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.

Comparison of critical adsorption scaling functions obtained from neutron reflectometry and ellipsometry

Carpenter et al. [Phys. Rev. E 59, 5655 (1999); 61, 532 (2000)] managed to explain ellipsometric critical adsorption data collected from the liquid-vapor interface of four different critical binary liquid mixtures near their demixing critical temperature using a single model. This was the first time a single universal function had been found which could quantitatively describe the surface critical behavior of many different mixtures. There have also been various attempts to investigate this surface critical behavior using neutron and x-ray reflectometries. Results have been mixed and have often been at variance with Carpenter et al. In this paper, the authors show that neutron reflectometry data collected from a crystalline quartz-critical mixture interface, specifically deuterated water plus 3-methylpyridine, can be quantitatively explained using the model of Carpenter et al. derived from ellipsometric data.

Ellipsometric search for vapor layers at liquid-hydrophobic solid surfaces

We use precision ellipsometry to evaluate the existence of nanometer thick vapor films at the surface between a liquid and a hydrophobic alkylsilane coated Si wafer. We find no evidence for such vapor films. All of our fluid-solid ellipsometry measurements can be explained using a double layer model consisting of an oxide plus silane layer between the fluid and bulk Si substrate. We have carefully checked our ellipsometer for residual phase shifts which might, under certain circumstances, cause a mis-interpretation of the experimental results. We find that the most reliable ellipsometric results for thin films (which are relatively immune to the presence of small residual phase shifts) are collected at the Brewster angle. The dielectric constant of the native oxide coating is also compared with similar measurements for two thick (approximately 100-300 nm) thermally grown oxide coatings on a Si wafer.

Adsorption at the liquid-vapor surface of a binary liquid mixture

In a binary liquid mixture, the component possessing the lowest surface tension preferentially adsorbs at the liquid-vapor surface. In the past this adsorption behavior has been extensively investigated for critical binary liquid mixtures near the mixture's critical temperature T(c). In this fluctuation-dominated regime the adsorption is described by a universal function of the dimensionless depth zxi where xi is the bulk correlation length. Fewer studies have quantitatively examined adsorption for off-critical mixtures because, in this case, one must carefully account for both the bulk and surface crossover from the fluctuation-dominated regime (close to T(c)) to the mean-field dominated regime (far from T(c)). In this paper we compare extensive liquid-vapor ellipsometric adsorption measurements for the mixture aniline+cyclohexane at a variety of critical and noncritical compositions with the crossover theory of Kiselev and co-workers [J. Chem. Phys. 112, 3370 (2000)].

Critical adsorption at silicon surfaces in binary liquid mixtures

In critical binary liquid mixtures the preferential adsorption that occurs at liquid-vapor or liquid-solid surfaces is expected to be described by a universal surface scaling function. In this paper, we show that aniline strongly adsorbs at an oxide-coated Si wafer surface from a critical mixture of aniline + cyclohexane where this solid-liquid adsorption can be described by the same universal function found at liquid-vapor surfaces. For a tetrabromoethane + n-dodecane critical mixture the n-dodecane adsorption on an alkylsilane coated Si wafer cannot be described by previously determined adsorption functions. We speculate that this discrepancy is caused by chemical heterogeneities at the alkylsilane surface due to differing surface distributions of -CH3 and -CH2- groups within the silane layer.

X-ray specular reflectivity study of a critical binary fluid mixture

We have used direct inversion of x-ray reflectivity data to extract the liquid-vapor interface composition profile and the related critical scaling function of a binary mixture of dodecane and tetrabromoethane. The mixture was in the one-phase region above its critical point. The results indicate the formation of a monolayer of the lower surface tension component followed by an abrupt change to a mixed composition which gradually relaxes to the bulk composition deep within the fluid.

Casimir force in a critical film formed from an electrolytic solution

We have studied the thickness of vapor adsorbed films of the critical binary liquid mixture acetic acid plus nonane adsorbed onto a silicon wafer substrate as a function of temperature near the critical temperature. This critical film possesses opposite boundary conditions (+-) at its two surfaces and, due to the dissociation of acetic acid, both the electrostatic force and the dispersion force affect the adsorbed film thickness. On approaching the critical temperature T(c), an increase in the film thickness L is observed, implying that the sign of the universal Casimir amplitude Delta(+-) is positive, consistent with theoretical predictions. However, we find quantitative discrepancies in the value of Delta(+-) and the form of the critical Casimir pressure scaling function vartheta(+-) compared with previous experimental results. We attribute these discrepancies to the complex nature of the critical system studied in this experiment.

Critical adsorption in the weak surface field limit

We study critical adsorption in the small surface field (h(1)) limit using a homologous series of critical liquid mixtures. The experiment data, in the one-phase regime, is accurately described by a universal surface scaling function G+(z/xi(+),z/l(h)) at distance z from the interface with correlation length xi(+) and surface field length l(h) approximately absolute value of (h(1))(-nu/Delta(1)), where h(1) approximately Deltasigma, the surface energy difference between the two components.

