THE MASTER EQUATION FOR LINEAR ADSORPTION AND DESORPTION OF GASES ON SOLID-SURFACES

A Markovian model has been derived for a process involving reversible physisorption and irreversible chemical adsorption of simple gaseous molecules on a solid surface, which obey linear rate laws. The model is written in terms of the conditional probability of transition between two populations, physisorbed and chemisorbed molecules. The resultant expression, the master equation of the process, has given rise to the governing differential equations for the mean and variance of the coverage of the solid surface by the gaseous molecules; these equations have been solved analytically. The variance or coefficient of variation, expressing the magnitude of fluctuations, is substantial for a small-size system, e.g., a highly evacuated and/or dilute system. It is not uncommon to find such a system at the commencement and conclusion of any process; these periods are the most critical from the standpoint of operation, monitoring and control. © 1991, Taylor & Francis Group, LLC. All rights reserved.