Overlimiting current due to electro-diffusive amplification of the second Wien effect at a cation-anion bipolar membrane junction

Abstract

Numerical simulations are presented for the transient and steady-state response of a model electrodiffusive cell with a bipolar ion-selective membrane under electric current. The model uses a continuum Poisson-Nernst-Planck theory including source terms to account for the catalytic second Wien effect between ionogenic groups in the membranes and resolves the Debye layers at interfaces. The resulting electric field at the membrane junction is increased by as much as four orders of magnitude in comparison to the field external to the membrane. This leads to a significant amplification of the second Wien effect, creating an increased ionic flux due to the catalytic decomposition of water. The effect also induces an exaltation effect wherein the salt ion flux undergoes a concomitant increase as well. The interplay of effects results in a unique over-limiting current mechanism due to concentration polarization internal, rather than external, to the membranes. In addition to the case of two equal but oppositely charged membranes under the standard simplifying assumption of equal ionic diffusivities, two variations on this model are studied. Asymmetric diffusivities, representative of the actual mobility difference in dissociated water ions, and the effect of the membrane charge density ratio were also considered. The latter elucidates an overlimiting current shift mechanism for DNA adsorption on anion-selective membranes proposed by Slouka et al. [Langmuir 29, 8275 (2013)]. The former provides more realistic picture of multi-ion transport and demonstrates a surprising steady-state effect due to the asymmetry in the diffusivity of hydroxide and hydronium.

Understanding Multi-Ion Transport Mechanisms in Bipolar Membranes

“…Modeling efforts for reverse bias BPMs attempted to replicate 4-probe experiments by solving the Poisson equation locally near the junction 47,53 or with continuum transport models of the entire BPM based on a modified Poisson-Nernst-Planck formulation that includes the Second Wien Effect. 36,37,48,[54][55][56][57] Unfortunately, there is a dearth of studies that have attempted to simulate the electrochemical characteristics of BPMs under the high applied pH gradients relevant to implementation in water electrolyzers. Furthermore, the multicomponent nature of the multi-ion transport in the BPM under these conditions necessitates a more complex formalism that accounts for the myriad of interactions present.…”

Novel electroosmotic micromixer configuration based on ion‐selective microsphere

“…Though attention here was restricted to the case of ideal, cationselective membranes, considering generalizations of the basic design to a microreactor, both cation-and anion-selective membranes could be used. The latter are known to lead to water-splitting via the second Wien effect [27], which in addition to the usual pH gradients occurring with concentration polarization offer a means to modulate local pH during mixing. Thus, the basic design itself offers the possibility of a number of microdevices for integrated fluids processing, concentration sensing, or small-scale energy harvest.…”

Ion Transport and Process of Water Dissociation in Electromembrane System with Bipolar Membrane: Modelling of Symmetrical Case

“…Thirdly, in a sufficiently large number of works [11,13,16,[34][35][36][37] to describe the process of water dissociation in the region of the space charge of bipolar membranes, the dependence of the rate constant of water dissociation on the electric field strength, predicted by the Onsager theory for the second Wien effect, is used [38]. The value of the rate constant of the reverse reaction -the recombination of ions -is considered independent of the field strength.…”

“…The first mathematical models for describing the current-voltage characteristics of a bipolar membrane were based on the assumption of the appearance of a space-charge region at the cation-exchanger/anion-exchanger interface, by analogy with the p-n junction region in semiconductors (depleted layer model) [8][9][10][11][12][13][14]. According to this model, in the space charge region, the concentration of mobile ions is very low compared to the Disclaimer/Publisher's Note: The statements, opinions, and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s).…”