Kinetic Diffusion in Polymer Gels

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Abstract

Heuristics for determining whether of not Fick’s first law can govern the diffusion of small molecules in polymers are discussed. Two types of integrals of Fickian diffusion equations are known to exhibit the characteristics of non-Fickian diffusion; integrals of each type are given for a nonlinear asymptotic description of Fickian swelling in free volume limited materials. Kinetic criteria, based on the Kramers theory of activated processes, are used to characterize types of molecular relaxations that can be represented by such “non-Fickian” solutions to Fick’s second law. It is concluded that these solutions cannot represent the swelling dynamics of typical polymeric materials.