Size effect on electric-double-layer capacitances of conducting structures

The charge storage in an electrical double-layer capacitor is dependent on the accumulation of ions on the interface between electrolyte and conducting material and the spatial distribution of ions in electrolyte. In this work, we study the effect of local curvature on the concentration of ions on the interface between electrolyte and electrode from the framework of thermodynamics and incorporate the concentration of ions on the interface in the analysis of the spatial distribution of ions for symmetric binary electrolytes. Semi-analytical results of the integral electrical-double-layer capacitances per unit area under the condition of large Debye-Hückel constant are obtained for spherical particle and cylindrical rod, which reveal the contribution of interface energy between the conducting material and the electrolyte to the storage of charge. For spherical cavity and cylindrical pore at small electric potential, the solution of the electric potential for linearized Poisson-Boltzmann equation is used in the calculation of the integral electrical-double-layer capacitances per unit area, which are dependent on the sizes of the cavity and pore and independent of the interface energy between the conducting material and the electrolyte. For spherical cavity and cylindrical pore at large electric potential, the integral double-layer capacitances are dependent on the interface energy.