Fractional Solution
Soxhlet-type extraction by using mixed solvent.
Reverse GPC : from low molecular weight fraction
to high molecular weight fraction
Fractional Solution (Soxhlet Apparatus)
1: Stirrer bar/antibumping granules
2: Still pot (extraction pot)
- still pot should not be
overfilled and the volume
of solvent in the still pot
should be 3 to 4 times the
volume of the soxhlet
chamber.
3: Distillation path
4: Soxhlet Thimble
5: Extraction solid
(residue solid)
6: Syphon arm inlet
7: Syphon arm outlet
8: Expansion adapter
9: Condenser
10: Cooling water in
11: Cooling water out
Fractional Precipitation
Dilute polymer solution is precipitated by variable nonsolvent mixture.
Precipitate is decanted or filtered
Reverse fractional solution : from high molecular weight
fraction to low molecular fraction
Affinity Chromatography
Thin-layer Chromatography (TLC)
Alumina- or silica gel coated plate.
Low cost and simplicity.
Preliminary screening of polymer samples or
monitoring polymerization processes.
Determination of MW Without Calibration
Electromagnetic radiation
Transmission
Reflection
Absorption
Scattering
Incident Radiation
1.
2.
3.
4.
transmission: transmitted radiation passes through the medium unaltered.
absorption: energy from the incident beam is taken up, resulting in: (1)heating, (2) reemitting at another wavelength (fluorescence, phosphorescence), (3)supporting
chemical reactions.
scattering: scattering is non-specific, meaning the incident radiation is entirely reemitted 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)
Now we focus on the light scattering.
Application of Light Scattering for Analysis
1.Classical Light Scattering (CLS) or Static Light Scattering (SLS)
2.Dynamic Light Scattering (DLS)
CLS
• Scattering center = small volumes of material that scatters light. Such as
individual molecule in a gas.
• Consequences of the interaction of the beam with the scattering center:
depends, among other things, on the ratio of the size of the scattering center to
the incident wavelength (λo). Our primary interest is the case where 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). This condition is satisfied by dissolved
polymer coils of moderate molar mass radiated by VISIBLE light. 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. Scattering under these circumstances is called
Rayleigh scattering. The light which is not scattered is transmitted: I o  I s  I t
, where Is and It are the intensity of the scattered and transmitted light,
respectively.
Elastic Scattering
Scattering
Transmission
• Oscillating electric field of incident beam interacts
with scattering center, induces a synchronous
oscillating dipole, which re-emits electromagnetic
energy in all directions.
I =Is+It
Io
Rayleigh scattering: (1+cos2θ), scattering center observer.
• 1944, Debye
I
• Rearrange:
Io
 1  cos2  

] 
2

r


I
[
Io


r


 1  cos2    [


1 + cos2
350.00 2.0
340.00
330.00
1.8
2
320.00
]
(2)
[
 
310.00





20.00
30.00
40.00
50.00
1.2
300.00

 RTc
 
c T

 
2
1.6
10.00
1.4
60.00
1.0
0.8
290.00
 2 2 
 no dn
]   4
dc
 o N A 
0.00
70.00
0.6
0.4
280.00
80.00
0.2
270.00
(3)
90.00
0.0
260.00
100.00
250.00
110.00
240.00
Constant, K
120.00
230.00
130.00
220.00
λo , dn/dc = refractive index increment
no: refractive index, π, c = [g/mL]
210.00
200.00
190.00
140.00
180.00
150.00
160.00
170.00
Then
I
Io

r2

 1  cos 2 

  2 2


 4
  o N A
 

dn

 no
dc


  RTc 
2

c
T




Iθ is inversely proportional to λo. Shorter wavelength scatters more than longer wavelength
Assume: system is dilute, the net signal at the point of observation is sum of all scattering
intensities from individual scatterer - no multiple scattering (scattered light from one
center strike another center causing re-scattering, etc.).
I
Io

