Phase behaviour in ionic solutions: Restricted primitive model of ionic liquid in explicit neutral solvent

Boundary-Monte Carlo Method for Neutral and Charged Confined Fluids

In this work, we describe a new Monte Carlo (MC) simulation method to investigate highly coupled fluids in confined geometries at a constant chemical potential. This method is based on so-called multi-scale Hamiltonian methods, wherein the chemical potential is determined using a more amenable Hamiltonian for a fluid in an "outer" region, which facilitates standard methods, such as grand canonical MC simulations or Widom's particle insertion method. The (inner region) fluid of interest is placed in diffusive contact with the simpler outer fluid via a boundary zone wherein the Hamiltonian is transformed. The current method utilizes an ideal fluid for the outer regions, which allows for implicit rather than explicit simulations. Only the boundary and inner region need explicit consideration; hence, the nomenclature used is boundary-Monte Carlo. We illustrate the utility of the method for simple neutral and charged fluids in cylindrical and planar pores. In the latter case, we use a dense room-temperature ionic liquid model and illustrate how the boundary zone establishes a proper Donnan equilibrium between inner and outer fluids in the presence of charged planar electrodes. Thus, the method allows direct calculation of properties such as the differential capacitance, without the need for additional difficult calculations of the requisite Donnan potential.

Local Grand Canonical Monte Carlo Simulation Method for Confined Fluids

We describe a new local grand canonical Monte Carlo method to treat fluids in pores in chemical equilibrium with a reference bulk. The method is applied to Lennard-Jones particles in pores of different geometry and is shown to be much more accurate and efficient than other techniques such as traditional grand canonical simulations or Widom's particle insertion method. It utilizes a penalty potential to create a gas phase, which is in equilibrium with a more dense liquid component in the pore. Grand canonical Monte Carlo moves are employed in the gas phase, and the system then maintains chemical equilibrium by "diffusion" of particles. This creates an interface, which means that the confined fluid needs to occupy a large enough volume so that this is not an issue. We also applied the method to confined charged fluids and show how it can be used to determine local electrostatic potentials in the confined fluid, which are properly referenced to the bulk. This precludes the need to determine the Donnan potential (which controls electrochemical equilibrium) explicitly. Prior approaches have used explicit bulk simulations to measure this potential difference, which are significantly costly from a computational point of view. One outcome of our analysis is that pores of finite cross-section create a potential difference with the bulk via a small but nonzero linear charge density, which diminishes as ∼1/ln(L), where L is the pore length.