Transcript No Slide Title

APPLICATION OF
PHOTON CORRELATION SPECTROSCOPY
IN SOFT MATTER RESEARCH
Irena Drevenšek-Olenik
Faculty of Mathematics and Physics, University of Ljubljana
and J. Stefan Institute, Ljubljana, Slovenia
LIGHT SCATTERING WITH COHERENT SOURCE
random
refractive index
variation n(r)
Coherent
radiation
(e.g. laser)
Random
diffraction
pattern
(speckle pattern )
To observe speckle pattern, coherent
illumination of the scattering medium is needed.
All radiation is at least partially coherent.
• Longitudinal (temporal) coherence
Longitudinal
coherence length
• Transverse (spatial) coherence
Transverse
coherence length
LIGHT SCATTERING WITH PARTIALLY COHERENT
SOURCE
• 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.
EXPERIMENTAL RESTRICTIONS
speckles

=scattering angle
To see speckle at 0 <  < 2, requires
To see speckle at 0 <  < m (SAXS,...), requires
m
2
T
m
DYNAMIC LIGHT SCATTERING (DLS)
Incident wave
r1(t)
r2 (t)
r1(t+)
r2(t+)
moving scattering objects
produce 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
Scattered waves

detector
(specle size!!!)
Count rate (kHz)
Example:
Brownian motion of
macromolecules in solution
t(ms)
PHOTON CORRELATION SPECTROSCOPY
small 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 FUNCTIONS
Intensity correlation function G(2)()
Usually normalised function is measured.
example of
measured g(2) (t).
FIELD CORRELATION FUNCTION
detector at distance R
from sample
n
Field correlation function: G(1)()=
n = refractive
index contrast
RELATION BETWEEN g(1) and g(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?
DLS detects fluctuations of refractive index of the medium: n(r,t)=n(q,t)eiqr
q
Maximum cross
section for
sample
Laser
H
H
V


kf

ki
n(q=qs) .
 

qS  k f  ki
Detector (I(t)|Es(t) |2)
measurement
g(2)(t)=<I(t’)I(t’+t)>/<I>2=1+ (g(1)(t))2
 E s (t')Es (t' t) 
(1)
g (t) 

 E s (t')  E s (t' t) 
C e
l
(  t /  l ) Sl
l
l
Information on dynamic modes related to n(q,t) on the time scale 10-9 –103 s .
FLUCTUATIONS OF REFRACTIVE INDEX
n(r,t)=n(q,t)eiqr
The main challenge of DLS investigations is to
deduce the origin of refractive index
fluctuations n(r,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
OF BIOLOGICAL MOLECULES IN SOLUTION
In aqueous solutions (physiological conditions)
biological molecules often exhibit tendency to
self-organize into highly ordered supramolecular
structures (secondary, tertiary structure, ...)
Example of a 3D protein structure
Aggregation into 1D structures:
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,
....
SPECIFICITY OF THE 1D AGGREGATION
N
N
1D: N0,N =-(N-1)kT
2D: N0,N =-(N-N1/2)kT
1= 0,1+kTlnX1
N= N0,N + kTlnXN
nD: N0,N =-(N-Np)kT, p<1
Aggregate end effects
G=-(N 1) +N=0
condition of coexistence
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
ROD-SHAPED SCATTERERS
Diluted solution:
Polarized light scattering (VV):
Depolarized light scattering (VH):
g(1)( )
g(1)( )
Rotational
diffusion
j
Translational
diffusion
j
Model of Tirado and Garcia de la Torre (2<(p=L/d)<30)
SELF-ASSEMBLING OF GUANOSINE DERIVATIVES
cell 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 PHASE
I
50
Ch
H
T=23oC
I + Ch
T (0C)
Phase diagram for
dGMP (ammonium salt)
I+H
70
30
10
0
10
20
30
40
c=4 wt %
Concentration (wt%)
Studied by PCS in:
Concentration region: 0.1 wt% < c < 33 wt%
c=12 wt%
Temperature region: 290 K < T < 340 K.
Spherulite of the Ch phase
(Optical polarization microscopy)
DLS RESULTS– concentration dependence
In this system 2 dispersive modes are observed in polarized (VV) scattering
and 1 nondispersive mode is detected in depolarized (VH) scattering (in case of excess of salt)
Results for polarized scattering (VV): 1 wt% < c<12.5 wt%
fast VV mode = translational motion of G4 stacks
slow VV mode =translational motion of globules???
T = 298 K
EM, bar= 0.1 m
c= 3.5 wt% = CMC
D=1/(q2)
Length of stacks: L=368 nm
(approx. of dilute solution)
DLS RESULTS – added salt dependence
Results for polarized scattering (VV): added salt was KCl
K
fast VV mode
= translational motion of G4 stacks
Polyelectrolyte behaviour =
electrostatic interactions play a vital role.
Length of stacks: L=345 nm
(approx. of complete polyion screening)
Translational diffusion of charged rods (macroions) in the solution of small ions.
Standard diffusion term
Electrostatic term
Theory of coupled
dynamic modes
Approximate analytical
solution: Lin-Lee-Schur
Poisson-Boltzmann equation
31P NMR study – added salt dependence
added salt was KCl
At cKCl=0.1 maximum possible
aggregation level of 75% is reached!
DLS RESULTS – added salt dependence
Results for depolarized scattering (VH): added salt was KCl
VH mode = orientational fluctuations of G4 stacks
(very nonexponential mode, gel-like structure)
Critical slowing-down due to approaching of the CI-Ch transition.
MELTING OF THE AGGREGATES
VV fast mode:
Temperature dependence
Why does DLS “see”
longer aggregates than
other techniques?
DLS
T<Tm (Rh~3Rg)
T>Tm (Rh~Rg)
15 wt% GMP
23 wt% GMP
14
Apparent Rg (A)
12
10
8
6
4
~ 10
2
20
SAXS
25
30
35
40
45
50
0
Temperature ( C)
55
60
65
nm
AFM dGMP (Na)
?
Discrepancy SAXS/DLS - search for explanation
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”) !!
Effective viscosity of the “soup” = 3H2O ??
•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
IN LIQUID CRYSTALS
LIQUID CRYSTALS (LC)
Solid phase (crystal)
heating
cooling
Liquid phase
Liquid crystal phase
n(r)

Optical
polarization
microscopy
LC orientational order is described by
nematic director field n(r) and scalar
order parameter S=<(3(cos2)-1)>/2.
OPTICAL BIREFRINGENCE OF
LIQUID CRYSTALS (LCs)
Liquid crystals (LC): usually commercial mixtures,
characterized by strong optical birefringence.
n(r)
typical LC molecule:
(pentyl-cianobiphenyl)
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 SCATTERING
orientational fluctuations
n(r)=n0(r)+n(r)
in a planarly aligned LC layer (D>>):
n(r)=n(q)eiqr
Thermaly induced
D
are related to increase of the elastic deformation energy of the LC director field n(r):
2+K q 2)+n (q)(K q 2+K q 2) 
Wd=(V/2)

