Surface Diffusion at Finite Coverage: The Characteristic Function Method

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 surface coverage. In this context, the intermediate scattering function is identified as a characteristic function that is very well defined in probability theory. From this function, the generating functions of the moments and cumulants of the jump probability distribution are straightforwardly obtained at any order. This analysis is carried out in two stages. First, the dilute limit, corresponding to non-interacting adsorbates or very low surface coverage, is briefly reviewed. Second, the method is extended to low and intermediate coverages, where adsorbate-adsorbate interactions become relevant. A further consequence of the present analysis is that the static structure factor is also a characteristic function of the adsorbate separation distance distribution. This method thus provides a compact and physically transparent route for connecting scattering observables, diffusion coefficients, and coverage-dependent structural correlations.