APPLICATION OF APPLICATION OF PHOTON CORRELATION SPECTROSCOPY PHOTON CORRELATION SPECTROSCOPY

IN SOFT MATTER RESEARCHIN SOFT MATTER RESEARCH

APPLICATION OF APPLICATION OF PHOTON CORRELATION SPECTROSCOPY PHOTON CORRELATION SPECTROSCOPY

IN SOFT MATTER RESEARCHIN SOFT MATTER RESEARCH

Irena Drevenšek-OlenikFaculty of Mathematics and Physics, University of Ljubljana

and J. Stefan Institute, Ljubljana, Slovenia

LIGHT SCATTERING WITH COHERENT SOURCELIGHT SCATTERING WITH COHERENT SOURCELIGHT SCATTERING WITH COHERENT SOURCELIGHT SCATTERING WITH COHERENT SOURCE

Coherent radiation(e.g. laser)

Randomdiffraction pattern(speckle pattern )

random refractive index variation n(r)

To observe speckle pattern, coherent illumination of the scattering medium is needed.All radiation is at least partially coherent.

• Longitudinal (temporal) coherence

• Transverse (spatial) coherence

Longitudinal coherence length

Transversecoherence length

• Inside the coherence volume radiation can be described as a monochromatic plane wave.

• Field amplitudes and phases in different coherence volumes are uncorrelated !!!

To observe scattering in the form of speckle pattern, the scattering volume of the sample must lie within one coherence volume of the illumination source.

LIGHT SCATTERING WITH PARTIALLY LIGHT SCATTERING WITH PARTIALLY COHERENT SOURCECOHERENT SOURCE

LIGHT SCATTERING WITH PARTIALLY LIGHT SCATTERING WITH PARTIALLY COHERENT SOURCECOHERENT SOURCE

EXPERIMENTAL RESTRICTIONSEXPERIMENTAL RESTRICTIONSEXPERIMENTAL RESTRICTIONSEXPERIMENTAL RESTRICTIONS

=scattering angle

To see speckle at 0 < < 2, requires

To see speckle at 0 < < m (SAXS,...), requires

mTm 2

speckles

DYNAMIC LIGHT SCATTERING (DLS)DYNAMIC LIGHT SCATTERING (DLS)DYNAMIC LIGHT SCATTERING (DLS)DYNAMIC LIGHT SCATTERING (DLS)

r1(t)r1(t+)

r2 (t)

detector(specle size!!!)

moving scattering objectsproduce temporal variations of local refractive index n=n(r,t). Consequently, intensity of specles fluctuates with time.

r= r2 - r1

r (t+)- r (t) (/sin( /2)) relative phase coherence is lost

r2(t+)

Scattered waves

Incident wave

t(ms)

Count rate (kHz)

Brownian motion of macromolecules in solution

Example:

PHOTON CORRELATION SPECTROSCOPYPHOTON CORRELATION SPECTROSCOPYPHOTON CORRELATION SPECTROSCOPYPHOTON CORRELATION SPECTROSCOPYsmall size

Tc

Autocorrelation function of scattered light intensity I at selected scattering angle (scattering wave vector q) is measured.

G(2)()=

Operation is repeated for many different values of in the range 10-9 s < < 103 s (typical autocorrelator gives results for 256 values of ).

CORRELATION FUNCTIONSCORRELATION FUNCTIONSCORRELATION FUNCTIONSCORRELATION FUNCTIONS

Intensity correlation function G(2)()

Usually normalised function is measured.

example of measured g(2) (t).

FIELD CORRELATION FUNCTIONFIELD CORRELATION FUNCTIONFIELD CORRELATION FUNCTIONFIELD CORRELATION FUNCTION

detector at distance R from sample

Field correlation function:

n

G(1)()=

n = refractive index contrast

RELATION BETWEEN gRELATION BETWEEN g(1)(1) and g and g(2)(2)RELATION BETWEEN gRELATION BETWEEN g(1)(1) and g and g(2)(2)

For scattered field Es(q,t), which can be described as 2D random walk (Gaussian field), the following relation is valid:

Siegert relation

In practice we measure:

The value of depends on the details of the detection system.

