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Polymers 1m

0 3. nm 104chain units long molecules

H

CH

H

CH

H

CH

H

CH

H

CH

H

CH

H

CH

H

CH

O

CH2OH

HO OH

O

thin, flexible

polyethene

apolar

hydrophobic

thick, rigid

cellulose polarhydrophylic

10nm

coiled

O

CH2OH

HO OH

O

O

CH2OH

HO OH

O

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HCH

HCH

HCH

HC

HCH

HCH

CH

HCH

HCH

entanglement

Cross Links

cross links make a polymer insoluble

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crystalline

(no diffusion)

amorphous

with some space

open, that allowsmotion of permeants

0 < crystallinity < 1

depends on the

polymer and its his torydimensions 10 nm

Crystalline and Amorphous

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108

106

104

modulus of

elasticity

EN m 2

200 300 400 500

Tg Tm

glass rubber liquid

temperature

T

K

glass transition

melting

temperature

rigid creeping

flow

1010

102

with cross

linking

Glass Transition Point

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polymer (1) solvent (2)

solvent

activitya2

10 2 100

volume fraction

2

101

100

10 1

10 2

polymer and solvent

fit on a 3D lattice

factor 2.71

a V

V2 2

2

1

11

exp

V V2 1

linear

Flory-Huggins

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V

V

2

1

10 2

10 3

10 4

solvent

activity

10 2

10 4

10 6

10 0

10 2 100

10010 2volume

fraction

2

mole

fraction x2

a2 activity is a simple functionof the volume fraction

strong volume and non-

ideality effects if we usemole fractions

Do not use the

Polymer to defineMole Fractions

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a V

V2 2

2

1

1 1

21

exp

non-ideality parameter

0 solvent and polymerdislike each other

0 solvent and polymer

are similar

solvent and polymer

attract each other

0

solvent

activitya2

10 2 100

volume fraction

2

101

100

10 1

10 2

2

1

0-1

demixing!Non-ideality

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Swelling (1)

a BV

VC2 2 1 1

2 21

1 3

expB nc

1

2

number of chain units

between each cross link

a cross linked polymer:

little springs under an

internal stress

solvent

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Swelling (2)

1.0

0.1

0.01

0.0 1.0 2.0

0

1

2

swelling parameter

gels, protein separation media

reverse osmosis

pervaporation

gas separations

(high pressure)

2

BV

VC

2

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Solubility of Vapour in Polymer

activity of vapour 2 activity of 2 in polymer

a p

p2

2

2

a BV

VC2 2

21

exp

1

1

equilibrium

a a2 2

2 2

22

1

1

p

p BV

VCexp

Henry coefficient

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Distribution between Solvent and Polymer

polymer (1)

solvent (2)

solute (3)

1 02large

3small

12

3

equilibrium calculation: a a2 2

a a3 3

a V

VB

V

VC3 3 1

3

2

23

1

1 31

exp

swelling: Fig 15.10

a

V

V3 3

3

2

21 exp

3

3 constant

volume distribution

(Nernst) coefficient