We apply a different version of the density functional theory, given by Pizio, Patrykiejew, and Sokolowski [J. Chem. Phys. 121, 11957 (2004)], for a nonuniform restricted primitive model of an electrolyte solution to evaluate the temperature dependence of the capacitance of an electric double layer. We show that this theory is capable of reproducing the computer simulation data at a quantitative level. In particular, the reversal of the temperature dependence of the capacitance at low temperatures is predicted. This phenomenon has been difficult to predict from theory. Further, this theory also leads to an accurate description of the double layer structure.
An extension of the singlet-level equations for the density profile to the case of adsorption of polydisperse fluids on solid surfaces is presented. Explicit calculations and comparisons with canonical ensemble Monte Carlo data have been performed for a polydisperse hard sphere fluid in contact with a hard wall by using the Percus–Yevick, hypernetted chain, and a modified Verlet approximation. A numerical solution of the density profile equations makes use of the orthonormal polynomials with the weight function corresponding to the distribution function of the diameters of fluid particles.
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