A systematic Monte Carlo simulation study of the primitive model planar electrical double layer over an extended range of concentrations, electrode charges, cation diameters and valences (original) (raw)
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arXiv (Cornell University), 2017
The purpose of this study is to provide data for the primitive model of the electrical double layer, where ions are modeled as charged hard spheres, the solvent as an implicit dielectric background (with dielectric constant ε = 78.5), and the electrode as a smooth, uniformly charged, hard wall. We use canonical and Grand Canonical Monte Carlo simulations to compute the concentration profiles, from which the electric field and electrostatic potential profiles are obtained by solving Poisson's equation. We report data for an extended range of parameters including 1:1, 2:1, and 3:1 electrolytes at concentrations c = 0.0001 − 1 M near electrodes carrying surface charges up to σ = ±0.5 Cm −2. The anions are monovalent with a fixed diameter d − = 3Å, while the charge and diameter of cations are varied in the range z + = 1, 2, 3 and d + = 1.5, 3, 6, and 9Å (the temperature is 298.15 K). We provide all the raw data in the Supporting Information.
The Journal of Physical Chemistry B, 2004
The electrical double layer near a charged electrode formed by a binary electrolyte in which the cations and anions have different diameters varying between 1.5 and 4.25 Å is studied by Monte Carlo (MC) simulation. Our emphasis is on small electrode charge, where new phenomena may be expected. As one would expect, there is a nonzero potential at the point of zero charge (PZC). Such an effect is outside the popular Gouy-Chapman theory, although it can be introduced. It arises naturally in the mean spherical approximation (MSA). A comparison of the simulation results is made with the linearized modified Gouy-Chapman (LMGC) and MSA. Surprisingly, for monovalent ions, the LMGC theory yields more reliable electrode potentials than does the MSA. In the case when the cations and anions have different charge, a nonzero PZC potential results, even if the diameters of the ions are equal. This phenomenon is not reproduced by either of the theories but is predicted by the modified Poisson-Boltzmann (MPB5) theory. Results are presented for the competition of the effects resulting from the size and charge asymmetries of the ions. A comparison of the density and potential profiles, as obtained from MC and LMGC calculations, is reported.
Molecular Physics, 2005
To model the double layer near an electrode, theories and simulations must include the different dielectric coefficients of the electrode, the commonly-postulated 'inner' layer, and the electrolyte. Recently, Boda et al. ] developed a technique to include inhomogeneous dielectric coefficients in arbitrary geometries in a simulation. Here, Monte Carlo simulation results based on this method are reported for the density profiles of 1:1, 2:2 and 2:1 aqueous electrolytes. The simulations include two dielectric boundaries, one from an inner layer of low dielectric coefficient and one from an uncharged metal electrode. In addition, an extension of a Poisson-Boltzmann (PB) type theory due to Onsager and Samara [L. Onsager, N.N.T. Samara. J. chem. Phys., 2, 528, (1934)] is developed and compared with our simulation results. This approach works best for 1:1 salts at low concentrations.
Monte Carlo simulation of an ion-dipole mixture as a model of an electrical double layer
The Journal of Chemical Physics, 1998
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.
The Journal of Physical Chemistry B, 2012
Most theoretical studies of an electrical double layer, which is formed by an electrolyte in contact with a charged electrode, employ a primitive model in which the solvent is represented by a dielectric continuum. This implicit-solvent model is convenient because computations are comparatively simple. However, it suppresses oscillations in the density profiles of ionic species that result from the discreteness of the solvent molecules. Furthermore, the implicit-solvent model yields poor results for the capacitance. In comparison with experiment at fixed electrode charge density, it predicts a too small electrode potential, and the resultant capacitance is too large. This latter discrepancy can be compensated in part by postulating the existence of an often fictitious inner layer whose properties are parametrized to agree best with experiment. The use of an implicit solvent model and an inner layer helps in correlating experimental results but rests on a faulty microscopic picture. Unfortunately, explicit consideration of solvent molecules poses both theoretical and numerical difficulties and, as a result, studies using an explicit solvent model have been few and far between. In this study, we consider a simple nonprimitive or explicit solvent model in which each solvent molecule is represented by a dimer composed of touching positive and negative hard spheres, with a resulting dipole moment that is equal to that of a water molecule, and the ions are represented by charged hard spheres. The density profiles and charge−potential relationship of this model are examined using the classical density functional theory. We find that the introduction of an explicit solvent increases the electrode potential, at fixed electrode charge, without the need to postulate a parametrized inner layer. Because of the solvent polarity, the ion profiles become strong oscillatory and show local charge inversion near a highly charged electrode surface at all ion concentrations.
The Journal of Chemical Physics, 2008
We present the Monte Carlo simulation and density functional study of structure of cylindrical double layers considering solvent as the third component. We have chosen molecular solvent model, where ions and solvent molecules are considered as charged and neutral hard spheres, respectively, having equal diameter. The polyionic cylinder is modeled as an infinite, rigid, and impenetrable charged hard cylinder surrounded by the electrolyte and the solvent spheres. The theory is partially perturbative where the hard-sphere interactions are treated within the weighted density approach, the corresponding ionic interactions have been evaluated through second-order functional Taylor expansion with respect to the bulk electrolyte. The Monte Carlo simulations have been performed in canonical ensemble. The system is studied at varying concentrations of electrolyte ions and the solvent molecules, at different valences of the electrolyte, at different sizes of hard spheres, and at varying surface charge density. The theory and the simulation results are found to be in good agreement at different parametric conditions. The hard-sphere exclusion effects due to molecular nature of the solvent are shown to have special implications in characterizing diffuse layer phenomena such as layering and charge inversion.
The Journal of Chemical Physics, 2008
We present a systematic study of the structure of cylindrical double layers to envisage the distribution of small ions around a cylindrical polyion through canonical Monte Carlo simulation and density functional theory. The polyion is modeled as an infinite, rigid, and impenetrable charged cylinder surrounded by charged hard spheres of equal diameter modeled for small ions of the electrolyte. The solvent is considered as dielectric continuum. The theory is partially perturbative where the hard sphere contribution to the total excess free energy is evaluated using weighted density approximation, and the ionic interactions are calculated using quadratic Taylor expansion with respect to a uniform fluid. The system is studied over a wide range of parameters, viz., ionic concentrations, valences, and ionic sizes as well as for varying axial charge densities of the polyion. The theoretical predictions are observed to be in good agreement with that of simulation results. Some interesting phenomena relating to the width of the diffuse layer, mean electrostatic potential, and charge inversion have been observed to be dependent on different parametric conditions.