Scaling for Interfacial Tensions near Critical Endpoints

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.

arXiv comment42 pages, 6 figures, to appear in Physical Review E

References in corpus (7)

• The Theory of Boundary Critical Phenomena
• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• Coexistence Curve Singularities at Critical End Points
• Extension to order ${\beta }^{23}$ of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices
• Numerical equation of state and other scaling functions from an improved three-dimensional Ising model
• Field-Theoretical Analysis of Critical and Coexistence Singularities at Critical End Points
• Bulk singularities at critical end points: a field-theory analysis

Cited by in corpus (3)

• Topological Approach to Microcanonical Thermodynamics and Phase Transition of Interacting Classical Spins
• Interfacial Tensions near Critical Endpoints: Experimental Checks of EdGF Theory
• Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets