A Unified Rational-Function Approximation for Square-Well, Square-Shoulder, and Nonadditive Hard-Sphere Mixtures
Abstract
We develop a rational-function approximation for the structural properties of multicomponent fluids with narrow square-well and square-shoulder interactions, together with weakly nonadditive hard-sphere mixtures. The theory is obtained by reformulating the analytical Percus--Yevick solution for additive sticky hard-sphere mixtures so as to account for finite interaction widths, leading to a unified semianalytical framework for these classes of fluids. The approximation satisfies the exact low-density limit and preserves the continuity of the cavity functions; a simple local correction restores the continuity of their first derivatives. Comparison with Monte Carlo simulations for binary mixtures shows that the theory accurately describes both the radial distribution functions and their Fourier transforms for narrow wells and shoulders and for weak nonadditivity. The proposed formulation extends previous sticky-hard-sphere-based approaches while retaining their analytical simplicity.
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BibTeX
@misc{santos2026unified,
title = {{A Unified Rational-Function Approximation for Square-Well, Square-Shoulder, and Nonadditive Hard-Sphere Mixtures}},
author = {Andrés Santos and Santos B. Yuste and Ana M. Montero and Mariano López de Haro},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34914},
eprint = {2609.34914},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34914},
}
RIS
TY - UNPB
TI - A Unified Rational-Function Approximation for Square-Well, Square-Shoulder, and Nonadditive Hard-Sphere Mixtures
AU - Andrés Santos
AU - Santos B. Yuste
AU - Ana M. Montero
AU - Mariano López de Haro
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34914
UR - https://arxiv.org/abs/2609.34914
AB - We develop a rational-function approximation for the structural properties of multicomponent fluids with narrow square-well and square-shoulder interactions, together with weakly nonadditive hard-sphere mixtures. The theory is obtained by reformulating the analytical Percus--Yevick solution for additive sticky hard-sphere mixtures so as to account for finite interaction widths, leading to a unified semianalytical framework for these classes of fluids. The approximation satisfies the exact low-density limit and preserves the continuity of the cavity functions; a simple local correction restores the continuity of their first derivatives. Comparison with Monte Carlo simulations for binary mixtures shows that the theory accurately describes both the radial distribution functions and their Fourier transforms for narrow wells and shoulders and for weak nonadditivity. The proposed formulation extends previous sticky-hard-sphere-based approaches while retaining their analytical simplicity.
ER -