Kinetic Theory of Diffusion Controlled Reaction

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Diffusion controlled reaction process in liquid is treated as a many-body problem from a view point of stochastic process. The time development of the ensemble of the reaction systems is formulated by introducing the survival probability as a fundamental quantity which is derived from the Smoluchovski equation with pair-absorbing interaction. This equation has just the same form as the Bloch equation for the density matrix of hard-core system in which 1⁄kT and hard-core radius correspond to the diffusion constant D and reaction radius σ, respectively. The equation is solved by introducing the cluster integrals which are calculated by means of the binary collision expansion. The survival probability is obtained in the form of a power series of the reactive particle densities up to the 4th order under the condition of σ2⁄(Dt)<1.

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