Development of the new approach to the diffusion-limited reaction rate theory
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OLIDS AND LIQUIDS
Development of the New Approach to the DiffusionLimited Reaction Rate Theory1 M. S. Veshchunov Nuclear Safety Institute (IBRAE), Russian Academy of Sciences, Moscow, 115191 Russia Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow Region, 141700 Russia email: [email protected] Received July 20, 2011
Abstract—The new approach to the diffusionlimited reaction rate theory, recently proposed by the author, is further developed on the base of a similar approach to Brownian coagulation. The traditional diffusion approach to calculation of the reaction rate is critically analyzed. In particular, it is shown that the traditional approach is applicable only in the special case of reactions with a large reaction radius, r A RAB r B (where r A and r B are the mean interparticle distances), and becomes inappropriate in calculating the reaction rate in the case of a relatively small reaction radius, RAB r A , r B . In the latter case, most important for chemical reactions, particle collisions occur not in the diffusion regime but mainly in the kinetic regime characterized by homogeneous (random) spatial distribution of particles on the length scale of the mean interparticle dis tance. The calculated reaction rate for a small reaction radius in three dimensions formally (and fortuitously) coincides with the expression derived in the traditional approach for reactions with a large reaction radius, but notably deviates at large times from the traditional result in the planar twodimensional geometry. In application to reactions on discrete lattice sites, new relations for the reaction rate constants are derived for both threedimensional and twodimensional lattices. DOI: 10.1134/S1063776112020148 1
1. INTRODUCTION
We refine and further develop the new approach to the diffusionlimited reaction rate theory proposed in our paper [1]. For many chemical processes, the reaction pro ceeds from a reaction complex formed by collision of two or more reactants. Each reaction rate coefficient K has a temperature dependence, which is usually given by the Arrhenius equation K = K0 exp(–Ea/kT), where the preexponential factor K0 determines the collision frequency of reacting species and the exponential fac tor determines the number of collisions with the energy greater than the activation energy Ea of the complex (i.e., corresponds to the sticking probability of collisions). Diffusionlimited (or diffusioncontrolled) reac tions are reactions in which collisions of the reactants (determining the preexponential factor K0) are con trolled by their diffusion migration in suspending sol vent (rather than by freemolecule collisions typical for molecular reactions in gas mixtures). Diffusion limited reactions between two different species A and B (A + B C, where C does not affect the reaction) show up in a vast number of applications including not only chemical (see, e.g., [2]) but also biological (e.g., 1
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