous component.11

2D IR spectroscopy has been

extremely successful in understanding spectral diffusion in bulk water6-8,12-15

and other

hydrogen bonding systems,11,16,17

protein and other biological systems,18-26

as well as

systems that undergo chemical exchange or isomerization.27-32

Through a time-ordered series of three input electric fields (ultrafast laser

pulses), 2D IR spectroscopy can manipulate the quantum pathways by which a system

144

evolves. The first pulse excites a coherent superposition of the ground (0) and first

excited (1) vibrational states. After a time period τ, the evolution period, a second

pulse interacts with the sample and brings the system into population states, 0 and 1.

After a time period Tw, the waiting period, the third pulse interacts with the sample and

creates another coherent superposition. The generated echo signal emits at a time t ≤

τ, which is the detection time period. A fourth beam, known as the local oscillator, is

overlapped with the vibrational echo signal for heterodyned detection. In an

experiment, τ is scanned at a series of fixed Tw values. The molecules undergo

spectral diffusion during Tw due to dynamic structural evolution of the system. After

Fourier transformation of the temporal interferograms obtained during the experiment,

correlation spectra are obtained for the detection vs. initial excitation frequencies,

referred to as ωm (axis of echo emission, vertical axis) and ωτ (axis of interaction with

the first pulse, horizontal axis), respectively.

Various methods for extracting the FFCF from the 2D correlation spectra have

been developed. A rigorous, and consequently more cumbersome, method involves

choosing a trial function for the FFCF and using the nonlinear third order response

functions to calculate 2D spectra. The FFCF parameters are iteratively adjusted until

the calculated and experimental spectra agree.3,4,33

This procedure becomes even

more problematic when finite pulse durations must be taken into account. In addition,

the quality of convergence of the fit is questionable, given that there are multiple

adjustable parameters. The complexity surrounding the trial FFCF procedure have

encouraged the development of simpler methods for extracting the FFCF.

2D IR observables such as the ellipticity,34-37

eccentricity,35

and dynamic line

width7,8

have all been used to extract dynamical information from 2D IR correlation

spectra. Although these techniques are much simpler computationally compared to

using a trial FFCF, these techniques are susceptible to distortions from finite pulse

durations, sloping background absorption, Fourier filtering methods (such as

apodization) as well as the overlap between the 0-1 and 1-2 transition peaks. The full

FFCF, including a fast motionally narrowed (homogeneous) component, may be

obtained via these methods, but a full treatment using nonlinear response theory must

be used.

145

The center line slope (CLS) method has also been used to extract the FFCF

from 2D IR measurements.9,10

This method is particularly useful because the Tw-

dependent portion of the FFCF may be obtained directly from the spectra without any

response function calculations. The motionally narrowed component may be easily

obtained using the CLS in conjunction with the linear IR absorption spectrum. In the

CLS technique, slopes are calculated through the lines that connect the peak positions

of one-dimensional cuts parallel to the ωm axis for each correlation spectrum. This

variant of the method is referred to as CLSωm. When the cuts are taken parallel to the

ωτ axis, then the technique is called CLSωτ. In CLSωm, the slopes are plotted vs. Tw.

In CLSωτ, the inverse of the slopes vs. Tw are plotted. In either case, the CLS plot is

equal to the normalized Tw-dependent portion of the FFCF. Figure 7.1 shows the CLS

data for bulk water at two Tw’s. The dotted lines are the peak positions through which

the slope is calculated. In this thesis and in previous studies, 23-25,38

the CLSωm

technique is used because, unlike the CLSωτ technique, it is not prone to distortions

caused by the overlap of the 0-1 and 1-2 transitions. The CLSωm technique, and the

process by which the motionally narrowed component is obtained, will be discussed in

more detail in Section 7.2.

When a system is composed of a single vibrational component (such as the OD

stretch of dilute HOD in bulk water), then analysis of the 2D IR spectra with the CLS

method is relatively straightforward. Only one 0-1 peak is present in the spectrum, so

the CLS cuts are taken at a range of frequencies around the 2D IR maximum value for

each Tw. If a system has two separate components, and if the separation of peak

transition frequencies for the components is large enough such that the system shows

two distinct bands in the 2D IR spectrum, then the CLS analysis may be carried out on

each band independently to yield the dynamics for each component. The question

addressed in this chapter is how one should treat a system of two components that are

not spectrally resolved. In this scenario, the resulting spectrum only shows one 0-1

band, even though it is made up of two 0-1 bands, one from each component. 2D IR

spectra are additive, so the overall observed spectrum can be thought of as the

weighted average of two separate spectra. Each individual spectrum will in general

have its own distinct dynamics, which CLS analysis should be able to determine, if the

146

two components could be separated from one another. This chapter shows that the

CLS results for the observed experimental spectra of a system with two components

may be decomposed into contributions from each component, provided that the center

line data of one of the components is known. The vibrational lifetimes, linear IR

absorption spectra, and relative fractions of the components must also be known in

order for the algorithm to work. It should be noted here that the term “component”

here refers to a chemically distinct and separate vibrating species and not, for instance,

a system of coupled oscillators on the same molecule. An example of a system in

which the method can be applied is water in reverse micelles. Over the years,

experimentalists have used reverse micelles as model systems to probe the dynamics

of water molecules in confined environments,38-66

a topic that bears great significance

to biological and industrial applications in which the behaviors of small amounts of

water or water next to interfaces can severely impact the function of systems such as

proteins, pharmaceuticals, and fuel cell membranes. In a reverse micelle, a water pool

is surrounded by a shell of surfactant molecules that have hydrophilic head groups,

which can either be charged or neutral. The surfactant molecules are suspended in a

non-polar organic phase. A very popular surfactant for making reverse micelles is

Aerosol-OT (AOT) because it makes monodispersed, spherical reverse micelles of

easily tunable water pool diameters.67-69

The size of the reverse micelle water pool is

often denoted by the ratio of water to AOT, 0 2[H O]/[AOT]w .69

Water pool

diameters can range from 1.7 to 28 nm (w0=2 to w0=60). It has been shown that the

population and orientational dynamics of water inside large AOT reverse micelles

(diameters of 5.8 nm and greater) can be readily separated into bulk and interfacial

components, each with distinct dynamics.39,41

As of yet, there has been no analogous

method presented to separate bulk and interfacial contributions to spectral diffusion.

The extended CLS method presented in this chapter can be applied not only to large

reverse micelles which are composed of bulk and interfacial water environments but

also to other two component systems that show only one band in their absorption and

2D IR spectra.

147

Figure 7.1 Calculated 2D IR spectra for bulk water at Tw = 0.2 ps (a) and Tw = 2 ps (b). The solid

lines show the direction of cuts through the spectra for the CLSωm technique. The dotted lines show the

peak positions for a series of cuts parallel to the ωm axis (and the solid lines), also known as center line

data. As Tw lengthens, the spectra become more symmetric, and the slope through the center line data

approaches zero.

7.2 Theoretical Development

7.2.1 CLS Method for a Single Component System

The CLS method for systems of one component, or for systems with two

spectrally resolved components, has been discussed in detail by previous authors.9,10

As explained in Section 7.1, the CLSωm variant is used for analyzing 2D IR data

throughout this thesis. In this technique, cuts through the 2D IR correlation plots are

taken parallel to the ωm axis and fit to Gaussian line shape functions to find the

maximum at each frequency. Typically, the cuts are taken at a range of ωτ frequencies

surrounding the location of the maximum of the 2D spectrum. The set of peaks and

corresponding ωτ frequencies are referred to as center line data. The CLSωm

2300 2400 2500 2600 27002300

2400

2500

2600

2700

2300 2400 2500 2600 27002300

2400

2500

2600

2700

A Tw = 0.2 ps

B Tw = 2 ps

ωτ (cm-1)

ωm

(cm

-1)

ωm

(cm

-1)

148

technique is not sensitive to the overlap between the 0-1 and 1-2 bands, allowing cuts

to be taken on either side of the spectral maximum even if there is overlap of the 0-1

and 1-2 bands. The peak positions of the Gaussian line shape fits are plotted vs. their

corresponding ωτ frequencies, and the slope of the resulting line is calculated. This

process is repeated for each Tw, and a plot of slopes vs. Tw is obtained. The CLS plot

corresponds to the Tw-dependent portion of the normalized FFCF. Figure 7.1a and

7.1b show calculated 2D IR spectra for bulk water at Tw= 0.2 ps and 2 ps based on its

known FFCF.11

The center line data of ωm peak positions at each Tw are indicated by

the dotted lines. The direction of the cuts is denoted by the solid lines. Typically, the

center line data are found over a limited range of frequencies around the maximum in

the 2D IR spectrum. For water systems, a typical range is ± 30-40 cm-1

about the

maximum. Figure 7.2 shows the CLS decay for the bulk water system. The data

points in Figure 7.2 are the slopes calculated from the center line data of the 2D

spectra at each Tw. A fast homogeneous component causes the CLS to rapidly decay

at early Tw so that the data do not begin at 1.

Figure 7.2 CLS decay curve for bulk water. Spectral diffusion is relatively rapid and has mostly

decayed by ~2 ps. There is a large homogeneous component, as seen by the large drop from 1 of the

data.

0 1 2 3 4 50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Tw (ps)

CL

S

149

The FFCF is composed of both a homogeneous (motionally narrowed) and

inhomogeneous components. Using a sum of exponentials, the FFCF is

/2

1 10 10

2

( )( ) ( ) (0) ,it

i

i

tC t t e

T

(7.1)

where 10 10( ) (0)t is the correlation function for the fluctuating 0-1 transition

frequency, and ( ) ( )t t . The T2 parameter is the dephasing time given by,

*

2 2 1

1 1 1 1,

2 3 orT T T (7.2)

where *

2T is the pure dephasing time, T1 is the vibrational lifetime, and τor is the

orientational relaxation time constant. The delta function term that involves the

dephasing time in Equation 7.1 is the motionally narrowed component. The Δi terms

are frequency fluctuation amplitudes, and the τi terms are their associated time

constants. The time constants represent different time scales for processes that

contribute to spectral diffusion. The magnitude of a Δi term represents the

contribution to the line shape of each process.

CLS data are often fit to a multi-exponential decay, yielding a set of time

constants and associated amplitudes. The parameters obtained from the CLS data like

that shown in Figure 7.2 are used in the overall calculation that determines the

motionally narrowed component, yielding the full FFCF.9 The values of the time

constants are accurate, as well as the amplitude corresponding to the longer of the time

constants. Due to the short time approximation,9,34,70

the amplitude of the first

component can be pushed into the homogeneous contribution. Therefore, the CLS

method cannot accurately determine the exact amplitudes of the fast inhomogeneous

component and the homogeneous component. To determine these, the absorption line

shape is employed. The absorption spectrum is the Fourier transform of the linear

response function, R1(t),

10 12 ( )1

10( ) ,i t ig t

R t e e

(7.3)

where µ10 is the transition dipole moment of the 0-1 transition, 10 is the average 0-1

transition frequency, and g1 is the line shape function given by

150

2

1 2 1 10 10

0 0

( ) ( ) (0) .

t

g t d d t

(7.4)

Equation 7.4 shows the link between the absorption spectrum and the FFCF.

Using the amplitude of the fast inhomogeneous decay and the homogeneous

component as the only adjustable parameters, the absorption line shape of the system

is fit simultaneously with the CLS decay.9,11,38

This procedure is able to accurately

determine the motionally narrowed component as well as the amplitude of the first

inhomogeneous component. The CLS method assumes Gaussian fluctuations,9,10

which is not entirely accurate for water systems.71,72

However, simulations have

indicated that any errors introduced by making the Gaussian approximation have been

shown to be comparable to errors induced by using different water models.7,8,72,73

Though the CLS may be somewhat approximate, it is still a useful experimental

observable for comparing different systems and determining time scales for spectral

diffusion processes.

7.2.2 Extension of the CLS Method to Two Components

Following the work of Kwak, et al.,10

the 2D IR line shape function may be

expressed as

2

1/2 1/2

( , ) ( , )4 2 2 2( , ) exp exp .

( ) ( ) ( ) ( )

m mm

w w w w

A BsR

K T K T Q T Q T

(7.5)

In this expression, Δ is the anharmonic frequency shift of the 0-1 and 1-2 transitions,

and s = µ21/µ10, the ratio of transition dipole moments for the 1-2 and 0-1 transitions.

The remaining parameters are as follows,

2 2

1 1 1

2 2

1 2 3

2 2

1 1

2

1 3 2

( , ) ( (0) 2 ( ) (0) ),

( , ) ( (0)( ) 2 ( )( ) (0) ),

( ) (0) ( ) ,

( ) (0) (0) ( ) ,

m m w m

m m w m

w w

w w

A C C T C

B C C T C

K T C C T

Q T C C C T

(7.6)

where,

151

1 10 1 10

2 21 1 10

3 21 1 21

( ) ( ) (0) ,

( ) ( ) (0) ,

( ) ( ) (0) .

C t

C t

C t

(7.7)

The CLSωm technique finds the maximum value of the line shape function along a

slice taken parallel to the ωm axis. In other words, the derivative of Equation 7.5 with

respect to ωm is set to 0 according to

2

3/2 3/2

( , ) ( , ) ( , )4 2 2 20 exp exp .

( ) ( ) ( ) ( )

m m m

m w w m w w m

R A BA s B

K T K T Q T Q T

(7.8)

After some rearrangement of Equation 7.8, a set of ωm and ωτ that correspond to a

maximum in the slice parallel to ωm is defined by

3/2

1 2

2 3/2

1 1

2 ( ) ( , ) ( , ) 2 (0)( ) 2 ( )exp .

( ) ( ) ( ) 2 (0) 2 ( )

w m m m w

w w w m w

Q T A B C C T

s K T K T Q T C C T

(7.9)

As shown by Kwak, et al.10

the slope through the set of points described by Equation

7.9 may be found by finding the total derivative of Equation 7.9 with respect to ωτ and

then solving for md

d

. After simplification it is found that,

1 1 2 1 1

2

1 1

1 1 2 3

2 2 2

1 1 1 3 2

2

1 1 2 1

1

(0)( ( ) ( )) (0) ( )

( ( ) (0) )

( ) (0) ( )( ) (0)( , , , )

(0) ( ) (0) (0) ( )

(0)( ( ) ( )) (0)

( (

m

w w w

w m

w m w mm w

w w

w w m

d

d

C C T C T C C T

C T C

C T C C T CD T s

C C T C C C T

C C T C T C

C

2

1

1 1 2 3

2 2 2

1 1 1 3 2

) (0) )

( ) (0) ( ) (0)( )( , , , )

(0) ( ) (0) (0) ( )

w m

w w mm w

w w

T C

C T C C T CD T s

C C T C C C T

(7.10)

152

where,

2

1 3 2

2 2 2

1 1

2 2

1 1 1

2 2

1 1

2 2

1 2 3

2

1 3 2

2( (0) (0) ( )( , , , )

(0) ( )

(0) 2 ( ) (0)

2 (0) ( )exp .

