Efficient Stochastic Simulations of Complex Reaction Networks on Surfaces

Abstract

Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations, which are based on the mean-field approximation. However, in case that the surface is partitioned into a large number of disconnected microscopic domains, the number of reactants in each domain becomes small and it strongly fluctuates. This is, in fact, the situation in the interstellar medium, where some crucial reactions take place on the surfaces of microscopic dust grains. In this case rate equations fail and the simulation of surface reactions requires stochastic methods such as the master equation. However, in the case of complex reaction networks, the master equation becomes infeasible because the number of equations proliferates exponentially. To solve this problem, we introduce a stochastic method based on moment equations. In this method the number of equations is dramatically reduced to just one equation for each reactive species and one equation for each reaction. Moreover, the equations can be easily constructed using a diagrammatic approach. We demonstrate the method for a set of astrophysically relevant networks of increasing complexity. It is expected to be applicable in many other contexts in which problems that exhibit analogous structure appear, such as surface catalysis in nanoscale systems, aerosol chemistry in stratospheric clouds and genetic networks in cells.

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• Binomial moment equations for stochastic reaction systems
• Molecular Hydrogen Formation on Low Temperature Surfaces in Temperature Programmed Desorption Experiments
• Incorporation of stochastic chemistry on dust grains in the PDR code using moment equations
• A hybrid moment equation approach to gas-grain chemical modeling
• Accurate rate coefficients for models of interstellar gas-grain chemistry
• Stochastic Analysis of Dimerization Systems
• Diffusion-limited reactions on a two-dimensional lattice with binary disorder