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 nonclass ical reaction-diffusion formalism that includes spatial fluctuations. This paper addresses the case of a spatially random initial distributi on of reactants; correlated initial conditions are discussed in anothe r paper. For low dimensions (d less-than-or-equal-to 2) we find that b oth A + A --> 0 and A + B --> 0 reactions depart (swiftly) from the cl assical 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 beha vior with its peculiar rate laws. We give scaling laws for the crossov er time and crossover density, with explicit dependencies on the initi al density and on the dimension. Similarly, in three dimensions the cr ossover from the classical to the segregated Zeldovich regime is deriv ed for the A + B --> 0 reaction. Finite size effects differ significan tly for the segregated and nonsegregated regimes. In the former case w e obtain a relation between aggregate sizes and lattice sizes. Monte C arlo simulations bear out the scaling laws and provide the scaling coe fficients.