### Chapter 01_Polymer Characterization Part2

```There are many times in nature when a solvent
will pass spontaneously through a
semipermeable membrane, which is a
membrane permeable to solvent, but not solute.
The osmotic pressure, П, is the pressure that
must be applied to stop the influx of solvent.
1
Examples:
(a) Transport of fluids through living cell
membranes ,
(b) Basis of osmometry, determination of
molecular mass by measurement of osmotic
pressure.
2
h
pV = n R T
n = g/M
c = g/V
1
p = c R T (  A2c  ...)
M
Semipermeable membrane: stops polymers, passes solvent.
3
Osmosis
Eventually the pressure difference between
the arms stops osmosis.
4
5
However  A is now increasedby greaterpressure p  
 *A ( p)   A ( x A , p  )
accountfor thepresenceof solute
 A ( x A , p  )   *A ( p  )  RT ln x A
take theeffectof pressureintoaccount
p
 *A ( p  )   *A ( p) 
 V dp
m
p
where Vmis themolar volume of pure solventA
combiningequations,we have
p 
 RT ln x A 
 V dp
m
p
Dilute solutions: ln x A replacedby ln(1  x A )   xB andVm is constant
RTxB   Vm
6
RTxB  pVm
nB
When thesoluteis dilute, xB 
. Because n AVm  V ,
nA
totalvolumeof thesolvent,theequationsimplifiesto
p  [ B]RT
Van’t Hoff Eq.
nB
where[ B] 
is themolarconcent ration of thesolute
V
7
8
A solution of polystyrene in benzene contains
10 g/L. The equilibrium height of the column of
solution (density 0.88 g cm-3) in the osmometer
corrected for capillary rise is 11.6 cm at 25oC.
What is the molar mass of polystyrene,
assuming the solution is ideal.
The osmotic pressure of an aqueous solution
at 300 K is 120 kPa. Calculate the freezing
point of the solution.
9
Osmotic pressure is easily measured, and is quite large.
Osmometry can be applied for the determination of
molecular weights of large molecules (proteins, synthetic
polymers), which dissolve to produce less than ideal
solutions. The Van’t Hoff equation can be rewritten in the
virial form:
Π= [B] RT {1 + B [B] + ...}
where B is the empirically determined osmotic virial
coefficient
10
Consider poly (vinyl chloride) PVC, in cyclohexanone
at 298 K
Pressures are expressed in terms of heights of solution,
ρ=0.980 g cm-3 in balance with the osmotic pressure
c (g L-1)
h (cm)
1.00
0.28
2.00
0.71
4.00
2.01
7.00 9.00
5.10 8.00
Use Π = [B] RT {1 + B [B] + …} with [B] = c/M, where c
is the mass concentration and M is the molar mass. The
osmotic pressure is related to the hydrostatic pressure by
Π = ρgh, where g = 9.81 m s-2. Then:
11
h
RT  Bc  RT  RTB 
c

 
1   
2 
c gM  M  gM  gM 
Plot h/ c vs. c to find M, expecting a straight line with
intercept RT/ ρgM at c = 0.
Data set:
c(g L-1)
1.00 2.00 4.00 7.00 9.00
h/c(cm g-1 L) 0.28 0.36 0.53 0.729 0.889
12
The data give an
intercept of 0.21.
13
The data give an intercept of 0.21 cm g-1 L, which is equal
to RT/ ρgM
Thus:
RT
1
M 

g 0.21cm g1 L

8.314JK

1
1

m ol  (298K )
1

3
2
(980kgm )  (9.81m s ) 2.1103 m 4 kg 1
1
 1.2 10 kgm ol
2
where we have used 1 kg m2 s-2=1J
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15
16


(A) Ubbelohde, and
(B) Cannon-Fenske.
17

IUPAC suggested the terminology of solution
viscosities as following.
•
Relative viscosity :
rel =

o
=
t
to
 : solution viscosity
o: solvent viscosity
t : flow time of solution
t o: flow time of solvent
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Specific Viscosity
Reduced Viscosity
Inherent Viscosity
Intrinsic Viscosity
   0 t  t0
 sp 

  rel  1
0
t0
 sp  rel  1
 red 

c
c
 inh
ln  red

c
   lim
c 0
 sp
c
 liminh
c 0
19
   kM a
log   log k  a log M v
K and a are Viscosity- MolecularWieght Constant
Mw > Mv > Mn
?
