Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. [J. Phys. Chem. B 125, 2677 (2021)] developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible (Cayley tree) clusters and a percolating ionic network (gel). Here, we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition.
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