USING RAMAN SPECTROSCOPY TO PROBE THE INTERNAL STRUCTURE AND

EXCITONIC PROPERTIES OF LIGHT-HARVESTING AGGREGATES OF

TETRA(SULFONATOPHENYL)PORPHYRIN

By

CHRISTOPHER CHARLES RICH

A dissertation submitted in partial fulfillment of

the requirements for the degree of

DOCTOR OF PHILOSOPHY IN CHEMISTRY

WASHINGTON STATE UNIVERSITY

Department of Chemistry

MAY 2013

© Copyright by CHRISTOPHER CHARLES RICH, 2013

All Rights Reserved

© Copyright by CHRISTOPHER CHARLES RICH, 2013

All Rights Reserved

ii

To the Faculty of Washington State University:

The members of the Committee appointed to examine the dissertation/thesis of

CHRISTOPHER CHARLES RICH find it satisfactory and recommend that it be

accepted.

______________________________

Jeanne McHale, Ph.D., Chair

______________________________

Kirk Peterson, Ph.D.

______________________________

James Brozik, Ph.D.

______________________________

Helmut Kirchhoff, Ph.D.

iii

ACKNOWLEDGMENT

I would like to extend my deepest gratitude my advisor, Jeanne McHale, for her

guidance and support throughout my graduate career. I consider myself fortunate to have

had you as a mentor and it has been a privilege to have worked in your group. I would

also like to thank my committee members Kirk Peterson, James Brozik, and Helmut

Kirchhoff for their support, advice, and commitment.

To all of the faculty, staff, and professors in Fulmer Hall, I thank you all for your

guidance, assistance, and kindness that you have shown me throughout my graduate

career. To my fiancé, Amy, and my family in New England, to whom this thesis is

dedicated, thank you for all of your constant support and love – even from long distances

it means a lot to me that I always have a home with you. And lastly thank you to all of

my peers and friends that I have made in Pullman: through all the ups, downs, and

frustrating times, you have made my time here enjoyable. Thank you!

iv

USING RAMAN SPECTROSCOPY TO PROBE THE INTERNAL STRUCTURE AND

EXCITONIC PROPERTIES OF LIGHT-HARVESTING AGGREGATES OF

TETRA(SULFONATOPHENYL)PORPHYRIN

Abstract

by Christopher Charles Rich, Ph.D.

Washington State University

May 2013

Chair: Jeanne L. McHale

Borrowing ideas from light-harvesting aggregates in nature for use in

photovoltaics or solar fuels to improve light collection and solar energy efficiency is an

attractive prospect. However an incomplete understanding of the aggregate internal

structure and its relation to excitonic states hinders the progress in this field. In this work,

aggregates of a synthetic porphyrin called tetra(sulfonatophenyl)porphyrin (TSPP) are

used as a model system to probe this correlation using resonance Raman spectroscopy.

The hypothesized structure for these nanotubular aggregates is that of a hierarchical

assembly composed of circular aggregates of TSPP which are held together by

electrostatic forces. The formation of the observed nanotube structure then derives from

water-mediated hydrogen bonding. Ensemble, condensed phase resonance Raman

spectroscopy, single aggregate resonance Raman spectroscopy/microscopy, and surface-

enhanced resonance Raman spectroscopy (SERRS) prove to be powerful tools for testing

this proposed model of the aggregate structure and understanding its excitonic properties.

Analysis of Raman intensities and polarized Raman spectra, as well as models for the

v

electronic absorption spectra of these assemblies, provide intriguing insights on the

nature of the excitonic states and the influence of the local environment on the effective

coherence of the aggregate.

vi

TABLE OF CONTENTS

Page

ACKNOWLEDGMENT.................................................................................................... iii

ABSTRACT ....................................................................................................................... iv

LIST OF TABLES ............................................................................................................ vii

LIST OF FIGURES ........................................................................................................... ix

CHAPTERS

1 Introduction ............................................................................................................. 1

2 Influence of Hydrogen-Bonding on Excitonic Coupling and Hierarchical Structure

of a Light-Harvesting Porphyrin Aggregate ......................................................... 28

3 Resonance Raman Spectra of Individual Excitonically Coupled Chromophore

Aggregates ............................................................................................................ 73

4 Spectroscopic Behavior of Light Harvesting Molecular Aggregates in

Nonaqueous Solvents .......................................................................................... 107

5 Surface Enhanced Spectroscopy of Light Harvesting Porphyrin Aggregates .... 125

6 Electronic Absorption Spectrum and Raman Excitation Profiles of TSPP

Aggregates .......................................................................................................... 136

7 Summary, Conclusions, and Outlook ................................................................. 161

APPENDICES

A Experimental Details ........................................................................................... 171

B MATLAB Codes ................................................................................................. 184

vii

LIST OF TABLES

Table 2.1 Depolarization Ratios of Prominent Raman Modes of TSPP-h Aggregates at

Different Excitation Wavelengths. ........................................................................ 45

Table 2.2 Depolarization Ratio of Prominent Raman Modes of TSPP-d Aggregates at

Different Excitation Wavelengths. ........................................................................ 48

Table 2.3 Depolarization Ratios of Prominent Raman Modes of TSPP-h Aggregates

Excited at 514.5 nm and 496.5 nm. ...................................................................... 65

Table 2.4 Depolarization Ratios of Prominent Raman Modes of TSPP-d Aggregates

Excited at 514.5 nm and 496.5 nm. ..................................................................... 65

Table 3.1 Calibration of Internal External Standard Method with Acetonitrile (918 cm-1

mode) as the Sample and Cyclohexane (800 cm-1

mode) as the Standard with 488

nm wavelength excitation. .................................................................................... 77

Table 3.2 Measurement of Raman Cross Section of Sodium Perchlorate (932 cm-1

mode)

with Cyclohexane (800 cm-1

mode) as the Standard with 488 nm wavelength

excitation using k value determined from Acetonitrile measurement. ................. 78

Table 3.3 Absolute resonance Raman cross sections and corresponding depolarization

ratios () of prominent modes of TSPP aggregates excited with 488 nm and 514.5

nm excitation wavelength. .................................................................................... 84

Table 3.4 Absolute resonance Raman cross sections and corresponding depolarization

ratios () of prominent modes of TSPP diacid monomers excited with 454.5 nm

excitation wavelength. .......................................................................................... 85

viii

Table 4.1 Depolarization Ratio Values for the TSPP diacid monomer, TSPP aggregates

prepared from 0.75 M HCl in H2O, and TSPP aggregates prepared from DCM and

HCl vapor from resonance Raman data excited with 454.5 nm wavelength. ..... 122

Table 6.1 Absolute Resonance Raman Cross Sections (x 10-22

cm2/molecules) for TSPP-h

Aggregates with Excitation Wavelengths Spanning the J-band. ........................ 154

Table 6.2 Absolute Resonance Raman Cross Sections (x 10-22

cm2/molecules) for TSPP-d

Aggregates with Excitation Wavelengths Spanning the J-band ......................... 155

ix

LIST OF FIGURES

Figure 1.1 Diagram explaining transition dipole moment coupling V12 of neighboring

chromophores with both x- and y- polarized electronic transitions by the staircase

model....................................................................................................................... 3

Figure 1.2 Absorption spectra of the free base monomer, diacid monomer, and aggregate

forms of TSPP (left) and molecular diagram of TSPP for the free base and diacid

monomer (right). ..................................................................................................... 6

Figure 1.3 Ninety degree scattering geometry. ................................................................... 8

Figure 1.4 Generalized scattering geometry. ...................................................................... 9

Figure 1.5 Tapping mode atomic force microscopy images with cross-sectional data (left)

and a scanning tunneling microscopy image (right) of TSPP aggregates deposited

on Au(111) from Ref. 3. ....................................................................................... 16

Figure 1.6 Cartoon showing geometrical constraints of TSPP in circular N-mer

aggregates of radius R. Porphyrins are shown as bent line structures separated by

a distance s. ........................................................................................................... 17

Figure 1.7 Polarized and depolarized resonance Raman spectra of 50 M TSPP

aggregates in 0.75 M HCl excited with a 488 nm wavelength laser..................... 19

Figure 1.8 Electronic absorption spectra of different concentrations of TSPP in 0.75 M

HCl. ....................................................................................................................... 21

Figure 1.9 Proposed mechanism of TSPP aggregation from diacid monomer (a) to

circular N-mer (b) to helical nanotube (c) with the STM image of the nanotube on

Au(111) (d). .......................................................................................................... 23

x

Figure 2.1 Structure of the neutral zwitterion (H4TSPP) from the DFT calculation

reported in Ref. 11. Two of the four sulfonato groups are protonated in this

structure................................................................................................................. 30

Figure 2.2 Formation of a helical nanotube from the diacid of TSPP (a), which first

assembles into a cyclic 16-mer (b), then a helical nanotube, (c) where the 16-mers

are represented as strings of beads. The helical nanotube model captures the

structural features of the flattened nanotubes as imaged by STM, shown in (d).

The drawings in (b) and (d) are adapted with permission from Friesen, B. A.;

Nishida, K. A.; McHale, J. L.; Mazur, U. J. Phys. Chem. C 2009, 113, 1709-

1718.5 Copyright American Chemical Society 2009. ........................................... 32

Figure 2.3 10 m x 10 m AFM image of (a) TSPP-h and (b) TSPP-d aggregates on

mica, 1 m x 1 m AFM image of (c) TSPP-h and (d) TSPP-d aggregates on

mica, and corresponding nanotube cross section data for TSPP-h (e) and TSPP-d

(f) sampled at the white lines shown in the images c and d, respectively. ........... 38

Figure 2.4 Absorption spectra of 50 M TSPP aggregates prepared in 0.75 M HCl in H2O

(black) and in 0.75 M DCl in D2O (red). The inset shows the J-band on an

expanded scale. ..................................................................................................... 40

Figure 2.5 Polarized resonance Raman spectra of 50 M TSPP aggregates in 0.75 M HCl

and H2O (black) and in 0.75 M DCl and D2O (red) excited at 488 nm. The

prominent Raman modes are labeled in each spectrum and the spectrum of the

deuterated TSPP aggregates is offset by +3000 arbitrary intensity units. ............ 41

xi

Figure 2.6 Resonance Raman (RR) spectra of 50 M TSPP aggregates in 0.75 M HCl

excited at a) 488.0 nm, b) 476.5 nm, c) 472.7 nm, and d) 465.8 nm. The polarized

and depolarized spectra are shown in black and red respectively. ....................... 43

Figure 2.7 Resonance Raman spectra of 50 M TSPP aggregates in 0.75 M DCl in D2O

excited at a) 488 nm, b) 476.5 nm, c) 472.7 nm, and d) 465.8 nm. The polarized

and depolarized spectra are shown in black and red respectively. ....................... 48

Figure 2.8 Resonance Light Scattering spectra of 5 M TSPP aggregates prepared in 0.75

M HCl in H2O (black) and in 0.75 M DCl in D2O (red). RLS response is most

prominent at 491 nm for both protiated and deuterated aggregates...................... 49

Figure 2.9 Polarized (black) and depolarized (red) resonance light scattering (RLS)

spectra of 5 M TSPP aggregates in 0.75 M HCl in H2O (a) and in 0.75 M DCl in

D2O (b). The depolarization ratio as a function of wavelength is shown in blue. 50

Figure 2.10 a) Orthogonal Soret-band transition moments of the diacid monomer, b) in-

plane components of the transition moments μge,x lead to the degenerate J-band of

an individual cyclic N-mer, while c) transition moments polarized perpendicular

to the plane of the ring, μge,y lead to the N-mer H-band. d) Two-dimensional

hexagonal array of cyclic N-mers showing the alignment of the degenerate J-band

transition moments of the cyclic N-mer. The Z-axis depicted here becomes the

long axis of the nanotube when the sheet is rolled into a cylinder by overlapping

the origin and the tip of the vector C. ................................................................... 57

Figure 2.11. Absorbance spectra of 50 M TSPP diacid monomer in 0.001 M HCl in H2O

(black) and in 0.001 M DCl in D2O (red). Insets show the blue shift which occurs

upon deuteration for both the B- and Q-bands. ..................................................... 63

xii

Figure 2.12. Polarized resonance Raman spectra of 50 M TSPP diacid in 0.001 M HCl

in H2O (black) and 0.001 M DCl in D2O (red) excited at 444.7 nm. The D2TSPP2-

spectrum is offset by +20000. ............................................................................... 64

Figure 2.13 Polarized (black) and depolarized (red) resonance Raman spectra of TSPP-h

aggregates excited with (left) 496.5 nm (right) and 514.5 nm. ............................. 64

Figure 2.14 Polarized (black) and depolarized (red) resonance Raman spectra of TSPP-d

aggregates excited at (left) 496.5 nm and (right) 514.5 nm. ................................. 65

Figure 2.15 Polarized resonance Raman spectra of TSPP-h (black) and TSPP-d (red)

excited at 514.5 nm. The backgrounds were shifted to obtain overlap of the

intensities of the two low frequency modes. ......................................................... 66

Figure 2.16 Depolarization ratio dispersion graph for the seven prominent modes of the

TSPP-h aggregate resonance Raman spectrum. The six points for the six

excitation wavelengths implemented (465.8 nm, 472.7 nm, 476.5 nm, 488 nm,

496.5 nm, and 514.5 nm) are connected by a polynomial spline fit. .................... 67

Figure 2.17 As for Figure 2.16, but for the TSPP-d aggregate. ........................................ 68

Figure 3.1 Schematic of confocal “internal/external” standard method for measuring

absolute Raman cross sections. ............................................................................. 78

Figure 3.2 Schematic of the Raman microscopy set up, specifically for polarized Raman

experiments. .......................................................................................................... 79

Figure 3.3 Resonance Raman spectrum of aggregates prepared from 50 M TSPP in 0.75

M HCl with cyclohexane as the intensity standard excited with 488 nm

wavelength light (black) and 514.5 nm wavelength light (red). The inset shows

the resonance Raman spectrum of 50 M TSPP diacid monomer in 0.001 M HCl

xiii

with acetonitrile as the intensity standard excited with 454.5 nm excitation

wavelength (blue). The spectra have been background subtracted and asterisks

mark solvent Raman bands. .................................................................................. 83

Figure 3.4 Absorption spectra of the 50 M TSPP diacid monomer in 0.001 M HCl

(black) and the aggregate prepared from 50 M TSPP in 0.75 M HCl (red). (Inset)

3D model of a fully protonated TSPP diacid molecule. ....................................... 84

Figure 3.5 Single TSPP aggregate resonance Raman spectra obtained from 10 different

aggregates (left) and a false color epi-illuminated microscopy image of an

aggregate excited with 488 nm light (top right). In the bottom-right is a false color

optical microscope image of an individual TSPP aggregate. The bright spot in this

image is the excitation laser spot. ......................................................................... 87

Figure 3.6 (a) Single-aggregate resonance Raman intensities of 243 cm-1

(black), 316 cm-

1 (red), and 1534 cm

-1 (blue) modes measured at different aggregates; (b) data in

(a) normalized to the intensity of the corresponding peaks in Sample 9; (c)

intensity ratios of the three Raman modes. The sample numbers correspond to the

numbered spectra in Figure 3.5. The green lines in 3.6b address the approximate

integer variance in the Raman peak intensity of the 316 cm-1

mode between

samples. ................................................................................................................. 89

Figure 3.7 The resonance light scattering image of a TSPP aggregate (with 488 nm

wavelength excitation) showing the places on the aggregate where Raman spectra

were measured. ..................................................................................................... 90

Figure 3.8 Resonance Raman spectra corresponding to spots 1-5 in Fig. 3.7 with 488 nm

excitation. .............................................................................................................. 91

xiv

Figure 3.9 Histograms of (top) the Raman intensities of the seven prominent modes at

each spot on the aggregate in Fig. 3.7 excited with 488 nm wavelength laser and

(bottom) corresponding intensity ratios. ............................................................... 93

Figure 3.10 (Left) Resonance Raman spectra of the TSPP aggregate in Figure 3.7

measured at spot 1 with 0.75 mW of 488 nm wavelength laser light at the moment

of exposure (black) and 92 seconds later. (Right) The time profile of the

intensities of the 243 cm-1

, 316 cm-1

, and 1534 cm-1

modes over the course of the

“high power” exposure. ........................................................................................ 94

Figure 3.11 Histogram of the intenisty ratios of the 243 cm-1

:316 cm-1

modes (blue), 316

cm-1

:1534 cm-1

modes (red), and 243 cm-1

:1534 cm-1

(black) with gentle laser

exposure (1) and high power laser exposure at t = 0 s (2) and t = 92 s (3) at spot 1

on aggregate shown in Fig. 3.7. ............................................................................ 95

Figure 3.12 The RLS images of the aggregate in Fig. 3.7 before (left) and after (right)

laser heating at spot 1. ........................................................................................... 96

Figure 3.13 Polarized Raman spectra of an individual TSPP aggregate. V and H refer to

the vertical and horizontal polarization, respectively, of the incident excitation

(first letter) and scattered light (second letter) with respect to the orientation of the

nanotube long axis as illustrated in the inset. ....................................................... 98

Figure 3.14 Atomic force microscopy image of TSPP aggregates spin-cast on mica from

a 5 M TSPP solution with 0.75 M HCl. Red and blue cross section profiles

correspond to red line and blue line in the image. .............................................. 103

Figure 4.1 Absorbance Spectrum of the TSPP aggregates in ethanol and aqueous 1.0 M

HCl. ..................................................................................................................... 110

xv

Figure 4.2 Absorption spectra of 5 M of the dihydrochloride salt of TSPP dissolved in

ethanol over time. Arrows emphasize the trend of the changes in the peaks over

time. .................................................................................................................... 111

Figure 4.3 Absorption spectra of 5 M TSPP diacid dissolved in various mixtures of

ethanol and water with a constant concentration of 1.0 M HCl.......................... 112

Figure 4.4 Absorption spectrum of TSPP diacid dissolved in a mixture 10% ethanol by

volume and water with an overall concentration of 1.0 M HCl as it evolves in

time. .................................................................................................................... 113

Figure 4.5 Absorption spectrum of the tetrabutylammonium chloride salt of TSPP free

base in dichloromethane. .................................................................................... 114

Figure 4.6 Absorption spectrum 34.7 M of the TBA salt of TSPP in DCM exposed to

HCl vapor for 1 hour. .......................................................................................... 115

Figure 4.7 Resonance Raman spectrum of 34.7 M of the TBA salt of TSPP in DCM

exposed to HCl vapors for 1 hour excited with 454.5 nm wavelength laser. The

285 cm-1

, 700 cm-1

, and 738 cm-1

Raman modes are attributed to DCM vibrations.

............................................................................................................................. 116

Figure 4.8 Polarized (black) and depolarized (red) resonance Raman spectra of 34.7 M

of the TBA salt of TSPP in DCM exposed to HCl vapor for 1 hour excited with

454.5 nm wavelength laser. ................................................................................ 117

Figure 4.9 7 x 7 m (top) and 100 x 100 nm (middle) AFM images of the TBA salt of

TSPP deposited from DCM exposed to HCl vapor for 1 hour on mica with

corresponding cross section (bottom). ................................................................ 119

xvi

Figure 5.1 Electronic absorption spectrum of AuNPs which observe a surface plasmon at

about 520 nm....................................................................................................... 128

Figure 5.2 Normalized SERRS spectra of TSPP aggregates mixed with 3 nm AuNPs.

Black and red spectra are prepared via the sandwich method and blue and pink

spectra are prepared via the spin coat method. The green spectrum is an ensemble

resonance Raman spectrum................................................................................. 130

Figure 5.3 Histogram of the Raman intensities of the 243, 316, and 1534 cm-1

modes of

the 4 SERRS measurements in sample Fig. 5.2. ................................................. 131

Figure 5.4 Histogram of Raman intensity ratios of the 243, 316, and 1534 cm-1

modes of

the 4 SERRS measurements in Figure 5.2. ......................................................... 132

Figure 5.5 Schemes for possible hot spot formation of the gold nanoparticles (brown-red

circles) around the aggregate nanotube. The third nanotube from the left is the

case where the nanoparticles form hot spots within the wall of the aggregate such

that the nanoparticles lie in the circular N-mers or in interstitial regions between

circular N-mers as shown on the right. The polarization of the predicted

transitions for a hierarchical helical nanotube aggregate are displayed here for

reference. ............................................................................................................. 133

Figure 6.1 The electronic absorption spectrum for the TSPP diacid (black) and the best fit

calculated absorption spectrum for the TSPP diacid (red) using equation 6.1 with

the listed parameters for the calculation. ............................................................ 144

Figure 6.2 The calculated absorption spectrum of a TSPP circular 16-mer aggregate using

equation 6.10, incorporating 1- and 2-particle states, vibrational quanta v = 0, 1, 2

with two vibrational modes (236 cm-1

and 1234 cm-1

). ...................................... 145

xvii

Figure 6.3 Model absorption spectrum for the TSPP hierarchical helical nanotube

aggregate without vibrations defining excitonic coupling through the point dipole

approximation. .................................................................................................... 147

Figure 6.4 The electronic absorption spectrum of TSPP-h (black) and TSPP-d (red)

aggregates prepared from the 50 M concentrations of the corresponding diacid

monomer in 0.75 M HCl/DCl in H2O/D2O. ........................................................ 148

Figure 6.5 Background subtracted resonance Raman spectra of TSPP-h aggregates with

respective reference standard (acetonitrile or cyclohexane) excited with

wavelengths spanning the J-band. The reference standard used for excitation

wavelengths 454.5 nm, 457.9 nm, and 514.5 nm was acetonitrile (920 cm-1

mode

for reference). The reference standard used for excitation wavelengths 465.8 nm,

472.7 nm, 476.5 nm, 488 nm, and 496.5 nm) was cyclohexane (800 cm-1

mode for

reference). Intensities of Raman modes are raw intensities. Peaks with asterisks

above them are reference standard Raman modes. ............................................. 150

Figure 6.6 Background subtracted resonance Raman spectra of TSPP-d aggregates with

respective reference standard (acetonitrile or cyclohexane) excited with

wavelengths spanning the J-band. The reference standard used for excitation

wavelengths 454.5 nm, 457.9 nm, and 514.5 nm was acetonitrile (920 cm-1

mode

for reference). The reference standard used for excitation wavelengths 465.8 nm,

472.7 nm, 476.5 nm, 488 nm, and 496.5 nm) was cyclohexane (800 cm-1

mode for

reference). Intensities of Raman modes are raw intensities. Peaks with asterisks

above them are reference standard Raman modes. ............................................. 151

xviii

Figure 6.7 Electronic absorption spectra of the J-band of the TSPP-h (black) and TSPP-d

(red) aggregates with vertical lines indicating the excitation wavelengths used in

the aforementioned quantitative resonance Raman spectra. ............................... 152

Figure 6.8 Resonance Raman excitation profiles of the 243 cm-1

(black), 317 cm-1

(red),

698 cm-1

(blue), 983 cm-1

(pink), 1013 cm-1

(green), 1228 cm-1

(indigo), and 1534

cm-1

(violet) modes of TSPP-h aggregates. ........................................................ 154

Figure 6.9 Resonance Raman excitation profiles of the 239 cm-1

(black), 315 cm-1

(red),

697 cm-1

(blue), 957 cm-1

(pink), 1004 cm-1

(green), 1225 cm-1

(indigo), and 1534

cm-1

(violet) modes of TSPP-d aggregates. ........................................................ 155

Figure 6.10 The sum-over-modes REPs of TSPP-h aggregates (red) and TSPP-d

aggregates (black). Data points are connected by polynomial spline to guide the

eye. ...................................................................................................................... 156

Figure A.1 Photograph of confocal resonance Raman spectroscopy set up with triple

monochromator. .................................................................................................. 171

Figure A.2 Photograph of display interface for triple monochromator. ......................... 172

Figure A.3 Photograph of confocal backscattering geometry. Light is reflected into the

first 4x objective by the beamsplitter (moving right to left), focused on the

sample in the first cuvette holder, is collimated by the second 4x objective, and

then focused on to the second sample in the second cuvette holder by a 10x

objective. A motorized magnetic stirrer is position near the second cuvette holder.

............................................................................................................................. 174

Figure A.4 Photograph of collection optics including (from left to right) the beamsplitter

shown in Fig A.3, the polarizer, depolarizer, focusing lens, and fiber optic. ..... 176

xix

Figure A.5 Photograph of inverted confocal microscope set-up used for single aggregate

Raman spectroscopy and resonance light scattering microscopy. ...................... 179

Figure A.6 Photograph of the collection optics which present scattered light to the

spectrometer. For spectroscopic measurements, the scattered light must be

directed out of the side port of the microscope body. ......................................... 180

Figure A.7 Photograph of CCD camera used for imaging. Light presented to the camera

is directed out the back port of the microscope body. ........................................ 181

Figure A.8 Photograph of frosted glass and screwed-in lens (small black cylinder behind

frosted glass) placed in the path of the incoming beam to epi-illuminate the

sample for RLS imaging. .................................................................................... 183

xx

Dedication

To my fiancé Amy, my parents Charles and Patty, and my siblings Allison and Joseph for

their love and support and in memory of my grandfathers, Robert Frazier and Charles

Rich.

1

Chapter 1 Introduction

1.1: Introduction and Background

1.1.1: Light Harvesting Aggregates

One fundamental aspect of developing solar energy technology that is cost-

efficient, energy-efficient and environmentally sustainable is to perfect light-harvesting

properties, particularly in capturing infrared and red wavelengths. Dye-sensitized solar

cells (DSSCs) have been found to be an inexpensive, eco-friendly alternative to other

photovoltaic systems but struggle to capture the entire solar spectrum and generate

comparable photoconversion efficiencies. One reason for the low efficiencies of DSSCs

is that the redox chemistry of the sensitizing dye can result in its eventual degradation. In

nature, most photosynthetic organisms utilize chlorophyll-carotenoid aggregates to

capture sunlight and funnel the electronic excitation to the photosynthetic reaction center,

separating light-harvesting and electron transfer chemistry.1 The organization of the light-

harvesting aggregates allows for the collection of a broad spectral range of light. In

addition to photovoltaics, the use of solar energy for splitting water for hydrogen

production would benefit from emulating nature and using tunable light-harvesting

aggregates (LHAs) to provide renewable energy in a more effective and potentially more

environmentally sustainable way.

While natural light harvesting aggregates contain chlorophyll, artificial systems

(based on the closely related porphyrin molecule) provide convenient models for

studying the optical and electronic properties of these aggregates. Both chlorophyll

derivatives as well as synthetic porphyrins tend to self organize into ring- and rod-shaped

2

supramolecular nanostructures.2,3

Understanding the way these structures form, how to

control aggregation, how molecular structure influences aggregation, and how the

structure influences optical and electronic properties is crucial to uncovering the mystery

behind tunable light harvesting in nature. Thus the goal of this thesis is to demonstrate

how one can use spectroscopic and microscopic techniques to better understand this

correlation between supramolecular structure and the optical and electronic properties

of LHAs.

LHAs can be prepared via a variety of facile methods in solution (particularly

aqueous), in micellar media,4,5

at interfaces,6 on DNA templates,

7 and on solid

substrates8,9

. Aggregation of strong light absorbing molecules to form LHAs is a result of

non-covalent intermolecular interactions.10,11

Because the intermolecular forces within

these chromophores are not covalent, determining the link between aggregate structure

and corresponding electronic properties can be challenging. The environment in which

aggregates form highly influences their ultimate structure. This can complicate

spectroscopic and imaging measurements of LHAs coincidentally as spectroscopic

measurements are typically conducted in solution and microscopy measurements are

performed on a dry solid substrate. As a result, one cannot make a definite conclusion of

the structure of the aggregate in solution based on that observed in a scanning probe

image and vice versa. Furthermore, the structure of light harvesting aggregates has been

shown to depend on preparation conditions such as ionic strength, pH, counterions, and

solvent.8,12,13,14,16

For quantitative measurement of Raman spectra, this can limit if not

eliminate the number of choices for internal standards to determine relative Raman cross-

sections. Thus it is integral to this research that an understanding of interactions between

3

aggregate and solvent be achieved in order to determine the role that the environment

plays on the properties of the system.

1.1.2: Excitonic Coupling of Porphyrin Aggregates

The conventional model for excitonic coupling in porphyrin aggregates is the so-

called staircase model (See Figure 1.1). At this simple level of theory, the transition

dipole moments of each monomer align themselves parallel to the direction of

aggregation and perpendicular to it for a linear aggregate. The wavefunctions and

eigenvalues (energies) that result from this coupling of these excitations can be

determined by diagonalizing the aggregate Hamiltonian (here ħ=1)15

:

(1.1)

The first term addresses the diagonal components of the Hamiltonian where n and m,

which index the monomer in the aggregate, are equal and consists of energies of the

Figure 1.1 Diagram explaining transition dipole moment coupling V12 of

neighboring chromophores with both x- and y- polarized electronic transitions by

the staircase model.

x

y

y

J

agg

2

3

2

12 cos31r

Vge

H 3

2

12r

Vge

ruruuur

Vge ˆˆˆˆ3ˆˆ

21213

2

12

cos2

4

localized states composed of the 0-0 molecular transition energy corresponding to the

lowest optically allowed transition, ω0-0, the site shift in the aggregate due to nonresonant

intermolecular interactions, D, a disorder-induced change in the transition energy at site

n, Δn, and the energy of the symmetric intramolecular vibration, ω0, multiplied by its

vibrational quantum number, v. The second term addresses the off-diagonal components

of the Hamiltonian which addresses the excitonic coupling, with coupling strength Jmn,

which couples the state in which molecule n is electronically excited and the state in

which molecule m is electronically excited.

The excitonic coupling strength Jmn (which can also expressed as V12 as shown in

Fig. 1.1) can be described by the point dipole approximation:

(1.2)

In this equation, ge is the electronic transition dipole moment, r is the distance between

chromophores, is the unit vector in the direction of the dipole moment at

chromophore n, and is the unit vector in the direction of the distance between

chromophores. As shown in Figure 1.1, depending on the orientation of the transition

dipole with respect to the direction of aggregation, excitonic coupling may result in a red

shift of the monomer absorption band (J-band), when the dipole moment vector is nearly

aligned with aggregation distance vector, or a blue shift (H-band), when the dipole

moment vector and aggregation distance vector are orthogonal. As a result, the doubly

degenerate B-(or Soret) band of the monomer electronic absorption spectrum of a

porphyrin splits into red-shifted (J-band) and blue-shifted (H-band) electronic transitions

upon aggregation when stacked in the staircase pattern with angle for which cos2 >

5

1/3) where the respective shifts of excitonic states are proportional to the transfer integral

V12.

For aggregates of a sufficiently large number of molecules, N, periodic boundary

conditions can be applied and each exciton can be characterized by a wave vector

quantum number k:

(1.3)

The k = 0 state carries most of the oscillator strength for the perturbed electronic

transition of the J and H bands. The one-exciton wavefunctions of the aggregate can also

be expressed as linear combinations of wavefunctions in which one molecule is

electronically excited as well as the linear combinations of wavefunctions considering

two molecule terms to address the case where excitation results in vibronic excitation of

one molecule n and only vibrational excitation of neighboring molecule n’ (Ref. 15):

(1.4)

The coefficients

and

for the 1-particle term (first term) and 2-particle term

(second term) are solved from diagonalization of the aggregate Hamiltonian where α

indexes the eigenstate.

The theory aforementioned adequately accounts for the existence of both H and J

bands for tetra(carboxyphenyl)porphyrin (TCPP) aggregates in the presence of nitrate

counterions.16

But the lack of exchange narrowing and lower intensity of the H-band

compared to that of the J- band in electronic absorption spectroscopy are not explained by

the simple model. This also holds true for aggregates composed of

tetra(sulfonatophenyl)porphyrin (TSPP) (See Figure 1.2), a water soluble porphyrin

6

which is widely researched in porphyrin aggregate studies. Flow-induced linear

dichroism (FLID) of the J-band of TSPP aggregates shows incomplete polarization of the

J-band transition dipole moment.17

This incomplete polarization is also observed in the

linear dichroism spectra of these aggregates when they are aligned with a magnetic

field.18

Furthermore, the intensity of the Q-band increases upon aggregation, indicating

that either excitonic coupling perturbs the mixing of excited configurations that

contribute to both the B- and Q-band excited states or distortion of the monomer upon

aggregation resulting in a site shift type perturbation.19,20,21

Coherence number values, Nc,

(which account for the number of molecules sharing the exciton) for these aggregates are

not equal to the number of molecules in the aggregate, but rather increase for larger

coupling and decreases with increasing exciton-phonon coupling, which are reflected in

the resonance Raman intensities of vibrational modes associated with interchromophore

coupling.

