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)
2 phases
-condition
-temp.
(Ref.: S.L. Rosen, John Wiley&Sons 1993)
General Rules for Polymer Solubility
1.
Like dissolves like
[equilibrium phenomena]
•
Polar solvent-polar polymers
•
Nonpolar solvents-nonpolar polymers
–
Ex. PVA will dissolve in water
–
Ex. Polystyrene in toluene
2.
MW solubility of polymer
[equilibrium phenomena]
3.
MW
[rate phenomena]
4.
- crosslinking eliminates solubility.
rate of solubility
[equilibrium phenomena]
- crystallinity – need strong solvent to eliminate crystalline bond (can
also be done by heating toward crystalline melting point)
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
Water  highly polar liquid
Hexane  nonpolar
H O
(N C)
-CH2-CH2-….
Polar
Nonpolar
Therefore , the polarity when n
n
hexane absorption
n
water absorption
(ref.: S.L. Rosen, John Wiley & Sons 1993)
Thermodynamic basis of polymer solubility
• “dissolution can be explained by “Gibbs’ free energy”
G  H  TS
- Solution process is thermodynamically feasible if
G <0.
G = free energy of mixing
H = heat of mixing
S = entropy of mixing
(entropy change in forming a polymer solution)
S small molecule  S polymer
 G small molecule  G polymer
Easily dissolved
Difficult to dissolve
G  H  TS
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
H  E  12 1  2 
2
-TS= RT(n1ln1+ n2ln2)
 
3
cal / cm
Usually  0
<< 0 for small mol.
~ 0 for polymer
Solubility Parameter
H  E  12 1  2 
2
 
3
cal / cm
Applied only w/o specific interaction btw. solute and solvent
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)
Greatest chance
of being soluble
is when H  0
= (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
• 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)
For solvent mixtures:
mix 
 y i  i i
 y i i
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
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)
x 1n1
1 
x 1n1  x 2n 2
;
x 2n 2
2 
x 1n1  x 2n2
xi = number of segments in the species
(for monomeric solvent x1 =1)
For polydisperse polymer (x2) use
x n (avg. degree of
polymerization)
Latice model of solubility
S small molecule  S polymer
(Ref.: S.L. Rosen, John Wiley&Sons 1993)
Ex.3 Estimate the configurational entropy changes that occur
when
a. 500 g of toluene (T) are mixed with 500 g of styrene monomer
(S)
b. 500 g of toluene (T) are mixed with 500 g of polystyrene (PS),
Mn=100,000
c. 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)
Sol n
Gas constant
S* = -R(n1 ln1 + n2 ln2)
1 =
2 =
X1n1
X1n1 + X2n2
X1
X2
toluene
= 1
styrene monomer = 1
X2
polystyrene
X2
PPO
M0, PPO = 120
= 100,000
104
=
100,000
M0 PPO
X2n2
X1n1 + X2n2
ntol = 500/92
n stvrene = 500/104
nPS = 500/100000
nPPO = 500/100000

Solution
i
ni (mol)
xi
a. Toluene
5.44
1
0.531
Styrene
4.81
1
0.469
i
ΔS* = 14.1 cal.K
b. Toluene
PS
5.44
1
0.531
0.005
962
0.469
ΔS* = 6.85 cal.K
c. PS
PPO
0.005
962
0.536
0.005
833
0.464
ΔS* = 0.0138 cal.K
•  = Flory-Huggins interaction parameter (Chi-parameter):
= enthalpy of interaction (H) per mole of solvent
RT
H = RT2n1x1
Relationship btw.  and 
1   2 2

RT
v = molar volume of liquid
(vol/mol)
Substituting H , S into G 
G = RT(n1ln 1 + n2ln 2+ 2n1x1)
For polydisperse polymer (x2) use
x n (avg. degree of
polymerization)
Criterion for complete solubility:   0.5
G = RT(n1ln 1 + n2ln 2+ 2n1x1)
Configurational
Interaction contribution from
entropy contribution both enthalpy and entropy effects
theta()
solvent
 < 0.5
 = 0.5
 > 0.5
soluble
theta() condition (Solubility limit)
insoluble
• Limitation of Flory-Huggins theory:
–  depend on temperature, concentration, and MW of polymer.
(may be from assuming no volume change upon mixing)
-swollen polymer larger sizehigher soln. viscosity
Theta () condition
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
Properties of Dilute Solutions (not many entanglement)
• Be = []c > 1 for entanglements (normally ~ 2-3%)
-Strong 2nd force btw.
polymer segments and
solvent molecules
-spread out conformation
in solution
-Strong attractive force btw.
polymer segments
-chain segments ball up
tightly
(Theta condition)
Thermoreversible solution.
Concentrated Solutions : Plasticized Polymers
Plasticizer :
DOP
- External Plasticizer ex. DOP
High Tb
Low volatile
Mwsolvent < Mwplasticizer << Mwpolymer
Good
plasticizer
Polymer-Polymer-Common Solvent Systems
Depend on
-chemical nature of polymers and solvent
-MW of polymer
(Ref.: S.L. Rosen, John Wiley&Sons 1993)
Hansen’s three dimensional solubility
parameter
H  E       2
1 2
1
2
 
cal / cm3
- Use to get ΔH when
polymers/solvents have extra
forces beyond van der waal’s
force ex. Hydrogen bonding or
2 = 2d + 2 p + 2h
dipole moment
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)
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 FloryHuggins 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