Modified Debye-H\"uckel-Onsager Theory for Electrical Conductivity in Aqueous Electrolyte Solutions. Account of Ionic Charge Nonlocality

TL;DR

This paper extends the classical Debye-Hückel-Onsager theory to include ion specificity and nonlocal charge effects, providing a more accurate mean-field model for electrical conductivity in aqueous electrolyte solutions across various concentrations and temperatures.

Contribution

It introduces a modified theory incorporating ion charge nonlocality and hydration effects, improving the prediction of electrolyte conductivity beyond classical models.

Findings

The model reproduces Kohlrausch's limiting law at low concentrations.

Experimental conductivity data are well approximated with a single free parameter.

Good agreement with experimental data across different temperatures.

Abstract

The paper presents a mean field theory of electrolyte solutions, extending the classical Debye-H\"{u}ckel-Onsager theory to provide a detailed description of the electrical conductivity in strong electrolyte solutions. The theory systematically incorporates the effects of ion specificity, such as steric interactions, hydration of ions, and their spatial charge distributions, into the mean-field framework. This allows for calculation of ion mobility and electrical conductivity, while accounting for relaxation and hydrodynamic phenomena. At low concentrations, the model reproduces the well-known Kohlrausch's limiting law. Using the exponential (Slater-type) charge distribution function for solvated ions, we demonstrate that experimental data on the electrical conductivity of aqueous 1:1, 2:1, and 3:1 electrolyte solutions can be approximated over a broad concentration range by adjusting a single free parameter representing the spatial scale of the nonlocal ion charge distribution. Using the fitted value of this parameter at 298.15 K, we obtain good agreement with available experimental data when calculating the electrical conductivity across different temperatures. We also analyze the effects of temperature and electrolyte concentration on the relaxation and electrophoretic contributions to total electrical conductivity, explaining the underlying physical mechanisms responsible for the observed behavior.