1. No category

Molecular weight of polymers
Molecular weight of polymers
Light scattering
Light scattering
Electromagnetic radiation
대기중에 부유하고 있는 입자상 물질에 빛을 조사하면 입자상 물질에 의해 빛이 산란하
게 된다. 물리적 성질이 동일한 입자상 물질의 빛을 조사하면 산란광의 양은 질량 농도에
비례하게 된다. 이러한 원리를 이용하여 산란광의 양을 측정하고 그 값으로부터 입자상
물질의 양을 구하는 방법이다
Transmission
Reflection
Absorption
Scattering
- transmission: transmitted radiation passes through the medium unaltered.
- absorption: energy from the incident beam is taken up, resulting in:
(1)heating, (2) re-emitting at another wavelength (fluorescence,
phosphorescence), (3)supporting chemical reactions.
- scattering: scattering is non-specific, meaning the incident radiation is
entirely re-emitted in all direction with essentially no change in wavelength.
Scattering results simply from the optical inhomogeneity of the medium.
- reflection: scattering at the surface of a matter (not considered here)
- Scattering center = small volumes of material that scatters light.
ex. individual molecule in a gas
- If the radius of the scattering center, a, is much smaller than the
wavelength of the incident light (a < 0.05λo, less than 5% of λo);
→ When the oscillating electric field of the incident beam interacts with
the scattering center, it induces a synchronous oscillating dipole, which
re-emits the electromagnetic energy in all directions.(Rayleigh scattering)
- ex. dissolved polymer coils of moderate molar mass radiated by
VISIBLE light
88
89
Molecular weight of polymers
Molecular weight of polymers
Light scattering
Light scattering : point scattered, d<<λ
Rayleigh scattering
A. The intensity of scattered light or turbidity() is depend on :
For ideal polymer solution
The incident radiation is entirely reemitted in all direction with essentially
no change in wavelength (Iθ1 = Iθ2)
a. size
b. concentration
For non-ideal polymer solution
Light Scattering Data Processing
c. polarizability
Kc /R 
d. refractive index
e. angle
Slope=2A 2
f. solvent and solute interaction
Intercept=1/M
90
Concentration, c
: Rayleigh ratio (small particles)
K : a system constant that depends
only the solvent properties
c : concentration
M : MW
91
Molecular weight of polymers
Molecular weight of polymers
Light scattering
Light scattering
RGD(Rayleigh-Gans-Debye) scattering:
In case of polymer (a  /20, Rayleigh limit), there is inference
between scattered light from the different part of the same molecule
→ Correction by scattering factor P(θ) is necessary
Effect of particle size on intensity distribution
330
320
310
300
340 3502.0
0
10 20
1.5
60
70
0.5
280
270
80
0.0
90
260
Iθ1 ≠ Iθ2
(P1 ≠ P2)
100
250
Different part of more
extended domain (B)
produce scattered light
which interferes with that
produced by other part (A) constructive or destructive
240
230
220
210
40
50
1.0
290
30
110
200 190
For larger particles, intensity is
reduced at all angles except zero.
180
170 160
120
130
140
150
: Rayleigh ratio (small particles)
: Rayleigh ration (large particles)
: : scattering factor (<1), function of
size and shape of scattering volume
Small Particles
Large Particles
Now we start seeing the angle dependence of the scattered light !
Correction
by P(θ)
92
93
Molecular weight of polymers
Molecular weight of polymers
Light scattering : Zimm Plot
Light scattering : Zimm Plot
To get Mw, we do two extrapolations.
First, plotting Kc/Rθ as a function of sin2(θ/2) at constant c gives a straight
line with the following slope and intercept:
For random coil polymer
Final Rayleigh equation for random coil polymer
 Kc 
1



R
c
0

 θ  θ 0 M w
Next we plot the intercepts of the plots as a function of concentration. The
resulting plot should be a straight line with
:
94
95
Molecular weight of polymers
Molecular weight of polymers
Light scattering : Zimm Plot
Light scattering : Zimm Plot
Plot Kc/Rθ vs sin2(θ/2)+kc, where k is a constant.
k is chosen to spread out the plot and give equal weights to each variable
- There will be experimental
points at all grid points except
along the lower line (the θ = 0
line) and the left-most line (the
c = 0) line.
- Connecting all the grid lines
and extrapolating to the lowerleft corner, the intercept point
gives the molecular weight
(intercept = 1/MW).
The lines labeled θ1, θ2,… are lines at constant θ with
The lines labeled c1, c2,… are lines at constant concentration with
1
Mw
Double extrapolation
96
97
Molecular weight of polymers
Molecular weight of polymers
Light scattering : Zimm Plot
Light scattering : Zimm Plot
c c c5
c1 c2 3 4
θ4
θ3
Measured
at various θ & c
θ=0
θ6
θ5
c=0
θ2
θ1
Extrapolated
to θ=0
kc1 kc2 kc3 kc4 kc5
sin2(θ1/2)
= kc (at θ=0)
98
sin2(θ2/2)
Measured
at various θ & c
Extrapolated
to c=0
=sin2(θ/2) (at c=0)
sin2(θ3/2) sin2(θ4/2) sin2(θ5/2) sin2(θ6/2)
99
Molecular weight of polymers
Molecular weight of polymers
Light scattering : Zimm Plot
Light scattering : Zimm Plot
-3
c=0 c1
c5
c2 c3 c4
3.5x10
θ6
-3
θ3
θ2
θ1
θ=0
-3
2.5x10
Measured
at various θ & c
Kc/R
θ4
0.845
3.0x10
θ5
Extrapolated
to c=0 & θ=0
c 
0.50
 
2.0x10
-3
Mw = 704k
Rg = 35.8 nm
-3
1.0x10
Mw
1.203
mg/mL
-3
1.5x10
1
1.013
-4
3
2
A = 4.26 x 10 cm ·mol/g
-4
5.0x10
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
2
100
sin () + 100c
101