CLASSICAL LIGHT SCATTERING1st

1
CLASSICAL LIGHT SCATTERING1st ?????
3nd Presentation for LLS Book 2 p.2-19

• Overview
• A. Scattering Intensity (by gases or by
  macromolecules in solution)
• B. Concentration Dependence
• C. Size Dependence (Structure factors, Rg, Zimm
  Plots)

Atmospheric scattering
Sept. 4, 2006
For more infos please login on
http//www.che.ccu.edu.tw/rheology/entry_basic.ht
m
2
Preliminary Remarks

• Light scattering has provided an important method
  for characterizing macromolecules for at least
  three decades
• Through the use of laser light, spectrum
  analyzers, autocorrelators, and the technology
  for clarifying samples, experiments can now be
  used to study molecular motion
• We will have finished introducing the classical
  light scattering (?????) theories (especially
  their assumptions and limitations) in the next
  presentation (9/18)
• We will provide the basic concepts of dynamic
  light scattering (?????) on 9/18 and 10/2 before
  some applications of LLS (e.g., laser doppler
  velocimetry) and advanced theories (e.g., SAXS)
  are given

3
A. Scattering Intensity -???????????

• Scattering by an Isolated Dipole and by Gases
  -??????????

Ez interacts with electrons in an atom or
molecule to induce and electric dipole moment
pz which provides the source of the scattered
light
For one scatter per unit volume
?????,????????????
Scattering geometry
4

• Contd.
• Rayleigh Ratio (experimentally reported value)

For N scatters per unit volume
?????,N ???????????
?????????? ??????? ????????? x ?????
(scattering volume)
5

• Scattering by Macromolecules in Solution -??????

• Interference effects of scattered light in the
  particle become significant!
• The scattering centers undergo Brownian
  movement, which produces transient
• optical inhomogenities in the solution

The scattering intensity per unit volume
??????????
???????????
6
B. Concentration Dependence - ?????????????????

• The magnitude of the average concentration
  fluctuation will clearly depend on the energy to
  produce the fluctuation
• .

???
Finally, we arrive at
The scattering intensity per unit volume
??????????
7

• Applications
• Obtaining M and B2
• LS intensities are sometimes reported in terms of
  the turbidity
• The attenuation results from scattering in any
  direction except at ?s 0

8
C. Size Dependence - ???????????????????

• Structure Factors S(q)

Step 1 Write down the electric field of the light
scattered by the jth segment
aj contains factors such as the polarizability,
the distance R to the detector etc
FIG. The path difference for scattering from a
segment in a macromolecule
9
Step 2 Sum up the scattered waves from the P
segments within the particle Step 3 Calculate
the scattering intensity for one particle with a
fixed orientation Step 4 Calculate the
scattering intensity for an ensemble of randomly
oriented particles Step 5 Calculate the
scattering intensity (without interference) at
?s0

• See book 2 (p.14-16) for the derivation of the
  structure factor for a uniform sphere of radius R
  or a uniform rod of length L

The expression for the structure factor
(Divide Step 4 by Step 5)
10
TABLE Structure Factors and Radius of Gyration
for Various Particles
11
(No Transcript)
12
???????? ?? ?????, ???????????

• Radius of Gyration
• LS measurements (at sufficiently low ?s) permit
  Rg to be determined from S(q) without any
  assumptions about the shape of the molecule
• Zimm Plot
• Simultaneously extrapolating
• data to both ?s 0 and C 0

Valid at sufficiently low angles
C
C
C
C
FIG. Zimm plot for cellulose nitrate
13

• Contd.

??????????? (??????)