WHAT CAN BE INVESTIGATED by DLS?WHAT CAN BE INVESTIGATED by DLS?WHAT CAN BE INVESTIGATED by DLS?WHAT CAN BE INVESTIGATED by DLS?

ik

fk

ifS kkq

Laser

Detector (I(t)|Es(t) |2)

sample

t)(t'E)(t'E

t)(t')E(t'E(t)g

ss

ss(1)

l

tl

lSleC )/(

H

V

Information on Information on dynamic modesdynamic modes related to related to n(n(qq,t) ,t) on the time scale on the time scale 10-9 –103 s . .

Maximum cross section for

n(n(qq==qs)) . .

g(2)(t)=<I(t’)I(t’+t)>/<I>2=1+ (g(1)(t))2

measurement

l

DLS detects fluctuations of refractive index of the medium: nn((rr,t)=,t)=nn((qq,t)e,t)eiiqqrr

H

q

FLUCTUATIONS OF REFRACTIVE INDEXFLUCTUATIONS OF REFRACTIVE INDEXFLUCTUATIONS OF REFRACTIVE INDEXFLUCTUATIONS OF REFRACTIVE INDEX

nn((rr,t)=,t)=nn((qq,t)e,t)eiiqqrr

The main challenge of DLS investigations is to deduce the origin of refractive index fluctuations nn((rr,t) ,t) and to gain understanding on dynamic processes associated with them.

Some phenomena, which can cause refractive index changes:• thermaly induced density fluctuations of the medium• translational and rotational motion of the “scatterers” • mechanical stress/strain• birefringence fluctuations•...

DLS INVESTIGATION of SELF-ASSEMBLY DLS INVESTIGATION of SELF-ASSEMBLY OF BIOLOGICAL MOLECULES IN SOLUTIONOF BIOLOGICAL MOLECULES IN SOLUTION

DLS INVESTIGATION of SELF-ASSEMBLY DLS INVESTIGATION of SELF-ASSEMBLY OF BIOLOGICAL MOLECULES IN SOLUTIONOF BIOLOGICAL MOLECULES IN SOLUTION

Technologial challenges of 1D self-aggregation:Columnar aggregates exhibit strongly anisotropic electronic transport properties – prospective for applications as supramolecular nanowires, photoconductive switches, for polarized O-LEDs, ....

In aqueous solutions (physiological conditions) biological molecules often exhibit tendency to self-organize into highly ordered supramolecular structures (secondary, tertiary structure, ...)

Aggregation into 1D structures:Example of a 3D protein structure

SPECIFICITY OF THE 1D AGGREGATIONSPECIFICITY OF THE 1D AGGREGATIONSPECIFICITY OF THE 1D AGGREGATIONSPECIFICITY OF THE 1D AGGREGATION

1= 0,1+kTlnX1

1D: N0,N =-(N-1)kT

2D: N0,N =-(N-N1/2)kT

nD: N0,N =-(N-Np)kT, p<1

G=-(N 1) +N=0condition of coexistence

N= N0,N + kTlnXN

NN

Aggregate end effects

Critical aggregate (micellar) concentration CMC e-

for p<1, transition from monomers to N aggregates

for p=1, transition from monomers to finite size linear aggregates with

size distribution: XN=N(X1e)Ne-,

1D aggregates are modeled as rod-shaped objects.

DIFFUSION CONSTANTS OF THE DIFFUSION CONSTANTS OF THE ROD-SHAPED SCATTERERS ROD-SHAPED SCATTERERS

DIFFUSION CONSTANTS OF THE DIFFUSION CONSTANTS OF THE ROD-SHAPED SCATTERERS ROD-SHAPED SCATTERERS

Polarized light scattering (VV): g(1)( )

Translational diffusionRotational

diffusion

Model of Tirado and Garcia de la Torre (2<(p=L/d)<30)

jj

Diluted solution:

g(1)( )Depolarized light scattering (VH):

SELF-ASSEMBLING OF GUANOSINE DERIVATIVESSELF-ASSEMBLING OF GUANOSINE DERIVATIVESSELF-ASSEMBLING OF GUANOSINE DERIVATIVESSELF-ASSEMBLING OF GUANOSINE DERIVATIVEScell ageing, telomers, quadruplexes, G-quartets.....

Chromosome ends are made of G-rich sequences, which form quadruplex structures.

Self-assembly of guanosine monophosphate(GMP) in aqueous solutions.

ISOTROPIC COLUMNAR PHASEISOTROPIC COLUMNAR PHASEISOTROPIC COLUMNAR PHASEISOTROPIC COLUMNAR PHASE

01 0

C o nc e ntra tio n (wt% )

T (C

)0

1 0 2 0 3 0 4 0

3 0

5 0

7 0

HC hII +

Ch

I + HPhase diagram fordGMP (ammonium salt)

Spherulite of the Ch phase(Optical polarization microscopy)

c=12 wt%

c=4 wt %

Studied by PCS in:

Concentration region: 0.1 wt% < c < 33 wt%

Temperature region: 290 K < T < 340 K.

T=23oC

DLS RESULTS– concentration dependenceDLS RESULTS– concentration dependenceDLS RESULTS– concentration dependenceDLS RESULTS– concentration dependence

In this system 2 dispersive modes are observed in polarized (VV) scatteringand 1 nondispersive mode is detected in depolarized (VH) scattering (in case of excess of

salt)

fast VV mode = translational motion of G4 stacks

slow VV mode =translational motion of globules???

T = 298 K

c= 3.5 wt% = CMC

EM, bar= 0.1 m

Results for polarized scattering (VV): 1 wt% < c<12.5 wt%

D=1/(q2)Length of stacks: L=368 nm(approx. of dilute solution)

DLS RESULTS – added salt dependenceDLS RESULTS – added salt dependenceDLS RESULTS – added salt dependenceDLS RESULTS – added salt dependenceResults for polarized scattering (VV): added salt was KCl

fast VV mode= translational motion of G4 stacksPolyelectrolyte behaviour = electrostatic interactions play a vital role.

K

Translational diffusion of charged rods (macroions) in the solution of small ions.

Poisson-Boltzmann equation

Standard diffusion term Electrostatic term

Theory of coupled dynamic modes

Approximate analytical solution: Lin-Lee-Schur

Length of stacks: L=345 nm(approx. of complete polyion screening)

31P NMR study – added salt dependence31P NMR study – added salt dependence31P NMR study – added salt dependence31P NMR study – added salt dependence

At cKCl=0.1 maximum possible aggregation level of 75% is reached!

added salt was KCl

Results for depolarized scattering (VH): added salt was KCl

VH mode = orientational fluctuations of G4 stacks(very nonexponential mode, gel-like structure)

DLS RESULTS – added salt dependenceDLS RESULTS – added salt dependenceDLS RESULTS – added salt dependenceDLS RESULTS – added salt dependence

Critical slowing-down due to approaching of the CI-Ch transition.

MELTING OF THE AGGREGATESMELTING OF THE AGGREGATESMELTING OF THE AGGREGATESMELTING OF THE AGGREGATES

20 25 30 35 40 45 50 55 60 652

4

6

8

10

12

14 15 wt% GMP 23 wt% GMP

App

aren

t Rg

(A

)

Temperature (0C)

DLS

SAXS

VV fast mode: Temperature dependence

T<Tm (Rh~3Rg)T>Tm (Rh~Rg)

?

AFM dGMP (Na)

Why does DLS “see” longer aggregates thanother techniques?

~ 10 nm

Problem = Motion of columnar aggregates in a dense solution of non aggregated species? In GMP solutions the concentration region of the CI phase is quite narrow:c*~ 10 wt%, cCI-Ch ~ 25 wt% (Motion in a dense “soup”) !!

Discrepancy SAXS/DLS - search for explanationDiscrepancy SAXS/DLS - search for explanationDiscrepancy SAXS/DLS - search for explanationDiscrepancy SAXS/DLS - search for explanation

Effective viscosity of the “soup” = 3H2O ??

•I. Drevenšek-Olenik, L. Spindler, M. Čopič, H. Sawade, D. Kruerke, G. Heppke:Phys. Rev. E, 65, 011705-1-9 (2001).

•L. Spindler, I. Drevenšek-Olenik, M. Čopič, J. Cerar, J. Škerjanc, R. Romih, P. Mariani:Eur. Phys. J. E, 7, 95-102. (2002).

•L. Spindler, I. Drevenšek-Olenik, M. Čopič, J. Cerar, J. Škerjanc, R. Romih, P. Mariani:Eur. Phys. J. E, 13, 27-33 (2004).

