Molecular simulations of Supercapacitors

Supercapacitors are energy storage devices with the ability to deliver and store energy at a fast rate. Therefore, they are mainly utilised in applications where a fast response time is required, e.g. regenerative braking systems of vehicles and for balancing the supply and demand of intermittent renewable energy. Improving their modest energy density would allow for further widening of their applications. This work focuses on molecular simulations of supercapacitors, which give insight into the charging and discharging processes at molecular level and thereby can help optimise supercapacitors.
Firstly, in Chapter 3 we perform Brownian Dynamics (BD) simulations of aqueous electrolytes and compare the results with classical density functional theory (DFT) calculations. We find an excellent agreement between the properties of the supercapacitors, like the density profiles of the ions and the differential capacitances, obtained with both methods, for a wide range of system parameters. The computationally much cheaper DFT calculations are therefore a suitable method to study supercapacitors containing small spherical ions. We also show that the capacitance curve at constant numbers of ions differs from the capacitance curve at constant chemical potential.
Next, in Chapter 5 we optimise the constant potential method (CPM), an algorithm for applying a constant potential difference between electrodes in molecular simulations. We substitute the narrow Gaussian charge distributions of the electrode atoms traditionally used in CPM with point charges and an intra-atomic energy term quadratic in the charges. This allows for easy implementation of CPM using any efficient electrostatic solver, whereas the narrow Gaussian charges require re-coding of existing electrostatic solvers that were developed for the point charges routinely employed in Molecular Dynamics (MD). Therefore, we name our optimised algorithm the generalised constant potential method (GCPM). We find an excellent agreement between simulations using traditional CPM, based on Ewald summation, and simulations using GCPM, based on the particle-particle particle-mesh method (PPPM), for four different test systems, while the latter is substantially faster and has an improved scalability with system size in all four cases.
Finally, in Chapter 6 we develop the constant sum-charge method (CSCM) to conserve a constant total charge on the electrodes of the supercapacitor, with consequently a fluctuating potential difference between the electrodes in response to the perpetual movements of the electrolyte atoms. This method is of importance since during many (dis)charging processes one does not control the potential difference between the electrodes, as is done in CPM. Rather, this difference is dependent on the charges on the electrodes and the instantaneous electrolyte distribution in the capacitor. We show that the average potential difference in a CSCM simulation of a disconnected supercapacitor, with a fixed electrode charge, is in agreement with the potential difference that has to be imposed in a CPM simulation to result in an average electrode charge matching the fixed charge in the CSCM simulation. We also show that ensemble averages, like the ion distribution and differential capacitance, agree well. CSCM is further extended to simulate (dis)charging of the supercapacitor, by introducing an equation of motion to the sum charge. We observe a double exponential relaxation in the charge of the electrode and the potential difference during (dis)charging, with one relaxation mode related to the dynamics of the electrolyte whereas the other mode is related to the current in the external circuit. In addition, we propose an equivalent circuit model which captures the simulation results well and thus allows for fast calculations with regard to the (dis)charging behaviour of supercapacitors, in contrast to simulations that take days.