- Ionic liquids are solvent-free electrolytes, some of which possess an intriguing self-assembly at finite length scale due to Coulombic interactions. Using a continuum framework (based on Onsager's relations), it is shown that bulk nanostructures arise via linear (supercritical) and nonlinear (subcritical) bifurcations (morphological phase transitions), which also directly affect the electrical double layer structure. A Ginzburg-Landau amplitude equation is derived and the bifurcation type is related to model parameters, such as temperature, potential, and interactions. Specifically, the nonlinear bifurcation occurs for geometrically dissimilar ions and, surprisingly, is induced by perturbations on the order of thermal fluctuations. Finally, qualitative insights and comparisons to the experimentally decaying charge layers within the electrical double layer are discussed.