(0)( ) 2 ( )( ) (0)

2 (0) (0) ( )

wm w

w

m w m

w

m w m

w

C C C TD T s

s C C T

C C T C

C C T

C C T C

C C C T

(7.11)

Within the harmonic approximation for a three level vibrational system, all of the

correlation functions are equal to each other. In this situation,

1 2 3( ) ( ) ( ) ( )C t C t C t C t and the slope (Equation 7.10) becomes the normalized

FFCF,10

( ).

(0)

m wd C T

d C

(7.12)

When two species are involved, the 2D IR line shape becomes

2

1 11 1/2 1/2

1 1 1 1

2

2 21 1/2 1/2

2 2 2 2

( , ) ( , )4 2 2 2( , ) ( , ) exp exp

( ) ( ) ( ) ( )

( , ) ( , )4 2 2 2(1 ( , )) exp exp ,

( ) ( ) ( ) ( )

m mm w

w w w w

m mw

w w w w

A BsR f T

K T K T Q T Q T

A Bsf T

K T K T Q T Q T

(7.13)

where the Ai, Bi, Ki, and Qi parameters are defined in a similar manner as given above

(Equation 7.6) but correspond to different components with different sets of

correlation functions,

2 2

1 1 1

2 2

1 2 3

2 2

1 1

2

1 3 2

( , ) ( (0) 2 ( ) (0) ),

( , ) ( (0)( ) 2 ( )( ) (0) ),

( ) (0) ( ) ,

( ) (0) (0) ( ) ,

i i i

i m m w m

i i i

i m m w m

i i

i w w

i i i

i w w

A C C T C

B C C T C

K T C C T

Q T C C C T

(7.14)

where,

153

1 10 1 10

2 21 1 10

3 21 1 21

( ) ( ) (0) ,

( ) ( ) (0) ,

( ) ( ) (0) .

i i i

i i i

i i i

C t

C t

C t

(7.15)

Figure 7.3 Linear IR absorption spectra for water (5% HOD in H2O) inside the AOT w0=12

reverse micelle (black line). The overall spectrum may be decomposed into a linear combination of

the bulk water (5% HOD in H2O) spectrum (blue line) and the w0=2 spectrum (red line) in which all

waters interact with the surfactant head group interface.

The f1 term in Equation 7.13 corresponds to a frequency and Tw-dependent

fraction term. The fraction reflects the overall concentration of a species at a certain

frequency. In two component systems such as reverse micelles, the fraction can be

obtained from infrared spectral analysis.39,41,49

As a concrete example for calculating

the fraction term, the 2D IR spectrum of a large AOT reverse micelle will be used as a

model, although other parameters will be varied to illustrate the use of the method. As

discussed in the introduction, the water nanopool in a large AOT reverse micelle

consists of a bulk water core and water at the AOT interface. Each spectrum may be

thought of as a linear combination of the bulk water spectrum and the spectrum of w0

= 2, the smallest micelle. In the w0 = 2 system, essentially all of the waters interact

2200 2300 2400 2500 2600 2700

0.0

0.2

0.4

0.6

0.8

1.0 bulk water

interface (w0= 2)

w0=12

frequency (cm-1)

ab

sorb

an

ce

154

with surfactant head groups. Thus, the spectra are decomposed into “core” and “shell”

spectra.49

Figure 7.3 shows the component core and shell spectra for water in the w0 =

12 AOT reverse micelle. It should be noted that the water measured inside the reverse

micelle is the OD stretch of 5% HOD in H2O. Dilute HOD in H2O is used in

experiments to eliminate vibrational excitation transfer and so that there is a single

local stretching mode.74,75

The model calculations performed in this work use the OD

stretch of HOD in H2O.

The overall linear absorption spectrum of a two component system takes the

following form,

1 1 1 2 1 2( ) ( ) (1 ) ( ) ( ) ( ),totI a I a I S S (7.16)

where ( )iI are the component spectra, and a1 is a single weighting factor. For w0 =

12, a1=0.56.

Figure 7.4 Frequency and Tw-dependent fraction of bulk water for the AOT w0=12 reverse

micelle system.

Each ωτ will yield a different fraction of component i determined by the

overlap of the infrared spectra of the two components. The relative populations at a

particular time, Tw, are also dependent on the vibrational lifetimes. Each component

2200 2300 2400 2500 2600 27000.0

0.2

0.4

0.6

0.8

1.0 Tw = 0 ps

Tw = 0.2 ps

Tw = 1.5 ps

Tw = 7 ps

frequency (cm-1)

f 1

155

spectrum of the 2D correlation plot will decrease in amplitude at a rate defined by its

vibrational lifetime. The f1 term can be calculated by

11

1 21 1

/

11 / /

1 2

( )( , ) ,

( ) ( )

w

w w

T T

w T T T T

S ef T

S e S e

(7.17)

where the Si terms are the infrared spectra of components 1 and 2 defined in Equation

7.16, and the 1

iT terms are their associated vibrational lifetimes. Figure 7.4 illustrates

the behavior of Equation 7.17 with changing wavelength and Tw for the AOT w0 = 12

system.

The location of the maximum of a slice along the ωm axis is found by setting

the partial derivative of Equation 7.13 with respect to ωm to 0,

1 1

3/2

1 1

1 12

1 1

3/2

1 1

2 2

3/2

2 2

1

( , )

( , ) ( , )4 2exp

( ) ( )( , )

( , ) ( , )2 2exp

( ) ( )

( , ) ( , )4 2exp

( ) ( )(1 ( , ))

m

m

m m

w w m

w

m m

w w m

m m

w w

w

R

A A

K T K Tf T

B Bs

Q T Q T

A A

K T K Tf T

2

2 2

3/2

2 2

( , ) ( , )2 2exp

( ) ( )

0.

m

m m

w w m

B Bs

Q T Q T

(7.18)

where the Ai, Bi, Ki, and Qi parameters are defined by Equations 7.14 and 7.15.

Equation 7.18 defines a set of ωm and ωτ values that correspond to the location

of the maximum along a slice parallel to ωm. As before, we may take the derivative of

Equation 7.18 with respect to ωτ to obtain an equation for the slope of the curve

created by the maxima locations. After extensive rearrangement and using the

harmonic approximation for each set of correlation functions associated with a given

component, we obtain the following expression for md

d

:

156

11

1 1

11

1 1

( , ) ( , , , ) ( , , , )

( , ) ( , , , ) (1 ( , )) ( , , , )

(1 ( , )) ( , , , ) ( , , , )

( , ) ( , , , ) (1 ( , )) ( , , , )

w m w m w

m

w m w w m w

w m w m w

w m w w m w

dff T F T s G T s

d d

d f T J T s f T K T s

dff T H T s I T s

d

f T J T s f T K T s

(7.19)

Equation 7.19 is written in a highly condensed form where

1 /

1

1 2 1 2 3/2

1 1

/ 1 1 1 1

1 1 1 1

1 2 1 2 5/2

1 1

2 / 1 1 1 1

1 1 1 1

1 2 1 2 5/2

1 1

2 ( )( , , , )

( (0) ( ) )

4 ( (0) ( ) )( ( ) (0) )

( (0) ( ) )

2 ( ( ) (0)( ))( (0) ( )( )),

( (0) ( ) )

a b

wm w

w

a b

m w w m

w

c b

w m m w m

w

C T eF T s

C C T

e C C T C T C

C C T

s e C T C C C T

C C T

(7.20)

/ 1 1 / 2 1 1

1 1 1 1

1 2 1 2 3/2 1 2 1 2 3/2

1 1 1 1

2 ( (0) ( ) ) ( ( ) (0)( ))( , , , ) ,

( (0) ( ) ) ( (0) ( ) )

a b c b

m w w m mm w

w w

e C C T e s C T CG T s

C C T C C T

(7.21)

2 /

1

2 2 2 2 3/2

1 1

/ 2 2 2 2

1 1 1 1

2 2 2 2 5/2

1 1

2 / 2 2 2 2

1 1 1 1

2 2 2 2 5/2

1 1

2 ( )( , , , )

( (0) ( ) )

4 ( (0) ( ) )( ( ) (0) )

( (0) ( ) )

2 ( ( ) (0)( ))( (0) ( )( )),

( (0) ( ) )

d f

wm w

w

d f

m w w m

w

g f

w m m w m

w

C T eH T s

C C T

e C C T C T C

C C T

s e C T C C C T

C C T

(7.22)

/ 2 2 / 2 2 2

1 1 1 1

2 2 2 2 3/2 2 2 2 2 3/2

1 1 1 1

2 ( (0) ( ) ) ( ( ) (0)( ))( , , , ) ,

( (0) ( ) ) ( (0) ( ) )

d f g f

m w w m mm w

w w

e C C T e s C T CI T s

C C T C C T

(7.23)

157

/ 2 1 11 /

1 11

1 2 1 2 3/2 1 2 1 2 3/2

1 1 1 1

/ 1 1 2

1 1

1 2 1 2 5/2

1 1

/ 2 1 1 1 1

1 1 1 1

1

1

( (0) ( )2 (0)( , , , )

( (0) ( ) ) ( (0) ( ) )

4 ( (0) ( ) )

( (0) ( ) )

2 ( ( ) (0)( ))( (0)( ) ( ) )

( (

c ba b

wm w

w w

a b

m w

w

c b

w m m m w

e s C C TC cJ T s

C C T C C T

e C C T

C C T

e s C T C C C T

C

2 1 2 5/2

10) ( ) )wC T

(7.24)

/ 2 2 22 /

1 11

2 2 2 2 3/2 2 2 2 2 3/2

1 1 1 1

/ 2 2 2

1 1

2 2 2 2 5/2

1 1

/ 2 2 2 2 2

1 1 1 1

2

1

( (0) ( )2 (0)( , , , )

( (0) ( ) ) ( (0) ( ) )

4 ( (0) ( ) )

( (0) ( ) )

2 ( ( ) (0)( ))( (0)( ) ( ) )

( (

g fd f

wm w

w w

d f

m w

w

g f

w m m m w

e s C C TC cK T s

C C T C C T

e C C T

C C T

e s C T C C C T

C

2 2 2 5/2

10) ( ) )wC T

(7.25)

and

1 2 1 1 2

1 1 1(0) 2 ( ) (0) ,m w ma C C T C (7.26)

1 2 1 2

1 1(0) ( ) ,wb C C T (7.27)

1 2 1 1 2

1 1 1(0) 2 ( ) ( ) (0)( ) ,w m mc C C T C (7.28)

2 2 2 2 2

1 1 1(0) 2 ( ) (0) ,m w md C C T C (7.29)

2 2 2 2

1 1(0) ( ) ,wf C C T (7.30)

2 2 2 2 2

1 1 1(0) 2 ( ) ( ) (0)( ) .w m mg C C T C (7.31)

In these expressions, the 1

iC terms are correlation functions for the ith

component.

Equation 7.19 is not a very practical expression, especially for use in analyzing

2D spectra. It is extremely important to note that the resulting slope is neither a

simple weighted average of the slopes of both components nor an expression equal to

the normalized FFCF. The center line data points themselves are, however, a

weighted average of the center line data points for each component. If a center line

point corresponding to a maximum along ωm is denoted as *m , then this relationship

may be mathematically expressed by

158

* *

1 1

*1 2

( , , ) ( , ) ( , , )

(1 ( , )) ( , , )

mC m w w m m w

w m m w

T f T T

f T T

(7.32)

where *mC , *

1m , and *2m represent the sets of center line data for the experimentally

observed two component system, component 1 by itself, and component 2 by itself,

respectively. Differentiating Equation 7.32 with respect to ωτ recovers Equation 7.19,

* *1 1*

1 1

*2 1*

1 2

( , ) ( , , )

(1 ( , )) ( , , ) .

mC mw m m w

mw m m w

d d dff T T

d d d

d dff T T

d d

(7.33)

If one of the components can be measured or simulated independently from the

combined system, then the second component may be calculated from,

* *

2 1 1*2

1

( ( , , ) ( , ) ( , , ))( , , ) .

(1 ( , ))

m C m w w m m wm m w

w

T f T TT

f T

(7.34)

Equation 7.34 provides a simple and experimentally tractable expression for

back-calculating the center line data for the second component from known quantities.

The center line data may be calculated for Tw’s common to both the combined system

and the first component. From the resulting component 2 center line data, the CLS

values (slopes) may be calculated and plotted vs. Tw, from which the FFCF parameters

can be determined according to the procedures outlined in Section 7.2.1, effectively

isolating the dynamics of component 2 from component 1. Section 7.3 will test this

algorithm for a variety of cases.

7.2.3 Model Calculation Details

The two component CLS method was tested using sets of model cases in

which two different FFCF functions are formulated separately. For our purposes we

chose one of the FFCFs to be the FFCF for bulk water (Table 7.1, System 1). The

FFCF parameters are inserted into the third order response functions that describe the

emitted 2D IR signal electric field. 3,76,77

The response functions are used to construct

2D correlation plots on which CLS analysis may be performed. In addition to the

FFCF parameters, a center frequency, anharmonicity, and vibrational lifetime are also

required to calculate the 2D spectra. When generating spectra for a system with two

159

components (known as the combined system), the sets of response functions for each

component are weighted by a fractional concentration (a1 from Equation 7.16).

Calculated 2D spectra may be independently obtained for each component by itself as

well as the combined system. The FFCF of component 2 can be back-calculated using

the method outlined above, and then the procedure can be verified since the actual

starting FFCF parameters of component 2 are known.

Table 7.1 First Model Case FFCF Parameters.

It should be noted that to apply Equation 7.34 to a two component system,

none of the FFCFs actually need to be known. The only required information is the

set of center line data for one of the components (plus the vibrational lifetime and

other details). Here we examine model cases and begin by knowing the FFCFs of

both components so that the efficacy of the algorithm may be evaluated.

