Experimental Method:
Determination of : Osmotic Pressure
 1      V1
0
1
V1  Molar Volume
of the Solvent

0
2
(  1   1 )    V1  RT ln( 1  v 2 )  v 2 (1  1 )   v 2
x

ln( 1  v 2 )   v 2  v / 2
2
2
V 1
RT
1


 v 2      v 2  1 / x 
Polymer
 Solubility 
2
1
The osmotic
pressure data for
cellulose tricaproate
in
dimethylformamide
at three
temperatures. The
Flory temperature was
determined to be 41
± 1°C
 
1
2
 A 2V1 
2
2
Polymer Solubility
2
Modified Flory-Huggins theory
 Is temperature dependent
  Hmix 
2  

   RT 
N


 T
 S Mix
N

 v1 v 2


  T   
  R  n1 ln v1  n 2 ln v 2  v1 v 2 
 
 T  

Therefore, any temperature which causes =1/2 will
be the Flory  temperature
Polymer Solubility
3
Flory-Huggins Parameters
Polymer Solubility
4
An Example
Polymer Solubility
5
Applications of 
The Chain Expansion Ratio and -Temperature
The Expansion Ratio, r
r 
2
r
r
2
2
o
Polymer Solubility
6
Applications of 

r depends on balance between i) polymer-solvent and ii) polymerpolymer interactions

If (ii) are more favourable than (i)
 r < 1
 Chains contract
 Solvent is poor

If (ii) are less favourable than (i)
 r > 1
 Chains expand
 Solvent is good

If these interactions are equivalent, we have theta condition


r = 1
Same as in amorphous melt
Polymer Solubility
7
Applications of 


For most polymer solutions r depends on temperature, and
increases with increasing temperature
At temperatures above some theta temperature, the solvent is good,
whereas below the solvent is poor, i.e.,
T>q
r > 1
T=q
r = 1
T<q
r < 1
Often polymers will precipitate
out of solution, rather than contracting
Polymer Solubility
8
Applications of 
The Solvent Goodness:
A2  (
•
•
•
•
1
2
  )(
1
V1 
2
2
)
A Positive A2 indicates a good solvent, i.e. a solvent that gives rise to
an exothermic enthalpy of mixing. This arise when <1/2.
When A2=0 the solvent is nearly Ideal. This is important for use of
osmotic pressure to measure molar mass.
A negative A2 indicates a poor solvent (>1/2). The entalpy of mixing is
positive here.
The goodness of solvent can be adjusted by changing the temperature.
Polymer Solubility
9
Applications of 
Recall:
 H mix  RT  1 N 1v 2
 1  z  w12 / RT
 w12  2 ( w11 w12 )
1
2
 w11  w 22  ( w11 )
1/ 2
 ( w 22 )
1/ 2
Note that the energy terms w11, w22 and w12 are attractive
terms and are usually negative .
When Hmix =0 for a solvent -polymer system, thus w11=w22 and
the cohesive energy density.
Polymer Solubility
10
Summary
Solubility Parameters:
Thermodynamics of Mixing
 G Mix   H Mix  T  S Mix
 H Mix   kTN 1v 2
Polymer Solubility
11
Summary
Free Energy of Mixing:
   G Mix
 1    
  n1
0
1



 T ,P ,n2

2
1
(  1   )  RT ln( 1  v 2 )  v 2 (1 
)  v2
x
0
1
Polymer Solubility

12
Summary
Chemical Potential and Osmotic Pressure:
 1      V1
0
1
V 1
RT
1

 v 2      v 2  1 /

2
A2  (
1
2
  )(

x 

1
V1 
Polymer Solubility
2
2
)
13
Summary
Other Forms of Flory-Huggins Eqs:
0.35 (in older literature), or zero
Polymer Solubility
14
Properties of 




If the value of  is below 0.5, the polymer should be
soluble if amorphous and linear.
When  equals 0.5, as in the case of the polystyrene–
cyclohexane system at 34°C, then the Flory 
conditions exist.
If the polymer is crystalline, as in the case of
polyethylene, it must be heated to near its melting
temperature, so that the total free energy of melting
plus dissolving is negative.
For very many nonpolar polymer–solvent systems,  is
in the range of 0.3 to 0.4.
Polymer Solubility
15
Properties of 



For many systems,  has been found to
increase with polymer concentration and
decrease with temperature with a
dependence that is approximately linear
with, but in general not proportional to, 1/T.
For a given volume fraction 2 of polymer,
the smaller the value of , the greater the
rate at which the free energy of the solution
decreases with the addition of solvent.
Negative values of  often indicate strong
polar attractions between polymer and
solvent.
Polymer Solubility
16
Properties of 

The polymer–solvent interaction
parameter is only slightly sensitive to the
molecular weight.
Polymer Solubility
17
Molecular Weight Averages
Polymer Solubility
18
Molecular Weight Distribution
Polymer Solubility
19
Determination of Number Average
Mw
a) End-group Analysis
b) Colligative Properties
Polymer Solubility
20
Osmotic Pressure
Polymer Solubility
21
Flory q-Temperature
Polymer Solubility
22
Intrinsic Viscosity
Polymer Solubility
23
Some Definitions
Polymer Solubility
24
The Mark-Houwink Relationship
Polymer Solubility
25
Experimental Techniques
Polymer Solubility
26
Example
Polymer Solubility
27
Example (cont.)
Polymer Solubility
28
Gel Permiation Chromatography
Size Exclusion Chromatography
Polymer Solubility
29
Schematic View
Polymer Solubility
30
Calibration
GPC is a relative Molecular Weight
Method
 Narrow molecular weight distribution,
anionically polymerized polystyrenes are
used most often.
 Other Polymers: PMMA, Polyisoprene,
polybutadiene, Poly(ethylene oxide) and
sodium salts of PMA.

Polymer Solubility
31
Calibration Method
Polymer Solubility
32
Molecular Weight of a Suspension
Polymerized PS
Polymer Solubility
33
GPC of a Blend
Polymer Solubility
34
End of Chapter 2
Polymer Solubility
35