Transport-limited water splitting at ion-selective interfaces during concentration polarization

Approximate time-dependent current-voltage relations for currents exceeding the diffusion limit

The time-dependent behavior of one-dimensional ion transport into a permselective medium is theoretically modeled in this work for currents exceeding the diffusion limit. Leveraging the findings of Yariv [E. Yariv, Phys. Rev. E 80, 051201 (2009)10.1103/PhysRevE.80.051201], we derive three separate expressions for the potential drop for short, intermediate, and long times. We show that the potential drop correlates to the time evolution of the space-charge layer adjacent to the permselective interface. Our approximate models show remarkable correspondence to numerical simulations.

Theory of pH changes in water desalination by capacitive deionization

In electrochemical water desalination, a large difference in pH can develop between feed and effluent water. These pH changes can affect the long-term stability of membranes and electrodes. Often Faradaic reactions are implicated to explain these pH changes. However, quantitative theory has not been developed yet to underpin these considerations. We develop a theory for electrochemical water desalination which includes not only Faradaic reactions but also the fact that all ions in the water have different mobilities (diffusion coefficients). We quantify the latter effect by microscopic physics-based modeling of pH changes in Membrane Capacitive Deionization (MCDI), a water desalination technology employing porous carbon electrodes and ion-exchange membranes. We derive a dynamic model and include the following phenomena: I) different mobilities of various ions, combined with acid-base equilibrium reactions; II) chemical surface charge groups in the micropores of the porous carbon electrodes, where electrical double layers are formed; and III) Faradaic reactions in the micropores. The theory predicts small pH changes during desalination cycles in MCDI if we only consider phenomena I) and II), but predicts that these pH changes can be much stronger if we consider phenomenon III) as well, which is in line with earlier statements in the literature on the relevance of Faradaic reactions to explain pH fluctuations.

Morphological instability during steady electrodeposition at overlimiting currents

We present a linear stability analysis of a planar metal electrode during steady electrodeposition. We extend the previous work of Sundstrom and Bark by accounting for the extended space-charge density, which develops at the cathode once the applied voltage exceeds a few thermal voltages. In accordance with Chazalviel's conjecture, the extended space-charge region is found to greatly affect the morphological stability of the electrode. To supplement the numerical solution of the stability problem, we have derived analytical expressions valid in the limit of low and high voltage, respectively.

Sharp-interface model of electrodeposition and ramified growth

We present a sharp-interface model of two-dimensional ramified growth during quasisteady electrodeposition. Our model differs from previous modeling methods in that it includes the important effects of extended space-charge regions and nonlinear electrode reactions. The electrokinetics is described by a continuum model, but the discrete nature of the ions is taken into account by adding a random noise term to the electrode current. The model is validated by comparing its behavior in the initial stage with the predictions of a linear stability analysis. The main limitations of the model are the restriction to two dimensions and the assumption of quasisteady transport.

Ion transport through electrolyte/polyelectrolyte multi-layers

Ion transport of multi-ionic solutions through layered electrolyte and polyelectrolyte structures are relevant in a large variety of technical systems such as micro and nanofluidic devices, sensors, batteries and large desalination process systems. We report a new direct numerical simulation model coined E_nPE_n: it allows to solve a set of first principle equations to predict for multiple ions their concentration and electrical potential profiles in electro-chemically complex architectures of n layered electrolytes E and n polyelectrolytes PE. E_nPE_n can robustly capture ion transport in sub-millimeter architectures with submicron polyelectrolyte layers. We proof the strength of E_nPE_n for three yet unsolved architectures: (a) selective Na over Ca transport in surface modified ion selective membranes, (b) ion transport and water splitting in bipolar membranes and (c) transport of weak electrolytes.

Concentration polarization, surface currents, and bulk advection in a microchannel

We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behavior of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk advection and the surface current; without a surface current, bulk advection is strongly suppressed. The numerical simulations are supplemented by analytical models valid in the long channel limit as well as in the limit of negligible surface charge. By including the effects of diffusion and advection in the diffuse part of the electric double layers, we extend a recently published analytical model of overlimiting current due to surface conduction.

Spatiotemporal pH dynamics in concentration polarization near ion-selective membranes

We present a detailed analysis of the transient pH dynamics for a weak, buffered electrolyte subject to voltage-driven transport through an ion-selective membrane. We show that pH fronts emanate from the concentration polarization zone next to the membrane and that these propagating fronts change the pH in the system several units from its equilibrium value. The analysis is based on a 1D model using the unsteady Poisson-Nernst-Planck equations with nonequilibrium chemistry and without assumptions of electroneutrality or asymptotically thin electric double layers. Nonequilibrium chemical effects, especially for water splitting, are shown to be important for the dynamical and spatiotemporal evolution of the pH fronts. Nonetheless, the model also shows that at steady state the assumption of chemical equilibrium can still lead to good approximations of the global pH distribution. Moreover, our model shows that the transport of the hydronium ion in the extended space charge region is governed by a balance between electromigration and water self-ionization. On the basis of this observation, we present a simple model showing that the net flux of the hydronium ion is proportional to the length of the extended space charge region and the water self-ionization rate. To demonstrate these effects in practice, we have adopted the experiment of Mai et al. (Mai, J.; Miller, H.; Hatch, A. V. Spatiotemporal Mapping of Concentration Polarization Induced pH Changes at Nanoconstrictions. ACS Nano 2012, 6, 10206) as a model problem, and by including the full chemistry and transport, we show that the present model can capture the experimentally observed pH fronts. Our model can, among other things, be used to predict and engineer pH dynamics, which can be essential to the performance of membrane-based systems for biochemical separation and analysis.