Experimental results on the formation of molecular hydrogen on amorphous silicate surfaces are presented for the first time and analyzed using a rate equation model. The energy barriers for the relevant diffusion and desorption processes are obtained. They turn out to be significantly higher than those obtained earlier for polycrystalline silicates, demonstrating the importance of grain morphology. Using these barriers, we evaluate the efficiency of molecular hydrogen formation on amorphous silicate grains under interstellar conditions. It is found that unlike polycrystalline silicates, amorphous silicate grains are efficient catalysts of H 2 formation within a temperature range that is relevant to diffuse interstellar clouds. The results also indicate that the hydrogen molecules are thermalized with the surface and desorb with low kinetic energy. Thus, they are unlikely to occupy highly excited states.

Abstract. The three species ABC model of driven particles on a ring is generalized to include vacancies and particle-nonconserving processes. The model exhibits phase separation at high densities. For equal average densities of the three species, it is shown that although the dynamics is local, it obeys detailed balance with respect to a Hamiltonian with long-range interactions, yielding a nonadditive free energy. The phase diagrams of the conserving and nonconserving models, corresponding to the canonical and grand-canonical ensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit a transition from a homogeneous to a phase-separated state, although the phase diagrams are shown to differ from each other. This conforms with the expected inequivalence of ensembles in equilibrium systems with long-range interactions. These results are based on a stability analysis of the homogeneous phase and exact solution of the hydrodynamic equations of the models. They are supported by Monte-Carlo simulations. This study may serve as a useful starting point for analyzing the phase diagram for unequal densities, where detailed balance is not satisfied and thus a Hamiltonian cannot be defined.

A generalization of the ABC model, a one-dimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) density-conserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with long-range interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (density-conserving) and grand canonical (density nonconserving) ensembles, as expected in long-range interacting systems. The implications of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.

The study of the formation of molecular hydrogen on low-temperature surfaces is of interest both because it enables the exploration of elementary steps in the heterogeneous catalysis of a simple molecule and because of its applications in astrochemistry. Here, we report results of experiments of molecular hydrogen formation on amorphous silicate surfaces using temperature-programmed desorption (TPD). In these experiments, beams of H and D atoms are irradiated on the surface of an amorphous silicate sample. The desorption rate of HD molecules is monitored using a mass spectrometer during a subsequent TPD run. The results are analyzed using rate equations, and the energy barriers of the processes leading to molecular hydrogen formation are obtained from the TPD data. We show that a model based on a single isotope provides the correct results for the activation energies for diffusion and desorption of H atoms. These results are used in order to evaluate the formation rate of H2 on dust grains under the actual conditions present in interstellar clouds. It is found that, under typical conditions in diffuse interstellar clouds, amorphous silicate grains are efficient catalysts of H2 formation when the grain temperatures are between 9 and 14 K. This temperature window is within the typical range of grain temperatures in diffuse clouds. It is thus concluded that amorphous silicates are good candidates to be efficient catalysts of H2 formation in diffuse clouds.

Systems of reacting particles, which are well mixed or distributed homogeneously in space, are commonly modeled by deterministic rate equations. These equations, which are based on the mean-field approximation, are valid for macroscopic systems. However, they neglect fluctuations in the particle populations. As a result, under conditions of strong fluctuations, the reaction rates obtained from the rate equations are highly inaccurate. To account for the fluctuations, stochastic methods are required. However, these methods are computationally intensive and may become infeasible for complex reaction networks. Therefore, it is useful to identify the conditions under which the rate equations provide accurate results. Naively, one expects strong fluctuations when the average population sizes of some of the reactants are of order one or lower. Here we present a systematic approach, for testing the validity of the rate equations, in which we define characteristic scales in terms of the rate constants of the network. We show that the rate equations fail to accurately reproduce the reaction rates when the system size is reduced below these scales. Surprisingly, the rate equations are found to be applicable in a wider range than expected. Their validity depends not only on the population sizes of the reactive species but also on the kinetic properties of the reaction network.