Introduction to PHOTON CORRELATION SPECTROSCOPY Rikard Bergman Condensed Matter Physics Department o

1
Introduction toPHOTON CORRELATION
SPECTROSCOPYRikard BergmanCondensed
Matter PhysicsDepartment of Applied Physics
2
Important information

• Email f5xrb_at_fy.chalmers.se
• Office Soliden 2042
• Phone [phone]
• Mobile [phone]
• Room F7203 (7th floor Forskarhuset)

3
Outline

• Introduction to PCS
• What do we study?
• General concepts
• Light scattering theory
• Applications
• Brownian motion
• Dynamics in glasses and polymer solutions
• Experiment
• Data Analysis
• Projects

4
General Concepts of PCS

• A dynamic light scattering technique.
• Probes time variation of density and/or
  concentration fluctuations.

5
What can we study with PCS?

• Physics, chemistry, bio-physics,
• - nano-particle/colloidal solutions
• - liquids/liquid-glass transition
• - polymers/polymer solutions
• - gels
• - DNA
• Issues
• - particle size, radius of gyration, size of
  globule
• - diffusion of species
• - relaxational dynamics

6
Time and energy scales
Time scale (seconds) 10-13
10-7
elementary excitations tunneling
polymer reptation diffusion
glassy dynamics molecular
excitations libration
Excitation energy (eV) 1 10-1
10-2 10-3
10-6 10-9
7
Length scales
Length scale in nm 0.01 0.1 0.3
1.0 3.0 10
30 100
surfaces and multilayers micelles
critical phenomena
proteins
polymers
atomic structures
organic molecules pharmaceuticals
supermolecules
50 0.5
0.05
0.005 Momentum transfer (Å-1)
8
Spectroscopic techniques
9
Time range of PCS
PCS covers a very large time range! Typically
10-8 - 103 s! gt 11 decades in time!
10
Q-range of PCS
Q-range 10-3 Å-1 Length scales mm PCS
is suitable for diffusional studies of
macromolecules, such as polymers and large
bio-molecules!
11
Outline

• Introduction to PCS
• What do we study?
• General concepts
• Light scattering theory
• Applications
• Brownian motion
• Dynamics in glasses and polymer solutions
• Experiment
• Data Analysis
• Projects

12
Light Scattering
Interference!
13
Light Scattering
14
Siegerts relation
Einsteins theory describes the electric field
correlation function, g1(t).
PCS experiments probes the intensity correlation
function g2(t).
I(t)E(t) E(t) Gaussian approximation
15
Correlation function
16
Outline

• Introduction to PCS
• What do we study?
• General concepts
• Light scattering theory
• Applications
• Brownian motion
• Dynamics in glasses and polymer solutions
• Experiment
• Data Analysis
• Projects

17
Brownian Motion

• First observed in 1827 by the botanist Robert
  Brown. But Brown did not understand what was
  happening. He only observed pollen grains under a
  microscope.
• Desaulx in 1877 "In my way of thinking the
  phenomenon is a result of thermal molecular
  motion in the liquid environment (of the
  particles)."
• But it was not until 1905 that the mathematical
  theory of Brownian motion was developed by
  Einstein. (It was partly for this work he
  received the Nobel prize 1921.)

18
Brownian Motion

• Explanation
• A suspended particle is constantly and randomly
  bombarded from all sides by molecules of the
  liquid. If the particle is very small, the hits
  it takes from one side will be stronger than the
  bumps from other side, causing it to jump. These
  small random jumps are what make up Brownian
  motion.
• Statistical Mechanics!

19
Stoke-Einsteins relation

• D diffusion constant
• T temperature
• h viscosity of solvent
• r radius of particles

20
Light Scattering geometry
Diffusion constant (Brownian motion)
t relaxation time q scattered wave vector
21
PCS experiment

• t -from experiment - determine
• D diffusion constant
• T temperature
• h viscosity of solvent
• r radius of particles

22
Research performed at Chalmers

• Glass transition dynamics
• Thin free-standing polymer films
• Dynamics in gels and polymer solutions

23
Glass transition dynamics

• ?-relaxation
• cooperative intermolecular motion
• stretched exponential decay
• non-Arrhenius temp. dep.
• freezes at Tg
• ?-relaxations
• local motion
• broad response
• Arrhenius temp. dep.

24
Glass transition dynamics

• ?-relaxation
• cooperative intermolecular motion
• stretched exponential decay
• non-Arrhenius temp. dep.
• freezes at Tg
• ?-relaxations
• local motion
• broad response
• Arrhenius temp. dep.

log ?
?
2
?
?
PCS
?fast
-13
glass
liquid
1/T
1/Tg
25
Poly(propylene glycol)
26
Dynamics in Free-standing Polymer Films

• Polystyrene

• Dynamics of thin free-standing and supported
  polymer films

27
Polymer Gels

• Poly(methyl methacrylate) (PMMA) / Propylene
  Carbonate (PC)

28
Dynamics in aPolymer Gel Electrolyte
29
Experimental Set-Up
30
Experimental Set-Up
Optics
Sample Holder
Detector
Laser
31
Alignment of the set-up
32
Alignment of the set-up
a) Focus the laser beam in the sample!
a)
33
Alignment of the set-up
a) Focus the laser beam in the sample! b)
Maximize the scattered light in the detector
tube!
b)
34
For your own safety

• USE THE SAFETY GOGGLES!

