Poisson-Fermi Modeling of Ion Activities in Aqueous Single and Mixed Electrolyte Solutions at Variable Temperature

TL;DR

This paper introduces a Poisson-Fermi model that accurately predicts ion activities in aqueous electrolyte solutions across various concentrations and temperatures, using only three parameters related to ion solvation.

Contribution

The paper develops a Poisson-Fermi theory-based model that accounts for steric and correlation effects, reducing parameter complexity compared to traditional models.

Findings

Accurately fits experimental activity data with only three parameters.

Models ion activities across a wide concentration and temperature range.

Includes ion-water and ion-ion correlation effects.

Abstract

The combinatorial explosion of empirical parameters in tens of thousands presents a tremendous challenge for extended Debye-H\"uckel models to calculate activity coefficients of aqueous mixtures of most important salts in chemistry. The explosion of parameters originates from the phenomenological extension of the Debye-H\"uckel theory that does not take steric and correlation effects of ions and water into account. In 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.