Relaxing gap capacitor models of electrified interfaces

Abstract

Relaxing gap capacitor models emphasize the charge-induced variation of the effective gap of electric double layer capacitors. The first such model, the elastic capacitor, resolved the theoretical puzzle of negative differential capacitance by linking its origin to the charge-induced contraction of the effective gap. It also revealed the importance of treating the electrode charge density as a self-adjustable equilibrium quantity rather than as an independently fixed variable. We show that negative differential capacitance for fixed electrode charge density leads to a charging instability for fixed applied voltage. The “squishy capacitor” model, which allows for lateral variation of the effective gap, relates negative differential capacitance to instabilities in isolated systems, with a resultant lateral redistribution of surface charge. We review the origin of negative differential capacitance, discuss charging instabilities, and explore the analogy between the critical behavior of the squishy capacitor and first-order phase transitions.