Figure 1.2 Absorption spectra of the free base monomer, diacid monomer, and

aggregate forms of TSPP (left) and molecular diagram of TSPP for the free base

and diacid monomer (right).

7

1.1.3: Resonance Raman Spectroscopy

Raman scattering is a two-photon inelastic light scattering process in which the

incident excitation photon has a different frequency than the scattered photon. When the

scattered photon frequency νs is less than the incident photon frequency νi, then the

Raman scattering is denoted as Stokes Raman scattering (which will be the only type of

Raman scattering discussed in this thesis). The opposite case where the scattered photon

frequency νs is higher in energy than the incident photon frequency νi, then the scattering

is denoted as Anti-Stokes Raman scattering. The shifts in energy, called Raman shifts, are

the result of interactions of the incident light with molecular vibrations or phonons. Thus

peaks in Raman spectra with different Raman shifts identify different vibrational modes

of the probed molecule. The fundamental transitions in Raman spectroscopy are allowed

through the polarizability derivative , i.e., Raman scattering occurs when

there is a change in the polarizability of the probed molecule during the vibration. For the

rest of this document the prime will be neglected and the transition polarizability will be

simply denoted as α.

8

Figure 1.3 Ninety degree scattering geometry.

9

In a typical Raman experiment for a 90 degree scattering geometry (shown in

Figure 1.3), incident excitation light polarized along direction propagates along the X-

direction and the scattered light is detected along the Y-direction. As in a fluorescence

experiment, radiation is accounted for as being scattered into a sphere of 4π stearadians.

The net intensity of the scattered light will be determined by the cross-section for the

scattering, . The differential cross-section

depends on the polarization of the

scattered and incident radiation represented by and , respectively. The differential

cross section is related to the lab frame transition polarizability tensor by:

Figure 1.4 Generalized scattering geometry.

10

(1.5)

The differential cross section in this equation is in cm2 sr

-1 molecule

-1, is the solid

angle of the scattered light subtended by the detector, and c is the speed of light. To

determine the total cross section, R, the differential cross section must be integrated over

all possible angles22

:

(1.6)

To evaluate this, one must consider how the intensity of light varies with the scattering

angles (,) and the polarization. Figure 1.4 shows a generalized scattering geometry

similar to Figure 1.3 where the wave vector of the scattered radiation may have any

orientation, specified by polar and azimuthal angles and . The scattered light

polarization can be resolved into two components , which is chosen to be perpendicular

to and , and , which is perpendicular to and . The differential cross-section at

a given scattering angle is given as the sum of the differential cross-section for the two

polarization components:

(1.7)

The depolarization ratio, , is given by the ratio of the intensity of the scattered light

polarized perpendicular to the polarization of the incident light (depolarized, Idep) over the

intensity of the scattered light polarized parallel to the polarization of the incident light

(polarized, Ipol) which is proportional to the ratio of the respective differential cross-

sections:

11

(1.8)

Using the depolarization ratio and trigonometry on equation 3, the differential cross-

section at a given scattering angle can be expressed as:

(1.9)

Using equation 5 in equation 2, the total cross-section can be found by measuring the

differential cross-section and the depolarization ratio in a ninety degree (as well as

confocal) scattering geometry:

(1.10)

As E1-allowed (electric dipole-allowed) absorption and emission intensities

derive from the square of the transition dipole moment, Raman scattering intensity

depends on the square of the transition polarizability. The components of the transition

polarizability tensor, in the molecular frame, are given by the Kramers-Heisenberg-Dirac

(KHD) equation:

(1.11)

Here and are Cartesian directions and i, n, and f are labels for the initial, intermediate,

and final state of the Raman scattering process respectively. The frequency of the

incident photon is denoted as ω, whereas ωni and ωnf are the transition frequencies

between the initial state and intermediate state and between the final state and

intermediate state respectively. The components of the transition dipole moment vector

12

are labeled ,. n is a damping term which accounts for the finite lifetime 1/n of

the intermediate state.

In the resonance Raman scattering experiment, the frequency of the incident

photon is equal or nearly equal to the energy of the vertical transition from the electronic

ground state to the electronic excited state. In this scenario, the second term in equation

1.11 (the anti-resonance term) is very small relative to the first term (the resonance term)

and can be neglected. Limiting the sum over intermediate states to vibrational states v

within the resonant excited electronic state e the Albrecht A-term of the transition

polarizability is derived:

(1.12)

Here, and denote the vibrational states of the electronic ground state. Totally

symmetric modes are resonance Raman active as the Franck-Condon overlap integrals do

not vanish. Undisplaced modes, however, are not allowed by the A term as only cases

where would be permitted. Thus the totally symmetric modes which are

enhanced in resonance Raman spectra are those which correspond to the geometry

change of the molecule and are called “A term enhanced” or “Franck-Condon enhanced”.

If one includes the terms for the transition dipole moment which are linear in the normal

coordinate using the Herzberg-Teller formalism one obtains the Albrecht B term:

13

(1.13)

is the vibronic coupling matrix element for unperturbed electronic states e and r

coupled by vibrational mode i:

(1.14)

The Albrecht B-term allows for resonance Raman activity for nontotally symmetric

vibrations when the vibrations are responsible for vibronic coupling of two nearby

electronic states. B-term allowed resonance Raman modes are typically weaker than A-

term allowed modes since they depend on the breakdown of the Born-Oppenheimer

approximation.

In an ensemble condensed-phase Raman experiment determining the elements of

the molecular frame transition polarizability tensor is complicated by the random

orientation of the molecules tumbling in solution. It is thus necessary to convert the

molecule-frame tensor elements to lab-frame components. Using Wigner rotation

functions we can express rotational invariants, , as linear combinations of the spherical

tensor components

which are independent of reference frame:

(1.15)

14

Here J = 0, 1, and 2 and M = 0, ±1, and ±2. As a second-rank tensor, the polarizability

has three invariants:

(1.16a)

(1.16b)

(1.16c)

is the isotropic part of the polarizability and is proportional to the square of the trace

of the polarizability tensor. and are the antisymmetric and symmetric anisotropies,

respectively, and depend on the off-diagonal elements of the polarizability tensor. The

components of the lab-frame tensor and can be expressed as linear

combinations of the invariants:

(1.17a)

(1.17b)

The depolarization ratio is related to these lab frame components as

follows:

(1.18)

Thus the depolarization ratio can be expressed in terms of the invariants:

(1.19)

15

For nontotally symmetric modes in the off-resonance Raman case where Σ0 and Σ

1

vanish, the depolarization ratio must be = 3/4. For totally symmetric modes in the off-

resonance Raman case, where Σ0 ≠ 0, the depolarization ratio must be < 3/4. For the

resonance Raman case, the Raman tensor is not necessarily symmetric and thus the

depolarization ratio may exceed 3/4 due to anomalous polarization caused by B-term

enhancement. Moreover the degeneracy of the resonant electronic state can be predicted

from the depolarization ratio of a totally symmetric vibration. For a nondegenerate

electronic state where the transition moment has a unique direction in the molecule

frame, i.e. the z direction, the only nonzero component of the Raman tensor is the

diagonal component corresponding to that the direction, i.e. αzz. In this case the

depolarization ratio is expected to be = 1/3. For a doubly degenerate resonant electronic

state where two diagonal Raman elements are nonzero and equal, the depolarization is

expected to be = 1/8. However, when Raman intensity derives from more than one

excited electronic state, the depolarization ratio will depend on the excitation wavelength

which is called depolarization ratio dispersion.

16

1.2: Previous Results: Imaging and Spectroscopy of TSPP aggregates

Collaboration between the McHale and Mazur groups at Washington State

University has presented a wealth of information regarding TSPP and its aggregation and

poses a different model from the staircase model to address the observed optical

phenomena. Atomic force microscopy (AFM) and scanning tunneling microscopy (STM)

images (see Figure 1.5) of TSPP aggregates desposited on Au (111) show nanorods of

with a cross-sectional height of ~4 nm and widths of ~25 nm.3

High resolution STM

images show that these rods consist of disks which have a diameter of ~6 nm. What is

important to note here is that of the dimensions mentioned, none are equal to the size of

the TSPP diacid monomer (~2 nm), an observation which does not support the staircase

model. Furthermore, recent STM images of TSPP diacid monomers on Au (111) by the

Mazur lab show apparent saddling of the molecular structure,23

a phenomenon attributed

to steric hindrance due to protonation of the porphyrin core, which is not accounted for in

Figure 1.5 Tapping mode atomic force microscopy images with cross-sectional data

(left) and a scanning tunneling microscopy image (right) of TSPP aggregates

deposited on Au(111) from Ref. 3.

17

the staircase model as well. A circular model for the organizations of TSPP diacid

molecules has been proposed to account for the observed 6 nm disks which resemble the

aforementioned chlorophyll-based light harvesting aggregates in purple bacteria as shown

in Figure 1.6. The degree of puckering exhibited by each diacid molecule defines the size

of the disk and number of molecules and is defined by an angle

called the

“magic angle,” the angle at which each porphyrin deviates from planarity. The McHale

group proposes that these circular aggregates assemble further into the observed nanorods

in STM images. Recently, it has been postulated that these nanorods are actually

nanotubes which, upon deposition on the surface for STM measurements, are desiccated

resulting in observed collapsed nanotubes, accounting for the 4 nm height.24

Resonance Raman spectroscopy of TSPP aggregates in resonance with the J-band

(see Figure 1.7) exhibit depolarization ratios of ~ 0.5 for all of the observed mode

which is not consistent with either a singly or doubly degenerate totally symmetric state

Figure 1.6 Cartoon showing geometrical constraints of TSPP in circular N-mer

aggregates of radius R. Porphyrins are shown as bent line structures separated by a

distance s.

18

(=1/3 or =1/8, respectively) or a nontotally symmetric state (=3/4). Strong

enhancement of the low frequency modes at 243 cm-1

and 316 cm-1

are a common feature

in resonance Raman spectra and, while their specific assignment has not been

ascertained, they have been generally attributed to “ruffling” or “doming” modes of the

porphyrin. Reported red-shifts of these two bands in D2O evidence N-H(-D) motion

attributed to the bands25

, suggesting that they are out-of-plane vibrations that are strongly

coupled to the delocalized electronic transition via perturbation of the interchromophore

separation. However, the depolarization ratio of = 0.5 for the low frequency bands is

not in accord with a nondegenerate J-band polarized along the nanotube long axis.

19

Further insight into the J-band is provided by resonance Raman spectra on

Au(111).24

Utilizing surface selection rules outlined by Moskovitz,26,27

polarization

studies show that the PP:SS ratio is smaller than predicted for an aggregate with only one

J-band transition, contradicting the assumption that only one of the diagonal components

of the polarizability tensor is nonzero. This suggests that there are components of the J-

band dipole that are parallel and perpendicular to the nanotube axis. Further computation

of the relative magnitudes of the pertinent polarizabilities suggests that the J-band

transition is largely, but not completely, oriented along the long axis of the nanotube.

Figure 1.7 Polarized and depolarized resonance Raman spectra of 50 M TSPP

aggregates in 0.75 M HCl excited with a 488 nm wavelength laser.

20

The resonance Raman spectrum of the aggregate excited within the H-band is

significantly different from that of the J-band. For excitation at 413 nm, the low

frequency modes are weak and the higher frequency modes are strong. PP:SS:PS:SP

ratios from resonance Raman spectra excited within the H-band of TSPP on Au(111), for

the 314 cm-1

mode, suggests that off-diagonal components of the polarizability tensor

could contribute. Vibronic coupling of the H-band and the Q-band can result in off-

diagonal components of the polarizability tensor.

Strong resonance light scattering signal of the J-band and weak RLS signal of the

H-band indicates that the degree of coherence is larger for the J-band. This lack of

coherence in the H-band may suggest that the corresponding transition dipole moments

are not well aligned with one another. Discerning the reason for this lack of agreement is

difficult as the overlap of the residual monomer B-band the aggregate H-band inhibits

distinguishing contributions of each species, particularly in resonance Raman spectra.

21

Electronic absorption spectroscopy reveals further information on TSPP

aggregates. Isosbestic points suggest the occurrence of two absorbing species: the diacid

monomer and the aggregate (see Figure 1.8). Furthermore, the isosbestic points are not

blurry, in comparison to previous studies with TCPP,16

suggesting a precursor to the

formation of the overall aggregate which dominates the spectral perturbations, i.e., the

circular aggregates forming the helical nanotubes. Integrated absorption data of the diacid

monomer and the aggregate show unequal intensities for the H- and J-bands, inconsistent

with the circular aggregate model, suggesting that upon aggregation intensity is

apparently stolen by the Q-band from the B-band. Symmetry considerations of the H- and

J-bands have lead to the postulate that intensity sharing between the B- and Q- bands

occurs via vibronic coupling.

Figure 1.8 Electronic absorption spectra of different concentrations of TSPP in 0.75

M HCl.

22

Based on a combination of spectroscopic and imaging methods, the McHale

group has deduced that TSPP exhibits aggregation into a hierarchical helical nanotube

(see Figure 1.9). Circular dichroism of the aggregates in the presence of chiral substances

suggests a left- or right-handedness to the aggregates which would be consistent with a

helical nanotube structure.28,29

However, how these aggregates maintain their structure

without a template or molecular scaffolding has not been revealed. The solvent

environment likely plays an important role in maintaining the structural integrity of these

self-assemblies. Additionally, the overlap of the H-band of the aggregate and the B-band

of the diacid monomer results in some uncertainty in the oscillator strength of the H-

band. This problem highlights the challenge of analysis of one absorbing species in a

heterogeneous mixture of many. Single-aggregate resonance Raman spectroscopy may

provide a technique which may overcome this problem and better illuminate

spectroscopic results of not only aggregates of TSPP but more complex natural

aggregates as well. Thus the research described in the following chapters attempts to

resolve the Raman spectrum of a single light harvesting aggregate in order to best

discern the correlation between its electronic, optical, and structural properties.

23

1.3: Hypothesis and Research

The proposed scheme for assembly of the TSPP aggregates shown in Fig. 1.9

involves, first, the formation of circular N-mers via electrostatic interactions between the

negatively-charged peripheral sulfonato groups and the positively-charged core

protonated pyrrole nitrogens of neighboring TSPP diacid monomers. The naturally

saddled geometric conformation of the porphyrin, and likely additional distortion that

occurs due to aggregation, causes the aggregate to wrap around on itself forming a

circular aggregate, similar to what is observed in LHCs of purple photosynthetic bacteria.

As a result, these aggregates have a doubly degenerate transition for which the two

orthogonal transition moments are polarized in the plane of the ring, related to J-type

Figure 1.9 Proposed mechanism of TSPP aggregation from diacid monomer (a) to

circular N-mer (b) to helical nanotube (c) with the STM image of the nanotube on

Au(111) (d).

24

excitonic coupling, and an orthogonal transition, related to H-type excitonic coupling.

The circular N-mers (consisting of about ~16 monomers to account for the 6 nm diameter

observed in STM images of the aggregate on gold) then further assemble into the helical

nanotube structure, shown in Fig. 7c, via hydrogen bonding interactions with the

surrounding water molecules and protons in the acidic aqueous environment.

Consequently, J-type excitonic coupling of the in plane transition dipole moments of the

N-mers would result in three transition dipole moments: one oriented along the long axis

of the nanotube aggregate and doubly degenerate transition dipole moments which are

oriented along the short axis. To probe the link between the structural and electronic

properties of these aggregates as well as ascertain the validity of this model, I have

utilized a combination of spectroscopic and microscopic techniques, specifically related

to resonance Raman scattering. The goals of this research include:

Determining the role of water on the structural and excitonic properties of TSPP

aggregates by measuring their spectroscopic properties in a protiated environment

(0.75 M HCl in water) and in a deuterated environment (0.75 M DCl in heavy

water).

Understanding the general role of solvent environment on the aggregate structure

by probing TSPP aggregates dissolved in organic solvents (i.e., dichloromethane,

ethanol, methanol,…)

Resolving the heterogeneity of aggregates in solution by measuring single

aggregate resonance Raman spectra and surface-enhanced resonance Raman

spectra (SERRS) to determine the spectroscopic properties of individual

aggregates.

25

Utilizing the Frenkel Polaron model15

and to fit a structural model (i.e., the

circular N-mer and nanotube) to the experimentally determined spectroscopic

parameters.

Combining the knowledge obtained from experiment and theory to assess the

structure and electronic properties of TSPP aggregates.

The findings of these experiments are detailed in the following data chapters (Chapters 2,

3, 4, 5, and 6 respectively) with a summation of the results, conclusions, and future work

addressed in Chapter 7.

1.4 References

1. Hu, X.; Schulten, K., “How Nature Harvests Sunlight,” Phys. Today 1997, 50, 28-34.

2. McDermott, G.; Prince, S. M.; Freer, A. A.; Hawthornthwaite-Lawless, A. M.; Papiz,

M. Z.; Cogdell, R. J.; Isaacs, N. W., Nature 1995, 374, 517.

3. Friesen, B. A.; Nishida, R. A.; McHale, J. L.; Mazur, U., J. Phys. Chem. C, 2009, 113,

1709-1718.

4. Li, X.; Zheng, Z.; Han, M.; Chen, Z.; Zuo, G., J. Phys. Chem. B, 2007, 111, 4342-

4348.

5. Voigt, B.; Krikunove, M.; Lokstein, H., Photosynth. Res., 2008, 95, 317-325.

6. Huijser, A.; Marek, P.L; Savenije, T. J.; Siebbeles, L. D. A.; Scherer, T.; Hauschild,

R.; Szymytkowski, J.; Kalt, H.; Hahn, H. Balaban, T. S., J. Phys. Chem. C, 2007, 111,

11726-11733.

7. Chowdury, A.; Yu, L.; Raheem, I.; Peteanu, L.; Liu, L. A.; Yaron, D. J., J. Phys.

Chem. A, 2003, 107, 3351-3362.

26

8. Doan, S. C.; Shanmugham, S.; Aston, D. E.; McHale, J. L., J. Am. Chem. Soc., 2005,

127, 5885-5892.

9. Higgins, D. A.; Kerimo, J.; Vavden Bout, D. A.; Barbara, P. F., J. Am. Chem. Soc.,

1996, 118, 4049-4058.

10. Kasha, M.; Rawls, H. R.; El-Bayoumi, M. A., Pure Applied Chem., 1965, 11, 371.

11. McRae, E. G.; Kasha, M., J. Phys. Chem. B, 1958, 28, 721-722.

12. Maiti, N. C.; Mazumdar, S.; Periasamy, N., J. Porphy. Phthalo., 1998, 2, 369-376.

13. Castriciano, M. A.; Romeo, A.; Villari, V.; Micali, N.; Scolaro, L. M., J. Phys. Chem.

B, 2003, 107, 8765-8771.

14. Castriciano, M. A.; Donato, M. G.; Villari, V.; Micali, N.; Romeo, A.; Scolaro, L. M.,

J. Phys. Chem. B, 2009, 113, 11173-11178.

15. Spano, F. C., Acc. Chem. Res., 2010, 43, 429-439.

16. Choi, M. Y.; Pollard, J. A.; Webb, M. A.; McHale, J. L., J. Am. Chem. Soc., 2003,

125, 810-820.

17. Ohno, O.; Kaizu, K.; Kobayashi, H., J. Chem. Phys., 1993, 99, 4128-4139.

18. Kitahama, Y.; Kimura, Y.; Takazawa, K., Langmuir, 2006, 22, 7600-7604.

19. Gouterman, M., J. Mol. Spect., 1961, 6, 138-163.

20. Gouterman, M.; Wagniere, G.; Snyder, L. C., J. Mol. Spect., 1963, 11, 108-127.

21. Yildirum, H.; İşeri, E. İ.; Gülen, D., Chem. Phys. Lett., 2004, 391, 302-307.

22. McHale, J. L., Molecular Spectroscopy, Prentice Hall, New Jersey, 1999.

23. Friesen, B. A.; Wiggins, B.; McHale, J. L.; Mazur, U.; Hipps, K. W., J. Am. Chem.

Soc., 2010, 132, 8554-8556.

27

24. Friesen, B. A.; Rich, C. C.; Mazur, U.; McHale, J. L., J. Phys. Chem. C, 2010, 114,

16357-16366.

25. Chen, D.-M.; He, T.; Cong, D.-F.; Zhang, Y.-H.; Liu, F.-C., J. Phys. Chem. A, 2001,

105, 3981-3988.

26. Moskovits, M., J. Chem. Phys., 1982, 77, 4408-4416.

27. Moskovits, M.; Suh, J. S., J. Phys. Chem., 1984, 88, 5526-5530.

28. Zhang, L.; Liu, M., J. Phys. Chem. B, 2009, 113, 14015-14020.

29. El-Hachemi, Z.; Escudero, C.; Orteaga, O.; Canillas, A.; Crusats, J.; Mancini, G.;

Purrello, R.; Sorrenti, A.; S’Urso, A.; Ribó, J. M., Chirality, 2009, 408-412.

28

Chapter 2 Influence of Hydrogen-Bonding on

Excitonic Coupling and Hierarchical Structure

of a Light-Harvesting Porphyrin Aggregate

Reprinted (adapted) with permission from Rich, C. C.; McHale, J. L., Phys. Chem. Chem.

Phys., 2012, 14, 2362-2374. Copyright © 2012 Royal Society of Chemistry.

Abstract

Helical porphyrin nanotubes formed from the diacid of tetrakis(4-

sulfonatophenyl)porphyrin (TSPP) were examined in DCl/D2O solution using resonance

Raman and resonance light scattering spectroscopy to probe the influence of hydrogen

bonding on the excitonic states. Atomic force microscopy reveals similar morphology

for aggregates deposited from DCl/D2O and from HCl/H2O solution. Deuteration results

in subtle changes to the aggregate absorption spectrum but large changes in the relative

intensities of Raman modes in the J-band excited resonance Raman spectra, revealing

relatively more reorganization along lower-frequency vibrational modes in the protiated

aggregate. Depolarization ratio dispersion and changes in the relative Raman intensities

for excitation wavelengths spanning the J-band demonstrate interference from

overlapping excitonic transitions. Distinctly different Raman excitation profiles for the

protiated and deuterated aggregates reveal that isotopic substitution influences the

excitonic structure of the J-band. The deuterated aggregate exhibits a nearly two-fold

increase in intensity of resonance light scattering as a result of an increase in the

coherence number, attributed to decreased exciton-phonon coupling. We propose that

strongly coupled cyclic N-mers, roughly independent of isotopic substitution, largely

29

decide the optical absorption spectrum, while water-mediated hydrogen bonding

influences the further coherent coupling among them when they are assembled into

nanotubes. The results show that, similar to natural light-harvesting complexes such as

chlorosomes, hydrogen bonding can have a critical influence on exciton dynamics.

KEYWORDS: Helical nanotubes, porphyrin aggregates, exciton coupling

2.1 Introduction

The tendency of porphyrins to self-assemble in solution has provided a rich

platform for the study of excitonic coupling relevant to antenna complexes of

photosynthetic organisms, which are comprised of structurally related chlorophylls and

bacteriochlorophylls. Perhaps the best studied synthetic porphyrin aggregate is that of

tetrakis(4-sulfonatophenyl)porphyrin (TSPP), which forms in acidic aqueous solution and

gives rise to a sharp, excitonically coupled red-shifted Soret band known as the J-

band.1,2,3,4

We have recently used resonance Raman spectroscopy and scanning tunneling

microscopy (STM) to probe the hierarchical structure of this aggregate,5,6,7

and find that it

shares some of the key structural features of light-harvesting complexes in photosynthetic

bacteria. Our results are consistent with a model in which circular aggregates of the

zwitterionic porphyrin diacid, H2TSPP2−

, are first assembled into ~6-nm diameter rings

reminiscent of the light-harvesting complexes of purple photosynthetic bacteria.8 These

rings, envisioned to be cyclic N-mers, then assemble into helical nanotubes (somewhat

similar to chlorosomes of green bacteria9) that are imaged as collapsed nanorods in AFM

and STM.5 The driving force for formation of the cyclic N-mers, where N is

hypothesized to be on the order of 16, is the electrostatic interaction of the protonated

porphyrin core with the negatively charged overlapping sulfonato groups on neighboring

30

molecules. The formation of rings rather than a linear staircase, as is typically depicted in

cartoons of J-aggregates, is postulated to be the result of nonplanarity of the porphyrin

diacid. It has been shown that protonation of the pyrrole nitrogens of

tetraphenylporphyrins results in saddled or ruffled geometries which are distorted from

planarity by as much as 20 to 30°,10

a key aspect of our model for the formation of the

cyclic N-mer.5

We recently reported experimental confirmation of the nonplanarity of the diacid

monomer of TSPP.11

As illustrated by the structure in Fig. 2.1 and revealed by high-

resolution STM images of individual diacid monomers on graphite, the protonated

monomer of TSPP adopts a saddled conformation. We hypothesize that the monomer

shape and electrostatic and hydrogen bonding forces dictate the hierarchical structure of

the self-assembled aggregate. Atomic force microscopy (AFM) and low-resolution STM

images of the TSPP aggregate deposited from acidic aqueous solution reveal nanorods of

variable length but uniform height (~ 4 nm) and width (~33 nm).5 Based on the fact that

STM images occasionally reveal intact nanotubes, we conclude that the “nanorods”

Figure 2.1 Structure of the neutral zwitterion (H4TSPP)

from the DFT calculation reported in Ref. 11. Two of

the four sulfonato groups are protonated in this

structure.

31

obtained in AFM and STM images are collapsed nanotubes, a conclusion shared by a

number of other investigators.12,13,14,15

However, though the existence of hierarchical

structure in the TSPP aggregate is widely recognized16,17,18,19

the challenge remains to

determine how the internal structure accounts for consistent widths and heights of

individual flattened nanotubes deposited from aggregate solutions of varying

concentration and ionic strength.4 Hydrogen-bonding is an example of highly-directional

intermolecular force that is known to control supramolecular structure in a variety of self-

assembled systems, including porphyrin aggregates.20,21,22

The present work employs

isotopic substitution to explore the possible role of hydrogen bonding in the TSPP

aggregate.

In addition, models for the supramolecular structure of the TSPP aggregate must

account for the important influence of water on the structure and optical properties.23,24

TSPP aggregates assembled on glass in the absence of water reveal a similar optical

spectrum to that of the aqueous phase aggregates but very different morphology

compared to aggregates deposited from water.25

TSPP aggregates assembled in water-

free acidic dichloromethane reveal a J-band at a wavelength similar to that of the aqueous

aggregate, but with a larger spectral width.26

TSPP aggregates formed in neat ethanol

have an optical spectrum which is somewhat perturbed from that of the aqueous system,

but the aggregates are imaged as shorter and wider nanorods in AFM.27

Even in ionic

liquids containing up to 40% water and HCl, the optical spectrum of the aggregate is

quite different from that in aqueous acid.28

It is therefore reasonable to propose that water

influences the hierarchical assembly of strongly-coupled microaggregates through

participation in highly directional hydrogen-bonding interactions between cyclic N-mers.

32

In the present work, we explore this hypothesis based on the model shown in Fig.

2.2, which we have previously used to interpret the images and resonance Raman spectra

of the TSPP aggregate deposited on Au(111).6

The formation of a porphyrin nanotube

from cyclic N-mers is analogous to the formation of a carbon nanotube by rolling up a

sheet of graphene, with the two-dimensional hexagonal array of cyclic N-mers serving as

the graphene sheet. Here, the mean porphyrin planes are arranged perpendicular to the

surface of the nanotube, accounting for the collapsed nanotube thickness on the order of

twice the porphyrin dimension, which is about 2 nm. In the proposed structure, two

Figure 2.2 Formation of a helical nanotube from the diacid of TSPP

(a), which first assembles into a cyclic 16-mer (b), then a helical

nanotube, (c) where the 16-mers are represented as strings of beads.

The helical nanotube model captures the structural features of the

flattened nanotubes as imaged by STM, shown in (d). The drawings

in (b) and (d) are adapted with permission from Friesen, B. A.;

Nishida, K. A.; McHale, J. L.; Mazur, U. J. Phys. Chem. C 2009, 113,

1709-1718.5 Copyright American Chemical Society 2009.

33

opposite sulfonato groups are engaged in electrostatic interactions with the protonated

pyrroles of neighboring porphyrins (Fig. 2.2b), leaving the –SO3− groups oriented

perpendicular to the planes of the cyclic N-mers available to participate in water-

mediated hydrogen-bonding between adjacent rings. The fixed width of the flattened

nanotubes, in this model would be enforced by an angle of about 140° between the planes

of adjacent N-mers.

The hierarchical model we propose appears to explain the wide range of reported

coherence numbers, ranging from 11 to about 500,29,30,31,32

and the appearance of an

isosbestic point in optical absorption, since the optical spectrum is largely, but not

completely, decided by the strong excitonic coupling within the putative cyclic N-mer.

Estimates of the coherence length from the exchange-narrowing of the J-band, in our

model, are too small because this band is split into axial and transverse components as

expected for a helical aggregate.33,34,35

If hydrogen bonding involving water influences

the excitonic coupling among the 6-nm disks, then deuteration could influence the

spectroscopy and perhaps also the structure of the aggregate. Though literature suggests

that deuteration may have only a small effect on the distance between hydrogen-bonded

moieties,36,37,38,39

deuteration of the diacid porphyrin core also leads to red-shifts3 in the

vibrational frequencies of the so-called “ruffling” and “doming” modes, at about 240 and

314 cm-1

respectively, which dominate the resonance Raman spectrum excited at 488

nm. These two modes are implicated in the vibronic coupling and intensity borrowing of

the Soret and Q bands of the aggregate.40,41

Strongly coupled vibrations; i.e., those which

dominate the resonance Raman spectrum, can influence the delocalization of the

excitonic state.42

In chlorosomes, natural light-harvesting aggregates of green bacteria,

34

hydrogen-bonding between bacteriochlorophylls provides a pathway for exciton

transport.9 Thus in addition to structural considerations, we seek to understand the

possible role of H-bonding on the excited state dynamics of the aggregate, through

comparison of the AFM images, resonance Raman, resonance light-scattering and optical

spectra of the H4TSPP2−

aggregate in H2O/HCl with that of D4TSPP2−

in D2O/DCl. (Note

that the four explicitly noted hydrogens and deuteriums represent those at the porphyrin

core, and the net charge of -2 results from the assumption that all four sulfonato groups

are deprotonated.) We refer to these below as the TSPP-h and TSPP-d aggregates. To

explore the possible splitting of the J-band into parallel and perpendicularly polarized

helical excitons,33

we obtain the resonance Raman spectra of TSPP-h and TSPP-d at a

range of wavelengths spanning the J-band. The results are discussed in terms of the

structure and dynamics of the aggregate and provide strong support for a structural model

which is entirely different from the conventional linear staircase array.

2.2 Experimental

2.2.1 Sample Preparation. Meso-tetra(4-sulfonatophenyl)porphine dihydrochoride was

purchased from Frontier Scientific. Deuterium oxide (D2O; D, 99.9%) and deuterium

chloride (DCl; D, 99.5%) were purchased from Cambridge Isotope Laboratories, Inc. To

prepare the aggregates, solutions of H2TSPP2-

and D2TSPP2-

diacid monomer were first

prepared by dissolving TSPP in Millipore ()water with HCl and in D2O with DCl,

respectively, to yield concentrations of 50 to 100 M of porphyrin and 1 x 10-3

M of the

respective acid. Concentration was measured by UV-visible absorbance spectroscopy via

Beer’s Law using the diacid monomer molar absorptivity which was 4.43 x 105 L mol

-1

cm-1

at the Soret band maximum of 434 nm. The diacid solutions were combined with

35

more HCl or DCl to induce aggregation and diluted with H2O or D2O to yield aggregate

solutions consisting of 5 M or 50M concentrations of porphyrin and 0.75 M HCl or

DCl, as noted in the text.

2.2.2 UV-visible absorption spectroscopy. Electronic absorption spectra were obtained

using a Shimadzu UV-2501PC UV-visible spectrophotometer. Spectra of aggregate

solutions were measured in 1 cm and 1 mm path length quartz cells for 5 M and 50 M

concentrations respectively.

