Diffuse charge and Faradaic reactions in porous electrodes

Thermodynamic relation between voltage-concentration dependence and salt adsorption in electrochemical cells

Electrochemical cells containing two electrodes dipped in an ionic solution are widely used as charge accumulators, either with polarizable (supercapacitor) or nonpolarizable (battery) electrodes. Recent applications include desalination ("capacitive deionization") and energy extraction from salinity differences ("capacitive mixing"). In this Letter, we analyze a general relation between the variation of the electric potential as a function of the concentration and the salt adsorption. This relation comes from the evaluation of the electrical and mechanical energy exchange along a reversible cycle, which involves salt adsorption and release by the electrodes. The obtained relation thus describes a connection between capacitive deionization and capacitive mixing. We check this relation with experimental data already reported in the literature, and moreover by some classical physical models for electrodes, including polarizable and nonpolarizable electrodes. The generality of the relation makes it very useful in the study of the properties of the electric double layer.

Ions Transport and Adsorption Mechanisms in Porous Electrodes During Capacitive-Mixing Double Layer Expansion (CDLE)

A model of the electro-diffusion of ions in porous electrodes is applied to analyze the dynamics of capacitive-mixing extraction of energy from salinity gradients with carbon porous electrodes. The complex time-evolution of the cell voltage observed in experiments is satisfactorily described. The asymmetry on the duration of the solution-change steps performed in open circuit is found to be due to the nonlinear voltage-concentration relationship of the electric double layers and to a current that redistributes the counterions along the depth of the electrode leading to nonuniform charge and salt adsorption. The validated model is an essential tool for the design and optimization of renewable energy extraction by this technique.

Water desalination using capacitive deionization with microporous carbon electrodes

Capacitive deionization (CDI) is a water desalination technology in which salt ions are removed from brackish water by flowing through a spacer channel with porous electrodes on each side. Upon applying a voltage difference between the two electrodes, cations move to and are accumulated in electrostatic double layers inside the negatively charged cathode and the anions are removed by the positively charged anode. One of the key parameters for commercial realization of CDI is the salt adsorption capacity of the electrodes. State-of-the-art electrode materials are based on porous activated carbon particles or carbon aerogels. Here we report the use for CDI of carbide-derived carbon (CDC), a porous material with well-defined and tunable pore sizes in the sub-nanometer range. When comparing electrodes made with CDC with electrodes based on activated carbon, we find a significantly higher salt adsorption capacity in the relevant cell voltage window of 1.2-1.4 V. The measured adsorption capacity for four materials tested negatively correlates with known metrics for pore structure of the carbon powders such as total pore volume and BET-area, but is positively correlated with the volume of pores of sizes <1 nm, suggesting the relevance of these sub-nanometer pores for ion adsorption. The charge efficiency, being the ratio of equilibrium salt adsorption over charge, does not depend much on the type of material, indicating that materials that have been identified for high charge storage capacity can also be highly suitable for CDI. This work shows the potential of materials with well-defined sub-nanometer pore sizes for energy-efficient water desalination.

Numerical study on the bulk instability of constant-current conduction in cation-exchange membranes

Numerical simulation of two-dimensional bulk instability of the one-dimensional conduction state in an electrolyte confined between a pair of cation-exchange membranes subjected to an external voltage is conducted under an assumption of constant current. By employing variable grids, we resolve the problem of sensitive dependence of the numerical solutions to the grid refinement in particular at a current close to the limiting value. In fact, the full range of parameters, i.e., Schmidt number, Peclet number, diffusivity ratio, and current, is considered in this study in obtaining the stability chart. It turns out that the Schmidt number exerts almost no influence on the results. From the neutral curves in the chart of the parameter space (current versus diffusivity ratio, i.e., cation diffusivity divided by anion diffusivity) we confirm that the system tends to be unstable at high Peclet numbers, high currents, and low diffusivity ratios. As the diffusivity ratio is increased the instability mode switches from the monotonic to the oscillatory type, and the critical diffusivity ratio for the switching is found to be decreased as the Peclet number decreases. At the switching, no jump in the neutral curves is found, contrary to the earlier result, because the wave number is set free to change in this study. The stability chart obtained in this study represents the true boundaries in discriminating the stable from the unstable parameter sets because the critical eigenvalues constituting the chart are sought for the entire possible range of the wave numbers and the frequencies.

Deionization shocks in microstructures

Salt transport in bulk electrolytes is limited by diffusion and advection, but in microstructures with charged surfaces (e.g., microfluidic devices, porous media, soils, or biological tissues) surface conduction and electro-osmotic flow also contribute to ionic fluxes. For small applied voltages, these effects lead to well known linear electrokinetic phenomena. In this paper, we predict some surprising nonlinear dynamics that can result from the competition between bulk and interfacial transport at higher voltages. When counterions are selectively removed by a membrane or electrode, a "deionization shock" can propagate through the microstructure, leaving in its wake an ultrapure solution, nearly devoid of coions and colloidal impurities. We elucidate the basic physics of deionization shocks and develop a mathematical theory of their existence, structure, and stability, allowing for slow variations in surface charge or channel geometry. Via asymptotic approximations and similarity solutions, we show that deionization shocks accelerate and sharpen in narrowing channels, while they decelerate and weaken, and sometimes disappear, in widening channels. These phenomena may find applications in separations (deionization, decontamination, biological assays) and energy storage (batteries, supercapacitors) involving electrolytes in microstructures.