Solute and penetrant diffusion in swellable polymers. I. Mathematical modeling

TLDR

A mathematical model was developed to describe diffusion of a penetrant and a solute in a swellable polymer slab, applied to a hydrophilic polymer loaded with a soluble bioactive agent where water is sorbed and the solute desorbed. The model incorporates arbitrary diffusion coefficients and predicts dimensional changes, with swelling initially confined to one dimension by a glassy core and later becoming isotropic as penetrant sorption plasticizes the material. An exponential Fujita‑type dependence on penetrant concentration was selected and demonstrated to adequately predict a range of transport behavior.

Abstract

Abstract A mathematical model was developed to describe diffusion of a penetrant and a solute in a swellable polymer slab. The model was applied to the case of a hydrophilic polymer loaded with a soluble bioactive agent, in which the penetrant (water) is sorbed and solute is desorbed. The model allows the incorporation of any appropriate form of the diffusion coefficients. A Fujita‐type exponential dependence on penetrant concentration was chosen and shown to be adequate for prediction of a range of transport behavior. Dimensional changes in the sample were predicted by allowing each spatial increment to expand according to the amount of penetrant sorbed. During the initial period of release, the swelling was restricted to one dimension by the glassy core of the sample. At a later point in the process, the center of the sample had sorbed enough penetrant to plasticize it, and the sample relaxed to an isotropically swollen state; thereafter swelling was three‐dimensional.