(70b) Monte Carlo Simulation in the Constant Voltage Ensemble: Application to Porous Electrodes

We performed Monte Carlo simulation of electrolytes in the constant-voltage grand-canonical ensemble in order to study the thermodynamics of electrolytes in porous electrodes. In most simulation studies on electrolytes with electrodes in literature, the surface charge density on the electrode planes and the number of ions are kept constant. However, in experimental studies, it is the voltage rather than the surface charge density that is controlled. The number of ions in the electrode planes varies with the voltage and temperature rather than being constant. Therefore, the constant-voltage grand-canonical ensemble, where the voltage and the chemical potential of ions are the controlled thermodynamic parameters, represents the experimental situation in the most realistic way. The thermodynamic properties such as the formation of the electrical double layers, the capacitance, or the change of the electrical potential near the cathode and near the anode can be calculated in a natural fashion in this ensemble. In this paper, we present two interesting phenomena in porous electrodes that would not have been easily found without applying this new simulation technique. The first finding is that the capacitance of porous electrodes increases as the pore size decreases in a medium of a low dielectric constant. On the other hand, the capacitance of porous electrodes decreases as the pore size decreases in a medium of a high dielectric constant. Such contrasting behaviors are explained in terms of the balance between the electrostatic and volume exclusion interactions. The second finding is that there are peculiar phase behaviors for the surface charge density and the ion density in the porous electrodes depending on the voltage and the pore size. Porous electrodes play important roles in modern technologies such as batteries, capacitors, and fuel cells. However, the basic properties of porous electrodes have not been thoroughly investigated yet. Monte Carlo simulation in the constant-voltage grand-canonical ensemble would be a useful tool in investigating and designing porous electrodes.