Reaction under vacancy-assisted diffusion at high quencher concentration

Abstract

The theory of diffusion-mediated reactions is already established for the target problem in the dilute limit, where the immobile target is surrounded by many quenchers. For lattice random walks in the crowded situation, each quencher is surrounded by other quenchers differently. As a result, each quencher migrates differently in the presence of site blocking effects. However, in the conventional theory, such difference is ignored and quenchers are assumed to move independently of each other. In this paper, theory of diffusion-mediated reactions of target problem is developed by taking into account the site blocking effects for quencher migration and the difference in the configuration of quenchers around each quencher. Our result interpolates between those in high and low limits of quencher concentrations and is a lower bound of the survival probability. In the static limit, the exact result is reproduced for a localized sink. In the presence of diffusion, the approximation is better when intrinsic reaction rates are low.

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.…”

Survival, Absorption, and Escape of Interacting Diffusing Particles

“…2. Earlier works [37][38][39][40][41] on the target survival for the SSEP only established some bounds on P(n = 0, T, ρ 0 ). 14), of the target survival probability for the SSEP.…”

From single-particle stochastic kinetics to macroscopic reaction rates: fastest first-passage time of $N$ random walkers

“…Exceptions are provided by several particular reaction schemes in which, under some rather restrictive constraints, so-called fluctuation-induced behaviour emerges, see, e.g., [25][26][27][28][29][30][31][32][33][34] and references therein. One particular question concerns the possible concentrationdependence of the effective reaction rates [15,[35][36][37][38]. Indeed, the original Smoluchowski approach and many of its generalisations are only plausible for sufficiently low albeit finite concentrations.…”