Modeling electric double-layer capacitors using charge variation methodology in Gibbs ensemble

Abstract

Supercapacitors deliver higher power than batteries and find applications in grid integration and electric vehicles. Recent work by Chmiola et al. (2006) has revealed unexpected increase in the capacitance of porous carbon electrodes using ionic liquids as electrolytes. The work has generated curiosity among both experimentalists and theoreticians. Here, we have performed molecular simulations using a recently developed technique (Punnathanam, 2014) for simulating supercapacitor system. In this technique, the two electrodes (containing electrolyte in slit pore) are simulated in two different boxes using the Gibbs ensemble methodology. This reduces the number of particles required and interfacial interactions, which helps in reducing computational load. The method simulates an electric double-layer capacitor (EDLC) with macroscopic electrodes with much smaller system sizes. In addition, the charges on individual electrode atoms are allowed to vary in response to movement of electrolyte ions (i.e., electrode is polarizable) while ensuring these atoms are at the same electric potential. We also present the application of our technique on EDLCs with the electrodes modeled as slit pores and as complex three-dimensional pore networks for different electrolyte geometries. The smallest pore geometry showed an increase in capacitance toward the potential of 0 charge. This is in agreement with the new understanding of the electrical double layer in regions of dense ionic packing, as noted by Kornyshev's theoretical model (Kornyshev, 2007), which also showed a similar trend. This is not addressed by the classical Gouy-Chapman theory for the electric double layer. Furthermore, the electrode polarizability simulated in the model improved the accuracy of the calculated capacitance. However, its addition did not significantly alter the capacitance values in the voltage range considered.