Phase diagram and criticality of the modified primitive electrolyte model in bulk and in inert and conducting confinement

Ionic fluids under conductive confinement are central to technologies such as batteries, supercapacitors, and fuel cells. Their interfacial behavior governs energy storage and electrochemical processes. Despite their importance, the thermodynamics of even simple models-such as the charged Lennard-Jones fluid-remain underexplored in this regime. We present an extended Wang-Landau sampling approach to efficiently compute the density of states of charged mixtures with respect to the particle number. The method supports simulations in both bulk and confined geometries. Combined with the constant potential method, it also enables the study of effects due to confining electrodes. We employ this approach to study symmetric, binary mixtures of charged Lennard-Jones particles-the modified restricted primitive model-in bulk, in inert confinement, and in conductive confinement at the potential of zero charge. Our results show that confinement shifts the vapor-liquid critical point to lower temperatures and higher densities compared to bulk, in line with the classical concept of capillary condensation. Importantly, conductive boundaries significantly lower the chemical potential of coexistence relative to inert confinement. For both confinement types, we find a minimal pore size below which no phase transition occurs, corresponding to a super-critical fluid. These findings offer deeper insight into the phase behavior of ionic fluids in energy-relevant porous environments.