35
Experimental Data
Filename.alv (binary file)
Correlator
Filename.dat (ascii file)
36
Experimental Data
Filename.alv (binary file)
Correlator
Filename.dat (ascii file)
37
Experimental Data
Filename.alv (binary file)
Correlator
Filename.dat (ascii file)
FILE Latex Spheres in Water DATE 180598
MODE REAL CORR AUTO 0 MULTIPLE TAU OFL0 NO
OVERFLOW CONC .001 TEMP 293.000 PRES
1.000 ANGL 90.000 R.I. 1.330 WAVE
488.000 STC .800 NPNT 191 SAMP
343707. MONB 465494000. GENERAL
1.00, .8480350000, 137.33 2.00,
.6785989000, 151.19 3.00,
.5840300000, 160.21 4.00,
.7849890000, 142.18 5.00,
.8165120000, 139.71 6.00,
.7692275000, 143.44 7.00,
.8007505000, 140.93 8.00,
.6510164000, 153.71 9.00,
.6155530000, 157.09 10.00,
.5722089000, 161.42
38
Experimental Data
Filename.dat (ascii file)
FILE Latex Spheres in Water DATE 180598
MODE REAL CORR AUTO 0 MULTIPLE TAU OFL0 NO
OVERFLOW CONC .001 TEMP 293.000 PRES
1.000 ANGL 90.000 R.I. 1.330 WAVE
488.000 STC .800 NPNT 191 SAMP
343707. MONB 465494000. GENERAL
1.00, .8480350000, 137.33 2.00,
.6785989000, 151.19 3.00,
.5840300000, 160.21 4.00,
.7849890000, 142.18 5.00,
.8165120000, 139.71 6.00,
.7692275000, 143.44 7.00,
.8007505000, 140.93 8.00,
.6510164000, 153.71 9.00,
.6155530000, 157.09 10.00,
.5722089000, 161.42
General Info
39
Experimental Data
Filename.dat (ascii file)
FILE Latex Spheres in Water DATE 180598
MODE REAL CORR AUTO 0 MULTIPLE TAU OFL0 NO
OVERFLOW CONC .001 TEMP 293.000 PRES
1.000 ANGL 90.000 R.I. 1.330 WAVE
488.000 STC .800 NPNT 191 SAMP
343707. MONB 465494000. GENERAL
1.00, .8480350000, 137.33 2.00,
.6785989000, 151.19 3.00,
.5840300000, 160.21 4.00,
.7849890000, 142.18 5.00,
.8165120000, 139.71 6.00,
.7692275000, 143.44 7.00,
.8007505000, 140.93 8.00,
.6510164000, 153.71 9.00,
.6155530000, 157.09 10.00,
.5722089000, 161.42
General Info
t STC X
g2(t)-1
40
Experimental Data
Filename.dat (ascii file)
FILE Latex Spheres in Water DATE 180598
MODE REAL CORR AUTO 0 MULTIPLE TAU OFL0 NO
OVERFLOW CONC .001 TEMP 293.000 PRES
1.000 ANGL 90.000 R.I. 1.330 WAVE
488.000 STC .800 NPNT 191 SAMP
343707. MONB 465494000. GENERAL
1.00, .8480350000, 137.33 2.00,
.6785989000, 151.19 3.00,
.5840300000, 160.21 4.00,
.7849890000, 142.18 5.00,
.8165120000, 139.71 6.00,
.7692275000, 143.44 7.00,
.8007505000, 140.93 8.00,
.6510164000, 153.71 9.00,
.6155530000, 157.09 10.00,
.5722089000, 161.42
41
Curve-fitting exponential function

• A relaxation strength
• t relaxation time

42
Curve-fitting KWW function
Kohlrausch-Williams-Watts

• A relaxation strength
• t relaxation time
• b stretch parameter

43
Curve-fitting sum of KWW
44
Curve-fitting sum of KWW
Theory
Exp Data
45
Task 1 Spheres in water

• Determine the size of spheres dissolved in water.
• Use PCS to determine relaxation time.
• Calculate the diffusion constant.
• Use Stoke-Einsteins relation to calculate the
  radius.
• Error estimation in the report!

46
Task 2 Free Project

• Anything that you can convince me could work!
• sugar molecules
• asymmetric particles
• micro-emulsions
• distribution of sphere-sizes
• relaxation in supercooled liquid

47
What are you supposed to do? (I)

• Before the lab
• Brownian motion
• Stoke-Einstein relation
• Correlation function
• Curve-fit procedures
• Project preparations

48
What are you supposed to do? (II)

• During the lab
• Align the set-up
• Determine size of spheres diluted in water
• Free project

49
What are you supposed to do? (III)

• After the lab
• Analyze data
• Write report

50
Safety Goggles!

• USE THEM!