NEUTRALIZATION OF ISOLATED ION PAIR IN POLAR MEDIA .I. THEORY OF YIELD OF SOLVATED ELECTRONS

Motion of an isolated ion pair in a polar medium is described here through the Smoluchowski equation with a time-dependent dielectric constant. The time dependence is taken as appropriate to constant charge rather than to constant external field. Explicit solution of the problem is obtained in the framework of prescribed diffusion. This solution, in the infinite time limit, gives the escape probability. The yield of escaped electrons is identified with the solvated electron yield. Known yields in various polar media are used to calculate the respective thermalization distances and effective dielectrc constants. Dielectric relaxation time is explicitly used in the present formulation. Two diffusion constants are used, one prior and one after relaxation. Calculated results are compared with experiment. Physical concepts derived from the present model relate to thermalization length, effective dielectric constant, and diffusion-relaxation length.