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.
Categories: cond-mat.stat-mech