Organic electrolytes such as tetraethylammonium tetrafluoroborate dissolved in acetonitrile (TEA-BF4/ACN) are widely used in commercial supercapacitors and academic research, but conflicting experimental results have been reported regarding the dependence of surface-area-normalized capacitance on the pore size. Here we show from a classical density functional theory the dependence of capacitance on the pore size from 0.5 to 3.0 nm for a model TEA-BF4/ACN electrolyte. We find that the capacitance-pore size curve becomes roughly flat after the first peak around the ion diameter, and the peak capacitance is not significantly higher than the large-pore average. We attribute the invariance of capacitance with the pore size to the formation of an electric double-layer structure that consists of counterions and highly organized solvent molecules. This work highlights the role of the solvent molecules in modulating the capacitance and reconciles apparently conflicting experimental reports.

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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.

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A recently proposed local second contact value theorem [Henderson D., Boda D., J. Electroanal. Chem., 2005, 582, 16] for the charge profile of an electric double layer is used in conjunction with the existing Monte Carlo data from the literature to assess the contact behavior of the electrode-ion distributions predicted by the density functional theory. The results for the contact values of the co-and counterion distributions and their product are obtained for the symmetric valency, restricted primitive model planar double layer for a range of electrolyte concentrations and temperatures. Overall, the theoretical results satisfy the second contact value theorem reasonably well, the agreement with the simulations being semi-quantitative or better. The product of the co-and counterion contact values as a function of the electrode surface charge density is qualitative with the simulations with increasing deviations at higher concentrations.