  We develop a simple Landau-Ginzburg-type continuum theory of solvent-free
ionic liquids and use it to predict the structure of the electrical double
layer. The model captures overscreening from short-range correlations, dominant
at small voltages, and steric constraints of finite ion sizes, which prevail at
large voltages. Increasing the voltage gradually suppresses overscreening in
favor of the crowding of counterions in a condensed inner layer near the
electrode. The predicted ion profiles and capacitance-voltage relations are
consistent with recent computer simulations and experiments on room-temperature
ionic liquids, using a correlation length of order the ion size.
