  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.
