1. Introduction to PHOTON CORRELATION SPECTROSCOPY
Start the CLOCK!!!!
Christer Svanberg, Materials Physics,....
Emphasize the experimental technique
Lab-PM
Info-paper
Preliminary schedule // 12 hours during 4 days//

2. Outline Introduction to PCS Applications Experiment What do we study?
General concepts
Light scattering theory
Applications
Brownian motion
Dynamics in glasses and polymer solutions
Experiment
Data Analysis
Projects
Start the CLOCK!!!!
Christer Svanberg, Materials Physics,....
Emphasize the experimental technique
Lab-PM
Info-paper
Preliminary schedule // 12 hours during 4 days//

3. General Concepts of PCS
A dynamic light scattering technique.
Probes time variation of density and/or concentration fluctuations.

4. 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

5. Time and energy scales:
Time scale (seconds)
elementary excitations
tunneling polymer reptation
diffusion glassy dynamics
molecular excitations libration
Excitation energy (eV)

6. Length scales: Length scale in nm 0.01 0.1 0.3 1.0 3.0 10 30 100
atomic structures
organic molecules
pharmaceuticals
supermolecules
surfaces and multilayers
micelles critical phenomena
proteins
polymers
Momentum transfer (Å-1)

7. Spectroscopic techniques

8. Time range of PCS PCS covers a very large time range!
LOG(TIME (s))
-14
-10 -6 -2 2
Neutrons
Raman
Brillouin
Photon Correlation
Dielectric
NMR
PCS covers a very large time range!
Typically: s! => 11 decades in time!

9. 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!

10. Outline Light scattering theory Introduction to PCS Applications
What do we study?
General concepts
Light scattering theory
Applications
Brownian motion
Dynamics in glasses and polymer solutions
Experiment
Data Analysis
Projects
Start the CLOCK!!!!
Christer Svanberg, Materials Physics,....
Emphasize the experimental technique
Lab-PM
Info-paper
Preliminary schedule // 12 hours during 4 days//

11. Light Scattering
Interference!

12. Time-dependent interference!
Light Scattering
Time-dependent interference!

13. Siegert´s 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

14. Correlation function

15. Outline Applications Introduction to PCS Experiment What do we study?
General concepts
Light scattering theory
Applications
Brownian motion
Dynamics in glasses and polymer solutions
Experiment
Data Analysis
Projects
Start the CLOCK!!!!
Christer Svanberg, Materials Physics,....
Emphasize the experimental technique
Lab-PM
Info-paper
Preliminary schedule // 12 hours during 4 days//

16. 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.)

17. 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!

18. Stoke-Einsteins relation
D diffusion constant
T temperature
h viscosity of solvent
r radius of particles

19. Light Scattering geometry
initial polarisation
final polarisation
scattered wave-vector
Diffusion constant:
(Brownian motion)
Scattered Wave vector:
n refractive index of the solvent
l wave-length of the laser
q scattering angle
t relaxation time
q scattered wave vector

20. PCS experiment t -from experiment - determine: D diffusion constant
T temperature
h viscosity of solvent
r radius of particles

21. Research performed at Chalmers
Glass transition dynamics
Thin free-standing polymer films
Dynamics in gels and polymer solutions

22. 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 
1/T
1/Tg   2
-13 
liquid
glass

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.
log   2  
PCS
fast
-13
glass
liquid
1/T
1/Tg

24. Poly(propylene glycol)
0,2
0,4
0,6
0,8 1 10 -6 -4 -2 2 4
Time (s)
221 K
192 K
Temp.

25. Dynamics in Free-standing Polymer Films
Polystyrene Å
Dynamics of thin free-standing and supported polymer films

26. Polymer Gels
Poly(methyl methacrylate) (PMMA) / Propylene Carbonate (PC)

27. Dynamics in a Polymer Gel Electrolyte

28. Experimental Set-Up

29. Experimental Set-Up
Optics
Sample Holder
Detector
Laser

30. Alignment of the set-up
IMPORTANT
Detects microscopic density fluctuations
Density fluctuations ->scattered light intensity flucuations
Laser focused into a sample
Scattered light polarised and focused into a detection system
Light intensity registered by a Photo-Multiplication tube and digitalized
The correlator calculates the auto-correlation function in real time
1) Polarizer
2) Alignment
3) Correlator

31. Alignment of the set-up
a) Focus the laser beam in
the sample!
IMPORTANT
Detects microscopic density fluctuations
Density fluctuations ->scattered light intensity flucuations
Laser focused into a sample
Scattered light polarised and focused into a detection system
Light intensity registered by a Photo-Multiplication tube and digitalized
The correlator calculates the auto-correlation function in real time
1) Polarizer
2) Alignment
3) Correlator a)

