Scaling laws for carbon-based electric double layer capacitors

This paper presents scaling laws for the integral capacitance of electric double layer capacitors (EDLCs) supported by rigorous analysis and experimental data for porous carbon-based electrodes. First, dimensionless similarity parameters were identified based on dimensional analysis of the modified Poisson-Boltzmann model for binary and symmetric electrolytes. Then, a correlation for the equilibrium potential at the Stern/diffuse layer interface near planar electrodes and near cylindrical and spherical pores was obtained as a function of previously identified dimensionless numbers for a wide range of parameters. Similarly, an analytical expression was proposed for the dimensionless double layer integral capacitance of planar electrodes. Finally, scaling analysis was applied to experimentally measured integral capacitance of mesoporous carbon electrodes with a wide range of morphology and different electrolytes. To maximize the integral areal capacitance, the electrolyte should have small ion effective diameter and large dielectric constant. The electrode pore diameter should be tailored to match the ion diameter.