A note on the kinetics of heavy atom reactions on interstellar grains

The assumption made in many surface chemistry models, that the reactive population of heavy atoms and/or molecules on a grain surface at any instant can be restricted to only zero, one, or two, species, is most likely in serious error. It is shown that the validity of this restriction is based upon the combination of an optimistic selection of the parameters governing the surface diffusion of heavy atoms and, more importantly, upon an erroneous application of results from the theory of random walks on regular lattices. It is shown that the latter leads to a gross overestimate of the importance of surface reactions involving heavy atoms unless interstellar grains are fractal and have a spectral dimension greater than two. Diffusion-controlled reactions involving C, O and N atoms are much less efficient on grain surfaces, and the predicted abundances of several molecules, formed in many published models of grain surface chemistry have to be revised downwards.