The Role of Ion-Ion Correlations for the Differential Capacitance of Ionic Liquids

We employ the quasi-chemical approximation to incorporate ion ion correlations into a lattice gas model for the electric double layer formed by a compact, size-symmetric ionic liquid. The resulting differential capacitance, which we calculate for planar and weakly curved electrodes up to first order in curvature, transitions from a bell shape to a camel-shape profile for increasing correlation strength. No such transition is present if the quasi-chemical approximation is replaced by a random mixing approximation. The bell-to-camel shape transition is, up to first order, independent of curvature. If Coulomb interactions dominate on molecular length scales, the differential capacitance has a tendency to adopt a camel-shape profile. Hence, our model offers a physical interpretation for the observed camel shape (or even U-shape) of the differential capacitance in many ionic liquids. Correlations also cause underscreening where the characteristic decay length of the electric double layer grows with the correlation strength and can become much larger than the size of a single ion.