Mathematical functions for optimisation of conducting polymer/activated carbon asymmetric supercapacitors

Equations routinely used to describe the properties of conventional symmetric electrochemical double-layer capacitors (EDLCs) are expanded to develop straightforward mathematical functions that can effectively describe the performance characteristics of asymmetric supercapacitors based on electrically conducting polymer and activated carbon (ECP–AC) electrodes. Formulae are developed to describe cell parameters (based on total active material mass) such as maximum specific capacitance (F g−1), maximum specific energy (Wh kg−1), and optimum electrode mass ratios that can be used for maximising the specific energy of asymmetric cells. The electrode mass ratios are found to have a significant impact on the swing voltages across the positive and negative electrodes. Illustrative EDLC and ECP–AC devices are explored and employed to verify the derived equations that serve to predict essential parameters of both symmetric and asymmetric systems, irrespective of electrolyte ion concentration, solvent or species and independent of voltage. The utility of the equations is demonstrated by predicting cell parameters for a number of theoretical asymmetric ECP–AC systems and used to correlate experimentally obtained parameters.