Subdiffusion-assisted reaction kinetics in disordered media

Abstract

We present a theory for describing the reaction process occurring in disordered media with energetically disordered trapping sites and spatial constraints. The theory is based on a generalized fractional reaction-diffusion equation, which describes the time evolution of the mean distribution of a particle performing a continuous time random walk on a fractal network. The motion of a particle is subdiffusive because of the spatial constraints and/or the random detrapping times described by a waiting time distribution given by psi(t) similar to t(-(1+alpha)) with 0 < a < 1. Assuming that the reaction occurs at a separation of contact, the reaction and transport processes are decoupled and the kinetic information for the reaction is expressed in terms of the reaction-free Green's function obtained with the reflecting boundary condition at the separation of contact. The survival probability of a reactant pair is shown to decay asymptotically as tau(-alpha vertical bar ds/2-1 vertical bar), where d(s) is the fracton dimension of the fractal network under consideration. We also check the validity of the analytical results by comparison with Monte Carlo simulation results.