7.3 Testing the Two Component CLS Method

7.3.1 Practical Application of the Two Component CLS Algorithm

The flow chart in Figure 7.5 illustrates the chain of events for back-calculating

the FFCF of component 2 using calculated 2D IR and linear IR data. The algorithm is

easily adaptable to experimental data as long as 2D and linear IR spectra for the

combined system and for one of the components can be measured independently (see

Chapter 8 for such experimental applications). Again, in an experimental situation it

is not actually necessary to know the FFCF of component 1; only the center line data

are required. Each block in Figure 7.5 is referenced with a letter so that the reader can

follow along with the description presented in this section. In the first step (a), the

required pieces of information are collected. FFCF parameters are chosen for each

component (the bulk water FFCF parameters are used for component 1 while

component 2 is hypothetical). In addition, the center frequencies, vibrational

lifetimes, and the anharmonicity values between the 0-1 and 1-2 transitions must also

System Γ (cm

-1) Δ

1 (cm

-1) t

1 (ps) Δ

2 (cm

-1) t

2 (ps) ω

0 (cm

-1) a1 T

1 (ps)

1 76 41 0.38 34 1.7 2509 0.5 1.8 2 40 45 0.9 30 5 variable 0.5 4.5

160

be known. Reasonable values were chosen for the second component. The last piece

of required information is the fractional concentration of species used to weight the

linear and 2D IR spectra (a1 from Equation 7.16). The starting information is used to

calculate the linear absorption spectra of the components that make up the combined

system spectrum, according to Equation 7.16, as well as center line data for

components 1 and 2 separately and the combined system (b). From the linear

absorption spectra, the f1 fraction terms may then be calculated using Equation 7.17

and the vibrational lifetimes of the two components (c). The center line data

calculated from the 2D spectra for component 1 and the combined system are used in

Equation 7.34 to back-calculate the center line data for component 2 (c). Figure 7.6

shows representative results for the center line back-calculation. The black circles are

the center line data from the calculated 2D IR spectrum of the model combined

system. The blue circles are the center line data for component 1 by itself. The green

circles are the back-calculated center line data for component 2 by itself using

Equation 7.34. The red line that passes through the black circles is the reconstructed

center line data for the combined system obtained by combining the back-calculated

component 2 center line and the known component 1 center line with the correct

fraction terms. The red line exactly reproduces the data represented by the black

circles, showing the virtually quantitative agreement of the calculation.

The back-calculated center line data for component 2 is then subjected to CLS

analysis (d). The CLS is calculated for ~30-40 cm-1

range around the center frequency

of component 2 (one of the pieces of starting information). For spectra with smaller

bandwidths, a smaller range should be chosen. The CLS is then simultaneously fit

with the IR spectrum of component 2 (obtained in step b) in order to obtain the FFCF

(e).

161

Figure 7.5 Flow chart illustrating the algorithm that calculates the center line data and FFCF for

a second component from known information (Equation 7.34). Because the model systems are

calculated from known FFCF parameters, the accuracy of the algorithm may be easily verified.

Starting Information

1. FFCF parameters (including motional narrowing), center

frequencies, anharmonicity values, and vibrational

lifetimes for:

a) Component 1

b) Component 2

2. Weighting factor of components (a1 from eq. 7.16)

Calculate 2D IR center line data and linear IR spectra (S1 and

S2 in eq. 7.16) for:

1. Component 1

2. Component 2

3. Combined System

Calculate f1 fractions using eq. 7.17 and then the center line

data for component 2 using eq. 7.34

Calculate the CLS around the IR peak position of component 2

Simultaneously fit the IR spectrum of component 2 and the

CLS to obtain the FFCF for component 2

a

b

c

d

e

162

Figure 7.6 Representative center line data used in the two component CLS algorithm. The known

center line data for bulk water are the blue circles, while the center line data for the known combined

system are shown by the black circles. After applying the algorithm, the center line data for component

2 are produced (green circles). The calculated center line data can then be recombined with the known

bulk water data to reproduce the known combined data (red line).

7.3.2 Non-Overlapping Bands

In some systems, the constituent components yield spectrally resolved line

shapes. For example, the red and blue states of the CO stretching mode of horseradish

peroxidase (HRP) give rise to narrow peaks at 1903.7 cm-1

and 1932.7 cm-1

,

respectively.35

The bandwidths of these peaks are 10 and 15 cm-1

, so the peaks are

readily distinguishable. In this situation, CLS analysis is performed independently on

each peak to obtain the individual FFCFs.9 It will be seen shortly that the model cases

tested in this study involve a bulk water-like component with a much broader

absorption spectrum compared to the HRP system. We would like to stress that the

modified CLS analysis and relevant discussions presented here can apply to many two

component systems and not just those with water.

2520 2540 2560 2580 2600

2520

2540

2560

2580

2600

component 1, calculation

combined system, calculation

component 2, back-calculated

reconstructed combined system

ωτ (cm-1)

ωm

(cm

-1)

Tw = 0.2ps

163

Figure 7.7 Calculated 2D IR spectra for non-overlapping bands at Tw = 0.2 ps (a) and Tw = 5 ps

(b). The bulk water system is the set of peaks on the left side of the spectra (lower frequency). Because

the two components have different vibrational lifetimes, the spectra decay at different rates.

Table 7.1 lists FFCF parameters that were used to construct a series of

calculated spectra for testing the two component CLS method. The set of FFCF

parameters in Table 7.1 is collectively referred to as the first model case, but it is used

to generate four separate situations involving different component 2 center

frequencies. The first row contains the known FFCF parameters for bulk water11

as

well as the center frequency (2509 cm-1

) and the vibrational lifetime, T1. Each

concentration (a1) was set to a fraction of 0.5. The only parameter varied in each

scenario is the center frequency (ω0) for the second component. In the non-

overlapping case, the center frequency of component 2 was set to 2700 cm-1

. Figure

7.7 displays calculated 2D IR spectra for this system at Tw = 0.2 and 5 ps. The 0-1 and

1-2 bands due to bulk water (component 1) are located on the red side of the plot and

by 5 ps are almost completely depleted due to a faster vibrational lifetime. T1 for

component 2 is 5 ps, while T1 for bulk water is 1.8 ps.39

Spectra were also calculated

separately for component 1 and component 2. If CLS analysis is performed on the

2300 2400 2500 2600 2700 28002300

2400

2500

2600

2700

2800

2300 2400 2500 2600 2700 28002300

2400

2500

2600

2700

2800

ωτ (cm-1)

ωm

(cm

-1)

A. Tw = 0.2 ps

B. Tw = 5 psω

m(c

m-1

)

164

individual bands of the combined spectra shown in Figure 7.7, then the resulting CLS

curves essentially match the CLS curves calculated for the separate sets of spectra for

bulk water and component 2. Figure 7.8 shows the excellent agreement of these CLS

calculations. There is no need to apply the algorithm presented in Figure 7.5. Since

the peaks basically have no overlap, it is not surprising that the CLS for each peak can

be readily extracted.

Figure 7.8 Model case 1 for non-overlapping bands (centers of 2509 and 2700 cm-1

): CLS decay

curves for bulk water (a) and component 2 (b). The red dots are the CLS calculations performed on

the spectra when both components are present, while the blue dots denote the CLS calculated on the

calculated bulk water and component 2 systems by themselves. Because the peaks are well-separated,

the CLS results for each component (blue vs. red) match almost perfectly.

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

CL

SC

LS

Component 1 (bulk water)

from combined spectra

from single Component 1 spectrum


from single Component 2 spectrum

Component 2

Tw (ps)

165

Figure 7.9 Model case 1 for overlapped but distinguishable bands (centers of 2509 and 2650 cm-

1): Calculated 2D IR spectrum at Tw = 0.2 ps (a) and the CLS results for the system (b). The red

dots are the CLS calculated for component 2 from the combined system 2D IR spectra. The green dots

are the CLS curve obtained from the calculated 2D spectra of component 2 by itself. The black dots are

the CLS for component 2 after applying Equation 7.34.

7.3.3 Overlapping But Distinguishable Bands

Figure 7.9a shows a 2D IR spectrum for the combined system (Table 7.1) with

the center of the second component set to 2650 cm-1

. In this situation, two bands can

be distinguished, but there is significant overlap between them. Despite this overlap,

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

Tw = 0.2 ps

ωτ (cm-1)

ωm

(cm

-1)

A.

B. Component 2


from single component 2 spectrum

back-calculated using eq. 7.34

CL

S

Tw (ps)

2300 2400 2500 2600 2700 28002300

2400

2500

2600

2700

2800

166

the CLS can still be calculated separately from the individual peaks. The accuracy is

improved if the CLS is calculated slightly more to the blue of the center for

component 2 and more to the red of the center for component 1. Figure 7.9b shows

the CLS results for component 2. The red circles are the CLS calculated from the 2D

IR spectra (Figure 7.9a) between 2650 and 2730 cm-1

. The green circles are the CLS

calculated from single 2D IR spectra of component 2 by itself. The black circles are

the CLS from the center line data back-calculated using Equation 7.34. Again, there is

excellent agreement between the data sets. The important result here is that the CLS

can be obtained accurately from each band individually even though there is

substantial overlap. In this case, it is not necessary to know the parameters for

component 1. The CLS curves of both component 1 and component 2 can be

obtained.

7.3.4 Unresolved Overlapping Bands

Figure 7.10a shows a 2D IR spectrum when the center of component 2 (Table

7.1) is set to 2600 cm-1

. The central lobe is quite elongated, but there is no clear

separation into two bands. Figure 7.11a corresponds to the case where the center of

component 2 (Table 7.1) is set to 2550 cm-1

and resembles a spectrum that might arise

from a single component. The two peaks are so overlapped that there is no indication

that there are two components. In such a situation, it is necessary to know whether

two species contribute. In these strongly overlapping cases, Equation 7.34 can be used

to obtain the CLS for component 2. The results for these two cases (7.10a and 7.11a)

are presented in Figures 7.10b and 7.11b. The green circles are the calculated CLS

from the single component 2 spectra without component 1. The black circles are the

results from applying Equation 7.34. The results from Equation 7.34 (black circles)

differ slightly from the component 2 simulation results (green circles). Table 7.2 lists

the FFCF parameters obtained from simultaneously fitting the CLS curves resulting

from Equation 7.34 and the FT IR spectra of component 2 at the two center positions

(2600 and 2550 cm-1

). Because the curves do not exactly agree, there is some error in

the magnitude of the homogeneous component, but the remaining parameters (Δ’s and

time constants) have excellent agreement with the starting parameters for the model

167

case listed in Table 7.1. Given that the two bands are completely indistinguishable in

either the linear IR spectrum or in the 2D IR spectra, the accuracy of the extracted

component 2 parameters demonstrates the usefulness of the method.

Figure 7.10 Model case 1 for overlapping bands (centers of 2509 and 2600 cm-1

): Calculated 2D

IR spectrum at Tw = 0.2 ps (a) and the CLS results for the system (b). The green dots are the CLS

from the calculated 2D spectra of component 2 by itself. The black dots are the component 2 results

after applying Equation 7.34.

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

2300 2400 2500 2600 2700 28002300

2400

2500

2600

2700

2800 Tw = 0.2 ps

ωτ (cm-1)

ωm

(cm

-1)

A

B

CL

S

Component 2



Tw (ps)

168

Figure 7.11 Model case 1 for overlapping bands (centers of 2509 and 2550 cm-1

): Calculated 2D

IR spectrum at Tw = 0.2 ps (a) and the CLS results for the system (b). The green dots are the CLS

from the calculated 2D spectra of component 2 by itself. The black dots are the component 2 results

after applying Equation 7.34.

In verifying the method, many model calculations with various input

parameters were used. These all gave good agreement between the extracted

component 2 FFCF parameters and the component 2 FFCF parameters used in the

calculations. Table 7.3 illustrates a different model system with two components,

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

Component 2



ωτ (cm-1)B

CL

S

Tw (ps)

2300 2400 2500 2600 2700 28002300

2400

2500

2600

2700

2800 Tw = 0.2 ps

ωm

(cm

-1)

A

169

collectively referred to as the second model case. Component 1 is the same as in

Table 7.1, but the second component consists of a homogeneous component, an

exponential decay, and a static offset (Δs) as given in Table 7.3. The resulting 2D IR

spectra are so close together that the spectrum consists of a single 0-1 peak, just as in

the other model cases in this section. Figure 7.12 shows that the CLS calculation

using only the component 2 spectra and the back-calculation (Equation 7.34) of the

CLS have some error. However, simultaneously fitting with the CLS and IR spectrum

recovers the homogeneous component quite accurately. The FFCF parameters

obtained from the Equation 7.34 CLS results are listed in the third row of Table 7.3.

The agreement is essentially quantitative.

Table 7.2 Parameters Obtained for Component 2 Via Eq.7.34 and Simultaneous Fitting.

Table 7.3 Second Model Case Parameters.

One interesting question is what happens when the CLS is calculated around

the 2D IR centers of the spectra of the combined system, without decomposing the

dynamics into two components? Figure 7.13 shows the CLS decay for the first model

case (Table 7.1) with centers frequencies of 2509 and 2550 cm-1

. Each CLS data point

was calculated for ±40 cm-1

around the peak position of the corresponding spectrum.

Because there are two components that decay with different vibrational lifetimes, the

center steadily shifts from ~2530 cm-1

at Tw = 0.2 ps to 2550 cm-1

at Tw = 10 ps. When

the curve in Figure 7.13 is fit with a biexponential decay, the fit parameters are a1 =

0.30, t1 = 0.6 ps, a2 = 0.39, t2 = 4.3 ps, where the ai and ti terms are amplitudes and

decay constants for a given component, respectively. The time constants fall between

the known starting values for each component in Table 7.1, but without knowledge of

any of the components, no further information can be gained. The fit parameters

Component

2 center Γ

(cm

-1) Δ

1 (cm

-1) t

1 (ps) Δ

2 (cm

-1) t

2 (ps)

2600 (cm-1

) 47 49 0.8 27 5.1 2550 (cm

-1) 45 46 0.9 29 4.9

System Γ (cm

-1) Δ

1 (cm

-1) t

1 (ps) Δ

2 (cm

-1) t

2 (ps) Δ

s (cm

-1) ω

0 (cm

-1) a1 T

1 (ps)

1 76 41 0.38 34 1.7 - 2509 0.56 1.8 2 35 55 1.9 - - 20 2565 0.44 4.5

2 FFCF 36 60 1.9 - - 19.3 - - -

170

could be used to calculate an FFCF, but the resulting processes would be nonspecific

to the different environments in a system and instead indicate a type of average

behavior. Much more information can be gained by separating out the components

using Equation 7.34.

Figure 7.12 CLS results for the second model case of overlapping bands (Table 7.3 with

component 2 center at 2565 cm-1

) at Tw = 0.2 ps. The green dots are the CLS from the calculated 2D

spectra of component 2 by itself. The black dots are the component 2 results after applying Equation

7.34.

Figure 7.14 shows the CLS curve for the second model case (Table 7.3),

calculated around the peak position for each spectrum. The resulting curve can be fit

to a biexponential decay plus an offset, but it is unclear what the fit parameters can tell

us about the system, since there appears to be a kink in the curve around 2 ps,

indicating that a strictly biexponential fit plus an offset is not the correct functional

form for the FFCF. This is not surprising because the CLS points reflect the

combination of two distinct FFCFs. This kink is most likely due to the relatively

faster FFCF of bulk water dying out more quickly than the FFCF for component 2.

