X-ray reflectivity study of thermal capillary waves on liquid surfaces

New Design of a Sample Cell for Neutron Reflectometry in Liquid–Liquid Systems and Its Application for Studying Structures at Air–Liquid and Liquid–Liquid Interfaces

Knowledge of interfacial structures in liquid–liquid systems is imperative, especially for improving two-phase biological and chemical reactions. Therefore, we developed a new sample cell for neutron reflectometry (NR), which enables us to observe the layer structure around the interface, and investigated the adsorption behavior of a typical surfactant, sodium dodecyl sulfate (SDS), on the toluene-d8-D2O interface under the new experimental conditions. The new cell was characterized by placing the PTFE frame at the bottom to produce a smooth interface and downsized compared to the conventional cell. The obtained NR profiles were readily analyzable and we determined a slight difference in the SDS adsorption layer structure at the interface between the toluene-d8-D2O and air-D2O systems. This could be owing to the difference in the adsorption behavior of the SDS molecules depending on the interfacial conditions.

2D reflectometry for the investigation of polymer interfaces: off-specular neutron scattering

Specular and off-specular neutron reflectometry have been used in a combined approach to study thin polymer films. Our goal in this work is to illustrate the power of the off-specular scattering technique to probe the properties of the buried interface of immiscible polymer bilayers of deuterated polystyrene and protonated poly(methyl methacrylate) (h-PMMA). The diffuse scattering stemming from these systems is discussed in relation to thermal fluctuations at the polymer/polymer interface, providing a means to extract in-plane correlation lengths from buried interfaces. In addition the onset of hole formation in the top layer is evidenced by the diffuse scattering, not easily detectable by specular reflection alone.

In situ determination of the structure and composition of Langmuir monolayers at the air/water interface by neutron and X-ray reflectivity and ellipsometry

This review focuses on the description of the structure and composition of a variety of Langmuir monolayers (LMs) deposited at the air/water interface by using ellipsometry, Brewster Angle microscopy and scattering techniques, mainly neutron and X-ray reflectometry. Since the first experiment done by Angels Pockels with a homemade trough in her home kitchen until today, LMs of different materials have been extensively studied providing not only relevant model systems in biology, physics and chemistry but also precursors of novel materials via their deposition on solid substrates. There is a vast amount of surface-active materials that can form LMs and, therefore, far from a revision of the state-of-the-art, we will emphasize here: (i) some fundamental aspects to understand the physics behind the molecular deposition at the air/water interface; (ii) the advantages in using in situ techniques, such as reflectometry or ellipsometry, to resolve the interfacial architecture and conformation of molecular films; and, finally, (iii) a summary of several systems that have certain interest from the experimental or conceptual point of view. Concretely, we will report here advances in polymers confined to interfaces and surfactants, from fatty acids and phospholipids monolayers to more unconventional ones such as graphene oxide.

Temperature-dependence of the static contact angle: A transition state theory approach

HYPOTHESIS

The temperature dependence of the static contact angle could a priori be predicted by using surface tension partitioning. An original model based on the transition state theory is also introduced. This model considers thermocapillary fluctuations on the droplet surface near the triple line and the self-affine pinning of this triple line against a solid substrate modeled with a pseudo-periodic distribution of adsorption sites.

EXPERIMENTS

The temperature dependence of the static contact angle was studied for a representative range of liquids with different polarities and on a wide array of solid substrates for temperatures ranging from 25 to 240 °C. Atomic force microscopy (AFM) was also used to quantify the surface roughness of the solid substrates.

FINDINGS

Whereas the surface tension partitioning failed to bring consistent results above room temperature, the transition state model proved very useful, thereby opening a way to yield predictive contact angle values with temperature variations. The introduction of a topological dimension in the equations yields a unified model that covers normal wetting (perfectly bonded liquids on smooth surfaces) but also the onset of Cassie-Baxter and Wenzel states on real surfaces. Moreover, the model encompasses the transition to complete wetting.

Near-Field Probe of Thermal Fluctuations of a Hemispherical Bubble Surface

We report measurements of resonant thermal capillary oscillations of a hemispherical liquid gas interface obtained using a half bubble deposited on a solid substrate. The thermal motion of the hemispherical interface is investigated using an atomic force microscope cantilever that probes the amplitude of vibrations of this interface versus frequency. The spectrum of such nanoscale thermal oscillations of the bubble surface presents several resonance peaks and reveals that the contact line of the hemispherical bubble is pinned on the substrate. The analysis of these peaks allows us to measure the surface viscosity of the bubble interface. Minute amounts of impurities are responsible for altering the rheology of the pure water surface.

Elastic properties of symmetric liquid-liquid interfaces

The mean (κ) and Gaussian (κ[over ¯]) bending rigidities of liquid-liquid interfaces, of importance for shape fluctuations and topology of interfaces, respectively, are not yet established: Even their signs are debated. Using the Scheutjens Fleer variant of the self-consistent field theory, we implemented a model for a symmetric L-L interface and obtained high-precision (mean-field) results in the grand-canonical (μ,V,T) ensemble. We report positive values for both moduli when the system is close to critical where the rigidities show the same scaling behavior as the interfacial tension γ. At strong segregation, when the interfacial width becomes of the order of the segment size, κ[over ¯] turns negative. The length scale λ≡sqrt[κ/γ] remains of the order of segment size for all strengths of interaction; yet the 1/sqrt[N] chain length correction reduces λ significantly when the chain length N is small.

Surface structure evolution in a homologous series of ionic liquids

Interfaces of room temperature ionic liquids (RTILs) are important for both applications and basic science and are therefore intensely studied. However, the evolution of their interface structure with the cation's alkyl chain length [Formula: see text] from Coulomb to van der Waals interaction domination has not yet been studied for even a single broad homologous RTIL series. We present here such a study of the liquid-air interface for [Formula: see text], using angstrom-resolution X-ray methods. For [Formula: see text], a typical "simple liquid" monotonic surface-normal electron density profile [Formula: see text] is obtained, like those of water and organic solvents. For [Formula: see text], increasingly more pronounced nanoscale self-segregation of the molecules' charged moieties and apolar chains yields surface layering with alternating regions of headgroups and chains. The layering decays into the bulk over a few, to a few tens, of nanometers. The layering periods and decay lengths, their linear [Formula: see text] dependence, and slopes are discussed within two models, one with partial-chain interdigitation and the other with liquid-like chains. No surface-parallel long-range order is found within the surface layer. For [Formula: see text], a different surface phase is observed above melting. Our results also impact general liquid-phase issues like supramolecular self-aggregation and bulk-surface structure relations.

Capillary fluctuations of surface steps: An atomistic simulation study for the model Cu(111) system

Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number (k) dependence of the mean squared capillary-wave amplitudes and associated relaxation times, is calculated for 〈110〉 and 〈112〉 steps on the {111} surface of elemental copper near the melting temperature of the classical potential model considered. Step stiffnesses are derived from the MD results, yielding values from the largest system sizes of (37±1)meV/A[over ˚] for the different line orientations, implying that the stiffness is isotropic within the statistical precision of the calculations. The fluctuation lifetimes are found to vary by approximately four orders of magnitude over the range of wave numbers investigated, displaying a k dependence consistent with kinetics governed by step-edge mediated diffusion. The values for step stiffness derived from these simulations are compared to step free energies for the same system and temperature obtained in a recent MD-based thermodynamic-integration (TI) study [Freitas, Frolov, and Asta, Phys. Rev. B 95, 155444 (2017)2469-995010.1103/PhysRevB.95.155444]. Results from the capillary-fluctuation analysis and TI calculations yield statistically significant differences that are discussed within the framework of statistical-mechanical theories for configurational contributions to step free energies.

Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.

