Electric double layer capacitors (EDLCs) store energy via ion adsorption in the electric double layer forming at the electrode/electrolyte interfaces in highly porous carbon electrodes. This charge storage mechanism is very fast and highly reversible resulting in large power density and long cycle life. Applications range from regenerative breaking for hybrid electric vehicles to the smart grid. The architecture of the carbon electrodes is known to have a significant effect on the performance of EDLCs. Unfortunately, experimental optimization can be time consuming and challenging due to the large number of design parameters. Numerical simulations could offer a faster and less costly alternative.

This study aims to demonstrate the use of numerical tools to simulate transient three-dimensional interfacial and transport phenomena in EDLCs with realistic electrode architecture. It also aims to derive design rules for EDLC porous electrodes. To do so, cyclic voltammograms were numerically generated for EDLCs consisting of electrodes with highly-ordered spherical carbon nanoparticles arranged in simple cubic (SC) or face-centered cubic (FCC) packing in LiClO₄/propylene carbonate electrolyte. Simulations were performed for different carbon nanoparticles diameter, electrode thickness, and scan rate. The continuum model was based on the modified Poisson-Nernst-Planck model and accounted for (i) the Stern layer at the electrode/electrolyte interface, (ii) finite ion size, (iii) binary and symmetric electrolyte, and (iv) three-dimensional electrode morphologies. In all cases, the areal capacitance was independent of scan rate at low scan rate but decreased beyond a critical scan rate corresponding to the diffusion-limited regime when ion transport cannot follow the rapid changes in electric potential. The results indicate that the areal capacitance (in F/m²) increased with decreasing sphere diameter below 40 nm due to the increasing surface curvature resulting in larger surface electric field. In addition, FCC packing featured larger capacitance that SC packing thanks to larger surface electric field for given sphere diameter and low scan rate . However, the ion diffusion regime was reached at lower scan rates in FCC packing because of the higher turtuosity limiting the ion transport in the electrode.