Competitive reversible binding: A theoretical study of density effects on the long-time relaxation

Abstract

Competitive reversible binding is studied for a one-dimensional continuum model. Taking the reaction as a stochastic two-state process (free or occupied binding site), from many-body equations by superposition a closed system of three coupled reactive equations is derived. Linearized versions of these equations are used to get low density approximations for the long-time kinetics. Starting point is an approximation (a) from which a Szabo–Zwanzig type t−1/2 long-time law can be followed. On the basis of an approximate relation between the state-specific distribution functions obtained in (a), a higher order in density approximation (b) is derived which prescribes a concentration effect on the long-time kinetics. According to (b) the t−1/2 law is also asymptotically valid for t→∞, but with a different concentration-dependent amplitude. For time windows in an intermediate long-time range the relaxation to equilibrium appears as satisfying a modified power law (∝ t−α with α≠1/2). These analytic results, which are interesting with respect to deviations from a predicted t−3/2 decay law observed for photoexcited proton transfer in water [D. Huppert et al., Phys. Rev. Lett. 68, 3932 (1992)], are related to recent Brownian simulations of the pseudounimolecular reaction.