Current-induced membrane discharge

Possible mechanisms for over-limiting current (OLC) through aqueous ion-exchange membranes (exceeding diffusion limitation) have been debated for half a century. Flows consistent with electro-osmotic instability (EOI) 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. Salt depletion leads to a large electric field which expels water co-ions, causing the membrane to discharge and lose its selectivity. Since salt co-ions and water ions contribute to OLC, CIMD interferes with electrodialysis (salt counter-ion removal) but could be exploited for current-assisted ion exchange and pH control. CIMD also suppresses the extended space charge that leads to EOI, so it should be reconsidered in both models and experiments on OLC.Comment: 4.5 page

Time-dependent ion selectivity in capacitive charging of porous electrodes

In a combined experimental and theoretical study, we show that capacitive charging of porous electrodes in multicomponent electrolytes may lead to the phenomenon of time-dependent ion selectivity of the electrical double layers (EDLs) in the electrodes. This effect is found in experiments on capacitive deionization of water containing NaCl/CaCl2 mixtures, when the concentration of Na+ ions in the water is five times the Ca2+-ion concentration. In this experiment, after applying a voltage difference between two porous carbon electrodes, first the majority monovalent Na+ cations are preferentially adsorbed in the EDLs, and later, they are gradually replaced by the minority, divalent Ca2+ cations. In a process where this ion adsorption step is followed by washing the electrode with freshwater under open-circuit conditions, and subsequent release of the ions while the cell is short-circuited, a product stream is obtained which is significantly enriched in divalent ions. Repeating this process three times by taking the product concentrations of one run as the feed concentrations for the next, a final increase in the Ca2+/Na+-ratio of a factor of 300 is achieved. The phenomenon of time-dependent ion selectivity of EDLs cannot be explained by linear response theory. Therefore, a nonlinear time-dependent analysis of capacitive charging is performed for both porous and flat electrodes. Both models attribute time-dependent ion selectivity to the interplay between the transport resistance for the ions in the aqueous solution outside the EDL, and the voltage-dependent ion adsorption capacity of the EDLs. Exact analytical expressions are presented for the excess ion adsorption in planar EDLs (Gouy-Chapman theory) for mixtures containing both monovalent and divalent cations

Imposed currents in galvanic cells

We analyze the steady-state behavior of a general mathematical model for reversible galvanic cells, such as redox flow cells, reversible solid oxide fuel cells, and rechargeable batteries. We consider not only operation in the galvanic discharging mode, spontaneously generating a positive current against an external load, but also operation in two modes which require a net input of electrical energy: (i) the electrolytic charging mode, where a negative current is imposed to generate a voltage exceeding the open-circuit voltage, and (ii) the “super-galvanic” discharging mode, where a positive current exceeding the short-circuit current is imposed to generate a negative voltage. Analysis of the various (dis-)charging modes of galvanic cells is important to predict the efficiency of electrical to chemical energy conversion and to provide sensitive tests for experimental validation of fuel cell models. In the model, we consider effects of diffuse charge on electrochemical charge-transfer rates by combining a generalized Frumkin-Butler-Volmer equation for reaction kinetics across the compact Stern layer with the full Poisson-Nernst-Planck transport theory, without assuming local electroneutrality. Since this approach is rare in the literature, we provide a brief historical review. To illustrate the general theory, we present results for a monovalent binary electrolyte, consisting of cations, which react at the electrodes, and non-reactive anions, which are either fixed in space (as in a solid electrolyte) or are mobile (as in a liquid electrolyte). The full model is solved numerically and compared to analytical results in the limit of thin diffuse layers, relative to the membrane thickness. The spatial profiles of the ion concentrations and electrostatic potential reveal a complex dependence on the kinetic parameters and the imposed current, in which the diffuse charge at each electrode and the total membrane charge can have either sign, contrary perhaps to intuition. For thin diffuse layers, simple analytical expressions are presented for galvanic cells valid in all three (dis-)charging modes in the two subsequent limits of the ratio δ of the effective thicknesses of the compact and diffuse layers: (i) the “Helmholtz limit” (δ → ∞) where the compact layer carries the double layer voltage as in standard Butler-Volmer models, and (ii) the opposite “Gouy-Chapman limit” (δ → 0) where the diffuse layer fully determines the charge-transfer kinetics. In these limits, the model predicts both reaction-limited and diffusion-limited currents, which can be surpassed for finite positive values of the compact layer, diffuse layer and membrane thickness

Ionic currents exceeding the diffusion limitation in planar nano-cavities

Theory predicts that ionic currents through electrochemical cells at nanometer scale can exceed the diffusion limitation due to an expansion of the interfacial electrostatic double layer. Corresponding voltammetry experiments revealed a clear absence of a plateau for the current, which cannot be described by the classical Butler–Volmer approach using realistic values for the transfer coefficient. We show that extending the classical approach by considering the double layer structure using the Frumkin correction leads to an accurate description of the anomalous experimental data. Keywords: Frumkin–Butler–Volmer equation, Double layer, Poisson–Nernst–Planck theory, Diffusion-limiting current, Nano-electrochemistr

Theory of electrochemical cells and its application to plastic-encapsulated IC reliability

