Theory of Bimolecular Reaction Processes in Liquids

A theoretical approach to the problem of diffusion controlled bimolecular reactions is presented. In order to take into account the time correlation of reaction process of our many-particle system, the probability of the first reaction is introduced as a fundamental quantity. Time development of the ensemble of our system is formulated using the probability of the first reaction. An approximation which reduces the general formula to a problem of Markov process is adopted. Then it is shown that, if we assume stationary reaction rate, the usual phenomenological kinetic equation, i.e. the so called law of mass action can be derived as the first order approximation, and as the second order approximation the deviation from the law of mass action is examined. For the general case, in order to obtain the probability of the first reaction in an explicit form, it becomes necessary to solve the multidimensional diffusion equation with pair absobing interactions, which is calculated using the binary collision expansion method.