Bimolecular Diffusion-Limited Reaction Kinetics at Steady-State
Physics of condensed matter offers numerous examples of reactive systems where the transport of reactants such as atoms, molecules or any localized excitation, is of the diffusive type. In general these systems exhibit two distinct time scales. One is a typical time of reaction between reactants and the other is a characteristic time associated with the microscopic erratic movements of the particles, often referred to as a time of jump The limiting process is calleddiffusion limited when at the time scale characterizing a microscopic jump, particles seem to react “instantaneously” when they are in contact at a microscopic distance (reaction radius). Bimolecular diffusion-limited reactions of the type Ai+Aj->Product, where Aiand Ajare distinct or similar rectants, are extensively investigated since they represent many important physical situations. The product formed by the reaction can be an aggregate, a third particle Ak, a particle Ai or Aj, or both particles may annihilate in pairs and leave the system. The range of applications spanned by these models covers particle aggregation, gelation of sols, coalescence of aerosols, electron-hole recombination in semi-conductors, soliton-antisoliton annihilation in polymers, exciton fusion in molecular crystals, etc…. Classically, the point of view associated with these different physical situations is essentially the same.
KeywordsPercolation Cluster Conservation Constraint Steady State Density Reaction Radius Distinct Time Scale
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