Synchronous vs asynchronous diffusion-reaction processes involving geminate radical pairs

We report lattice Monte Carlo calculations to study the efficiency of diffusion-controlled reactive processes involving geminate radical pairs. Whereas our earlier study [J.J. Kozak, C. Nicolis, G. Nicolis, N.J. Turro, J. Phys. Chem. 105 (2001) 10949] focused on factors affecting the reaction efficiency when a pair of coreactants moved synchronously on a surface modeled as a d=2 dimensional square planar lattice subject to periodic boundary conditions, we document here differences in reaction efficiency when a pair of coreactants can move synchronously or asynchronously on surfaces which are topologically different but characterized by the same number N of sites. As before, the first surface is taken to be a d=2 square planar lattice; the second surface considered is a Cartesian shell, the bounded surface of a cube. When studied as a function of system size, we find that synchronous dynamics are more efficient than asynchronous dynamics in optimizing diffusion-reaction processes; and, reactions on planar, periodic surfaces are more efficient than on cubic shells. The relevance of these conclusions to experimental studies on two radiation-induced, radical decay reactions [the one cited above and A.J. Frank, M. Grätzel, J.J. Kozak, J. Am. Chem. Soc. 98 (1976) 3317] is noted and discussed.