Mesoscale modeling of electric double layer capacitors with three-dimensional ordered structures

Abstract

This paper presents general mathematical formulations for simulating electric double layer capacitors (EDLCs) with three-dimensional ordered structures. For the first time, a general set of boundary conditions was derived in order to account for the Stern layer without simulating it in the computational domain. These boundary conditions were valid for planar, cylindrical, and spherical electrode particles or pores. They made possible the simulations of EDLCs with complex geometries while rigorously accounting for both the Stern and diffuse layers. The model also simultaneously accounted not only for 3D electrode morphology but also for finite ion size and field-dependent electrolyte dielectric permittivity. It was used to faithfully simulate the complex structure of an EDLC electrode consisting of ordered bimodal mesoporous carbon featuring both macropores and mesopores. Areal and gravimetric capacitances were predicted based on non-solvated and solvated ion diameters. These two cases set the upper and lower bounds for the predicted capacitances. The capacitances predicted using non-solvated ion diameter were found to be in good agreement with experimental data reported in the literature. All surfaces contributed to the overall capacitance of EDLCs. The gravimetric capacitance of different bimodal carbons increased linearly with increasing specific surface area corresponding to constant areal capacitance.