A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores

Abstract

We employ a field-theoretical variational approach to study the behavior of ionic solutions in the grand canonical ensemble. To describe properly the hardcore interactions between ions, we use a cutoff in Fourier space for the electrostatic contribution of the grand potential and the Carnahan-Starling equation of state with a modified chemical potential for the pressure one. We first calibrate our method by comparing its predictions at room temperature with Monte Carlo results for excess chemical potential and energy. We then validate our approach in the bulk phase by describing the classical "ionic liquid-vapor" phase transition induced by ionic correlations at low temperature, before applying it to electrolytes at room temperature confined to nanopores embedded in a low dielectric medium and coupled to an external reservoir of ions. The ionic concentration in the nanopore is then correctly described from very low bulk concentrations, where dielectric exclusion shifts the transition up to room temperature for sufficiently tight nanopores, to high concentrations where hardcore interactions dominate which, as expected, modify only slightly this ionic "capillary evaporation".

References in corpus (2)

• Ionic transport through sub-10 nm diameter hydrophobic high-aspect ratio nanopores: experiment, theory and simulation
• Electrostatics of ions inside the nanopores and trans-membrane channels

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• Poisson-Boltzmann theory with non-linear ion correlations
• Projective-truncation-approximation study of the one-dimensional ${\varphi }^4$ lattice model
• Phase behaviour of primitive models of molecular ionic liquids in porous media: effects of cation shape, ion association and disordered confinement
• Non-electrostatic interactions as random fields in charged liquids
• Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores