Differential capacitance of an electrical double layer with asymmetric ion sizes in the presence of hydration interactions
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The differential capacitance is a fundamental property of an electrical double layer and thus important for the development of more efficient and environment-friendly energy storage devices. In addition to the bare electrostatic interactions, the differential capacitance is affected by a complex interplay of ion-specific effects that arise from ion size, shape, and hydration. We employ Monte Carlo simulations to calculate the differential capacitance for size-asymmetric spherical ions, thereby modeling hydration-mediated interactions using Yukawa pair potentials. We also propose a corresponding mean-field theory that includes ion-specific Yukawa pair potentials and accounts for ion size mismatch on the basis of a recently proposed lattice model. Comparison of the two approaches – Monte Carlo simulations and mean-field theory – yields qualitative agreement, irrespective of ion size and size mismatch between cations and anions. The agreement includes the regime of weakly charged electrodes, where we find a growing differential capacitance with growing ion sizes, a behavior that is not consistent with the widely used Stern layer concept. Hence, our study reinforces the predictive power of mean-field theory, but only when the influence of correlations due to excluded volume interactions is diminished by the presence of soft, hydration-mediated ion-ion interactions.