On the equivalence of self-consistent equations for nonuniform liquids: a unified description of the various modifications

Abstract

A variety of self-consistent (SC) equations have been proposed for non-uniform states of liquid particles under external fields, including adsorbed states at solid substrates and confined states in pores. External fields represent not only confining geometries but also fixed solutes. We consider SC equations ranging from the modified Poisson-Boltzmann equations for the Coulomb potential to the hydrostatic linear response equation for the equilibrium density distribution of Lennard-Jones fluids. Here, we present a unified equation that explains the apparent diversity of previous forms and proves the equivalence of various SC equations. This unified description of SC equations is obtained from a hybrid method combining the conventional density functional theory and statistical field theory. The Gaussian approximation of density fluctuations around a mean-field distribution is performed based on the developed hybrid framework, allowing us to derive a novel form of the grand-potential density functional that provides the unified SC equation for equilibrium density.

28 pages, 1 figure

References in corpus (10)

• Interfacial layering in the electric double layer of ionic liquids
• Local molecular field theory for effective attractions between like charged objects in systems with strong Coulomb interactions
• The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
• Charge Oscillations in Ionic Liquids: A Microscopic Cluster Model
• Structural interactions in ionic liquids linked to higher order Poisson-Boltzmann equations
• Statistical field theory of ion-molecular solutions
• Dipolar correlations in structured solvents under nanoconfinement
• The double-layer structure of overscreened surfaces by smeared-out ions
• Transverse density fluctuations around the ground state distribution of counterions near one charged plate: stochastic density functional view
• Gas-liquid critical point of the ultrasoft restricted primitive model from analytic theory

Cited by in corpus (1)

• Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation