Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores

Abstract

A variational theory is developed to study electrolyte solutions, composed of interacting point-like ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and non-linear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image charge repulsion. Our variational equations thus go beyond the mean-field theory. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. i) A single neutral air-water interface with an asymmetric electrolyte. A charge separation and thus an electrostatic field gets established due to the different image charge repulsions for coions and counterions. Both charge distributions and surface tension are computed and compared to previous approximate calculations. For symmetric electrolyte solutions close to a charged surface, two zones are characterized. In the first one, with size proportional to the logarithm of the coupling parameter, strong image forces impose a total ion exclusion, while in the second zone the mean-field approach applies. ii) A symmetric electrolyte confined between two dielectric interfaces as a simple model of ion rejection from nanopores. The competition between image charge repulsion and attraction of counterions by the membrane charge is studied. For small surface charge, the counterion partition coefficient decreases with increasing pore size up to a critical pore size, contrary to neutral membranes. For larger pore sizes, the whole system behaves like a neutral pore. The prediction of the variational method is also compared with MC simulations and a good agreement is observed.

This version is accepted for publication in Phys. Rev. E.

References in corpus (2)

• Statics and Dynamics of Strongly Charged Soft Matter
• Charge Inversion of Divalent Ionic Solutions in Silica Channels

Cited by in corpus (44)

• Perspective: Coulomb fluids -- weak coupling, strong coupling, in between and beyond
• Ionic transport through sub-10 nm diameter hydrophobic high-aspect ratio nanopores: experiment, theory and simulation
• Interacting Ions in Biophysics: Real is not Ideal
• Ions at hydrophobic interfaces
• On the theoretical description of weakly charged surfaces
• Dependence of DNA persistence length on ionic strength of solutions with monovalent and divalent salts: a joint theory-experiment study
• Ionic Capillary Evaporation in Weakly Charged Nanopores
• Electrostatic correlations in inhomogeneous charged fluids beyond loop expansion
• Solving Fluctuation-Enhanced Poisson-Boltzmann Equations
• Ion size effects at ionic exclusion from dielectric interfaces and slit nanopores
• Ionic exclusion phase transition in neutral and weakly charged cylindrical nanopores
• Electrostatic correlations on the ionic selectivity of cylindrical membrane nanopores
• Electrostatic correlation induced ion condensation and charge inversion in multivalent electrolytes
• The Poisson-Boltzmann Theory for Two Parallel Uniformly Charged Plates
• On the nature of overcharging and charge inversion in electrical double layers
• Inhomogeneous screening near a dielectric interface
• Correlation-induced DNA adsorption on like-charged membranes
• Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory
• Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations
• A Brief Review of Continuous Models for Ionic Solutions: the Poisson-Boltzmann and Related Theories
• Interactions between Charged Particles with bathing Multivalent Counterions: Experiments {\it vs} Dressed Ion Theory
• Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions
• Ionic Interactions in Biological and Physical Systems: a Variational Treatment
• Ion correlation driven like-charge attraction in multivalent salt solutions
• The renormalized Jellium model of colloidal suspensions with multivalent counterions
• A variational approach to the liquid-vapor phase transition for hardcore ions in the bulk and in nanopores
• Distribution of counterions and interaction between two similarly charged dielectric slabs: Roles of charge discreteness and dielectric inhomogeneity
• Dipolar depletion effect on the differential capacitance of carbon based materials
• Ion filling of a one-dimensional nanofluidic channel in the interaction confinement regime
• Generating true minima in constrained variational formulations via modified Lagrange multipliers
• The Correlation Potential of a Test Ion Near a Strongly Charged Plate
• Excluded volume effects in macromolecular forces and ion-interface interactions
• Pimples reduce and dimples enhance flat dielectric surface image repulsion
• Poisson-Boltzmann theory with non-linear ion correlations
• Electrostatic energy barriers from dielectric membranes upon approach of translocating DNA molecules
• Life's Solutions are Complex Fluids. A Mathematical Challenge
• Electrostatic interactions in charged nanoslits within an explicit solvent theory
• Desalination due to Electrical Image Forces
• Charged Plate in Asymmetric Electrolytes: One-loop Renormalization of Surface Charge Density and Debye Length due to Ionic Correlations
• Classical theory of electron-ion correlations at electrochemical interfaces: Closing the circuit from double-layer charging to ion adsorption
• Poisson-Boltzmann Equation with a Random Field for Charged Fluids
• Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores
• Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations
• Non-electrostatic interactions as random fields in charged liquids