2003/04/30 by Jonathan L. Bentz, John J. Kozak, E. Abad +2
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1016/s0378-4371(03)00271-1
15 pages, 8 figures, uses revtex4, accepted for publication in Physica A
openalex publication_date 2003/04/30 · arxiv created 2003/07/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The role of dimensionality (Euclidean versus fractal), spatial extent, boundary effects and system topology on the efficiency of diffusion-reaction processes involving two simultaneously-diffusing reactants is analyzed. We present numerically-exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via application of the theory of finite Markov processes, and via Monte Carlo simulation. As a general rule, we conclude that for sufficiently large systems, the efficiency of diffusion-reaction processes involving two synchronously diffusing reactants (two-walker case) relative to processes in which one reactant of a pair is anchored at some point in the reaction space (one walker plus trap case) is higher, and is enhanced the lower the dimensionality of the system. This differential efficiency becomes larger with increasing system size and, for periodic systems, its asymptotic value may depend on the parity of the lattice. Imposing confining boundaries on the system enhances the differential efficiency relative to the periodic case, while decreasing the absolute efficiencies of both two-walker and one walker plus trap processes. Analytic arguments are presented to provide a rationale for the results obtained. The insights afforded by the analysis to the design of heterogeneous catalyst systems are also discussed.