A theory of case II diffusion

A theory is proposed to explain the transport behaviour of organic penetrants in glassy polymers in terms of two basic parameters: the diffusivity of the penetrant, D, and the viscous flow rate of the glassy polymer, 1/170. The rate controlling process for transport in these systems is considered to be diffusion of solvent down an activity gradient coupled with time-dependent mechanical deformation of the polymer glass in response to the swelling stress. The theory combines these two factors and is able to predict a wide range of observed transport phenomena from Fickian diffusion kinetics at one extreme to so-called Case II and Super-Case II behaviour at the other. The existence of a sharp front separating swollen and unpenetrated polymer is shown to result from the concentration dependence of the viscous flow rate.