The Structure of Ionic Liquids at Electrified Interfaces - A Continuum Theory Based Approach

Abstract

Here, we discuss the role of competing energy scales for the structure of the EDL. For this purpose, we supplement our numerical simulations by an analytic investigation of the integral formulation, using higher order gradients in the ion distribution. Thereby, we identify three energy scales related to short-ranged ion-correlations, accounting for excluded volume of hardcore ions, to the thermal energy, and to the electrostatic energy of Coulombic interactions. The relative magnitudes of these energy scales account for the resulting charge-profile in the EDL. We predict the emergence of three screening-phases, consisting of a saturation-profile (crowding), followed by an exponentially decay towards the bulk, a profile of damped oscillations (overscreening), and a crystalline phase of undamped oscillations, which constitutes ion separation. Our analytic investigation gives precise predictions for the damping ratio and the frequency of the oscillations. We compare the analytic discussion with numerical simulations, and show that the analytic description is highly accurate.