Kinetic transitions in diffusion-reaction space. II. Geometrical effects

We extend the stochastic master equation approach described earlier [J. J. Kozak and R. Davidson, J. Chem. Phys. 101, 6101 (1994)] to examine the infl uence on reaction efficiency of multipolar correlations between a fixed tar get molecule and a diffusing coreactant, the latter constrained to move on the surface of a host medium (e.g., a colloidal catalyst or molecular organ izate) modeled as a Cartesian shell [Euler characteristic, chi = 2]. Our mo st comprehensive results are for processes involving ion pairs, and we find that there exists a transition between two qualitatively different types o f behavior in diffusion-reaction space, viz., a regime where the coreactant 's motion is totally correlated with respect to the target ion, and a regim e where the coreactant's motion is effectively uncorrelated. This behavior emerges both in the situation where correlations between the ion pair are s trictly confined to the surface of the host medium or where correlations ca n be propagated through the host medium. The effects of system size are als o examined and comparisons with diffusion-reaction processes taking place o n surfaces characterized by Euler characteristic chi = 0 are made. In all c ases studied, the most dramatic effects on the reaction efficiency are unco vered in the regime where the Onsager (thermalization) length is comparable to the mean displacement of the coreactant, a conclusion consistent with r esults reported in earlier work. (C) 1999 American Institute of Physics. [S 0021-9606(99)50506-0].