A rate process with an entropy barrier

Abstract

This paper presents a simple dynamical model of a rate process in which the rate appears to be controlled by an entropy barrier, rather than an energy barrier. The model consists of independent particles moving in a two-dimensional region bounded by four reflecting disks. The particles collide elastically with the walls. A bottleneck separates the region into reactants and products. The extent of the reaction is followed by using computer simulations to get the time dependence of the number correlation function of reactants. The particle dynamics are either frictionless (inertial), moderately frictional (Langevin dynamics), or strongly frictional (Brownian dynamics). For small bottlenecks, the number correlation function generally decays in time as a single exponential. The transition rate in the frictionless limit is predicted correctly by microcanonical transition state theory. As the strength of the friction is increased, the rate changes to the diffusive limit without the usual Kramers turnover.