A modified Poisson–Boltzmann analysis of the capacitance behavior of the electric double layer at low temperatures

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions

In this work, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions

In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

Temperature dependence of differential capacitance in the electric double layer.Symmetric valency 1:1 electrolytes

The differential capacitance of an electric double layer formed by an aqueous solution of KNO₃ on a glassy carbon electrode is measured by impedance analysis at constant frequency. Results are obtained at electrolyte concentrations of 0.1 mol/dm³, 0.5 mol/dm³, and 1.0 mol/dm³, and at a series of temperatures, viz., 288 K, 298 K, 308 K, 318 K, and 328 K. The differential capacitance envelopes reveal a rich, complex pattern of maxima, minima, and local minima, whose magnitude and position change with a change in solution concentration. At the two lower concentrations, the temperature dependence of the capacitance, for example, at zero electrode potential, shows an alternating positive-negative behavior, while at the highest concentration of 1.0 mol/dm³, the slope of the differential capacitance-electrode potential curve is always positive. The experimental results are supplemented by a numerical grand canonical Monte Carlo simulation study of a restricted primitive model double layer but with an off-center cationic charge achieved by displacing the charge center from the ion sphere center toward its surface. The simulations, performed at the electrolyte concentration of 1.0 mol/dm³ and constant cation charge center displacement, and at varying electrode potentials and temperatures, show, in general, a negative temperature dependence of the differential capacitance. However, this temperature dependence can also be positive for a negative electrode charge and for a sufficiently large gradient of the cation charge center displacement with temperature. This feature is seen to be associated with an increase in the entropy of formation of the double layer.

Theoretical insight into the origin of the electrochemical promotion of ethylene oxidation on ruthenium oxide

In EPOC the adsorption energies of the reactants and products are modified by applying an electrochemical potential to the catalyst. DFT computations unveil that the C–C and O–O bond dissociation are accelerated under positive and negative potential, respectively.

ISFET pH Sensitivity: Counter-Ions Play a Key Role

The Field Effect sensors are broadly used for detecting various target analytes in chemical and biological solutions. We report the conditions under which the pH sensitivity of an Ion Sensitive Field Effect transistor (ISFET) sensor can be significantly enhanced. Our theory and simulations show that by using pH buffer solutions containing counter-ions that are beyond a specific size, the sensor shows significantly higher sensitivity which can exceed the Nernst limit. We validate the theory by measuring the pH response of an extended gate ISFET pH sensor. The consistency and reproducibility of the measurement results have been recorded in hysteresis free and stable operations. Different conditions have been tested to confirm the accuracy and validity of our experiment results such as using different solutions, various oxide dielectrics as the sensing layer and off-the-shelf versus IC fabricated transistors as the basis of the ISFET sensor.

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The venerable theory of electrokinetic phenomena rests on the hypothesis of a dilute solution of point-like ions in quasi-equilibrium with a weakly charged surface, whose potential relative to the bulk is of order the thermal voltage (kT/e approximately 25 mV at room temperature). In nonlinear electrokinetic phenomena, such as AC or induced-charge electro-osmosis (ACEO, ICEO) and induced-charge electrophoresis (ICEP), several V approximately 100 kT/e are applied to polarizable surfaces in microscopic geometries, and the resulting electric fields and induced surface charges are large enough to violate the assumptions of the classical theory. In this article, we review the experimental and theoretical literatures, highlight discrepancies between theory and experiment, introduce possible modifications of the theory, and analyze their consequences. We argue that, in response to a large applied voltage, the "compact layer" and "shear plane" effectively advance into the liquid, due to the crowding of counterions. Using simple continuum models, we predict two general trends at large voltages: (i) ionic crowding against a blocking surface expands the diffuse double layer and thus decreases its differential capacitance, and (ii) a charge-induced viscosity increase near the surface reduces the electro-osmotic mobility; each trend is enhanced by dielectric saturation. The first effect is able to predict high-frequency flow reversal in ACEO pumps, while the second may explain the decay of ICEO flow with increasing salt concentration. Through several colloidal examples, such as ICEP of an uncharged metal sphere in an asymmetric electrolyte, we show that nonlinear electrokinetic phenomena are generally ion-specific. Similar theoretical issues arise in nanofluidics (due to confinement) and ionic liquids (due to the lack of solvent), so the paper concludes with a general framework of modified electrokinetic equations for finite-sized ions.