ORIENTATIONAL FLUCTUATIONS ORIENTATIONAL FLUCTUATIONS IN LIQUID CRYSTALSIN LIQUID CRYSTALS

ORIENTATIONAL FLUCTUATIONS ORIENTATIONAL FLUCTUATIONS IN LIQUID CRYSTALSIN LIQUID CRYSTALS

LIQUID CRYSTALS (LC)LIQUID CRYSTALS (LC)LIQUID CRYSTALS (LC)LIQUID CRYSTALS (LC)

coolingSolid phase (crystal) Liquid phase

Liquid crystal phase

Opticalpolarization microscopy

heating

LC orientational order is described bynematic director field n(r) and scalarorder parameter S=<(3(cos2)-1)>/2.

n(r)

OPTICAL BIREFRINGENCE OFOPTICAL BIREFRINGENCE OFLIQUID CRYSTALS (LCs)LIQUID CRYSTALS (LCs)

OPTICAL BIREFRINGENCE OFOPTICAL BIREFRINGENCE OFLIQUID CRYSTALS (LCs)LIQUID CRYSTALS (LCs)

Liquid crystals (LC): usually commercial mixtures,

characterized by strong optical birefringence.

typical LC molecule:

(pentyl-cianobiphenyl)

n(r)

Nematic director field n(r) can be strongly modified by low external voltages. Variation of n(r) causes large modification of optical properties. This specific property of LCs represents a basic principle of operation of LCD devices.

ORIENTATIONAL FLUCTUATIONS and LIGHT SCATTERINGORIENTATIONAL FLUCTUATIONS and LIGHT SCATTERING ORIENTATIONAL FLUCTUATIONS and LIGHT SCATTERINGORIENTATIONAL FLUCTUATIONS and LIGHT SCATTERING

n0

q

Wd=(V/2)n1(q)(K1q 2+K3q 2)+n2(q)(K2q 2+K3q 2)

1 2

kT

dWd/dni=-ini/t, i=1,2

Relaxation rate: (1/ )(K/)q2

10-5 cm2/s

Thermaly induced orientational fluctuationsin a planarly aligned LC layer (D>>): n(r)=n0(r)+n(r) nn((rr)=)=nn((qq)e)eiiqrqr

2 2

q

kT

are related to increase of the elastic deformation energy of the LC director field n(r):

Ki 10-11 N

10-6 –1 s

nn((qq,t,t))==nn((qq,0,0))ee-t/-t/

D

Relaxation of the fluctuations :

PDLC

Photopolymerization of the prepolymer/LC mixture induces phase separation of the constituents.

This process results in formation of liquid crystal droplets, embedded in a polymer matrix.

light beam (UV)

POLYMER DISPERSED LIQUID CRYSTALS (PDLCs)

CONFINED LIQUID CRYSTALSCONFINED LIQUID CRYSTALSCONFINED LIQUID CRYSTALSCONFINED LIQUID CRYSTALS

HOLOGRAPHIC POLYMER DISPERSED LIQUID CRYSTALS (HPDLCs)

inhomogeneous phase separation

Planes with LC droplets separated by planes of more or less pure polymer

SEM image

SWITCHABLE DIFFRACTION IN HPDLCsSWITCHABLE DIFFRACTION IN HPDLCsSWITCHABLE DIFFRACTION IN HPDLCsSWITCHABLE DIFFRACTION IN HPDLCsImage of diffraction pattern observed on a far field screen: a) E=0, b) E=100 V/m.

a) b)HPDLC quasicrystal structure with 10-fold symmetry.(20 m HPDLC layer between ITO coated glass plates)

Polymer matrix:SEM-image

Standard open problem = size and structure of LC domains.

A) Spherical droplets of radius R qmin/R, (1/ )min (K/)R-2

B) Thin planar layer of thickness D

For ellipsoidal droplets one expects a situation intermediate between A) and B)

0 2 4 6 8 10 12

1/

qR

0 2 4 6 8 10 12

qs=(0,0,qz)1

/1

/

qsD

qs=(qx,0,0)

EFFECT OF CONFINEMENT ON FLUCTUATIONSEFFECT OF CONFINEMENT ON FLUCTUATIONSEFFECT OF CONFINEMENT ON FLUCTUATIONSEFFECT OF CONFINEMENT ON FLUCTUATIONS

?

qmin/D, (1/ )min (K/)D-2

s

TYPICAL EXAMPLE OF TYPICAL EXAMPLE OF g(1)(t) FOR H-PDLCFOR H-PDLC TYPICAL EXAMPLE OF TYPICAL EXAMPLE OF g(1)(t) FOR H-PDLCFOR H-PDLC

