Effect of current-induced coion transfer on the shape of chronopotentiograms of cation-exchange membranes

Abstract

Chronopotentiometry using pulses of a constant current of density j is a powerful method for characterizing ion-exchange membranes (IEMs). We report on the influence of coion transport on the shape of chronopotentiogram (ChP) and the consequent new possibility of quantifying coion transport based on ChP analysis. We show that in the case where the bathing solution contains Ca2+ or Mg2+ ions, the ChPs of the homogeneous (CMX) and heterogeneous (MK-40) cation-exchange membranes at overlimiting current densities have a maximum (a peak), which appears a few seconds after the transition time. The time required to reach a stationary state is of the order of d2/D‾2 (where d is the membrane thickness and D‾2 is the coion diffusion coefficient in the membrane); this time under our experiment conditions is about 300–400 s. We show that the cause of the maximum is the increase in coion transfer caused by the current-induced concentration polarization of the bathing solution. This increase in coion transfer results in increasing the limiting current density jlim, which at j = const leads to a reduction in the resistance of the depleted diffusion layer over time and the appearance of a maximum on the ChP. 1D mathematical modeling is based on the Nernst-Planck-Poisson equations. The main assumption inspired by the works of Levich and Amatore is that the apparent electrolyte diffusion coefficient in the depleted solution increases with increasing electroconvection. The stationary value of this diffusion coefficient is found from the I–V curve. The only fitting parameter is the critical potential difference, which refers to the onset of intensive electroconvection.