Generally, the parameters in the interaction potential between like molecules in a mixture can be determined in a relatively straightforward manner from the properties of the pure components. However, the determination of the parameters in the interaction potential between the unlike pairs in the mixtures is more difficult. As a result, these parameters are usually estimated from averages of the like parameters. The most common recipes are the Lorentz–Berthelot mixing rules, where the energy and molecular size parameters are presumed to be geometric and arithmetic averages, respectively. There have been some studies of the consequences of deviations from the energy rule but almost no studies of the consequences of deviations from the size rule. Here, we study the effects of deviations from both rules on the radial distribution functions of a simple mixture. We find from simulations that, for this mixture, the effect of deviations from the energy rule on the radial distribution function are rather small but that the effect of deviations from the size rule can be significant and are interesting.

The efficient calculation of induced charges in an inhomogeneous dielectric is important in simulations and coarse-grained models in molecular biology, chemical physics, and electrochemistry. We present the induced charge computation (ICC) method for the calculation of the polarization charges based on the variational formulation of Allen et al. [Phys. Chem. Chem. Phys. 3, 4177 (2001)]. We give a different solution for their extremum condition that produces a matrix formulation. The induced charges are directly calculated by solving the linear matrix equation $A\mathbf{h}=\mathbf{c},$ where $\mathbf{h}$ contains the discretized induced charge density, $\mathbf{c}$ depends only on the source charges—the ions moved in the simulation—and the matrix A depends on the geometry of dielectrics, which is assumed to be unchanged during the simulation. Thus, the matrix need be inverted only once at the beginning of the simulation. We verify the efficiency and accuracy of the method by means of Monte Carlo simulations for two special cases. In the simplest case, a single sharp planar dielectric boundary is present, which allows comparison with exact results calculated using the method of electrostatic images. The other special case is a particularly simple case where the matrix A is not diagonal: a slab with two parallel flat boundaries. Our results for electrolyte solutions in these special cases show that the ICC method is both accurate and efficient.

Despite the fact that our conceptual understanding of the electrical double layer has advanced during the past few decades, the interpretation of experimental and applied work is still largely based on the venerable Poisson–Boltzmann theory of Gouy, Chapman and Stern. This is understandable since this theory is simple and analytic. However, it is not very accurate because the atomic/molecular nature of the ions/solvent and their correlations are ignored. Simulation and some theoretical studies by ourselves and others that have advanced our understanding are discussed. These studies show that the GCS theory predicts a narrow double layer with monotonic profiles. This is not correct. The double layer is wider, and there can be substantial layering that would be even more pronounced if explicit solvent molecules are considered. For many years, experimental studies of the double layer have been directed to the use of electrochemistry as an analytical tool. This is acceptable for analytic chemistry studies. However, the understanding of electrochemical reactions that typically occur at the electrode surface, where simulation and theory indicate that the GCS theory can have substantial errors, requires modern approaches. New, fundamental experimental studies that would lead to deeper insights using more novel systems would be desirable. Further, biophysics is an interesting field. Recent studies of the selectivity of ion channels and of the adsorption of ions in a binding sites of a protein have shown that the linearized GCS theory has substantial errors.

Monte Carlo (MC) and density functional theory (DFT) results are reported for an electrolyte, consisting of charged hard spheres of diameter 3 Å with the solvent modeled as a dielectric continuum, near a charged flat uniformly charged electrode. These results are more interesting than the earlier MC results of Torrie and Valleau [J. Chem. Phys. 73, 5807 (1980); J. Phys. Chem. 86, 3251 (1982)] for 4.25 Å spheres because the popular Gouy–Chapman (GC) theory is less successful for this system. The DFT results are in good agreement with the MC results. Both the MC and DFT results show particularly interesting features when the counterions are divalent. For such divalent counterions, the diffuse layer potential passes through a maximum magnitude, then declines, and ultimately has a sign that is opposite to that of the electrode charge. The consequences of this behavior are discussed. In contrast, the well-known GC theory consistently overestimates the magnitude of the diffuse layer potential, does not have any unusual behavior, and is in poor agreement with the simulation results.

Canonical Monte Carlo simulations were performed for a nonprimitive model of an electrical double layer. The ions and the solvent molecules are modeled as charged and dipolar hard spheres, respectively, while the electrode as a hard, impenetrable wall carrying uniform surface charge. We found that the ion-dipole model gives a reasonable description of the double layer for partially charged ions with small to moderate dipole moments, or equivalently for an "effective" dielectric constant. Density, polarization and mean electrostatic potential profiles are reported. Strong layering structure, and at higher charges, charge inversion in the second layer were found. With appropriate choices of charge and solvent parameters, states corresponding to the primitive or the solvent primitive model can be produced, and the results agreed well with literature data. At higher effective charges and dipole moments, the dipolar solvent has difficulties in preventing the ions from clustering. More realistic models of water and other solvents are necessary to study the double layer. © 1998 American Institute of Physics.published_or_final_versio