Similar shapes have been observed for multi-component anisotropy decays where one

component reorients faster than the second.39,43,78

Figure 7.13 and 14 show an

important aspect of multi-component systems. In Figure 7.14, the shape of the CLS

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

Component 2



CL

S

Tw (ps)

171

data obtained from a series of 2D IR spectra hints the data are not arising from a single

component system. However, the plot in Figure 7.13 does not provide an indication

that the system has two components. The curve can be fit very nicely to a sum of

exponentials. However, treating the CLS as a one component system does not provide

the correct FFCF parameters for either component. Therefore, the algorithm presented

in this paper is not a cure-all for ambiguous data sets but rather a tool for analysis of

two components systems that can be used when critical pieces of information are

known beforehand or can be reasonably simulated.

Figure 7.13 CLS decay, calculated around the 2D IR maxima, for the first model case (Table 7.1

with component 2 center at 2550 cm-1

) without decomposing the data into different components.

A biexponential fit to the curve yields ambiguous information.

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

CL

S

Tw (ps)

first model case (centers 2509 & 2550 cm-1)

biexponential fit, no decomposition

172

Figure 7.14 CLS decay, calculated around the 2D IR maxima, for the second model case (Table

7.3 with component 2 center at 2565 cm-1

) without decomposing the data into different

components. Note the kink in the curve around 2 ps. It is unclear what functional form this CLS curve

should take, indicating that decomposing the CLS data into separate components can yield more useful

information.

7.3.5 Degree of Error in the Two Component CLS Method

The model cases discussed above show that in non-overlapping and even in

significantly overlapping cases with resolvable 2D IR spectra, the CLS for each

component can be directly calculated from the spectra separately for each component.

It appears that when the separation of the 0-1 peaks for the two components exceeds

50% of the FWHM of one of the components, then the CLS curves may be calculated

directly from the spectra. This is certainly the case for the red and blue states of HRP

referenced earlier because the spectral separation is several times larger than the

bandwidth of the peaks.35

Figure 7.9 suggests that the results are the same whether or

not the CLS is obtained from the spectra or Equation 7.34. In cases where the

separation of components is less than 50% of one of the FWHM values, then Equation

7.34 should be used to obtain the correct center line data. A general rule of thumb is

that if one cannot distinguish separate peaks, then the algorithm should be used.

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

CL

S

Tw (ps)

second model case (centers 2509 & 2565 cm-1)

173

Another point of interest is how much error can be introduced into the FFCF

parameters after doing the simultaneous fit of the CLS data and the IR spectrum. The

extracted parameters using Equation 7.34 that are presented in Tables 7.2 and 7.3

show that the parameters are reasonably reproduced when compared to the initial

known values for component 2. It should be noted that the algorithm was tested for

quite a few other cases not presented here. For example, we tested the algorithm for

two components with similar vibrational lifetimes and found no change in accuracy.

Throughout our studies, it appeared that the algorithm typically returned Δ values

within ±5 cm-1

of the starting value with occasional deviants of ±10 cm-1

. The time

constants were generally within ±1 ps. As can be seen from Tables 7.1, 7.2, and 7.3,

there can be great error associated with the homogeneous component, but this degree

of error is similar to previously reported experimental error values for the

homogeneous component.11

Overall, the algorithm presented in this paper succeeds in

capturing the overall dynamics of a system (biexponential, single exponential, etc.)

and returns values that are reasonably close to the true parameters. When applied to

experimental systems, results can be trusted and the errors may not exceed

experimental error.


2D IR vibrational echo spectroscopy is a useful technique for studying the

dynamics of molecules in liquids, solids, and biological systems. The dynamics of a

system are described by the frequency-frequency correlation function that can be

extracted from the 2D spectra using the CLS technique. The main benefit of the CLS

technique is that a full response function calculation is not needed to obtain the full

FFCF. In contrast to other methods, the CLS technique is insensitive to pulse

duration, Fourier filtering techniques, sloping absorptive background, and the overlap

of the 0-1 and 1-2 transition peaks.10

However, when more than one species is present

in a system, the CLS technique becomes more complicated, and normal application of

the CLS technique can yield ambiguous information. We have shown mathematically

that the peak location of a slice through a spectrum with two components is a weighted

combination of the peak locations of the individual components. The center line data

174

(set of peak locations vs. ωτ for a given Tw) for each component are weighted by

frequency and Tw-dependent fraction terms, which can be obtained from the linear

absorption spectra and vibrational lifetimes of the two components. Therefore, if one

of the components of a two component system is well characterized, and if other

parameters for both components are known, i.e., the center frequencies, vibrational

lifetimes, and IR spectra, then the set of center line data for the second component can

be readily back-calculated (using Equation 7.34) from experimental data of the

combined system. After the center line data for component 2 is back-calculated, CLS

analysis may be performed and the FFCF for the second component obtained.

We have tested this algorithm for a variety of model cases to show its accuracy

in reproducing sets of model data. Overall, the extracted FFCF parameters of the

unknown component are quite accurate. A significant implication of this algorithm is

the realization that the CLS curve for a multiple component system is not itself a

weighted average of individual CLS curves for each component separately. Therefore,

a traditional single CLS curve is not very useful in describing the dynamics of a

multiple component system. The algorithm developed here extracts an unknown

FFCF from a set of 2D IR data consisting of two contributing components. Chapter 8

will demonstrate the practical application of Equation 7.34 to experimental 2D IR data

for water inside of large AOT reverse micelles.

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M. Proc. Natl. Acad. Sci. USA 2008, 105, 1472.

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179

Chapter 8 Spectral Diffusion of Water

Molecules in Reverse Micelles

8.1 Introduction

The behavior and motions of interfacial water molecules are critical in many

chemical reactions, biological mechanisms, and industrial processes. For example,

water molecules facilitate proton transfer in the polyelectrolyte membranes of fuel

cells. Water molecules at mineral or zeolite interfaces are used for ion-exchange and

filtration applications as well as heterogeneous catalysis. In biology, water molecules

are found in crowded environments interacting with protein pockets or surfaces, cell

membranes, or pharmaceuticals. Processes in such nanoscopic systems depend upon

water’s ability to form and exchange hydrogen bonds. Bulk water consists of an

extended network of hydrogen bonds that are continually rearranging, requiring

concerted motions of both the first and second solvation shells.1,2

The presence of

interfaces or confined environments can disrupt pathways necessary for hydrogen

bond rearrangement, thus slowing down the rate of hydrogen bond exchange.3-7

Spectroscopic observables that report upon water dynamics include the vibrational

lifetime, orientational relaxation, and spectral diffusion of the water hydroxyl stretch,

all of which generally occur on the picosecond (ps) time scale. With its femtosecond

(fs) time resolution, ultrafast infrared spectroscopy is a useful technique for measuring

water dynamics.

One fundamental question is how the size of the confining environment affects

water hydrogen bond rearrangement dynamics. This topic has been explored quite

extensively with ultrafast pump-probe experiments that measure water reorientation

inside of reverse micelle systems.6,8-20

A reverse micelle consists of a nanoscopic

water pool surrounded by a layer of surfactant molecules. The surfactant has a

hydrophilic head group and a hydrophobic tail region. The head groups face in

towards the water pool, surrounding the nanoscopic pool of water and forming a layer

180

of interfacial water molecules. The tails are suspended in a non-polar organic phase.

A common surfactant used in making reverse micelles is sodium bis(2-ethylhexyl)

sulfosuccinate, also known as Aerosol-OT or AOT (Figure 8.1), which has charged,

sulfonate head groups. The AOT system makes monodispersed, spherical reverse

micelles and has been well-characterized. The size of the water pool diameter is easily

controlled by varying the w0 parameter which is equal to the ratio of concentrations of

starting materials: w0 = [H2O]/[surfactant].21-23

Sizes of reverse micelles can range

from essentially dry AOT (w0 = 0) up to w0 = 60, which has a water nanopool diameter

of 28 nm and contains roughly 350000 water molecules.10

Figure 8.1 Molecular structures for AOT and Igepal CO-520. AOT has charged, sulfonate head

groups while Igepal has neutral, hydroxyl head groups.

The spectral diffusion dynamics of water inside of w0 = 2 AOT reverse

micelles suspended in carbon tetrachloride (CCl4) were reported in Chapter 6.24

Spectral diffusion dynamics are described by the frequency-frequency correlation

function (FFCF) which indicates how quickly water molecules sample different

frequencies within the inhomogeneously broadened vibrational absorption band. The

frequency evolution is caused by structural changes that influence the vibrational

frequency of a molecule such as hydrogen bond rearrangement. Once the FFCF is

known, time-dependent diagrammatic perturbation theory can be used to calculate all

linear and nonlinear optical experimental observables.25

In addition to a fast,

homogeneous component, the FFCF for the w0 = 2 system was found to have ~1 ps

and ~10 ps components and an offset.24

The FFCF for bulk water has a homogeneous

component, a ~400 fs component, and a ~1.7 ps component (and no offset).26

The

181

short, ~400 fs, component is attributed to fast local hydrogen bond fluctuations,

mainly in the lengths of hydrogen bonds,27,28

while the 1.7 ps component arises from

hydrogen bond network randomization.26

While it is likely that the ~1 ps component

in the w0 = 2 system arises from fast hydrogen bond fluctuations, the 10 ps component

has no analog in the bulk water system. It was proposed this ~10 ps process was due

to water molecules accommodating topography roughness of the surfactant interface,

but other possibilities will be discussed below. The offset was attributed to extremely

slow reorientation and diffusion processes of water molecules. Overall, the dynamics

in the very small w0 = 2 reverse micelles (~40 water molecules) are extremely slow

compared to bulk water because virtually all of the water molecules are interacting

with the interface.

It was shown in Chapter 6 that the dynamics inside the AOT reverse micelles

are insensitive to the identity of the non-polar phase.24

AOT reverse micelles may be

made in a variety of solvents, including isooctane, decane, carbon tetrachloride, and

toluene without significantly changing the size of the water pool.29,30

Isooctane is a

popular solvent used in experiments and in molecular dynamics (MD) simulations.31,32

However, it was discovered that interactions between AOT and isooctane cause extra

signals that interfere with the measurements of the hydroxyl stretch spectral diffusion,

although it is still possible under the right circumstances to effectively background-

subtract the extra signals and determine the FFCF.24

This procedure that corrects for

the distortions in the isooctane system has been described in detail in Chapter 6.24

When carbon tetrachloride (CCl4) is used as the solvent instead, the distortions are not

present. To ascertain whether the identity of the non-polar phase changes the

dynamics of the water pool, the steady state and dynamic data were compared for

AOT reverse micelles made in isooctane and in CCl4. It was found that the FT IR

absorption spectra, vibrational lifetime behavior, reorientation dynamics, and spectral

diffusion are identical for the two solvents within experimental error. Thus,

experimental data obtained in CCl4 may be directly compared to experiments

performed with isooctane.

Here, spectral diffusion dynamics of water inside a wide range of AOT reverse

micelle sizes, w0 = 16.5, 12, 7.5, 4, and 2, are compared. CCl4 cannot support reverse

182

micelles of w0’s greater than 10,10,33

so cyclohexane was used as the organic phase for

w0 = 12 and 16.5. Based on the previous solvent-dependence study, the change to

cyclohexane will not affect the water pool dynamics. Spectral diffusion of water was

also measured in reverse micelles of w0 = 12 made with the nonionic surfactant Igepal

CO-520 (Figure 8.1), which has the same water pool diameter as AOT w0 = 16.5 (5.8

nm). With these different systems, we examine how both water pool size and the

chemical composition of the interface affect water spectral diffusion, and therefore

structural evolution, in confined environments.


Carbon tetrachloride (CCl4), cyclohexane, H2O, D2O (Sigma-Aldrich), and

Igepal CO-520 were used as received. AOT (Sigma-Aldrich) was purified by first

dissolving the compound in methanol and stirring overnight with activated charcoal.

The charcoal was removed by vacuum filtration, and the methanol was removed with

a rotary evaporator. The AOT was stored in a vacuum desiccator. 0.5 M stock

solutions of AOT were prepared in CCl4 and in cyclohexane. A 0.3 M stock solution

of Igepal CO-520 was prepared in cyclohexane. The residual water contents of the

stock solutions were measured via Karl-Fischer titration. The reverse micelle samples

were prepared by mass by adding appropriate amounts of a solution of 5% HOD in

H2O to measured quantities of the AOT or Igepal stock solutions to obtain the desired

w0. The AOT/CCl4 stock solution was used to make w0 = 2, 4, and 7.5 (diameters of

1.7, 2.3, and 3.3 nm, respectively) while the AOT/cyclohexane stock solution was

used to make w0 = 12 and 16.5 (diameters of 4.6 and 5.8 nm, respectively). To

compare the effects of the chemical composition of the interface, Igepal reverse

micelles with w0 = 12 were also made. Like AOT, Igepal also makes monodispersed

spherical reverse micelles.34

The w0 = 12 Igepal reverse micelles have the same 5.8

nm diameter as AOT w0 = 16.5. The w0 = 12 Igepal reverse micelles are not the same

size as the w0 = 12 AOT reverse micelles because the two surfactants have different

aggregation numbers. The experimental samples are contained between two calcium

fluoride windows that are separated by a Teflon spacer. The thickness of the Teflon

183

spacer is chosen such that the optical density of the OD stretch region is ~0.1 for the

echo experiments.

In the ultrafast experiments, the OD stretch of 5% HOD in H2O is probed

because it prevents vibrational excitation transfer processes from artificially causing

decay of the orientational correlation function and observables related to spectral

diffusion.35,36

MD simulations indicate that a dilute amount of HOD does not perturb

the structure and properties of H2O and that the OD stretch reports on the dynamics of

water.37

The laser system used to generate the infrared light that excites the OD

hydroxyl stretch consists of a Ti:Sapphire oscillator that seeds a regenerative

amplifier. The output of the regenerative amplifier pumps an optical parametric

amplifier which generates near-infrared wavelengths that are difference frequency

mixed in a AgGaS2 crystal. The resulting mid-infrared pulses are centered at ~4 µm

(2500 cm-1

) but are tuned to the peak of the absorption spectrum for a given sample

(for instance, 2565 cm-1

for w0 = 2).

The experimental layout and procedures of the 2D IR vibrational echo

experiment have been described in detail elsewhere24,38

and also in Chapters 2 and 3 of

this thesis. In brief, the mid-IR light is beam split into three time-ordered excitation

beams and a fourth beam called the local oscillator (LO). The first excitation pulse

creates a coherence state between the v = 0 and v = 1 vibrational levels of the OD

stretch. During the evolution period τ that follows, the phase relationships between

the oscillators decay. At time τ the second pulse creates a population state in both the

v = 0 or v = 1 vibrational levels. The waiting period Tw elapses before the third pulse

arrives to create a final coherence state, partially restoring the phase relationships.

The rephasing of the oscillators causes the vibrational echo to be emitted at a time t ≤ τ

after the third pulse. The OD oscillators undergo spectral diffusion during the Tw

period as the molecules sample different environments due to structural evolution of

the system. The vibrational echo signal is spatially and temporally overlapped with

the LO for heterodyned detection. The heterodyned signal is frequency dispersed by a

monochromator and detected on a 32 element mercury cadmium telluride detector. At

a series of fixed Tw values, τ is scanned to generate 2D IR spectra. The time evolution

of the spectra as Tw is increased yields information on spectral diffusion.

