Wien dissociation in very low intensity electric fields

Abstract

Recent work by MciIroy on mathematical models of the conduction of the nervous impulse employ Onsager's well known equation for the dependence of the dissociation constant of a weak electrolyte as a function of the applied electric field intensity (Wien effect). Onsager's result, however, possesses a discontinuity in the derivative with respect to the applied field strength which makes a full analysis of the nerve models impossible at present. In this paper, by treating the dissociation of oppositely charged ion pairs of the weak electrolyte as a rate process across the shielded coulombic potential of the ion pairs, a result for the dependence of the dissociation constant on the strength of the applied field in the case of extremely small fields is derived which is free of the aforementioned discontinuity and which resembles a conjectural equation proposed by Onsager for this range of field strength.