The swelling of polymer systems in solvents. II. Mathematics of diffusion

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Abstract
Data from complete swelling–time curves for crosslinked polymers in solvents are used to calculate diffusion coefficients for the penetrant at 25°C. Diffusion coefficients for constant diffusion and concentration‐dependent diffusion are obtained from Fick's law in a manner similar to that employed by Crank. For concentration‐dependent diffusion, solutions of solvent and nonsolvent in various proportions (cyclohexane and acetone for butyl vulcanizates) was employed. Although it is known that some of the nonsolvent is sorbed by the polymer from the solvent‐nonsolvent solution, the method still is applicable, in form, for determination of the diffusion coefficient of the solvent at zero solvent concentration. The sorption of liquid by the elastomer is shown to be a rather sharp advancing front, with the concentration of penetrant at the center of the sample remaining nearly zero until equilibrium is approached. This behavior is a direct consequence of the exponential dependence of diffusion on concentration.

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