Examination of the equations for calculation of chronopotentiometric transition time in membrane systems. (1st September 2020) - Butylskii, D.Yu.; Skolotneva, E.D.; Mareev, S.A.; Gorobchenko, A.D.; Urtenov, M.K.; Nikonenko, V.V.
Abstract: Transition time, τ, is a very crucial characteristic in chronopotentiometry; it is important to have a simple equation to calculate this value. As early as in 1901, Sand has deduced his famous equation for calculating τ in electrode/solution systems with infinitely large diffusion layer. The exact analytical solution for the case of finite diffusion-layer thickness was obtained by Sheldeshov et al. in 1986. However, τ enters this solution as an implicit function of the current density, i . Recently, van Soestbergen and coauthors proposed an approximate formula where the transition time is an explicit function of i . In this paper, we examine the above equations along with our numerical solution by comparing the calculated values of τ with our experimental data for homogeneous (Fuji CEM Type I, Type II, Type X, Neosepta CMX) and heterogeneous (MK-40) membranes. A large gamma of current densities (from i = 1.0 i lim to 2.5 i lim, where i lim is the limiting current density) is applied. The most simple in use is the formula of van Soestbergen et al., which, however, gives at i > 1.0 i lim the values of τ slightly (about 0.7%) lower than the exact analytical solution of Sheldeshov et al. We show that a better approximation to the exact solution is obtained when the first-order approximation of the analytical solution (obtained by van Soestbergen et al.) is applied in the range of i from 1.0 to 1.9 i lim, while for i > 1.9 i lim, the Sand equation is used. We find nevertheless that the experimental values of τ are higher than the theoretical ones for all the studied membranes. The causes of this deviation, which are mainly electroconvection and surface electric heterogeneity, are discussed.