2.2.3 Resonance Raman Spectroscopy. Resonance Raman scattering (RRS) spectra were

measured in a confocal backscattering arrangement using a 1 cm path length quartz cell

and excited with vertically polarized light from an Argon ion (Ar+) gas laser.

Specifically, the 514.5 nm, 496.5 nm, 488 nm, 476.5 nm, 472.7 nm, and 465.8 nm laser

lines were used to probe different parts of the aggregate J-band. A magnetic cuvette

spinner was used to mix the aggregate solution in the quartz cell so as to avoid potential

photodegradation due to prolonged laser exposure. Both parallel and perpendicularly

polarized Raman scattering (which will be referred to as polarized and depolarized

scattering here) were detected by using a polarizer. Scattered light was dispersed using a

SPEX Triplemate triple monochromator system and detected using a liquid nitrogen

cooled CCD. 50 M concentrations of porphyrin aggregate solutions were used for

Raman measurements to ensure optimal signal. Depolarization ratios of the Raman

modes were determined by dividing the background subtracted depolarized Raman peak

intensity by the background subtracted polarized Raman peak intensity. Subtraction of

fluorescence background was performed using the Peak Analyzer program in Origin Pro

8 using a user-defined fit traced along the observed emission. Resonance Raman spectra

36

of the monomer diacid were obtained in a backscattering arrangement using a 1 cm path

length quartz cell and excited with vertically polarized light from a diode laser at 444.7

nm. Scattered light was dispersed by an Acton SpectroPro 2300i single monochromator

and detected by a thermoelectrically-cooled CCD. Depolarization ratios were checked by

measuring the known depolarization ratios for the Raman modes of cyclohexane and

carbontetrachloride. Both triple and single monochromators were calibrated by measuring

the Raman spectrum of cyclohexane (specifically the 384 cm-1

, 426 cm-1

, 800 cm-1

, 1027

cm-1

, 1155 cm-1

, 1263 cm-1

, 1344 cm-1

, and 1442 cm-1

modes) to a pixel value and fitting

the data to a linear least squares fit.

2.2.4 Resonance Light Scattering. Resonance light scattering (RLS) spectra were

measured with a PTI Quanta Master Fluorimeter using a 1 cm quartz cuvette. RLS

intensities were obtained by synchronous scan of the excitation and emission

monochromators, using a wavelength offset of = 10 nm, from 250 nm to 800 nm. 5

M porphyrin aggregate solutions were used for these experiments to minimize self-

absorption. Polarized and depolarized RLS spectra were also collected using polarizers

for the excitation and emission. The excitation polarizer selected only vertically polarized

light while the emission polarizer selected either vertically or horizontally polarized light

to obtain polarized and depolarized spectra respectively. A depolarizer was implemented

downstream of the emission polarizer to negate polarization bias.

2.2.5 Atomic Force Microscopy Imaging. AFM images were obtained using a Digital

Instruments Atomic Force Microscope in tapping mode. Silicon cantilevers with a spring

constant 42 N m-1

and a resonance frequency of ~330 kHz were employed for imaging. 5

37

M aggregate solutions were deposited on mica substrates and immediately spun dry for

30 s. This procedure yielded highly dispersed images of porphryin aggregates.

38

Figure 2.3 10 m x 10 m AFM image of (a) TSPP-h and (b) TSPP-d

aggregates on mica, 1 m x 1 m AFM image of (c) TSPP-h and (d) TSPP-d

aggregates on mica, and corresponding nanotube cross section data for TSPP-

h (e) and TSPP-d (f) sampled at the white lines shown in the images c and d,

respectively.

39

2.3 Results

2.3.1 Atomic Force Microscopy. Figure 2.3 compares the AFM images of TSPP-h and

TSPP-d aggregates deposited on mica. Both protiated and deuterated porphyrin

aggregates are imaged as nanorods on mica with widths and heights that are the same

within experimental error. Average widths, taken to be the full width at half-height of line

scans such as those shown in Fig. 2.3, were found to be 32.04 ± 2.12 nm for TSPP-h and

32.31 ± 2.23 nm for TSPP-d, and cross-sectional heights were found to be 3.54 ± 0.16 nm

for TSPP-h and 3.62 ± 0.16 nm for TSPP-d. Note that the widths determined from AFM

are slightly larger than the ~27 nm width determined using STM5 owing in part to the

larger apex size of the AFM tip. The average heights and widths were collected from 8

and 10 TSPP-h and TSPP-d nanotubes, respectively and are in accord with previously

published AFM images of the TSPP-h aggregate.5,43,44

The lengths of the nanotubes are

much more broadly distributed than the widths and heights but are on the order of 200

nm, on average, for both the deuterated and protiated aggregates. It is apparent that

deuteration of the porphyrin core and formation of the aggregate in D2O rather than H2O

does not lead to structural differences that can be discerned at the resolution of AFM.

40

2.3.2 Electronic absorption spectroscopy. As shown in Fig. 2.4, the electronic absorption

spectrum of the aggregate is slightly different for the deuterated and protiated forms. For

concentrations that are identical based on the optical spectra of the parent diacid

monomer in H2O and D2O, the aggregate in D2O that forms on addition of 0.75 M DCl

gives a lower peak intensity for the J-band and slightly less absorbance of residual

monomer at 434 nm, which appears as a shoulder to the H-band at 420 nm. These subtle

differences in the optical spectra of TSPP-h and TSPP-d were found to be reproducible

and were also observed in less-concentrated (5 μM) solutions of the aggregate. The H-

band and the strongly red-shifted Q-band, which are characteristic of aggregation, are

similar for the TSPP-h and TSPP-d aggregates. Taken with slightly lower intensity of the

Figure 2.4 Absorption spectra of 50 M TSPP aggregates prepared in

0.75 M HCl in H2O (black) and in 0.75 M DCl in D2O (red). The inset

shows the J-band on an expanded scale.

41

434 nm shoulder in TSPP-d, this suggests that the lower peak intensity of the J-band is

not a consequence of reduced tendency to aggregate in the deuterated system. Rather,

there is a slight increase in the full-width at half maximum (FWHM) of the J-band from

343 cm-1

to 408 cm-1

on deuteration such that the area under the optical spectrum is

conserved. The optical spectra of the monomer diacid in HCl/H2O and DCl/D2O are

shown in Fig. 2.11 of Supporting Information and reveal minor effects of isotopic

substitution, i.e., small blue shifts of the B and Q bands of the deuterated diacid

monomer.

Figure 2.5 Polarized resonance Raman spectra of 50 M TSPP aggregates in

0.75 M HCl and H2O (black) and in 0.75 M DCl and D2O (red) excited at 488

nm. The prominent Raman modes are labeled in each spectrum and the spectrum

of the deuterated TSPP aggregates is offset by +3000 arbitrary intensity units.

42

2.3.3 Resonance Raman Spectroscopy. While subtle differences in the absorption spectra

of TSPP-h and TSPP-d are found, much larger changes in the resonance Raman

scattering (RRS) spectra are observed, as seen in Fig. 2.5, which depicts the polarized

resonance Raman spectra excited at 488 nm, near the 490 nm absorption maximum of the

J-band. Fig. 2.5 reveals frequency shifts of some of the prominent Raman modes as well

as changes in the relative intensities of the Raman modes upon deuteration. The most

notable frequency shifts observed are those of the 983 cm-1

and 1013 cm-1

modes in the

protiated aggregate which shift to 957 cm-1

and 1004 cm-1

in TSPP-d. These two modes

are pyrrole breathing modes and thus the red shifts can be attributed to the substitution of

deuterium ions with the labile protons in the porphyrin core. The putative ruffling and

doming modes are shifted from 243 and 316 cm-1

to 239 and 315 cm-1

on deuteration.

Additionally, deuteration results in an increase in the intensity of the higher frequency

modes, most notably the 697 cm-1

and 957 cm-1

modes, relative to the low-frequency

modes at 239 cm-1

and 315 cm-1

. As shown in Fig. 2.12 of Supporting Information,

isotopic substitution to form the monomer diacid D2TSPP2−

in D2O does not greatly

perturb the relative intensities (with exception of the 933/952 cm-1

mode). This leads to

the conclusion that the differences in relative Raman intensities shown in Fig. 2.5 result

from the effect of isotopic substitution on the excited state structure and dynamics of the

aggregate. In general, larger isotope shifts are found for vibrational modes of the

monomer than for the aggregate.

43

Examining the polarized and depolarized Raman spectra of the protiated TSPP

aggregates at different excitation wavelengths (Fig. 2.6) we observe changes in the

relative intensity of different Raman modes as the excitation wavelength is varied from

488 nm to 465.8 nm. The broad background peaking at an absolute wavelength of 492

nm is the fast-relaxing (~360 fs) J-band fluorescence previously observed by Kano and

Kobayashi.45

The Stokes shift observed here is less than 100 cm-1

in agreement with Ref.

45. The maximum in this fluorescence background (that is, the absolute frequency) is

roughly independent of excitation wavelength, though the width and shape vary. It is

apparent that even accounting for the changing fluorescence background, there is

Figure 2.6 Resonance Raman (RR) spectra of 50 M TSPP aggregates in 0.75 M

HCl excited at a) 488.0 nm, b) 476.5 nm, c) 472.7 nm, and d) 465.8 nm. The

polarized and depolarized spectra are shown in black and red respectively.

44

considerable variation in the relative intensities with excitation wavelength, whereby the

low-frequency modes decrease in intensity and the higher frequency modes increase in

intensity as the excitation wavelength decreases. Furthermore, as the excitation

wavelength is scanned, the intensities of Raman modes that overlap the J-band

fluorescence are enhanced while modes with scattering frequencies outside the

fluorescence band are relatively less intense. It should be stressed that these changes in

relative intensities with excitation wavelength are not the result of differential self-

absorption of the scattered light, the effects of which are minimized in the confocal

backscattering geometry used. Owing to the small half-width of the J-band and its peak at

490 nm, it can be seen that only the low-frequency modes in the 488 nm spectrum are

significantly attenuated by self-absorption, yet they have the greatest relative intensity at

this excitation wavelength. Changes in the relative Raman intensities as the excitation

wavelength is varied suggest overlapping resonant excited states, as expected for a helical

nanotube in which the J-band of the isolated cyclic N-mer is split into closely-spaced

longitudinal and transverse excitons.6 For example, the trends seen in Figs. 2.6 and 2.7

could be interpreted to be due to stronger coupling of higher frequency vibrations to the

higher energy component of the J-band while the low-frequency modes have larger

displacements in the lower energy excitonic state. To address this question, Raman

spectra were obtained at 496.5 and 514.5 nm (Figs. 2.13, 2.14, and 2.15 of Supporting

Information), on the red edge of the J-band, where there is little interference from

fluorescence. As seen in Fig. 2.13 and 2.14, lower relative intensities of the low-

frequency modes of TSPP-d compared to TSPP-h are also observed at excitation

wavelengths of 496.5 and 514.5 nm. Fig. 2.15 compares the RRS spectra of TSPP-h and

45

TSPP-d at 514.5 nm, showing larger intensity of higher-frequency modes for the latter. In

addition, the apparent increase in relative intensity of ruffling and doming modes,

observed for both aggregates as the wavelength is tuned from 465.8 to 488 nm, does not

continue when the excitation is tuned further to the red. Instead, the intensities of the

ruffling and doming modes in the 514.5 nm spectrum are comparable to but generally

less than those of modes above 700 cm-1

. This suggests that the intensities of Raman

modes are indeed boosted when their absolute frequencies overlap the J-band

fluorescence. This phenomenon, as explained further below, would not be expected in the

case of resonance via a single excited electronic state.

Table 2.1 Depolarization Ratios of Prominent Raman Modes of TSPP-h Aggregates

at Different Excitation Wavelengths.

Wavelength (nm)\Raman Shift (cm-1)

243 316 698 983 1013 1228 1533

488.0 0.45 0.44 0.41 0.48 0.45 0.53 0.61

476.5 0.45 0.48 0.45 0.40 0.37 0.42 0.44

472.7 0.50 0.52 0.44 0.39 0.39 0.40 0.44

465.8 0.55 0.61 0.71 0.46 0.52 0.41 0.41

Further evidence for the composite nature of the J-band is provided by the

excitation wavelength dependence of the depolarization ratio as shown in Table 2.1. As

previously shown,6 at an excitation wavelength of 488 nm, the low-frequency modes

give values of that are significantly larger than , which shows that the J-band is not

the result of a transition to a single nondegenerate excited state. Instead, the values in

Table 2.1 are consistent with the expectation for a helical aggregate, which should have a

Raman tensor for which xx = yy zz, where the xx and yy components derive from the

transverse component of the J-band and the zz component is resonant with the

longitudinally polarized transition. Depolarization ratios thus change as the excitation

46

frequency is scanned owing to different wavelength-dependence of the components of the

Raman tensor. However, one should note that for each mode, the depolarization ratio

tends to be lowest when the mode is closest to the peak maximum of the J-band

fluorescence, with the exception of the 698 cm-1

mode, suggesting that changes in

depolarization ratio may also be influenced by contributions of the fast-relaxing

fluorescence. The depolarization ratio for the fluorescence is also significant as it reveals

the angle between the transition dipole for absorption and emission, discussed further

below. We find ρ ≈ 0.5 from a fit to the fluorescence background in the polarized and

depolarized spectra at the three lower excitation wavelengths. The width of the observed

fluorescence background (fitted to a polynomial function) varies with excitation

wavelength, which along with the small Stokes shift reveals the unrelaxed nature of this

emission. It was not possible to fit the observed fluorescence background to a single

Gaussian independent of excitation wavelength.

Fig. 2.7 shows the polarized and depolarized resonance Raman spectra of TSPP-d

as a function of wavelength as in Fig. 2.6. Similar trends are seen for TSPP-d and TSPP-

h, i.e.; relative intensities of Raman modes vary with excitation wavelength such that

modes which overlap the fluorescence tend to be more intense. Table 2.2 shows that the

TSPP-d aggregate Raman modes also exhibit depolarization ratio dispersion similar to

that seen for TSPP-h. For example, ρ for both the 1227 and 1534 cm-1

modes is highest at

488 nm and decreases with decreasing excitation wavelength. In most cases, for the same

mode and excitation frequency, depolarization ratios are slightly larger for the deuterated

aggregate. Additionally, depolarization ratios tend to be lowest when the mode is closest

to the J-band fluorescence peak maximum. The dispersion in the depolarization ratios is

47

plotted as a function of excitation wavelength and is shown in Figs. 2.16 and 2.17 of

Supporting Information, including the values at excitation wavelengths to the red of the J-

band. These graphs reveal fairly smooth trends in ρ with excitation wavelength, and an

apparent convergence of ρ for different modes to values near either ~0.3 or ~0.5 at the

longest excitation wavelengths used.

For both TSPP-h and TSPP-d, the depolarization ratio of the fast-relaxing

fluorescence ρ = Iperp/Ipar is about 0.5, where Iperp (Ipar) is the emitted light polarized

perpendicular (parallel) to the polarization direction of the incident light. In the

conventional notation for fluorescence anisotropy, this translates to r = (Ipar − Iperp)/ (Ipar

+ 2Iperp) ≈ 0.25. Given the fast relaxation of the J-band fluorescence and the large size of

the aggregate, it is assumed that the rotational motion of the aggregate during the lifetime

of the excited state can be ignored and thus r = r0 = 0.2(3cos2α − 1) is a function of the

angle α between the absorption and emission transition dipoles.46

The data is consistent

with an angle α of 30°. If the absorption and emission transition dipoles were parallel,

we would see r = 0.4 (ρ = 1/3), while perpendicular transition dipoles would result in r =

−0.2 and ρ =2.

48

Table 2.2 Depolarization Ratio of Prominent Raman Modes of TSPP-d Aggregates

at Different Excitation Wavelengths.

Wavelength (nm)\Raman Shift (cm-1)

239 315 697 957 1004 1225 1534

488.0 0.50 0.48 0.48 0.52 0.52 0.57 0.62

476.5 0.50 0.49 0.44 0.40 0.36 0.44 0.45

472.7 0.49 0.52 0.48 0.41 0.41 0.40 0.47

465.8 0.54 0.52 0.59 0.50 0.53 0.42 0.40

Figure 2.7 Resonance Raman spectra of 50 M TSPP aggregates in 0.75 M DCl in

D2O excited at a) 488 nm, b) 476.5 nm, c) 472.7 nm, and d) 465.8 nm. The

polarized and depolarized spectra are shown in black and red respectively.

49

2.3.4 Resonance Light Scattering. Resonance light scattering (RLS) of chromophore

aggregates is a powerful measure of the coherence of the excited electronic state.47,48

Fig.

2.8 displays the RLS spectra of TSPP-h and TSPP-d obtained by synchronous scan of the

emission and excitation wavelengths in a fluorimeter. (Note that the very weak

fluorescence background seen in the resonance Raman spectra of Figs. 2.6 and 2.7 makes

an entirely negligible contribution to the very strong RLS signal shown in Fig. 2.8.) In

agreement with previous reports,49

strong RLS signal is observed in the vicinity of the J-

band (the dominant peak at 491 nm) and weaker intensity is seen at the wavelength of the

H-band (the small peak at 416 nm). The dip at about 490 nm is the result of self-

absorption by the strong J-band, and the jagged features just to the blue of this dip are

Figure 2.8 Resonance Light Scattering spectra of 5 M TSPP aggregates

prepared in 0.75 M HCl in H2O (black) and in 0.75 M DCl in D2O (red).

RLS response is most prominent at 491 nm for both protiated and

deuterated aggregates.

50

variations in the lamp intensity. There is a striking enhancement of the RLS signal from

TSPP-d aggregates, which is nearly twice the magnitude of the RLS from TSPP-h

aggregates. Though RLS intensity does increase with the physical size of the

aggregate,47,50

AFM images show that TSPP-h and TSPP-d aggregates are similar in size.

Thus, as discussed further below, the differences in RLS shown in Fig. 2.8 must be the

result of increased excitonic coherence of the deuterated aggregate.

As shown in Fig. 2.9, polarized and depolarized RLS data were obtained for both

TSPP-h and TSPP-d aggregates, using vertically polarized excitation and detecting the

parallel and perpendicular components of the scattering. Both protiated and deuterated

aggregates exhibit depolarization ratio dispersion, where the depolarization ratio is ~0.15

at the J-band peak maximum, increasing as the wavelength decreases across the J-band.

This observed increase in the depolarization ratio of resonance Rayleigh scattering at

higher energies has been reported previously by Stanton et al.51

who calculated the

depolarization ratio for a model system with axial symmetry. Well within the respective

Figure 2.9 Polarized (black) and depolarized (red) resonance light scattering

(RLS) spectra of 5 M TSPP aggregates in 0.75 M HCl in H2O (a) and in 0.75 M

DCl in D2O (b). The depolarization ratio as a function of wavelength is shown in

blue.

a b

51

H- and J-bands, the depolarization ratio for RLS should reflects the symmetry of the

polarizability tensor, just as for resonance Raman spectra. The J-band value of the

depolarization ratio of 0.15 found here is similar to the value of 0.17 reported for the

TSPP aggregate in Ref. 47 and is consistent with an axially symmetric polarizability

tensor for which αzz is on the order of five times larger than αxx = αyy. However, in Ref.

47, the result was interpreted using a linear staircase model with a nonzero slip angle,

giving components of the transition moment both parallel and perpendicular to the chain.

Such a model is inconsistent with the structural data from scanning probe microscopy and

with the nonplanarity of the monomer diacid porphyrin. We also note that dispersion of

the RLS depolarization ratio across the J-band is in accord with the composite nature of

the band. On the blue side of the J-band, the depolarization ratio tends toward a value of

1/3, the limiting value for a single nondegenerate resonant state. On the red side of the J-

band, on the other hand, the trend is toward a depolarization ratio typical of a doubly

degenerate transition (1/8), in good agreement with expectations for a helical aggregate.

Curiously, the weak RLS signal in the vicinity of the H-band shows no

perpendicular component. This is the behavior expected for a spherically symmetric

polarizability tensor. It is attractive to consider this possibility, as it would explain the

reported low flow-induced linear dichroism of the H-band,1,12

as well as our own

polarized surface RRS data6 which show little dependence on the polarization of the

incident and scattered light when the Raman spectrum of the surface-adsorbed aggregate

is excited within the H-band.

52

2.4 Discussion

Though AFM images of the TSPP-h and TSPP-d aggregates reveal little effect of

isotopic substitution on the ground state structure, changes to the optical absorption,

resonance Raman, and resonance light scattering spectra reveal significant differences in

the excited state structure and dynamics. The increase in the width of the J-band for the

deuterated aggregate, taken alone, might be considered to reflect decreased coherence of

the excited electronic state, since exchange narrowing should result in a reduction of the

absorption linewidth by approximately 2/1

cN , where Nc is the coherence number.52,53

However, this conclusion conflicts with the enhanced RLS of TSPP-d over TSPP-h,

which indicates a larger coherence number for TSPP-d. We speculate that this results

from stronger coupling among the putative cyclic N-mers which comprise the helical

nanotube, resulting in greater splitting of the overlapping longitudinal and transverse

helical excitonic transitions and hence a slightly broader absorption band. Excitonic

coupling leads to an increase in the transition moment by a factor of 2/1

cN , and the RLS

signal scales as the fourth power of the transition moment. Hence, the roughly two-fold

increase in RLS for TSPP-d reflects an increase in the coherence number by a factor of

about 1.4.

What is the basis for increased coherence in the deuterated aggregate? Spano et

al.54,55

have shown that increased exciton-phonon coupling leads to a decrease in the

coherence number. The strength of exciton-phonon coupling is proportional to the

amplitude of relevant phonon modes. Several prominent modes of H2TSPP2−

are

enhanced in the RRS of the aggregate and undergo red-shifts on deuteration, notably the

low-frequency modes at ~240 and 314 cm-1

and the pyrrole vibrations near 980 and 1000

53

cm-1

. In addition, if water is the “glue” responsible for the hierarchical structure of the

aggregate, then very low-frequency phonon modes associated with hydrogen bonds

would be expected to be strongly coupled to the exciton, contributing to different values

of Nc for TSPP-h and TSPP-d. Regardless of the nature of the relevant vibrations, the

increase in the coherence number on deuteration also explains the slight increase in

width, by a factor of ~1.2, of the J-band. The value of Nc is proportional to the strength of

the intermolecular transition-dipole coupling.56

If indeed it is the water-mediated

excitonic coupling of cyclic N-mers that is strengthened in the deuterated aggregate, then

we can also understand the increased width of the J-band to be a result of a slight increase

in the splitting of the longitudinal and transverse helical excitons. Similarly, the FWHM

of the RLS spectrum is slightly larger for TSPP-d (~480 cm-1

) than for TSPP-h (390 cm-

1), also suggesting increased separation of the J-band components.

Isotope effects on the resonance Raman spectra of the aggregate provide

additional insight into the exciton coherence. The relative RRS intensities of the

monomer diacid are quite similar for H4TSPP2−

and D4TSPP2−

, but the Raman spectra of

the aggregate are very dependent on isotopic substitution. Overall, we see greater

enhancement of out-of-plane vibrations (low-frequency modes) relative to other

vibrations in TSPP-h than in TSPP-d, regardless of excitation wavelength. RRS

intensities are determined by the dimensionless displacements (Huang-Rhys factors) of

the various normal modes, and these too influence the coherence number of the

aggregate.52

Increasing diagonal disorder diminishes Nc, more so as the Huang-Rhys

factor increases. The larger relative intensity of the ruffling and doming modes in TSPP-h

could therefore also contribute to lower coherence compared to TSPP-d.

54

For both TSPP-h and TSPP-d, depolarization ratios and relative Raman intensities

vary as the excitation wavelength is tuned across the J-band. Overlapping resonant

electronic states lead to interference effects; i.e., the total Raman intensity is obtained by

adding the amplitudes of the transition polarizability contributed by each resonant state,

then squaring the result. Such interference effects lead to relative Raman intensities

which vary strongly with excitation wavelength.57,58

In addition, resonance via two or

more excited states with different transition moment directions results in wavelength

dependence of the depolarization ratio. Thus our RRS strongly suggests that the J-band

derives from transitions to more than one excited electronic state polarized in different

directions. Owing to the interference of these overlapping states, the observed subtle

differences in the shape of the absorption spectrum translate into large variations in the

relative intensities of different Raman modes as a function of excitation wavelength.

However, the observed increase in intensity of Raman modes that overlap the

weak J-band fluorescence merits further consideration. The small Stokes shift and short

lifetime of this fluorescence highlights the common theoretical roots of these two

spontaneous light emission (SLE) processes.59,60,61

The ability to write the total SLE as a

sum of Raman-like (RL) and fluorescence-like (FL) terms is an approximation that is

justified when the ratio of the vibrational to the electronic linewidths is negligible. The

exchange narrowing of the J-band strains this approximation somewhat, but the total J-

band width of over 300 cm-1

exceeds the typical half-width of a Raman band by at least

an order of magnitude. Following Mukamel61

we write the cross section for SLE as:

(2.1)

where ω0 and ωS are the incident and scattered light frequencies, respectively, and

55

220

,,22

0

24

0

)(

ˆ4)(2

)(

1),(

Sbc

Sac

bca ba

cbbageSSLE vvvvaPS

(2.2)

Eq. 2.2 was obtained from expressions in Ref. 60 and 61 with the assumption of a single

excited electronic state, where a and c label the initial and final vibrational states within

the ground electronic state, respectively, and b is a vibrational state within the resonant

electronic state. ge is the transition dipole moment in the Condon approximation, P(a) is

the fraction of molecules in initial state a, /)( iffi EE , and ba vv and ab vv are

Franck-Condon overlaps. Γ, and γ are the total dephasing rate, pure dephasing rate,

and inverse lifetime, respectively.

Eq. 2.2 assumes spectral broadening in the homogeneous (fast modulation) limit which

seems reasonable for the exchange-narrowed J-band. In addition, the inverse lifetimes of

vibrational states a and c were considered negligible, resulting in the RL component

being approximated by the delta function spikes in Eq. 2.2, centered at Raman shifts ω0 –

ωS which match the frequencies ωca of vibrational transitions. The FL component, on the

other hand, is given by the second term in the curly brackets of Eq. 2.2 and results in SLE

which is distributed over a range of wavelengths with a FWHM of 2Γ. Though the

assumption that Γ is independent of frequency is likely to be invalid for excitonically

coupled molecules,50

Eq. 2.2 is useful to consider because it shows that resonance with a

single electronic state can’t lead to an interference between the RL and FL components as

they are clearly additive. On the other hand, simultaneous resonance with overlapping

excitonic states requires the addition of the RL and FL terms at the amplitude level and

56

the square of the sum would result in cross-terms which mix the RL contribution from

one excited state with the FL contribution from the other. We propose that this is the

mechanism whereby the Raman modes undergo a boost in intensity when the scattered

light frequency overlaps the fluorescence. Along with the depolarization ratios and their

dispersion, this is further evidence for the composite nature of the J-band.

The intensity and width of the J-band fluorescence at a given excitation

wavelength is not very different for TSPP-h and TSPP-d. This conclusion is subject to

further investigation using a suitable intensity standard, but comparison of the data in

Figs. 2.6 and 2.7 do not indicate isotope effects on the intensity of the fluorescence

background as large as those seen in RLS. Further, the depolarization ratio of this

fluorescence indicates rotation of the transition moment (~30°) within the <400 fs

lifetime of the excited state. We also observe an increase in the width of this fluorescence

(~450 to 500 cm-1

depending on excitation wavelength) over that of the J-band. We

propose that this is the result of exciton-phonon scattering which relaxes the selection

rules for excitonic transitions and thus distributes the J-band fluorescence over a greater

range of wavelengths.

57

The dramatic differences in the relative Raman intensities of TSPP-h and TSPP-d

at all excitation wavelengths within the J-band, despite only subtle differences in the

absorption spectrum, highlight the composite nature of the J-band in the helical nanotube.

Fig. 2.10 outlines the spectroscopic consequences of the model shown in Fig. 2.2. The

degenerate Soret band of the monomer diacid (Fig. 2.10a) is split into a doubly

degenerate J-band (Fig. 2.10b) in the cyclic N-mer, with components in the X and Y

directions defined in the plane of the N-mer. The monomer transition moments oriented

perpendicular to the ring (Fig. 2.10c), lead to a nondegenerate blue-shifted transition (H-

band) of the cyclic N-mer. Experiment suggests that the perpendicular transition moment

is reduced on assembly, accounting for the weak coherence of the H-band.6

Further

coupling of the J-band components of the rings on assembly into the nanotube is

envisioned with the help of the two-dimensional hexagonal array shown in Fig. 2.2d. A

helical nanotube with dimensions in accord with our STM images (2 nm shell thickness,

Figure 2.10 a) Orthogonal Soret-band transition moments of the diacid

monomer, b) in-plane components of the transition moments μge,x lead to the

degenerate J-band of an individual cyclic N-mer, while c) transition moments

polarized perpendicular to the plane of the ring, μge,y lead to the N-mer H-

band. d) Two-dimensional hexagonal array of cyclic N-mers showing the

alignment of the degenerate J-band transition moments of the cyclic N-mer.

The Z-axis depicted here becomes the long axis of the nanotube when the

sheet is rolled into a cylinder by overlapping the origin and the tip of the

vector C.

58

flattened widths of about 27 nm) can be achieved by rolling the sheet to overlap the

origin with the tip of the C vector.

A rough estimate of the splitting of the J- and H-bands in an isolated cyclic N-mer

can be obtained with a point transition dipole model, where the coupling strength of

adjacent molecules is given by

ruruuuhcr

Vμ

ge ˆˆˆˆ3ˆˆ21213

2

(2.3)

where iu is a unit vector in the direction of the transition moment of molecule i, r is the

distance between neighboring molecules, and r is the corresponding unit vector in that

direction. Clearly, the coupling strength VJ for the transition moments depicted in Fig.

2.2b is negative, while VH (Fig. 2.2c) is positive. The nonplanarity of the monomers and

uncertainty about the orientation and magnitudes of the transition moments μge,x and μge,y

after assembly into the ring prevents us from using Eq. 2.3 to make quantitative

predictions about the splitting of the H and J band in the isolated N-mer. However, we

are only interested in an order of magnitude estimate here. Assuming a ring of 16

monomers that is 6 nm in diameter, r = 1.2 nm is the separation between the molecular

centers. This results in a coupling strength on the order of 32 / hcrge 420 cm-1

, assuming

that μge,x and μge,y are both equal to the monomer value of about 12 Debye. For a cyclic

aggregate with even N, the excitonic states are indexed by the quantum number k = 0,

1, 2,….N/2, and the resulting transitions corresponding to the split Soret band are given

by62

)/2cos(2/~)/2cos(2/~

NkVhcE

NkVhcE

HBH

JBJ

(2.4)

59

For the sake of discussion, assume that the in-plane transition moments make an angle of

zero with respect to r, leading to VJ on the order of −800 for a cyclic 16-mer. VH is then

420 cm-1

if it is assumed that μge,x = μge,y. For the in-plane transition moments (J-band),

only the 1k excitonic states are allowed, while the H-band results in one allowed

transition to the k = 0 excited state. Thus the ballpark estimate of the splitting of the

Soret band in the cyclic N-mer with N = 16, is on the order of 2400 cm-1

, compared to the

observed difference of 3400 cm-1

between the H-band (420 nm) and the J-band (490 cm).

Next consider the further coupling of the J-band excitonic transitions of the N-

mers when they are assembled into the helical nanotube as depicted in Fig. 2.2d. Theory

shows that for a helical nanotube of infinite length, transitions polarized both parallel and

perpendicular to the long axis are expected.63

The former result from the component of

the monomer transition moment parallel to the long-axis, while the component of the

monomer transition dipole moment perpendicular to this axis results in a doubly-

degenerate, perpendicularly polarized transition. In the present case the “monomers” that

comprise the helical aggregate are cyclic N-mers for which the transition dipole moment

is amplified by a factor of N1/2

. Taken with the fact that the distance between coupled

units is 6 nm (compared to about 1 nm in the N-mer), the coupling strength for adjacent

N-mers is reduced from that of adjacent monomers by a factor 16/63 = 0.074, i.e. V is on

the order of a few hundred cm-1

. This translates into a splitting of the J-band in the

nanotube into longitudinal and transverse components which are separated by only about

5 nm.

