Double-Layer Capacitances Caused by Ion–Solvent Interaction in the Form of Langmuir-Typed Concentration Dependence

Variations of the double layer capacitances (DLCs) at a platinum electrode with concentrations and kinds of salts in aqueous solutions were examined in the context of facilitating orientation of solvent dipoles. With an increase in ionic concentrations, the DLCs increased by ca. a half and then kept constant at concentrations over 1 mol dm−3. This increase was classically explained in terms of the Gouy–Chapman (GC) equation combined with the Stern model. Unfortunately, measured DLCs were neither satisfied with the Stern model nor the GC theory. Our model suggests that salts destroy hydrogen bonds at the electrode–solution interface to orient water dipoles toward the external electric field. A degree of the orientation depends on the interaction energy between the salt ion and a water dipole. The statistical mechanic calculation allowed us to derive an equation for the DLC as a function of salt concentration and the interaction energy. The equation took the Langmuir-type in the relation with the concentration. The interaction energy was obtained for eight kinds of salts. The energy showed a linear relation with the interaction energy of ion–solvent for viscosity, called the B-coefficient.

Parallel Combination of Inner Capacitance and Ionic Capacitance, Apparently Inconsistent with Stern’s Model

A double layer capacitance (DLC) has mainly been brought about in the Helmholtz layer rather than in the diffuse layer, as was demonstrated with the invariance of DLC to salt concentration, c, less than 0.5 M (M = mol dm−3). The DLC measured here increased with concentrations of KCl and HCl solutions as high as 1 M at a platinum electrode by the ac impedance method. It was represented as a sum of the Helmholtz capacitance and the ionic one which had 0.7 power of the concentrations. The simple addition implies that the Helmholtz contribution and the ionic one should be represented by a parallel combination rather than a series one such as in the Stern model. The disagreement of the experimental values of the DLC with the Gouy–Chapman theory at high concentrations has been conventionally attributed to the effects of packing of ions over their sizes. In this paper, a model of avoiding the packing was introduced, in which ions were distributed in the direction normal to the electrode in the balance of electric motive force and the thermal energy, keeping the uniform distribution on a plane projected to the electrode. The energy balance was taken by using the grand canonical ensemble in statistical mechanics. The ionic contribution had a linear relation with the applied voltage rather than exponential dependence. When a series combination was applied to the Helmholtz capacitance and the ionic one under the condition of difference between the locally anionic DLC and the cationic one, we obtained approximately a parallel combination of the two capacitances because either the anionic or the cationic DLC works predominantly.

Participation in Negative Capacitance of Diffusion-Controlled Voltammograms of Hemin

Hemin in dimethyl sulfoxide solution has exhibited voltammograms controlled by diffusion at glassy carbon electrodes for slow scan rates, although it is adsorbed slightly. In contrast, voltammograms for high scan rates, v > 1 V s^-1, were governed by some kinds of kinetics judging from the scan rate dependence of peaks. The kinetics is close to that of a ferrocenyl derivative, in which the currents include the capacitive component with negative values. The capacitive one can be identified with the proportionality to the scan rates. The variation of the peak currents with v yielded -200 μF cm^-2. This negative value, being associated with the charge transfer reaction, makes cyclic voltammograms deviated downward from the diffusion-controlled behavior, resembling an irreversible reaction of the Butler-Volmer kinetics. Double layer capacitances are generally formed so that the applied electric field may be relaxed. The reduction of hemin forms a dipole coupled with a cation of the salt. The dipole orients from the electrode to the bulk, whereas the solvent dipoles orients in the opposite direction. Therefore, the capacitance is observed negatively. The capacitance determined by ac impedance took also negative values when the applied dc potential was only in the potential domain for the charge transfer. These complications can be avoided in electrocatalysis by use of such slow voltammetry as scan rates of 0.1 V s^-1 and ac frequency of 0.2 Hz.

Structure of the Electrical Double Layer Revisited: Electrode Capacitance in Aqueous Solutions

The structure of the electrical double layer at the interface of planar electrodes and aqueous solutions is investigated. Electrical impedance spectroscopy is used to measure the impedance of aqueous solutions of sodium chloride and two different surfactants over a wide range of concentrations. The electrode capacitance is directly inferred from the admittance spectra as well as by regression of the impedance spectra to an equivalent circuit. It is found that the electrode capacitance remains on the same order of magnitude over the entire range of investigated concentrations. This is contradictive to the predictions of the Gouy-Chapman-Stern theory which predicts that, at low concentrations, the electrode capacitance should be determined by the diffuse layer. It is concluded that the Stern layer capacitance always dominates the electrode capacitance, even at very low concentrations, and the establishment of a diffuse layer capacitance requires an ionic strength of around 1 mM.

Potential Step for Double-Layer Capacitances Obeying the Power Law

Potential-step chronoamperometry was made at a platinum wire electrode in KCl aqueous solution at the aim of finding the behavior of the power law of the time or the constant phase element for the double-layer (DL) capacitances. The logarithmic current decays linearly with the time shorter than 0.1 ms, and then it obeys the power law in which it has a linear relation with the logarithmic time in the millisecond time domain. The transition from the exponential decay to the power law was expressed theoretically for the model of a series combination of the resistance and the DL capacitance. The expression predicts that the double logarithmic plots of the current-time provide a capacitance value at 1 s from the intercept, independent of the resistance. This prediction was demonstrated experimentally in KCl solutions of which concentrations ranged from 1 mM to 0.5 M. The capacitance can be evaluated simply by chronoamperometry on a 1 s time scale without considering any resistance effect. The capacitance values did not vary with the applied potential.