Current-induced concentration polarization of interfaces between non-ideally perm-selective ion-exchange media and electrolyte solutions

Analysis of electrolyte transport through charged nanopores

We revisit the classical problem of flow of electrolyte solutions through charged capillary nanopores or nanotubes as described by the capillary pore model (also called "space charge" theory). This theory assumes very long and thin pores and uses a one-dimensional flux-force formalism which relates fluxes (electrical current, salt flux, and fluid velocity) and driving forces (difference in electric potential, salt concentration, and pressure). We analyze the general case with overlapping electric double layers in the pore and a nonzero axial salt concentration gradient. The 3×3 matrix relating these quantities exhibits Onsager symmetry and we report a significant new simplification for the diagonal element relating axial salt flux to the gradient in chemical potential. We prove that Onsager symmetry is preserved under changes of variables, which we illustrate by transformation to a different flux-force matrix given by Gross and Osterle [J. Chem. Phys. 49, 228 (1968)JCPSA60021-960610.1063/1.1669814]. The capillary pore model is well suited to describe the nonlinear response of charged membranes or nanofluidic devices for electrokinetic energy conversion and water desalination, as long as the transverse ion profiles remain in local quasiequilibrium. As an example, we evaluate electrical power production from a salt concentration difference by reverse electrodialysis, using an efficiency versus power diagram. We show that since the capillary pore model allows for axial gradients in salt concentration, partial loops in current, salt flux, or fluid flow can develop in the pore. Predictions for macroscopic transport properties using a reduced model, where the potential and concentration are assumed to be invariant with radial coordinate ("uniform potential" or "fine capillary pore" model), are close to results of the full model.

Teorell instability in concentration polarization

We investigate the development of electro-osmotic (Teorell) oscillations at a weakly charged microporous membrane without a preimposed transmembrane electrolyte concentration drop. This drop, necessary for the occurrence of oscillations, develops spontaneously as a result of concentration polarization in the solution layers adjacent to the membrane. A three-layer model comprising a membrane flanked by two diffusion layers is proposed and analyzed for galvano- and potentiostatic regimes of operation.

Coating of Nafion membranes with polyelectrolyte multilayers to achieve high monovalent/divalent cation electrodialysis selectivities

Electrodialysis (ED) membranes typically exhibit modest selectivities between monovalent and divalent ions. This paper reports a dramatic enhancement of the monovalent/divalent cation selectivities of Nafion 115 membranes through coating with multilayer poly(4-styrenesulfonate) (PSS)/protonated poly(allylamine) (PAH) films. Remarkably, K(+)/Mg(2+) ED selectivities reach values >1000, and similar monovalent/divalent cation selectivities occur with feed solutions containing K(+) and Ca(2+). For comparison, the corresponding K(+)/Mg(2+) selectivity of bare Nafion 115 is only 1.8 ± 0.1. However, with 0.01 M KNO3 and 0.01 M Mg(NO3)2 in the source phase, as the applied current density increases from 1.27 to 2.54 mA cm(-2), the K(+)/Mg(2+) selectivities of coated membranes decrease from >1000 to 22. Water-splitting at strongly overlimiting current densities may lead to a local pH increase close to the membrane surface and alter film permeability or allow passage of Mg(OH)x species to decrease selectivity. When the source phase contains 0.1 M KNO3 and 0.1 M Mg(NO3)2, the K(+) transference number approaches unity and the K(+)/Mg(2+) selectivity is >20,000, presumably because the applied current is below the limiting value for K(+) and H(+) transport is negligible at this high K(+) concentration. The high selectivities of these membranes may enable electrodialysis applications such as purification of salts that contain divalent or trivalent ions.

Current-induced membrane discharge

Possible mechanisms for overlimiting current (OLC) through aqueous ion-exchange membranes (exceeding diffusion limitation) have been debated for half a century. Flows consistent with electro-osmotic instability have recently been observed in microfluidic experiments, but the existing theory neglects chemical effects and remains to be quantitatively tested. Here, we show that charge regulation and water self-ionization can lead to OLC by "current-induced membrane discharge" (CIMD), even in the absence of fluid flow, in ion-exchange membranes much thicker than the local Debye screening length. Salt depletion leads to a large electric field resulting in a local pH shift within the membrane with the effect that the membrane discharges and loses its ion selectivity. Since salt co-ions, H(+) ions, and OH(-) ions contribute to OLC, CIMD interferes with electrodialysis (salt counterion removal) but could be exploited for current-assisted ion exchange and pH control. CIMD also suppresses the extended space charge that leads to electro-osmotic instability, so it should be reconsidered in both models and experiments on OLC.