Three-Dimensional Cyclic Voltammetry Simulations of EDLC Electrodes Made of Ordered Carbon Spheres

Abstract

This study aims to investigate the effect of electrode nanoarchitecture on the performance of electric double layer capacitor (EDLC) porous electrodes consisting of highly-ordered monodisperse spherical carbon nanoparticles. To do so, cyclic voltammograms, reproducing three-electrode measurements, were numerically generated for electrodes with different thicknesses and nanoparticle diameters arranged in either simple cubic (SC) or face-centered cubic (FCC) packing structure. The transient three-dimensional simulations of interfacial and transport phenomena in the porous electrodes were based on a continuum model accounting for (1) binary symmetric electrolytes with finite ion size, (2) electric field-dependent dielectric constant of the electrolyte, (3) the Stern layer at the electrode/electrolyte interface, along with (4) Ohmic potential drop in the electrode. For both FCC and SC packing structures, the areal capacitance (in μF/cm2) increased with decreasing sphere diameter. In addition, for a given sphere diameter, FCC packing featured larger equilibrium capacitance than SC packing. These observations were attributed to larger electric field at the carbon sphere surface for smaller spheres and/or FCC packing. In all cases, the areal capacitance remained constant at low scan rates but decreased beyond a critical scan rate. The latter rate-dependent regime was reached at lower scan rates for thicker electrodes due to resistive losses across the electrode. Interestingly, limitation due to ion diffusion through the porous electrode was not observed. Finally, dimensional analysis was performed by scaling the CV cycle period by the time scale for electron transport in the electrode. This study illustrates powerful numerical simulation tools that can be used to select materials and electrolytes and to design and optimize EDLC electrodes.