A Systematic Way to Extend the Debye–Hückel Theory beyond Dilute Electrolyte Solutions

Abstract

An extended Debye-Hückel theory with fourth order gradient term is developed for electrolyte solutions, namely the electric potential ϕ(r) of the bulk electrolyte solution can be described byr), where the parameters κ and L Q are chosen to reproduce the first two roots of the dielectric response function of the bulk solution. Three boundary conditions for solving the electric potential problem are proposed based upon the continuity conditions of involving functions at the dielectric boundary, with which a boundary element method for the electric potential of a solute with a general geometrical shape and charge distribution is derived. Solutions for the electric potential of a spherical ion and a diatomic molecule are found and used to calculate their electrostatic solvation energies. The validity of the theory is successfully demonstrated when applied to binary as well as multi-component primitive models of electrolyte solutions.

Electric-field-induced oscillations in ionic fluids: a unified formulation of modified Poisson–Nernst–Planck models and its relevance to correlation function analysis

“…One is to improve the Poisson equation for the Coulomb interaction potential ψ ( r , t ) experienced by an ion (the higher-order Poisson eqn (15)). 5–10,21–24 The other is to make a self-energy correction to the Coulomb interaction term in the PNP equations (the self-energy term determined by the generalized Debye–Hückel eqn (21)), 10,25 thereby providing theoretical descriptions of ionic transport in agreement with simulation results; however, these modifications are empirical, and correlation functions have been beyond the scope due to the absence of stochastic current. Meanwhile, our self-energy-modified PNP equations, derived from the basic formulation of the SDFT (see Appendix A for details), verify the stochastic dynamics and encompass the above modifications.…”

“…As shown in Appendix A2, eqn (14) transforms towhen performing the low wavenumber expansion of ω ( k ), similarly to the transformation from the finite-spread Poisson–Boltzmann equation to the higher-order one for one-component fluids. 24 Eqn (15) will be referred to as the higher-order Poisson equation 5–10,21–24 for comparison with the finite-spread Poisson eqn (14), though often called either the Poisson-Fermi equation or the Bazant–Storey–Kornyshev equation. 21…”

“…(ii) Ion–ion Coulomb correlations are taken into account by modified Poisson equations such as higher-order Poisson equation. 21–24 (iii) Dielectric boundary effects are investigated according to a generalized Born theory which evaluates solvation energy from an ionic self-energy. 25…”

“…The essential achievement in terms of the theoretical formalism is clarified in Section IID. As detailed in Appendix A, the hybrid framework of the field-theoretic approach, the equilibrium 37,38 and dynamic 11 DFTs, and the liquid state theory justifies the modified Poisson equations 5–10,23,24,39–41 and the generalized Debye–Hückel equation for the self-energy. 10,25…”

Ionization Difference between Weak and Strong Electrolytes as Perturbed by Conductivity Spectra Analysis

“…This behavior is usually explained by the Kohlrausch law (KL) and the Debye–Hückel–Onsager (DHO) conductivity theory for dilute solutions, which classifies the electrolytes by a degree of dissociation (Figure b). Various modifications of the Debye–Hückel theory have been developed for the past decades. ,− They extend the range of modeling to the high concentrations but still account for the dc data only.…”