Concentration fluctuations in reaction kinetics

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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 (D A=0) and the trapping (D B=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.

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