Line tension approaching a first-order wetting transition: experimental results from contact angle measurements

The line tension values of n-octane and 1-octene on a hexadecyltrichlorosilane coated silicon wafer, are determined by contact angle measurements at temperatures near a first-order wetting transition T(w). It is shown experimentally that the line tension changes sign as the temperature increases toward T(w) in agreement with a number of theoretical predictions. A simple phenomenological model possessing a repulsive barrier at l(0)=5.1+/-0.2 nm and a scale factor of B=78+/-6 provides a quantitative description of the experiments.

Dipole orientational order at the critical interface

We present experimental evidence that dipoles exhibit orientational order at the critical interface of mixtures of polar plus nonpolar liquids using the technique of ellipsometry. In this technique the ellipticity rho; at the critical interface for all nonpolar or weakly polar fluids or fluid mixtures diverges as t(beta-nu) where t=(Tc-T)/Tc is the reduced temperature relative to the critical temperature Tc and beta=0.328, nu=0.632 are critical exponents. For polar fluids, however, the dipole-image dipole interaction at the interface can cause long-range orientational order resulting in deviations from this power-law divergence. Theoretical results predict that the surface orientational order parameter alpha2(z) approximately m(*4)[d2v(z)/dz2], where m(*) is the reduced dipole moment and v(z) is the local composition at position z within the interface. We find quantitative agreement with these predictions for two different critical binary liquid mixtures composed of a highly polar plus nonpolar component.

Casimir effect in critical films of binary liquid mixtures

We present experimental evidence for the Casimir effect within critical films of binary liquid mixtures possessing opposite boundary conditions (+-) by studying the thickness of these vapor-adsorbed films on a silicon wafer as a function of temperature near the critical temperature. Our results for two different critical mixtures demonstrate that the critical Casimir pressure scaling function vartheta(+-)(y) scales with y=L/xi, where L is the equilibrium film thickness and xi is the bulk correlation length. Additionally, on approaching the critical temperature T(c) an increase in the film thickness L is observed, implying that the sign of the universal Casimir amplitude Delta(+-)=vartheta(+-)(0)/2 at T(c) is positive, consistent with theoretical predictions. However, the magnitude of the Casimir amplitude that we measure is approximately two orders of magnitude smaller than that given by prevailing theories. In the two-phase region of the liquid mixture, preliminary evidence suggests that the adsorbed film undergoes a surface phase transition from a film near the critical composition at T less, similarT(c) to a film near one of the bulk phases at T<<T(c). This low temperature film composition most likely corresponds to the bulk phase rich in the component that preferentially adsorbs at the silicon surface.

Evidence for dipole surface orientational order at critical interfaces

At the critical interface of dipolar systems theory predicts that the amplitude of the surface orientational order alpha(2)(z) approximately m(*4)d(2)v(z)/dz(2), where m(*) is a reduced dipole moment and v(z) is the local composition at position z within the interface. We find quantitative agreement with these predictions for two different critical binary liquid mixtures composed of a highly polar and a nonpolar component.

Ellipsometric determination of universal critical adsorption scaling functions

In this paper we determine and compare a number of theoretical models which describe the universal scaling functions for critical adsorption in the strong surface field limit. The P1 and P3 models, which are continuous up to and including the first and third derivatives, respectively, provide excellent descriptions of the ellipsometric data for four different critical binary liquid mixtures. The exponential-Pade model, initially proposed by Liu and Fisher [Phys. Rev. A 40, 7202 (1989)], provides a reasonable but less accurate description of the one-phase experimental data. This later model has the advantage, however, that it is continuous in all derivatives.

Spreading dynamics of terraced droplets

The liquid crystal (-)7S5 spreads as a two-terraced droplet on an oxide covered (100) Si wafer. The thickness of the upper and lower terraces are respectively approximately 200 and approximately 40 A. This is the simplest system for which the de Gennes and Cazabat (dGC) terraced spreading model [C. R. Acad. Sci. II 310, 1601 (1990)] is applicable. We find that soon after the upper terrace acquires a flat top a hole develops in the center of this terrace. The hole propagates down to the depth of the first terrace. In this contribution we demonstrate that the dGC model is unstable to the formation of a hole in the center of the upper terrace for a two-terraced droplet. Our extended dGC model, which includes a hole in the upper terrace, provides a reasonable description of the average spreading dynamics for this system. However, this model has difficulties quantitatively accounting for all of the features exhibited by the dynamics, perhaps because experimentally the inner and outer borders of the upper terrace become irregular with time. These irregularities in the borders have not been included within the model.

Universal surface scaling function for critical adsorption

We present an accurate determination of the one- and two-phase universal surface scaling function which describes critical adsorption at noncritical interfaces of critical binary liquid mixtures in the strong surface field limit. The 95% confidence levels for this function are also determined. This function quantitatively describes ellipsometric critical adsorption data for three upper critical and one lower critical binary liquid mixtures.