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Abstract.We have used the master equation approach to study a moderately complex network of diffusive reactions occurring on the surfaces of interstellar dust particles. This network is meant to apply to dense clouds in which a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen atoms, oxygen atoms, and CO molecules are allowed to accrete onto dust particles and their chemistry is followed. The stable molecules produced are oxygen, hydrogen, water, carbon dioxide (CO 2 ), formaldehyde (H 2 CO), and methanol (CH 3 OH). The surface abundances calculated via the master equation approach are in good agreement with those obtained via a Monte Carlo method but can differ considerably from those obtained with standard rate equations.

We have studied deuterium fractionation on interstellar grains with the use of an exact method known as the direct master equation approach. We consider conditions pertinent to dense clouds at late times when the hydrogen is mostly in molecular form and a large portion of the gas‐phase carbon has already been converted to carbon monoxide. Hydrogen, oxygen and deuterium atoms, as well as CO molecules, are allowed to accrete on to dust particles and react there to produce various stable molecules. The surface abundances, as well as the abundance ratios between deuterated and normal isotopomers, are compared with those calculated with the Monte Carlo approach. We find that the agreement between the Monte Carlo and the direct master equation methods can be made as close as desired. Compared with previous examples of the use of the direct master equation approach, our present method is much more efficient. It should now be possible to run large‐scale gas–grain models in which the diffusive dust chemistry is handled ‘exactly’.

Abstract. We present a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In the model, the gas-phase chemistry is treated via rate equations while the diffusive granular chemistry is treated stochastically. The two phases are coupled through accretion and evaporation. A small network of surface reactions accounts for the surface production of the stable molecules water, formaldehyde, methanol, carbon dioxide, ammonia, and methane. The calculations are run for a time of 10 7 years at three different temperatures: 10 K, 15 K, and 20 K. The results are compared with those produced in a totally deterministic gas-grain model that utilizes the rate equation method for both the gas-phase and surface chemistry. The results of the different models are in agreement for the abundances of the gaseous species except for later times when the surface chemistry begins to affect the gas. The agreement for the surface species, however, is somewhat mixed. The average abundances of highly reactive surface species can be orders of magnitude larger in the stochastic-deterministic model than in the purely deterministic one. For non-reactive species, the results of the models can disagree strongly at early times, but agree to well within an order of magnitude at later times for most molecules. Strong exceptions occur for CO and H 2 CO at 10 K, and for CO 2 at 20 K. The agreement seems to be best at a temperature of 15 K. As opposed to the use of the normal rate equation method of surface chemistry, the modified rate method is in significantly better agreement with the stochastic-deterministic approach. Comparison with observations of molecular ices in dense clouds shows mixed agreement.

Abstract.It is well known that the rate equations for diffusive reactions on grain surfaces can be inappropriate under certain circumstances because they do not take the discrete nature of grains into account. A previous modification of the rate equations developed by us to treat surface chemistry on grains more accurately contains an error in the probability of evaporation from grain surfaces. With the rate of evaporation handled correctly, we show for a simple system in which only O and H atoms accrete on grain surfaces and react to form H2, OH, and O2 that the modified rate method is in reasonable agreement with a corrected Monte Carlo approach through 20 K and in excellent agreement with a new master equation approach at 10 K.