Surface Diffusion with Coverage: The Method of the Characteristic Function

In this work, the so-called characteristic function method is proposed as a new approach to describe and interpret the diffusion process with interacting adsorbates in terms of the surface coverage. In this context, the intermediate scattering function is shown to be a characteristic function of probability theory which is also the generating function of the moments and cumulants of the jump probability distribution. The theoretical analysis carried out here consists of reviewing very briefly firstly the case of non-interacting adsorbates or very low surface coverages and extending secondly this method to low and intermediate surface coverages. As a direct consequence of this analysis, it is shown that the static structure factor is also a characteristic function of the adsorbate separation distances.