Permselectivity of bilayered ion-exchange membranes in ternary electrolyte

The work aims to study the competitive ions transfer through bilayer ion-exchange membranes, both in theory and in an experiment. The transport of ions was described within the framework of the Nernst-Planck model in a four-layer membrane system formed by a bilayer membrane and two diffusion layers. For the two cases, when the current is much smaller than the limiting one and for the limiting current, we obtained analytical solutions of the problem. In these two cases, one can calculate the ions separation coefficients, effective transport numbers and permselectivity coefficients using the thermodynamic and kinetic properties of the individual layers of a bilayer membrane. For an arbitrary current density, a numerical solution of the boundary value problem is obtained. The numerical solution allowed calculating the dependencies of the permselectivity coefficient on the current density for membranes with different thicknesses of the modifying layer. The theory was verified experimentally in an electromembrane system with a bilayer membrane in a ternary solution of CaCl2+NaCl electrolyte. Quantitatively and qualitatively, the causes and the mechanism of permselectivity coefficient reduction are analyzed. For bilayer membranes at currents close to the limiting one, it is determined by the diffusion coefficients of the separated counterions in solution and by the charge numbers of counterions and coions.