  The first off-lattice Monte Carlo kinetics model of interstellar dust-grain
surface chemistry is presented. The positions of all surface particles are
determined explicitly, according to the local potential minima resulting from
the pair-wise interactions of contiguous atoms and molecules, rather than by a
pre-defined lattice structure. The model is capable of simulating chemical
kinetics on any arbitrary dust-grain morphology, as determined by the
user-defined positions of each individual dust-grain atom. A simple method is
devised for the determination of the most likely diffusion pathways and their
associated energy barriers for surface species. The model is applied to a
small, idealized dust grain, adopting various gas densities and using a small
chemical network. Hydrogen and oxygen atoms accrete onto the grain, to produce
H2O, H2, O2 and H2O2. The off-lattice method allows the ice structure to evolve
freely; ice mantle porosity is found to be dependent on the gas density, which
controls the accretion rate. A gas density of 2 x 10^{4} cm^{-3}, appropriate
to dark interstellar clouds, is found to produce a fairly smooth and non-porous
ice mantle. At all densities, H2 molecules formed on the grains collect within
the crevices that divide nodules of ice, and within micropores (whose extreme
inward curvature produces strong local potential minima). The larger pores
produced in the high-density models are not typically filled with H2. Direct
deposition of water molecules onto the grain indicates that amorphous ices
formed in this way may be significantly more porous than interstellar ices that
are formed by surface chemistry.