r2

 1  cos 2 

 2 2





 4 N

A
 o
 

dn

 no
dc


RTc

 
c

 
2

T




Define “Rayleigh ratio” Rθ
R
 2 2
 
 4 N
A
 o
? 6:
 

dn

 no
dc


RTc

 
c

 
2

T




What does do the osmosis pressure in here?
1.Turbidimetery (or spectrophotometer)
2.Light scattering
1. Turbidimeter experiment (Transmitted light intensity, It is measured)
Sample Cell
Detector
Monochromatic
light source
Photomultiplier tube
measures It
= 1 - (It/Io) = (16/3) R
• "Turbidity",  = fraction of incident light which is scattered out = 1-(It/Io)

is obtained by integrating Iθ over all angles:    16  R
 3 
 32 3
Substitute R :   
4
 3o N AV
 1 

  RTc    Bc    
 M 



2
 dn
 RTc 
 no

dc  


c T 


 

 32 3    dn 
 no  
   4

3

N
 o av    dc 
 Substitute:
2


c


 1  2 A2 c  ....... 
 M

 32 3    dn 
Hc
 no     
Define : H  
4

1  2A c  
 3o N av    dc 
2
M
2
Solution is dilute, so higher order concentration terms can be ignored.

Hc
1
M
 2 A2c    

Hc


1
 2 A2c
M
Procedure: Measure  at various conc.  Plot Hc / vs. c (straight line)  Determine
M from intercept, 2nd virial coeff., A2 from slope

Hc
1
M
 2 A2c    

Hc


1
 2 A2c
M
Hc/τ
Turbidity Data Processing
Slope=2A2
Intercept=1/M
Concentration, c
2. Light Scattering experiment (measure Iθ at certain θ and r)
Rθ
RTc


K
c T


Light Scattering Data Processing
(4)
 1 

  

  RT    A2c    
 c T
 M 

Kc 1

 2 A2 c (7)
Rθ M
Kc/R
 1 

  RTc    A2c     ( 5 )
 M 

(6)
Slope=2A2
Intercept=1/M
Concentration, c
Light Scattering Data Examples
PS in cyclohexane
4.4
T(o C)=55
3.9
(Kc/Rq )x107
T(o C)=45
T(oC)=38
3.4
T(o C)=34
2.9
T(o C)=32.
2.4
0
0.1
0.2
0.3
0.4
0.5
0.6
Concentration, c x 103 (g/cm3 )
The slope of the plot
θ-condition
Kc
vs. c
R
can be either positive or negative.
For polydisperse sample, Turbidity (light scattering) is contributed by
molecules of different MW.
τ i
Define: turbidity →
Hci
1
 2 A2 ci    
Mi
If ci  0  2A2ci  0  i Hci Mi   total  i   Hci Mi   H  ci Mi 
H  ci M i   ci M i 
  total 

 

H  ci
 ci
 Hctotal  c 0
(Hc)/ vs. c
 mi
Substitute ci 
mi
V


Mi 
 V
 cons tan t

 mi 
  V 
  V
m M   N M M   N M 




 weight  average MW






m
N
M
N
M



2
i
i
i
i
i
i
i
i
turbidity light scattering weight-average MW
i
i
i
i
Rayleigh-Gans-Debye (RGD scattering) : when the scattering centers are larger than
Rayleigh limit
Plain Polarized Light
A
B
2
1
Different part of more extended domain (B) produce scattered light which interferes with that
produced by other part (A) - constructive or destructive
Effect of particle size on intensity distribution
Distribution is symmetrical for small
particles (<λ/20).
For larger particles, intensity is
reduced at all angles except zero.
2.0
1.5
1.0
R RGD  R RayleighP ( )
0.5
0.0
(8)
Contributions from two scattering
centers can be summed to give
the net scattering intensity. The
result is a net reduction of the
scattered intensity
Small Particles
Pθ = "shape factor" or "form factor"
Large Particles
Always Pθ < 1, function of size and shape of scattering volume.
seeing the angle dependence of the scattered light !
Now we start
Kc
11