MicroelectronicsElectrical Engineering, Mathematics and Computer Scienc

Frumkin–Butler–Volmer Theory and Mass Transfer in Electrochemical Cells1

An accurate mathematical description of the charge transfer rate at electrodes due to an electrochemical reaction is an indispensable component of any electrochemical model. In the current work we use the generalized Frumkin-Butler–Volmer (gFBV) equation to describe electrochemical reactions, an equation which, contrary to the classical Butler–Volmer approach, includes the effect of the double layer composition on the charge transfer rate. The gFBV theory is transparently coupled to the Poisson–Nernst–Planck ion transport theory to describe mass transfer in an electrochemical cell that consists of two parallel plate electrodes which sandwich a monovalent electrolyte. Based on this theoretical approach we present analytical relations that describe the complete transient response of the cell potential to a current step, from the first initial capacitive charging of the bulk electrolyte and the double layers all the way up to the steadystate of the system. We show that the transient response is characterized by three distinct time scales, namely; the capacitive charging of the bulk electrolyte at the fastest Debye time scale, and the formation of the double layers and the subsequent redistribution of ions in the bulk electrolyte at the longer harmonic and diffusion time scales, respectively.Materials Innovation InstituteMechanical, Maritime and Materials Engineerin

Dissolution properties of cerium dibutylphosphate corrosion inhibitors

The corrosion inhibitor cerium dibutylphosphate, Ce(dbp)3, prevents corrosion by cerium and dbp deposition at the alkaline cathode and acidic anode respectively. The pH dependent Ce(dbp)3 solubility seems to play an essential role in the inhibition degree. We found that Ce(dbp)3 scarcely dissolves in water with a ~1 mM solubility limit between pH 2 and 9, whereas at pH 1, we found ~3 mM due to protonation of dbp, and for pH >9, the cerium precipitated as Ce(OH)3. We believe that the Ce(dbp)3 dissolution process is an important aspect for understanding its release from coatings and thus the corrosion inhibition. In case of a pressed Ce(dbp)3 tablet, its dissolution is dominated by transport of dissolved Ce(dbp)3 across a stagnant diffusion layer. The chemical bond strength between cerium and dbp is a major factor in their transport. The infrared spectrum of Ce(dbp)3 powder revealed a covalent-like bond, while the molar conductivity showed complete dissociation, so Ce(dbp)3 transports in water as separate ions

Diffuse-charge effects on the transient response of electrochemical cells

We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or “space charge”) near the electrodes on Faradaic reaction kinetics. The full model is based on the classical Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions to describe electron-transfer reactions across the Stern layer at the electrode surface. In practical situations, diffuse charge is confined to thin diffuse layers (DLs), which poses numerical difficulties for the full model but allows simplification by asymptotic analysis. For a thin quasi-equilibrium DL, we derive effective boundary conditions on the quasi-neutral bulk electrolyte at the diffusion time scale, valid up to the transition time, where the bulk concentration vanishes due to diffusion limitation. We integrate the thin-DL problem analytically to obtain a set of algebraic equations, whose (numerical) solution compares favorably to the full model. In the Gouy-Chapman and Helmholtz limits, where the Stern layer is thin or thick compared to the DL, respectively, we derive simple analytical formulas for the cell voltage versus time. The full model also describes the fast initial capacitive charging of the DLs and superlimiting currents beyond the transition time, where the DL expands to a transient non-equilibrium structure. We extend the well-known Sand equation for the transition time to include all values of the superlimiting current beyond the diffusion-limiting current.Materials Innovation Institute M2i (Project No. MC3.05236)National Science Foundation (U.S.) (Contract No. No. DMS-0855011)National Science Foundation (U.S.) (Contract No. DMS-0842504

Effect of interfacial transport on the diffusivity of highly filled polymers

The diffusivity of substances, such as moisture, through polymer composites is often described by an effective macroscopic quantity, even though microscopically the diffusivity might be far from uniform. In this work, we study the theoretical example of a permeable matrix containing equal-sized impermeable spheres. We assume that, due to interface effects, the diffusivity of the matrix in the vicinity of the spheres is higher than its bulk matrix diffusivity. Using numerical simulations of the composite's diffusivity, we show that upon the formation of large clusters of the highly permeable interfaces, i.e. near percolation of the spheres, the diffusivity of the composite rises sharply. For even higher values of the volume fraction of the spheres, up to the close-packing limit, the diffusivity decreases due to the increased tortuosity. This effect is well described by an analytical solution for the composite's diffusivity

Inhibition of electrokinetic ion transport in porous materials due to potential drops induced by electrolysis

In this work we present non-destructive measurements of sodium ion concentration profiles during the electrokinetic removal of sodium chloride from porous materials using Nuclear Magnetic Resonance (NMR). The effect of both protons and hydroxyl ions, generated due to the electrolysis of water, on the transport of the salt ions is studied by tracking the acidic and alkaline fronts using pH-indicator paper. In addition, the electrical potential distribution within the specimen is monitored to assess its influence on the process. To support the observations we compare the experimental results with a theoretical model based on the Poisson–Nernst–Plank equations. In this model we use the chemical equilibrium condition for the self-electrolysis of water in the description of the transport of protons and hydroxyl ions. In addition we use the electro-neutrality condition to compute the transport of salt ions through the material. At the edges of the system the electrical current is distributed over the chemical active species, i.e. protons, hydroxyl and chloride ions, according to the Butler–Volmer description for charge transfer at electrodes. Both the experimental and model results show in the final stage of the electrokinetic remediation process a sharp transition from the acidic to alkaline region at one third of the length of the specimen away from the positively biased electrode, i.e. the anode. From the model results we found that the formation of chlorine gas at the anode does not influence the position of this transition area. In this transition region we also observe a large gradient in electrical potential and a corresponding local deficit of ions. As a result of the large potential gradient in this small transition zone the electrical field in the acidic and alkaline region diminishes. Consequently, electrokinetic ion transport though the material will stagnate