Lonely adatoms in space

There is a close relation between the problems of second layer nucleation in epitaxial crystal growth and chemical surface reactions, such as hydrogen recombination, on interstellar dust grains. In both cases standard rate equation analysis has been found to fail because the process takes place in a confined geometry. Using scaling arguments developed in the context of second layer nucleation, I present a simple derivation of the hydrogen recombination rate for small and large grains. I clarify the reasons for the failure of rate equations for small grains, and point out a logarithmic correction to the reaction rate when the reaction is limited by the desorption of hydrogen atoms (the second order reaction regime).