An analytical longitudinal dielectric function of primitive electrolyte solutions and its application in predicting thermodynamic properties

A multiple decay-length extension of the Debye–Hückel theory: to achieve high accuracy also for concentrated solutions and explain under-screening in dilute symmetric electrolytes

“…Most of these approximations have been used to obtain thermodynamical quantities, distribution functions and/or the mean electrostatic potential. 15,16,27,28,[31][32][33]37,39,[42][43][44][45][46][47] Xiao and Song [48][49][50] have developed a linear theory that exploits all decay modes obtained in many of these approximations to calculate thermodynamical quantities for electrolytes. We will return to some of these linear, approximate theories later.…”

A molecular Debye-Hückel theory and its applications to electrolyte solutions: The size asymmetric case

“…Our MDH theory is applicable to the solutes with general geometry and charge density and has been tested for several systems. [25][26][27][28] With the above excess properties, it is possible to evaluate other thermodynamic properties of an electrolyte solution. The averaged excess internal energy per particle is…”

“…Note that χ(k) in most case is not analytically known, an empirical function χ(k) = a 0 k 2 k 4 + (a 1 k 2 − a 2 )Cos(kb) + a 3 Sin(kb) + a 2 can be used to fit the response function χ(k), and then the pole k = ik n can be determined by solving k 4 + (a 1 k 2 a 2 )Cos(kb) + a 3 Sin(kb) + a 2 = 0 numerically. 27,28 (2) The hard sphere contribution to the charge density ρ hs j (k) = n i q i x i h hs ij (k) can be evaluated using the analytical correlation function h hs ij (k) from the Percus-Yevick (PY) theory or other integral equation theory for hard sphere mixtures, 15 and then the cumulate charge Q hs j ≡ ∫ ρ hs j (r)4πr 2 dr and the electric potential ψ hs j ≡ ∫ ρ hs j (r) r 4πr 2 dr can be determined. The parameters ρ hs e and a d of the effective surface charge are evaluated by ρ hs e = (ψ hs j ) 2 /(4πQ hs j ) and a d = Q hs j /ψ hs j .…”

“…Such a prescription has been applied successfully to the various ionic fluids. [25][26][27][28] In this contribution, we extend the MDH theory to the size asymmetric case, so that the cation and anion of the electrolyte solutions can have different sizes. It is known that the size asymmetry leads to a border zone around a solute ion, where the charge density is nonzero even for a neutral solute.…”

A molecular Debye-Hückel theory of solvation in polar fluids: An extension of the Born model

“…from MD simulation is fitted to a half empirical function [52][53][54] which is the function form of the MSA response function for a dipolar hard sphere fluid. The fitted parameters are found to be a 1 = 7.1953, a 2 = 120.58, a 3 = 10.431, a 4 = 619.04, b 1 = 3.2588, and b 2 = 0.300 96.…”