10-4 10-3 10-2 10-1 1 10 102 103 104

0.0

0.2

0.4

0.6

0.8

1.0

sample VIS, =0.78 m

g(1) (t

)

t (ms)

10-4

10-3

10-2

10-1 1 10 10

210

310

40.0

0.2

0.4

0.6

0.8

1.0 =0.27 ms

S=0.91

10-4 10-3 10-2 10-1 1 10 102 103 1040.0

0.2

0.4

0.6

0.8

1.0 slow

=36 msS

slow=0.15

Fit: g(1)(t)=A+Bexp((-t/)S)+Bslowexp( (-t/slow)Sslow)

fast process: 0.1-1 msS > 0.75

Two different orientational relaxation processes are detected

slowprocess: 10-103msS: 0.1-0.2

10-4

10-3

10-2

10-1 1 10 10

210

310

4

0.0

0.2

0.4

0.6

0.8

1.0

H(V)V scattering, =20o

VIS =0.78 m

UV-2B =0.78 m

g1 (t)

t (ms)

SLOW RELAXATIONSLOW RELAXATION – – DIFFUSION OFDIFFUSION OF THE THE AVERAGE AVERAGE LC DROPLET LC DROPLET ORIENORIENTATION <TATION <nn((rr)>.)>.

SLOW RELAXATIONSLOW RELAXATION – – DIFFUSION OFDIFFUSION OF THE THE AVERAGE AVERAGE LC DROPLET LC DROPLET ORIENORIENTATION <TATION <nn((rr)>.)>.

1 10 102

103

104

0.00

0.02

0.04

- Sensitive to “imperfections” of the LC-polymer interface and to interpore orientational coupling.

M. Avsec, I. Drevensek-Olenik, A. Mertelj, S. Gorkhali, G. P. Crawford, M. Copic: Phys. Rev. Lett. 98, 173901-1-4 (2007).

(Quasi)periodic network results

in band structure of the modes.

FAST RELAXATIONFAST RELAXATION – decay of the – decay of the normal modes of nematic director field normal modes of nematic director field nn((qq,t).,t).

FAST RELAXATIONFAST RELAXATION – decay of the – decay of the normal modes of nematic director field normal modes of nematic director field nn((qq,t).,t).

- Dispersion is observed at large scattering angles – relaxation time decreases with increasing scattering angle .

10-3 10-2 10-1 1 10 102

0.0

0.2

0.4

0.6

0.8

1.0

1.2 =20

o

=120o

g(1) (t

)

t (ms)

- Signal from “intrapore” orientational fluctuations.

DISPERSION OF THE FAST MODE (DISPERSION OF THE FAST MODE (sample sample =0.8 =0.8 mm))DISPERSION OF THE FAST MODE (DISPERSION OF THE FAST MODE (sample sample =0.8 =0.8 mm))

z

y

dz 250 nmdy 600 nm

SEM

Analysis of dispersion data revealssize and shape of the LC domains.

1 1 mm

0,0 5,0x106 1,0x107 1,5x107 2,0x1070

2

4

6

8

10

12

14

qz,min

1/ f (

kHz)

1/ f (

kHz)

q (m-1)

qs II K

g

0

2

4

6

8

10

12

14

VIS

qy,min

qs K

g

s

qi,min (/ di)

1) I. Drevensek-Olenik, M. E. Sousa, A. K. Fontecchio, G. P. Crawford,M. Copic: Phys. Rev. E, 69, 051703-1-9 (2004).

2) “Dynamic processes in confined liquid crystals”, M. Vilfan, I. Drevenšek Olenik, M. Čopič: in "Time-resolved Spectroscopy in Complex Liquids - An Experimental Perspective", edited by R. Torre, p. 185-216 (Springer 2008).

CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS• Photon correlation spectroscopy is a very convenient tool to probe refractive index fluctuations in different materials in the time range from nanoseconds to hundreds of seconds.

• It requires illumination of the sample by coherent radiation and detection of the scattered light within the region smaller from a speckle size (photomultipliers, avalanche photodiodes, ...)

• It is one of the standard techniques used to deduce the shape and size (size distribution) of submicrometer particles in solutions (studies of polymers, proteins, nanotubes, ...)

• It is a convenient probe of liquid crystal orientational and viscoelastic properties in all kinds of mesophases and structures.

• In astronomy PCS can be used to investigate...........?