When Raman spectra are resonant with a single excited electronic state, the

excitation profiles are directly related to the absorption profile.64,65

If this were the case

60

here, the similar absorption spectra of TSPP-h and TSPP-d would have correlated to

similar relative Raman intensities, in contrast to our results. Interference from resonance

via two or more closely spaced excited states, on the other hand, results in relative Raman

intensities and, for different directions of the transition moments, depolarization ratios

that vary with excitation wavelength. Weak splitting of the J-band into parallel and

perpendicular components, owing to the coupling of the transition moments of

hierarchical subunits, is strongly supported by the present results. We further propose that

this splitting is different for the aggregate in protiated and deuterated environments.

Stronger coupling among the sub-units in the latter case explains the larger coherence

number deduced from RLS and larger width of the J-band. In addition to explaining our

own polarized surface Raman data,6 the model accounts for the widely-reported

incomplete polarization of the J-band for aligned aggregates.1,12,13

Our model can be contrasted with others that have attempted to account for the

existence of hollow nanotubes. Kitahama et al.13

proposed that the nanotubes result from

alignment of linear arrays of conventional J-aggregates arranged in lengthwise stripes in a

tubular fashion. However, a linear array is not supported by the known nonplanarity of

the monomers, and the model proposed in Ref. 13 would not lead to a splitting of the red-

shifted component of the Soret band. Based on their small-angle X-ray study, Gandini et

al.15

proposed a tubular structure constructed from stacked rings of circular arrays in

which the porphyrin planes are arranged perpendicular to the tube axis. While such a

structure could explain the ~2 nm shell thickness observed in STM5,6

and cryo-electron

microscopy,12

this model can not account for the presence of a transition polarized

parallel to the long axis. Rotomskis et al.14

interpreted their AFM data with a model in

61

which a linear array (conventional staircase aggregate) of 60 or 70 molecules curls

around to form a 20-nm diameter ring. These rings were then presumed to stack into

nanotubes which were flattened on the surface and imaged as rectangular nanorods. The

authors do not explain what determines the fixed diameter of the rings or the 4 nm

thickness of the flattened tubes. Vlaming et al.12

, on the other hand, formed a helical

nanotube from rolling up a two-dimensional lattice of overlapping porphyrins, presumed

to be planar, and varied the tilt angles to get a calculated spectrum in good agreement

with experiment. The small tilt angles they derived could not explain the 2-nm shell

thickness that they observed in their cryo-electron microscopy data, which they attributed

to the presence of condensed water. Though the models of Ref. 14 and 15, and to some

extent that of Ref. 12 agree with low-resolution (AFM) structural data, none can account

for the wavelength-dependence of polarized resonance Raman spectra. To our

knowledge, our hierarchical structural model is the only one that can account for a small

splitting of the J-band. In addition, our model is based on detailed structural data

showing that the nanotubes are comprised of 6-nm disks which are ~2-nm thick.

2.5 Conclusions

In this work, the possible influence of water-mediated hydrogen bonds on the

structure and optical properties of the TSPP aggregate have been investigated. While

structural differences in the aggregate deposited from DCl/D2O and HCl/H2O cannot be

discerned from AFM images, and deuteration only slightly perturbs the optical spectrum,

significant effects on the resonance Raman, and resonance light scattering spectra are

found. Invoking a model in which cyclic N-mers of strongly coupled porphyrins are held

together in a helical nanotube by hydrogen bonds which permit further excitonic

62

coupling, our results are consistent with an increase in the coherence number and increase

in excitonic interactions between cyclic N-mers in the deuterated system. This increased

coupling leads to a larger splitting of the transverse and longitudinal helical excitons and

enhanced resonance light scattering for the deuterated aggregate. In addition, variations

in the relative Raman intensities between the protiated and deuterated aggregate suggest

relatively more reorganization along low-frequency vibrations in TSPP-h than in TSPP-d,

which may also contribute to higher exciton-phonon coupling and lower coherence in the

protiated aggregate. To our knowledge, this is the first report of the influence of isotopic

substitution on exciton coupling, and the results herein provide strong evidence for the

role of exciton-phonon coupling in limiting coherence. Further, spectroscopic data

presented here provide evidence that water-mediated hydrogen bonds influence the

hierarchical structure of the aggregate and the resulting excitonic coupling.

2.6 Acknowledgments:

The support of the National Science Foundation through grant CHE 0848511 is gratefully

acknowledged. We also thank the National Science Foundation for support for the

atomic force microscope through grant CHE 0234726. We are grateful to our colleague

Prof. James Brozik for the use of his triple monochromator.

63

2.7 Supporting Information

Figure 2.11. Absorbance spectra of 50 M TSPP diacid monomer in 0.001 M HCl

in H2O (black) and in 0.001 M DCl in D2O (red). Insets show the blue shift which

occurs upon deuteration for both the B- and Q-bands.

B-band

Q-band

64

Figure 2.13 Polarized (black) and depolarized (red) resonance Raman spectra of

TSPP-h aggregates excited with (left) 496.5 nm (right) and 514.5 nm.

Figure 2.12. Polarized resonance Raman spectra of 50 M

TSPP diacid in 0.001 M HCl in H2O (black) and 0.001 M

DCl in D2O (red) excited at 444.7 nm. The D2TSPP2-

spectrum is offset by +20000.

65

Table 2.3 Depolarization Ratios of Prominent Raman Modes of TSPP-h Aggregates

Excited at 514.5 nm and 496.5 nm.

Wavelength (nm)\Raman Shift (cm-1)

243 316 698 983 1013 1228 1533

514.5 0.51 0.47 0.51 0.38 0.51 0.36 0.40

496.5 0.41 0.41 0.52 0.52 0.58 0.54 0.53

Table 2.4 Depolarization Ratios of Prominent Raman Modes of TSPP-d Aggregates

Excited at 514.5 nm and 496.5 nm.

Wavelength (nm)\Raman Shift (cm-1)

239 315 697 957 1004 1225 1534

514.5 0.53 0.47 0.52 0.36 0.51 0.38 0.49

496.5 0.39 0.40 0.44 0.45 0.53 0.49 0.56

Figure 2.14 Polarized (black) and depolarized (red) resonance Raman spectra of

TSPP-d aggregates excited at (left) 496.5 nm and (right) 514.5 nm.

66

Figure 2.15 Polarized resonance Raman spectra of TSPP-h (black) and

TSPP-d (red) excited at 514.5 nm. The backgrounds were shifted to obtain

overlap of the intensities of the two low frequency modes.

67

Figure 2.16 Depolarization ratio dispersion graph for the seven

prominent modes of the TSPP-h aggregate resonance Raman

spectrum. The six points for the six excitation wavelengths

implemented (465.8 nm, 472.7 nm, 476.5 nm, 488 nm, 496.5

nm, and 514.5 nm) are connected by a polynomial spline fit.

68

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73

Chapter 3 Resonance Raman Spectra of

Individual Excitonically Coupled Chromophore

Aggregates

Abstract

We report resonance Raman spectra of individual porphyrin nanotubular

aggregates of meso-tetra(4-sulfonatophenyl)porphyrin (TSPP) deposited on glass. Using

a novel internal/external standard method for aqueous phase aggregate, we show that

absolute Raman cross-sections per molecule for low-frequency vibrational modes are

enhanced with excitation which is resonant with the J-band. Large Raman cross sections

of the prominent Raman modes allow for the determination of single-aggregate resonance

Raman spectra without surface enhancement. Variations in the relative intensities of low-

and high-frequency Raman modes and images of the resonance light scattering in epi-

illumination reveal local variations in the exciton coherence and allow the possible

correlation between Raman intensity and coherence to be explored. Polarized Raman

spectra of individual aggregates confirm that the J-band is a composite of two closely-

spaced vibronically coupled transitions polarized parallel and perpendicular to the long

axis of the aggregate, in accordance with our structural model of a hierarchical helical

nanotube. Our experimental results provide insight into the concept of aggregation-

enhanced Raman scattering.

Keywords: porphyrin aggregate, single-aggregate Raman, excitons, helical nanotubes

74

3.1 Introduction

Excitonic coupling of strongly allowed electronic transitions in chromophore

aggregates results in a number of interesting optoelectronic properties, such as excited

state delocalization, enhanced light-harvesting and efficient energy transfer. These

properties depend strongly on the aggregate supramolecular structure and on static and

dynamic disorder within the assembly, which limit the coherence number, Ncoh, the

number of molecules over which the exciton is delocalized.1,2,3

While images from

scanning probe4,5,6,7

and electron microscopy8,9

experiments reveal the gross morphology

of molecular aggregates, determination of their internal structure, for example by X-ray

diffraction methods,10

is challenging, and thus intermolecular configurations are often

inferred from perturbations to the optical spectra. The contribution of structural

heterogeneity in an ensemble of aggregates complicates the attempt to use optical spectra

to determine intermolecular couplings, which dictate shifts in the optical spectra, and

coherence numbers, which influence spectral linewidths. Single-aggregate Raman

spectroscopy provides a means to obtain information about internal structure and the

nature of the resonant electronic transition without complications from aggregate

heterogeneity.

We have recently reported the results of scanning probe microscopy and polarized

resonance Raman spectroscopy studies of the excitonically coupled aggregate of meso-

tetra(4-sulfonatophenyl)porphyrin (TSPP).4,11,12,13,14

Raman spectra and images are

consistent with a hierarchical structural model in which cyclic N-mers assemble into a

helical nanotube which is flattened when deposited on a surface. In the present work, we

show that a combination of excitonic coupling, which serves to concentrate the resonance

75

Raman enhancement into a narrow wavelength range, and self-assembly, which

concentrates the molecules within the focal volume, enables the determination of Raman

spectra of single TSPP aggregates and small bundles thereof, without the use of surface

enhancement via noble metals. We report variations in the Raman spectra of individual

aggregates and spectral perturbations that are suggestive of aggregate-to-aggregate

variations in coherent coupling. Polarized single-aggregate Raman measurements reveal a

J band which is incompletely polarized along the long axis of the flattened nanotube,

consistent with our previous model of a helical nanotube built up from cyclic N-mers.

We also present a novel internal/external standard approach for determining the

Raman cross-sections of the aggregate and monomer, enabling us to make a quantitative

assessment of the significance of aggregation-enhanced Raman scattering, or AERS. As

proposed by Akins15

and explored in a number of publications from his group16,17,18

and

others,19,20,21

excitonic coupling has the potential to lead to enhancements in the

resonance Raman intensity. In addition to reporting the absolute Raman cross-sections of

the solution phase monomer and aggregate at similar detunings, we use resonance light

scattering and resonance Raman spectra of individual aggregate of TSPP on glass to

explore the role of coherence in the heterogeneity of the Raman intensities.

3.2 Experimental

3.2.1 Materials. Meso-tetra(4-sulfonatophenyl)porphyrin in its diacid form was

purchased from Frontier Scientific. Aqueous solutions of TSPP aggregates were prepared

by combining aqueous solutions of TSPP diacid and hydrochloric acid (HCl) so that the

concentration of HCl was 0.75 M and the concentration of TSPP was 50 M for the

quantitative resonance Raman experiments. Aggregates samples for single aggregate

76

spectroscopy were prepared from solutions containing 5 M TSPP and 0.75 M HCl

which were drop-cast onto glass coverslips and allowed to dry.

3.2.2 Quantitative Resonance Raman Spectroscopy. Absolute Raman cross sections of

the aggregate in solution, computed on a per-molecule basis, were determined using an

internal/external standard method shown in Figure 3.1. Resonance Raman spectra of the

aqueous aggregates or monomers and a transparent reference (either neat cyclohexane or

acetonitrile) were measured simultaneously using 488 nm light from an Ar ion laser. The

scattered light was dispersed with a SPEX Triplemate triple monochromator and detected

with a liquid nitrogen cooled CCD camera. Polarized spectra were collected using a

Melles-Griot polarizer for polarization selection followed by a Thorlabs DPU-25

depolarizer for scrambling to avoid polarization bias. Cross section measurements and

calculations were performed using OriginPro 8 and Mathcad.

Absolute resonance Raman cross sections were calculated by first determining the

differential Raman cross section of the sample using the following equation:

(3.1)

is the differential Raman cross section of a Raman band indexed by (

,2 is the sample and reference, respectively), is the intensity of the Raman mode

defined by the peak area, is the index of refraction and is the concentration in

moles of monomer per liter. The absolute resonance Raman cross section is then derived

from the differential Raman cross section by:

(3.2)

77

where is the absolute resonance Raman cross section and is the depolarization ratio

of the Raman mode in question.

Determination of absolute resonance Raman cross sections is a precise

measurement and requires calibration. To take into account the differences in light

collection between each lens, one must measure the absolute cross section of a standard

with a reported cross section and compare it to a known literature value. A correction

factor k is then determined by taking the ratio of the measured cross section to the

literature value cross section.

(3.3)

The absolute Raman cross section of the aggregate is then determined by dividing the

calculated cross section by k.

(3.4)

To assure a consistent k value for the aggregate measurement and the calibration

measurement, the aggregate sample is measured first so that the beam focus is the same

in the calibration measurement. The k values were checked by measuring the absolute

Raman cross section of another reference with a known cross section using the previously

determined k value. Shown in Tables 3.1 and 3.2 is an example of this check with

acetonitrile and 1 M sodium perchlorate with 488 nm excitation using cyclohexane as a

reference standard.

Table 3.1 Calibration of Internal External Standard Method with Acetonitrile (918

cm-1

mode) as the Sample and Cyclohexane (800 cm-1

mode) as the Standard with

488 nm wavelength excitation.

R,expt R,lit k

7.54 cm2/molecule 13.4 cm2/molecule 0.56

78

Table 3.2 Measurement of Raman Cross Section of Sodium Perchlorate (932 cm-1

mode) with Cyclohexane (800 cm-1

mode) as the Standard with 488 nm wavelength

excitation using k value determined from Acetonitrile measurement.

R,expt R,lit R,corr

75.4 cm2/molecule 136.9 cm2/molecule 134.8 cm

2/molecule

3.2.3 Single Aggregate Resonance Raman Spectroscopy. TSPP aggregates were first drop

cast onto glass cover slips and then allowed to dry. Spectra and images were measured

using an Olympus IX70 inverted confocal microscope with an Olympus 100x oil

immersion objective (See Figure 3.2). Images were visualized using a thermoelectrically-

cooled Andor CCD camera. Raman spectra were dispersed with an Acton SpectraPro

i2300 single monochromator and collected with a thermoelectrically-cooled CCD

camera. For experiments in which we wanted to negate the polarization dependency of

the aggregates, a quarter wave plate was used to transform the linearly polarized incident

light into circularly polarized light. Polarized spectra were recorded by using a half-wave

plate to rotate the polarization of the incident light so that it was either parallel or

perpendicular to an the long axis of an individual aggregate. A polarizer followed by a

Figure 3.1 Schematic of confocal “internal/external” standard method for measuring

absolute Raman cross sections.

79

scrambler was used to select and then randomize scattered light that was either parallel or

perpendicular to the incident light polarization. The source of laser light for both the

ensemble and single aggregate experiments were provided by an argon ion laser.

3.2.4 Resonance Light Scattering Microscopy. Resonance light scattering (RLS) images

were obtained using the microscope set up described above except that the incident beam

was first diffused through frosted glass and passed through a lens before entering the

100x objective. This provided a broadened, diffuse laser spot to epi-illuminate a large

area of the imaged sample. The scattered light was passed through a 500 nm long pass

filter for laser light rejection. Images were collected with a thermoelectrically-cooled

Andor CCD camera.

3.3 Results

3.3.1 Condensed-Phase Absolute Raman Cross Sections. Typically, it is quite difficult, if

not impossible, to produce single molecule Raman spectra without the use of surface

Figure 3.2 Schematic of the Raman microscopy set up, specifically for polarized

Raman experiments.

80

enhancement (a notable exception being carbon nanotubes22

). Even with surface or

resonance enhancement, imaging molecules with fluorescence or Raman microscopy is a

challenge, since the molecules are typically smaller than the diffraction limit. We show

here that aggregates of TSPP, however, have rather large absolute resonance Raman cross

sections, on the order of 10-22

cm2/molecule with 488 nm excitation. (Cross-sections here

are reported on the basis of the known concentration of monomers used to prepare the

aggregate sample.) While the TSPP nanotubes are only ~20 nm in diameter (~34 nm wide

and 4 nm high when flattened on the surface)4,11

, they can be several microns long and

are thus visible in optical microscopy.

Figure 3.3 shows the background subtracted ensemble resonance Raman spectrum

of TSPP aggregates in aqueous solution with 0.75 M HCl, excited at 488 nm, which is

resonant with the sharp J-band of the aggregate, and excited at 514.5 nm, which is 930

cm-1

to the red of the absorption maximum of the J-band. The inset shows the resonance

Raman spectrum of the diacid monomer excited at 454.4 nm, near the Soret band at 434

nm (1039 cm-1

to the red of the absorption maximum of the Soret band). Table 3.3 lists

the absolute resonance Raman cross sections per porphyrin molecule of each of the seven

prominent modes of the aggregate, determined using a novel internal/external standard

method. Raman spectra were obtained by simultaneously measuring a solution of either

the diacid monomer or the aggregate and a transparent Raman reference standard

(cyclohexane or acetonitrile, respectively), using reported cross section data from Refs.

23 and 24. Depolarization ratios for the prominent modes of the TSPP aggregate, which

have been previously reported in Ref 12, show dispersion at excitation wavelengths

across the J-band, with values that deviate from what would be expected for resonance

81

via a single nondegenerate excited state. These results provided initial evidence that the J-

band consists of two closely-spaced excitonic transitions.

It should be noted that the resonance Raman cross section data for the diacid

monomer, shown in Table 3.4, are for the Raman spectrum excited by 454.4 nm

wavelength laser light, while the absorption maximum of the diacid monomer Soret band

is at 434 nm. The Raman spectrum of the aggregate is obtained with more favorable

resonance conditions than that of the monomer. However, the Raman spectrum of the

aggregate with excitation wavelength of 514.5 nm is obtained with nearly equivalent

resonance conditions as that of the monomer, probing the red wing of the J-band. The

cross sections of the prominent modes of the aggregates excited with 514.5 nm

wavelength light are lower than those observed in the monomer in nearly similar

resonance conditions, considerably so for the low frequency modes which differ by an

order of magnitude. This observation seems to dispute observations of aggregation-

enhanced Raman spectroscopy. However, as reported in Ref. 15, the absolute Raman

cross sections of the low frequency modes are dramatically enhanced by nearly 3 orders

of magnitude when the excitation wavelength is close to the absorption maximum while

the high frequency modes are only enhanced by about one order of magnitude. It is likely

that an increase in Raman cross section on aggregation derives from the concentration of

the total Raman cross section into a more narrow range of excitation wavelengths in the

case of the aggregate. To the extent that the absorption band of the aggregate is

exchange-narrowed by coherent coupling, this enhancement on aggregation represents a

correlation between exciton coherence and resonance Raman intensity. See Figure 3.4 in

Supporting Information for a comparison of the monomer diacid and aggregate spectra.

82

Note that the comparison of the bandwidths of J band and the monomer diacid

Soret band would underestimate the coherence number owing to the composite nature of

the J band. It is also significant that the low-frequency modes of the TSPP diacid at 234

and 316 cm-1

, which may involve out-of-plane motion of the hydrogens in the porphyrin

core, are significantly enhanced in the aggregate compared to the monomer. Excitonically

coupled chromophores often show large enhancements of low-frequency modes in their

resonance Raman spectra.5,15,25,26,27,28,29

We have previously shown12

that the 243 and 316

cm-1

vibrations of the TSPP aggregate exhibit strong exciton-phonon coupling. Their A-

term enhancement in the resonance Raman spectrum is expected since these out-of-plane

vibrations perturb the interchromophore separation which in turn modulates the coherent

coupling that leads to delocalization of the excited electronic state. In agreement with

previous work,4 the 243 cm

-1 mode of the aggregate is blue-shifted by 9 cm

-1 compared to

its value in the monomer diacid, while the 316 cm-1

mode of the diacid is not shifted

appreciably on aggregation. We have also previously shown that the 243 cm-1

mode of

the aggregate prepared in HCl/H2O (referred to as TSPP-h in that work) shifts to 239 cm-1

in DCl/D2O solution (the TSPP-d aggregate), while the 316 cm-1

is negligibly red-shifted

in the deuterated environment.12

Thus of the two low-frequency modes, the 243 cm-1

mode is apparently more perturbed by either the environment or isotopic substitution.

83

Figure 3.3 Resonance Raman spectrum of aggregates prepared from 50 M TSPP in

0.75 M HCl with cyclohexane as the intensity standard excited with 488 nm

wavelength light (black) and 514.5 nm wavelength light (red). The inset shows the

resonance Raman spectrum of 50 M TSPP diacid monomer in 0.001 M HCl with

acetonitrile as the intensity standard excited with 454.5 nm excitation wavelength

(blue). The spectra have been background subtracted and asterisks mark solvent

Raman bands.

84

Table 3.3 Absolute resonance Raman cross sections and corresponding

depolarization ratios () of prominent modes of TSPP aggregates excited with 488

nm and 514.5 nm excitation wavelength.

Raman Shift, cm-1

243 316 698 983 1013 1228 1534

Raman cross section, 10-23

cm2/molecule (488 nm)

26.2

=0.45

19.6

=0.44

5.78

=0.41

6.37

=0.48

2.86

=0.45

6.84

=0.53

12.0

=0.61

Raman cross section, 10-23 cm2/molecule (514.5 nm)

0.0241

=0.51

0.0508

=0.47

0.0578

=0.51

0.184

0.0799

=0.51

0.169

=0.36

0.983

=0.40

Figure 3.4 Absorption spectra of the 50 M TSPP diacid monomer in 0.001 M HCl

(black) and the aggregate prepared from 50 M TSPP in 0.75 M HCl (red). (Inset)

3D model of a fully protonated TSPP diacid molecule.

85

Table 3.4 Absolute resonance Raman cross sections and corresponding

depolarization ratios () of prominent modes of TSPP diacid monomers excited with

454.5 nm excitation wavelength.

Raman Shift, cm-1

234 316 1234 1540

Raman cross section, 10-23 cm2/molecule

0.245

=0.14

0.354

=0.17

0.653

=0.14

1.45

=0.55

3.3.2. Single Aggregate Resonance Raman Spectroscopy and RLS images. Figure 3.5

shows the resonance Raman spectrum of 10 aggregate individuals with an image of a

typical filament-like individual. Rod-like structures observed by optical microscopy may

be separate aggregates or small bundles as observed in AFM images (see Fig 3.14 in

Supporting Information). However, since their width dimension is too small to be seen

via optical microscopy, whether they are single aggregates or bundles cannot be readily

distinguished. The large Raman cross sections of the TSPP aggregate allow for detection

of individual or small bundles of aggregates via Raman microscopy without the presence

of Raman signal enhancing techniques such as surface-enhanced Raman scattering

(SERS). The spectra in Fig. 3.5 were obtained with circularly polarized excitation to

eliminate polarization bias resulting from aggregates with different orientations, such that

the intensity might be proportional to the number of aggregates in the focal volume.

However, depending on the aggregate measured, the peak height of the 243 cm-1

mode

varies somewhat with respect to that of the 316 cm-1

mode. Additionally the relative

intensities of the high frequency modes (698 cm-1

to 1534 cm-1

) to the low frequency

modes (243 cm-1

and 316 cm-1

) vary significantly among different samples.

The epi-illuminated image of a TSPP aggregate excited with 488 nm wavelength

light in Figure 3.5 reflects the intensity of resonance light scattering (RLS) along the

86

length of the nanotube. Variations in the RLS intensity arise from heterogeneity in the

coherence number, with hot spots reflecting regions of enhanced coherence. We propose

that these same variations in coherence affect the relative Raman intensities of different

aggregates, in addition to changes in the number of bundled nanotubes. To explore the

effects of coherence versus bundling, we examined the Raman spectra from different

nanotubes (Figure 3.5) as well as from different spots along the length of a given

nanotube (Figure 3.7).

87

Figure 3.6 shows that both the overall intensities and the relative intensities of

various Raman modes, determined from the background-subtracted peak areas, are

different for the 10 different sampled nanotubes. Figure 3.6a shows the intensities of the

two low frequency modes and the 1534 cm-1

mode for the 10 different aggregates

expressed as histograms. If coherence or structural heterogeneity played no role in the

Figure 3.5 Single TSPP aggregate resonance Raman spectra obtained from 10

different aggregates (left) and a false color epi-illuminated microscopy image of an

aggregate excited with 488 nm light (top right). In the bottom-right is a false color

optical microscope image of an individual TSPP aggregate. The bright spot in this

image is the excitation laser spot.

88

Raman intensity, then we would expect the Raman intensities of each mode to vary in

proportion to the number of bundled tubes. Figure 3.6b shows the intensities of these

three modes compared to their values in sample 9, which exhibits the lowest Raman

intensities of the 10 samples. It is apparent that the relative intensities of the three modes

vary greatly from one aggregate to another. Of the three modes considered in Figure 3.6,

only the 316 cm-1

mode displays intensities which vary by approximately integral

multiples, as shown in Fig. 3.6b. Figure 3.6c shows a histogram of the relative intensities

of the three modes. While the relative intensities of the two lowest frequency modes are

relatively constant from one aggregate to another (± 10%), there is a larger variation in

the relative intensity of either low-frequency mode to that of the 1534 cm-1

mode, more

than ± 20%. We conclude that while there are indications in Figure 3.6 that the number of

bundled nanotubes probably varies for the 10 different probed regions, local variations in

coherence also contribute to different Raman intensities from different spots.

89

Figure 3.6 (a) Single-aggregate resonance Raman intensities of 243 cm

-1 (black),

316 cm-1

(red), and 1534 cm-1

(blue) modes measured at different aggregates; (b)

data in (a) normalized to the intensity of the corresponding peaks in Sample 9; (c)

intensity ratios of the three Raman modes. The sample numbers correspond to the

numbered spectra in Figure 3.5. The green lines in 3.6b address the approximate

integer variance in the Raman peak intensity of the 316 cm-1

mode between

samples.

90

Figure 3.7 The resonance light scattering image of a TSPP aggregate (with 488

nm wavelength excitation) showing the places on the aggregate where Raman

spectra were measured.

91

To investigate the observed heterogeneity in the coherence of the aggregates and

its correlation to Raman intensities, we measured the Raman spectra of five spots along

the length of the nanotube shown in Figure 3.7 (corresponding resonance Raman spectra

in Fig. 3.8). The stage translation of the microscope requires precise manual adjustments,

making precise aim of the laser focus experimentally difficult. The laser spot diameter, as

observed by optical images (see Fig. 3.5), is approximately 500 nm. The intensities of the

Figure 3.8 Resonance Raman spectra corresponding to spots 1-5 in Fig.

3.7 with 488 nm excitation.

92

seven prominent modes of each Raman spectrum are shown in the histogram in Figure

3.9 as well as the intensity ratios of the two low frequency modes and the 1534 cm-1

mode with respect to one another. The large intensities of the Raman modes for spot 1

corresponds with the overlap of an observed coherence hot spots and the diminished

intensities for spots 3 and 4 correspond with the observed diminished coherence in those

spots. This would seem to suggest that in spots where effective coherence is large the

Raman intensities, particularly of the low frequency modes, will be strong. However the

large Raman intensities of spots 2 and 5, where there is no coherence hot spot, are

inconsistent with this statement. Furthermore, the Raman intensity ratios of the low

frequency modes to 1534 cm-1

mode in Fig. 3.9 do not show any particular trend between

spots. In fact, spot 3, which exhibits low coherence in the RLS image, exhibits rather

strong low frequency modes with respect to the high frequency mode. Since we are

limited in optical microscopy in imaging the aggregates, due to the thin ~34 nm width of

the collapsed nanotube which is well below the diffraction limit, increases in intensity in

spots with apparently weak coherence may be due to measurements of bundles of

aggregate nanotubes.

93

Figure 3.9 Histograms of (top) the Raman intensities of the seven

prominent modes at each spot on the aggregate in Fig. 3.7 excited

with 488 nm wavelength laser and (bottom) corresponding

intensity ratios.

94

Since water-mediated hydrogen bonds are hyothesized to maintain the

nanotubular structure of TSPP aggregates, it is crucial to ascertain the effect on the

coherence and the Raman intensities as water is forcibly driven away. To do this we have

measured RLS images and Raman spectra of spot 1 of the aggregate in Figure 3.7 while

exposing it to a 0.75 mW power 488 nm wavelength laser, rather than 0.75 W for

typical single aggregate Raman experiments. Figure 3.10 shows the Raman spectra of the

aggregates at the beginning and at the end of a 92 s exposure to this “high power” laser

and the intensities of the 243 cm-1

, 316 cm-1

, and 1534 cm-1

modes measured every 0.5 s

over the course of the exposure. It is evident that over this laser heating period the Raman

mode intensities undergo decay but level off at certain intensities which may be

indicative of disaggregation of the nanotubes into the diacid monomer. With weaker laser

exposure used in previous experiments the intensity of Raman modes do not change with

time. However, as shown in Figure 3.11, the Raman intensity ratios of the low and high

Figure 3.10 (Left) Resonance Raman spectra of the TSPP aggregate in Figure 3.7

measured at spot 1 with 0.75 mW of 488 nm wavelength laser light at the moment

of exposure (black) and 92 seconds later. (Right) The time profile of the intensities

of the 243 cm-1

, 316 cm-1

, and 1534 cm-1

modes over the course of the “high power”

exposure.

95

frequency modes do not change throughout the laser heating experiment. But these

intensity ratios differ from the intensity ratios obtained with gentler laser exposure where

the low frequency modes are much stronger than the 1534 cm-1

mode. Since

disaggregation occurs with laser heating, the diminishing relative intensities of the low

frequency modes seems consistent with the so-called aggregation-enhanced Raman

scattering of low frequency modes presented by Akins.15

Additionally, Figure 3.12 shows

the RLS image of the aggregate before and after laser heating showing the vanishing

coherence after the high power laser exposure.

Figure 3.11 Histogram of the intenisty ratios of the 243 cm

-1:316

cm-1

modes (blue), 316 cm-1

:1534 cm-1

modes (red), and 243

cm-1

:1534 cm-1

(black) with gentle laser exposure (1) and high

power laser exposure at t = 0 s (2) and t = 92 s (3) at spot 1 on

aggregate shown in Fig. 3.7.

96

Figure 3.13 shows the results of using vertically (V) and horizontally (H)

polarized incident light, with respect to the nanotube long axis, to excite an aggregate. As

shown in the figure, the scattered light in each case was detected with polarization either

parallel (VV and HH) or perpendicular (VH and HV) to the incident light polarization.

The polarization ratios (VV:HV:VH:HH) for the 243 cm-1

, 316 cm-1

, and 1534 cm-1

modes are 5.4:2.4:2.4:1, 7.6:3.4:2.4:1, and 6.0:2.6:2.0:1, respectively. Referring to the

long-axis of the aggregate as the z direction, the VV spectrum selects for the zz

component of the polarizability tensor and is the most intense of the four polarized

spectra. However, the HH spectrum is also significant demonstrating the xx component

of the polarizability, where x is perpendicular to the long axis of the aggregate and

Figure 3.12 The RLS images of the aggregate in Fig. 3.7 before (left) and after

(right) laser heating at spot 1.

97

parallel to the surface. We presume for an intact helical nanotube aggregate that the x and

y components of the J transition are degenerate. However, this is not the case for

aggregates deposited on a surface since the nanotubes are usually flattened when

deposited on a surface.11

A nonzero ratio of αxx to αzz is in accord with our previously

determined depolarization ratios for the aggregate in solution. The values of (αxx/αzz)2

obtained here are in the range 0.13 to 0.18, in agreement with our previous study of TSPP

aggregates deposited on Au(111).11

However, the nonzero intensities for the VH and HV

polarizations reveal off-diagonal components of the polarizability αxz and αzx, which

could not be determined in previous work using ensemble spectroscopy. These off-

diagonal components of α indicate vibronic coupling of the z- and x-polarized J-band

excited states, which contribute to the observed depolarization ratio dispersion and

relative intensity changes of the ensemble resonance Raman spectrum of the aggregate

when probed with wavelengths spanning the J-band.12

While the intensities of the VH

and HV spectra are nearly equivalent for the 243 cm-1

mode, the VH and HV intensities

are different for the 316 cm-1

and 1534 cm-1

modes. It is possible that similar magnitudes

of αzx and αxz reflect increased delocalization for the 243 cm-1

mode, in accord with its

stronger dependence on nanotube environment compared to the 316 cm-1

mode.

