Coarse-Grained Electrostatic Model Including Ion-Pairing Equilibrium That Explains DC and AC X-ray Photoelectron Spectroscopy Measurements on Ionic Liquids

The dynamics of the electrochemical double layer in ionic liquids can be experimentally probed by a number of experimental techniques. Earlier, we reported on the results of an X-ray photoelectron spectroscopic investigation under applied square-wave bias of two distinct frequencies. Our studies had revealed counterintuitive properties involving the physical and temporal progression of the effect of the electrochemical double layer that could not be modeled with conventional equivalent-circuit approaches. Herein, we present a new coarse-grained modeling methodology that accounts for particle diffusion, migration, and ion association equilibrium. Our model is computationally efficient enough to be used to predict and match the results at extended time scales and distances of the experiment. Modeling efforts predict that a crucial component of the behavior is controlled by the ion-pairing equilibrium, an often overlooked aspect of ionic liquids.