Nanoscale Structure of the Oil-Water Interface

X-ray reflectivity (XR) and atomistic molecular dynamics (MD) simulations, carried out to determine the structure of the oil-water interface, provide new insight into the simplest liquid-liquid interface. For several oils (hexane, dodecane, and hexadecane) the XR shows very good agreement with a monotonic interface-normal electron density profile (EDP) broadened only by capillary waves. Similar agreement is also found for an EDP including a sub-Å thick electron depletion layer separating the oil and the water. The XR and MD derived depletions are much smaller than reported for the interface between solid-supported hydrophobic monolayers and water.

Surfactant-induced phases in water-supported alkane monolayers: II. Structure

The structure of the Langmuir-Gibbs films of normal alkanes C(n) of length n = 12-21 formed at the surface of aqueous solutions of C(m)TAB surfactants, m = 14, 16, and 18, was studied by surface-specific synchrotron X-ray methods. At high temperatures, a laterally disordered monolayer of mixed alkane molecules and surface-adsorbed surfactant tails is found, having thicknesses well below those of the alkanes' and surfactant tails' extended length. The mixed monolayer undergoes a freezing transition at a temperature T(s)(n,m), which forms, for n ≤ m + 1, a crystalline monolayer of mixed alkane molecules and surfactant tails. For n ≥ m + 2, a bilayer forms, consisting of an upper pure-alkane, crystalline monolayer and a lower liquidlike monolayer. The crystalline monolayer in both cases consists of hexagonally packed extended, surface-normal-aligned chains. The hexagonal lattice constant is found to decrease with increasing n. The films' structure is discussed in conjunction with their thermodynamic properties presented in an accompanying paper.

Disjoining pressure and the film-height-dependent surface tension of thin liquid films: new insight from capillary wave fluctuations

In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications.

Contact angle patterns on low-energy surfaces

It is well-known that on a given low-energy solid surface, the contact angles of different organic liquids follow a regular pattern. The experimental evidence for this, and semi-empirical equations describing the pattern, are reviewed. Theoretical and computational efforts to explain the pattern are discussed, and a simplified analytical approach is presented. The main pattern of contact angles is seen to arise from two factors: a common combining rule for liquid-solid molecular interactions, and the reduced density of liquid molecules adjacent to a lower-energy solid surface. Irregular departures from the main pattern are due to chemical effects originating in molecular structure.

A novel X-ray diffractometer for studies of liquid-liquid interfaces

The study of liquid-liquid interfaces with X-ray scattering methods requires special instrumental considerations. A dedicated liquid surface diffractometer employing a tilting double-crystal monochromator in Bragg geometry has been designed. This diffractometer allows reflectivity and grazing-incidence scattering measurements of an immobile mechanically completely decoupled liquid sample, providing high mechanical stability. The available energy range is from 6.4 to 29.4 keV, covering many important absorption edges. The instrument provides access in momentum space out to 2.54 Å(-1) in the surface normal and out to 14.8 Å(-1) in the in-plane direction at 29.4 keV. Owing to its modular design the diffractometer is also suitable for heavy apparatus such as vacuum chambers. The instrument performance is described and examples of X-ray reflectivity studies performed under in situ electrochemical control and on biochemical model systems are given.

A study of the ice–water interface using the TIP4P/2005 water model

The structure and fluctuations of the ice–water interface are studied by means of computer simulations using the TIP4P/2005 model.

Formation of iron containing aggregates at the liquid-air interface

The early stages of the formation of inorganic aggregates, composed of iron compounds at the solution-air interface, were investigated in situ. The properties of the solution-air interface were changed by using different Langmuir layers. In order to get insight into the evolution of the sample system in situ, the processes were studied by X-ray scattering and spectroscopy techniques. The formation of aggregates was detected under cationic as well as under anionic Langmuir layers. The observed compounds lack long range order which indicates the formation of amorphous structures. This is supported by extended X-ray absorption fine structure measurements showing only minor order in the formed aggregates.

In situ X-ray studies of adlayer-induced crystal nucleation at the liquid-liquid interface

Crystal nucleation and growth at a liquid-liquid interface is studied on the atomic scale by in situ Å-resolution X-ray scattering methods for the case of liquid Hg and an electrochemical dilute electrolyte containing Pb(2+), F(-), and Br(-) ions. In the regime negative of the Pb amalgamation potential Φ(rp) = -0.70 V, no change is observed from the surface-layered structure of pure Hg. Upon potential-induced release of Pb(2+) from the Hg bulk at Φ > Φ(rp), the formation of an intriguing interface structure is observed, comprising a well-defined 7.6-Å-thick adlayer, decorated with structurally related 3D crystallites. Both are identified by their diffraction peaks as PbFBr, preferentially aligned with their axis along the interface normal. X-ray reflectivity shows the adlayer to consist of a stack of five ionic layers, forming a single-unit-cell-thick crystalline PbFBr precursor film, which acts as a template for the subsequent quasiepitaxial 3D crystal growth. This growth behavior is assigned to the combined action of electrostatic and short-range chemical interactions.

The mechanical response of liquids depositing on a reed

A composite reed flexural vibration method is used to investigate the dynamic mechanical responses of deposited liquids. The composite vibration system consists of a substrate reed with a hole and of liquids deposited inside the hole. The mechanical response of the composite system was monitored in the process of evaporation of deposited liquids such as deionized water, n-propanol and ethanol. The mechanical energy dissipation increases firstly and shows a sudden decrease nearly at the end of the evaporation process. The main contribution to the mechanical energy dissipation is identified to be the damping of liquid surface wave when liquids are inside the hole. This work provides a convenient way to investigate the damping of liquid surface wave by the composite reed vibration method.

A neutron reflection study of surface enrichment in nematic liquid crystals

The interfacial adsorption properties of several different dopants in cyanobiphenyl liquid crystals have been measured using specular neutron reflection. It was found that a partly fluorinated analogue of 11OCB, called F17, adsorbed strongly at the interface between 5CB and air but it was not adsorbed at the interface between 5CB and a solid substrate treated with cetyl trimethyl ammonium bromide (CTAB). The concentration dependence of the adsorption at the air interface was well described by the Brunauer, Emmett and Teller (BET) model, adapted for solutions rather than the gas phase. The isotherms are determined by two equilibrium constants: K(S) for adsorption of the dopant directly at the interface and K(L) for adsorption onto previously adsorbed dopant. The temperature dependence of K(S) indicated that the adsorption enthalpy is not influenced by the phase of the 5CB and its value of -29 kJmol(-1) is consistent with physical adsorption. The value of K(L) is zero in the isotropic phase but increases rapidly on cooling in the nematic phase suggesting that the F17 is less compatible with nematic than isotropic 5CB. The smallest layer thicknesses (~18 Å) suggest that the F17 molecules are approximately perpendicular to the surface. The other dopants studied were components of the E7 mixture: 8OCB and 5CT. No adsorption was found for 8OCB but 5CT showed adsorption at a CTAB treated solid interface when present in 5CB at the 10% level. In this case, the value of K(S) was much smaller than for F17 but the value of K(L) was such that an exponential concentration profile (predicted by the BET model) was observed with characteristic thickness of ~200 Å. The results demonstrate the potential for very precise control of surface properties in liquid crystal devices by using appropriate dopants.

Checkerboard self-patterning of an ionic liquid film on mercury

Å-resolution studies of room temperature ionic liquid (RTIL) interfaces are scarce, in spite of their long-recognized importance for the science and many applications of RTILs. We present an Å-resolution x-ray study of a Langmuir film of an RTIL on mercury. At low (high) coverage [90 (50) Å2/molecule] a mono-(bi)layer of surface-parallel molecules is found. The molecules self-assemble in a lateral ionic checkerboard pattern, unlike the uniform-charge, alternate-ion layers of this RTIL at its bulk-solid interface. A 2D-smectic order is found, with molecules packed in parallel stripes, forming long-range order normal to, but none along, the stripes.

Modification of deeply buried hydrophobic interfaces by ionic surfactants

Hydrophobicity, the spontaneous segregation of oil and water, can be modified by surfactants. The way this modification occurs is studied at the oil-water interface for a range of alkanes and two ionic surfactants. A liquid interfacial monolayer, consisting of a mixture of alkane molecules and surfactant tails, is found. Upon cooling, it freezes at T(s), well above the alkane's bulk freezing temperature, T(b). The monolayer's phase diagram, derived by surface tensiometry, is accounted for by a mixtures-based theory. The monolayer's structure is measured by high-energy X-ray reflectivity above and below T(s). A solid-solid transition in the frozen monolayer, occurring approximately 3 °C below T(s), is discovered and tentatively suggested to be a rotator-to-crystal transition.

Sticking polydisperse hydrophobic magnetite nanoparticles to lipid membranes

The formation of a layer of hydrophobic magnetite (Fe(3)O(4)) nanoparticles stabilized by lauric acid is analyzed by in situ X-ray reflectivity measurements. The data analysis shows that the nanoparticles partially disperse their hydrophobic coating. Consequently, a Langmuir layer was formed by lauric acid molecules that can be compressed into an untilted condensed phase. A majority of the nanoparticles are attached to the Langmuir film integrating lauric acid residue on their surface into the Langmuir film. Hence, the particles at the liquid-gas interface can be identified as so-called Janus beads, which are amphiphilic solids having two sides with different functionality.

Control of thin liquid film morphology during solvent-assisted film deposition

Liquid films of different silicate esters were deposited from volatile solvents on hydroxylated and hydrogen-passivated silicon surfaces. We show that adsorption of silicate ester molecules and the resulting structural morphology of the liquid films not only are determined by attractive van der Waals forces with contributions from electrostatic interactions between the silicone ester moieties and oxide surface sites but also can be tuned by modifying the substrate surface or by changing the liquid-solvent interactions. Our results also show the importance of the conformational properties of liquid molecules and their rearrangements at the liquid/solid interface for controlled solvent-assisted film deposition.

Surface layering at the mercury-electrolyte interface

X-ray reflectometry reveals atomic layering at a liquid-liquid interface--mercury in a 0.01 M NaF solution. The interface width exceeds capillary wave theory predictions and displays an anomalous dependence on the voltage applied across it, displaying a minimum positive of the potential of zero charge. The latter is explained by electrocapillary effects and an additional intrinsic broadening of the interface profile, tentatively assigned to polarization of the conduction electrons due to the electric field of the electrochemical double layer at the interface.

Structural signal of a dynamic glass transition

Pentaphenyl trimethyl trisiloxane is an isotropic liquid at room temperature with a dynamic glass transition at 224 K. Using x-ray reflectivity, we see surface density oscillations (layers) develop below 285 K, similar to those seen in other metallic and dielectric liquids and in computer simulations. The layering threshold is approximately 0.23 times the liquid-gas critical temperature. Upon cooling further, there is a sharp increase at 224 K in the persistence of the surface layers into the bulk material, i.e., an apparently discontinuous change in static structure at the glass transition.

Thermally excited capillary waves at vapor/liquid interfaces of water-alcohol mixtures

The density profiles of liquid/vapor interfaces of water-alcohol (methanol, ethanol and propanol) mixtures were studied by surface-sensitive synchrotron x-ray scattering techniques. X-ray reflectivity and diffuse scattering measurements, from the pure and mixed liquids, were analyzed in the framework of capillary wave theory to address the characteristic length scales of the intrinsic roughness and the shortest capillary wavelength (alternatively, the upper wavevector cutoff in capillary wave theory). Our results establish that the intrinsic roughness is dominated by average interatomic distances. The extracted effective upper wavevector cutoff indicates capillary wave theory breaks down at distances of the order of bulk correlation lengths.

