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
)
Random diffraction pattern
(speckle pattern )
Coherent radiation
(e.g. laser)
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
r 1
(t)
r 1
(t+
)
r= r 2
- r
1
r (t+
)-
r (t)
(
/sin (
/2 ) )
relative phase coherence is lost r 2
(t)
r 2
(t+
) Scattered waves
moving scattering objects
produce temporal variations of local refractive index n=n(r,t). Consequently,
intensity of specles fluctuates with time
.
Count rate (kHz)
detector
(specle size!!!) Example: Brownian motion of macromolecules in solution
t(ms)
PHOTON CORRELATION SPECTROSCOPY
small size T c Autocorrelation function of scattered light intensity scattering angle (scattering wave vector
q
I
at selected ) is measured.
G (2) (
)=
Operation is repeated for many different values of
10 -9 s <
< 10 3 s
( typical
autocorrelator
in the range 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
E
s (
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)e i
qr q Laser
H
sample
H V
k
f k
i
q S
k
f
k i
Maximum cross section for n(
q= q s
) .
Detector ( I(t)
|E s (t) | 2 ) measurement
g (2) (t)=
l C l e
(
t
/
l
)
l l
Information on dynamic modes related to
n(
q
,t)
on the time scale 10 -9 –10 3 s .
FLUCTUATIONS OF REFRACTIVE INDEX
n(
r
,t)= n(
q
,t)e i
qr 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, ....
N
SPECIFICITY OF THE 1D AGGREGATION
N 1D : N 0,N =-(N-1) kT 2D : N 0,N =-(N-N 1/2 ) kT 1 = 0,1 +kTlnX 1 nD : N 0,N =-(N-N p ) kT, p<1 N = N 0,N + kTlnX N G=-(N 1 ) + N =0
condition of coexistence
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:
X N =N(X 1 e
) N e -
, 1D aggregates are modeled as
rod-shaped objects
.
DIFFUSION CONSTANTS OF THE ROD-SHAPED SCATTERERS
Diluted solution:
Polarized light scattering (VV):
g (1)
( )
Depolarized light scattering (VH):
g (1)
( ) Rotational diffusion Translational diffusion
j 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.
70 50 I
ISOTROPIC COLUMNAR PHASE
I + H Ch H Phase diagram for dGMP (ammonium salt) T=23 o C 30 10 0 10 20 30 40 Conc entration (wt%)
c=4 wt %
Studied by PCS in: Concentration region: 0.1 wt% < c < 33 wt% Temperature region: 290 K < T < 340 K.
c=12 wt%
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/( q 2 ) 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
Poisson-Boltzmann equation
Approximate analytical solution: Lin-Lee-Schur
31P NMR study – added salt dependence
added salt was KCl
At c
KCl
=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 14 12 10 8 6 4 15 wt% GMP 23 wt% GMP 2 20 SAXS 25 30 35 40 45 50 Temperature ( 0 C) 55 60 65 T
~ 10 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%, c CI-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)
heating Solid phase (crystal) cooling Liquid phase
Optical polarization microscopy
Liquid crystal phase n
(
r
) LC orientational order is described by nematic director field
n
(
r
) and scalar order parameter S=<(3(cos 2 )-1)>/2.
OPTICAL BIREFRINGENCE OF 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 SCATTERING
Thermaly induced
orientational fluctuations in a planarly aligned LC layer (D>> ):
n
(
r
)=
n
0 (
r
)
+
n
(
r
)
n
(
r
)=
n
(
q
)e i
qr
D are related to increase of the elastic deformation energy of the LC director field
n
(
r
): W d =(V/2) q n 1 (
q
) 2 (K 1 q 2 +K 3 q 2 ) + n 2 (
q
) 2 (K 2 q 2 +K 3 q 2 ) dW d /dn i = i n i / t, i=1,2
kT Relaxation of the fluctuations
: K i 10 -11 N
kT
n 0
n
(
q,t
)=
n
(
q,0
)e -t/ Relaxation rate : (1/ ) (K/ )q 2
1
q
2 10 -6 –1 s
10 -5 cm 2 /s
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.
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.
Polymer matrix: SEM-image
EFFECT OF CONFINEMENT ON FLUCTUATIONS
A) Spherical droplets of radius R q min
/R, (1/ ) min (K/ )R -2
q min
/D, (1/ ) min (K/ )D -2
B) Thin planar layer of thickness
D
q s
=(q x ,0,0)
?
0 2 4 6 qR s 8 10 12
For ellipsoidal droplets one expects a situation intermediate between A) and B)
0 2 4 6 q s D
q s
=(0,0,q z ) 8 10 12
TYPICAL EXAMPLE OF
g (1) (t)
FOR H-PDLC
fast process
:
0.1-1 ms
S >
0.75
sample VIS, =0.78 m 1.0
0.8
0.6
1.0
0.8
0.6
0.4
0.2
0.0
10 -4 10 -3 10 -2 10 -1 1
slow =36 ms S slow =0.15
10 10 2 10 3 10 4 0.4
0.2
1.0
0.8
=0.27 ms S=0.91
0.6
0.4
0.2
0.0
10 -4 10 -3 10 -2 10 -1 0.0
10 -4 10 -3 1 10 10 2 10 3 10 4 10 -2 10 -1 1 t (ms) 10 10 2 10 3 10 4
slow process
:
10-10 3 ms
S:
0.1-0.2
Fit: g (1) (t)=A+B exp((-t/ ) S )+B slow exp( (-t/ slow ) Sslow )
Two different orientational relaxation processes are detected
SLOW RELAXATION – DIFFUSION OF THE AVERAGE LC DROPLET ORIENTATION < n
(
r
)>.
1.0
0.8
H(V)V scattering, =20 o VIS =0.78 m UV-2B =0.78 m Sensitive to “imperfections” of the LC polymer interface and to interpore orientational coupling.
0.6
0.4
0.04
0.2
0.02
0.00
1 0.0
10 10 2 10 3 10 4 10 -4 10 -3 10 -2 10 -1 1 t (ms) 10 10 2 10 3 10 4 (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
1.0
0.8
0.6
0.4
0.2
0.0
10 -3 10 -2 10 -1 t (ms) 1 =20 o =120 o 10 10 2 Dispersion is observed at large scattering angles – relaxation time decreases with increasing scattering angle .
Signal from “intrapore” orientational fluctuations.
DISPERSION OF THE FAST MODE (
sample
=0.8
m
)
y 14 12 10
q s
K
g
4 2 8 6
q y,min
0 14 12 10 8 6 4 2 0 0,0 q
s
II K
g
5,0x10 6
q z,min
1,0x10 7 q (m s -1 ) 1,5x10 7
VIS
2,0x10 7
1
m
z
d z d y
250 nm 600 nm SEM q i,min
(
/ d i ) Analysis of dispersion data reveals size and shape of the LC domains.
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).
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...........?