Unusual properties of the electric double layer in an extremely narrow nanotube. A grand canonical Monte Carlo and classical DFT study

Abstract

A grand canonical Monte Carlo (GCMC) simulation technique at a constant electrode–electrolyte potential drop and classical density functional theory (CDFT) have been employed to study the ion distribution and the differential capacitance of an electric double layer (EDL) in extremely narrow nanotubes. In the applied constant-potential GCMC method, to preserve the electroneutrality of the system after a single ion exchange, the electrode charge is suitably modified. The resulting charge fluctuations are used to calculate the differential capacitance of the EDL. Results for the ion distributions and differential capacitance in the nanotubes are reported for symmetric +1: 1 ionic valences with a common ionic diameter of 0.4 nm at electrolyte concentrations of 0.1 m, 1.0 m, and 2.5 m, a cylinder radius of 0.6 nm, potential drop varying from −0.6 V to 0.6 V, a relative permittivity of 78.5, and a temperature of 298.15 K. These results are compared with corresponding data for size-asymmetric systems with cations of diameters of 0.32 nm and 0.48 nm and ion-valence asymmetric systems of +2: 1 and +3: 1. At higher electrode surface charges, the counter-ion density distributions show an unusual accumulation along the axis of the nanotube. Differential capacitance plots have four or fewer, often three, maxima. The central minimum surrounded by two maxima undergoes a transition from a minimum to a maximum as the electrolyte concentration is increased. The positions of the side maxima indicate the electrode potential at which the rate of the unusual counter-ion accumulation is at its highest. Comparison between the results of simulations and CDFT suggests the latter to be reliable for investigation of the electrical capacitance properties of extreme nanoscale supercapacitors, even if its degree of accuracy for particle distributions decreases with increasing surface charge.