Analytical solutions to mathematical models of the surface and bulk erosion of solid polymers

Abstract

AbstractThe process by which polymeric materials hydrolyze and disappear into their environments is often called erosion. Two types of erosion have been defined according to how the hydrolysis takes place. If hydrolysis occurs throughout the entire specimen at the same time, it is called bulk erosion. If the hydrolysis is mainly confined to a region near the surface of the specimen and the surface continuously degrades by moving inward, it is termed surface erosion. In this article, a kinetic relationship for bulk erosion is developed. This relationship provides a method for estimating the hydrolysis kinetic constants for bulk‐eroding polymers. This same relationship is also applicable to surface erosion at a microscopic level. Through its combination with a diffusion–reaction equation and the provision of moving boundary conditions, an analytical solution to the steady‐state surface‐erosion problem is obtained. The erosion rate, erosion front width, and induction time can all be expressed as simple functions of the rate of polymer bond hydrolysis, water diffusivity, and solubility, plus other parameters that can be experimentally determined. The erosion front width is the product of the induction time and the erosion rate. The ratio of the erosion front width to the polymer specimen thickness is a parameter that determines whether the specimen undergoes surface or bulk erosion. Theoretical results are compared with experimental observations from the literature, and agreement is found. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 383–397, 2005