  2Bc  (8' )
R P  M

Qa        (9)
1
 1
P
5
2
a=
Q = scattering vector = (4π/λ)sin(θ/2)rg (10)
1
Random coil
5 2
a    rg
3
(11)
Scattering factor, P ( )
Effect of Angular Asymmetry on MW Measurements
MW
1
10k
100k
200k
400k
0.9
600k
0.8
0.7
0.6
0
10
20
30
40
50
60
Scattering Angle, 
• p(θ) decreases with θ.
• p(θ) decreases more for higher MW.
70
80
90
Effect of MW and Chain Conformation on Pθ, and on measured MW at 90o.
MW (g/mol)
RG (nm)
P(90o)
MW(90o)
Polystyrene
51K
8
0.98
51K
Polystyrene( θ-condition)
420K
19
0.95
400K
PMMA
680K
36
0.70
480K
Polyisoprene(~70% cis)
940K
48
0.56
530K
66K
3
1.00
66K
10700K
12
0.98
10500K
Poly- -benzyl-L-glutamate
130K
26
0.91
118K
Myosin
493K
47
0.74
365K
DNA
4000K
117
0.35
1400K
Conformation
Random coil
Spherical
Bovine serum albumin
Bushy stunt virus
Rod shaped
1
Random coil ,
5 2
a    rg (11)
 3
 
2

Kc  1
   16  2
2 


 2 A2 c  1  
r
sin
2  g
2
R  M
   3 

(12)
Final Rayleigh equation for random coil polymer
[Case 1] θ→0:
Kc  1

   2 A2c 
R  M

Plot Kc /Rθ vs. c: Intercept=1/M, Slope=2A2
[Case 2] c→0:
 
Kc 1   16 2  2 2  
rg sin

1  
2
R M   3M2 

Plot Kc /Rθ vs. sin2(θ/2): y-=1/M, Intercept = (16π2/3Mλ2) rg2
Three information!
 
2

Kc  1
   16  2
2 


 2 A2 c  1  
r
sin
2  g
2
R  M
   3 

(12)
 
2

Kc  1
   16  2
2 


 2 A2 c  1  
r
sin
2  g
2
R  M
   3 

(12)
(1) Rθ.
(2) Kc/Rθ vs. c, Kc/Rθ vs. sin2(θ /2) plot.
(3) θ =0 c =0 extrapolate.
Kc/Rθ vs. c
Kc/Rθ vs. sin2(θ /2)
Zimm plot:
: extrapolated points
Cases
1. Small polymers: (Horizontal line)
Zimm plot for PMMA in butanone
λo=546 nm, 25℃, no ~1.348, dn/dc = 0.112 cm3/g
(Kc/Rθ) vs. c
Mw and A2
2. Small polymers in θ-solvent.
Zimm plot of poly(2-hydroxyethyl methacrylate) in
isopropanol
λo=436 nm, 25℃, no ~1.391, dn/dc = 0.125 cm3/g
θ-solvent : A2= 0
-Calculated values : Mw = 66,000 g/mol
A2 = 0 mol cm3/g2
- Kc/Rθ at small angles fall mostly
below the horizontal line plotted
through the points from medium and
large angles.
3. Larger polymers in good solvent.
Zimm plot of polystyrene in toluene
λo=546 nm, 25℃, no ~1.498, dn/dc = 0.110 cm3/g
4. Polymers in poor solvent: A2
Zimm plot of polybutadiene in dioxane
λo=546 nm, 25℃, no ~1.422, dn/dc = 0.110 cm3/g
 Polymer
Physics, M. Rubinsein and R.H.
Colby.
 Introduction to Physical Polymer Science ,
L.H. Sperling.