n
(q)(K
q
1
1 
3 
2
2 
3 
q
2
2
kT
Ki  10-11 N
kT
Relaxation of the fluctuations :
n0
dWd/dni=-ini/t, i=1,2
1
n(q,t)=n(q,0)e-t/
Relaxation rate: (1/ )(K/)q2
10-6 –1 s
10-5 cm2/s
q
2
CONFINED LIQUID CRYSTALS
POLYMER DISPERSED LIQUID CRYSTALS (PDLCs)
light beam (UV)
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.
PDLC
HOLOGRAPHIC POLYMER DISPERSED LIQUID CRYSTALS (HPDLCs)
Planes with LC
droplets separated
by planes of more
or less pure
polymer
inhomogeneous phase separation
SEM image
SWITCHABLE DIFFRACTION IN HPDLCs
Image of diffraction pattern observed on a far field screen: a) E=0, b) E=100 V/m.
Polymer matrix:
SEM-image
a)
b)
HPDLC quasicrystal structure with 10-fold symmetry.
(20 m HPDLC layer between ITO coated glass plates)
Standard open problem =
size and structure of LC domains.
EFFECT OF CONFINEMENT ON FLUCTUATIONS
A) Spherical droplets of radius R
qmin/R, (1/ )min (K/)R-2
qmin/D, (1/ )min (K/)D-2
1/
B) Thin planar layer of thickness D
1/
qs=(qx,0,0)
0
2
4
6
8
10
12
qR
s
For ellipsoidal droplets one expects a
situation intermediate between A) and B)
1/
?
qs=(0,0,qz)
0
2
4
6
qsD
8
10
12
TYPICAL EXAMPLE OF g(1)(t) FOR H-PDLC
slow
process
sample VIS, =0.78 m
1.0
: 10-103ms
S: 0.1-0.2
slow=36 ms
Sslow=0.15
1.0
0.8
0.6
0.8
0.4
0.0
-4
-3
-2
-1
10 10 10 10
0.6
(1)
g (t)
0.2
1.0
0.4
0.8
1
10 102 103 104
10
2
=0.27 ms
S=0.91
0.6
0.2
fast process
: 0.1-1 ms
S > 0.75
0.0
0.4
0.2
0.0
-4
-3
-2
-1
10 10 10 10
10
-4
10
-3
1
10 102 103 104
10
-2
10
-1
1
10
10
3
10
4
t (ms)
Fit: g(1)(t)=A+Bexp((-t/)S)+Bslowexp( (-t/slow)Sslow)
Two different orientational relaxation processes are detected
SLOW RELAXATION – DIFFUSION OF THE
AVERAGE LC DROPLET ORIENTATION <n(r)>.
H(V)V scattering, =20
- Sensitive to “imperfections” of the LC-
o
polymer interface and to interpore
orientational coupling.
VIS =0.78 m
UV-2B =0.78 m
1.0
1
g (t)
0.8
0.6
0.4
0.04
0.02
0.2
0.00
1
10
2
10
3
4
10
10
0.0
10
-4
10
-3
10
-2
10
-1
1
10
10
2
10
3
10
4
t (ms)
(Quasi)periodic network results
in band structure of the modes.
M. Avsec, I. Drevensek-Olenik, A. Mertelj, S. Gorkhali, G. P. Crawford, M. Copic: Phys. Rev. Lett. 98, 173901-1-4 (2007).
FAST RELAXATION – decay of the
normal modes of nematic director field n(q,t).
1.2
=20
1.0
- Signal from “intrapore” orientational
o
=120
fluctuations.
o
(1)
g (t)
0.8
0.6
0.4
0.2
0.0
-3
10
10
-2
10
-1
1
10
10
2
t (ms)
- Dispersion is observed at large
scattering angles – relaxation time
decreases with increasing
scattering angle .
DISPERSION OF THE FAST MODE (sample =0.8 m)
y
14
1/f (kHz)
12
z
qs  K g
10
1 m
8
6
4
SEM
2
1/f (kHz)
VIS
qy,min
0
14
12
qi,min (/ di)
qs II Kg
Analysis of dispersion data reveals
size and shape of the LC domains.
10
8
6
4
2
0
0,0
dz  250 nm
dy  600 nm
1) I. Drevensek-Olenik, M. E. Sousa, A. K. Fontecchio, G. P. Crawford,
M. Copic: Phys. Rev. E, 69, 051703-1-9 (2004).
qz,min
6
5,0x10
7
1,0x10
s -1
q (m )
7
1,5x10
7
2,0x10
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).
CONCLUSIONS
• 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...........?