Effect of reactant size on discrete stochastic chemical kinetics

This paper is aimed at understanding what happens to the propensity functions (rates) of bimolecular chemical reactions when the volume occupied by the reactant molecules is not negligible compared to the containing volume of the system. For simplicity our analysis focuses on a one-dimensional gas of N hard-rod molecules, each of length l. Assuming these molecules are distributed randomly and uniformly inside the real interval [0,L] in a nonoverlapping way, and that they have Maxwellian distributed velocities, the authors derive an expression for the probability that two rods will collide in the next infinitesimal time dt. This probability controls the rate of any chemical reaction whose occurrence is initiated by such a collision. The result turns out to be a simple generalization of the well-known result for the point molecule case l=0: the system volume L in the formula for the propensity function in the point molecule case gets replaced by the "free volume" L-Nl. They confirm the result in a series of one-dimensional molecular dynamics simulations. Some possible wider implications of this result are discussed.