Preferential affinity of calcium ions to charged phosphatidic acid surface from a mixed calcium/barium solution: X-ray reflectivity and fluorescence studies

X-ray reflectivity and fluorescence near total reflection experiments were performed to examine the affinities of divalent ions (Ca(2+) and Ba(2+)) from aqueous solution to a charged phosphatidic acid (PA) surface. A phospholipid (1,2-dimyristoyl-sn-glycero-3-phosphate, DMPA), spread as a monolayer at the air/water interface, was used to form and control the charge density at the interface. We find that, for solutions of the pure salts (i.e., CaCl(2) and BaCl(2)), the number of bound ions per DMPA at the interface is saturated at concentrations that exceed 10(-3) M. For 1:1 Ca(2+)/Ba(2+) mixed solutions, we find that the bound Ca(2+)/Ba(2+) ratio at the interface is 4:1. If the only property determining charge accumulation near PA were the ionic charges, the concentration of mixed Ca(2+)/Ba(2+) at the interface would equal that of the bulk. Our results show a clear specific affinity of PA for Ca compared to Ba. We provide some discussion on this issue as well as some implications for biological systems. Although our results indicate an excess of counterion charge with respect to the surface charge, that is, charge inversion, the analysis of both reflectivity and fluorescence do not reveal an excess of co-ions (namely, Cl(-) or I(-)).

Dynamics and critical damping of capillary waves in an ionic liquid

The dynamics of thermal capillary waves (CWs) on an ionic liquid's surface are studied at the transition from propagating to overdamped CWs by x-ray photon correlation spectroscopy. The analysis considers both homodyne and heterodyne contributions, and yields excellent full line-shape experiment-theory agreement for the structure factor. The CWs' Brillouin scattering becomes extinct at a critical temperature Tc JK approximately 10 K above Tc LL , the propagating modes' hydrodynamic limit, in agreement with linear response theory. Surprisingly, the same power law applies at both Tc. The results rule out the presence of a suggested surface dipole layer.

Structure of the liquid-vapor interfaces of Ga, In and the eutectic Ga-In alloy-an ab initio study

We report the results of ab initio molecular dynamics simulations for the liquid-vapor interface of the liquid metals Ga, In and the eutectic binary alloy Ga-In (16.5% In) for which experimental data are available. The study was performed by using samples of 3000 particles in a slab geometry with periodic boundary conditions. In those systems, the total ionic density distributions along the normal to the interface display some layering and in the case of the Ga-In alloy there appears a highly enriched layer of the lower surface tension component located outermost at the interface. The results are compared with the available experimental data.

Wetting of liquid-crystal surfaces and induced smectic layering at a nematic-liquid interface: an x-ray reflectivity study

We report the results of a synchrotron x-ray reflectivity study of bulk liquid-crystal surfaces that are coated by thin wetting films of an immiscible liquid. The liquid-crystal subphase consisted of the nematic or isotropic phase of 4-octyl- 4;{'} -cyanobiphenyl (8CB), and the wetting film was formed by the fluorocarbon perfluoromethylcyclohexane (PFMC), a volatile liquid. The thickness of the wetting film was controlled by the temperature difference DeltaT(micro) between the sample and a reservoir of bulk PFMC, contained within the sealed sample cell. Phase information on the interfacial electron density profiles has been extracted from the interference between the scattering from the PFMC-vapor interface and the surface-induced smectic order of the 8CB subphase. The liquid-crystal side of the nematic-liquid (8CB-PFMC) interface is characterized by a density oscillation whose period corresponds to the smectic layer spacing and whose amplitude decays exponentially toward the underlying nematic subphase. The decay length xi of the smectic amplitude is independent of the PFMC film thickness but increases as the nematic-smectic- A transition temperature T(NA) is approached, in agreement with the longitudinal correlation length xi(parallel) proportional, variant(T-T(NA))(-0.7} for the smectic fluctuations in the bulk nematic. The results indicate that the homeotropic orientation of the 8CB molecules is preferred at the 8CB-PFMC interface and that the observed temperature dependence of the smectic layer growth is consistent with the critical adsorption mechanism. The observed DeltaT(micro) dependence of the PFMC film thickness, L proportional, variant(DeltaT(micro))(-1/3) , implies that PFMC completely wets the 8CB surface and is dominated by the nonretarded dispersion interactions between hydro- and fluorocarbons. The complete wetting behavior of PFMC is nearly independent of the degree of interfacial smectic order in the subphase.

