Role of Thermodynamic Activity in Rate Processes

Abstract

This paper contains an investigation of the relation between rates of diffusion and evaporation and thermodynamic activity. The method of proceeding involves the use of the one-dimensional Ising model for which an exact statistical treatment can be given. The actual system treated may be thought of as an edge dislocation with adsorbed impurity atoms. As a by product, some interesting results concerning the formation of cluster and pinning points along a dislocation are derived. However, the main purpose of this work remains the investigation of the connection between rate and activity. For the one-dimensional model (for any degree of coupling between molecules) it can be shown exactly that the rate of evaporation is proportional to the thermodynamic activity with constant coefficient and that the rate of diffusion is similarly proportional to the gradient of the thermodynamic activity with constant coefficient. These results, which have been suggested before, therefore receive theoretical justification in terms of this simple model. Certain not-too-restrictive conditions must be applied, however. The most important of these is the requirement that every subsystem of the system be at equilibrium with respect to all variations save the one which corresponds to the rate process.