  Water-in-salt electrolytes (WiSEs) are a class of super-concentrated
electrolytes that have shown much promise in replacing organic electrolytes in
lithium-ion batteries. At the extremely high salt concentrations of WiSEs,
ionic association is more complicated than the simple ion pair description. In
fact, large branched clusters can be present in WiSEs, and past a critical salt
concentration, an infinite percolating ionic network can form spontaneously. In
this work, we simplify our recently developed thermodynamic model of reversible
ionic aggregation and gelation, tailoring it specifically for WiSEs. Our
simplified theory only has a handful of parameters, all of which can be readily
determined from simulations. Our model is able to quantitatively reproduce the
populations of ionic clusters of different sizes as a function of salt
concentration, the critical salt concentration for ionic gelation, and the
fraction of ions incorporated into the ionic gel, as observed from molecular
simulations of three different lithium-based WiSEs. The extent of ionic
association and gelation greatly affects the effective ionic strength of
solution, the coordination environment of active cations that is known to
govern the chemistry of the solid-electrolyte interface, and the thermodynamic
activity of all species in the electrolyte.
