Postulation of optimal charging protocols for minimal charge redistribution in supercapacitors based on the modelling of solid phase charge density

Abstract

Supercapacitors featured with high power density and long cycle life have been used as a complement to batteries in a wide range of applications. One of the outstanding issues with supercapacitors is voltage decay due to charge redistribution (CR). In this work, a physics-based model was developed to study CR in a supercapacitor. A version of the Smoluchowski drift–diffusion equation was employed to resolve the non-linear distribution of solid-phase electric charge inside the electrodes of a supercapacitor. The model is used to quantify the effect of various factors on self-discharge due to CR. These included: magnitude of the charging current, length of constant voltage hold and initial state. Complex relationships were observed, with the redistribution of solid phase charge density predicted to be a driving mechanism. Finally, the coupled relationship between constant charging current (CCC) and constant voltage hold (CVH) on CR was investigated. These were then used as the basis for an optimised charging protocol that minimised voltage decay due to CR. A CVH of any duration was only found to be helpful with longer charging times (at least 1200 s). Otherwise, for shorter charging times, using the longest possible CCC process (i.e. the lowest possible charging current) was identified as the ideal charging protocol.