The Dielectric Constant of Ionic Solutions: A Field-Theory Approach

Abstract

We study the variation of the dielectric response of a dielectric liquid (e.g. water) when a salt is added to the solution. Employing field-theoretical methods we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. We predict analytically the dielectric decrement which depends on the ionic strength in a complex way. Furthermore, a qualitative description of the hydration shell is found and is characterized by a single length scale. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles.

5 pages, 2 figures

References in corpus (1)

• Dielectric decrement as a source of ion specific effects

Cited by in corpus (46)

• Comparative Roles of Charge, $\pi$ and Hydrophobic Interactions in Sequence-Dependent Phase Separation of Intrinsically Disordered Proteins
• Dependence of the dielectric constant of electrolyte solutions on ionic concentration - a microfield approach
• Differential capacitance of the electric double layer: The interplay between ion finite size and dielectric decrement
• Surface Tension of Electrolyte Interfaces: Ionic Specificity within a Field-Theory Approach
• A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes
• Dielectric Constant of Ionic Solutions: Combined Effects of Correlations and Excluded Volume
• Molecular Mean-Field Theory of Ionic Solutions: a Poisson-Nernst-Planck-Bikerman Model
• Dipolar Poisson-Boltzmann Approach to Ionic Solutions: A Mean Field and Loop Expansion Analysis
• Bjerrum Pairs in Ionic Solutions: a Poisson-Boltzmann Approach
• The multilevel four-stroke swap engine and its environment
• Fundamental measure theory for the electric double layer: implications for blue-energy harvesting and water desalination
• A modified Poisson-Boltzmann theory: Effects of co-solvent polarizability
• Charged Membranes: Poisson-Boltzmann theory, DLVO paradigm and beyond
• A close look into the excluded volume effects within a double layer
• Computing Coulomb Interaction in Inhomogeneous Dielectric Media via a Local Electrostatics Lattice Algorithm
• Microscopic formulation of non-local electrostatics in polar liquids embedding polarizable ions
• A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and its Ramifications for Dielectric Effects in Biomolecular Condensates
• On the theory of electric double layer with explicit account of a polarizable co-solvent
• Statistical field theory of ion-molecular solutions
• Dipolar correlations in structured solvents under nanoconfinement
• Kinetic and ion pairing contributions in the dielectric spectra of electrolyte aqueous solutions
• Nonlocal statistical field theory of dipolar particles in electrolyte solutions
• Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces: the nonlinear Poisson-Boltzmann approach
• Mean-field electrostatics beyond the point-charge description
• Beyond Poisson-Boltzmann: fluctuations and fluid structure in a self-consistent theory
• A Brief Review of Continuous Models for Ionic Solutions: the Poisson-Boltzmann and Related Theories
• Alteration of gas phase ion polarizabilities upon hydration in high dielectric liquids
• Nonlinear Dielectric Decrement of Electrolyte Solutions: an Effective Medium Approach
• Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions
• Ion Solvation in Dipolar Poisson models in a dual view
• Dipolar depletion effect on the differential capacitance of carbon based materials
• Stochastic density functional theory for ions in a polar solvent
• Nonlocal statistical field theory of dipolar particles forming chain-like clusters
• Nonlinear conductivity of aqueous electrolytes: beyond the first Wien effect
• Variational functional theory for coulombic correlations in the electric double layer
• Electrostatic interactions in charged nanoslits within an explicit solvent theory
• Effect of Bjerrum pairs on electrostatic properties in an electrolyte solution near charged surfaces: A mean-field approach
• Brownian dynamics simulations of electric double-layer capacitors with tunable metallicity
• Polar Liquids at Charged Interfaces: A Dipolar Shell Theory
• Debye-Hückel Theory of Weakly Curved Macroions: Implementing Ion Specificity through a Composite Coloumb-Yukawa Interaction Potential
• Unraveling the behavior of the individual ionic activity coefficients on the basis of the balance of ion-ion and ion-water interactions
• Competition between Born solvation, dielectric exclusion, and Coulomb attraction in spherical nanopores
• Non-electrostatic interactions as random fields in charged liquids
• Effect of variable relative permittivity on the thermodynamics of asymmetric valency aqueous salts
• A model of an optical biosensor detecting environment
• Beyond Poisson-Boltzmann: Numerical sampling of charge density fluctuations