Typical Phase Behavior in Polymer-Solvent Systems

2 phases

2 phases

(single phase)

LCST-well above normal boiling point of solvent-difficult to observe experimentally

Chapter 7 : Polymer Solubility and Solutions

(Ref.: S.L. Rosen, John Wiley&Sons 1993)

-condition-temp.

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 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)

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

[ 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.

SolutionWater highly polar liquid Hexane nonpolar

H O

( N C )

Polar

-CH2-CH2-….

Nonpolar

Therefore , the polarity when n

n hexane absorption

n water absorption

(ref.: S.L. Rosen, John Wiley & Sons 1993)

H O

Thermodynamic basis of polymer solubility

• “dissolution can be explained by “Gibbs’ free energy”

STHG - Solution process is thermodynamically feasible if <0.G

S

H

G

= free energy of mixing

= heat of mixing

= entropy of mixing (entropy change in forming a polymer solution)

polymermoleculesmall SS polymermoleculesmall GG

Easily dissolved Difficult to dissolve

STHG

Small molecule: ΔS helps G 0

Large molecule: ΔS doesn’t help.(ΔS ~ 0)

322121 cm/calEH

-TS= RT(n1ln1+ n2ln2)

Formula for H and S

Usually 0

G must be 0 to be soluble (G 0 ละลาย)

<< 0 for small mol.~ 0 for polymer

Solubility Parameter

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)

322121 cm/calEH

= (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

Applied only w/o specific interaction btw. solute and solvent

Greatest chance of being soluble is when H 0

• 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:

ii

iiimix y

y

Where yi = mole fraction of component ii = molar volume of component ii = 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(n1ln1+ n2ln2)

where i = volume fractions, ni = no. of mole (1-solvent, 2-solute)

2211

111 nxnx

nx

2211

222 nxnx

nx

;

xi = number of segments in the species (for monomeric solvent x1 =1) For polydisperse polymer (x2) use (avg. degree of

polymerization)

nx

Latice model of solubility

polymermoleculesmall SS

(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)

X2 polystyrene =

100,000

104

X2 PPO = 100,000

M0 PPO

X1 toluene

= 1X2 styrene monomer

= 1

S* = -R(n1 ln1 + n2 ln2)

1 = X1n1 2 = X2n2

X1n1 + X2n2 X1n1 +

X2n2

Sol n

Gas constant

ntol = 500/92

n stvrene = 500/104

nPS = 500/100000

nPPO = 500/100000M0, PPO = 120

i ni (mol) xi i

a. Toluene 5.44 1 0.531

Styrene 4.81 1 0.469

ΔS* = 14.1 cal.K

b. Toluene 5.44 1 0.531

PS 0.005 962 0.469

ΔS* = 6.85 cal.K

c. PS 0.005 962 0.536

PPO 0.005 833 0.464

ΔS* = 0.0138 cal.K

Solution

= Flory-Huggins interaction parameter (Chi-parameter):

= enthalpy of interaction (H) per mole of solventRT

H = RT2n1x1

Relationship btw. and

Substituting H , S into G

G = RT(n1ln 1 + n2ln 2+ 2n1x1)

RT

221

For polydisperse polymer (x2) use (avg. degree of polymerization)nxCriterion for complete solubility: 0.5

v = molar volume of liquid (vol/mol)

• Limitation of Flory-Huggins theory: depend on temperature, concentration, and MW of polymer.

(may be from assuming no volume change upon mixing)

G = RT(n1ln 1 + n2ln 2+ 2n1x1)

Configurational entropy contribution

Interaction contribution from both enthalpy and entropy effects

< 0.5 soluble = 0.5 theta() condition > 0.5 insoluble

(Solubility limit)theta() solvent

Theta () condition

Theta () condition: condition that G=0 (or H = TS)-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

-swollen polymer larger sizehigher soln. viscosity

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 conformationin solution

-Strong attractive force btw. polymer segments -chain segments ball up tightly

(Theta condition)

Thermoreversible solution.

Concentrated Solutions : Plasticized Polymers

Plasticizer : - External Plasticizer ex. DOP

High Tb Low volatile

Good plasticizerDOPDOP

MwMwsolventsolvent < Mw < Mwplasticizerplasticizer << << MwMwpolymerpolymer

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

(Ref.: S.L. Rosen, John Wiley&Sons 1993)

- Use to get ΔH when

polymers/solvents have extra

forces beyond van der waal’s

force ex. Hydrogen bonding or

dipole moment

322121 cm/calEH

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

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