Ellipsometric measurement of universal critical adsorption integrals

We present an experimental determination of the universal critical adsorption integrals F ${\mathit{P}}_{+}$=F ${\mathit{P}}_{+}$(x)dx and F ${\mathit{P}}_{\mathrm{-}}$=F[${\mathit{P}}_{\mathrm{-}}$(x)-1]dx, where ${\mathit{P}}_{\pm }$(x) are the one-phase (+) and the two-phase (-) universal functions that scale the variation of the local order parameter near a free surface in the vicinity of the Ising critical end point. From ellipsometric measurements on three critical binary liquid mixtures we obtain F ${\mathit{P}}_{+}$=1.86±0.11, F ${\mathit{P}}_{\mathrm{-}}$=1.61±0.04, and ${\mathit{R}}_{\mathit{M}\mathit{A}}$=1.19±0.04 for their ratio, where the quoted uncertainties represent one standard deviation. These values are compared with recent theoretical and computational results. The renormalization-group calculation of Diehl and Smock [Phys. Rev. B 47, 5841 (1993)] obtained F ${\mathit{P}}_{+}$=1.91, F ${\mathit{P}}_{\mathrm{-}}$=1.44, and ${\mathit{R}}_{\mathit{M}\mathit{A}}$=1.33, while a Monte Carlo simulation [M. Smock, H. W. Diehl, and D. P. Landau, Ber. Bunsenges. Phys. Chem. 98, 486 (1994)] obtained F ${\mathit{P}}_{+}$=2.18, F ${\mathit{P}}_{\mathrm{-}}$=1.97, and ${\mathit{R}}_{\mathit{M}\mathit{A}}$=1.11. An interpolation to dimension d=3 of exact calculations for d=2 and 4 [G. Flöter and S. Dietrich, Z. Phys. B 97, 213 (1995)] obtained F ${\mathit{P}}_{+}$=2.27±0.33, F ${\mathit{P}}_{\mathrm{-}}$=1.84±0.33, and ${\mathit{R}}_{\mathit{M}\mathit{A}}$=1.32±0.07.