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Interfacial layering in the electric double layer of ionic liquids

Ions in ionic liquids and concentrated electrolytes reside in a crowded, strongly-interacting environment, leading to the formation of discrete layers of charges at interfaces. Here, we propose a continuum theory that captures the transition from overscreening-- alternating layers of excess charge at low surface potential, to overcrowding-- the formation of dense layers of charge of the same sign at high surface potential. The model outputs slowly-decaying oscillations in the charge density with a wavelength of single ion diameters, as shown by analysis of the gradient expansion. The gradient expansion suggests a new structure for partial differential equations describing the electrostatic potential at charged interfaces. We find quantitative agreement between the theory and molecular simulations in the differential capacitance and concentration profiles.