Ion-dipole Mixture Research Articles

An ion-dipole mixture against a charged hard wall with specific adsorption

The electric double layer is modelled by a hard-sphere ion–dipole mixture in the neighbourhood of a uniformly charged plane hard wall. Specific adsorption of the ions and dipoles are treated using Baxter's sticky potential. The theory is investigated for 1:1 electrolytes in the mean-field approximation. The inclusion of different ion sizes and dipole adsorption leads to a variety of differential capacitance curves. In some situations a maximum can occur in the capacitance which is reminiscent of a ‘hump’ observed in experimental work.

A theoretical study of the solid–electrolyte solution interface. I. Structure of a hard sphere ion–dipole mixture near an uncharged hard wall

In this paper we investigate the density and orientational structure of a molecular model electrolyte solution consisting of a mixture of charged hard spheres in a dipolar hard sphere solvent, located in the vicinity of a neutral hard wall. The electrolyte is symmetrically charged and all particles have the same size. The statistical mechanical treatment is the reference hypernetted-chain (RHNC) approximation for the bulk fluid and, respectively, the linearized RHNC (LRHNC) and the full RHNC approximations for the wall–molecule and the wall–ion correlation functions. Our results for the pure solvent are in good agreement with previous theoretical work and available computer simulations. It is found that in addition to the steric effects due to the molecular solvent, image forces play an essential role in the determination of the ionic density profile near the wall. Moreover, at moderate ionic concentrations, our results indicate that beyond the first layer of solution this electrostatic effect may be well described by a continuum description of the solvent.

Statistical mechanics of ion–dipole mixtures: An exactly solvable model in one dimension

The statistical mechanics of a mixture of hard core ions and dipoles, with or without an applied external field, is solved exactly in one dimension using the generating function technique of Baxter. This function is shown to be the solution of a nonlinear Hill-type equation. In the plasma limit we obtain explicit expressions for the thermodynamic properties of the bulk phase and the potential drop and differential capacitance of the electrical double layer as well. The expressions obtained resemble the mean spherical approximation results.

On sum rules and Stillinger–Lovett conditions for inhomogeneous Coulomb systems

We show that, for the case of a Coulomb fluid bounded by a planar surface, the inhomogeneous Stillinger–Lovett condition is a consequence of the dipole moment sum rule of Blum et al. [J. Chem. Phys. 75, 5974 (1981)]. We also give a new derivation of the Stillinger–Lovett condition, valid for both homogeneous and inhomogeneous systems, which is entirely analogous to the derivation of the dipole moment sum rule. Our new derivation enables us to clarify certain subtleties that arise when image forces are present. We comment briefly on the generalization of these sum rules to systems of particles with higher multipole moments (e.g., ion–dipole mixtures).

Towards a mean electrostatic potential treatment of an ion-dipole mixture or a dipolar system next to a plane wall

The basic equations are formulated for a mean electrostatic potential treatment of a mixture of charged hard spheres and dipolar hard spheres or solely dipolar hard spheres near a uniformly charged plane wall. The Kirkwood hierarchy of equations are closed using an approximation analogous to that of Loeb for the primitive model electrolyte. A linear form of the ion-dipole theory supports the mean spherical approximation that a damped oscillatory behaviour can occur in the charge density and polarization density which depends crucially upon the solvent molecules. The potential theory also appears to be useful technique for treating a pure dipolar fluid.

The modelling of solvent structure in the electrical double layer

A Civilized Model electrolyte is one in which the ions and solvent molecules are regarded as distinct molecular species and treated on an equal basis. Recent efforts to use a Civilized Model to study the effects of solvent structure in the properties of the electrical double layer are discussed. By modelling the electrolyte as a simple ion-dipole mixture, it is possible to gain valuable insight in areas such as: 1) the successes and limitations of the Gouy-Chapman-Stern picture; 2) the derivation as opposed to a postulation of the Stern layer; 3) the influence of the charged surface on the magnitudes of the apparent Stern capacities (e.g. the “low” capacitances of the mercury/solution interface vs. the “high” capacitance of inorganic oxides); 4) the effect of solvent structure on the potential profile in the diffuse layer; 5) the interpretation of the electrokinetic potential; and 6) the role of solvent orientation on the x potential.

Ionic and dipolar adsorption from an ion–dipole mixture. A model for the stern layer

The details of solvent structure in the electrical double layer are investigated using a molecular model electrolyte which consists of a fluid mixture of hard spheres with embedded point charges in a solvent of hard spheres with embedded point dipoles. The charged surface is modelled as a hard wall with a uniform surface charge density. Effects due to the specific adsorption of ions and the specific adsorption and preferential orientation of solvents at the surface are also considered. The statistical mechanical treatment is the Mean Spherical Approximation. Simple analytic expressions, valid at low electrolyte concentrations and near the point of zero charge, are obtained for the effective Stern-layer capacitance for various types of charged surfaces. In this model the Stern layer is a derived rather than a postulated entity. Structural quantities such as potential and polarization profiles at the charged surface indicate that while the Stern model can correctly parameterize the thermodynamic properties of the double layer, it may not be an appropriate visualization of the microstructure of the interfacial region.

Explicit solution of the mean spherical model for ions and dipoles

It is shown that the solution of the mean spherical approximation for the ion-dipole mixtures obtained by Blum, Adelman, and Deutch has an explicit closed form solution which is one of the roots of a cubic equation.

The structure of electrolytes at charged surfaces: Ion–dipole mixtures

The detailed structure of the double layer is investigated using a model fluid consisting of hard spheres with embedded point charges in a solvent of hard spheres with embedded point dipoles against a hard wall with smeared-out surface charge. Such a model treats solute and solvent particles on an equal basis, unlike the primitive model of electrolytes. The statistical mechanics is solved using the mean spherical approximation for all interactions. This limits the validity of any results to the regime of low ionic concentrations, where, in this approximation, the model fluid has the correct limiting behavior for bulk thermodynamic quantities. In this regime, simple analytic results for the surface properties are given, which are correct to order (κR). In particular, the surface potential has the classical Stern layer form, with solvent structuring responsible for the inner layer capacitance. This result is the first derivation, as opposed to postulation, of Stern layer behavior. In addition, the polarization density oscillates about the continuum theory result for 3–4 molecular diameters away from the surface. Such behavior shows the difficulty in defining a local dielectric constant close to the surface.

On the theory of dipolar fluids and ion–dipole mixtures

The Stillinger–Lovett condition for the second moment of ion–ion distribution functions is obtained from first principles for an ion–dipole mixture. The Debye–Hückel form for the asymptotic behavior of the potential of mean force between ions is shown to emerge for arbitrary density of the dipolar solvent in the limit of low ionic concentration.