Onsager's Contribution to Reaction-Rate Theory

As is true in so many cases, Onsager's major contribution to reaction-rate theory, [17], represented an attack on a significant physical problem that at the same time required the solution to a non-trivial mathematical problem. The physical problem, as originally stated, is that of calculating the probability that an electron, initially removed from a charged particle, will ultimately recombine with that particle in the presence of a constant field. The interaction potential is assumed to be Coulombic.

Notwithstanding its very specific formulation, Onsager's results have been applied to a wide variety of problems in solid state physics^1-4, and physical chemistry⁵. In mathematical terms, the probability that the two particles do not combine is known as a splitting probability. A general discussion of such probabilities as calculated for systems whose evolution is described by the Smoluchowski equation is to be found in the text by Gardiner⁶…