Primitive model electrolytes. A comparison of the HNC approximation for the activity coefficient with Monte Carlo data

TL;DR

This study evaluates the accuracy of the Hansen-Vieillefosse-Belloni equation within the HNC approximation for activity coefficients in primitive model electrolytes, comparing results with Monte Carlo data across various concentrations.

Contribution

It demonstrates the validity of the HNC approximation for activity coefficients and compares its thermodynamic consistency with Monte Carlo data and other theoretical models.

Findings

HNC results agree well with Monte Carlo data for activity coefficients.

Gibbs-Duhem-based calculations slightly outperform the Hansen-Vieillefosse-Belloni expression.

HNC provides consistent excess internal energies and osmotic coefficients.

Abstract

Accuracy of the mean activity coefficient expression (Hansen-Vieillefosse-Belloni equation), valid within the hypernetted chain (HNC) approximation, was tested in a wide concentration range against new Monte Carlo (MC) data for +1:-1 and +2:-2 primitive model electrolytes. The expression has an advantage that the excess chemical potential can be obtained directly, without invoking the time consuming Gibbs-Duhem calculation. We found the HNC results for the mean activity coefficient to be in good agreement with the machine calculations performed for the same model. In addition, the thermodynamic consistency of the HNC approximation was tested. The mean activity coefficients, calculated via the Gibbs-Duhem equation, seem to follow the MC data slightly better than the Hansen-Vieillefosse-Belloni expression. For completeness of the calculation, the HNC excess internal energies and osmotic coefficients are also presented. These results are compared with the calculations based on other theories commonly used to describe electrolyte solutions, such as the mean spherical approximation, Pitzer's extension of the Debye-H\"uckel theory, and the Debye-H\"uckel limiting law.