32. Alignment of the set-up
a) Focus the laser beam in
the sample!
b) Maximize the scattered light
in the detector tube! b)
IMPORTANT
Detects microscopic density fluctuations
Density fluctuations ->scattered light intensity flucuations
Laser focused into a sample
Scattered light polarised and focused into a detection system
Light intensity registered by a Photo-Multiplication tube and digitalized
The correlator calculates the auto-correlation function in real time
1) Polarizer
2) Alignment
3) Correlator

33. For your own safety:
USE THE SAFETY GOGGLES!

34. Filename.alv (binary file) Filename.dat (ascii file)
Experimental Data
Filename.alv (binary file)
Correlator
Filename.dat (ascii file)

35. Filename.alv (binary file) Filename.dat (ascii file)
Experimental Data
Filename.alv (binary file)
Correlator
Filename.dat (ascii file)

36. Filename.alv (binary file) Filename.dat (ascii file)
Experimental Data
Filename.alv (binary file)
Correlator
Filename.dat (ascii file)
FILE Latex Spheres in Water
DATE
MODE REAL CORR AUTO 0 MULTIPLE TAU
OFL0 NO OVERFLOW
CONC
TEMP
PRES
ANGL
R.I
WAVE
STC
NPNT
SAMP
MONB
GENERAL
1.00, ,
2.00, ,
3.00, ,
4.00, ,
5.00, ,
6.00, ,
7.00, ,
8.00, ,
9.00, ,
10.00, ,

37. Filename.dat (ascii file)
Experimental Data
Filename.dat (ascii file)
FILE Latex Spheres in Water
DATE
MODE REAL CORR AUTO 0 MULTIPLE TAU
OFL0 NO OVERFLOW
CONC
TEMP
PRES
ANGL
R.I
WAVE
STC
NPNT
SAMP
MONB
GENERAL
1.00, ,
2.00, ,
3.00, ,
4.00, ,
5.00, ,
6.00, ,
7.00, ,
8.00, ,
9.00, ,
10.00, ,
General Info

38. Filename.dat (ascii file)
Experimental Data
Filename.dat (ascii file)
FILE Latex Spheres in Water
DATE
MODE REAL CORR AUTO 0 MULTIPLE TAU
OFL0 NO OVERFLOW
CONC
TEMP
PRES
ANGL
R.I
WAVE
STC
NPNT
SAMP
MONB
GENERAL
1.00, ,
2.00, ,
3.00, ,
4.00, ,
5.00, ,
6.00, ,
7.00, ,
8.00, ,
9.00, ,
10.00, ,
General Info
t = STC · X
g2(t)-1

39. Filename.dat (ascii file)
Experimental Data
Filename.dat (ascii file)
FILE Latex Spheres in Water
DATE
MODE REAL CORR AUTO 0 MULTIPLE TAU
OFL0 NO OVERFLOW
CONC
TEMP
PRES
ANGL
R.I
WAVE
STC
NPNT
SAMP
MONB
GENERAL
1.00, ,
2.00, ,
3.00, ,
4.00, ,
5.00, ,
6.00, ,
7.00, ,
8.00, ,
9.00, ,
10.00, ,

40. Curve-fitting: exponential function
A : relaxation strength
t : relaxation time

41. Curve-fitting: KWW function
Kohlrausch-Williams-Watts
A : relaxation strength
t : relaxation time
b : stretch parameter

42. Curve-fitting: sum of KWW

43. Curve-fitting: sum of KWW
Theory
Exp Data

44. 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!

45. 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
………

46. What are you supposed to do? (I)
Before the lab:
Brownian motion
Stoke-Einstein relation
Correlation function
Curve-fit procedures
Project preparations
IMPORTANT
Detects microscopic density fluctuations
Density fluctuations ->scattered light intensity flucuations
Laser focused into a sample
Scattered light polarised and focused into a detection system
Light intensity registered by a Photo-Multiplication tube and digitalized
The correlator calculates the auto-correlation function in real time
1) Polarizer
2) Alignment
3) Correlator

47. What are you supposed to do? (II)
During the lab:
Align the set-up
Determine size of spheres diluted in water
Free project
IMPORTANT
Detects microscopic density fluctuations
Density fluctuations ->scattered light intensity flucuations
Laser focused into a sample
Scattered light polarised and focused into a detection system
Light intensity registered by a Photo-Multiplication tube and digitalized
The correlator calculates the auto-correlation function in real time
1) Polarizer
2) Alignment
3) Correlator

48. What are you supposed to do? (III)
After the lab:
Analyze data
Write report
IMPORTANT
Detects microscopic density fluctuations
Density fluctuations ->scattered light intensity flucuations
Laser focused into a sample
Scattered light polarised and focused into a detection system
Light intensity registered by a Photo-Multiplication tube and digitalized
The correlator calculates the auto-correlation function in real time
1) Polarizer
2) Alignment
3) Correlator

49. Safety Goggles!
USE THEM!