Polymers in SolutionChapter 10

Polymers in Solution

Chapter 10

Ch 10 Sl 2

Solution thermodynamics



solution = mixing solvent (1) and solute (2)



∆G

= G

– (G

+ G

)



∆G

= ∆H

– T ∆S



∆S

> 0 always



∆H

> 0 almost always

 “like dissolves like”

 ∆H_m = 0 at best (when solute is the same to solvent)

 if not, ∆H_m > 0

 ∆H_m < 0 only when specific interaction like H-bonding exists



For solution, ∆H

< T ∆S

 G₁₂ < (G₁ + G₂)

Ch 10 Sl 3

Solubility parameter  ∆H _m



∆H

= V

[(∆E

/V

)

– (∆E

/V

)

]

φ

φ

= V

[δ

– δ

]

φ

φ

 φ ~ volume fraction



∆E ~ cohesive energy ~ energy change for vaporization

 ∆E = ∆H_vap – P∆V ≈ ∆H_vap – RT [J]



∆E/V ~ cohesive energy density



δ ~ solubility parameter

 δ (∆E, CED) depends on intermolecular interaction

 dispersion force

 polar interaction

 H-bonding

Eqn (10.58) p250

Ch 10 Sl 4



For solution,



∆H

< T ∆S



without specific interaction

 δ₁ = δ₂  ∆H_m = 0  ∆G_m < 0

 ∆δ < 20 MPa^½ for solvent/solvent solution

 ∆δ < 2 MPa^½ for solvent/polymer solution

 Why? smaller ∆S_m

 ∆δ ≈ 0 for polymer/polymer solution

Ch 10 Sl 5



PP soluble in cx? No.

Semicrystalline polymers are not soluble at RT.

 positive ∆H_fusion  ∆H_fusion + ∆H_m > T ∆S_m

 soluble at higher temperature ~ PP in p-xylene at above 100 °C

 solubilize using specific interaction ~ PET in formic acid (H-bonding)

for amorphous state at 25 ºC

Ch 10 Sl 6



ideal solution ~ ∆H

= 0



size of 1 and 2 the same



interaction energy, h

= h

= h



∆G

of ideal solution



∆G

= µ

– µ

= RT ln X

∆G

= µ

– µ

= RT ln X



∆G

= n

∆G

+ n

∆G

= RT (n

ln X

+ n

ln X

)



∆S

of ideal solution



∆H

= 0 

µ ~ chemical potential n ~ number of moles X ~ mole fraction X₁ = n₁/(n₁+n₂)

Ideal solution

Ch 10 Sl 7

∆S _m from statistical thermodynamics



lattice model



filling N

and N

molecules in N

+N

=N

cells

 volume of 1 ≈ volume of 2 (for small molecules)



Boltzmann relation, S = k ln Ω

 S ~ combinatorial [configurational] entropy

 Ω ~ number of (distinguishable) ways



= S

– S

– S

 S₁ = k ln Ω₁ = k ln (N₁!/N₁!) = 0 = S₂

 S₁₂ = k ln Ω₁₂ = k ln [(N₁+N₂)!/N₁!N₂!]

Fig 10.1 p230

Ch 10 Sl 8

∆S _m of polymer solution



developed by Flory and Huggins



lattice model



filling N

solvents and N

polymers in N

+ xN

= N

cells

 volume of 1 << volume of 2 (by x; x ~ deg of polym’n)



∆S

= S

– S

– S

= k ln [Ω

/Ω

Ω

] = k ln [Ω

/Ω

]

 Ω₁ = 0; Ω₂ ≠ 0 (connected)



x (mol wt ) 

 ∆S





for polymer/polymer soln,

∆S

even smaller (n

& n

)

n ~ number of moles φ ~ volume fraction φ₁ = N₁/(N₁+xN₂)

pp239-243 for derivation

Ch 10 Sl 9

∆H _m



∆G

= ∆H

– T ∆S



in original F-H theory

∆H

= N

z X

[h

– ½(h

+h

)]

= kT N

φ

^χ



modified  entropy change with interaction

 χ ~ (F-H polymer-solvent) interaction parameter

 χ   ∆H_m   solvent power 

 ∆H_m = V_m [δ₁ – δ₂]²

φ

φ

χ = χ₁ = χ₁₂ χ = χ_H + χ_S

Ch 10 Sl 10

Flory-Huggins equation



∆G

= ∆H

– T ∆S



F-H theory predicts polymer solution property,

 solubility, miscibility, phase separation, fractionation, ---

 vapor pressure, boiling point, ---



but not that precisely.

 due to drawbacks of theory like

 no volume change, self-intersection, changing χ

 especially for dilute polymer solution

 Chains are separated in dilute soln.