Diffusion and binding of molecules to sites within homogeneous thin films

In this paper we consider the process of a chemical species diffusing into a thin homogeneous film which contains fixed sites on to which the species can reversibly bind. We consider the situation in which the interaction of the diffusing species and the sites is described by the Langmuir isotherm. The differential equations that describe this nonlinear diffusion reaction problem are studied. The find that the problem may be conveniently divided into six cases. Each case is presented and approximate analytical solutions for the concentration profiles are given as a function of time for both adsorption and desorption. These solutions are relevant in situations of practical importance, including the binding of substrates to immobilized enzymes, the operation of polymeric gas sensors, and the vapour phase doping of conducting polymers.