1. Chapter 7 : Polymer Solubility and Solutions
Typical Phase Behavior in Polymer-Solvent Systems
2 phases
LCST
well above normal
boiling point of solvent
difficult to observe
experimentally
(single phase)
-condition
-temp.
2 phases
(Ref.: S.L. Rosen, John Wiley&Sons 1993)

2. General Rules for Polymer Solubility
Like dissolves like [equilibrium phenomena]
Polar solvent-polar polymers
Nonpolar solvents-nonpolar polymers
Ex. PVA will dissolve in water
Ex. Polystyrene in toluene
MW solubility of polymer [equilibrium phenomena]
MW rate of solubility [rate phenomena]
4. - crosslinking eliminates solubility. [equilibrium phenomena]
- crystallinity – need strong solvent to eliminate crystalline bond (can also be done by heating toward crystalline melting point)

3. Solution n hexane absorption n water absorption
Ex1. The polymers of -amino acids are termed “nylon n”,
where n is the number of consecutive carbon atoms in the chain. Their general formula is
H O
[ N C ( CH2 )n-1 ] x
The polymers are crystalline, and will not dissolve in either water or hexane at room temperature. They will, however, reach an equilibrium level of absorption when immersed in each liquid. Describe how and why water and hexane absorption will vary with n.
Solution
Therefore , the polarity when n
n hexane absorption
n water absorption
Water  highly polar liquid
Hexane  nonpolar
H O
( N C )
-CH2-CH2-….
Polar
Nonpolar
(ref.: S.L. Rosen, John Wiley & Sons 1993)

4. Thermodynamic basis of polymer solubility
“dissolution can be explained by “Gibbs’ free energy”
- Solution process is thermodynamically feasible if
<0.
= free energy of mixing
= heat of mixing
= entropy of mixing
(entropy change in forming a polymer solution) 
Easily dissolved
Difficult to dissolve

5. G must be  0 to be soluble (G  0 ละลาย)
Small molecule: ΔS helps G  0
Large molecule: ΔS doesn’t help.(ΔS ~ 0)
Formula for H and S
Usually  0
-TS= RT(n1ln1+ n2ln2)
<< 0 for small mol.
~ 0 for polymer

6. Solubility Parameter = (CED)1/2 = (Ev/v)1/2
Applied only w/o specific interaction btw. solute and solvent
Greatest chance of being soluble is when H  0
where E = change in internal energy/vol solution
i = volume fraction
i = solubility parameters [=] (cal/cm3)1/2 i =1 for solvent, i=2 for solute(polymer)
= (CED)1/2 = (Ev/v)1/2
where CED = cohesive energy density
(strength of inermolecular forces holding the molecules together in liq. state)
Ev = molar change in internal energy of vaporization
v = molar volume of liquid

7. For linear and branched polymer: The greatest tendency of a polymer to dissolve occur when its solubility parameter matches that of the solvent (1= 2)
For lightly crosslinked polymer: when 1= 2,, polymers swell the most.
(Ref.: S.L. Rosen, John Wiley&Sons 1993)

8. “Cosolvent”=mixtures of 2 or more solvents
For solvent mixtures:
Where yi = mole fraction of component i
i = molar volume of component i
i = volume fraction of component i
Mixed solvent is used to adjust mix to be closest to that of the polymers
“Cosolvent”=mixtures of 2 or more solvents

9. The Flory-Huggins Theory
Based on the lattice model
S*--configurational entropy change (due to geometry alone): obtained from the statistical evaluation of the number of arrangement possible on the lattice.
S*= -R(n1ln1+ n2ln2)
where i = volume fractions, ni = no. of mole (1-solvent, 2-solute) ;
xi = number of segments in the species
(for monomeric solvent x1 =1)
For polydisperse polymer (x2) use (avg. degree of
polymerization)

10. Latice model of solubility
(Ref.: S.L. Rosen, John Wiley&Sons 1993)

11. Ex.3 Estimate the configurational entropy changes that occur when
500 g of toluene (T) are mixed with 500 g of styrene monomer (S)
500 g of toluene (T) are mixed with 500 g of polystyrene (PS), Mn=100,000
500 g of PS, Mn=100,000 are mixed with 500 g of polyphynylene oxide (PPO), Mn=100,000 (rare example that 2 high MW can be soluble.)
(Given that molecular wt of phynylene oxide monomer = 120)

