Reacting hard sphere dynamics: Liouville equation for condensed media

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Abstract
A rigorous formalism is presented for analyzing a model of chemical reactions that may occur upon classical hard sphere impact. Between hard sphere encounters, the particles interact via a continuous potential. Reaction of the type A+X→B+Y are allowed to occur if threshold energy or steric criteria are satisfied. Third body effects such as catalysis or solvent mediation are accounted for via the dependence of the latter criteria. Using methods of hard sphere kinetic theory, we formulate a (pseudo‐)Liouville equation, valid for all densities. This equation allows for the use of a variety of analytical procedures to generate kinetic and correlation function equations. A projection operator technique is used to derive exact chemical kinetic results valid for slow reactions and the reciprocal limit of diffusion limited reaction, both valid at all densities. We find that Enskog‐like reaction rates are valid for all densities in a special case of the slow reaction limit. For this case, the overall rate in a mustistep process can be written as a sum of terms, each associated with an elemental reaction process but having concentration dependent rate coefficients.