The Primitive Model in Classical Density Functional Theory: Beyond the Standard Mean-Field Approximation

Abstract

The primitive model describes ions by point charges with an additional hard-core interaction. In classical density-functional theory the mean-field electrostatic contribution can be obtained from the first order of a functional perturbation of the pair potential for an uncharged reference system of hard spheres. This mean-field electrostatic term particularly contributes at particle separations that are forbidden due to hard-core overlap. In this work we modify the mean-field contribution such that the pair potential is constant for distances smaller than the contact distance of the ions. We motivate our modification by the underlying splitting of the potential, which is similar to the splitting of the Weeks-Chandler-Andersen potential and leads to higher-order terms in the respective expansion of the functional around the reference system. The resulting formalism involves weighted densities similar to the ones found in fundamental measure theory. To test our modifications, we analyze and compare density profiles, direct and total correlation functions, and the thermodynamic consistency of the functional via a widely established sum rule and the virial pressure formula for our modified functional, for established functionals, and for data from computer simulations. We found that our modifications clearly show improvements compared to the standard mean-field functional, especially when predicting layering effects and direct correlation functions in high concentration scenarios; for the latter we also find improved consistency when calculated via different thermodynamic routes. In conclusion, we demonstrate how modifications towards higher order corrections beyond mean-field functionals can be made and how they perform, by this providing a basis for systematic future improvements in classical density-functional theory for the description of electrostatic interactions.

References in corpus (15)

• The Electrostatic Screening Length in Concentrated Electrolytes Increases with Concentration
• ESPResSo 4.0 -- An Extensible Software Package for Simulating Soft Matter Systems
• Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
• Underscreening in concentrated electrolytes
• Tension and stiffness of the hard sphere crystal-fluid interface
• Interfacial layering in the electric double layer of ionic liquids
• Primitive Model Electrolytes in the Near and Far Field: Decay Lengths from DFT and Simulations
• The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
• Free energies, vacancy concentrations and density distribution anisotropies in hard--sphere crystals: A combined density functional and simulation study
• Screening Lengths in Ionic Fluids
• Fundamental measure theory for the electric double layer: implications for blue-energy harvesting and water desalination
• Mean-Field Theory of Inhomogeneous Fluids
• Monte Carlo simulation of the nonadditive restricted primitive model of ionic fluids: Phase diagram and clustering
• Anisotropic pair correlations in binary and multicomponent hard-sphere mixtures in the vicinity of a hard wall: A combined density functional theory and simulation study
• Statistical thermodynamics of supercapacitors and blue engines

Cited by in corpus (6)

• Anomalous Underscreening in the Restricted Primitive Model
• Learning classical density functionals for ionic fluids
• Adsorption of polyelectrolytes in the presence of varying dielectric discontinuity between solution and substrate
• In-plane structure of the electric double layer in the primitive model using classical density functional theory
• Variational functional theory for coulombic correlations in the electric double layer
• Poisson-Nernst-Planck charging dynamics of an electric double layer capacitor: symmetric and asymmetric binary electrolytes