A molecular Debye-Hückel theory and its applications to electrolyte solutions

Abstract

In this report, a molecular Debye-Hückel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Hückel theory which is related to the dressed ion theory in the static case. Due to the multi-pole structure of dielectric function of ionic fluids, the electric potential around a single ion has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Hückel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to binary as well as multi-component primitive models of electrolyte solutions demonstrated the accuracy of our approach. More importantly, for electrolyte solution models with soft short-ranged interactions, it is shown that the traditional perturbation theory can be extended to ionic fluids successfully just as the perturbation theory has been successfully used for short-ranged systems.

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

“…In our previous study, it is found that the inclusion of several DH modes (typically L = 2 or 4) are capable to predict the thermodynamics of electrolyte solutions or molten salts [25,8,9], and so one can always safely truncate the elements in Eq. (25) to a finite number.…”

“…We consider a restricted primitive model of electrolyte solution and denote ϕ j (r) as the mean electric potential of a single ion j with charge q j and diameter σ. The electric potential ϕ j (r) of the ion is expanded by a set of DH-like modes [25], such that…”

“…The longitudinal dielectric function ϵ l (k) of an isotropic solution is the wave-number-dependent longitudinal component of the wave-vector-dependent static dielectric tensor ϵ αβ (k), which describes the charge response of a bulk k 2 D k 2 D +k 2 can be found from the Debye-Hückel(DH) theory [25], which describes the dielectric response by a linearized Poisson-Boltzmann equation as ▽ 2 ϕ(r) = k 2 D ϕ(r), with ϕ(r) = q ϵs e −k D r r a Yukawa electric potential and k D the inverse Debye length that related to the ionic strength [26]. However, such a dielectric function is only valid for dilute solution, and is not suitable for concentrated electrolytes.…”

“…Using analytical constraints on k 1,2 from various statistical theories, actually we find a family of analytical dielectric function. Furthermore, this dielectric function is combined with our molecular Debye-Hückel(MDH) theory [25] to give a mean field description of the electrolyte solutions, where the dielectric response is characterized by a linear combination of DH-like response modes, and another analytical expression of dielectric function is derived. Our study establishes a relationship between the microscopic structure parameters such as the first two decay parameters k 1,2 and the thermodynamic properties of an electrolyte solution.…”

Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

“…Numerous theoretical frameworks for aqueous electrolyte solution modelling have been described in the literature; recent examples include the publications of Afanas'ev (2011), Fraenkel (2011, Haghtalab et al (2011), Hsieh and Lin (2011), Hu et al (2011), Lamperski and Pluciennik (2011), Li et al (2011), Partanen (2012), Sun and Dubessy (2012), Tian et al (2012) and Xiao and Song (2011). Of the various approaches proposed none has been more widely adopted than that of Pitzer (1973).…”