diffusion and permeability in polymers

8/11/2019 Diffusion and Permeability in Polymers

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GCH 6101- Polymer Diffusion PM Wood-Adams 1

Permeation Rate at which a gas or vapor passes through a polymer Consists of 3 processes:

Absorption of the permeating species into the polymer Diffusion through the polymer Desorption of the permeating species from the polymer

surface and removal

Factors affecting permeability of a polymer: Solubility and diffusivity of the small molecule in the

polymer

Chain packing and side group complexity, polarity,crystallinity, orientation, fillers, humidity andplasticization


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Essential factors for permeation

Free volume: in order for any molecules to move in amaterial there must be holes available

Continuous path through the polymer

increasing elapsed time

Example ofdiffusion:

After some time:


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Ficks Laws Steady State:

Unsteady state:xc

DJ=

Schematic of steady state diffusion

=

x

cD

xt

c

J is the flux of permeant [=] (mass/area/time)

D is the diffusivity: it depends on polymer, diffusing species,temperature and in some cases on concentration c.


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Example of diffusion in a rubbery polymer Studying the effect of dissolved CO 2 on viscosity of HDPE The CO 2 was diffused into the sample in the rheometer where

only the edges of the rectangular sample were exposed to the

gas Measurement of stress was performed at the center of the

sample needed to know when the concentration of thediffusant in the center of the sample had reached the solubility.

Reference: Effects of Pressure and Supercritical Fluids on the Viscosity of Polyethylene,

Park and Dealy, Macromolecules 2006, 39, 5438-5452

Gas diffuses in on the sides ofthe sample but not on the top

or bottom.


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DiffusionDiffusion

and Saturationand Saturation

+= 2

2

2

2

yc

xc D

t c

Saturation TimePrediction

Ficks Model

Polymer

ShearStresstransduceractivehead

High P and T chamber of rheometer

L-L

aL

-aL

Diffusant


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Solution toSolution to 22 DD -- Fick Fick s Diffusions Diffusion Model:Model:

Prediction of Level of SaturationPrediction of Level of Saturation

( ) ( ) ( ) ( )( )

++

++

=

=

= 0 2

22

0 2

22

4

12exp

12

14

4

12exp

12

141

),0,0(

m

m

n

n

aL

t m D

m L

t n D

nS

t C

Dimensionless center concentration with time:

Relative amount absorbed by polymer with timeto the absorbed quantity after infinite time:

( ) ( )( )

( )( )

( )

2 2

2 220

2 2

2 220

2 1( ) 81 exp

42 1

2 18 exp2 1 4

n

m

D n t M t

M Ln

D m t m aL

=

=

+ = +

+ +

( )( )

(0,0, ) and

M t C t

S M will be 0 at t = 0 and 1 after saturation. ( S is solubility.)


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Results of Ficks analysis


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Validation of Ficks analysisIn order to monitor the diffusion, viscosity measurementswere taken every few minutes. The CO2 causes adecrease in viscosity, as long as the concentration of CO2

in the middle of the sample is changing then the viscositywill change. When saturation is reached the viscosityreaches and remains constant.

Relative viscosity Viscosity w/o CO 2

Viscosity at saturation

Viscosity at time t


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Saturation with COSaturation with CO 22 : Prediction and Data: Prediction and Data

0

0.2

0.4

0.6

0.8

1

0 60 120 180 240 300 360t (min)

M ( t ) / M (

) , C

( 0

, 0 , t )

/ S , o

r R

D =9x10-5cm 2/s

HDPE with CO 2

180o

C, 18MPa (2600 psi)

)()0()()0(

t R

1s63.0 = &

99% Satu. time

M (t )/ M ( )C (0,0, t )/S

R: with CO 2 R : w/o CO 2


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Effect of continuous shearing on diffusion


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Permeability

Permeability coefficient, P = volume of vapour passingthrough a unit area of polymer per unit time, with a unitpressure difference across the sample

Solubility coefficient, S = volume of vapour per unit volume

of polymer per unit pressure

SDP =


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Permeability Data

=

RTE

expPP 0


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Effect of permeant sizeThe diffusion rate decreases with permeant size.Example from previous table for LDPE:

0.346 nm

Size of permeant

0.364 nm0.33 nm

0

2

4

6

8

10

0.32 0.33 0.34 0.35 0.36 0.37

Size of permeant

P


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Permeation in glassy polymers vs rubbery

polymers

Free volume ismuch lower inglassy polymers

than in rubberypolymers thereforediffusion tends tobe slower


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Permselectivity of polymer membranes and

gas separations

If the permeabilities of 2gases in one polymerare different then thispolymer may be used toseparate the gases to

some extent. This isproperty of the polymerdescribed by the gasselectivity, A/B.

B

ABA P

P=

Open circles are for rubbery polymers and closedcircles are for glassy polymers. Upper bound is an

empirical relation.


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Gas permeability in polymer blends

The gas permeability in polymer blends where onecomponent is dispersed in the other component will fall inbetween upper and lower bounds defined by the parallel

and series models respectively

Upper bound:

Lower bound:

The permeability of a blend can be maximized if thecontinuous phase is made up of the polymer with thehigher permeability.

diffusion and permeability in polymers

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