NUMERICAL-ANALYSIS OF ELLIPSOMETRIC CRITICAL ADSORPTION DATA

A recent study [Dan S. P. Smith and Bruce M. Law, Phys. Rev. E 54, 272 7 (1996)] presented measurements of the ellipsometric coefficient at t he Brewster angle <(rho)over bar> on the liquid-vapor surface of four different binary liquid mixtures in the vicinity of their liquid-liqui d critical point and analyzed the data analytically for large reduced temperatures t. In the current report we analyze this (<(rho)over bar> , t) data numerically over the entire range of t. Theoretical universa l surface scaling functions P-+/-(x) from a Monte Carlo (MC) simulatio n [M. Smock, H. W. Diehl, and D. P. Landau, Ber. Bunsenges. Phys. Chem . 98, 486 (1994)] and a renormalization-group (RG) calculation [H. W. Diehl and M. Smock, Phys. Rev. B 47, 5841 (1993); 48, 6470(E) (1993)] are used in the numerical integration of Maxwell's equations to provid e theoretical (<(rho)over bar>, t) curves that can be compared directl y with the experimental data. While both the MC and RG curves are in q ualitative agreement with the experimental data, the agreement is gene rally found to be better for the MC curves. However, systematic discre pancies are found in the quantitative comparison between the MC and ex perimental (<(rho)over bar>, t) curves, and it is determined that thes e discrepancies are too large to be due to experimental error. Finally , it is demonstrated that <(rho)over bar> can be rescaled to produce a n approximately universal ellipsometric curve as a function of the sin gle variable xi(+/-)/lambda, where xi is the correlation length and la mbda is the wavelength of light. The position of the maximum of this c urve in the one-phase region, (xi(+)/lambda)(peak), is approximately a universal number. It is determined that (xi(+)/lambda)(peak) is depen dent primarily on the ratio c(+)/P-infinity,P-+ where P-+(x)congruent to c(+x)(-beta/nu) for x much less than 1 and P-+(x)congruent to P(inf inity,+)e(-x) for x much greater than 1. This enables the experimental estimate of c(+)/P-infinity,P-+ = 0.90 +/- 0.24, which is significant ly large compared to the MC and RG values of 0.577 and 0.442, respecti vely.