Nonextensive local composition models in theories of solutions

TL;DR

This paper introduces nonextensive Tsallis statistics into local composition models for solutions, generalizing Wilson's, NRTL, and UNIQUAC models to better fit experimental data with a new temperature dependence.

Contribution

It proposes a novel nonextensive framework for local composition models, incorporating an additional parameter q to improve thermodynamic predictions.

Findings

The q-models fit experimental activity coefficients better than traditional models.

The generalized models reduce to classical ones when q approaches 1.

Application to ethanol solutions demonstrates improved accuracy.

Abstract

Thermodynamic models present binary interaction parameters, based on the Boltzmann weight. Discrepancies from experimental data lead to empirically consider temperature dependence of the parameters, but these modifications keep unchanged the exponential nature of the equations. We replace the Boltzmann weight by the nonextensive Tsallis weight, and generalize three models for nonelectrolyte solutions that use the local composition hypothesis, namely Wilson's, NRTL, and UNIQUAC models. The proposed generalizations present a nonexponential dependence on the temperature, and relies on a theoretical basis of nonextensive statistical mechanics. The $q$-models present one extra binary parameter $q_{ij}$, that recover the original cases in the limit $q_{ij} \to 1$. Comparison with experimental data is illustrated with two examples of the activity coefficient of ethanol, infinitely diluted in toluene, and in decane.