  Ionic liquids are solvent-free electrolytes, some of which possess an
intriguing self-assembly property. Using a mean-field framework (based on
Onsager's relations) we show that bulk nano-structures arise via type-I and II
phase transitions (PT), which directly affect the electrical double layer (EDL)
structure. Ginzburg-Landau equation is derived and PT are related to
temperature, potential and interactions. The type-I PT occurs for geometrically
dissimilar anion/cation ratio and, surprisingly, is induced by perturbations on
order of thermal fluctuations. Finally, we compare the insights with the
decaying charge layers within the EDL, as widely observed in experiments.
