Computer investigations on the asymptotic behavior of the rate coefficient for the annihilation reaction A + A → product and the trapping reaction in three dimensions

Abstract

We have performed intensive computer simulations of the irreversible annihilation reaction: A + A → C + C and of the trapping reaction: A + B → C + B for a variety of three-dimensional fluids composed of identical spherical particles. We have found a significant difference in the asymptotic behavior of the rate coefficients for these reactions. Both the rate coefficients converge to the same value with time t going to infinity but the convergence rate is different: the O(t(-1/2)) term for the annihilation reaction is higher than the corresponding term for the trapping reaction. The simulation results suggest that ratio of the terms is a universal quantity with the value equal to 2 or slightly above. A model for the annihilation reaction based on the superposition approximation predicts the difference in the O(t(-1/2)) terms, but overestimates the value for the annihilation reaction by about 30%. We have also performed simulations for the dimerization process: A + A → E, where E stands for a dimer. The dimerization decreases the reaction rate due to the decrease in the diffusion constant for A. The effect is successfully predicted by a simple model.

Influence of the force interaction on accumulation of macroscopic correlations in elementary reaction A + B → C

“…However, binary scaling has shown that it is beyond the limits of binary description accuracy, and thus is insignificant at small density parameter. Such an effect is to manifest itself with increasing concentration, as is shown by numerical calculations [20,[46][47][48]. Making allowance for initial correlations in full agreement with general kinetic theory gave rise to the inhomogeneous source in the kinetic equation vanishing with time.…”

“…The influence of the interaction of the reacting pair AB with other particles (including products C) is insignificant, since taking it into consideration is beyond the limits of making allowance for two-particles only. Of course, as the density parameter increases (in this case ET is inapplicable) such a consideration becomes essential, and this is confirmed by numerical calculations available in the literature [20,[46][47][48]. However, even at small density parameters, ignoring the above force interactions in the more general GET theory that considers the dependence of pair encounters of reactants in solution determined by the contribution of three-particle correlations into the kinetics is not so apparent.…”

Concentration effects on the rates of irreversible diffusion-influenced reactions

“…26,27 Seki et al investigated the EV effect (site blocking effect) on diffusionmediated reactions based on a lattice model with prohibited double occupancy of the lattice sites. [28][29][30][31] They considered the effects of excluded volumes of inert particles as well as those of reactants, and the theoretical rate expressions were assessed by Monte Carlo simulations.…”