98

3.4 Discussion

The changes in the relative peak height of the 243 cm-1

mode, as well as the

changes in the relative intensity of the low frequency modes to the high frequency modes

may suggest environmental perturbations to the aggregate and the degree of disassembly

of the nanotube into constituent circular N-mers or porphyrin monomers. In Ref 12, we

reported that water serves a role in both the aggregate structure as well as in excitonic

coupling and exciton-phonon coupling as shown by the large changes in the relative

intensities of the low frequency modes and the intensity of the resonance light scattering

for aggregates prepared in water and HCl compared to those prepared in D2O and DCl. In

Figure 3.13 Polarized Raman spectra of an individual TSPP aggregate. V and H

refer to the vertical and horizontal polarization, respectively, of the incident

excitation (first letter) and scattered light (second letter) with respect to the

orientation of the nanotube long axis as illustrated in the inset.

99

the same vein of thought the varying intensity ratios of the high and low frequency modes

seen in this work may reflect heterogeneity amongst the aggregates in terms of exciton-

phonon coupling depending on the dryness of the local environment of the aggregate and

the degree to which the aggregates have collapsed due to the absence of water. The

observed hot spots along the epi-illuminated image of the aggregate may be an indication

of localized areas of increased coherence which are reported by increased resonance light

scattering intensity. It is also possible that these hotspots may be overlapping nanotubes,

which may result in an increase in the resonance light scattering signal if the excited

states are delocalized over more than one nanotube. The AFM images in Fig. 3.14 show

breaks in some of the aggregates which could limit coherence, potentially accounting for

places where the RLS is weak. Since the resonance Raman spectrum in the laser heating

experiment shows considerably more intensity from high-frequency modes than low-

frequency modes compared to the gentler laser power experiments, we suggest that

Raman spectra from aggregates which show relatively more intense high frequency

modes may indicate partial disaggregation. However, a clear relationship between the

intensity of the coherence hot spots in the RLS images and the intensities of the

resonance Raman modes is not entirely apparent.

The absolute Raman cross sections measured here are, to our knowledge, the first

instance of quantitative Raman intensity comparison for aggregates of TSPP and it diacid

monomer. Comparison of the Raman cross sections of the diacid monomer and aggregate

under similar resonance conditions seem to suggest no aggregate-enhanced Raman

scattering exists here. However the dramatic enhancement of the low frequency modes

with resonance with the J-band absorption maximum is consistent with previous

100

observations and suggests some relation of low frequency modes Raman intensities with

the effective coherence of the aggregate. The variation in the relative Raman intensities

of the low frequency modes and high frequency modes in single aggregate

measurements, particularly with the diminishing relative intensity of low frequency

modes compared to that of the high frequency modes in laser heating experiments, seem

to suggest some relation of the low frequency modes to the effective coherence of the

aggregate. But with the influence of exciton-phonon coupling, which reduces coherence,

inherent in the intensities of the low frequency Raman modes, in addition to the

considerably lower absolute Raman cross section of the low frequency modes of the

aggregate compared to those of the monomer under the same resonance conditions, it is

difficult to make an argument that Raman intensities are enhanced solely due to

aggregation. Rather, enhancement of Raman modes which are relevant to assembly (i.e.,

the low frequency modes) occurs only when the excitation wavelength is resonant with

the exciton transition.

The polarization ratios of the single aggregate resonance Raman spectra of TSPP

aggregates reflect the multicomponent nature of the J-band transition as well as the

hierarchical structure of the aggregate. This incomplete polarization of the J-band has

been observed here and in other studies including ensemble resonance Raman spectra of

the aggregate on Au(111)11

, in resonance Raman data of the aqueous aggregate excited at

wavelengths spanning the J-band12

, and in flow-induced linear dichroism.30,31

Partial

polarization along the short axis must be attributed to a J-band which has more than one

component. We argue that the J-band consists of two excitonic components as expected

101

for a helical aggregate: one is a transition polarized parallel to the nanotube long axis and

the other a doubly degenerate transition polarized along the nanotube short axis.

3.5 Conclusion

As aforementioned, the goal of this work was to provide insight into the structural

and electronic properties of the hierarchical TSPP aggregates without the hindrance of

aggregate heterogeneity found in ensemble spectroscopic methods. In this Chapter, we

have reported for the first time single aggregate resonance Raman spectroscopy showing

variations in the relative intensity of Raman modes reflecting heterogeneity in exciton

coherence and exciton-phonon coupling. A range of relatively large coherence numbers

have been previously reported for the TSPP aggregate,14

for example a value of about

500 was derived from Stark spectroscopy.32

Our findings show that this coherence varies

within and among different aggregates when deposited on a surface. We speculate that

these differences arise from the role of water in the structure of the assembly. If

aggregation-enhanced Raman scattering is valid, it appears to be very excitation

wavelength dependent. Large enhancement of low frequency modes when the excitation

wavelength is tuned to resonance with the J-band absorption maximum illustrates this

effect. However, it is important to recognize that resonance with the exciton state causes

this enhancement of vibrational modes which are relevant to aggregate formation (i.e.

out-of-plane distortions) and not the assembly of the aggregate itself, as shown in the

comparison of the resonant Raman cross-sections of the monomer and aggregate at

similar resonance conditions. Polarized Raman spectra of an individual porphyrin

nanotube proves the multicomponent nature of the J-band transition and reveals strong

coupling of the parallel and perpendicular polarized J-band excitons. Though the finer

102

details of the internal structure of the aggregate remain to be fully understood, our results

support the idea that TSPP aggregates imaged in scanning probe microscopy are

collapsed helical nanotubes for which the J-band is split into two closely spaced

components. The standard cartoon of a J-aggregate as a staircase of planar porphyrin

molecules is inconsistent with our Raman polarization data and with numerous

previously reported scanning probe images. Combining the present results on individual

TSPP aggregates with the information gathered from ensemble measurements and with

theory that properly describes the excitonic coupling will lead to better understanding of

light-harvesting in these self-assembled nanostructures.

3.6 Acknowledgments

The support of the National Science Foundation (CHE-1149013) is gratefully

acknowledged.

103

3.7 Supporting Information

Figure 3.14 Atomic force microscopy image of TSPP aggregates spin-cast

on mica from a 5 M TSPP solution with 0.75 M HCl. Red and blue cross

section profiles correspond to red line and blue line in the image.

104

3.8. References

1. Spano, F.; Kuklinski, J.; Mukamel, S. Phys. Rev. Lett. 1990, 65, 211-214.

2. de Boer, D.; Wiersma, D. Chem. Phys. Lett. 1990, 165, 45-53.

3. Heijs, D.; Malyshev, V.; Knoester, J. Phys. Rev. Lett. 2005, 95, 177402.

4. Friesen, B. A. Nishida, K. A.; McHale, J. L.; Mazur U. J. Phys. Chem. C 2009, 113,

1709-1718.

5. Doan, S. C.; Shanmugham, S.; Aston, D. E.; McHale, J. L. J. Amer. Chem. Soc. 2005,

127, 5885-5892.

6. Rotomskis, R.; Augulis, R.; Snitka, V.; Valiokas, R.; Liedberg, B. J. Phys. Chem. B

2004, 108, 2833-2828.

7. Schwab, A. D.; Smith, D. E.; Rich, C. S.; Young, E. R.; Smith, W. F.; de Paula, J. C. J.

Phys. Chem. B 2003, 107, 11339-11345.

8. Franco, R.; Jacobsen, J. I.; Wang, H.; Wang, Z.; István, K.; Schore, N. E.; Song, Y.;

Medforth, C. E.; Shelnutt, J. A. PhysChemChemPhys 2010, 12, 4072-4077.

9. Wang, C.; Tauber, M. J. J. Am. Chem. Soc. 2010, 132, 13988-13991.

10. Gandini, S. C. M.; Gelamo, E. L.; Itri, R.; Tabak, M. Biophys. J. 2003, 85, 1259-

1268.

11. Friesen, B. A.; Rich, C. C.; Mazur, U.; McHale, J. L. J. Phys. Chem. C 2010, 114,

16357-16366.

12. Rich, C. C.; McHale, J. L., Phys. Chem. Chem. Phys. 2012, 14, 2362-2373.

13. McHale, J. L. J. Phys. Chem. Lett. 2012, 3, 587-597.

105

14. “Hierarchical Structure of Light-Harvesting Porphyrin Aggregates,” Ch. 3 in “J-

Aggregates,” Vol. 2, pp. 77-118, ed. T. Kobayashi, World Scientific Press, Singapore,

2012.

15. Akins, D. A. J. Phys. Chem. 1986, 90, 1530-1534.

16. Aydin, M.; Fleumingue, J.-M.; Stevens, N.; Akins, D. L. J. Phys. Chem. B 2004, 108,

9695-9702.

17. Akins, D. L.; Zhuang, Y. H.; Zhu, H.-R.; Liu, J. Q. J. Phys. Chem. 1994, 98, 1068-

1072.

18. Akins, D. L.; Zhu, H.-R.; Guo, C. J. Phys. Chem. 1996, 100, 5420-5425.

19. Puntharod, R.; Webster, G. T.; Asghari-Khiavi, M.; Bambery, K. R.; Safinejad, F.;

Rivadehi, S.; Langford, S. J.; Haller, K. J.; Wood, B. R. J. Phys. Chem. B 2010, 114,

12104-12115.

20. Webster, G. T.; McNaughton, D.; Wood, B. R. J. Phys. Chem. B 2009, 113, 6910-

6916.

21. Coles, D. M.; Meijer, A. J. H. M.; Tsoi, W. C.; Charlton, M. D. B.; Kim, J.-S.;

Lidzey, D. G. J. Phys. Chem. A 2010, 114, 11920-11927.

22. Hartschuh, A.; Pedrosa, H. N.; Novotny, L.; Krauss, T. D., Science, 2003, 301, 1354-

1356.

23. Trulson, M. O.; Mathies, R.A., J. Chem. Phys. 1986, 84, 2068-2074.

24. Dudik, J. M.; Johnson, C. R.; Asher, S. A., J. Chem. Phys., 1985, 82, 1732-1740.

25. Akins, D. A. J. Phys. Chem. 1986, 90, 1530-1534.

26. Kano, H.; Saito, T.; Kobayashi, T. J. Phys. Chem. A 2002, 106, 3445-3453.

106

27. Choi, M. Y.; Pollard, J. A.; Webb, M. A.; McHale, J. L. J. Am. Chem. Soc. 2003, 125,

819-820.

28. Novoderezhkin, V.; Monshouwer, R.; van Grondelle, R. J. Phys. Chem. B 2000, 104,

12056-12071.

29. Aydin, M.; Dede, O.; Akins, D. L. J. Chem. Phys. 2011, 134, 064325/1-12.

30. Ohno, O.; Kaizu, Y.; Kobayashi, H., J. Chem. Phys., 1993, 99, 4128-4139.

31. Vlaming, S. M.; Augulis, R.; Stuart, M. C. A.; Knoester, J.; van Loosdrecht, P. H. M.

J. Phys. Chem. B 2009, 113, 2273-2283.

32. Katsumata, T.; Nakato, N.; Ogawa, T.; Koiki, K.; Kobayashi, T. Chem. Phys. Lett.

2009, 477, 150-155.

107

Chapter 4 Spectroscopic Behavior of Light

Harvesting Molecular Aggregates in

Nonaqueous Solvents

4.1 Introduction

Nanotubular aggregates of meso-tetrakis(sulfonatophenyl)porphyrin (TSPP),

which are prepared in acidic aqueous solutions (pH < 1), are a well studied light-

harvesting assembly whose structure and excitonic properties show dependence on its

aqueous environment.1,2,3,4

A previous study in our group has shown that changing the

solvent from a protiated environment (0.75 M HCl in H2O) to a deuterated environment

(0.75 M DCl in D2O) results in an increase in the coherence of the aggregate as well as a

decrease in exciton-phonon coupling.5 However, the aggregates of TSPP that form in the

absence of water have been shown to have different structure and spectroscopic

properties. When molecules of TSPP on a surface are exposed to HCl vapor, the

characteristic exchange-narrowed, red-shifted J-band and weak, blue-shifted H-band in

the absorption spectrum are observed, but the typical nanotube structure is not visible in

the surface-probe microscopy images.6 Furthermore porphyrin aggregates prepared in

various solvents7,8

, embedded in materials9, and prepared in ionic liquids

10 have shown

changes in the spectroscopic features of the aggregate including changes in the relative

intensities of the J- and H-bands or a blue-shifted J-band from what is observed in

aqueous preparations. In this work we will attempt to explain these observations by

looking at the spectroscopic properties of aggregates prepared in nonaqueous conditions.

108

4.2 Experimental

4.2.1 Sample Preparation. Meso-Tetra(4-sulfonatophenyl)porphyrin dihydrochloride was

purchased from Frontier Scientific. Ethanol (200 proof) was purchased from Decon

Laboratories, Inc. Dichloromethane (DCM) was purchased from J. T. Baker. Mixtures of

TSPP and ethanol were prepared by adding the TSPP diacid dihydrochloride salt to

straight ethanol. Mixtures of ethanol and 18 M water with hydrochloric acid (HCl) were

prepared by combining various volumes of ethanol and water while adding enough HCl

to maintain an overall 1.0 M concentration of the acid. Mixtures of TSPP in

dichloromethane were prepared following the procedure outlined by De Luca and co

workers.11

The tetrabutylammonium salt of TSPP was prepared by combining

tetrabutylammonium chloride with TSPP diacid dihydrochloride salt in a 4:1 mole ratio

in an aqueous solution with NaOH added to bring the solution to pH = 5 to convert the

diacid to the free base form. Water is then removed with a rotary evaporator and the

resulting red crystals are dissolved in dichloromethane. The resulting suspension is

acidified by exposing it to HCl vapor for 1 hour.

4.2.2 UV-visible absorption spectroscopy. Electronic absorption spectra were obtained

using a Shimadzu UV-2501PC UV-visible spectrophotometer. Spectra of aggregate

solutions were measured in 1 cm and 1 mm path length quartz cells for 5 M

concentrations and 35 M concentrations.

4.2.3 Resonance Raman Spectroscopy. Resonance Raman scattering (RRS) spectra were

measured in a confocal backscattering arrangement using a 1 cm path length quartz cell

and excited with vertically polarized light from a 454.5 nm wavelength argon ion (Ar+)

gas laser. A magnetic cuvette spinner was used to mix the aggregate solution in the quartz

109

cell so as to avoid potential photodegradation due to prolonged laser exposure. Both

parallel and perpendicularly polarized Raman scattering (which will be referred to as

polarized and depolarized scattering here) were detected using a polarizer. Scattered light

was dispersed using a SPEX Triplemate triple monochromator system and detected using

a liquid nitrogen cooled CCD. The spectral resolution of the triple monochromator is 4

cm-1

. Depolarization ratios of the Raman modes were determined by dividing the

background subtracted depolarized Raman peak area by the background subtracted

polarized Raman peak area. Background subtraction was performed using the Peak

Analyzer program in Origin Pro 8 using a user-defined fit traced along the observed

background emission.

4.2.4 Atomic Force Microscopy. AFM images were obtained using a Digital Instruments

Atomic Force Microscope in tapping mode. Silicon cantilevers with a spring constant of

42 N m-1

and a resonance frequency of ~330 kHz were employed for imaging. Aggregate

preparations in DCM were deposited on mica substrates and allowed to dry.

4.3 Results

4.3.1 Aggregates Prepared in Ethanol. Figure 4.1 shows the absorption spectra of the

same concentration of the dihydrochloride salt of TSPP dissolved in 0.75 M HCl in H2O

and in neat ethanol (EtOH). Both spectra indicate the presence of aggregates with a

strong, exchange-narrowed, and red-shifted J-band and a red-shifted Q-band. However,

the apparent H-band appears to be stronger in the case of the ethanolic aggregates than in

the aqueous aggregates and seemingly at the expense of the intensity of the J-band and

the diacid monomer B-band.

110

Figure 4.1 Absorbance Spectrum of the TSPP aggregates in ethanol and aqueous 1.0

M HCl.

111

Figure 4.2 shows the change of the absorption spectrum of the aggregate in

ethanol over time. As time progresses, the J-band and Q-band diminish while the “H-

band” increases. However, “H-band” is a misnomer for this peak as its absorption

maximum occurs around 413 nm similar to that of the free base monomer. Thus it

appears as though while ethanol permits aggregation of TSPP initially, over time the

aggregates disassemble into the free base monomer form. It is possible that protons in the

TSPP diacid monomers are removed by the ethanol in the environment turning them into

the free base form.

Figure 4.2 Absorption spectra of 5 M of the dihydrochloride salt of TSPP dissolved

in ethanol over time. Arrows emphasize the trend of the changes in the peaks over

time.

112

Figure 4.3 shows absorption spectra of TSPP diacid dissolved in various mixtures

of ethanol and water with a concentration of HCl sufficient to induce aggregation.

Despite the acidity of the mixture, aggregation is prevented in mixtures containing

greater than 25% ethanol by volume. However, aggregation appears to be no longer

inhibited when the mixture contains 20% ethanol by volume or less. Furthermore, with

small amounts of ethanol in the mixture the aggregation process slows, as shown in Fig.

4.4 for the 10% ethanol mixture.

Figure 4.3 Absorption spectra of 5 M TSPP diacid dissolved in various mixtures of

ethanol and water with a constant concentration of 1.0 M HCl.

113

4.3.2. Aggregates Prepared in Dichloromethane. Figure 4.5 shows the absorption

spectrum of the free base form of TSPP prepared in dichloromethane (DCM). Figures

4.6, 4.7, and 4.8 show the absorption, resonance Raman, and polarized resonance Raman

spectra of TSPP aggregates prepared in DCM. Since water plays a role in the assembly of

the circular N-mers into nanotubes, preparing the aggregates in an acidified environment

without water should not permit the formation of the nanotubes.

Figure 4.4 Absorption spectrum of TSPP diacid dissolved in a mixture 10% ethanol

by volume and water with an overall concentration of 1.0 M HCl as it evolves in

time.

114

Figure 4.5 Absorption spectrum of the tetrabutylammonium chloride salt of TSPP

free base in dichloromethane.

115

Figure 4.6 Absorption spectrum 34.7 M of the TBA salt of TSPP in DCM

exposed to HCl vapor for 1 hour.

116

Figure 4.7 Resonance Raman spectrum of 34.7 M of the TBA salt of TSPP in

DCM exposed to HCl vapors for 1 hour excited with 454.5 nm wavelength laser.

The 285 cm-1

, 700 cm-1

, and 738 cm-1

Raman modes are attributed to DCM

vibrations.

117

The absorption and Raman spectra of these aggregates show differences in

aggregates prepared in an organic environment as opposed to those prepared in an acidic

aqueous environment. The aggregate absorption peak is considerably blue shifted in the

organic environment as opposed to the aqueous environment (~455 nm vs. 491 nm).

Furthermore, the resonance Raman spectrum of the organic aggregates contrasts

considerably with that of the aqueous aggregates, with far less intense low frequency

modes relative to the high frequency modes. Additionally, the depolarization ratios of the

organic phase aggregates are considerably different from the aqueous phase aggregates,

Figure 4.8 Polarized (black) and depolarized (red) resonance Raman spectra of

34.7 M of the TBA salt of TSPP in DCM exposed to HCl vapor for 1 hour

excited with 454.5 nm wavelength laser.

118

with the most prominent modes having > 0.5 with the exception of the 240 cm-1

mode

which has = 0.26.

However, the dryness of these samples should be called into question, and while

the spectra collected are certainly identical to that measured by Scolaro and coworkers,11

the procedure does not immediately assure a completely dry sample as the preparation

and measurements were not performed under a dry inert gas environment or in vacuo.

Shown in Figure 4.9 are AFM images of the resulting aggregates prepared in DCM. The

aggregates show up as small round features with fairly consistent dimensions. While the

shape of aggregates is different, appearing as small ~34 nm diameter dots, the height of

the aggregates is quite similar to that of the aggregates deposited from aqueous solution

(about 4 nm).12

This might suggest that with what little water is in the mixture, smaller

aggregates similar to the nanotube aggregates observed in water may be forming or that

the small substituent circular N-mer aggregates may be arranging themselves around

droplets of water in a micellar fashion.

119

Figure 4.9 7 x 7 m (top) and 100 x 100

nm (middle) AFM images of the TBA

salt of TSPP deposited from DCM

exposed to HCl vapor for 1 hour on mica

with corresponding cross section

(bottom).

120

4.4 Discussion

Considering the formation of aggregates by the previously mentioned model, if

water mediated hydrogen bonding drives the formation of nanotubes from the circular N-

mer building blocks, then reducing or eliminating the amount of water in the environment

or increasing the lyophilicity of environment would prevent nanotubes from forming.

Moreover, if solvent mediated hydrogen bonding is a driving force for aggregation of the

hierarchical subunits, then there must be differences between aggregates prepared in

protonated polar solvents, such as short chain alcohols, where the driving force may still

exist, and nonpolar solvents, where only intermolecular electrostatics determine

aggregation.

For the ethanolic aggregates, the decay of the J-band and the increase of the

freebase monomer band over time reflect the strength of the acidity of the diacid against

that of the ethanol. Since ethanol is a considerably weaker acid (stronger base) than that

of the diacid (pKa = 5 for diacid,13

pKa = 16 for ethanol14

) ethanol will scavenge protons

from the diacid monomer causing the observed formation of the free base monomer over

time. As a result in mixtures of ethanol and 1.0 M HCl (aq) where the amount of ethanol

is larger, ethanol will scavenge protons from the diacid monomer and the environment,

reducing the acidity and ionic strength of the solution and preventing aggregation. Even

with small amounts of ethanol, the aggregation process occurs slowly compared to

completely aqueous preparations as ethanol competes with the diacid porphyrin for

protons. These observations further emphasize the importance the acidity or ionic

strength of the environment on aggregate assembly.

121

When the system is devoid of water (or nearly devoid of water as is the case here)

such as when the aggregates are prepared in acidified DCM, aggregates appear to take on

a different structure and different spectroscopic properties. The smaller red-shift of the J-

band for the aggregates prepared in DCM compared to the red-shift of the J-band for the

aggregates prepared in the aqueous environment may indicate only the formation of the

circular N-mers in the absence of water. The fact that nanotubes are not observed in the

AFM images aggregates deposited from DCM is consistent with dependence of water-

mediated hydrogen bonding on aggregate formation. If electrostatic forces alone drive

aggregation it is presumed, based on our hierarchical model, that only the circular

aggregate structures form. An absorption maximum at ~460 nm has been observed in

ionic liquids where water is also absent (Ref 10). This could be a characteristic feature of

the circular N-mers when they do not assemble into a nanotubular aggregate. The

depolarization ratios for the modes measured with 454.5 nm wavelength excitation are

different than that measured for the diacid15

and for the nanotube aggregates (see Table

4.1). However the depolarization ratios of the lowest frequency mode of = 0.26 is

inconsistent with a J-state that should be doubly degenerate for a circular N-mer, which

would result in a depolarization ratio of = 1/8 for a totally symmetric mode. The

unexpected depolarization ratio values for the prominent resonance Raman modes of the

aggregates prepared in DCM may arise from non-Condon contributions to the transition

polarizability which derives from vibronic coupling of the excitons of the observed

aggregates. But it is also likely that these depolarization ratios arise from the overlap of

many closely spaced bands, which, if the circular aggregates form in this environment,

could be the J-band, H-band, and Soret band from residual monomer. Additionally, since

122

these aggregate samples are not completely dry, some partial nanotube formation around

small amounts of water, which may explain the small features observed in the AFM

images, could lead to excitonic coupling between circular N-mers. The widths and

heights of the aggregates in AFM images almost resemble a fraction of the nanotube

aggregate as though a circular portion of an aggregate were cut out.

Table 4.1 Depolarization Ratio Values for the TSPP diacid monomer, TSPP

aggregates prepared from 0.75 M HCl in H2O, and TSPP aggregates prepared from

DCM and HCl vapor from resonance Raman data excited with 454.5 nm

wavelength.

Raman Shift (cm-1) (diacid/aq. agg./DCM agg.)

234/243/ 240

316/316/ 312

1234/1228/1229

1540/1534/1534

TSPP diacid 0.14 0.17 0.14 0.55

TSPP agg. (aq.) -- -- 0.63 0.63

TSPP agg. (DCM)

0.26 0.5 0.72 0.65

4.5 Conclusion

Nonaqueous environments and the absence of assembly-mediating hydrogen-

bonding have been shown to suppress aggregation of TSPP beyond what is permissible

through electrostatic interactions. In the presence of ethanol, aggregation is slowed or

prevented due to the proton scavenging nature of the relatively basic alcohol. Preparation

of TSPP aggregates in a relatively nonaqueous solvent, DCM, with HCl vapor produces

aggregates with unique electronic absorption signature compared to what is observed in

aggregates prepared in an acidic aqueous solution. Resonance Raman spectra of these

aggregates show some unique Raman shifts for prominent modes with unique

depolarization ratios demonstrating these organic phase aggregates observe distinct

structural and excitonic properties. The observation of small features with similar cross-

123

sectional widths and heights as the TSPP aggregate nanotube suggests the assembly about

small amounts of water in DCM. We propose that in the absence of water, aggregation is

driven only by electrostatic interactions. By our proposed model for the assembly of

TSPP aggregates, we would expect that the spectroscopic properties of aggregates

prepared in DCM would reflect that of the circular N-mers. However, the questionable

dryness of the solvent, the depolarization ratios, and the observed assembly in AFM

images of the TSPP aggregates prepared in DCM complicate identifying their internal

structure and excitonic properties. Future work will require improving the dryness of the

solvent as well as investigating aggregates prepared in nonaqueous, acidic environments

such as ionic liquids to gain better understanding of the assembly of these aggregates in

the absence of water-mediated hydrogen bonding and potentially of the internal structure

of the hierarchical subunits which make up TSPP aggregates prepared in acidic aqueous

media.

4.6 References

1. Ohno, O.; Kaizu, Y.; Kobayashi, H., J. Chem. Phys., 1993, 99, 4128-4139.

2. Akins, D. L.; Zhu, H.-R.; Guo, C., J. Phys. Chem., 1994, 98, 3612-3618.

3. Chen, D.-M.; He, T.; Cong, D.-F.; Zhang, Y.-H.; Liu, F.-C., J. Phys. Chem. A, 2001,

105, 3981-3988.

4. Schwab, A. D.; Smith, D. E.; Rich, C. S.; Young, E. R.; Smith, W. F.; de Paula, J. C.,

J. Phys. Chem. B, 2003, 107, 11339-11345.

5. Rich, C. C.; McHale, J. L., Phys. Chem. Chem. Phys., 2012, 14, 2362-2374.

6. Kalimuthu, P.; John, S. A., ACS Appl. Mater. Interfaces, 2010, 2, 3348-3351.

124

7. Castriciano, M. A.; Romeo, A.; Villari, V.; Micali, N.; Scolaro, L. M., J. Phys. Chem.

B, 2003, 107, 8765-8771.

8. Castriciano, M. A.; Donato, M. G.; Villari, V.; Micali, N.; Romeo, A.; Scolaro, L. M.,

J. Phys. Chem. B, 2009, 113, 11173-11178.

9. Castriciano, M. A.; Carbone, A.; Saccà, A.; Donato, M. G.; Micali, N.; Romeo, A.; De

Luca, G.; Scolaro, L. M., J. Mater. Chem., 2010, 20, 2882-2886.

10. Ali, M.; Kumar, V.; Baker, S. N.; Baker, G. A.; Pandey, S., Phys. Chem. Chem.

Phys., 2010, 12, 1886-1894.

11. De Luca, G.; Romeo, A.; Scolaro, L. M., J. Phys. Chem. B, 2006, 110, 7309-7315.

12. Friesen, B. A.; Nishida, K. R. A.; McHale, J. L.; Mazur, U., J. Phys. Chem. C, 2009,

113, 1709-1718.

13. Maiti, N. C.; Ravikanth, M.; Mazumdar, S.; Periasamy, N., J. Phys. Chem., 1995, 99,

17192-17197.

14. Ballinger, P.; Long, F. A., J. Amer. Chem. Soc., 1960, 82, 795-798.

15. Rich, C. C.; McHale, J. L., J. Phys. Chem. C, 2013, submitted.

125

Chapter 5 Surface Enhanced Spectroscopy of

Light Harvesting Porphyrin Aggregates

5.1 Introduction

In order to accurately probe the link between chromophore aggregate structure

and light-harvesting properties, a technique must be implemented which may overcome

the heterogeneity of the aggregate/monomer solutions. Surface-enhanced resonance

Raman spectroscopy (SERRS) combines resonance enhancement and surface

enhancement on noble metal nanoparticles to yield high quality single molecule Raman

data with enhancements reported as high as 107

for rhodamine 6G.1 Surface-enhancement

by Raman spectra using noble metal colloidal nanoparticles is an attractive method for

measuring single aggregate Raman spectroscopy of light-harvesting aggregates (LHAs).

With expected fluorescence quenching, surface-enhanced (resonance) Raman

spectroscopy (SERRS) provides the advantage of investigating LHAs without

background emission.

Surface enhancement and resonance enhancement in a combined technique has

enabled the observation of high quality SM-SERRS spectra.2,3

This technique has been

utilized for various dye molecules,4,5,6

green fluorescence protein,7 and carbon

nanotubes.8,9,10

The surface enhancement phenomenon of the adsorbate occurs as a result

of enhancement of the electric field provided by excited localized surface plasmons. As

the frequency of excitation approaches resonance with the plasmon frequency, the field

enhancement increases. In order for this phenomenon to occur, the surface cannot be

smooth and flat as the plasmon oscillations must be perpendicular to the surface in order

126

for enhancement to occur. For this reason, roughened surfaces and colloidal nanoparticle

assemblies are employed for SERS experiments as they provide surfaces in which the

localized surface oscillations can take place. Enhancement for colloidal metal

nanoparticles occurs in the form of “hot spots” associated with adsorbates located in

interstitial regions of nanoparticles.11

An advantage to using colloidal metal nanoparticles

is that their surface plasmon resonances are tunable by altering their size and shape,

allowing for adjustment of surface plasmon resonances to overlap with the absorption

bands of the adsorbate.

5.2 Experimental

5.2.1 Materials. Meso-tetra(4-sulfonatophenyl)porphine (TSPP) dihydrochoride was

purchased from Frontier Scientific. Tetrachloroauric acid, sodium citrate, and sodium

borohydride were purchased from Sigma Aldrich.

5.2.2 Preparation of gold colloids. Synthesis of ~4 nm gold nanoparticles was conducted

following the procedure in Ref. 12. Briefly, a 20 mL aqueous solution containing 2.5 x

10-4

M HAuCl4 and 2.5 x 10-4

M sodium citrate was prepared in a conical flask. Then 0.6

mL of ice-cold, freshly prepared 0.1 M sodium borohydride was added to the solution

while stirring. The solution turned pink immediately after adding sodium borohydride

indicating particle formation.

5.2.3 UV-vis electronic absorption spectroscopy. Electronic absorption spectra were

obtained using a Shimadzu UV-2501PC UV-visible spectrophotometer. Spectra of gold

nanoparticle solutions were measured in 1 cm path length quartz cells.

5.2.4 Surface-enhanced resonance Raman spectroscopy. Solutions for SERRS

measurements were prepared by combining half of the total volume of gold nanoparticle

127

(AuNP) solution with enough TSPP diacid solution and HCl so that the final

concentrations of TSPP and HCl in solution were 5 M and 0.75 M, respectively. The

acidic solution encourages aggregation of the TSPP into nanotube aggregates and also

encourages aggregation of the AuNPs which is beneficial for forming the necessary hot

spots required for surface enhancement. SERRS experiments use an inverted confocal

microscope set up with a 100x oil-immersion objective with scattered light dispersed by a

single monochromator and images collected by a CCD camera. Due to the

photosensitivity of the TSPP aggregates, excitation for SERRS measurements is provided

by 2 mW, 488 nm wavelength laser light passed through a 4.0 neutral density filter to

further reduce the laser power to 0.2 W. Samples were prepared by either spin coating

solutions of 5 M TSPP, 0.75 M HCl mixed with AuNPs on glass cover slips or by

“sandwiching” drops of solution between two glass cover slips.

