Poisson-Fermi modeling of ion activities in aqueous single and mixed electrolyte solutions at variable temperature

Abstract

The combinatorial explosion of empirical parameters in tens of thousands presents a tremendous challenge for extended Debye-Hückel models to calculate activity coefficients of aqueous mixtures of the most important salts in chemistry. The explosion of parameters originates from the phenomenological extension of the Debye-Hückel theory that does not take steric and correlation effects of ions and water into account. By contrast, the Poisson-Fermi theory developed in recent years treats ions and water molecules as nonuniform hard spheres of any size with interstitial voids and includes ion-water and ion-ion correlations. We present a Poisson-Fermi model and numerical methods for calculating the individual or mean activity coefficient of electrolyte solutions with any arbitrary number of ionic species in a large range of salt concentrations and temperatures. For each activity-concentration curve, we show that the Poisson-Fermi model requires only three unchanging parameters at most to well fit the corresponding experimental data. The three parameters are associated with the Born radius of the solvation energy of an ion in electrolyte solution that changes with salt concentrations in a highly nonlinear manner.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

“…We have recently developed a molecular mean-field theory called—Poisson-Nernst-Planck-Bikerman (PNPB) theory—that can describe the size, correlation, dielectric , and polarization effects of ions and water in aqueous electrolytes at equilibrium or nonequilibrium all within a unified framework [ 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 ]. Water and ions in this theory can have different shapes and volumes necessarily with intermolecular voids.…”

Review and Modification of Entropy Modeling for Steric Effects in the Poisson-Boltzmann Equation

“…Let us denote (55) as the specific-ion-size Bikerman model 2 (SISBM2) for convenience. Note that a similar model was also obtained in [ 18 , 19 ] without a rigorous derivation.…”

“…Notice, under , SISBM3 is actually same as SISBM1, but with a rigorous derivation now. This model has been useful and proven to fit the experimental data quite well [ 16 , 17 , 18 ]. Although here we just discussed steric-effect modifications for PB, modifications for PNP can be likewise derived.…”

“…The steric potential , first described in [ 16 , 17 , 18 , 19 ], characterizes the crowding of ions and their finite-size effect by a bulk-to-local water fraction ratio. Larger local ion concentrations would have a larger steric potential.…”

“…Researchers have tried to address this shortcoming with specific ion sizes, and many of them simply extended original Bikerman model by replacing the identical ion size with specific ones without any rigorous justification. Although the resultant model has a better agreement with experiments than the original Bikerman model [ 16 , 17 , 18 ], it does not have a Helmholtz free energy to support it. Here modifications of the Bikerman model to include specific ion sizes have been developed iteratively in Section 4 , Section 5 and Section 6 , preceded by derivations of classical PB in Section 2 , and the original Bikerman model in Section 3 .…”