Counterion layering at high surface charge in an electric double layer. Effect of local concentration approximation

Electrostatic correlations in electrolytes: Contribution of screening ion interactions to the excess chemical potential

A new theory for the electrostatic component of the chemical potential for homogeneous electrolytes modeled with the primitive model is developed. This Mean Countershell Approximation (MCSA) is an analytic theory derived by including the interactions between the ions' screening clouds. At molar concentrations, these contribute substantially to the excess chemical potential but are absent in classical Debye-Hückel and Mean Spherical Approximation (MSA) theories. Simulations show that the MCSA is highly accurate, including at the low dielectric constants of ionic liquids. While sharing a mathematical framework with the MSA, the MCSA has simpler formulas and is qualitatively more accurate when there is ion size asymmetry.

Selecting ions by size in a calcium channel: the ryanodine receptor case study

Many calcium channels can distinguish between ions of the same charge but different size. For example, when cations are in direct competition with each other, the ryanodine receptor (RyR) calcium channel preferentially conducts smaller cations such as Li(+) and Na(+) over larger ones such as K(+) and Cs(+). Here, we analyze the physical basis for this preference using a previously established model of RyR permeation and selectivity. Like other calcium channels, RyR has four aspartate residues in its GGGIGDE selectivity filter. These aspartates have their terminal carboxyl group in the pore lumen, which take up much of the available space for permeating ions. We find that small ions are preferred by RyR because they can fit into this crowded environment more easily.

High energy conversion efficiency in nanofluidic channels

It is proposed that the layering of large ions at the wall/liquid interface of nanofluidic channels can be used to achieve high efficiency (possibly >50%) in the conversion of hydrostatic energy into electrical power. Large ions tend to produce peaks and troughs in their concentration profiles at charged walls, producing high concentrations far from the walls where the ions' pressure-driven velocity is high. This increases the streaming conductance and the energy conversion efficiency.

The weighted correlation approach for density functional theory: a study on the structure of the electric double layer

Within the framework of density functional theory, a weighted correlation approach is developed in order to obtain the density distributions of an inhomogeneous fluid. It results in a formally exact expression, by means of the concept of a weighted pair correlation function, used to evaluate the change of the single-particle direct correlation function of the system relative to that of a reference state. When applying the approach for practical use, however, an approximation of the pair correlation function has to be made, along with an appropriate definition of a weight function. Noticeably, combining this approach with fundamental measure theory gives rise to a new method, which we call the FMT/WCA-k(2) approach, for studying the structural and thermodynamic properties of a charged hard-sphere fluid subjected to a spatially varying external potential. Application of the FMT/WCA-k(2) approach in a range of electrolyte concentrations and surface charge densities, against the Monte Carlo simulations, shows that it is superior to the typical approaches of density functional theory in predicting the ionic density profiles of both counter-ions and co-ions near a highly charged surface. It is capable of capturing the fine features of the structural properties of the electric double layers, to well reproduce the layering effect and the charge inversion phenomenon, also in strongly coupled cases where divalent counter-ions are involved. In addition, it is found that the FMT/WCA-k(2) approach even has an advantage over the anisotropic, hyper-netted chain approaches in giving better agreement with the Monte Carlo results.

Comparing the Predictions of the Nonlinear Poisson-Boltzmann Equation and the Ion Size-Modified Poisson-Boltzmann Equation for a Low-Dielectric Charged Spherical Cavity in an Aqueous Salt Solution

The ion size-modified Poisson Boltzmann equation (SMPBE) is applied to the simple model problem of a low-dielectric spherical cavity containing a central charge, in an aqueous salt solution to investigate the finite ion size effect upon the electrostatic free energy and its sensitivity to changes in salt concentration. The SMPBE is shown to predict a very different electrostatic free energy than the nonlinear Poisson-Boltzmann equation (NLPBE) due to the additional entropic cost of placing ions in solution. Although the energy predictions of the SMPBE can be reproduced by fitting an appropriatelysized Stern layer, or ion-exclusion layer to the NLPBE calculations, the size of the Stern layer is difficult to estimate a priori. The SMPBE also produces a saturation layer when the central charge becomes sufficiently large. Ion-competition effects on various integrated quantities such the total number of ions predicted by the SMPBE are qualitatively similar to those given by the NLPBE and those found in available experimental results.

Local semi-empirical formulae for the contact values of the singlet distribution functions of a double layer

The electrochemical double layer is an important practical and theoretical problem. Generally speaking, experiment gives valuable information about quantities, such as potential differences, that involve integrals of density and charge profiles but does not provide direct information about the profiles themselves. Computer simulations have given numerical information about these profiles. However, explicit expressions are useful in understanding these data. For some years an exact expression has been known for the contact value of total density profile of the ions in the double layer but, until recently, an expression for the contact value of the more important charge profile has been lacking. A few years ago, a semi-empirical local result for the charge profile, valid at low electrode charge, was proposed and, very recently, extended to higher electrode charge. This expression contains a parameter; the effect of variations in this parameter is explored in this paper and the result is compared with a large set of simulation data for the contact values of various profiles that we have accumulated in the past few years. The agreement of the semi-empirical expression with our simulation results is excellent. The best values for this parameter are fairly close to the value suggested by theory.

The electric double-layer differential capacitance at and near zero surface charge for a restricted primitive model electrolyte

The behavior of the differential capacitance of a planar electric double layer containing a restricted primitive model electrolyte in the neighborhood of zero surface charge is investigated by theory and simulation. Previous work has demonstrated that at zero surface charge the differential capacitance has a minimum for aqueous electrolytes at room temperature but can have a maximum for molten salts and ionic liquids. The transition envelope separating the two situations is found for a modified Poisson-Boltzmann theory and a Poisson-Boltzmann equation corrected for the exclusion volume term. Good agreement is found between simulation and the modified Poisson-Boltzmann theory in the neighborhood of the envelope at the reduced temperature of 0.8, while the exclusion volume corrected Poisson-Boltzmann theory shows correct qualitative trends.

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.

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.

Relaxation of the electrical double layer after an electron transfer approached by Brownian dynamics simulation

In this paper, the dynamical properties of the electrochemical double layer following an electron transfer are investigated by using Brownian dynamics simulations. This work is motivated by recent developments in ultrafast cyclic voltammetry which allow nanosecond time scales to be reached. A simple model of an electrochemical cell is developed by considering a 1:1 supporting electrolyte between two parallel walls carrying opposite surface charges, representing the electrodes; the solution also contains two neutral solutes representing the electroactive species. Equilibrium Brownian dynamics simulations of this system are performed. To mimic electron transfer processes at the electrode, the charge of the electroactive species are suddenly changed, and the subsequent relaxation of the surrounding ionic atmosphere are followed, using nonequilibrium Brownian dynamics. The electrostatic potential created in the center of the electroactive species by other ions is found to have an exponential decay which allows the evaluation of a characteristic relaxation time. The influence of the surface charge and of the electrolyte concentration on this time is discussed, for several conditions that mirror the ones of classical electrochemical experiments. The computed relaxation time of the double layer in aqueous solutions is found in the range 0.1 to 0.4 ns for electrolyte concentrations between 0.1 and 1 mol L(-1) and surface charges between 0.032 and 0.128 C m(-2).

Density-functional theory of spherical electric double layers and ζ potentials of colloidal particles in restricted-primitive-model electrolyte solutions

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high.