Rate-equation models are a widely-used and inexpensive tool for the simulation of interstellar chemistry under a range of physical conditions. However, their application to grain-surface chemical systems necessitates a number of simplifying assumptions, due to the requirement to treat only the total population of each species, using averaged rates, rather than treating each surface particle as an independent entity. While the outputs from rate-equation models are strictly limited to such population information, the inputs — in the form of the averaged rates that control the time-evolution of chemical populations — can be guided by the results from more exact simulation methods. Here, we examine the effects of back-diffusion, wherein particles diffusing on a surface revisit binding sites on the lattice, slowing the total reaction rate. While this effect has been studied for two-particle systems, its influence at greater surface coverage of reactants has not been explored. Results from two Monte Carlo kinetics models (one a 2-D periodic lattice, the other the surface of a three dimensionally-realized grain) were used to develop a means to incorporate the grain-surface back-diffusion effect into rate-equation methods. The effects of grain size, grain morphology, and surface coverage on the magnitude of the back-diffusion effect were studied for the simple H+H reaction system. The results were fit with expressions that can be easily incorporated into astrochemical rate-equation models to reproduce accurately the effects of back-diffusion on grain-surface reaction rates. Back-diffusion reduces reaction rates by a maximum factor of around 5 for the canonical grain of $\sim$10$^6$ surface sites, but this falls to unity at close to full surface coverage.
E. Willis and R. Garrod
Thu, 20 Apr 17
Comments: 14 pages, 6 figures, accepted for publication in The Astrophysical Journal