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[hal-01360415] A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores.

(19/10/2021)  
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.”

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Keywords

Scalar field theory Phase separation Polytrope Stability Perturbation theory Violent relaxation Random tilings 9530Sf DNA Critical phenomena 9536+x 9535+d Statistical and Nonlinear Physics TASEP 9880-k Computational modelling Generalized thermodynamics Transition vitreuse Persistence Théorème du viriel Entropy Marcheur aléatoire Scattering length Poisson equation Diffusion Structure Formation Wave function Statistical mechanics Interacting agents Energy high Random walker Gravitation self-force Physique statistique Denaturation Competition Metastable states Black hole Collapse Fokker-Planck Quantum mechanics Thermodynamics Dark matter Hydrodynamics Cosmology Gravitational collapse Atmosphere Game theory Nanofiltration Euler-Maclaurin Statistical Mechanics Brownian motion Potential quantum Quasicrystals Parametrization Keller-Segel Wisdom of crowds Self-organization Gravitation collapse Dark matter halo Self-gravitating systems Numerical calculations Mouvement brownien Bethe ansatz Temperature Einstein Nonrelativistic Turbulence Ions close to interfaces Quantum chromodynamics axion Evaporation Effondrement gravitationnel Fermi gas Membrane transport Phase transition Bose–Einstein condensates Catastrophe theory Axion Chemotaxie Random process 9862Gq Long-range interactions Chemotaxis Field theory scalar Dissipation Collisionless stellar-systems Axion star General relativity Smoluchowski-Poisson Suppression Virial theorem Processus stochastique Cosmological model Glass transition Gravitation Rotation Scalar field Smoluchowski equation Condensation Bose-Einstein Dark matter condensation