Scaling for Interfacial Tensions near Critical Endpoints

TL;DR

This paper develops parametric scaling models for interfacial tensions near fluid critical endpoints, incorporating nonclassical exponents and universal ratios, and addresses previous theoretical shortcomings to better match experimental observations.

Contribution

It introduces an extended local-functional theory that rectifies prior scaling defects and models complete wetting behavior near critical endpoints.

Findings

Predicts an amplitude ratio of -3.25 ± 0.05 for vapor-liquid interfacial tension.

Includes nonclassical critical exponents and universal amplitude ratios.

Addresses and corrects previous scaling treatment deficiencies.

Abstract

Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the \textit{full} neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both} of temperature \textit{and} of density/order parameter \textit{or} chemical potential/ordering field. Accurate \textit{nonclassical critical exponents} and reliable estimates for the \textit{universal amplitude ratios} are included naturally on the basis of the ``extended de Gennes-Fisher'' local-functional theory. Serious defects in previous scaling treatments are rectified and complete wetting behavior is represented; however, quantitatively small, but unphysical residual nonanalyticities on the wetting side of the critical isotherm are smoothed out ``manually.'' Comparisons with the limited available observations are presented elsewhere but the theory invites new, searching experiments and simulations, e.g., for the vapor-liquid interfacial tension on the two sides of the critical endpoint isotherm for which an amplitude ratio $-3.25 \pm 0.05$ is predicted.