# Structural and electrical properties of an electric double layer formed inside a cylindrical pore investigated by Monte Carlo and classical density functional theory

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## Abstract

We present the properties of an electrical double layer formed by ions inside a charged cylindrical pore studied by the grand canonical Monte Carlo simulation and classical density functional theory. The cylinder radius is 3000 pm. The wall is hard, perfectly smooth. The ions are modelled by hard spheres with a point electric charge at the centre. The hard sphere diameter is fixed at 400 pm. The monovalent ions are immersed in a continuous dielectric medium of the relative permittivity *ε*_{r}. The temperature is 298.15 K and the electrolyte concentration takes the following values: 1.0, 2.5 and 4.0 M. The surface charge density varies in the range from − 1.0 to + 1.0 C/m^{2}. The ion singlet distribution results show adsorption of counter-ions and desorption of co-ions from the cylindrical electrode. At high electrode charges the second layer of counter-ions is formed, while for high electrolyte concentration the co-ion distribution curve has a small maximum at some distance from the electrode surface. In comparison to the planar electrode, the concave one attracts stronger the counter-ions and repels the co-ions. At high electrolyte concentration, the profiles of the volume charge density have a positive hump, while those of the mean electrostatic potential have a negative minimum, which indicates the overscreening effect. For low electrolyte concentrations, the differential capacitance curve has a minimum at *σ* = 0 surrounded by two maxima. With increasing concentration, the minimum transforms into a maximum. The differential capacitance curves run above the curves for the planar electrode at small electrode charges and below them for high negative and positive charges. The very good agreement of all the grand canonical Monte Carlo to the classical density functional theory results presented in the paper indicates the reliability of the latter approach in cylindrical pore as well as planar geometry.

## Keywords

Electrical double layer Cylindrical pore Grand canonical Monte Carlo simulation Classical density functional theory Differential capacitance curve## Notes

### Acknowledgements

The authors would like to thank genuinely the anonymous reviewers for the constructive comments which help in deepening the discussions. SL gratefully acknowledges the financial support from the Faculty of Chemistry, Adam Mickiewicz University in Poznań. This project is supported by the National Natural Science Foundation of China (Nos. 21373274 and 21673299).

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