X-ray and ellipsometric study of strong critical adsorption

Carpenter [Phys. Rev. E 61, 532 (2000)] succeeded in determining a single universal model, called the P1 model, that could describe the ellipsometric critical adsorption data from the liquid-vapor interface of four different critical binary liquid mixtures near their critical demixing temperatures. The P1 model also recently has been used to describe neutron reflectometry data from a critical liquid mixture/crystalline quartz interface. However, in another recent study, the P1 model failed to simultaneously describe x-ray reflectometry and ellipsometry data from the liquid-vapor surface of the critical mixture n -dodecane + tetrabromoethane (DT). In this paper, we resolve this discrepancy between x-ray and ellipsometric data for the DT system. At large length scales (far from the interface) the local concentration is described by the P1 model in order to correctly reproduce the temperature dependence of the ellipsometric data. Close to the interface, however, the molecular structure must be correctly accounted for in order to quantitatively explain the x-ray data. An important conclusion that arises from this study is that neutron or x-ray reflectometry is most sensitive to short-range interfacial structure, but may provide misleading information about long-range interfacial structure. Ellipsometry provides a more accurate measure of this long-range interfacial structure. Complex interfacial structures, possessing both short- and long-range structure, are therefore best studied using multiple techniques.