Abstract
Theoretical and computer simulation studies of annihilation reactions with traps on two and in three dimensional lattice systems are reported for the following reactions: (1) Bimolecular trapping/annihilation: A+A→*; A+T→AT; A+AT→T; (2) unimolecular trapping/annihilation: A+A→*; A→AT; A+AT→*. The mean field analysis and combinatorial calculations of the rate constants given previously for a square lattice are generalized to lattices in two and three dimensions. It is found that the kinetics of trapped A’s can be described by mean field theory for bimolecular but not for unimolecular trapping reactions. The kinetics of free A’s obeys mean field theory at short times, but at longer times and at low trap densities the free A population decays as a stretched exponential at when large density fluctuations dominate the reaction. This stretched exponential behavior of the Donsker–Varadhan from A(t)∼exp(−td/(d+2)), where d is the dimensionality, already found for the reactant decay in A–A annihilation reactions with traps on a square lattice [Rasaiah et al., J. Phys. Chem. 94, 652 (1990)] was tested for universality by studying triangular and hexagonal lattices in two dimensions (2D) and a cubic lattice in three dimensions (3D). The same behavior is also observed when the free particle annihilation is turned off. The effect of a finite staying probability ps on the kinetics of these reactions are also investigated.
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