Non-mean-field theory of anomalously large capacitance at the metal/ionic conductor interface

Recent experiments on capacitors made with ion-conducting glasses have demonstrated a remarkably high capacitance at the metal/glass interface [1]. Such large capacitance cannot be explained by mean-field theories of the ionic double layer, since it implies a double-layer thickness that is significantly smaller than the ion radius. We propose an alternate theory of the ionic double-layer which allows for the binding of discrete ions to their image charges in the metal. We show that at small voltages the capacitance of the double-layer is limited only by the relatively weak dipole-dipole repulsion between bound ions. At large voltages the depletion of bound ions from one of the capacitor electrodes triggers a collapse of the capacitance to a much smaller value, in agreement with experiment. [1] C. R. Mariappan, T. P. Heins, and B. Roling, arxiv:cond-mat/0904.3856v2