Derive The MHS equation (use Phys. Chem references
20
Representative Viscosity-Molecular Weight Constants
Polymer
Solvent
Polystyrene
(atactic)c
Polyethylene
(low pressure)
Poly(vinyl chloride)
98% cis-1,4, 2% 1,2
97% trans-1,4, 3% 1,2
Polyacrylonitrile
Poly(methyl methacrylate-costyrene)
30-70 mol%
71-29 mol%
Poly(ethylene terephthalate)
Nylon 66
Molecular Weight
Range  10-4
8-42e
4-137e
3-61f
3-100e
K 103
Cyclohexane
Cyclihexane
Benzene
Decalin
Temperature,
oC
35 d
50
25
135
Benzyl alcohol
Cyclohexanone
155.4d
20
4-35e
7-13f
156
13.7
0.50
1.0
Toluene
Toluene
DMFg
DMF
30
30
25
25
5-50f
5-16f
5-27e
3-100f
30.5
29.4
16.6
39.2
0.725
0.753
0.81
0.75
1-Chlorobutane
1-Chlorobutane
M-Cresol
M-Cresol
30
30
25
25
5-55e
4.18-81e
0.04-1.2f
1.4-5f
80
26.9
9.52
67.7
17.6
24.9
0.77
240
a
0.50
0.599
0.74
0.67
0.67
0.63
0.95
0.61
cAtactic
defined
temperature.
eWeight average.
fNumber average.
gN,N-dimethylformamide.
d
21
22
?
Prepare a report with the definitions for: 1) Dynamic Viscosity;
2) Shear Viscosity; 3) Bulk Viscosity and 4) Extensional Viscosity.
23
Viscosity; is Thickness:
“Thin” like water, “Thick” like honey
24
25
After a hurricane, many trees fall over and
bend into a river. Also, a cow and a dog
fall into a flooded river. Which one
reaches the ocean first, cow or dog?
Moo!
Woof!
26
•Solvent flow carries molecules from left to right; big ones come
out first while small ones get caught in the pores.
•It is thought that particle volume controls the order of elution.
27
28
•The following plot of relative amount of
the large solute (blue) and of the
smaller solute (red) goes with the
animation.
•Larger solutes elute EARLIER, smaller
solutes LATER, from a size exclusion
column.
29
Molecular Weight Distribution
Gel Permeation Chromatography (GPC)
a. GPC or SEC (size exclusion chromatography)
b. GPC method is modified column chromatography.
c. Packing material: Poly(styrene-co-divinylbezene),
glass or silica bead swollen and porous surface.
d. Detector : RI, UV, IR detector, light scattering detector
e. Pumping and fraction collector system for elution.
f. By using standard (monodisperse polystyrene),
we can obtain Mn , Mw .
30
Schematic representation of a gel permeation chromatograph.
31
c
log10M
c
DRI
Ve
c
degas
pump
injector
log10M
32
PS standard samples
Mw
Vendor
Specified
3105
6207
10300
43900
102000
212000
170000
422000
929000
1600000
1971000
2145000
Mw/Mn
1.14
1.03
1.03
1.01
1.02
1.01
1.01
1.02
1.01
1.16
1.03
1.1
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34
Detector
response
Typical gel permeation chromatogram. Dotted lines
represent volume “counts.”
Baseline
Elution volume (Vr) (counts)
35
Typical semilogarithmic calibration plot of molecular weight versus retention
volume.
Molecular weight (M)
106
105
104
103
Retention volume (Vr) (counts)
36
37
109




Polystyrene (linear)
Polystyrene (comb) 
 Polystyrene (star)
 Heterograft copolyner 
 Poly (methyl methacrylate)
Poly (vinyl chloride)




107


108


Log([η]M)
Universal calibration for gel permeation chromatography.
THF, tetrahydrofuran.
Styrene-methyl methacrylate graft copolymer
106
105
18
20
22
24
26
28
Elution volume ,5 ml counts, THF solvent
30
38
Universal calibration method
[η]1M1 = [η]2M2
1
logM2 = ( 1 + a
2
KK
12
)log( ) + ( 11 ++ aa1 )logM1
2
39
[]AMA = []SMS= f (Ve)
[] = KM a
Mark-Houwink Relation
K A M Aa A 1  K S M SaS 1
 K S M SaS 1 

MA 
 KA 


Universal Calibration
A = analyte; S = standard
1
a A 1
Combine to get these two
equations, useful only if
universal calibration works!
40
41
```