128

5.3 Results and Discussion

Gold nanoparticles were chosen as a SERRS substrate for TSPP aggregates

because their surface plasmon resonances (520 nm as shown in Fig. 5.1) lie close to J-

band absorption maximum (491 nm) which may allow for both surface enhancement as

well as resonance enhancement. Figure 5.2 shows a comparison of four SERRS spectra

(SERRS 1 and 2 using the sandwich technique, SERRS 3 and 4 using the spin coat

technique) and an ensemble RR spectrum. Figure 5.3 and Figure 5.4 show histograms of

the intensities of the 243, 316, and 1534 cm-1

modes and the intensity ratios of those

modes, respectively. Since water plays an integral role in the structural and excitonic

Figure 5.1 Electronic absorption spectrum of AuNPs which observe a surface

plasmon at about 520 nm.

129

properties of these aggregates,13,14

analyzing nominally dry (in the case of the spin coated

samples) and wet (in the case of the “sandwiched” samples) samples may lead to further

insight on the influence of water in individual or small bundle of nanotubes. For both dry

and wet samples the relative intensities of the lowest frequency mode (243 cm-1

) and the

highest frequency mode (1534 cm-1

) appear to be connected. When the lowest frequency

mode intensity is large relative to the 316 cm-1

mode, the high frequency modes are

relatively less intense (SERRS 1 and SERRS 3). However, when the 243 cm-1

is less

intense relative to the 316 cm-1

mode the high frequency modes are more intense (SERRS

2 and SERRS 4). For the dry samples, specifically for SERRS 4, the intensity for the 243

cm-1

mode is less intense than the 316 cm-1

and a red shifted shoulder on the 243 cm-1

mode appears. Since the 243 cm-1

mode has been shown to be sensitive to the

environment of the aggregate, as demonstrated when the protons in the acidic aqueous

environment are isotopically substituted with deuterium in Ref. 13 and in single

aggregate resonance Raman spectra of aggregates in environments of reduced water

content in Ref. 14, the observed Raman intensity changes can be linked to disaggregation

induced by reduced water-mediated hydrogen bonding. This heterogeneity amongst the

resonance Raman intensities of the prominent modes of different aggregates has been

observed in single aggregate resonance Raman spectra in Ref. 14.

130

Figure 5.2 Normalized SERRS spectra of TSPP aggregates mixed with 3 nm

AuNPs. Black and red spectra are prepared via the sandwich method and blue and

pink spectra are prepared via the spin coat method. The green spectrum is an

ensemble resonance Raman spectrum.

131

Figure 5.3 Histogram of the Raman intensities of the 243, 316, and 1534 cm

-1

modes of the 4 SERRS measurements in sample Fig. 5.2.

132

It is worth mentioning that the some of the changes in the relative intensities of

the Raman modes may be due in part to the geometry of the hot spot formed by gold

nanoparticles. Hot spot formation by nanoparticles for surface enhancement requires that

the nanoparticles be within a few nanometers of each other.15

As the particles spread

apart, the localized field becomes more diffuse and surface enhancement is weakened. As

a result, optimal surface enhancement may require that the hot spots form in such a way

that the two nanoparticles are positioned around (or within) the wall of the aggregate

nanotube as shown in Fig. 5.3. The orientation of the hotspot interparticle axis and with

respect to the polarization of one of the J-band transitions could result in interactions

between the exciton and the localized electric field which may enhance the intensities of

Figure 5.4 Histogram of Raman intensity ratios of the 243, 316, and 1534 cm

-1

modes of the 4 SERRS measurements in Figure 5.2.

133

certain Raman modes. Furthermore as the polarization of the incident light was not

circularly polarized, the polarization bias of the aggregate will also influence the

observed Raman intensities depending on the polarization of the laser light with respect

to the polarization of the aggregate transitions.

5.4 Conclusion

Changes in the relative intensities of the low frequency modes with respect to

high frequency modes and the emergence of a red shifted shoulder near the 243 cm-1

mode in dry samples may reflect disaggregation in the aggregates due to changes in the

local environment of the aggregate probed which affect water-mediated hydrogen

bonding which influences both the structure and excitonic properties of the aggregate.

The influence of the localized surface plasmons from interparticle hot spots of gold

nanoparticles may also influence Raman intensities, however what this influence may be

Figure 5.5 Schemes for possible hot spot formation of the gold nanoparticles

(brown-red circles) around the aggregate nanotube. The third nanotube from the left

is the case where the nanoparticles form hot spots within the wall of the aggregate

such that the nanoparticles lie in the circular N-mers or in interstitial regions

between circular N-mers as shown on the right. The polarization of the predicted

transitions for a hierarchical helical nanotube aggregate are displayed here for

reference.

134

is difficult to discern without the ability to determine the number of hot spots at a given

sampling volume or the geometry of the hot spot. In further pursuit of understanding the

influence of surface enhancement on aggregates, in particular the interaction between the

localized electric field generated by hot spots and the excitons of the aggregate, we will

look at the SERRS spectra of individual aggregates on nanostructured surfaces, where the

polarization of the local electric field between hot spots may be more uniform, and use

polarized SERRS.

5.5 References

1. Nie, S.; Emory, S. R., Science, 1997, 275, 1102-1105.

2. Jiang, J.; Bosnick, K.; Maillard, M.; Brus, L., J. Phys. Chem. B, 2003, 107, 9964-9972.

3. Michaels, A. M.; Jiang, J.; Brus, L., J. Phys. Chem. B, 2000, 104, 11965-11971.

4. Michaels, A. M.; Nirmal, M.; Brus, L. E., J. Am. Chem. Soc., 1999, 121, 9932-9939.

5. Kneipp, K.; Kneipp, H., Appl. Spectrosc., 2006, 60, 322A-334A.

6. Moskovits, M.; Tay. L. L.; Yang, J.; Haslett, T., Topics in Appl. Phys., 2002, 82, 215-

226.

7. Hbuchi, S.; Cotlet, M.; Gronheid, R.; Dirix, G.; Michiels, J.; Vanderleyden, J.; de

Schryver, F. C.; Hofkens, J., J. Am. Chem. Soc., 2003, 125, 8446-8447.

8. Hartschuh, A.; Pedrosa, H. N.; Novotny, L.; Krauss, T. D., Science, 2003, 301, 1354-

1359.

9. Dresselhaus, M. S.; Dresselhaus, G.; Jorio, A.; Souza Filho, A. G.; Pimenta, M. A.;

Saito, R., Acc. Chem. Res., 2002, 35, 1070-1078.

10. Wu, Y.; Maultzsch, J.; Knoesel, E.; Chandra, B.; Huang, M.; Sfeir, M. Y.; Brus, L.

E.; Hone, J.; Heinz, T. F., Phys. Rev. Lett., 2007, 99, 027042.

135

11. Wang, Z.; Pan, S.; Krauss, T. D.; Du, H.; Rothberg, L. J., Proc. Natl. Acad. Sci.,

2003, 100, 8638-8643.

12. Jana, N. R.; Gearheart, L.; Murphy, C. J., Langmuir, 2001, 17, 6782-6786.

13. Rich, C. C.; McHale, J. L., Phys. Chem. Chem. Phys., 2012, 14, 2362-2374.

14. Rich, C. C.; McHale, J. L., J. Phys. Chem. C, 2013, submitted.

15. Etchegoin, P. G.; Le Ru, E. C., Phys. Chem .Chem. Phys., 2008, 10, 6079-6089.

136

Chapter 6 Electronic Absorption Spectrum and

Raman Excitation Profiles of TSPP Aggregates

6.1 Introduction

A main thrust of this thesis is to understand the correlation between the structure

of TSPP nanotube aggregates and their light harvesting properties. A plethora of studies

have looked at these aggregates using different techniques to examine this relationship,

from surface probe imaging techniques such as AFM and STM1,2

, to spectroscopic

techniques such as flow-induced linear dichroism spectroscopy,3 magnetic field induced

linear dichroism spectroscopy,4 and circular dichroism spectroscopy.

5 However, there is

little consensus on the internal structure of TSPP aggregates despite the large quantity of

data gathered by many researchers. Even more discouraging is that many proposed

models such as the “staircase” or “slipped deck of cards” model3,4

or the helical nanotube

model proposed by Vlaming and coworkers6 reflect some aspects of reported data but

ignore important spectroscopic features of the aggregate, thus neglecting some of the

unique complexities inherent to the system. We have proposed in previous works2,7

a

model of TSPP aggregates which consists of a hierarchical nanotube consisting of

helically arranged circular N-mer subunits which may reflect the hierarchical nature of

the nanotube observed in STM images and provide a sound model for the aggregate

excitonic properties derived from spectroscopic data, i.e. resonance Raman depolarization

ratio dispersion. In this chapter, I will attempt to utilize this model to calculate the

absorption spectrum for TSPP aggregates. Raman excitation profiles from TSPP

aggregates prepared from 0.75 M HCl in H2O (TSPP-h) and from 0.75 M DCl in D2O

137

(TSPP-d) will contribute further detail into the excitonic and vibrational properties of

these aggregates and provide further insight into the model for these aggregate.

6.2 TSPP Diacid Absorption Spectrum Model

To model the TSPP diacid absorption spectrum of the B-band, the following

equation was used to calculate the frequency dependent molecular absorptivity:

(6.1

)

where is the excitation frequency, and are the vibrational quanta of two

vibrational modes with frequencies and ; is the 0-0 electronic transition, is

Avogadro’s number, is the electronic transition dipole, is the speed of light (2.998

x 1010

cm/s), is the refractive index of water at room temperature (1.33), is Planck’s

constant h divided by 2and is the Gaussian inhomogeneous width. The square of

Franck-Condon factors and for the 0- transitions were

determined by the equation:

(6.2)

where is the dimensionless displacement for vibrational mode i.

In the calculation discussed in this chapter, the two modes examine will include

one low frequency mode and one high frequency mode observed in the resonance Raman

spectra of the TSPP diacid (234 cm-1

and 1234 cm-1

specifically). For the low frequency

mode we will include thermally populated vibrational quantum states in the electronic

ground state for vibrational quanta = 0, 1, and 2. The Franck-Condon factors for >

138

0 are determined using the formalism presented by Manneback.8 We calculate that the

population for these states can be determined by:

(6.3)

where kT = 206 cm-1

for thermal energy at room temperature. The normalized population

is then determined for a certain vibrational quantum number, i.e.,

(6.4)

The normalized population is then multiplied by the respective Franck-Condon factor

with the corresponding ground state vibrational quantum number to weight the

contribution of those Franck-Condon factors in calculating the absorption spectrum.

6.3 Frenkel Polaron Theory

The theory used in modeling the absorption spectra of the circular N-mer and

hierarchical helical nanotube aggregates was described previously by Spano9 and

Vlaming and coworkers6. In this theory a Frenkel exciton is defined as an excitation in a

molecular assembly which is comprised of a vibronically excited central molecule

surrounded by vibrationally, but not electronically, excited molecules. To quantitatively

account for exciton-vibrational coupling, or exciton-phonon coupling, we assume a

simple model in which the electronic ground state and excited states can be represented

by harmonic wells. To describe the collective excitations in the aggregate we employ a

multiparticle basis set consisting of one particle excitations, , where molecule n is

vibronically excited with excited state vibrational quanta and all other molecules are

electronically and vibrationally unexcited; and two particle excitations, ,

where molecule n is vibronically excited with excited state vibrational quanta ,

139

neighboring molecule is only vibrationally excited with ground electronic state

vibrational quanta , and all other molecules are unexcited. The two particle excitations

are necessary in describing the spatial extent of the vibrational distortion field

surrounding the central vibronic excitation. Thus the th eigenstate of the aggregate

Hamiltonian can be described as a linear combination of the one-particle and two-particle

basis states (for a single excited state):

(6.5)

where

and

are the coefficients for the one- and two-particle basis states.

For multiple excited states, as will be shown here for J- and H-exciton states, additional

one- and two-particle terms are added for each excited state. These coefficients can be

found from diagonalization of the aggregate Hamiltonian H.

The diagonal elements of the Hamiltonian consist of the energies of the localized

basis states:

(for one particle states) (6.6a)

(for two particle

states)

(6.6b)

where is the monomer molecular transition frequency, is monomer-to-aggregate

site shift due to nonresonant intermolecular interactions, is the frequency of an

intramolecular vibration with vibrational quanta and , and represents disorder-

induced change in the transition energy at site n. In this study, we neglect and in our

calculation of the diagonal elements of the Hamiltonian for simplicity but acknowledge

140

their importance. The off-diagonal elements of the Hamiltonian are determined by the

typical excitonic Hamiltonian:

(6.7a)

(6.7b)

(6.7c)

(6.7d)

for .

These off-diagonal elements allow for resonant transfer between one-particle states (Eq.

6.7a), two-particle states (Eq. 6.7b), as well as between one-particle and two particle

states (Eqs. 6.7c and 6.7d). m and n index the basis state where only molecule m or n are

in a vibronic excited state and m and n index a neighboring molecule which is only

vibrationally excited. is the excitonic coupling strength between mth and nth basis

states. In this study we determine the coupling strength using the point dipole

approximation:

(6.8)

where is the electronic transition dipole moment, is the distance between

molecules, is the unit vector for the direction of the transition dipole moment at

molecule n, and is the unit vector for the direction of the distance between molecules.

The overlap integrals are calculated by first separating the electronic and vibrational

parts, assuming the Born-Oppenheimer approximation applies here, to generate the

Franck-Condon overlaps for each transition from the ground state to the excited. The

Franck-Condon overlaps, or Franck-Condon factors, are evaluated using the formalism

141

established by Manneback.8 For the 1-particle-1-particle interactions, we assume the

ground state is both electronically and vibrationally unexcited ( ). For the 2-

particle-2-particle interactions, only elements in which and are

considered, as emphasized by the delta functions. If or , then one would

have to consider the overlap integral of or with the ground vibrational state,

which would reduce to delta functions, i.e.,

(6.9)

which implies that unless , the overlap vanishes as does the matrix element. The

same holds true for the 1-particle-2-particle elements. For the aggregate absorption

spectrum calculations the nearest neighbor approximation is invoked, i.e., ,

neglecting long distance coupling whose coupling strength tends to drop off precipitously

beyond coupling between neighboring molecules.

After diagonalization of the aggregate Hamiltonian to obtain the eigenvectors

(coefficients) and corresponding eigenvalues (energies for each eigenstate) one can

calculate the normalized electronic absorption spectrum:

(6.10)

In equation 6.14, is the number of monomers in the aggregate, is the magnitude of

the transition dipole moment of the monomer, is the unit vector of the transition dipole

moment of the monomer in the aggregate, is the unexcited ground state, is the

exciton state, and is homogeneous lineshape broadening function which

depends on the excitation frequency, , and the frequency eigenvalues of the

142

eigenstates, . The lineshape broadening function which dresses each transition

with a Gaussian is expressed as:

(6.11)

where is the homogeneous broadening term defining the linewidth of the band. The

oscillator strength for each eigenstate is determined by . If the unit vectors

of the transition dipole moment are known and the coefficients have been calculated, then

the oscillator strength can be expressed as:

(6.12)

6.4 Experimental

6.4.1 Calculation. Electronic absorption spectra were calculated using original written

script programs on MATLAB R2012b. Due to the large size of the data sets, calculations

were performed in parallel on a server with 2 processors each with 12 cores (1 core

equivalent to 1 MATLAB worker).

6.4.2 Sample Preparation. Meso-tetra(4-sulfonatophenyl)porphine dihydrochoride was

purchased from Frontier Scientific. Deuterium oxide (D2O; D, 99.9%) and deuterium

143

chloride (DCl; D, 99.5%) were purchased from Cambridge Isotope Laboratories, Inc.

Preparation of the aggregate samples was previously described in Ref. 7. Briefly,

solutions of H2TSPP2-

and D2TSPP2-

diacid monomer were first prepared by dissolving

the dihydrochloride salt of TSPP in Millipore ()water with HCl and in D2O with

DCl, respectively, to yield concentrations of 50 to 100 M of porphyrin and 1 x 10-3

M of

the respective acid. Concentration was measured by UV-visible absorbance spectroscopy

via Beer’s Law using the diacid monomer molar absorptivity which was 4.43 x 105 L

mol-1

cm-1

at the Soret band maximum of 434 nm. The diacid solutions were combined

with more HCl or DCl to induce aggregation and diluted with H2O or D2O to yield

aggregate solutions consisting of 5 M or 50M concentrations of porphyrin and 0.75 M

HCl or DCl.

6.4.3 Quantitative Resonance Raman Spectroscopy. The procedure for the internal-

external standard method for measuring absolute Raman cross sections was previously

reported.10

Resonance Raman spectra of the TSPP-h and TSPP-d aggregates and a

transparent reference (either neat cyclohexane or acetonitrile) were measured

simultaneously by first focusing the excitation beam on the transparent reference,

collimating the beam, and then refocusing the beam on the aggregate sample in a

confocal backscattering arrangement so that Raman scattering from both reference and

sample were collected by the spectrometer. The scattered light was dispersed with a

SPEX Triplemate triple monochromator and detected with a liquid nitrogen cooled CCD

camera. Polarized spectra were collected using a Melles-Griot polarizer for polarization

selection followed by a Thorlabs DPU-25 depolarizer for scrambling to avoid

polarization bias. Cross section measurements and calculations were performed using

144

OriginPro 8 and Mathcad. Laser lines of wavelengths 454.5 nm, 457.9 nm, 465.8 nm,

472.7 nm, 476.5 nm, 488 nm, 496.5 nm, and 514.5 nm were produced by an argon ion

gas laser.

6.5 Results and Discussion

6.5.1 Diacid Monomer Absorption Spectrum. Figure 6.1 shows the experimental

absorption spectrum of the TSPP diacid compared to the best fit calculated absorption

spectrum for the TSPP diacid. The two vibrational modes were chosen from the diacid

monomer absorption spectrum (see Refs. 7 and 10) to provide representation of both low

and high frequency modes. We assume here that the potential surfaces of the ground and

Figure 6.1 The electronic absorption spectrum for the TSPP diacid (black) and the

best fit calculated absorption spectrum for the TSPP diacid (red) using equation

6.1 with the listed parameters for the calculation.

145

electronic excited states can be represented by harmonic wells where the vibrational

energy levels in each potential have equal energy spacing. Franck-Condon factors for

each vibrational mode were determined with guesses for the dimensionless displacement,

, and including excited state vibrational quanta v = 1, 2, … 10. For the best fit to

experiment, the values for the dimensionless displacements, transition frequency (00),

homogeneous broadening (), and transition dipole moment (ge) are presented in Figure

1. For the low frequency mode, thermal populations for the v = 0, 1, and 2 vibrational

quanta in the ground state were considered whereas for the high frequency mode only the

v = 0 vibrational quanta in the ground state is considered.

Figure 6.2 The calculated absorption spectrum of a TSPP circular 16-mer

aggregate using equation 6.10, incorporating 1- and 2-particle states, vibrational

quanta v = 0, 1, 2 with two vibrational modes (236 cm-1

and 1234 cm-1

).

146

6.5.2 Circular 16-mer Absorption Spectrum. The absorption spectrum in Figure 6.2 was

calculated using the aforementioned model for circular 16- mer aggregate with two

vibrational modes (236 cm-1

and 1234 cm-1

) with vibrational quanta v = 0, 1, and 2 and

including 2-particle states. For a circular 16-mer, diacid monomers were projected around

in a circle with equal spacing, 22.5o between projections around the 3 nm radius circle.

The ~2 nm long porphyrin were oriented in such a way that the transition dipole moments

of the porphyrin within the plane of the ring made a 2/20, 18o, angle with the local

tangent. The orthogonal transition dipole moment of each diacid is then oriented

perpendicular to the plane of the ring. Both in-plane and out-of-plane transition dipole

moments for each diacid in the aggregate had magnitudes of 14.5 Debye, as calculated in

the diacid monomer absorption spectrum. In this calculation we only consider nearest-

neighbor coupling with boundary conditions that treat the 16th

porphyrin in the ring as the

nearest neighbor of the 1st porphyrin.

The calculated J-band transition occurs at 476 nm and is doubly degenerate. The

calculated H-band transition occurs at 415 nm and is nondegenerate. The combined

oscillator strength of the central H-band and its vibronic side bands is equivalent to the

combined oscillator strength of the J-band with its limited vibrational structure. Using the

point dipole approximation to determine nearest neighbor coupling, the coupling strength

for the in-plane transitions and out-of-plane transitions were determined to be -1106 cm-1

and 660 cm-1

, respectively, assuming that the in-plane and out-of-plane transition dipoles

for the monomer were equivalent in magnitude and neglecting possible site shifts due to

perturbations of the molecular geometry upon aggregation.

147

In the calculation of the circular 16-mer, the concentration of oscillator strength

into a single J-band for the in-plane transitions and the redistribution of oscillator strength

among the vibronic side bands of the H-band are consistent with stronger excitonic

coupling for the in-plane transitions and weaker excitonic coupling in the out-of plane

transitions. In strong excitonically coupled aggregates, the oscillator strength is mainly

concentrated in a single peak due to the absorption of a nearly free exciton. The exciton is

created with no change in the ground-state nuclear coordinates which results in

essentially no vibrational relaxation following vertical excitation because the excitation

resonantly jumps to a neighbor before nuclear relaxation can occur.9

Figure 6.3 Model absorption spectrum for the TSPP hierarchical helical nanotube

aggregate without vibrations defining excitonic coupling through the point dipole

approximation.

148

6.5.3 Nanotube Aggregate Absorption Spectrum. Modeling the absorption spectrum for

the nanotubular aggregate adds complexity to the aggregate as the number of basis states

increases with the length of the nanotube. In order to accurately replicate the

spectroscopic properties of the nanotube aggregate, the modeled nanotube has to be

sufficiently long. Incorporating two vibrational modes with the large number of circular

16-mers (which act as macromolecules) in conjunction with two particle terms results in

very large computations. To simplify the model, vibrations were left out of the

calculation for a hierarchical helical nanotube consisting of 270 circular 16-mer subunits,

for which the resulting absorption spectrum is shown in Figure 6.3. The parameters for

Figure 6.4 The electronic absorption spectrum of TSPP-h (black) and TSPP-d

(red) aggregates prepared from the 50 M concentrations of the corresponding

diacid monomer in 0.75 M HCl/DCl in H2O/D2O.

149

the magnitudes of the transition dipole moment of each circular N-mer, as well as the

frequency of the J- and H-transitions were manipulated so that the center of the circular

aggregate J-band was positioned at 492 nm (matching closely with the experimental J-

band in Fig. 6.4). The nanotube is constructed by taking a hexagonally closed packed

array of circular 16-mers and then wrapping the array on itself in such a way that subunits

form a helical structure with a chiral angle of about 5.8o and a nanotube radius of 8.2 nm,

matching the imaged dimension of the tube.1,2,6

Each circular N-mer is projected on to the

next with a helical angle of ~41.9o. The in-plane transition dipole moments of the circular

aggregates are oriented in such a way that one transition is polarized along the long axis

of the tube and the other transition is polarized along the short axis of the tube. The out-

of-plane, H-band transition dipole moments are polarized perpendicularly to the nanotube

wall.

The resulting nanotube J-band consists of two closely spaced transitions, a

nondegenerate transition polarized along the long axis (we will call this the z-axis) with a

wavelength of 494 nm and a doubly degenerate transition polarized along the x- and y-

axes with a wavelength of 491 nm. The H-band, which derives from doubly degenerate

orthogonal transitions polarized along the x- and y-axes, is centered at 400 nm, which is

much higher in energy than the H-band is experimentally. More work is being done on

this calculation to accurately obtain the transition frequencies, as well as the oscillator

strengths and transition dipole moments, of the J- and H-band of the circular N-mer and

aggregate nanotube that will assist in testing the validity of the proposed hierarchical

helical nanotube model. But what can be obtained from this preliminary calculation is

that as a result of excitonic coupling the in-plane transitions of the circular N-mer, the

150

resulting J-band transitions are closely spaced in energy and only shift slightly from the

circular aggregate J-band transition energy. Thus, if the model is correct, the diacid

monomers that make up the circular aggregate must undergo a site-shift, possibly due to

further symmetry distortion upon aggregation.

Figure 6.5 Background subtracted resonance Raman spectra of TSPP-h aggregates

with respective reference standard (acetonitrile or cyclohexane) excited with

wavelengths spanning the J-band. The reference standard used for excitation

wavelengths 454.5 nm, 457.9 nm, and 514.5 nm was acetonitrile (920 cm-1

mode for

reference). The reference standard used for excitation wavelengths 465.8 nm, 472.7

nm, 476.5 nm, 488 nm, and 496.5 nm) was cyclohexane (800 cm-1

mode for

reference). Intensities of Raman modes are raw intensities. Peaks with asterisks

above them are reference standard Raman modes.

151

Figure 6.6 Background subtracted resonance Raman spectra of TSPP-d aggregates

with respective reference standard (acetonitrile or cyclohexane) excited with

wavelengths spanning the J-band. The reference standard used for excitation

wavelengths 454.5 nm, 457.9 nm, and 514.5 nm was acetonitrile (920 cm-1

mode

for reference). The reference standard used for excitation wavelengths 465.8 nm,

472.7 nm, 476.5 nm, 488 nm, and 496.5 nm) was cyclohexane (800 cm-1

mode for

reference). Intensities of Raman modes are raw intensities. Peaks with asterisks

above them are reference standard Raman modes.

152

6.5.4 Raman Excitation Profiles. Figures 6.5 and 6.6 show the resonance Raman spectra

of TSPP-h and TSPP-d aggregates, respectively, using the internal-external standard

method with excitation frequencies spanning the J-band, shown in Fig. 6.7. Figures 6.8

and 6.9 show the Raman excitation profiles of the seven prominent modes of the TSPP-h

and TSPP-d aggregates respectively with their corresponding absolute Raman cross

sections listed in Table 6.1 and 6.2. In both protiated and deuterated aggregates the

Raman cross sections of the low frequency modes diminish quickly with respect to the

high frequency modes with less resonant excitation wavelength. As the out-of-plane

distortion of the diacid porphyrin factors greatly in interchromophore coupling in the

formation of the aggregate, it makes sense that the intensities of the low frequency

Figure 6.7 Electronic absorption spectra of the J-band of the TSPP-h (black) and

TSPP-d (red) aggregates with vertical lines indicating the excitation wavelengths

used in the aforementioned quantitative resonance Raman spectra.

153

modes, which correspond to out-of-plane vibrations, are dramatically enhanced when

resonant with the J-band transitions. As observed in the relative Raman intensities of

TSPP-h and TSPP-d aggregates in our previous work,7 the Raman cross sections of the

low frequencies modes relative to the high frequency modes are smaller in the TSPP-d

aggregates than in the TSPP-h aggregates. Moreover, when one compares the cross

sections of the low frequency modes between the TSPP-h and TSPP-d aggregates at 488

nm, the TSPP-h aggregate cross sections are larger than the TSPP-d aggregate cross

sections by a factor of ~1.5. Figure 6.10, which shows the Raman excitation profile of the

sum-over-all modes cross section data, shows the total absolute Raman cross section for

the TSPP-h aggregates is larger than that of the TSPP-d aggregates by a factor of ~1.4.

Previous resonance light scattering measurements have shown that TSPP-d aggregates

are ~1.4 times more coherent than the TSPP-h aggregates. As the intensity of relevant

Raman modes is proportional to the strength of exciton-phonon coupling and exciton-

phonon coupling leads to a decrease in coherence,11,12

the larger absolute Raman cross

sections, particularly along the low frequency modes, in the TSPP-h aggregates than in

the TSPP-d aggregates is consistent with stronger exciton phonon coupling and, as a

result, weaker coherence in the TSPP-h aggregates.

154

Table 6.1 Absolute Resonance Raman Cross Sections (x 10-22

cm2/molecules) for

TSPP-h Aggregates with Excitation Wavelengths Spanning the J-band.

Raman Shifts (cm-1)

243 317 698 983 1013 1228 1534

454.5 nm 0 0 0 0.0241 0.00644 0.135 0.354

457.9 nm 0 0 0 0.155 0.0485 1.03 1.84

465.8 nm 0.0262 0.0354 0.0627 0.649 0.347 1.48 1.10

472.7 nm 0.0568 0.0745 0.132 0.442 0.218 0.468 0.445

476.5 nm 0.0973 0.178 0.301 0.505 0.228 0.441 0.462

488 nm 2.63 1.96 0.578 0.637 0.286 0.684 1.20

496.5 nm 0.596 0.530 0.181 0.246 0.163 0.317 0.961

514.5 nm 0.00241 0.00508 0.00578 0.0184 0.00799 0.0169 0.0983

Figure 6.8 Resonance Raman excitation profiles of the 243 cm

-1

(black), 317 cm-1

(red), 698 cm-1

(blue), 983 cm-1

(pink), 1013 cm-

1 (green), 1228 cm

-1 (indigo), and 1534 cm

-1 (violet) modes of

TSPP-h aggregates.

155

Table 6.2 Absolute Resonance Raman Cross Sections (x 10-22

cm2/molecules) for

TSPP-d Aggregates with Excitation Wavelengths Spanning the J-band

Raman Shift (cm-1)

239 315 697 957 1004 1225 1534

454.5 nm 0 0 0 0.0455 0.0136 0.123 0.549

457.9 nm 0.00705 0.00579 0.0166 0.112 0.0259 0.304 0.992

465.8 nm 0.0296 0.0334 0.0481 0.416 0.109 0.850 0.850

472.7 nm 0.0441 0.0574 0.242 0.613 0.133 0.325 0.315

476.5 nm 0.0957 0.127 0.281 0.527 0.0983 0.274 0.343

488 nm 1.52 1.15 0.359 0.627 0.126 0.358 0.892

496.5 nm 0.495 0.398 0.154 0.354 0.0981 0.172 0.829

514.5 nm 0.00198 0.00379 0.00535 0.0163 0.00559 0.0121 0.106

Figure 6.9 Resonance Raman excitation profiles of the 239 cm

-1

(black), 315 cm-1

(red), 697 cm-1

(blue), 957 cm-1

(pink), 1004 cm-

1 (green), 1225 cm

-1 (indigo), and 1534 cm

-1 (violet) modes of

TSPP-d aggregates.

156

Increases in the Raman cross section of the high frequency modes at bluer

excitation wavelengths track with their overlap of the fast-relaxing fluorescence shown in

Ref. 7. This “fluorescence-induced enhancement” complicates an already complicated

picture of the excitonic properties of these aggregates. Both resonance Raman and

fluorescence may be expressed as a , nonlinear spectroscopic process called

spontaneous light emission13,14

which may allow mixing of the fluorescence-like part

with the Raman-like part when the fluorescence lifetime is sufficiently short:

Figure 6.10 The sum-over-modes REPs of TSPP-h aggregates (red) and

TSPP-d aggregates (black). Data points are connected by polynomial

spline to guide the eye.

157

(6.13)

This equation is only valid in the fast modulation limit which is thought to be the case for

these aggregates due to the observed exchange-narrowing of the J-band. However, in the

slow modulation limit a third term in the spontaneous light emission equation arises

related to a phenomenon called “broad Raman”.15,16

Broad Raman consists of a series of

progressively broader lineshapes centered around Raman lines whose classification as

either fluorescence or Raman depends on the correlation time of the bath relative to the

lifetime of the excited electronic state. In the slow modulation limit, when the correlation

time of the solvent is very long relative to the lifetime of the excited electronic state,

broad Raman consists of a series of very narrow lineshapes, thus behaving more like

Raman modes. One other possible explanation for this observed enhancement may arise

from phonon-mediated interactions with a dark excitonic state, similar to what is

observed in single walled carbon nanotubes,17

which may cause enhancement of phonon

modes which couple to the exciton. If high frequency mode vibrations couple strongly to

this dark exciton then an enhancement in their Raman intensities would result.