Simulational and theoretical study of the spherical electrical double layer for a size-asymmetric electrolyte: the case of big coions

Monte Carlo simulations of a spherical macroion, surrounded by a size-asymmetric electrolyte in the primitive model, were performed. We considered 1:1 and 2:2 salts with a size ratio of 2 (i.e., with coions twice the size of counterions), for several surface charge densities of the macrosphere. The radial distribution functions, electrostatic potential in all the space and at the Helmholtz surfaces, and integrated charge are reported. We compare these simulational data with original results obtained from the Ornstein-Zernike integral equation, supplemented by the hypernetted chain-hypernetted chain (HNC-HNC) and hypernetted chain-mean spherical approximation (HNC-MSA) closures, and with the corresponding calculations using the modified Gouy-Chapman and unequal-radius modified Gouy-Chapman theories. The HNC-HNC and HNC-MSA integral equations formalisms show good concordance with Monte Carlo "experiments," whereas the notable limitations of point-ion approaches are evidenced. Most importantly, the simulations confirm our previous theoretical predictions of the nondominance of the counterions in the size-asymmetric spherical electrical double layer [J. Chem. Phys. 123, 034703 (2005)], the appearance of anomalous curvatures at the outer Helmholtz plane, and the enhancement of the charge reversal and screening at high colloidal surface charge densities due to the ionic size asymmetry.

"Squishy capacitor" model for electrical double layers and the stability of charged interfaces

Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of sigma control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, sigma. The contradiction is only apparent; in fact local sigma cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage phi (phi control) or total surface charge q (q control). NC predictions in studies based on sigma control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of phi control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under q control, clarifying the basic picture using an exactly solvable "squishy capacitor" toy model. We find that phi can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL's critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by sigma control.

Effect of the surface charge discretization on electric double layers: A Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups, a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.

Testing one component plasma models on colloidal overcharging phenomena

In this paper, the mechanisms of overcharging of a colloidal macroion in the presence of multivalent counterions are investigated by means of Monte Carlo simulations. This computational technique appears as a powerful tool for probing the validity of semianalytical models developed for this issue. In particular, the simulations performed are compared with the predictions of two different models based on the one component plasma (OCP) theory. Therein, the multivalent ionic atmosphere confined at the macroion surface is approximated by a two-dimensional Wigner crystal. These kinds of models are largely used in the literature since (in some cases) they present quite simple equations to describe the electric double layer (EDL) of macroions with different geometries in the presence of much smaller (but still multivalent) ions. In this sense, charge inversion phenomena of membranes, polyelectrolytes, DNA molecules, etc., are straightforwardly predicted in terms of these expressions. Unfortunately, comparisons between these predictions and experimental results are scarce, mostly due to the difficulty to reproduce the experimental conditions in the laboratory. Accordingly, the goal of the present paper is to simulate EDLs under real conditions (in which overcharging phenomena are expected to happen) and use the results obtained in this way for comparing with those obtained from OCP models.

Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging

The classical Poisson-Boltzmann (PB) theory of electrolytes assumes a dilute solution of point charges with mean-field electrostatic forces. Even for very dilute solutions, however, it predicts absurdly large ion concentrations (exceeding close packing) for surface potentials of only a few tenths of a volt, which are often exceeded, e.g., in microfluidic pumps and electrochemical sensors. Since the 1950s, several modifications of the PB equation have been proposed to account for the finite size of ions in equilibrium, but in this two-part series, we consider steric effects on diffuse charge dynamics (in the absence of electro-osmotic flow). In this first part, we review the literature and analyze two simple models for the charging of a thin double layer, which must form a condensed layer of close-packed ions near the surface at high voltage. A surprising prediction is that the differential capacitance typically varies nonmonotonically with the applied voltage, and thus so does the response time of an electrolytic system. In PB theory, the differential capacitance blows up exponentially with voltage, but steric effects actually cause it to decrease while remaining positive above a threshold voltage where ions become crowded near the surface. Other nonlinear effects in PB theory are also strongly suppressed by steric effects: The net salt adsorption by the double layers in response to the applied voltage is greatly reduced, and so is the tangential "surface conduction" in the diffuse layer, to the point that it can often be neglected compared to bulk conduction (small Dukhin number).

Planar electric double layer for a restricted primitive model electrolyte at low temperatures

Monte Carlo simulation and the modified Poisson-Boltzmann theory are used to investigate the planar electric double layer for a restricted primitive model electrolyte at low temperatures. Capacitance as a function of temperature at low surface charge is determined for 1:1, 2:2, 2:1, and 3:1 electrolytes. Negative adsorption can occur for 1:1 electrolytes at low surface charge with low electrolyte concentration. The 1:1 electrolyte diffuse layer potential as a function of surface charge displays a maximum at low densities. At high densities, the diffuse layer potential is negative with a negative slope. The Gouy-Chapman-Stern theory fails in this low-temperature regime, whereas the modified Poisson-Boltzmann theory is fairly successful in this regard.