Dependence of ion concentration on growth of crystallites formed during discharge of an idealized electrode

Abstract

Calculations are made showing the time dependence of the ion concentration of an electrolytic solution in which a model electrode is immersed. The model electrode consists of two parts: firstly of the ion source function which can be thought to be calculated as an average of an amount of ion sources statistically distributed over a volume, secondly of the ion sink function which is calculated from size and quantity of crystallites formed by the discharge product. The crystallites are assumed to be spherical and of uniform size. The special case of diffusional controlled growth is considered explicitly. The problem is reduced to the discussion of two differential equations and the initial conditions by which the time dependence of concentration and volume of the discharge product is controlled. After having reached a maximum in certain cases the concentration decreases slowly. When time proceeds the volume of the discharge product becomes asymptotically linear with time. The range of applications to real electrodes is discussed. It is shown that a great amount of crystallites of the discharge product is desirable in order to keep the ion concentration and thus the concentration overvoltage low.