6.6 Conclusion

Modeled electronic absorption spectra of TSPP circular 16-mers show a doubly

degenerate J-band which exhibits strong excitonic coupling and a nondegenerate H-band

which exhibits weak excitonic coupling, as demonstrated by the redistribution of its

158

oscillator strength among vibronic side bands. Without perturbation of the diacid

monomer electronic transition upon aggregation, which would be accounted for by the

inclusion of a site shift, the resulting transition frequencies of the J- and H-band in the

calculated electronic absorption spectrum of the circular 16-mer is blue-shifted from the

experimental TSPP aggregate J- and H-band transition frequencies (476 nm vs. 491 nm

for the J-band, 415 nm vs 423 nm for the H-band). A simple calculation of the absorption

spectrum of the hierarchical, helical nanotube aggregate demonstrates small shifts in the

long axis J-band transition and the short axis J-band transition from the original circular

16-mer J-band transition as a result of excitonic coupling of the circular 16-mer subunits.

These observations suggest that the inclusion of a site shift in the calculation of the

circular 16-mer, resulting perhaps from geometry distortion of the diacid porphyrin

monomer upon aggregation, may be necessary for producing a more accurate model of

the nanotube aggregates. Raman excitation profiles of the prominent modes of TSPP-h

and TSPP-d aggregates show smaller absolute Raman cross sections, and thus weaker

exciton-phonon coupling, along the low frequency modes for the TSPP-d aggregates. The

enhancement of the observed fluorescence-enhanced Raman scattering for the high

frequency modes is still a mystery. Spontaneous light emission provides a mechanism by

which constructive interference with fluorescence, or broad Raman, may enhance Raman

modes. Phonon-mediated interactions with dark exciton states in the J-band through high

frequency vibrational modes may also lead to this high energy feature in the REPs. To

bring about a better understanding of the REPs of these aggregates, and completing the

picture started with the modeling of the absorption spectrum, future work will focus on

modeling these REPs utilizing both a interpretation of Raman scattering as well as a

159

linear spectroscopy interpretation which incorporates both A-term Raman scattering and

B-term Raman scattering to accurately portray the influence of phonon-mediated

processes.

6.7 References

1. Friesen, B. A.; Nishida, K. A.; McHale, J. L.; Mazur, U. J. Phys. Chem. C, 2009, 113,

1709-18.

2. Friesen, B. A.; Rich, C. C.; Mazur, U.; McHale, J. L. J. Phys. Chem. C 2010, 114,

16357-16366.

3. Ohno, O.; Kaizu, K.; Kobayashi, H., J. Chem. Phys., 1993, 99, 4128-4139.

4. Kitahama, Y.; Kimura, Y.; Takazawa, K., Langmuir, 2006, 22, 7600-7604.

5. Ali, M.; Kumar, V.; Baker, S. N.; Baker, G. A.; Pandey, S. Phys. Chem. Chem. Phys.

2010, 12, 1886-1894.

6. Vlaming, S. M.; Augulis, R.; Stuart, M. C. A.; Knoester, J.; van Loosdrecht, P. H. M.,

J. Phys. Chem. B, 2009, 113, 2273-2283.

7. Rich, C. C.; McHale, J. L., Phys. Chem. Chem. Phys., 2012, 14, 2362-2374.

8. Manneback, C., Physica, 1951, 17, 1001.

9. Spano, F. C., Acc. Chem. Res., 2010, 43, 429-439.

10. Rich, C. C.; McHale, J. L., J. Phys. Chem. C., 2013, submitted.

11. Spano, F. C.; Kuklinski, J. R.; Mukamel, S., J. Chem. Phys., 1991, 94, 7534-7544.

12. Spano, F. C.; Silvestri, L.; Spearman, P.; Raimondo, L.; Tavazzi, S., J. Chem. Phys.,

2007, 127, 184703.

13. Mukamel, S., Principles of Nonlinear Optical Spectroscopy, Oxford University Press,

New York, 1995.

160

14. Mukamel, S., J. Chem. Phys., 1985, 82, 5398-5408.

15. Sue, J.; Yan, Y. J.; Mukamel, S., J. Chem. Phys., 1986, 85, 462-474.

16. Sue, J.; Mukamel, S., J. Chem. Phys., 1988, 88, 651-665.

17. Blackburn, J. L.; Holt, J. M.; Irurzun, V. M.; Resasco, D. E.; Rumbles, G., Nano

Letters, 2012, 12, 1398-1403.

161

Chapter 7 Summary, Conclusions, and Outlook

7.1 Summary of Results

The goal of this dissertation was to discern the internal structure of TSPP

aggregates and determine the corresponding excitonic properties using (primarily) Raman

spectroscopy as a probe. To reiterate, my hypothesized scheme for the aggregate of TSPP

aggregates prepared in aqueous acidic conditions (as referred to in Chapters 1 and 2 as

well as Refs. 1, 2, and 3) involves, first, the assembly of porphyrin diacid monomers into

circular N-mers via intermolecular electrostatic interactions between the positively

charged, protonated porphyrin core of one porphyrin and the negatively charged

peripheral sulfonato groups of the neighboring porphyrin. The circular shape of this

hierarchical subunit is defined by the out-of-plane distortion of the each diacid porphyrin.

Thus, these circular aggregates have doubly degenerate in-plane transitions (X,Y) and a

nondegenerate out-of-plane transition (Z) which correspond to the J-band and H-band

respectively. As a result of water mediated hydrogen bonds, these circular N-mers

organize into a hexagonally closed packed sheet which wraps around on itself to form a

helical nanotube of with a ~18 nm diameter and ~2 nm wall thickness. Excitonic coupling

of these circular N-mers result in a composite J-band consisting of a nondegenerate

transition aligned along the long axis of the nanotube (the z-axis) and doubly denegerate

transitions aligned along the short axis (x and y-axes). Do the results of the previously

described experiments provide evidence to justify this model? To answer this question, I

will summarize the results of this dissertation, state the overall conclusions from project

162

as a whole, and project an outlook on what questions remain and what future should be

conducted to pursue their answers.

Preparations of TSPP dihydrochloride salt in 0.75 M HCl in H2O and in 0.75 M

DCl in D2O produce aggregates (which will be refered to as TSPP-h and TSPP-d

aggregates, respectively) which in atomic force microscope (AFM) images appear

structurally similar. Electronic absorption spectroscopy, however, shows a subtle

broadening of the J-band for the TSPP-d aggregates compared to the TSPP-h aggregates

with dramatic relative intensity changes in J-band resonance Raman modes revealing

more reorganization along low frequency vibrational modes in the protiated aggregates.

Depolarization ratio dispersion and Raman intensity changes for excitation wavelengths

spanning the J-band evidence interference from overlapping transitions. The resonance

light scattering intensity of the J-band for the TSPP-d aggregates is twice as strong as that

for the TSPP-h aggregates which, since resonance light scattering is proportional to the

square of the coherence number, , corresponds to an increase in coherence by a factor

of ~1.4 for deuterated aggregates. Since the amplitude of the relevant Raman modes is

proportional to the exciton-phonon coupling in the aggregate,4,5

the increased coherence

in the TSPP-d aggregates may be explained by the less intense low frequency modes,

related to out-of-plane distortion vibrations, which are related to diminished exciton-

phonon coupling. The stronger coherence in the deuterated aggregates also explains the

broadening of the electronic absorption spectrum which would increase splitting between

the composite transitions of the J-band. The influence of isotopic substitution on the

exciton-phonon coupling and effective coherence of the aggregate highlights the

163

importance of water-mediated hydrogen bonding not only on the structure of the TSPP

aggregates but also on their exciton dynamics.

Measurement of large absolute resonance Raman cross sections of TSPP-h

aggregates on the order of 10-22

cm2/molecule, provide impetus for single aggregate

resonance Raman spectroscopy without the need of Raman intensity enhancement, such

as SERS.6 Comparison of the absolute Raman cross sections of TSPP-h aggregates with

514.5 nm wavelength excitation to the absolute Raman cross section of H2TSPP2+

diacid

with 454.5 nm wavelength (both excitations are in the red wing of the respective

absorption bands) show very little evidence for aggregation-enhanced Raman scattering.

The cross sections of the prominent modes of the aggregate being considerably less than

that of the diacid with exception of two of the high frequency modes (1228 cm-1

and 1534

cm-1

for the aggregate, 1234 cm-1

and 1540 cm-1

for the diacid).

Single aggregate resonance Raman spectra of TSPP-h aggregates were deposited

to dryness on a glass cover slip. Changes in the relative Raman intensities of the low and

high frequency modes measured at different aggregates as well as different spots on an

aggregate reflect heterogeneity within each aggregate nanotube. Resonance light

scattering images of the aggregates show coherence hot spots along the length of the

nanotube. Since these aggregates are probed in environments of limited water content,

these hot spots could be spots with sufficient water to maintain structural integrity and

strong excitonic coupling. However, since relative Raman intensities of the low and high

frequency modes do not appear to track with coherence it is also possible that bundles of

nanotubes, which cannot be resolved with optical spectroscopy since the widths of the

nanotubes are diffraction limited, may cause changes in intensities related to the number

164

of aggregates in the scattering. Laser heating of aggregate individuals, which perturbs the

water-mediated hydrogen bonding around the aggregate, causes a decrease in the relative

Raman intensities of the low frequency modes compared to the high frequency modes.

This further implies the importance of water-mediated hydrogen bonding on the structure

and excitonic properties of the nanotube aggregates. Surface-enhanced resonance Raman

spectra (SERRS) of TSPP-h aggregates prepared in nominally dry and wet environments

show variations in the relative Raman intensities for the low and high frequency modes

similar to what is observed in the single aggregate measurements. Perturbations to the

local environment by the localized surface plasmon formed by the hot spot may

contribute to further intensity changes in the Raman modes. Polarized single aggregate

resonance Raman spectroscopy confirm excitons aligned along the long axis and the short

axis but also indicates that off diagonal components of the transition polarizability for the

prominent modes are nonzero, indicating that vibronic coupling occurs between the long

axis J-band transition and the short axis J-band transition through those vibrations.

Preparation of aggregates of TSPP in ethanol and in dichloromethane show that

aggregation can occur in nonaqueous solvents, but it is either inhibited by interaction

with the nonaqueous environment or results in entirely unique aggregation from what is

observed in acidic aqueous preparations. In neat ethanol, aggregates of TSPP will form

that have similar spectroscopic characteristics of the aqueous preparation with an

exchange-narrowed strong J-band and weak H-band. But over time the ethanol, which

has a considerably lower pKa than the diacid monomer, will pull the protons off of the

diacid monomer converting it into the free base monomer of TSPP, resulting in

disaggregation. With a sufficient amount of water combined with ethanol with 0.75 M

165

HCl, aggregation will stabilize but will occur more slowly. When preparing the

tetrabutylammonium free base salt in dichloromethane and exposing the mixture to HCl

vapor for 1 hour, round aggregates with diameters and cross section heights similar to the

nanotube aggregate (~35 nm and ~4 nm respectively) form with a different absorption

spectrum. The resulting absorption spectrum for these aggregates has a peak maximum at

~450 nm. Furthermore, depolarization ratios for the resonance Raman modes excited

with 454.5 nm wavelength show depolarization ratios unique to these aggregates.

The model for the absorption spectrum of the circular 16-mer aggregate was

calculated using the Frenkel polaron theory presented by Spano.7 This calculation shows

that for a circular 16-mer, the J-band derives from a doubly degenerate transition which

exhibits strong excitonic coupling, where the oscillator strength is concentrated mostly in

a single band, and the H-band derives from a nondegenerate transition which exhibits

weak excitonic coupling, where the oscillator strength is redistributed amongst the

vibronic side bands as well. While this calculated spectrum does not reflect the properties

of the nanotube aggregate, the strong excitonic coupling in the J-band and the weak

excitonic coupling in the H-band is consistent with what was observed in the resonance

light scattering spectrum of the TSPP nanotube aggregates. The small splitting of the

circular 16-mer J-band into longitudinal and transverse components upon formation of

the nanotube aggregate suggests that the transition frequency of the J-band for the 16-mer

should be centered near the observed nanotube aggregate J-band. Thus it is likely that a

site shift occurs upon assembly of the 16-mer due to perturbations of the geometry of the

diacid monomer.

166

The TSPP-h and TSPP-d aggregate Raman excitation profiles (REPs) show that

the absolute Raman cross sections of the low frequency modes diminish dramatically

further from resonance than the high frequency modes owing to the role of out-of-plane

distortion in intermolecular coupling in the aggregates. The total absolute Raman cross

section over all of the Raman modes for all excitation frequencies is larger for the TSPP-

h aggregates than the TSPP-d aggregates, corresponding to the stronger exciton-phonon

coupling in the protiated aggregates. Due to what appears to be overlap with a fast-

relaxing fluorescence, the high frequency Raman modes become enhanced resulting in a

blue shifted feature in the Raman excitation profile in Figure 6.10. “Fluorescence-

enhanced” Raman scattering may derive from the influence of fluorescence or broad

Raman on Raman scattering through a (3) interpretation of Raman spectroscopy.

8,9,10,11

7.2 Conclusions

One of the central themes of this work is that the environment in which the

aggregate is prepared matters. For the nanotube aggregates of TSPP, water-mediated

hydrogen bonding plays an immense role in both their structure and excitonic properties.

The intimate role of water is reflected in the heterogeneity of the coherence along a

nanotube aggregate under nominally dry conditions, the dramatic influence on exciton-

phonon coupling and the effective coherence revealed in resonance Raman and resonance

light scattering intensities of TSPP aggregates, and in the different structural and

spectroscopic properties of TSPP aggregates prepared in nonaqueous systems. In our

model, water molecules not only function in assembly of the circular N-mer subunits into

the hierarchical helical nanotube, but also allow for excitonic coupling between these

aggregates, thus influencing their light harvesting properties.

167

Resonance Raman spectroscopy has proven to be a useful tool in providing

insight into the excitonic structure of TSPP aggregates as well as providing evidence

which defends the proposed hierarchical, helical nanotube model. Changes in the relative

and absolute Raman intensities and depolarization ratios with the excitation wavelength

spanning the J-band support a composite J-band consisting of closely spaced transitions

which is consistent with the proposed model for aggregate assembly as theory predicts

that the J-band consists of two closely spaced transition related to a nondegenerate long

axis (z-axis) transition and doubly degenerate short axis (x- and y-axes) transitions.

Polarized single aggregate resonance Raman spectroscopy further supports this

hypothesis as polarized resonance Raman intensity ratios of the 243 cm-1

, 316 cm-1

, and

1534 cm-1

modes suggests the presence of a strong z-polarized transition with a x-

polarized (or y-polarized) transition that is ~ weaker as indicated by the relative

magnitudes of the diagonal elements of the transition polarizability tensor (

). The nonzero polarized resonance Raman intensities for scattering with

perpendicular polarization with respect the excitation further imply nonzero off-diagonal

components of the transition polarizability, which arise in the case of vibronic coupling

between two excited electronic states which are close in energy through B-term

enhancement.

The strong excitonic coupling predicted for the J-band transition and the weak

excitonic coupling predicted for the H-band transition for the circular 16-mer is

consistent with strong RLS signals with respect to the J-band observed for the aqueous

TSPP nanotube aggregates and provides impetus for future modeling of the nanotube

aggregate absorption spectrum.

168

7.3 Outlook and Future Work

The structural and spectroscopic complexity of these aggregates shown in this

work leads to many interesting questions that require further experimentation to answer.

What mechanism causes the enhancement of high frequency resonance Raman modes at

short excitation wavelengths in between the J-band and diacid monomer Soret-band

transition? What is the internal structure of aggregates prepared in nonaqueous media?

Are they simply circular N-mers or something entirely unique? To answer these questions

further modeling will be attempted to calculate the electronic absorption spectrum of a

hierarchical helical aggregate and determine if the hypothesized internal structure is

valid. Utilizing parameters from this calculation, the REPs reported in Chapter 6 will be

modeled to diagnose the identity of the high energy feature and determine what causes

enhancement of high frequency modes at lower wavelengths: does it stem from

interaction between the fluorescence and Raman scattering or vibration- or phonon-

mediated interaction with a dark exciton or a yet unforeseen process entirely? Models

utilizing both a linear spectroscopy interpretation of Raman scattering, including both A-

term and B-term Raman scattering, as well as a (3) nonlinear spectroscopy approach will

be useful tools for investigation. Spectroscopic measurements and images of aggregates

prepared in dry, organic solvents will be conducted to obtain further insight into the

effect of the internal structure of the resulting assemblies of TSPP in the absence of

water-mediated hydrogen bonding. Aggregates prepared in ionic liquids provide an

interesting system to study as the environment would provide the necessary ionic strength

to induce aggregation and yet nanotube formation would be expected to be hindered to

the absence of water. Resonance Raman spectra with excitation resonant with the H-band

169

and the Q-band, and the depolarization ratios of the prominent modes, would provide

further detail into the excitonic and structural properties of these aggregates provided the

sufficient excitation wavelengths are available for analysis.

7.4 References

1. Friesen, B. A.; Nishida, R. A.; McHale, J. L.; Mazur, U., J. Phys. Chem. C, 2009, 113,

1709-1718.

2. Friesen, B. A.; Rich, C. C.; Mazur, U.; McHale, J. L., J. Phys. Chem. C, 2010, 114,

16357-16366.

3. Rich, C. C.; McHale, J. L., Phys. Chem. Chem. Phys., 2012, 14, 2362-2374.

4. Spano, F. C.; Kuklinski, J. R.; Mukamel, S. J. Chem. Phys. 1991, 94, 7534.

5. Spano, F. C.; Silvestri, L.; Spearman, P.; Raimundo, L. Tavazzi, S. J. Chem. Phys.

2007, 127, 184703.

6. Rich, C. C.; McHale, J. L., J. Phys. Chem. C, 2013, submitted.

7. Spano, F. C., Acc. Chem. Res., 2010, 43, 429-439.

8. Mukamel, S., Principles of Nonlinear Optical Spectroscopy, Oxford University Press,

New York, 1995.

9. Mukamel, S., J. Chem. Phys., 1985, 82, 5398-5408.

10. Sue, J.; Yan, Y. J.; Mukamel, S., J. Chem. Phys., 1986, 85, 462-474.

11. Sue, J.; Mukamel, S., J. Chem. Phys., 1988, 88, 651-665.

APPENDICES

A. Experimental Details

B. MATLAB Codes

171

Appendix A Experimental Details

A.1: Raman Spectroscopy with the Triple Monochromator

A.1.1 Instrumentation. Samples are excited with either a Lexel Model 95 Argon Ion laser

(wavelengths: 454.5 nm, 457.9 nm, 465.8 nm, 472.7 nm, 476.5 nm, 488 nm, 496.5 nm,

501.7 nm, 514.5 nm, and 528.7 nm), a Spectra-Physics BeamLock 2060 Krypton Ion

laser (wavelengths: 350.7 nm, 406.7 nm, 413.1 nm, 520.8 nm, 530.9 nm, 568.2 nm, 647.1

nm, and 676.4 nm), or a CrystaLaser diode laser (wavelength: 444.7 nm). The beam

splitter used in the confocal optical train is a ThorLabs Pellicle beam splitter which

transmits 92% of incident light and 8% of reflected light (for visible wavelengths).

Polarization selection is conducted with a Melles-Griot polarization analyzer and

Figure A.1 Photograph of confocal resonance Raman spectroscopy set up with

triple monochromator.

172

polarization scrambling is performed by a Thorlab DPU-25 depolarizer. Scattered light is

collected and dispersed by a Spex Triplemate Triple monochromator and is detected by a

liquid nitrogen cooled CCD camera. Samples prepared in cuvettes are placed in the

cuvette holder. For samples which can drop out of solution, it is strongly recommended to

place a clean cuvette magnetic stir bar into the cuvette and used the magnetic spinner to

keep the solution stirring during measurement.

A.1.2 Triple Monochromator Operation. The CCD camera power and cooler must both

be turned on first. After which the camera dewar must be filled with liquid nitrogen. The

camera then must be allowed to cool down for approximately 1 hour to assure total noise

suppression. The camera should stay cool for approximately 12 hours. The spectrometer

can then be turned on.

Figure A.2 Photograph of display interface for triple monochromator.

173

To set the digital display (shown in Figure A.2) to the wavelength value in the

calibration window, first press the CAL button, press the SEL DIG button to select the

digit you wish to change, and press the INC DIG button to increase the number of the

selected digit. Once the digital display reads the same wavelength value as the calibration

window, press the ENT button. The digital GRATING display should read “4”.

Initiate the WinSpec program on the computer. This is the software used to

capture spectra, however it will not move the gratings to measure spectra at a different

wavelength. Moving the gratings is performed manually by pressing the UP and DOWN

buttons on the spectrometer which will increase the value of the wavelength in the

calibration window. The wavelength value in the calibration window represents the

wavelength value at the center of a spectrum window. Before taking measurements, you

will want to set this value so that it is at least 1000 cm-1

red-shifted of your excitation

wavelength.

174

A.1.3 Off-resonance/Resonance Raman spectroscopy. With exception of the diode laser,

which does not require plasma line suppression, all laser light must pass through a magic

cube or a holographic bandpass filter. Magic cubes are rated for 488 nm, 514.5 nm, 457.9

nm, and 413.1 nm. Thus laser lines that do not match the rated wavelength of the magic

cube will require additional mirrors to bring the laser to the correct optical table as those

laser lines will not enter and leave the magic cube at a 90o angle. For nonquantitative off-

resonance and resonance Raman scattering measurement, the laser must reflect off the

beamspltter and through the 4x objective and focus on the sample (see Fig. A.3). For the

best signal, especially with highly light absorbing or scattering samples, the focal plane

should be as close to the front wall of the cuvette as possible. As this is a confocal

Figure A.3 Photograph of confocal backscattering geometry. Light is reflected

into the first 4x objective by the beamsplitter (moving right to left), focused on

the sample in the first cuvette holder, is collimated by the second 4x objective,

and then focused on to the second sample in the second cuvette holder by a 10x

objective. A motorized magnetic stirrer is position near the second cuvette holder.

175

spectroscopy set up, scattered light will pass through the same 4x objective, becoming

collimated, and pass through the beam splitter. For measurements not requiring

polarization analysis, collimated scattered light will be focused by a lens into a

multimodal fiber optic which will bring the light to the entrance slits of the spectrometer.

For polarization measurements requiring polarization analysis, the polarizing analyzer

and depolarizer should be placed between the beam splitter and the focal lens as shown in

Fig. A.4. The polarizer will select a specific scattered light polarization which will be

pseudo-randomized by the depolarizer to avoid the polarization bias of the gratings in the

spectrometer. To obtain polarized Raman spectra, the scattered light polarization selected

is parallel to the polarization of the incident laser light. To obtain the depolarized Raman

spectra, the scattered light polarization selected is perpendicular to the polarization of the

incident laser light.

176

A.1.4 X-axis Calibration. Since the spectrometer gratings are moved manually, the

WinSpec software will not keep track of the values of the x-axis. Thus the x-axis must be

calibrated manually. To do this, once you have moved the gratings to the appropriate

configuration for measurement, measure a Raman spectrum of a reference standard with

Raman modes with known Raman shifts (i.e., cyclohexane). Go to Calibrate > Setup to

open the calibration window. The go to Display>Layout>Axes and turn off the

Calibration to set the window x-axis value to Pixels. Then pick out the peaks in the

Raman spectrum of the reference standard and assign the corresponding Pixel value in

the calibration window. Once this is done, check that the calibration window is set to the

appropriate excitation wavelength and click OK. The spectrum window will now display

Figure A.4 Photograph of collection optics including (from left to right) the

beamsplitter shown in Fig A.3, the polarizer, depolarizer, focusing lens, and fiber

optic.

177

the x-axis with values that match the configuration of the gratings. This procedure must

be performed every time the spectrometer optics are moved.

A.1.5 Quantitative Raman/Resonance Raman Spectroscopy. For measurement of absolute

resonance Raman cross sections, utilize the internal-external standard set up, shown in

Chapter 3 (see Fig. 3.1). In this setup a second 4x objective is placed behind the cuvette

holder to recollimate the transmitted light. A 10x objective is used to focus the light on

another cuvette to probe a second sample. For this set up to work, the first sample must

have a known Raman cross section for the excitation wavelength used and must be

optically transparent so suppress self-absorption. This set up requires precise alignment

of the laser through the objectives and thus it is important to calibrate the Raman cross

section using a sample with a known absolute Raman cross section. For the best results

measure the combined resonance Raman spectrum of the sample solution and external

standard first so that the cross section calibration uses the same alignment and focus as

used for the experiment. Replace the sample with a second reference standard and

measure the combined Raman spectrum. Then calculate the differential cross section of

the second reference standard with the following equation:

(A.1)

where is the differential cross section for sample m, is the measured

Raman mode peak area, is the refractive index of sample m, and is the

concentration of sample m. Solving for the differential cross section of the second

reference, one can then calculate the absolute Raman cross section:

178

(A.2)

where is the depolarization ratio of the second reference standard. To account for

optical inefficiencies or alignment issues, a correction factor k is then calculated by

dividing the measured absolute Raman cross section of the reference by its known

literature value:

(A.3)

Using this correction factor, one can then calculate the absolute Raman cross section of

the sample with unknown Raman cross section by using the same strategy as before but

incorporating the correction factor:

(A.4)

A good way to check the validity of these correction factors is to use the correction factor

to calculate the absolute cross section of another known sample and see if the corrected

cross section matches literature values. An example of this check is shown in the proof of

concept in the Supporting Info section of Chapter 3 (Tables 3.3 and 3.4).

179

A.2: Raman Spectroscopy with the Inverted Confocal Microscope Set-up

A.2.1. Instrumentation. Samples are prepared by either drop-casting a solution of the

sample on to a glass cover slip and allowing the sample to dry on the surface or pressing

a drop of the sample between two glass cover slips (the “wet” sample preparation).

Excitation radiation is supplied by the same laser sources as described previously in

section A.1.1. Focusing of the beam onto the sample is performed by an Olympus 100x,

Figure A.5 Photograph of inverted confocal microscope set-up used for single

aggregate Raman spectroscopy and resonance light scattering microscopy.

180

oil-immersion objective. The microscope is an Olympus IX70 inverted confocal

microscope (see Fig. A.5 and Fig. 3.2). The scattered light from the sample is collected

out of the side port, focused on an aperture pinhole, collimated and refocused on the

entrance slits of the spectrometer. Scattered light is dispersed by an Acton SpectraPro

2300i single monochromator and detected by a thermoelectrically-cooled CCD. The

spectrometer is controlled using Winspec software and does not require the extensive

calibration needed for the triple monochromator.

A.2.2 Raman Measurements. Similar to the set up discussed in section A.1, radiation from

gas lasers are passed through a magic cube to suppress plasma lines. Depending on the

experiment, a choice of wave plate to control the polarization of the excitation beam is

implemented before entering into the microscope body. For circular polarization, a

Figure A.6 Photograph of the collection optics which present scattered light to

the spectrometer. For spectroscopic measurements, the scattered light must be

directed out of the side port of the microscope body.

181

Thorlabs achromatic quarter wave plate is used. To rotate the polarization of the beam by

ninety degrees, a Thorlabs half wave plate is used. When not using circularly polarized

light, the polarization bias of the optics must be taken into account. In the body of the

microscope are two beamsplitters: one which reflects the beam into the objective and one

which reflects the scattered light out the side port to the spectrometer. The first

beamsplitter reflects and transmits 50% of light polarized perpendicular to the optical

table and reflects 20% and transmits 80% of the light polarized parallel to the optical

table. The second beam splitter reflects 66% of perpendicular polarized light and 77% of

parallel polarized light. Figure A.6 shows a photograph of the collection optics bringing

the scattered light to the spectrometer. To detect scattered light of a particular

polarization, a polarizer and depolarizer are placed in the path of the collimated light

before the last focusing lens.

Figure A.7 Photograph of CCD camera used for imaging. Light presented to the

camera is directed out the back port of the microscope body.

182

A.2.3 Imaging. All images are collected by an Andor thermoelectrically-cooled CCD

camera posited at the back port of the microscope body (see Fig. A.7). Backlit optical

images utilize a white light fiber optic to provide backlighting. Resonance light scattering

imaging requires epi-illumination of the sample with the excitation wavelength used. For

epi-illumination, diffuse the beam and expand the laser spot to fit the field of view. To

diffuse the beam, frosted glass is positioned at about 5 cm away from the entrance of the

microscope. The diffuse laser then passes through a screwed-in lens at the entrance

before encountering the first beamsplitter leading to the objective to expand the focused

laser spot (see Fig. A.8).

183

Figure A.8 Photograph of frosted glass and screwed-in lens (small black

cylinder behind frosted glass) placed in the path of the incoming beam to epi-

illuminate the sample for RLS imaging.

