Density functional theory study of the capacitance of single file ions in a narrow cylinder

The differential capacitance of a model organic electrolyte in a cylindrical pore that is so narrow that the ions can form only a single file is studied by means of density functional theory (DFT). Kornyshev (2013), has studied this system and found the differential capacitance to have only a double hump shape (the so-called camel shape) whereas other geometries show this behavior only at low ionic concentrations that are typical for aqueous electrolytes. However, his calculation is rather approximate. In this DFT study we find that the double hump shape occurs only at low ionic concentrations. At high concentrations, the capacitance has only a single hump. Kornyshev considers a metallic cylinder and approximately includes the contributions of electrostatic images. Electrostatic images are not easily incorporated into DFT. As a result, images are not considered in this study and the question of whether Kornyshev's result is due to his approximations or images cannot be answered. Simulations to answer this question are planned.