Modelling of surface chemistry on an inhomogeneous interstellar grain

Context. Many interstellar molecules are formed through grain surface reactions. These reactions are usually modelled using rate equations, while considering a homogeneous grain with only one type of binding site for each species. However, amorphicity and the irregular character of interstellar dust grains make inhomogeneous grain surfaces much more likely. Aims. The aim of this study is to investigate the effect of surface inhomogeneity on surface reaction rates. The formation of molecular hydrogen is here taken as an example. Methods. The continuous-time random-walk Monte Carlo method is used to study the dependence of the H-2 formation rate on surface size, fraction of strong binding sites and the distribution of these sites for different temperatures and bond strengths. Classical rate equations and modified rate equations are applied to try to reproduce these results. Results. The H-2 formation efficiency is strongly affected by the introduction of a second type of binding site. This effect depends on the strength of the binding energy and the fraction of strong binding sites. The way in which the sites are distributed can change the formation rate by as much as four orders of magnitude. Classical rate equations fail to reproduce the formation rate for all tested situations. Modified rate equations are able to obtain a reasonable agreement with the Monte Carlo results for inhomogeneous surfaces with randomly distributed sites consisting of less than 30% strong sites. Conclusions. Since the different types of binding sites on interstellar grains are probably randomly distributed, we recommend the use of modified rate equations in gas grain models to include the effect of surface inhomogeneity. This method reproduces the most important features while being computationally inexpensive.