Thermodynamic Relation between Voltage-Concentration Dependence and Salt Adsorption in Electrochemical Cells

Abstract

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.

Modification of the surface of activated carbon electrodes for capacitive mixing energy extraction from salinity differences

“…φ L > φ H ) and negative (φ L < φ H ) potential rise, respectively; in all the studied cases, this means that they adsorb anions and cations, respectively. The relation between the voltage rise and the salt adsorption has been recently studied [18]. It's worth noting that the notion of positive-and negative-potential-rise does not mean that the electrode is the "positive" or the "negative" electrode of a given couple, like in batteries, nor is it related to the behavior as "anode" or "cathode" in an electrochemical cell.…”

“…In particular, an accurate modeling of the experimental results, which was developed for CDI [40], predicts also in this case two plateaus at ±80 mV for the potential rise. It is worth noting that there is a thermodynamical relation [18] between the desalination charge efficiency of the above-mentioned models [40] and the potential rise of CAPMIX, that holds in equilibrium conditions. The apparent discrepancy that we observe between the capacitive deionization experiments and our CAPMIX potential rises should lead to the conclusion that the latter are not obtained in equilibrium conditions; indeed, they are measured on time scales that are shorter than that of the CDI experiments.…”

“…This process can be described as a capacitormediated mixing, hence the name "capacitive mixing". It is thus evident that the energy is extracted at the expense a 000000 000000 000000 000000 000000 000000 000000 000000 of the free energy of the solutions; indeed, it has been shown that the voltage rise is connected with the ability of the electrodes to store the salt inside them, when they are charged during phase A [18].…”

Electric Double-Layer Structure in Primitive Model Electrolytes: Comparing Molecular Dynamics with Local-Density Approximations

“…ex (8) which, when nondimensionalized by 2qen B , is given by (13) Closing the LDA description requires a form for the excess chemical potentials μẽ x ± , after which the LDA equations can be solved self-consistently by imposing constraints on the electrostatic potential at the charged interface (14) and in the bulk…”

“…1,18 As described by Gillespie in a recent review, 19 they can also fail on more basic theoretical grounds near interfaces or electrodes if locally averaged concentrations are not used, where the averaging is performed over an ion-sized volume. Despite these well-known shortcomings, LDA models have been proposed to treat shortranged enthalpic 20 and steric interactions between equisized 21,22 and asymmetric 23 ions for ionic liquids, 24 electrochemical cells, 6,13 and liquid−liquid interfaces. 8,10 We recently showed that all EDLs described by any particular LDA have self-similar scaling and thus collapse onto a single master curve when plotted against suitably derived similarity coordinates.…”