We extend Tachiya’s method for treating totally diffusion-controlled recombination of a pair of particles to partially diffusion-controlled recombination. The differential equation satisfied by the survival probability of the pair is derived, and solved for several cases of practical interest. Recent experiments on the solvated electron yield in liquid ammonia are analyzed by use of the present theory. It is confirmed that the rather high yield of solvated electrons in irratiated liquid ammonia is due to the slowness of the recombination reaction e−s+NH+4.

Diffusion-controlled reactions of a pair of particles on a spherical surface are studied. An analytical expression for the pair survival probability is derived in the case of a pair of freely diffusing particles. The decay of the pair survival probability is found to be well approximated by a single exponential. A simple approximate method for calculating the decay time which characterizes the exponential is presented. The decay time of a pair of particles interacting with each other by an arbitrary force is derived by use of this method. The results are applied to analyze available experimental data on reactions occurring on micellar surfaces, including the dismutation reaction of Br2− on the surface of cationic micelles and that of Ag2+ on the surface of anionic micelles, and the diffusion coefficients of these species on the micellar surfaces are estimated.

The present paper aims at constructing a theoretical model in terms of which the relationship between the free-ion yield and electron mobility may be understood for high-mobility liquids. The framework chosen for that purpose is the Fokker-Planck equation with the Coulomb field of the electron and the sibling cation built into it. This equation describes, in general, the distribution function for the electrons in both the configurational and velocity spaces. Starting from a given initial position and velocity, one can calculate the distribution of thermalization distances through the use of a relaxation time. The same relaxation time appears in the mobility equation. implying the similarity of energy-loss processes of low-energy electrons following an ionization event and of electrons slightly heated up by the external field. The model therefore provides, in principle. a connection between the electron mobility and the free-ion yield. In practice the agreement between theory and experiment is reasonably good for molecular hydrocarbons but is poor for liquefied rare gases.

The escape probabilities or the recombination probabilities in diffusion-controlled reactions are obtained for some special systems which are not centrosymmetric. Specifically, we calculate (1) the escape probability of an electron from N fixed cations, (2) the recombination probability of a pair of radicals in an anisotropic medium, (3) the recombination probability of a radical with each of two statics sinks, and obtain (4) approximate expressions for the recombination probability of a radical with N static sinks in particular configurations. As a by-product, we obtain the bulk reaction rate for each system. Of special note is our result for the first system listed above. With the proviso that the cation radii are vanishingly small, we find the escape probability to be equal to the reciprocal of the Boltzmann factor for the system. This result factors into a product of isolated geminate ion pair escape probabilities. No competitive effects due to the geometric distribution of the cations appear.

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