The pair approach applied to kinetics in restricted geometries: strengths and weaknesses of the method

Preprint
Publisher Website
Google Scholar
  • 12 February 2003
Abstract
In the rapidly emerging field of nanotechnology, as well as in biology where chemical reaction phenomena take place in systems with characteristic length scales on the nanometer range, understanding of chemical kinetics in restricted geometries is of increasing interest. We studied the two-species reaction-diffusion system A+B->0 in a one-dimensional restricted geometry. Particles A and B are set to move on a line by diffusion (with equal diffusion constants) and annihilate when within reaction range. To avoid boundary effects, the line is closed into a ring. The size of the system (ring) varies from very large, where the system size L is much larger than the size of reactants a, towards the situation where molecules are pressed into tiny volumes (L of the order of a). To simplify algebra we do not consider exclusion effects at this stage. The two types of initial conditions are studied with (i) equal initial number of A and B particles N_{0,A}=N_{0,B} and (ii) initial number of particles is only equal in average = . In both cases we assume that in the initial state the particles are well mixed. We observe exponential decay of particle concentration for both types of initial conditions. In the case of the type (ii) initial condition, the results of the pair-like analytical model agrees qualitatively with computer experiment (Monte Carlo simulation), while less agreement was obtained for the type (i) initial condition.

This publication has 0 references indexed in Scilit: