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Simulations for the density and potential profiles of the ions in the planar electrical double layer of a model electrolyte or an ionic liquid are reported. The ions of a real electrolyte or an ionic liquid are usually not spheres; in ionic liquids, the cations are molecular ions. In the past, this asymmetry has been modelled by considering spheres that are asymmetric in size and/or valence (viz., the primitive model) or by dimer cations that are formed by tangentially touching spheres. In this paper we consider spherical ions that are asymmetric in size and mimic the asymmetrical shape through an off-center charge that is located away from the center of the cation spheres, while the anion charge is at the center of anion spheres. The various singlet density and potential profiles are compared to (i) the dimer situation, that is, the constituent spheres of the dimer cation are tangentially tethered, and (ii) the standard primitive model. The results reveal the double layer structure to be substantially impacted especially when the cation is the counterion. As well as being of intrinsic interest, this off-center charge model may be useful for theories that consider spherical models and introduce the off-center charge as a perturbation.Key words: electrical double layer, simulations, density functional theory, off-center charged spheres PACS: 61.20.Qj, 82.45.Fk, 82.45.Gj, 82.45.Jn This article is dedicated to our colleague and friend, Stefan Sokołowski, in commemoration of his 65th birthday. DH first met and collaborated with "Don Esteban" in Mexico City but had admired his work long before that. Stefan has been our good friend and frequent collaborator since that time. We wish him a happy birthday and continued good health and productivity.

The structure of a planar electric double layer formed by a 2:2 valency dimer electrolyte in the vicinity of a uniformly charged planar hard electrode is investigated using density functional theory and Monte Carlo simulations. The dimer electrolyte consists of a mixture of charged divalent dimers and charged divalent monomers in a dielectric continuum. A dimer is constructed by two tangentially tethered rigid spheres, one of which is divalent and positively charged and the other neutral, whereas the monomer is a divalent and negatively charged rigid sphere. The density functional theory reproduces well the simulation results for (i) the singlet distributions of the various ion species with respect to the electrode, and (ii) the mean electrostatic potential. Comparison with earlier results for a 2:1/1:2 dimer electrolyte shows that the double layer structure is similar when the counterion has the same valency.

The properties of the singlet ion distributions at and around contact in a restricted primitive model double layer are characterized in the modified Poisson-Boltzmann theory. Comparisons are made with the corresponding exact Monte Carlo simulation data, the results from the Gouy-ChapmanStern theory coupled to an exclusion volume term, and the mean spherical approximation. Particular emphasis is given to the behaviour of the theoretical predictions in relation to the contact value theorem involving the charge profile. The simultaneous behaviour of the coion and counterion contact values is also examined. The performance of the modified Poisson-Boltzmann theory in regard to the contact value theorems is very reasonable with the contact characteristics showing semi-quantitative or better agreement overall with the simulation results. The exclusionvolume-treated Gouy-Chapman-Stern theory reveals a fortuitous cancellation of errors, while the mean spherical approximation is poor. KeywordsElectric double layer; Contact value theorems; Density profile; Charge profile; Monte Carlo Alongside exact numerical simulations, exact analytical conditions are invaluable in statistical mechanics of Coulomb fluids in comparative assessment of different theories and/ or further theoretical development. These exact conditions can also help provide additional, useful checks on the consistency of simulations. One such condition in the electric double layer phenomenon is our principal concern in this paper. An electric double layer is formed when a charged electrode is brought in contact with a charged fluid and an ionic atmosphere develops in the vicinity of the electrode. The phenomenon has practical significance for a spectrum of systems in biology and industrial chemical processes. Here ρ s , d s and g s are, respectively, the average number density, the diameter and the electrode-ion distribution function of ionic species s, p is the bulk osmotic pressure and σ is the uniform surface charge density on the electrode with ε 0 and ε r , respectively, being the vacuum permittivity and relative permittivity of the solvent. Also, k B is the Boltzmann constant and T the absolute temperature. The relation was derived from force balance considerations at the electrode-electrolyte interface. It is local, easy to implement and, as a consequence, has been useful in checking theoretical descriptions of the electric double layer over the past three decades 1 .The other, relatively recent condition concerns the contact value of the charge profile in the planar double layer. This was derived by Holovko, Badiali and di Caprio4,5 (HBC), and Holovko and di Caprio6 starting from the Bogoliubov-Born-Green-Yvon (BBGY) hierarchy of equations7. For a double layer containing a restricted primitive model (RPM) electrolyte (the ions of the PM are now restricted to having a common diameter), and for symmetric valency salts -our interest in this paper, their relation is particularly simple, viz.,where g sum (x) = (1/2)(g ctr (x) + g co (x)), g diff (x...

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