Simulations of phase transitions and capacitance, of simple ionic fluids in porous electrodes

In this work, we simulate the capacitance of a simple charged fluid model consisting of equal-sized, spherical monovalent ions, immersed in an implicit solvent. Apart from Coulomb forces, the particles interact via a truncated and shifted Lennard-Jones potential. This is a possible crude model for hydrophobic ions (assuming an implicit aqueous solvent) and allows for a possible demixing transition in the solution. Such a phase separation may be driven by charging a narrow slit-like pore, immersed in a dilute ("gas-like") bulk phase, akin to a capillary condensation. We highlight the dramatic effect that boundary conditions and regulatory control have on electrical properties (e.g., the differential capacitance) at the point of transition. For example, the surface potential displays a vertical (first-order) transition, as a function of surface charge density, when the latter is constrained to be uniform over the pore surfaces. At short separations, the transition is gradual (i.e., not first-order), which leads to a regime with an apparent "non-physical" negative differential capacitance. Under conditions of constant surface potential, the negative capacitance region becomes inaccessible, as a first-order (horizontal) transition is reasserted. This is true for both conducting and non-conducting surfaces.