Chronopotentiometry of ion-exchange membranes in the overlimiting current range. Transition time for a finite-length diffusion layer: modeling and experiment

• 1D transient model based on the Nernst-Planck-Poisson equations is proposed.
• Diffusion layer thickness decreases with time due to electroconvection.
• An excellent agreement between calculated and experimental transition time is found.
• The Sand equation holds for current densities more than 1.5 times higher than jlim.

This paper presents a simple method for simulation of chronopotentiograms at underlimiting and overlimiting current densities. The model is based on the Nernst-Planck-Poisson (NPP) equations. The idea consists in the presentation of the diffusion layer thickness, δ, as a function of the Donnan potential drop (PD) at the membrane/depleted solution interface, ΔφDon. When an overlimiting current density, j, is applied and the time approaches the transition time, τ, electroconvection arises near the depleted interface and causes a decrease of δ. The δ(ΔφDon) function is assumed linear one and containing two adjustable parameters: the threshold value of ΔφDon, which relates to the onset of electroconvection, and the value of ΔφDon related to the steady state reached under a given j. It is shown that the model describes well experimental chronopotentiograms of a CMX homogeneous cation-exchange membrane at all applied overlimiting current densities. If the solution is not too dilute (>0.001 M), the thickness of the interfacial space charge region (SCR) may be neglected and the local electroneutrality (LEN) assumption may be applied. Thus, the overlimiting current chronopotentiograms are for the first time described under the LEN assumption. We show that the Sand equation for calculating τ is applicable only for j at least 1.5 times higher than the limiting current density. The reason is in convection transfer, which is not taken into account in Sand’s theory, but allowed for by fitting δ in our model.

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