Constant Potential and Constrained Charge Ensembles for Simulations of Conductive Electrodes

Constant potential method molecular dynamics simulation (CPM MD) enables the accurate modeling of atomistic electrode charges when studying the electrode-electrolyte interface at the nanoscale. Here, we extend the theoretical framework of CPM MD to the case in which the total charge of each conductive electrode is controlled, instead of their potential difference. We show that the resulting thermodynamic ensemble is distinct from that sampled with a fixed potential difference but they are rigorously related as conjugate ensembles. This theoretical correspondence, which we demonstrate using simulations of an ionic liquid supercapacitor, underpins the success of recent studies with fixed total charges on the electrodes. We show that equilibration is usefully sped up in this ensemble and outline some potential applications of these simulations in the future.