Charging and discharging a supercapacitor in molecular simulations

As the world moves more toward unpredictable renewable energy sources, better energy storage devices are required. Supercapacitors are a promising technology to meet the demand for short-term, high-power energy storage. Clearly, understanding their charging and discharging behaviors is essential to improving the technology. Molecular Dynamics (MD) simulations provide microscopic insights into the complex interplay between the dynamics of the ions in the electrolyte and the evolution of the charge distributions on the electrodes. Traditional MD simulations of (dis)charging supercapacitors impose a pre-determined evolving voltage difference between the electrodes, using the Constant Potential Method (CPM). Here, we present an alternative method that explicitly simulates the charge flow to and from the electrodes. For a disconnected capacitor, i.e., an open circuit, the charges are allowed to redistribute within each electrode while the sum charges on both electrodes remain constant. We demonstrate, for a model capacitor containing an aqueous salt solution, that this method recovers the charge-potential curve of CPM simulations. The equilibrium voltage fluctuations are related to the differential capacitance. We next simulate a closed circuit by introducing equations of motion for the sum charges, by explicitly accounting for the external circuit element(s). Charging and discharging of the model supercapacitor via a resistance proceed by double exponential processes, supplementing the usual time scale set by the electrolyte dynamics with a novel time scale set by the external circuit. Finally, we propose a simple equivalent circuit that reproduces the main characteristics of this supercapacitor.