184

Appendix B MATLAB Codes

B.1: Absorption spectrum for TSPP diacid monomer

%DiacidAbsThermal2modes.m is a script which calculates the Absorption spectrum of the %diacid monomer using the expression for the molar absorptivity including thermal %influences for low frequency modes. %Constants and parameters%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% N_A=6.022e23; %Avogadro's number muge=14.5e-18; %transition dipole moment of diacid in esu-cm c=3e10; %speed of light in cm/s n_r=1.33; %refractive index of water h=6.626e-27; %Planck's constant hbar=h/(2*pi); %h-bar nu00=22950; %origin of transition in wavenumbers sigma=210; %width of gaussian in wavenumbers prefac=(4*pi^2*N_A*muge^2)/(3*2303*c*n_r*hbar); %prefactor in molar absorptivity expression %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Vibrational Energies and Franck-Condon Factors%%%%%%%%%%%%%%%%%%%%%%%%%%%% nmodes=2; %number of Raman modes nuvib=[236 1234]; %vibrational energies in wavenumbers from RR of diacid excited with 444.7 nm excitation del=[1.0 0.43]; %guess for dimensionless displacements based on relative Raman intensities of four prominent Raman modes %Create Franck-Condon factor matrix %Find the <0|0> FC factors for i=1:nmodes FCF(i,1)=exp(-del(i)*del(i)/2); end %Find the <0|v> elements vmax=11; %the max number of vibrational quanta for i=1:nmodes for v=1:vmax vfac=prod(1:v); %v-factorial term delsq=del(i)*del(i); FCF(i,v+1)=(1/vfac)*(delsq/2)^v*FCF(i,1); end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Include v=0,1,2 of 234 cm modes%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [C236,d236,o236]=fcfunc(vmax,nuvib(1),nuvib(1),del(1)); FCm236=C236'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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%Thermal populations%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for i=1:3 vi=i-1; P1(i)=exp(-(vi*nuvib(1))/206); end for i=1:3 %normalize P1norm(i)=P1(i)/(P1(1)+P1(2)+P1(3)); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Molar Absorptivity Spectrum%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% numin=19600; %~510 nm in wavenumbers numax=31750; %~315 nm in wavenumbers deltanu=25; %calculate abs every 25 cm^-1 num=(numax-numin)/deltanu+1; %number of data points for j=1:num nu(j)=numin+(j-1)*deltanu; espnu=0; for v1low=1:3 v1in=v1low-1; Prob=P1norm(v1low); for vi=1:vmax if v1low==1 FC1=FCF(1,vi); else FC1=(FCm236(v1low,vi))^2; end for vj=1:vmax v1=vi-1; v2=vj-1; vibE=(v1-v1in)*nuvib(1)+v2*nuvib(2); %vibrational energy part of gaussian term FCFtot=FC1*FCF(2,vj); %Franck-Condon Factor products gausarg=(-(nu00+vibE-nu(j))^2)/(2*sigma*sigma); %Argument in gaussian term gaus=(1/(sqrt(2*pi)*sigma))*exp(gausarg); %gaussian term espnu=espnu+(FCFtot*gaus*Prob); end end end molabs(j)=prefac*nu(j)*espnu; %molar absorptivity end plot(nu,molabs,'r') legend('Calc. Mol. Abs.') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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B.2: Franck-Condon Factor Calculation

%FCfunc.m A function to calculate Franck-Condon Factors %following Mannebeck, Physica 17, 1001 (1951) %C is a square matric of dimension vmax by vmax %May 10, 2005 %Checked Sept. 13, 3011 - OKAY! %Modified Sept. 26,2011 to get the C(2,2) term %-------------------------------------------- function [C, d, o] = fcfunc(vmax,nug,nue,M) k = (nug - nue)/(nue + nug); kplus = 2*sqrt(nug*nue)/(nug + nue); a = M*sqrt(2*nug/(nue + nug)); b = M*sqrt(2*nue/(nue + nug)); %Note Matlab doesn't permit 0 indices, so C(n,m) is %the FC factor for n-1,m-1 C(1,1) = exp(-0.5*M*M)*sqrt(kplus) % This is <0|0> C(2,1) = -a*C(1,1) % This is <1|0> C(2,2) = kplus*C(1,1) + b*C(2,1); %This is <1|1> %generate C(3,1)=<2|0>,C(4,1)=<3|0>,...C(8,1)= <7|0> for vp = 1:vmax-2 C(vp+2,1) = -sqrt(vp/(vp+1))*k*C(vp,1) -a*C(vp+1,1)/sqrt(vp+1); end C(1,2) = b*C(1,1); % This is <0|1> %generate C(1,3),C(1,4),...C(1,7) = <0|2>,<0,3>,...<0,7> for vpp = 1:vmax-2 C(1,vpp+2) = sqrt(vpp/(vpp+1))*k*C(1,vpp) + b*C(1,vpp+1)/sqrt(vpp+1); end %generate the rest of the C-matrix %Y = 0 for v = 1:vmax-2 if v ~= 1 Y = C(v-1,v+1); else Y = 0; end C(v+1,v+1) = -sqrt(v/(v+1))*k*Y + kplus*C(v,v) - sqrt(1/v)*a*C(v,v+1); for vp = 1:vmax-2 C(vp+2,v+1) = -sqrt(vp/(vp+1))*k*C(vp,v+1) +sqrt(v/(vp+1))*kplus*C(vp+1,v) - sqrt(1/(vp+1))*a*C(vp+1,v+1); C(v+1,vp+2) = sqrt((vp)/(vp+1))*k*C(v+1,vp)+sqrt(v/(vp+1))*kplus*C(v,vp+1)+ sqrt(1/(vp+1))*b*C(v+1,vp+1); end end for v = 1:vmax for vp = 1:vmax stuff = 0; for n = 1:vmax stuff = stuff + C(n,v)*C(n,vp); end fcsum(v,vp) = stuff; end

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end X = fcsum sumdiag = 0; sumoffdiag = 0; for vi = 1:vmax for vj = 1:vmax if vi == vj sumdiag = sumdiag + fcsum(vi,vj); else sumoffdiag = sumoffdiag + fcsum(vi,vj); end end end avediag = sumdiag/vmax; aveoffdiag = sumoffdiag/(vmax*(vmax-1)); d = avediag o = aveoffdiag Cdisplay = C disp('Done- okay')

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B.3: Normalized Absorption Spectrum for a Circular 16-mer

% HANDABSCIRCAGGVEC3NOABSPTDIPOLE.m is a script which calculates the the Hamiltonian, then % calculates the absorption spectrum of a TSPP Circular N-mer. tic; %Vibrational Energies and Franck-Condon Factors%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Vibrational information from diacidabsthermal4modes.m nmodes=2; %number of Raman modes vmax=4; nuvib=[236 1234]; %vibrational energies in wavenumbers from RR of diacid excited with 444.7 nm excitation del=[0.1 0.43]; %guess for dimensionless displacements based on relative Raman intensities of four prominent Raman modes %Create Franck-Condon factor matrices %For 236 mode nug=nuvib(1); nue=nuvib(1); M=del(1); k = (nug - nue)/(nue + nug); kplus = 2*sqrt(nug*nue)/(nug + nue); a = M*sqrt(2*nug/(nue + nug)); b = M*sqrt(2*nue/(nue + nug)); %Note Matlab doesn't permit 0 indices, so C(n,m) is %the FC factor for n-1,m-1 C(1,1) = exp(-0.5*M*M)*sqrt(kplus); % This is <0|0> C(2,1) = -a*C(1,1); % This is <1|0> C(2,2) = kplus*C(1,1) + b*C(2,1); %This is <1|1> %generate C(3,1)=<2|0>,C(4,1)=<3|0>,...C(8,1)= <7|0> for vp = 1:vmax-2 C(vp+2,1) = -sqrt(vp/(vp+1))*k*C(vp,1) -a*C(vp+1,1)/sqrt(vp+1); end C(1,2) = b*C(1,1); % This is <0|1> %generate C(1,3),C(1,4),...C(1,7) = <0|2>,<0,3>,...<0,7> for vpp = 1:vmax-2 C(1,vpp+2) = sqrt(vpp/(vpp+1))*k*C(1,vpp) + b*C(1,vpp+1)/sqrt(vpp+1); end %generate the rest of the C-matrix %Y = 0 for v = 1:vmax-2 if v ~= 1 Y = C(v-1,v+1); else Y = 0; end C(v+1,v+1) = -sqrt(v/(v+1))*k*Y + kplus*C(v,v) - sqrt(1/v)*a*C(v,v+1); for vp = 1:vmax-2 C(vp+2,v+1) = -sqrt(vp/(vp+1))*k*C(vp,v+1) +sqrt(v/(vp+1))*kplus*C(vp+1,v) - sqrt(1/(vp+1))*a*C(vp+1,v+1); C(v+1,vp+2) = sqrt((vp)/(vp+1))*k*C(v+1,vp)+sqrt(v/(vp+1))*kplus*C(v,vp+1)+ sqrt(1/(vp+1))*b*C(v+1,vp+1); end end

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for v = 1:vmax for vp = 1:vmax stuff = 0; for n = 1:vmax stuff = stuff + C(n,v)*C(n,vp); end fcsum(v,vp) = stuff; end end X = fcsum; sumdiag = 0; sumoffdiag = 0; for vi = 1:vmax for vj = 1:vmax if vi == vj sumdiag = sumdiag + fcsum(vi,vj); else sumoffdiag = sumoffdiag + fcsum(vi,vj); end end end avediag = sumdiag/vmax; aveoffdiag = sumoffdiag/(vmax*(vmax-1)); d = avediag; o = aveoffdiag; Cdisplay = C; C236=C; d236=d; o236=o; %For 1234 mode nug=nuvib(2); nue=nuvib(2); M=del(2); k = (nug - nue)/(nue + nug); kplus = 2*sqrt(nug*nue)/(nug + nue); a = M*sqrt(2*nug/(nue + nug)); b = M*sqrt(2*nue/(nue + nug)); %Note Matlab doesn't permit 0 indices, so C(n,m) is %the FC factor for n-1,m-1 C(1,1) = exp(-0.5*M*M)*sqrt(kplus) % This is <0|0> C(2,1) = -a*C(1,1) % This is <1|0> C(2,2) = kplus*C(1,1) + b*C(2,1); %This is <1|1> %generate C(3,1)=<2|0>,C(4,1)=<3|0>,...C(8,1)= <7|0> for vp = 1:vmax-2 C(vp+2,1) = -sqrt(vp/(vp+1))*k*C(vp,1) -a*C(vp+1,1)/sqrt(vp+1); end C(1,2) = b*C(1,1); % This is <0|1> %generate C(1,3),C(1,4),...C(1,7) = <0|2>,<0,3>,...<0,7> for vpp = 1:vmax-2 C(1,vpp+2) = sqrt(vpp/(vpp+1))*k*C(1,vpp) + b*C(1,vpp+1)/sqrt(vpp+1); end %generate the rest of the C-matrix %Y = 0

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for v = 1:vmax-2 if v ~= 1 Y = C(v-1,v+1); else Y = 0; end C(v+1,v+1) = -sqrt(v/(v+1))*k*Y + kplus*C(v,v) - sqrt(1/v)*a*C(v,v+1); for vp = 1:vmax-2 C(vp+2,v+1) = -sqrt(vp/(vp+1))*k*C(vp,v+1) +sqrt(v/(vp+1))*kplus*C(vp+1,v) - sqrt(1/(vp+1))*a*C(vp+1,v+1); C(v+1,vp+2) = sqrt((vp)/(vp+1))*k*C(v+1,vp)+sqrt(v/(vp+1))*kplus*C(v,vp+1)+ sqrt(1/(vp+1))*b*C(v+1,vp+1); end end for v = 1:vmax for vp = 1:vmax stuff = 0; for n = 1:vmax stuff = stuff + C(n,v)*C(n,vp); end fcsum(v,vp) = stuff; end end X = fcsum sumdiag = 0; sumoffdiag = 0; for vi = 1:vmax for vj = 1:vmax if vi == vj sumdiag = sumdiag + fcsum(vi,vj); else sumoffdiag = sumoffdiag + fcsum(vi,vj); end end end avediag = sumdiag/vmax; aveoffdiag = sumoffdiag/(vmax*(vmax-1)); d = avediag; o = aveoffdiag; Cdisplay = C; C1234=C; d1234=d; o1234=o; FCm236=C236'; FCm1234=C1234'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Molecular Position Vector%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% R=3e-7; %radius of circular aggregate in cm N=16;

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phi=2*pi/N; %angle between projections theta=2*pi/20; %angle between in plane transition dipole moment and local tangent angle=zeros(N,1); d=zeros(3,N); for n=1:N d(:,n)=[R*cos((n-1)*phi); R*sin((n-1)*phi); 0]; %distance column vector angle(n,:)=(pi/2)-theta-(n-1)*phi; %the angle that the n-th dipole makes with respect to X end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Transition Dipole Moment Vector%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Values determined from best fit data from diacid monomer absorption %calculation numon=22950; %monomer diacid molar B-band in wavenumbers muBpar=14.5e-18; %component of the B-band transition moment which is parallel to the ring plane in esu*cm muBperp=14.5e-18; %compoent of the B-band transition moment which is perpendicular to the ring plane in esu*cm muB1=zeros(N,3); %parallel component dipole moment vector muB2=zeros(N,3); %perpendicular component dipole moment vector for n=1:N muB1(n,:)=[muBpar*cos(angle(n)),-muBpar*sin(angle(n)),0]; %row vector muB2(n,:)=[0,0,muBperp]; %also row vector end muB1u=muB1/muBpar; %muB1 unit vector muB2u=muB2/muBperp; %muB2 unit vector N1=N*vmax^nmodes; %number of 1 particle basis sets N2=2*N*vmax^nmodes*(vmax^nmodes-1); %number of 2 particle basis sets Ntot=N1+N2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Frenkel Polaron Hamiltonian%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %H consists of two Hamiltonians, Hpar and Hperp %Index the 2-particle states |nn, vn: nm, vm>%%%%%%%%%%%%%%%%%%%%%%%%%%%%% indexnm=zeros(N2,2); %saves the molecule numbers for the n-th 2-part state indexvv=zeros(N2,4); %saves the vibrational quantum numbers for both modes for the n-th 2-part state (plus 1) n = 0; for nn=1 for nm=N for vnm = 1:vmax %index first mode for vnp = 1:vmax %index second mode for vmm = 1:vmax %index first mode for vmp = 1:vmax %index second mode if vmm+vmp>2 n = n+1; indexvv(n,:) = [vnm,vnp,vmm,vmp]; %saves the vibrational quantum numbers vn, vm for both modes indexnm(n,:) = [nn,nm]; %saves the molecule numbers nn, nm

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end end end end end end end for nn = 1:N for nm = 1:N if abs(nm - nn) == 1 %np and nj must be near-neighbors for vnm = 1:vmax %index first mode for vnp = 1:vmax %index second mode for vmm = 1:vmax %index first mode for vmp = 1:vmax %index second mode if vmm+vmp>2 n = n+1; indexvv(n,:) = [vnm,vnp,vmm,vmp]; %saves the vibrational quantum numbers vn, vm for both modes indexnm(n,:) = [nn,nm]; %saves the molecule numbers nn, nm end end end end end end end end for nn=N for nm=1 for vnm = 1:vmax %index first mode for vnp = 1:vmax %index second mode for vmm = 1:vmax %index first mode for vmp = 1:vmax %index second mode if vmm+vmp>2 n = n+1; indexvv(n,:) = [vnm,vnp,vmm,vmp]; %saves the vibrational quantum numbers vn, vm for both modes indexnm(n,:) = [nn,nm]; %saves the molecule numbers nn, nm end end end end end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hpar%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hpar=zeros(Ntot,Ntot); H11matpar=zeros(N1,N1); H12matpar=zeros(N1,N2); H22matpar=zeros(N2,N2); %1-particle/1-particle diagonal matrix elements

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for nn=1:N for vn=1:vmax; for vm=1:vmax; v1=vn-1; v2=vm-1; n=vm+(vn-1)*vmax+(nn-1)*vmax^nmodes; H11matpar(n,n)=numon+v1*nuvib(1)+v2*nuvib(2); end end end %1-particle/1-particle off-diagonal matrix elements %Float a value for coupling strength, J0par, in wavenumbers Jnmpar=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmpar(n,m)=0; else dnm=d(:,n)-d(:,m); Dnm=(dnm'*dnm)^0.5; %magnitude of vector dnm dnmu=dnm/Dnm; %dnm unit vector Jnmpar(n,m)=5.034e15*(muBpar^2/Dnm^3)*(muB1u(n,:)*muB1u(m,:)'-3*(muB1u(n,:)*dnmu)*(muB1u(m,:)*dnmu)); end end end for nn=1:N for vnm=1:vmax %index vibrational level of first mode for vnp=1:vmax %index vibrational level of second mode n=vnp+(vnm-1)*vmax+(nn-1)*vmax^nmodes; nm=nn-1; %nearest neighbor approximation if nm==0 nm=N; end for vmm=1:vmax %index vibrational level of first mode for vmp=1:vmax %index vibrational level of second mode m=vmp+(vmm-1)*vmax+(nm-1)*vmax^nmodes; H11matpar(n,m)=Jnmpar(nn,nm)*FCm236(1,vnm)*FCm236(1,vmm)*FCm1234(1,vnp)*FCm1234(1,vmp); H11matpar(m,n)=H11matpar(n,m); end end end end end %1-particle/2-particle matrix elements for nn=1:N for vnm=1:vmax %index vibrational level of first mode for vnp=1:vmax %index vibrational level of second mode n=vnp+(vnm-1)*vmax+(nn-1)*vmax^nmodes; %1-part index |nn,vn> for m=1:N2 % |nm,vm;np,vp> 2-part vmm=indexvv(m,1); %first mode vmp=indexvv(m,2); %second mode vpm=indexvv(m,3); %first mode

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vpp=indexvv(m,4); %second mode nm=indexnm(m,1); np=indexnm(m,2); if nn==np flag=1; else flag=0; end H12matpar(n,m)=Jnmpar(nn,nm)*FCm236(vpm,vnm)*FCm236(1,vmm)*FCm1234(vpp,vnp)*FCm1234(1,vmp)*flag; end end end end %2-particle/2-particle diagonal matrix elements for n=1:N2 vnm=indexvv(n,1); %first mode particle 1 vnp=indexvv(n,2); %second mode particle 1 vmm=indexvv(n,3); %first mode particle 2 vmp=indexvv(n,3); %second mode particle 2 H22matpar(n,n)=numon+(vnm-1+vmm-1)*nuvib(1)+(vnp-1+vmp-1)*nuvib(2); end %2-particle/2-particle off-diagonal matrix elements for n=2:N2 %<nn,vn;nm,vm| vnm=indexvv(n,1); %first mode particle 1 vnp=indexvv(n,2); %second mode particle 1 vmm=indexvv(n,3); %first mode particle 2 vmp=indexvv(n,4); %second mode particle 2 nn=indexnm(n,1); nm=indexnm(n,2); for m=1:n-1 %|np,vp;nq,vq> vpm=indexvv(m,1); %first mode particle 1 vpp=indexvv(m,2); %second mode particle 1 vqm=indexvv(m,3); %first mode particle 2 vqp=indexvv(m,4); %second mode particle 2 np=indexnm(m,1); nq=indexnm(m,2); if nq==nn flag1=1; else flag1=0; end if nm==np flag2=1; else flag2=0; end H22matpar(n,m)=Jnmpar(nn,np)*FCm236(vqm,vnm)*FCm236(vmm,vpm)*FCm1234(vqp,vnp)*FCm1234(vmp,vpp)*flag1*flag2; H22matpar(m,n)=H22matpar(n,m); end end Hpar=[H11matpar H12matpar; H12matpar' H22matpar];

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hperp%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hperp=zeros(Ntot,Ntot); H11matperp=zeros(N1,N1); H12matperp=zeros(N1,N2); H22matperp=zeros(N2,N2); %1-particle/1-particle diagonal matrix elements for nn=1:N for vn=1:vmax; for vm=1:vmax; v1=vn-1; v2=vm-1; n=vm+(vn-1)*vmax+(nn-1)*vmax^nmodes; H11matperp(n,n)=numon+v1*nuvib(1)+v2*nuvib(2); end end end %1-particle/1-particle off-diagonal matrix elements %Float a value for coupling strength, J0perp, in wavenumbers Jnmperp=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmperp(n,m)=0; else dnm=d(:,n)-d(:,m); Dnm=(dnm'*dnm)^0.5; %magnitude of vector dnm dnmu=dnm/Dnm; %dnm unit vector Jnmperp(n,m)=5.034e15*(muBperp^2/Dnm^3)*(muB2u(n,:)*muB2u(m,:)'-3*(muB2u(n,:)*dnmu)*(muB2u(m,:)*dnmu)); end end end for nn=1:N for vnm=1:vmax %index vibrational level of first mode for vnp=1:vmax %index vibrational level of second mode n=vnp+(vnm-1)*vmax+(nn-1)*vmax^nmodes; nm=nn-1; %nearest neighbor approximation if nm==0; nm=N; end for vmm=1:vmax %index vibrational level of first mode for vmp=1:vmax %index vibrational level of second mode m=vmp+(vmm-1)*vmax+(nm-1)*vmax^nmodes; H11matperp(n,m)=Jnmperp(nn,nm)*FCm236(1,vnm)*FCm236(1,vmm)*FCm1234(1,vnp)*FCm1234(1,vmp); H11matperp(m,n)=H11matperp(n,m); end end end end

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end %1-particle/2-particle matrix elements for nn=1:N for vnm=1:vmax %index vibrational level of first mode for vnp=1:vmax %index vibrational level of second mode n=vnp+(vnm-1)*vmax+(nn-1)*vmax^nmodes; %1-part index |nn,vn> for m=1:N2 % |nm,vm;np,vp> 2-part vmm=indexvv(m,1); %first mode vmp=indexvv(m,2); %second mode vpm=indexvv(m,3); %first mode vpp=indexvv(m,4); %second mode nm=indexnm(m,1); np=indexnm(m,2); if nn==np flag=1; else flag=0; end H12matperp(n,m)=Jnmperp(nn,nm)*FCm236(vpm,vnm)*FCm236(1,vmm)*FCm1234(vpp,vnp)*FCm1234(1,vmp)*flag; end end end end %2-particle/2-particle diagonal matrix elements for n=1:N2 vnm=indexvv(n,1); %first mode particle 1 vnp=indexvv(n,2); %second mode particle 1 vmm=indexvv(n,3); %first mode particle 2 vmp=indexvv(n,3); %second mode particle 2 H22matperp(n,n)=numon+(vnm-1+vmm-1)*nuvib(1)+(vnp-1+vmp-1)*nuvib(2); end %2-particle/2-particle off-diagonal matrix elements for n=2:N2 %<nn,vn;nm,vm| vnm=indexvv(n,1); %first mode particle 1 vnp=indexvv(n,2); %second mode particle 1 vmm=indexvv(n,3); %first mode particle 2 vmp=indexvv(n,4); %second mode particle 2 nn=indexnm(n,1); nm=indexnm(n,2); for m=1:n-1 %|np,vp;nq,vq> vpm=indexvv(m,1); %first mode particle 1 vpp=indexvv(m,2); %second mode particle 1 vqm=indexvv(m,3); %first mode particle 2 vqp=indexvv(m,4); %second mode particle 2 np=indexnm(m,1); nq=indexnm(m,2); if nq==nn flag1=1; else flag1=0; end if nm==np flag2=1;

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else flag2=0; end H22matperp(n,m)=Jnmperp(nn,np)*FCm236(vqm,vnm)*FCm236(vmm,vpm)*FCm1234(vqp,vnp)*FCm1234(vmp,vpp)*flag1*flag2; H22matperp(m,n)=H22matperp(n,m); end end Hperp=[H11matperp H12matperp; H12matperp' H22matperp]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% H=[Hpar zeros(Ntot,Ntot); zeros(Ntot,Ntot) Hperp]; %combine Hamiltonians %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Eigenvectors and eigenvalues%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [vec,en]=eig(H); lams=eig(H); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% t=toc; n=0; for nn=1:N for vnm=1:vmax for vnp=1:vmax n=n+1; indexn(n,:)=nn; indexv(n,:)=[vnm,vnp]; end end end for n=1:N1 indexmu1(n,:)=muB1u(indexn(n),:); indexmu2(n,:)=muB2u(indexn(n),:); end for n=1:N2 indexmu1(N1+n,:)=muB1u(indexnm(n,1),:); indexmu2(N1+n,:)=muB2u(indexnm(n,1),:); end muBu=zeros(2*Ntot,3); muBu=[indexmu1;indexmu2]; FCFm=zeros(2*Ntot,2); for n=1:N1 FCFm(n,:)=[FCm236(1,indexv(n,1)),FCm1234(1,indexv(n,2))]; FCFm(Ntot+n,:)=[FCm236(1,indexv(n,1)),FCm1234(1,indexv(n,2))]; end for n=1:N2 if indexvv(n,3)==1 delta1=1; else

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delta1=0; end if indexvv(n,4)==1 delta2=1; else delta2=0; end FCFm(N1+n,:)=[FCm236(1,indexvv(n,1))*delta1,FCm1234(1,indexvv(n,2))*delta2]; FCFm(Ntot+N1+n,:)=[FCm236(1,indexvv(n,1))*delta1,FCm1234(1,indexvv(n,2))*delta2]; end tic; %Find Absorption Strengths%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% muk=zeros(2*Ntot,1); parfor k=1:2*Ntot summu=zeros(2*Ntot,2*Ntot); summu=(vec(:,k)*conj(vec(:,k))').*(muBu*conj(muBu)').*((FCFm(:,1).*FCFm(:,2))*(FCFm(:,1).*FCFm(:,2))'); muk(k,1)=sum(sum(summu),2); end tt=toc; %Sort according to dipole strength tic; [Int,ki]=sort(muk); for a=1:2*Ntot b=2*Ntot-a+1; k=ki(b); MuX=0; MuY=0; MuZ=0; for n=1:2*Ntot MuX=MuX+vec(n,k)*muBu(n,1); MuY=MuY+vec(n,k)*muBu(n,2); MuZ=MuZ+vec(n,k)*muBu(n,3); end Muk(k,:)=[MuX;MuY;MuZ]; Energy=lams(k); Intensity=muk(k); Out(a,:)=[k,Energy,Intensity,MuX,MuY,MuZ]; end sum=0; for a=1:2*Ntot b=2*Ntot-a+1; k=ki(b); sum=sum+muk(k); end TotInt=sum; clear sum %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ttt=toc;

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tic; %Absorption Spectrum%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% numax=30000; %maximum frequency numin=16000; %minimum frequnecy nuint=151; %frequency interval nu=linspace(numin,numax,nuint); %frequencies scanned sigma=210; %broadening factor in wavenumbers A=zeros(nuint,1); for x=1:nuint alphasum=zeros(10,1); arg=zeros(10,1); arg=(nu(x)-Out(1:10,2)).^2; alphasum=Out(1:10,3).*exp(-arg/(sigma^2)); A(x)=1/N*sum(alphasum); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tttt=toc;

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B.4: Normalized Absorption Spectrum of the Hierarchical Helical Nanotube

Aggregate

%HNANOTUBEAGG0MODES.m calculates the absorption spectrum %of the nanotube aggregates using the method outlined in F. C. Spano's Frenkel %Polaron article (Spano, FC, Acc. Chem. Res. 2010, 43, 429-439). tic; %Molecular Position Vector rn%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% R=8.2e-7; %radius of nanotube in cm n1stop=270; %max number of rings on which N-mers reside n2stop=1; %max number of helices on which N-mers lie N=n1stop*n2stop; phi2=2*pi/n2stop; rc=3e-7; %radius of circular N-mer in cm dc=2*rc; %diameter of circular N-mer in cm h=0.61e-7; %height between rings in cm gamma=2*pi/8.6; %angle between projections n1=[1:1:n1stop]'; n2=[1:1:n2stop]'; norigin=N/2+1; p=zeros(N,1); for n=1; p(1:n2stop,1)=n2*phi2+(-norigin+n1(n))*gamma; end for n=2:n1stop; p((n*n2stop-(n2stop-1)):(n*n2stop),1)=n2*phi2+(-norigin+n1(n))*gamma; end for n=1:n1stop; rnz((n*n2stop-(n2stop-1)):(n*n2stop),1)=(-norigin+n1(n))*h; end rn=zeros(N,3); rn=[R.*cos(p) R.*sin(p) rnz]; %Denote first and second column as rnx and rny rnx=rn(:,1); rny=rn(:,2); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Transition Dipole Moment Vectors munx, muny, munz%%%%%%%%%%%%%%%%%%%%%%%%% mux=37.2e-18; %magnitude of transition dipole moment x muy=37.2e-18; %magnitude of transition dipole moment y muz=100e-18; %magnitude of transition dipole moment z for k=1:n1stop; p((k*n2stop-(n2stop-1)):(k*n2stop),1)=n2*phi2+(-norigin+n1(k))*gamma; pz((k*n2stop-(n2stop-1)):(k*n2stop),1)=n2*phi2+(-norigin+n1(k))*gamma-(pi/2); end munx=[-mux.*sin(p) mux.*cos(p) zeros(N,1)]; muny=[zeros(N,1) zeros(N,1) muy*ones(N,1)]; munz=[-muz.*sin(pz) muz.*cos(pz) zeros(N,1)];

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Frenkel Exciton Polaron Hamiltonian H%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %H=sum(omega0*bndag*bn)+sum(J(n-m)*bndag*bn) (in atomic units) %hbar=1 nu0x=20291; nu0y=20291; nu0z=23663; %Hxx%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hxx=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hxx(n,n)=nu0x; end %1-particle/1-particle off-diagonal matrix elements Jnmxx=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmxx(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector munxu=munx/mux; %munx unit vector Jnmxx(n,m)=5.034e15*(mux^2/Rnm^3)*(munxu(n,:)*munxu(m,:)'-3*(munxu(n,:)*rnmu')*(munxu(m,:)*rnmu')); Hxx(n,m)=Hxx(n,m)+Jnmxx(n,m); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hyy%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hyy=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hyy(n,n)=nu0y; end %1-particle/1-particle off-diagonal matrix elements Jnmyy=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmyy(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector

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munyu=muny/muy; %munx unit vector Jnmyy(n,m)=5.034e15*(muy^2/Rnm^3)*(munyu(n,:)*munyu(m,:)'-3*(munyu(n,:)*rnmu')*(munyu(m,:)*rnmu')); Hyy(n,m)=Hyy(n,m)+Jnmyy(n,m); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hzz%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hzz=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hzz(n,n)=nu0z; end %1-particle/1-particle off-diagonal matrix elements Jnmzz=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmzz(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector munzu=munz/muz; %munx unit vector Jnmzz(n,m)=5.034e15*(muz^2/Rnm^3)*(munzu(n,:)*munzu(m,:)'-3*(munzu(n,:)*rnmu')*(munzu(m,:)*rnmu')); Hzz(n,m)=Hzz(n,m)+Jnmzz(n,m); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hxy%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hxy=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hxy(n,n)=0; end %1-particle/1-particle off-diagonal matrix elements Jnmxy=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmxy(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector

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Jnmxy(n,m)=5.034e15*(mux*muy/Rnm^3)*(munxu(n,:)*munyu(m,:)'-3*(munxu(n,:)*rnmu')*(munyu(m,:)*rnmu')); Hxy(n,m)=Hxy(n,m)+Jnmxy(n,m); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hxz%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hxz=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hxz(n,n)=0; end %1-particle/1-particle off-diagonal matrix elements Jnmxz=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmxz(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector Jnmxz(n,m)=5.034e15*(mux*muz/Rnm^3)*(munxu(n,:)*munzu(m,:)'-3*(munxu(n,:)*rnmu')*(munzu(m,:)*rnmu')); Hxz(n,m)=Hxz(n,m)+Jnmxz(n,m); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hyx%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hyx=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hyx(n,n)=0; end %1-particle/1-particle off-diagonal matrix elements Jnmyx=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmyx(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector Jnmyx(n,m)=5.034e15*(muy*mux/Rnm^3)*(munyu(n,:)*munxu(m,:)'-3*(munyu(n,:)*rnmu')*(munxu(m,:)*rnmu')); Hyx(n,m)=Hyx(n,m)+Jnmyx(n,m);

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end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hyz%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hyz=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hyz(n,n)=0; end %1-particle/1-particle off-diagonal matrix elements Jnmyz=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmyz(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector Jnmyz(n,m)=5.034e15*(muy*muz/Rnm^3)*(munyu(n,:)*munzu(m,:)'-3*(munyu(n,:)*rnmu')*(munzu(m,:)*rnmu')); Hyz(n,m)=Hyz(n,m)+Jnmyz(n,m); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hzx%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hzx=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hzx(n,n)=0; end %1-particle/1-particle off-diagonal matrix elements Jnmzx=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmzx(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector Jnmzx(n,m)=5.034e15*(muz*mux/Rnm^3)*(munzu(n,:)*munxu(m,:)'-3*(munzu(n,:)*rnmu')*(munxu(m,:)*rnmu')); Hzx(n,m)=Hzx(n,m)+Jnmzx(n,m); end end end

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Hzy%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Hzy=zeros(N,N); %1-particle/1-particle diagonal matrix elements for n=1:N Hzy(n,n)=0; end %1-particle/1-particle off-diagonal matrix elements Jnmzy=zeros(N,N); for n=1:N; for m=1:N; if n==m; Jnmzy(n,m)=0; else rnm=rn(n,:)-rn(m,:); Rnm=(rnm*rnm')^0.5; %magnitude of vector rnm rnmu=rnm/Rnm; %rnm unit vector Jnmzy(n,m)=5.034e15*(muz*muy/Rnm^3)*(munzu(n,:)*munyu(m,:)'-3*(munzu(n,:)*rnmu')*(munyu(m,:)*rnmu')); Hzy(n,m)=Hzy(n,m)+Jnmzy(n,m); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% H=[Hxx Hxy Hxz; Hyx Hyy Hyz; Hzx Hzy Hzz]; %combine Hamiltonians %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Eigenvectors and eigenvalues%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [vec,en]=eig(H); lams=eig(H); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% t=toc; tic; %Absorption Spectrum%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% numax=30000; %maximum frequency numin=16000; %minimum frequnecy nuint=151; %frequency interval nu=linspace(numin,numax,nuint); %frequencies scanned sigma=210; %broadening factor in wavenumbers A=zeros(nuint,1); indexn=zeros(N,1); indexmu1=zeros(N,3);

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indexmu2=zeros(N,3); indexmu3=zeros(N,3); n=0; for nn=1:N n=n+1; indexn(n,:)=nn; end for n=1:N indexmu1(n,:)=munxu(indexn(n),:); indexmu2(n,:)=munyu(indexn(n),:); indexmu3(n,:)=munzu(indexn(n),:); end mu=zeros(3*N,3); mu=[indexmu1; indexmu2; indexmu3]; parfor x=1:nuint alphasum=zeros(3*N,1); for k=1:3*N arg=(nu(x)-lams(k))^2; absum=zeros(3*N,3*N); absum=(vec(:,k)*conj(vec(:,k))').*(mu*conj(mu)'); alphasum(k,1)=sum(sum(absum),2)*exp(-arg/(sigma^2)); end A(x)=1/N*sum(alphasum); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% tt=toc; tic; %Find Absorption Strengths%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% muk=zeros(3*N,1); parfor k=1:3*N summu=zeros(3*N,3*N); summu=(vec(:,k)*conj(vec(:,k))').*(mu*conj(mu)'); muk(k,1)=sum(sum(summu),2); end %Sort according to dipole strength [Int,ki]=sort(muk); for a=1:3*N b=3*N-a+1; k=ki(b); MuX=0; MuY=0; MuZ=0; for n=1:3*N MuX=MuX+vec(n,k)*mu(n,1); MuY=MuY+vec(n,k)*mu(n,2); MuZ=MuZ+vec(n,k)*mu(n,3); end Muk(k,:)=[MuX;MuY;MuZ]; Energy=lams(k); Intensity=muk(k); Out(a,:)=[k,Energy,Intensity,MuX,MuY,MuZ];

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end sum=0; for a=1:3*N b=3*N-a+1; k=ki(b); sum=sum+muk(k); end TotInt=sum; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ttt=toc;