DIFFUSION-LIMITED BINARY REACTIONS - THE HIERARCHY OF NONCLASSICAL REGIMES FOR RANDOM INITIAL CONDITIONS

We derive a hierarchy of kinetic regimes and crossover conditions for elementary A + A --> 0 and A + B --> 0 batch reactions from a nonclassical reaction-diffusion formalism that includes spatial fluctuations. This paper addresses the case of a spatially random initial distribution of reactants; correlated initial conditions are discussed in another paper. For low dimensions (d less-than-or-equal-to 2) we find that both A + A --> 0 and A + B --> 0 reactions depart (swiftly) from the classical behavior toward a ''depletion zone regime'' with non-Hertzian nearest neighbor distributions and nonclassical rate laws. Eventually the (A-B) density difference fluctuations take over in the A + B --> 0 case and lead to the segregated Ovchinnikov-Zeldovich asymptotic behavior with its peculiar rate laws. We give scaling laws for the crossover time and crossover density, with explicit dependencies on the initial density and on the dimension. Similarly, in three dimensions the crossover from the classical to the segregated Zeldovich regime is derived for the A + B --> 0 reaction. Finite size effects differ significantly for the segregated and nonsegregated regimes. In the former case we obtain a relation between aggregate sizes and lattice sizes. Monte Carlo simulations bear out the scaling laws and provide the scaling coefficients.