184

Spectral diffusion may be described by the frequency-frequency correlation

function (FFCF), which can take the form:

2 /

1 10 10 *2

( )( ) ( ) (0) .it

i

i

tC t t e

T

(8.1)

The Δi are the frequency fluctuation amplitudes of each component, and the τi are

their associated time constants. If the product Δτ < 1for a given component in the

FFCF, then Δ and τ cannot be determined separately and instead contribute a

motionally narrowed homogeneous component to the absorption spectrum with a pure

dephasing line width of * 2 *

21/ T where *

2T is the pure dephasing time.

Contributions from vibrational lifetime, orientational relaxation, and pure dephasing

may be combined into the total homogeneous dephasing time, T2, which is given by

*

2 2

1 1 1 1,

2 3vib orT T (8.2)

where *

2T , vib , and or are the pure dephasing time, vibrational lifetime, and

orientational relaxation time, respectively. The total homogeneous line width is given

by 21/ . T

The FFCF (Equation 8.1) can be determined from the Tw dependence of the 2D

IR correlation spectra via center line slope (CLS) analysis.38-40

In this technique, the

2D correlation spectrum at a given Tw is sliced parallel to the ωm axis (the vertical

detection axis) over a range of frequencies about the 2D IR center. Each slice is fit to

a Gaussian line shape function to obtain its peak position. This particular variant of

the CLS method is known as CLSωm. The peak positions are plotted versus the ωτ

frequencies (the horizontal initial excitation axis) that the slices intercept. The set of

peak positions (ωτ, m) are referred to as center line data. The resulting line is fit with

a linear regression to find the slope. Slopes of this nature are obtained for each Tw.

From the plot of slopes vs. Tw, the FFCF can be determined. The procedures

describing the extraction of the FFCF from CLS data have been detailed previously39

and in Chapter 7. In brief, the CLS decay is fit with a multi-exponential decay. The

decay constants are the FFCF decay constants. To obtain the homogeneous

component of the FFCF, amplitudes and time constants of the CLS are used to

185

simultaneously fit the CLS data and the system’s linear FT IR absorption spectrum.

The FT IR spectrum is fit via the Fourier transform of the linear response function. A

homogeneous component is also included in the fit so that the full FFCF is

determined.

The CLSωm method is a convenient tool for obtaining the FFCF of a system

because it avoids using the nonlinear response function formalism to fit the 2D IR

data, and it is insensitive to finite pulse durations, sloping background absorption,

Fourier filtering methods (such as apodization), and overlap between the 0-1 and 1-2

transition peaks.39,40

It should be noted that the CLS methodology was developed

under the assumption of Gaussian fluctuations.39,40

In systems such as bulk water,

non-Condon effects and deviations from Gaussian fluctuations may influence

experimental spectral observables to some extent.41,42

Non-Condon effects account for

a varying transition dipole with absorption frequency.41,42

MD simulations have

shown that the variations in calculated observables obtained via different water models

are just as large as simulations that do or do not use the Gaussian approximation.28,42-44

In aqueous systems that are even more complex than bulk water, such as water

nanopools in reverse micelles, it is extremely difficult to extract usable information

from 2D spectra using simulations alone. While obtaining the FFCF via the CLS

method involves certain approximations, the CLS is still an easily accessible

experimental observable that can discern time scales of structural fluctuations and can

be used to compare different systems. Furthermore, the CLS is a valid observable that

can be the target of simulations regardless of whether it is used to determine the FFCF.

Polarization and wavelength selective pump-probe experiments are used to

determine the vibrational lifetime and orientational relaxation time of water molecules

inside the reverse micelle environments. In these experiments, the IR light is split into

a weak probe pulse and an intense pump pulse. The pump is polarized at 45° relative

to the horizontally polarized probe. The two beams cross in the sample, and the

parallel and perpendicular components (+/ 45°) of the probe are resolved using a

computer-controlled rotation stage. Before entering the monochromator, the

polarization of the probe is set to horizontal to eliminate problems from diffraction and

reflection efficiencies of the optics inside the monochromator for different

186

polarizations. The frequency dispersed signal is detected on the 32 element mercury

cadmium telluride detector. The measured parallel and perpendicular signals yield

information about the population relaxation and orientational dynamics of the water

molecules (HOD) and are given by

2( ) ( )(1 0.8 ( )),I t P t C t (8.3)

2( ) ( )(1 0.4 ( )),I t P t C t (8.4)

where P(t) is the vibrational population relaxation and C2(t) is the second Legendre

polynomial orientational correlation function for a dipole transition. These two

signals may be combined to yield the pure population relaxation,

( ) ( ) 2 ( ).P t I t I t (8.5)

The anisotropy, from which C2(t) may be extracted, is given by

2

( ) ( )( ) 0.4 ( ).

( ) 2 ( )

I t I tr t C t

I t I t

(8.6)

For two component systems consisting of bulk-like water in the core and water at the

interface of large reverse micelles, Equations 8.5 and 8.6 must be modified, as

discussed below, to account for the contributions of different sub-ensembles of water

molecules.


8.3.1 Linear Absorption and Pump-Probe Spectroscopy

Figure 8.2a displays the FT IR absorption spectra for the OD stretch of HOD in

H2O in the range of w0’s of AOT reverse micelles studied in this work along with bulk

water for comparison. The hydrogen bonding interaction between water (HOD) and

the sulfonate head groups at the micelle interface causes the OD spectrum to blue

shift. As the reverse micelles become smaller, a greater proportion of water molecules

interact with the sulfonate head groups and cause a greater blue shift. Previous

analysis has shown that the water spectra in AOT reverse micelles can be decomposed

into a bulk water spectrum and an interfacial water spectrum. The interfacial spectrum

is approximated as the w0 = 2 spectrum6,8,10

because in this system virtually all of the

187

water molecules interact with the head groups. In describing the absorption spectrum

the only adjustable parameter is a fractional population corresponding to the amounts

of interfacial and bulk water in a given reverse micelle. This model is often referred to

as the core/shell or two component model. This model takes the following

mathematical form,

1 1 1 2 1 2( ) ( ) (1 ) ( ) ( ) ( ),totI a I a I S S (8.7)

where a1 is the fractional population, and I1 and I2 are the component spectra for bulk

water and w0 = 2, respectively. Figure 8.2b shows the decomposition of the AOT w0 =

12 spectrum. The blue and red curves are the bulk water and w0 = 2 spectra,

respectively. The circles are the w0 = 12 spectrum, and the black curve is the weighted

sum of the bulk water and w0 = 2 spectra. The figure shows excellent agreement for

the model embodied in Equation 8.7. For AOT reverse micelles, a1 = 0.56 for w0 = 12

and 0.74 for w0 = 16.5.

Figure 8.3 compares the linear FT IR absorption spectra of AOT w0 = 16.5 and

Igepal w0 = 12. Both samples have water pool diameters of 5.8 nm. Even though the

water pool sizes are identical, the spectra are not the same because the head group

regions are different. The spectrum for Igepal w0 = 12 is less blue shifted than AOT

w0 = 16.5. The difference is caused by the different nature of the interfacial

interactions for the two surfactants.

Population relaxation and rotational dynamics can provide considerable insight

into the dynamics and interactions of water molecules in confinement. Population

relaxation is described via the vibrational lifetime, a time constant that measures how

quickly vibrational energy dissipates in a system. The vibrational energy goes into a

combination of low frequency modes, such as bending modes, torsions, and bath

modes that sums to the original energy.45,46

In bulk water, vibrational energy

dissipates relatively easily through these pathways. Confinement or the presence of

solutes can modify vibrational relaxation because certain pathways that were available

in bulk water may no longer be accessible. As a result, the vibrational lifetime is

extremely sensitive to local environments. Figure 8.4 shows the population decays for

AOT w0 = 12, AOT w0 = 16.5, and Igepal w0 = 12 at a high frequency of 2589 cm-1

where the contribution from water at the interface is enhanced. As demonstrated by

188

Moilanen et al., the population decay of water in large reverse micelles can be

decomposed into contributions from the bulk water core and the interfacial water

molecules at the head groups,

1 2/ /

1 1( ) (1 ) ,vib vibt tP t Ae A e

(8.8)

where A1 is a fractional population and τvib1 and τvib2 are the vibrational lifetimes of

bulk water and water at the head group interface, respectively. In larger AOT reverse

micelles, the time constants do not change with wavelength, but the fractional

population A1 does change with wavelength. In Equation 8.8, A1 is not the same as a1

in Equation 8.7 because A1 changes with wavelength while a1 is a single value. At all

wavelengths, τvib1 is fixed at the literature value of 1.8 ps for bulk water,6,8

and τvib2 is

determined to be ~4.5 ps for both AOT reverse micelle sizes (w0 = 12 and 16.5), as

summarized by Table 8.1. This interfacial vibrational lifetime is consistent with a

previous value obtained for large reverse micelles in isooctane.6,8

Figure 8.4 shows

that the population decay for AOT w0 = 12 is slightly slower than that for AOT

w0=16.5 at the same wavelength. This behavior arises because there is more

interfacial water in AOT w0 = 12 and therefore a greater contribution of the

component with a slower decay. The population decays in Figure 8.4 have been

corrected for a well-understood long time non-zero baseline that arises from the

deposition of heat into the system from the vibrational relaxation.10,13,47-52

Table 8.1 Population and Orientational Relaxation Parameters for Large and Intermediate

Reverse Micelles.

AOT w0=16.5 AOT w0=12 AOT w0=7.5

τvib1 (ps) 1.8 1.8 2.1

τvib2 (ps) 4.5 4.7 5.5

τor1 (ps) 2.6 2.6 4.4

τor2 (ps) 15 23 30 Error bars are ±0.2 for τvib1, τvib2, and τor1; ± 5 for τor2

The population relaxation parameters for AOT w0 = 7.5 are also listed in

Table 8.1, which have been published previously.24

AOT w0 = 7.5 can also be

decomposed into core and interfacial environments, but the vibrational lifetime

associated with the core is slightly slower (2.1 ps) than the value for bulk water (1.8

ps). The vibrational lifetime at the interface also slows down (5.5 ps). The AOT w0 =

189

7.5 reverse micelle is too small to support a purely bulk-like water core, but it is still

large enough to have separate environments with different dynamics. The w0 = 7.5

system can be considered an intermediate-sized reverse micelle. In the spectral

diffusion analysis in the next section, AOT w0 = 7.5 will be analyzed in two ways as

both a small and large reverse micelle.

Figure 8.2 Linear IR absorption studies. a) Linear FT IR absorption spectra for the range of reverse

micelles sizes studied, in addition to bulk water. The smaller reverse micelles, w0=2, 4, and 7.5 were

made in carbon tetrachloride (CCl4) while w0= 12 and 16.5 were made in cyclohexane. There is a

systematic blue shift of the spectra as water content decreases. b) Two component decomposition of the

AOT w0 = 12 spectrum into the bulk water (blue) and AOT w0 = 2 (red) spectra. The black dots are the

original spectrum, and the black line is the two component fit.

0.0

0.2

0.4

0.6

0.8

1.0

frequency (cm-1)

abso

rbance (norm

.)abso

rbance (norm

.)

A

B

2300 2400 2500 2600 27000.0

0.2

0.4

0.6

0.8

1.0

bulk water

w0 = 2

w0 = 12 data

and fit

water

w0 = 16.5

w0 = 12

w0 = 7.5

w0 = 4w0 = 2

190

Figure 8.3 Linear FT IR absorption spectra for Igepal w0=12 (blue) AOT w0= 16.5 (red). Even

though these two reverse micelles both have a 5.8 nm water pool diameter, the Igepal spectrum is red

shifted because the head group regions are different between the two surfactants.

Figure 8.4 Population relaxation decays for AOT w0=12 (green), AOT w0=16.5 (red), and Igepal

w0=12 (blue) at a detection wavelength of 2589 cm-1

. AOT w0=12 has the slowest decay and Igepal

w0=12 has the fastest.

Table 8.2 lists the vibrational relaxation parameters for smaller reverse

micelles, AOT w0 = 2 and w0 = 4. These reverse micelles present a situation where,

even though the water molecules exist in a mainly interfacial environment without a

core region, the vibrational lifetime still has two components. For both reverse

2300 2400 2500 2600 27000.0

0.2

0.4

0.6

0.8

1.0

frequency (cm-1)

abso

rban

ce (n

orm

.) Igepal w0 = 12 AOT w0 = 16.5

0 1 2 3 4 5 6 7 8 9 100.0

0.2

0.4

0.6

0.8

1.0

t (ps)

P(t

) (n

orm

.)

Igepal w0 = 12

2589 cm-1

AOT w0 = 16.5, 2589 cm-1

AOT w0 = 12, 2589 cm-1

191

micelles, there is one lifetime of 2 ps and a slower lifetime of ~7 ps for w0 = 2 and

~6.5 ps for w0 = 4. The faster (2 ps) lifetime is attributed to OD hydroxyls that are

hydrogen bonded to the oxygens of water molecules, while the second, slower lifetime

is attributed to ODs bound to head groups. Unlike the larger reverse micelles, there is

a frequency dependence to the value of the second, longer lifetime. As the frequency

increases, the population of the 2 ps lifetime decreases, and the value of the slower

lifetime increases. At the highest frequencies for AOT w0 = 2, the population decay

becomes single exponential because only ODs bound to head groups are observed.

The two component behavior arises because the vibrational lifetime is extremely

sensitive to local environments. The water molecules in the small reverse micelles are

mostly hydrogen bonded to the interface, but they can sometimes form hydrogen

bonds to other water molecules. These water-hydroxyl interactions give rise to the

faster lifetime while water-interface interactions give rise to the slower lifetime. As

the frequency is tuned to the blue, the nature of the OD-head group interactions

change, which is reflected in an increasingly long lifetime.

Table 8.2 Population Relaxation Parameters for Small Reverse Micelles.