12. Sol n M0, PPO = 120 S* = -R(n1 ln1 + n2 ln2) 1 = X1n1 2 = X2n2
X1n1 + X2n X1n1 + X2n2
Sol n
Gas constant
X1 toluene = 1
X2 styrene monomer = 1
ntol = 500/92
n stvrene = 500/104
nPS = 500/100000
nPPO = 500/100000
X2 polystyrene = 100,000
104
X2 PPO = ,000
M0 PPO
M0, PPO = 120

13. Solution i ni (mol) xi a. Toluene 5.44 1 0.531 Styrene 4.81 0.469
ΔS* = 14.1 cal.K
b. Toluene PS
0.005
962
ΔS* = 6.85 cal.K
c. PS
0.536
PPO
833
0.464
ΔS* = cal.K

14. Criterion for complete solubility:   0.5
 = Flory-Huggins interaction parameter (Chi-parameter):
= enthalpy of interaction (H) per mole of solvent RT
H = RT2n1x1
Relationship btw.  and 
Substituting H , S into G 
G = RT(n1ln 1 + n2ln 2+ 2n1x1)
v = molar volume of liquid
(vol/mol)
For polydisperse polymer (x2) use (avg. degree of polymerization)
Criterion for complete solubility:   0.5

15. G = RT(n1ln 1 + n2ln 2+ 2n1x1)
Configurational
entropy contribution
Interaction contribution from
both enthalpy and entropy effects
< soluble
= theta() condition
> insoluble
(Solubility limit)
theta()
solvent
Limitation of Flory-Huggins theory:
 depend on temperature, concentration, and MW of polymer. (may be from assuming no volume change upon mixing)

16. Theta () condition
-swollen polymer larger sizehigher soln. viscosity
Theta () condition: condition that G=0 (or H = TS)
-boundary of good and poor solvent for polymer with infinite MW
-At this condition,
polymer-solvent interaction = polymer-polymer interaction
-Exponent “a = 0.5” for intrinsic viscosity []x=K(Mx)a
(good solvent a > 0.5)
-2nd virial coefficient = 0
Terminology
-temperature = UCST for polymer with infinite MW
-solvent = solvent that give theta-condition

17. Properties of Dilute Solutions (not many entanglement)
Be = []c > 1 for entanglements (normally ~ 2-3%)
-Strong attractive force btw.
polymer segments
-chain segments ball up
tightly
-Strong 2nd force btw.
polymer segments and
solvent molecules
-spread out conformation
in solution
(Theta condition)
Thermoreversible solution.

18. Concentrated Solutions : Plasticized Polymers
Plasticizer : - External Plasticizer ex. DOP
High Tb
Low volatile
Good plasticizer
DOP
Mwsolvent < Mwplasticizer << Mwpolymer

19. Polymer-Polymer-Common Solvent Systems
Depend on
-chemical nature of polymers and solvent
-MW of polymer
(Ref.: S.L. Rosen, John Wiley&Sons 1993)

20. Hansen’s three dimensional solubility parameter
- Use to get ΔH when polymers/solvents have extra forces beyond van der waal’s force ex. Hydrogen bonding or dipole moment
2 = 2d + 2 p + 2h
d = van der waal
p = dipole
h = hydrogen
[(p1-p2)2 + (h1-h2)2 + 4(d1-d2)2]1/2 < R
(Ref.: S.L. Rosen, John Wiley&Sons 1993)

21. HW 7. Polymer Solubility and Solution
Find out whether the following solvent-polymer systems will likely be soluble at 27 oC by considering from the Flory-Huggins parameter and Hansen’s Parameter
(Hint: Use polymer handbook)
(I) hexane - polyethylene
(II) acetone - natural rubber
(III) toluene – polystyrene
(IV) water – polyvinyl alcohol
(V) water - Nylon6,6
(VI) styrene - PVC