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Overlimiting Current and Shock Electrodialysis in Porous Media

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Overlimiting Current and Shock Electrodialysis in Porous Media ( overlimiting-current-and-shock-electrodialysis-porous-media )

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Langmuir Article the electron charge, D is the cation diffusion coefficient, c0 is the reservoir ion concentration, and L is the diffusion length from the reservoir to the selective surface. Above the thermal voltage, V ≫ kBT/e (= 26 mV at room temperature), the current saturates, I → Ilim, like a diode under reverse bias. In practice, an overlimiting current (OLC), which exceeds Ilim, is often observed, and its possible origins have long been debated.10 For bulk transport, the consensus is that OLC can arise from chemical effects, which create more ions10,13 or reduce membrane selectivity,14 or from convection by electro- osmotic instability near the membrane.15−18 More intriguingly, it has recently been predicted that surface transport can also sustain OLC in a microchannel by electroosmotic flow19 (EOF) or surface conduction12 (SC) along the side walls, depending on the aspect ratio and surface charge. The new theory12 may explain different ion concentration polarization (ICP) phenomena observed at micro/nanochannel junc- tions.20,21 A surprising feature of microfluidic experiments in the regime of overlimiting current is the tendency for the depleted region to form a very sharp boundary with the bulk electrolyte,20,22,23 which can be understood as a shock wave in the salt concentration, propagating against the flow.24−26 It has recently been predicted that stable “deionization shocks” can also propagate in porous media at constant current,27−29 and the theory predicts steady OLC in a finite system at constant voltage (Figure 1d−f).12,28,29 In this article, we investigate OLC experimentally in materials with a submicrometer mean pore size. The results are consistent with theoretical predictions and reveal some basic principles of nonlinear electrokinetics in porous media. Classical electrokinetic phenomena, such as the streaming potential and electroosmotic flow, are defined by the linear response of flow or current to a small applied voltage or pressure,9 but relatively little is known about the nonlinear response of a porous medium to a large voltage (V ≫ kBT/e = 26 mV at room temperature). In contrast to recent work on induced-charge electrokinetics in polarizable media,30 we focus on surfaces of (nearly) fixed charge and report the first experimental evidence that surface transport can sustain OLC and deionization shocks over macroscopic distances in a porous m■edium. THEORY Overlimiting Conductance. The classical theory of ICP assumes a homogeneous bulk electrolyte,9 but there is a growing realization that new nonlinear electrokinetic phenom- ena arise when the electrolyte is weakly confined by charged surfaces aligned with the applied current.12,19,24−29,31−33 Under strong confinement with overlapping double layers, a nano- channel or pore acts as a counterion-selective membrane because the pore is effectively “all surface”.34 Under weak confinement with thin double layers, it is well known that surface conduction plays only a small role in linear electro- kinetic phenomena because the total excess surface conductivity is much smaller than the total bulk conductivity (small Dukhin number).35 ICP alters this picture, and surprisingly, surface- driven transport can dominate at high voltage, even with initially thin double layers. A simple theory of OLC in a microchannel was recently proposed by our group.12 In thin or highly charged channels, the dominant mechanism is SC, and in thick or weakly charged channels, it is EOF, as long as the viscosity is also low enough Figure 2. Electroosmotic flow (EOF) mechanism for overlimiting current through a porous medium (brown) to an impermeable counterion-selective membrane (right). Strong EOF (red arrows) in the depleted region and pressure-driven back flow (green arrows) produce salty (blue) and depleted (white) fingers in eddies of transverse size, he, centered at lc. (a) Mean salt concentration profile. (b) In a regular microstructure, eddies are confined to parallel pores of size he ≈ hp. (c) In an irregular microstructure, eddies form around connected loops of width he ≈ hl. for sufficiently fast flow. In water with typical surface charges, the predicted transition from SC to EOF occurs at the scale of several micrometers for dilute electrolytes (mM) or tens of nanometers for concentrated electrolytes (M). For both mechanisms, the current−voltage relationship is approximately linear just above the limiting current ⎡ ⎛ zeV⎞⎤ I = Ilim⎢1 − exp⎜−k T⎟⎥ + σOLCV ⎣ ⎝B⎠⎦ (3) as if the surfaces provide a constant shunt resistance to bypass the diodelike response of ICP (Figure 1f). The scalings of σOLC with salt concentration and surface charge allow the mechanism to be distinguished (below), but first we must generalize the theory to porous media. Mechanism 1: Surface Conduction. Even during strong ICP the homogenized effect of SC in porous media without flow can be rigorously described by a volume-averaged electroneutrality condition.27−29 For 1D transport over a distance L from a reservoir to an ideal cation-selective surface in a dilute binary electrolyte, the exact solution yields eq 3 with 2zeAD q σSC≈ ms OLC kBTLhp (4) dx.doi.org/10.1021/la4040547 | Langmuir 2013, 29, 16167−16177 16168

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