The Current Passage Across an Electrode/Membrane/Solution System. Part 2: Steady-State Diffusion–Migration Current. Ternary Electrolyte

A recently proposed express method for experimental determination of diffusion coefficients of electrotive ions inside a membrane and their distribution coefficients at the membrane/solution interface (Russ. J. Electrochem., 2022, vol. 58, p. 1103) is based on the comparing of a measured non-stationary current across the electrode/membrane/electrolyte solution system upon applying a potential step with theoretical expressions for the time dependence of the current, the steady-state regime being included. In previous publications, the application of this method to the studies of the bromide anion transport across membrane is carried out under conditions of the membrane selective permeability (permselectivity) for non-electroactive counter-ions where the electrical field intensity inside it has been suppressed by their high concentration. Under this condition, the movement of electroactive co-ions (bromide anions), having a much lower concentration inside the membrane, takes place via the purely diffusion mechanism, for which analytical solutions have been available. When the concentrations of electroactive co-ions and supporting-electrolyte counter-ions inside the membrane are comparable, their transport is contributed by both diffusion and migration. In particular, such a situation takes place in a ternary system of monovalent ions where both ions of the supporting electrolyte M⁺ and A^–, as well as the electroactive anion X^–, penetrate the membrane from the external solution, their concentrations inside the membrane appeared being comparable. In this work, we derived analytical expressions for the steady-state distributions of the concentrations of all ionic components, as well as of the electrical field, inside the membrane as a function of the amplitude of the passing stationary current and of the ion concentrations in the bulk solution, as well as for the diffusion–migration limiting current density. In particular, it is shown that at a low concentration of co-ions at the membrane/electrolyte solution interface [compared to the concentration of fixed charged groups of the membrane: X_m \( \ll \) min (C_f, M_m)], the migration contribution into the flux of electroactive ions can be neglected. On this reason, the formulas derived in this work for the ternary electrolyte are reduced approximately to the corresponding expressions for the pure diffusional transport. If the opposite condition is fulfilled (X_m/C_f \( \gg \) 1), the migration contributions into the ion fluxes lead to a modification of the expression for the diffusion–migration limiting current.