A stochastic approach to surface reactions including energetic interactions: I. Theory

A stochastic model to describe surface reaction systems is introduced. The reactions may include mono-and bimolecular steps (i.e. adsorption, desorption, reaction and diffusion steps). Furthermore, energetic interactions between the adsorbed particles are allowed. The temporal evolution of the system is described by master equations using the Markovian behaviour of these systems. The resulting infinite chain of equations is truncated at a certain level by using an improved superposition approximation. The equations are solved in a small lattice region exactly and their solution is connected to continuous functions which represent the behaviour of the system for large distances. We define a standard model which can be used to model various surface reaction systems in a unique manner. This gives the possibility for a better and easier comparison between different models.