Abstract. A stochastic model of grain surface chemistry, based on a master equation description of the probability distributions of reactive species on grains, is developed. For an important range of conditions, rates of molecule formation are limited by low accretion rates, so that the probability that a grain contains more than one reactive atom or molecule is small. We derive simple approximate expressions for these circumstances, and explore their validity through comparison with numerical solutions of the master equation for H, O and H, N, O reaction systems. A more detailed analysis of the range of validity of several analytic approximations and numerical solutions, based on exact analytical results for a model in which H and H2 are the only species, is also made. Though the use of our simple approximate expressions is computationally efficient, the solution of the master equation under the assumption that no grain contains more than two particles of each species usually gives more accurate results in the parameter regimes where the deterministic rate equation approach is inappropriate. The implementation of sparse matrix inversion techniques makes the use of such a truncated master equation solution method feasible for considerably more complicated surface chemistries than the ones we have examined here.

In recent years it has become evident that large differences can exist between model results of grain‐surface chemistry obtained from a rate equation approach and from a Monte Carlo technique. This dichotomy has led to the development of a modified rate equation method, in which a key element is the artificial slowing down of the diffusion rate of surface hydrogen atoms. Recent laboratory research into the surface diffusion rate of atomic hydrogen suggests that atomic hydrogen moves more slowly on grains than heretofore assumed. This research appears to lessen the need for modifications to the rate equation method. Based on the new laboratory work, we have developed appropriate models of gas‐phase and grain‐surface chemistry in quiescent dense cloud cores to examine the chemical effects of slowing down the rate at which atomic H can scan over dust surfaces. Furthermore, we have investigated the effect of slowing down the rate at which all species can move over grain surfaces.

From observations of sulphur‐bearing and other molecular species and chemical models it has been established that elemental sulphur is roughly two orders of magnitude more depleted in the detectable parts of such regions than are elemental carbon, nitrogen and oxygen. It seems surprising that sulphur is so depleted but not entirely depleted. We suggest that the fact that much of the sulphur is in S+ in translucent clumps with hydrogen number densities of less than 103 cm−3 plays a significant role in determining why it is so depleted in denser sources. Ions collide more rapidly with grains and may stick more efficiently to them than neutrals; so, as a clump collapses, sulphur may become depleted in it more rapidly than elements that are not primarily ionized in translucent material. Eventually in the collapse, gas‐phase sulphur will become contained mostly in neutral species, which in our picture leads to a large decrease in its depletion rate and a remnant gas‐phase elemental fractional abundance high enough for sulphur‐bearing species in dense cores to be detectable.

A B S T R A C TSolid CO 2 is observed to be an abundant interstellar ice component towards both quiescent clouds and active star-forming regions. Our recent models of gas±grain chemistry, appropriate for quiescent regions, severely underproduce solid CO 2 at the single assumed gas density and temperature. In this paper, we investigate the sensitivity of our model results to changes in these parameters. In addition, we examine how the nature of the grain surface affects the results and also consider the role of the key surface reaction between O and CO. We conclude that the observed high abundance of solid CO 2 can be reproduced at reasonable temperatures and densities by models with diffusive surface chemistry, provided that the diffusion of heavy species such as O occurs efficiently.