  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 \textit{et al.} 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 regime dominated by free, crowded ions. This transition
from gelation to crowding is conceptually similar to the overscreening to
crowding transition.