Sample Parameter 2590 cm-1

2610 cm-1

2620 cm-1

2640 cm-1

AOT w0 = 2 A1 0.13 0.08 1.0 1.0

τvib1 (ps) 2.0 2.0 7.4 8.1

τvib2 (ps) 7.3 7.5 - -

AOT w0 = 4 A1 0.22 0.15 0.13 0.10

τvib1 (ps) 2.0 2.0 2.0 2.0

τvib2 (ps) 6.4 6.6 6.9 7.4 Error bars are ±0.2 ps for time constants; ±0.04 for amplitudes

Orientational relaxation, determined from the time dependent anisotropy

(Equation 8.6), provides information on how quickly water molecules rotate. In the

mechanism for hydrogen bond reorientation, large amplitude rotations occur via

concerted motions of the water molecules.1,2

Interfaces and solute molecules can

modify water orientational relaxation.5-8,10-14,26

Like the population dynamics,

Moilanen et al. found that the anisotropy decay of water inside of large reverse

micelles can be decomposed into two components.6,8

The two component anisotropy

192

model takes on a more complicated form than the two component population

decay,5,8,10

1 1 2 2

1 2

/ / / /

1 1

/ /

1 1

(1 )( )

(1 )

vib or vib or

vib vib

t t t t

t t

Ae e A e er t

Ae A e

(8.9)

where A1, τvib1, and τvib2 are defined by Equation 8.8, and τor1 and τor2 are the

orientational relaxation time constants for bulk water and interfacial water,

respectively. The full derivation of Equation 8.9 is shown in Appendix B. Because

A1, τvib1, and τvib2 can be determined separately via the population decay and τor1 = 2.6

ps from the literature,52

τor2 is the only adjustable parameter in Equation 8.9.

Typically, anisotropy decays for several wavelengths are fit simultaneously to extract

τor2.5,6,8,9

For large reverse micelles, τor2 ~20 ps, which is much slower than the bulk

water orientational relaxation time of 2.6 ps. The two component anisotropy decays

display an apparent plateau beginning at ~4 ps5,8

as seen in Figure 8.5. The plateau is

a result of the different lifetimes and orientational relaxation times for bulk and

interfacial water. At sufficiently long time, the anisotropy will decay to zero, but this

time is outside the experimental time window which is limited by the vibrational

lifetimes.

Figure 8.5 Anisotropy (orientational relaxation) data for AOT w0=12 (green), AOT w0=16.5 (red),

and Igepal w0=12 (blue) at a detection wavelength of 2589 cm-1

. All sets of data display a plateau

that is characteristic for multi-component anisotropy decays.

0 1 2 3 4 5 6 70.0

0.1

0.2

0.3

0.4

t (ps)

r(t)

–an

iso

tro

py

Igepal w0 = 12, 2589 cm-1

AOT w0 = 16.5, 2589 cm-1

AOT w0 = 12, 2589 cm-1

193

Table 8.3 Population and Orientational Relaxation Parameters for Igepal w0=12.

Subscript 1 – bulk water; subscript 2 – interfacial water; subscript 3 – OD head groups.

A1 τvib1 (ps) τor1

(ps)

A2 τvib2 (ps) τor2

(ps)

A3 τvib3 (ps)

0.71±0.02 1.8±0.2 2.6±0.2 0.25±0.02 3.7±0.3 15 ±3 0.04±0.02 4.1±0.3

AOT w0=7.5 also follows the two component anisotropy decay model, but

similar to the population relaxation behavior, the time constants for the core region are

slightly slower.24

The orientational relaxation time for the interface is also slower than

its counterpart in the larger reverse micelles. In addition to summarizing the

population relaxation parameters for AOT w0 =16.5, 12, and 7.5, Table 8.1 also lists

the orientational relaxation parameters for these three systems. The orientational

relaxation decays for the small reverse micelles (w0 = 2 and 4) follow a wobbling-in-a-

cone model10,19,53

which consists of a short ~1ps time constant decay followed by a

very slow component decay of ~100 ps.6,24

Even though the population decays for the

small reverse micelles follow a two component model, the anisotropy decays do not.

The essentially single ensemble orientational relaxation behavior for the smallest

reverse micelles is evidenced by a lack of wavelength dependence for the decays.6,24

The lifetime for the smallest reverse micelles depends on the hydrogen bonding of the

OD hydroxyl, which is either to a sulfonate or to a water oxygen. However, the

orientational relaxation depends on the concerted motion of many water molecules.

Because all of the water molecules in the smallest reverse micelles are either bound to

the interface or are bound to a water that is bound to the interface, none are truly

independent of the influences of the interface. For orientational relaxation, the water

nanopools of the smallest reverse micelles behave essentially as a single ensemble.

Figures 8.4 and 8.5 also display data for the Igepal w0=12 reverse micelles,

which have the same water pool diameter as AOT w0=16.5. An Igepal reverse micelle

is different from an AOT reverse micelle because the hydroxyl head groups can

exchange with HOD molecules in the water pool. The exchange of deuterium with the

head group interface creates a third vibrational species (deuterated hydroxyl head

groups) that contributes to the population decay and anisotropy signals. The overall

population of OD head groups is generally very small, but these head groups do make

194

a non-negligible contribution to the signal. The three component treatment of Igepal

reverse micelles has been discussed in detail previously17

and in Chapter 5. The

population decay for Igepal in Figure 8.4 indicates that even though the Igepal w0 = 12

and AOT w0=16.5 water pools are the same size, the population dynamics in Igepal

are slightly faster than those in AOT. The curve for Igepal w0 = 12 decays more

quickly than in AOT w0=16.5. Table 8.3 lists the population and orientation relaxation

parameters for Igepal w0 = 12. The parameters with a subscript of 1 are the bulk water

core parameters, parameters with a subscript of 2 are for waters at the interface, and

parameters with a subscript of 3 are for OD head groups. While the bulk water

component is the same regardless of the surfactant identity, the vibrational lifetime for

waters at the Igepal interface is faster than the interfacial vibrational lifetime in AOT.

The vibrational lifetime of the OD head groups is similar to that for waters at the AOT

interface and is similar to previous measurements.17

There is no orientational time

constant given for the OD head groups because it will be exceedingly slow; it is

assumed that it is equivalent to the overall rotation time of the reverse micelle, which

occurs on the order of nanoseconds. The anisotropy decays in Figure 8.5 indicate that

there is little difference between the rotational behaviors in Igepal and in AOT reverse

micelles of the same size, as the curves are virtually identical. However, because the

small effects from the OD head groups in Igepal must be taken into account, it cannot

be concluded that the dynamics in AOT and Igepal are exactly the same. Nonetheless,

it is clear that interaction with the interface significantly affects the rotational

dynamics of water while the chemical composition of the interface has substantially

less influence.

8.3.2 Spectral Diffusion in Large Reverse Micelles

2D IR vibrational echo correlation spectra were measured for each of the

reverse micelles (AOT w0 = 16.5, 12, 7.5, 4, and 2 and Igepal w0 = 12). 2D correlation

spectra for AOT w0 = 16.5 at a series of Tw’s are shown in Figure 8.6 and for AOT w0

= 2 in Figure 8.7. These samples provide representative spectra for the large and

small reverse micelles, respectively. Each spectrum consists of two peaks. The

positive (red) peak along the diagonal corresponds to the 0-1 vibrational transition

195

while the negative (blue) peak off the diagonal arises from vibrational echo emission

at the 1-2 transition frequency. The 1-2 peak appears off the diagonal and shifted

along the m axis due to the vibrational anharmonicity. At early Tw values, the spectra

are elongated along the diagonal, showing a strong correlation that an oscillator

excited at a certain frequency will retain that frequency after a short amount of time.

The spectra become more symmetric as Tw lengthens and the water molecules undergo

spectral diffusion because of structural evolution of the system. Bulk water generally

completes spectral diffusion within a few picoseconds.43,44

By 2 ps, the shape of the

bulk water spectrum has evolved from diagonally elongated to nearly symmetric

(circular). In contrast, none of the reverse micelles, from w0 = 2 through w0 = 16.5,

exhibit symmetric spectra at the end of their experimental Tw ranges, indicating that

spectral diffusion is not completed.

The large reverse micelles (w0 = 12 and 16.5) and intermediate reverse

micelles (w0 = 7.5) contain two types of water molecules: core waters and interfacial

waters. As shown by FT IR analysis, each of these regions is characterized by its own

absorption spectrum (see Figure 8.2b). In a 2D IR experiment, each of these

ensembles generates a 2D IR spectrum. The overall measured 2D spectrum is a

combination of the individual spectra. When the peak separation between components

is relatively small, the individual spectra are not resolved, and the 2D IR correlation

plots look as if there is a single species. In large reverse micelles, the component

spectra are bulk water and w0 = 2 (see Figure 8.2b).

Chapter 7 showed that the CLS method can be extended to two component

systems.54

Each two component 2D spectrum can be decomposed into its constituent

spectra, and each of these spectra has a characteristic CLS decay. In large reverse

micelles, the bulk water CLS is known, so it is possible to obtain the CLS decay (and

by extension, the FFCF) of the interfacial waters. In a system with two ensembles of

vibrations, i.e. bulk and interfacial water OD hydroxyl stretches, simply applying the

CLS method (calculating the slope around the 2D IR maximum location) does not

provide information on the interfacial water dynamics.54

The resulting multi-

exponential fit to the CLS curve yields a combination of the time constants of the bulk

196

water and interfacial water CLS decays that cannot be directly resolved into the time

constants and amplitudes for each ensemble.

Figure 8.6 2D IR correlation plots for AOT w0=16.5 at Tw = 0.2, 1, and 4 ps. At early Tw the spectra

are quite elongated, but the spectra do not complete spectral diffusion by the end of the experimental Tw

window.

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650

Tw = 0.2 ps

Tw = 1 ps

Tw = 4 ps

ωm

(cm

-1)

ωτ (cm-1)

ωm

(cm

-1)

ωm

(cm

-1)

197

Figure 8.7 2D IR correlation plots for AOT w0=2 at Tw = 0.2, 3, and 15 ps. At early Tw the spectra

are quite elongated, but the spectra do not complete spectral diffusion by the end of the experimental Tw

window. Data may be taken out longer for AOT w0=2 because of the sample’s longer vibrational

lifetime.

The theoretical work in Chapter 754

demonstrated that it is possible to extract

the unknown CLS and FFCF of one component if the center line data for the other

component is known; in this case, the center line data (and FFCF) for bulk water are

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650

2400 2450 2500 2550 2600 26502400

2450

2500

2550

2600

2650 Tw = 0.2 ps

Tw = 3 ps

Tw = 15 ps

ωm

(cm

-1)

ωτ (cm-1)

ωm

(cm

-1)

ωm

(cm

-1)

198

known. It was found that for the two component 2D IR spectrum (also called the

combined spectrum) the peak positions ( *mC ) of slices parallel to the ωm axis are

weighted combinations of the peak positions ( *1m ) of the bulk water spectrum and the

peak positions ( *2m ) of a second component:

* *1 1

*1 2

( , , ) ( , ) ( , , )

(1 ( , )) ( , , ).

mC m w w m m w

w m m w

T f T T

f T T

(8.10)

In the case of large reverse micelles, the second component is the ensemble of

interfacial water molecules. The set of peak positions for the slices are also known as

center line data. In Equation 8.10, f1 is the fractional population of bulk water, which

is both Tw and frequency-dependent. This fraction term may be obtained from the FT

IR absorption spectra of the two components and the measured vibrational lifetimes,

1

1 2

/

11 / /

1 2

( )( , ) ,

( ) ( )

w vib

w vib w vib

T

w T T

S ef T

S e S e

(8.11)

where S1 and S2 are defined by Equation 8.7. Since center line data for the combined

system and bulk water can be measured separately, Equation 8.10 can be rearranged to

obtain *2m for the interface:

* *

2 1 1*2

1

( ( , , ) ( , ) ( , , ))( , , ) .

(1 ( , ))

m C m w w m m wm m w

w

T f T TT

f T

(8.12)

To implement Equation 8.12 properly, the f1 fraction term must be known, requiring

that the vibrational lifetimes are known. In addition, the peak positions of the

interfacial water must also be known or reasonably approximated. When CLS

analysis is applied to the calculated interfacial water center line data, the CLS will be

calculated around the peak position of the interface water band, not the 2D IR

maximum. As shown in Figure 8.2b, the w0 = 2 spectrum is an excellent

approximation for the interfacial water spectrum. For w0 = 2, the peak position is

2565 cm-1

.

The raw CLS data that has not been decomposed into separate contributions

(calculated around the 2D IR centers for each correlation plot) for the AOT w0 = 16.5

and 12 systems each fit well to a single exponential to an offset. The raw CLS data for

AOT w0 = 7.5 fit well to a biexponential decay with an offset. The fit parameters to

199

these curves are given in Table 8.4. In addition to amplitudes and time constants, and

differences between 1 and the initial values at Tw = 0 are given as the a0 term in the

table. From these fit parameters, the raw CLS data may be reconstructed. These

parameters do not reflect the dynamics of either component of the two component

system. However, they could be useful for comparing MD simulations of the entire

system to the measured experimental data.

Table 8.4 Exponential Fit Parameters to Raw CLS Data for Large and Intermediate Reverse

Micelles. a0 – drop from 1; ai – amplitude; ti – time constant; y0 - offset

w0 a0 a1 t1 (ps) a2 t2 (ps) y0

7.5 0.30 0.14 1.1 0.47 6.4 0.09

12 0.28 0.57 2.5 - - 0.15

16.5 0.37 0.34 2.1 - - 0.29 Error bars are ±0.02 for a0, ai and y0; ± 0.2 for t1; ± 1 for t2.

Figure 8.8 Representative center line data for the back-calculation of the interfacial CLS. Shown

here are results for AOT w0=12 at Tw = 0.2 ps. The blue dots are bulk water center line data, and the

black circles are the experimentally measured center line data for AOT w0=12 at Tw = 0.2 ps. The green

dots are the back-calculated interfacial center line data using Equation 8.12. The red line is a

reconstruction of the calculated interfacial data with the bulk water data to reproduce the experimental

data.

2530 2540 2550 2560 2570 2580 2590

2520

2540

2560

2580

2600 bulk water

AOT w0=12 (experimental)

interface (back-calculated)

reconstructed AOT w0=12

ωτ (cm-1)

ωm

(cm

-1)

200

Figure 8.8 shows the results of Equation 8.12 when applied to AOT w0 = 12 at

Tw = 0.2 ps. The black circles are the actual measured experimental center line data

for the AOT w0 = 12 reverse micelle. The blue dots are the center line data for bulk

water, which was obtained separately. The bulk water CLS was used to determine the

bulk water FFCF, which was then used to obtain the bulk water center line data for

longer times because experimental data can only be measured out to 2 ps due to

vibrational lifetime limitations.54

The green dots are the interfacial water center line

data found by applying Equation 8.12. The red line is a verification of the algorithm.

The calculated interfacial water center line data and the center line data for bulk water

are recombined with the fraction terms to make sure that the original combined center

line data is reproduced. Because Equation 8.12 is simple linear algebra, the agreement

is virtually quantitative.

Figure 8.9 Interfacial CLS data for AOT w0=16.5, 12, and 7.5. The lines through the data are the

calculated interfacial FFCFs.

