Current Passage across Electrode/Membrane/Solution System. Part 3: Short-Time Evolution. Binary Electrolyte (Arbitrary Mobilities)
摘要
The recently proposed express-method for experimental determination of transport characteristics of ion-exchange membranes (Russ. J. Electrochem., 2022, vol. 58, p. 1103) is based on the comparison of measurements of the current transients in an electrode/membrane/electrolyte solution system after applying a large-amplitude potential step with theoretical predictions for this dependence. In previous studies, this approach was used in the study of the transport of bromide anions through a membrane under conditions of its pure diffusional mechanism owing to the electric-field suppression by background ions, for which analytical solutions are available. In this paper, both the solution and the membrane contain only two mobile single-charge ionic species: background cation (counterion) M and electroactive anion (co-ion) X which is subject to the redox-transformation into a neutral product at the electrode/membrane boundary. Then, the non-stationary electrodiffusion transport of these ions inside the membrane as a result of applying a potential step from the equilibrium state of the whole system to the transport-limited current regime is considered. Equilibrium with respect to the exchange of each ion across the membrane/solution boundary is assumed to be retained. It is established that within a short-time interval after the potential step, when the non-stationary diffusion layer thickness is significantly shorter than that of the membrane, the distributions of ion concentrations and electric field strength can be represented as functions of a self-similar variable, х/t1/2, where x is the spatial coordinate, t is the time. Dependence of these functions on the system parameters are found by numerical integration. The limiting current varies over time according to the Cottrell formula: I ~ t–1/2. The dependence of the dimensionless current amplitude on the system characteristics is found by numerical calculation. Explicit analytical formulas are derived for the cases of high and low cation concentrations in the membrane as compared with the concentration of immobile charged groups. If the counterion mobility strongly exceeds that of the electroactive component, an approximate analytical formula is proposed that is applicable within a wide range of system parameters. Estimates of the limits of applicability of the expressions obtained are given.