Concentration fluctuations in reaction kinetics

Abstract

We study the kinetics of the A+A → P and the A+B → P diffusion-limited reactions by modeling the dynamics through random walks on regular and on fractal lattices. For the pseudounimolecular reactions A(0)≪B(0) we present exact analytical expressions for the target (DA=0) and the trapping (DB=0) problems. The kinetics of trapping as well as of the bimolecular reactions are then determined through simulation calculations. In all cases, we relate the results to Smoluchowski-type forms. Whereas the target and the A+A → P problems are well described by such forms, the trapping and the strictly bimolecular A+B → P reaction show different behaviors at longer times, due to fluctuations in the particle densities.