Center line data for the interface, as displayed by Figure 8.8, were obtained for

AOT w0=16.5, 12, and 7.5 at all measured Tw’s. The interfacial CLS curves for these

three micelles are displayed in Figure 8.9. Overall, the interfacial CLS curves are very

similar for w0 = 12 and 16.5. The lack of a size dependence for the large reverse

micelles is consistent with a lack of size dependence for the interfacial orientational

relaxation and the vibrational lifetime.6,8

The w0 = 7.5 system is considerably smaller

in size, and its interfacial CLS seems to decay slightly slower than the larger reverse

0 1 2 3 4 5 6 7 8 9 10 11 120.0

0.2

0.4

0.6

0.8

1.0

AOT w0= 7.5 interface

AOT w0=12 interface

AOT w0=16.5 interface

Tw (ps)

CL

S

201

micelles. It should be noted that the bulk water center line data were used in the w0 =

7.5 calculation, even though our experiments suggest that the core is not exactly like

bulk water. We cannot measure the core of the w0 = 7.5 reverse micelle directly, so

bulk water is the best approximation for use in the calculation.

The interfacial CLS curves fit well to a single exponential decay plus an offset.

The FFCFs for w0 = 16.5, 12, and 7.5 were calculated by simultaneously fitting the

CLS curve and the w0 = 2 spectrum for each sample. Table 8.5 summarizes the FFCF

parameters for the large reverse micelles and w0=7.5. As suggested by examination of

the CLS curves, w0 = 12 and 16.5 yield very similar FFCF parameters. This similarity

indicates that, like the rotational and population relaxation dynamics,6,8

spectral

diffusion at the interface in large reverse micelles is independent of size. For large

reverse micelles there is a core of bulk-like water, and the curvature of the interface is

mild. The solvation of the head groups is independent of size.6,8,9

The result is that

the local water-interface interactions and dynamics do not change with size for

sufficiently large reverse micelles.

The exponential decay portion of the FFCF for w0 = 12 and 16.5 is ~1.6 ps,

which is within experimental error very similar to the FFCF long time constant of bulk

water, 1.7 ps. The 1.7 ps time constant in bulk water is attributed to global hydrogen

bond rearrangement.43,44

In the analysis of the orientational relaxation, lifetimes, and

spectra of interfacial water in large AOT reverse micelles, it was shown that the

interfacial layer is approximately one water molecule thick.6,8

The orientational

relaxation time at the interface is slow, ~20 ps. This result suggests that exchange of

water between the interfacial region and the bulk-like core occurs on this time scale or

slower. Therefore, on a time scale of 1.6 ps, there is a fixed ensemble of interfacial

water molecules that are bound to the sulfonate head groups but also interacting with

water molecules that are beyond the interfacial layer.

Table 8.5 Interfacial FFCF Parameters for Large and Intermediate Reverse Micelles.

w0 Γ (cm-1

) Δ1 (cm-1

) τ1 (ps) ΔS (cm-1

)

7.5 57 44 3.5 24

12 35 55 1.9 21

16.5 28 50 1.3 29 Error bars are ±5 for Γ and Δ’s; ± 0.5 for τ1.

202

Water molecules at the interface are hydrogen bonded to water molecules

beyond the interfacial layer, and the frequency of the interfacial water molecules will

be influenced by the dynamics of this more bulk-like water. Non-interfacial water

molecules will be making and breaking hydrogen bonds with the interfacial water

molecules as well as with other core water molecules. It is possible that the ~1.6 ps

component of the interfacial water FFCF is produced by the hydrogen bond

rearrangement of non-interfacial water molecules that are making and breaking

hydrogen bonds with the interfacial water molecules. This proposition, if correct,

indicates that water molecules immediately beyond the interfacial layer behave very

much like bulk water. Although these water molecules would have hydrogen bonds to

interfacial water molecules, they are also interacting with a large collection of

basically bulk-like core water molecules. Again, it is important to point out that

assigning the fast component of the interfacial FFCF to the hydrogen bond dynamics

of non-interfacial water molecules is a conjecture based on the similarity of the

observed interfacial spectral diffusion dynamical time scale and the known time scale

for bulk water hydrogen bond randomization.

In contrast to bulk water, the interfacial FFCF has an offset (ΔS in Table 8.5).

The offset is produced by dynamics that are too slow to measure because they are

outside the experimental time window that is set by the vibrational lifetime. It is not

surprising that the interfacial water has very slow dynamics. Complete spectral

diffusion within the interfacial inhomogeneous line requires sampling all of the

frequencies (see Figure 8.2b). As shown in Table 8.2, the vibrational lifetime of the

w0 = 2 reverse micelle becomes longer at the very blue side of the absorption line.

This shows that the interface is not a single environment. All environments must be

sampled for spectral diffusion to be complete. As mentioned above, the interfacial

orientational relaxation time for large reverse micelles is ~20 ps. Orientational

relaxation will require breaking a hydrogen bond to the interface (sulfonate head

group). Therefore, it is reasonable to conclude that the time required for a water

molecule to sample the range of interfacial environments will be quite slow.

For spectral diffusion to be truly complete, all frequencies must be sampled,

including both the interfacial frequencies and the core frequencies. Thus, there must

203

be exchange between the interfacial and core populations. Molecules at the interface

will have to move away from the interface and become core molecules, and core water

molecules will have to move toward the head groups and become interfacial water

molecules. Again, given the ~20 ps interfacial orientational relaxation time, the time

scale for interfacial-core exchange should be slow.

The exponential decay of the w0 = 7.5 FFCF has a time constant of ~3.5 ps,

which is significantly slower than that observed for the large reverse micelles. w0 =

7.5 is an intermediate size with a core that is well separated from the interface, but the

core does not have bulk-like water properties. Coupling of the slow dynamics at the

interface to water throughout the small nanopool slows the vibrational and

orientational relaxation at both the interface and in the core (see Table 8.1). The 3.5

ps component of the w0 = 7.5 FFCF may reflect hydrogen bond rearrangement of core

water molecules that are bonded to interfacial water molecules. The slowing of this

component of the FFCF would be in accord with the slowing of the core water

structural dynamics as evidenced by the slower orientational relaxation time.

8.3.3 Spectral Diffusion in Igepal Reverse Micelles

2D IR spectra were also measured for Igepal w0 = 12, a reverse micelle with

the same water pool diameter as AOT w0 = 16.5. Because of lifetime limitations, data

for AOT w0 = 16.5 can be taken out to about 5 ps, but the echo signal for Igepal w0 =

12 is not reliable past 2 ps. Given the limited experimental time window for Igepal, it

was impractical to apply Equation 8.12 and obtain an interfacial CLS. Instead, the

AOT w0 = 16.5 and Igepal w0 = 12 systems were analyzed with the CLS method in the

traditional manner as if there were a single ensemble. The CLS was obtained around

the 2D IR maxima for each Tw. Figure 8.10 displays these CLS curves. For the

limited range of Tw’s that could be measured, the CLS for the two samples are almost

identical. Given the small experimental time window, our limited results suggest that,

at least at early times, spectral diffusion is not too sensitive to the chemical nature of

the interface. This result is consistent with the similarity found for the interfacial

orientational relaxation times of water in AOT and Igepal reverse micelles.17

204

Figure 8.10 CLS data for Igepal w0=12 (blue squares) and AOT w0=16.5 (red circles), showing

close agreement between the samples. The CLS data presented in this figure have not been analyzed

with the modified two component CLS model.

8.3.4 Spectral Diffusion in Small Reverse Micelles

To quantify the changes in the 2D spectra, and to extract the FFCF, the CLS

was calculated for a ±30 cm-1

range around the 2D IR maximum location for w0 = 2, 4,

and 7.5. The CLS curves for these three AOT reverse micelles are shown in Figure

8.11. Orientational relaxation measurements for the w0 = 2 and 4 reverse micelles

show that the structural dynamics behave essentially as a single ensemble. In the

previous sections, we treated w0 = 7.5 approximately using the core-interface

decomposition approach for the 2D IR spectral diffusion dynamics. Here w0 = 7.5 was

treated in the same manner as w0 = 2 and 4 for comparison. The experimental Tw

range is limited by the vibrational lifetimes of each sample. Thus, data cannot be

taken at the same Tw values for each sample (see Figure 8.11).

The general trend of the CLS data is that spectral diffusion slows down as the

water pool size decreases. The CLS curves, in conjunction with the IR spectra of the

samples, can be used to extract the FFCF parameters.39,40

The FFCF parameters

determined for reverse micelles w0 = 2, 4, and 7.5 are listed in Table 8.6. The FFCF

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

Igepal w0=12

AOT w0=16.5

Tw (ps)

CL

S

205

for a small reverse micelle takes the form of a biexponential decay with a static offset

(ΔS) and a motionally narrowed (homogeneous) component. All three FFCFs have a

fast time constant of ~1 ps, and a slower time constant of ~6-10 ps. Bulk water has a

fast time constant of ~400 fs, which is attributed to very fast local hydrogen bond

fluctuations.27,28

Given the similarity in time scales and that the small reverse micelles

represent very constrained environments, it is reasonable to conclude that the ~1 ps

time scale is also due to local hydrogen bond fluctuations.

Figure 8.11 CLS data for small reverse micelles: AOT w0=2, 4, and 7.5. The lines through the data

are the calculated FFCFs. As reverse micelle size decreases, spectral diffusion slows down.

It is useful to note that neither treatment of the w0 = 7.5 reverse micelle is truly

correct. In this section, w0 = 7.5 is treated as a single ensemble in the same way as w0

= 2 and 4. However, in contrast to w0 = 2 and 4 for which the orientational relaxation

does not separate into interfacial and core components, w0 = 7.5 does separate into two

components. In the previous section, the CLS data were decomposed to obtain the

interfacial component. The two component CLS procedure requires that the spectral

diffusion is known for the core. Bulk water was used to model the core, but the

orientational relaxation data show that the core is not bulk-like in AOT w0 = 7.5.

Therefore, there are uncertainties associated with each model for AOT w0 = 7.5.

0 2 4 6 8 10 12 14 16 18 200.0

0.2

0.4

0.6

0.8

1.0

AOT w0=2

AOT w0=4

AOT w0=7.5

Tw (ps)

CL

S

206

Table 8.6 FFCF Parameters for Small and Intermediate Reverse Micelles.

w0 Γ (cm-1

) Δ1 (cm-1

) τ1 (ps) Δ2 (cm-1

) τ2 (ps) ΔS (cm-1

)

2 33 ± 5 19 ± 2 0.9 ± 0.1 36 ± 1 10 ± 1 37 ± 1

4 33 ± 5 21 ± 2 0.7 ± 0.4 44 ± 5 8.9 ± 3 26 ± 1

7.5 57 ± 2 25 ± 2 1.1 ± 0.2 47 ± 3 6.4 ± 1 20 ± 2

The static offset in the FFCF (not present in bulk water) arises from the

extremely slow motions of the water molecules in the small reverse micelles. For

spectral diffusion to be complete in any system, all water molecules must experience

all environments. Diffusion through the reverse micelles or exchange of populations

between an OD hydroxyl bound to the interface and one bound to another water

oxygen will occur very slowly in the highly confined environments of the smallest

reverse micelles. It is likely that slow diffusion and exchange contribute to the static

offset.

The slowest time scale for bulk water spectral diffusion is 1.7 ps,

corresponding to global hydrogen bond reorganization.26

It is possible that the

intermediate time scale decay of the FFCF, 6-10 ps, is caused by hydrogen bond

rearrangement of water molecules bound to the waters directly at the interface with

ones that have at least one or possibly both hydroxyls not bound to the interface. For

the large reverse micelles, this mechanism was proposed because of the similarity of

times for the interfacial and bulk water spectral diffusion. For the small reverse

micelles the dynamics will be slower and as the water nanopool becomes smaller, the

dynamics will become increasingly slow. Another possibility that was suggested

previously (Chapter 6) is that interfacial topography roughness contributes to the

inhomogeneous broadening and, by extension, motions of the surfactant head groups

will cause spectral diffusion.24

In addition to the time constants, the FFCF also contains frequency fluctuation

amplitudes (Δ terms) and a motionally narrowed component. Each time scale,

including the static offset, produces a significant amount of inhomogeneous

broadening. The motionally narrowed component (Γ) is roughly the same for w0 = 2

and 4, but is significantly greater for w0 = 7.5. Again, it needs to be noted that w0 =

7.5 is not strictly a small reverse micelle.

207


Spectral diffusion was measured for water inside of a range of AOT reverse

micelles from w0=16.5 (5.8 nm diameter) through w0=2 (1.7 nm diameter) using 2D IR

vibrational echo spectroscopy. We observe that the process of spectral diffusion,

described by the FFCF, undergoes significant changes as the water pool size inside the

reverse micelles increases. The 2D IR spectra for large reverse micelles (w0 = 12 and

16.5) are a combination of signals from a bulk water core and a shell of interfacial

waters at the surfactant the head groups. Each of these ensembles has its own FFCF.

Because the FFCF for bulk water is known, the FFCF for the interfacial region can be

calculated from known data and other experimentally measured parameters. It is

important to note that a CLS curve calculated on the actual experimental 2D spectra

does not yield a weighted average of the FFCF and that in order for meaningful

information to be obtained, the CLS for large reverse micelles must be decomposed

into bulk and interfacial contributions.

The similarity between the FFCFs for AOT w0 = 12 and 16.5 further

corroborates previous conclusions that the dynamics at the interface are virtually the

same for all AOT large reverse micelles.6,8,9

For the large reverse micelles, a

component of the interfacial spectral diffusion is very similar to that of bulk water,

which corresponds to hydrogen bond network randomization. It was postulated that

the ~1.6 ps component of the interfacial spectral diffusion is associated with hydrogen

bond rearrangement of core water molecules that are interacting with the interfacial

water molecules. Spectral diffusion was also compared for large Igepal and AOT

reverse micelles of diameter 5.8 nm (Igepal w0 = 12 and AOT w0 = 16.5). The results

suggest that dynamics that give rise to spectral diffusion are not affected much by the

chemical nature of the interface. This was found to be true for orientational relaxation

as well.17

The interfacial dynamic processes in large reverse micelles are mainly

determined by the presence of an interface rather than its chemical nature.

The w0 = 7.5 system was also treated as a large reverse micelle because based

on orientational relaxation experiments, the w0 = 7.5 water pool can be divided into

core and interfacial regions. However, the core region is not the same as bulk water.

208

The actual core region for w0 = 7.5 cannot be measured separately, so bulk water was

used as an approximation in the decomposition of the spectral diffusion dynamics to

obtain the interfacial FFCF. It is found that the interfacial FFCF for w0 = 7.5 is slower

than the interfacial FFCFs for w0 = 12 and 16.5, which are about the same. We have

presented two sets of FFCF results for AOT w0=7.5, treating it both as a large and a

small reverse micelle. Neither is precisely correct, but the results permit comparisons

to the larger and smaller reverse micelles.

In small reverse micelles (w0 = 2 and 4), the FFCF takes the form of a

biexponential decay plus an offset and a homogeneous component. A fast decay of ~1

ps is attributed to local hydrogen bond fluctuations (present in bulk water), but the

slower ~6-10 ps decay represents processes that are not present in bulk water, such as

surface topography fluctuations of the interface or slow hydrogen bond rearrangement

of water molecules bound to interfacial water molecules. The static offset also has no

analog in bulk water and is associated with very slow processes such as diffusion to

the interface and exchange between hydroxyl bound to the interface and ones that are

not.

Molecular dynamics (MD) simulations have been used to study the

orientational relaxation of water in AOT reverse micelles.31,32,55

In light of the new

extended two component CLS method, it would be very interesting to explore the

spectral diffusion dynamics of interfacial water molecules in large reverse micelles

using MD simulations.

8.5 References




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(4) Laage, D.; Stirnemann, G.; Hynes, J. T. J. Phys. Chem. B 2009, 113, 2428.


2009, 131, 5530.

(6) Moilanen, D. E.; Fenn, E. E.; Wong, D.; Fayer, M. D. J. Chem. Phys 2009,

131, 014704.


Natl. Acad. Sci. USA 2009, 106, 375.

209


113, 8560.


131, 8318.


Phys. Chem. A 2006, 110, 4985.







103, 15355.

(15) Piletic, I.; Tan, H.-S.; Moilanen, D. E.; Spry, D. B.; Fayer, M. D. In

Femtochemistry VII: Fundamental Ultrafast Processes in Chemistry, Physics,

and Biology; Castleman, A. W., Kimble, M. L., Eds.; Elsevier: Amsterdam,

2006, p 195.


(17) Fenn, E. E.; Wong, D. B.; Fayer, M. D. Proc. Natl. Acad. Sci. USA 2009, 106,

15243.


2007, 129, 14311.


(20) Tan, H.-S.; Piletic, I. R.; Fayer, M. D. J. Op. Soc. Am. B: Optical Physics

2005, 22, 2009.




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(29) Izquierdo, C.; Moya, M. L.; Usero, J. L.; Casado, J. Monatsh. Chem. 1992,

123, 383


Lett. 2005, 94, 057405.

(31) Pieniazek, P. A.; Lin, Y.-S.; Chowdhary, J.; Ladanyi, B. M.; Skinner, J. L. J.

Phys. Chem. B. 2009, 113, 15017.

(32) Abel, S.; Sterpone, F.; Bandyopadhyay, S.; Marchi, M. J. Phys. Chem. B 2004,

108, 19458.

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(33) Freda, M.; Onori, G.; Paciaroni, A.; Santucci, A. Chem. Phys. Lett. 2001, 348,

311.

(34) Lipgens, S.; Schubel, D.; Schlicht, L.; Spilgies, J.-H.; Ilgenfritz, G.; Eastoe, J.;

Heenan, R. K. Langmuir 1998, 14, 1041.






124503.

(40) Kwak, K.; Rosenfeld, D. E.; Fayer, M. D. J. Chem. Phys. 2008, 128, 204505.


044513(13).










108, 10957.

(48) Woutersen, S.; Emmerichs, U.; Bakker, H. J. J. Chem. Phys. 1997, 107, 1483.

(49) Gaffney, K.; Piletic, I. R.; Fayer, M. D. J. Phys. Chem. A 2002, 106, 9428.

(50) Gaffney, K. J.; Davis, P. H.; Piletic, I. R.; Levinger, N. E.; Fayer, M. D. J.

Phys. Chem. A 2002, 106, 12012.

(51) Loparo, J. J.; Fecko, C. J.; Eaves, J. D.; Roberts, S. T.; Tokmakoff, A. Phys.

Rev. B 2004, 70, 180201.



(54) Fenn, E. E.; Fayer, M. D. J. Chem. Phys. 2011, 135, 074502.

(55) Faeder, J.; Ladanyi, B. M. J. Phys. Chem. B 2000, 104, 1033.

211

Appendix A Derivation of the Homogeneous

and Inhomogeneous Components of the Line

Shape Function

A.1 Homogeneous Component

Recall that the line shape function, g1, is given by

2

1 2 1 10 10

0 0

( ) ( ) (0) ,

t

g t d d t

(A.1)

where

/2

1 10 10

2

( )( ) ( ) (0) .it

i

i

tC t t e

T

(A.2)

C1(t) is known as the frequency-frequency correlation function (FFCF). T2 is the

dephasing time (which includes orientation and vibrational lifetime effects), the Δi’s

are the frequency fluctuation amplitudes, and the τi’s are their associated time

constants. The motional narrowed (homogeneous component) is the first term of the

Equation A.2 involving the delta function. The pure dephasing time, T2* may be used

instead of T2 if one does not need to include orientation and vibrational lifetime

effects. Substituting the first term of Equation A.2 into Equation A.1 and performing

the integration will give us the pure homogeneous contribution to the line shape

function,

2

21 2 2

2 2 2 20 0 0 0

( ) 1( ) .

tt tt t

g t d dt dT T T T

(A.3)

The integration in equation A.3 uses the delta function integration,

0 0( ) ( ) ( ).dtf t t t f t (A.4)

212

A.2 Intermediate Components

To calculate the intermediate contribution to the line shape (when the FFCF

components fall between the homogeneous limit of Δτ < 1 and the inhomogeneous

limit of Δτ >> 1), the second term of Equation A.2 is integrated. To simplify the

derivation, i = 1,

22

1 1

2 1 2 1

1

1

/ /2 2

1 2 1 1 2 1

0 0 0 0

/ /2 2 2

1 2 1 1 1 1 1 20

0

/2 2 2

1 1 1 1

/2 2

1 1

1

( )

1 .

t t

t t

tt

t

t

g t d dt e d e

d e e

e t

te

(A.5)

As shown above, each intermediate component makes a contribution of

/2 2 1it

i i

i

te

to the line shape function.

A.3 Inhomogeneous Component

The FFCF containing all time scales of components will have the following

form

/2 2

1 10 10

2

( )( ) ( ) (0) ,it

i s

i

tC t t e

T

(A.6)

where the last term corresponds to a pure inhomogeneous, or static, component. To

get the proper contribution of the static component to the line shape, it is necessary to

Taylor expand to second order the exponential term in the last line of Equation A.5,

2 2 2 2 2 2

2 2

2 21 1 .

2 2 2

t t t t t

(A.7)

Note that the subscripts on the amplitude and time constant have been dropped for

generality. Equation A.7 shows that a static component contributes 2 2 / 2st to the line

shape function.

213

Appendix B Derivation of the Anisotropy for a

Two Component System

B.1 Anisotropy for a Single Component System

For a system consisting of one ensemble, the parallel and perpendicular signals

obtained from polarization-selective pump-probe spectroscopy (see Chapters 2 and 3)

are given by

2( ) ( )(1 0.8 ( )),I t P t C t (B.1)

2( ) ( )(1 0.4 ( )),I t P t C t (B.2)

where P(t) is the population relaxation and C2(t) is the second Legendre polynomial

orientational correlation function for a dipole transition. In the case of a single

ensemble, both P(t) and C2(t) follow single exponential decays, each with a

characteristic decay constant. Pure population relaxation is obtained from

3 ( ) ( ) 2 ( ).P t I t I t (B.3)

Computation of Equation B.3 eliminates all contributions from the orientational

correlation function, C2(t). The pure orientational correlation function is obtained via

the anisotropy,

( ) ( )

( ) ,( ) 2 ( )

I t I tr t

I t I t

(B.4)

where the denominator is the pure population relaxation (B.3). Written explicitly, we

see that dividing by Equation B.3 eliminates any contributions from population

relaxation to the anisotropy,

2 2

2 2

22

( )(1 0.8 ( )) ( )(1 0.4 ( ))( )

( )(1 0.8 ( )) 2 ( )(1 0.4 ( ))

1.2 ( ) ( )0.4 ( ).

3 ( )

P t C t P t C tr t

P t C t P t C t

P t C tC t

P t

(B.5)

Equation B.5 shows that for a single ensemble, calculating the anisotropy yields the

pure orientational correlation function.

214

B.2 Anisotropy for a Two Component System

For a system of two components, the parallel and perpendicular signals consist

separate contributions from each vibrating ensemble,

1 2

1 1 2 2 2 2( ) ( )(1 0.8 ( )) ( )(1 0.8 ( )),I t f P t C t f P t C t (B.6)

1 2

1 1 2 2 2 2( ) ( )(1 0.4 ( )) ( )(1 0.4 ( )),I t f P t C t f P t C t (B.7)

where P1(t) and P2(t) are the population relaxation decays for components 1 and 2,

respectively, and f1 and f2 are their respective fractional populations. 1

2 ( )C t and 2

2 ( )C t

are the orientational correlation functions for components 1 and 2, respectively. The

numerator of the anisotropy (Equation B.4) is given by

1 1

1 1 2 1 2

2 2

2 2 2 2 2

1 2

1 1 2 2 2 2

( ) ( ) ( )(1 0.8 ( )) ( )(1 0.4 ( ))

( )(1 0.8 ( )) ( )(1 0.4 ( ))

1.2( ( ) ( ) ( ) ( )).

I t I t f P t C t P t C t

f P t C t P t C t

f P t C t f P t C t

(B.8)

The denominator of the anisotropy is given by

1 1

1 1 2 1 1 2

2 2

2 2 2 2 2 2

1 1 2 2

( ) 2 ( ) ( )(1 0.8 ( )) 2 ( )(1 0.4 ( ))

( )(1 0.8 ( )) 2 ( )(1 0.4 ( ))

3( ( ) ( )).

I t I t f P t C t f P t C t

f P t C t f P t C t

f P t f P t

(B.9)

Putting the results of Equations B.8 and B.9 together, the two-component anisotropy

becomes

1 21 21 1

1 21 1

1 2

1 1 2 2 2 2

1 1 2 2

1 2

1 1 2 2 2 2

1 1 2 2

/ // /

1 2

/ /

1 2

1.2( ( ) ( ) ( ) ( ))( )

3( ( ) ( ))

( ) ( ) ( ) ( )0.4

( ) ( )

0.4 ,or ort tt T t T

t T t T

f P t C t f P t C tr t

f P t f P t

f P t C t f P t C t

f P t f P t

f e e f e e

f e f e

(B.10)

where the population relaxation terms and the orientational correlation functions have

been replaced with exponential decay terms. The time constants 1

1T and 2

1T are the

vibrational lifetimes of components 1 and 2, respectively. The 1or and 2or

parameters describe the orientational relaxation decay for components 1 and 2

respectively. Of particular note is that unlike in Equation B.5, the pure population

215

relaxation does not divide out in Equation B.10. For a two component system, the

anisotropy depends not only on the orientational correlation functions for each

component, but also the vibrational lifetimes for both components. The two

component model can be easily extended to systems with more than two components,

such as the Igepal system in Chapter 5. It should be noted that the addition of more

components can lead to more difficult and ambiguous analysis unless most of the

parameters can be fixed (see Chapter 5 for more details).

217

Appendix C Details for 2D IR Background

Subtraction

C. 1 Experimental Procedures

If 2D IR vibrational echo data produce beat signals as described in Chapter 6,

then 2D IR background subtraction may be required. To make the data analysis

procedure of background subtraction (also known as beat subtraction) as reliable as

possible, it is important that several experimental requirements are met. Two separate

echo experiments are required: one with the resonant sample and one with the

nonresonant sample. Both samples should have the same path length. The same

monochromator blocks, Tw’s, and τ scanning periods should be used. In the resonant

experiment, the nonresonant sample may be used for chirp correction and 1-2 re-

timing (unless severe distortions are present in the three pulse cross-correlation). In

the nonresonant experiment, the nonresonant sample itself can be used for 1-2 and 3-

LO retiming by just unplugging the BNC cable that links the relay circuit to the

solenoid valve that controls the pneumatic stage. That way, the nonresonant sample

remains in place during the 1-2 retiming process. Alternatively, a second, identical

nonresonant sample can be made and used normally in the nonresonant sample

position on the pneumatic stage. To set the focal depth, the resonant sample can be

used for both experiments. In the nonresonant experiment, the resonant sample will be

removed after setting the focal depth and then replaced with the nonresonant sample.

The experimentalist should also gauge whether the laser can remain stable over

the course of about two days. Each echo experiment can last up to 24 hours, and it is

important that the laser conditions (pulse duration, chirp, stability, and spectrum)

remain as identical as possible between experiments. As soon as the first echo

experiment finishes, immediately set up the second. Run the phasing pump-probe

experiment on the resonant sample after both echo experiments have completed.

218

C.2 MATLAB Routines

After both the resonant and nonresonant echo experiments have finished. The

interferograms must be pre-processed using the PhasingNormal1.2 program

(main). Specifically, a variant called PhasingNormal1.2_save_intfgrms1

must be used. This variant saves the averaged, base-lined, raw interferogram data

which are used for beat subtraction. These saved interferograms will not have been

smoothed or resampled. This does not matter because these procedures will be done

later on the beat subtracted interferograms. The original PhasingNormal1.2

program will not save the interferograms, so make sure to use the correct version. Be

sure to save the data.

Next, run the program beat_subtraction.m.2 This program requires the

names of the folders where the averaged data for both experiments is saved in addition

to a user-specified time region over which to perform fitting. This region should be a

well-defined beat region which, if beats were not present, should be equal to zero.

When the program is run, there will be prompts to select the averaged files for both

experiments as well as a pret0 and postt0 file for each. It does not matter which of

these pre- and postt0 files are chosen. They are required only to get the proper time

axes. The program will amplitude adjust and time-shift the nonresonant

interferograms such that when subtracted from the resonant interferograms, the

selected beat region will be zero. When the routine has finished, the program will

prompt the user to select a folder to save the output file. The quality of the beat

subtraction procedure may be visualized with the program graph_intfgrm.3

Once the beat subtraction program has run and the beat subtracted

interferograms saved, it is necessary to run another modified PhasingNormal1.2

program called PhasingNormal1.2_save_intfgrms_beatsub. 4 To use

this program, load in the original Mfile from the resonant echo experiment. This

Mfile is just used as a placeholder for things to come. Then, click ‘Avg Overlap Pix.’

If you want to change the resolution or do smoothing, make sure to enter in the desired

parameters before clicking this button. At the prompt, enter in the beat subtracted file

generated by beat_subtraction.m. At this point, the beat subtracted

219

interferograms will be processed normally and converted to 2D correlation plots which

can be phased with the pump-probe spectrum of the resonant sample.

C.3 Notes

The notes below are the folders in the author’s computer in which the

programs described above may be found.

(1)

C:\Fayer Group\Programs

(2)

C:\FayerGroup\Programs\echo_baseline_test\MatlabfromDavid\Phasing

Normal

(3)

C:\Fayer Group\Programs\echo_baseline_test\MatlabfromDavid \Phasing

Normal

(4)

C:\Fayer Group\Programs

NEW METHODS FOR EXTRACTING ULTRAFAST WATER …core and an interfacial water shell. Each region has...

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Transcript of NEW METHODS FOR EXTRACTING ULTRAFAST WATER …core and an interfacial water shell. Each region has...