Large enhancement of capacitance driven by electrostatic image forces.

Abstract

The purpose of this thesis is to examine the role of electrostatic images in determining the capacitance and the structure of the electrostatic double layer (EDL) formed at the interface of a metal electrode and an electrolyte. Current mean field theories, and the majority of simulations, do not account for ions to form image charges in the metal electrodes and claim that the capacitance of the double layer cannot be larger than that of the Helmholtz capacitor, whose width is equal to the radius of an ion. However, in some experiments, and simulations where the images are included, the apparent width of the capacitor is substantially smaller. Monte Carlo simulations are used to examine the interface between a metal electrode and a room temperature ionic liquid (RTIL) modeled by hard spheres (the “restricted primitive model”). Image charges for each ion are included in the simulated electrode. At moderately low temperatures the capacitance of the metal/RTIL interface is so large that the effective thickness of the electrostatic double-layer is up to 3 times smaller than the ion radius. To interpret these results, an approach is used that is based on the interaction between discrete ions and their image charges, which therefore goes beyond the mean-field approximation. When a voltage is applied across the interface, the strong image attraction causes counterions to condense onto the metal surface to form compact ion-image dipoles. These dipoles repel each other to form a correlated liquid. When the surface density of these dipoles is low, the insertion of an additional dipole does not require much energy. This leads to a large capacitance C that decreases monotonically with voltage V , producing a “bell-shaped” C(V ) curve. In the case of a semi-metal electrode, the finite screening radius of the electrode shifts the reflection plane for image charges to the interior of the electrode resulting in a “camel-shaped” C(V ) curve, which is parabolic near V = 0, reaches a maximum and then decreases. These predictions are in qualitative agreement with experiment. A similarly simple model is employed to simulate the EDL of superionic crystals. In this case only small cations are mobile and other ions form an oppositely charged background. Simulations show an effective thickness of the EDL that may be 3 times smaller than the ion radius. The weak repulsion of ion-image dipoles again plays a central role in determining the capacitance in this theory, which is in reasonable agreement with experiment. Finally, the problem of a strongly charged, insulating macroion in a dilute solution of multivalent counterions is considered. While an ideal conductor does not exist in the problem, and no images are explicitly included, simulations demonstrate that adsorbed counterions form a strongly correlated liquid of at the surface of the macroion and acts as an effective metal surface. In fact, the surface screens the electric field of distant ions with a negative screening radius. The simulation results serve to confirm existing non-mean-field theories.