  In concentrated electrolytes with asymmetric or irregular ions, such as ionic
liquids and solvent-in-salt electrolytes, ion association is more complicated
than simple ion-pairing. Large branched aggregates can form at significant
concentrations at even moderate salt concentrations. When the extent of ion
association reaches a certain threshold, a percolating ionic gel networks can
form spontaneously. Gelation is a phenomenon that is well known in polymer
physics, but it is practically unstudied in concentrated electrolytes. However,
despite this fact, the ion-pairing description is often applied to these
systems for the sake of simplicity. In this work, drawing strongly from
established theories in polymer physics, we develop a simple thermodynamic
model of reversible ionic aggregation and gelation in concentrated electrolytes
accounting for the competition between ion solvation and ion association. Our
model predicts the populations of ionic clusters of different sizes as a
function of salt concentration, it captures the onset of ionic gelation and
also the post-gel partitioning of ions into the gel. We discuss the
applicability of our model, as well as the implications of its predictions on
thermodynamic, transport, and rheological properties.