Wetting, mixing, and phase transitions in Langmuir-Gibbs films

Millimolar bulk concentrations of the surfactant cetyltrimethylammonium bromide (CTAB) induce spreading of alkanes, H(CH(2))(n)H (denoted C(n)) 12< or =n< or =21, on the water surface, which is not otherwise wet by these alkanes. The novel Langmuir-Gibbs film (LGF) formed is a liquidlike monolayer comprising both alkanes and CTAB tails. Upon cooling, an ordering transition occurs, yielding a hexagonally packed, quasi-2D crystal. For 11< or =n< or =17 this surface-frozen LGF is a crystalline monolayer. For 18< or =n< or =21 the LGF is a bilayer with a crystalline, pure-alkane, upper monolayer, and a liquidlike lower monolayer. The phase diagram and film structure were determined by x-ray, ellipsometry, and surface tension measurements. A thermodynamic theory accounts quantitatively for the observations.

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.

Spectra of the liquid cluster surface thermal fluctuations

Classification of cluster particles is proposed that introduces three particle types: the internal particles, surface particles, and virtual chains of particles. Thermal fluctuations of a surface passing through the surface particles of a Lennard-Jones liquid cluster are studied using a molecular dynamics simulation. It is shown that for large clusters, the Fourier spectral amplitude of these fluctuations decays faster than 1q, where q is the wave number. The frequency Fourier spectrum shows an overdamped system behavior, which is the evidence for the absence of thermal capillary waves for clusters comprising less than 10(5) particles. The time-averaged cluster density profile is given by an error function with the width parameter diverging as the logarithm of the cluster size.

The surface structure of ionic liquids: Comparing simulations with x-ray measurements

The surface-normal electron density profile of an ionic liquid, [bmim][PF6], derived from x-ray reflectivity measurements, is compared with two independent molecular-dynamics simulations. It is shown that a meaningful comparison requires a detailed accounting for both thermal and nonthermal surface roughening effects. The former is due to thermally excited capillary waves, and the latter is due to the molecular zero-point motion and form. These quantities influence very significantly, but differently, the simulated and measured density profiles. Stripping off these effects from both types of profiles yields the intrinsic structure factor of the surface. The simulated intrinsic structure factors are found to deviate considerably from the measured one. The introduction of additional ad hoc surface roughness to the simulated profiles greatly reduces the deviation, however, no physical origin for this effect can be identified. The method employed in this study should prove useful for simulation-experiment comparisons of other liquid surfaces, provided they obey capillary-wave theory, as do almost all liquid surfaces studied to date by x-ray reflectivity.

Capillary wave fluctuations and intrinsic widths of coupled fluid-fluid interfaces: an x-ray scattering study of a wetting film on bulk liquid

An x-ray specular reflectivity (XR) and off-specular diffuse scattering (XDS) study of the coupled thermal capillary fluctuations and the intrinsic profiles of two interacting fluid-fluid interfaces is presented. The measurements are carried out on complete wetting films of perfluoromethylcyclohexane (PFMC) on the surface of bulk liquid eicosane (C20), as a function of film thickness 30<D<160 A. In order to facilitate the analysis and interpretation of the data with minimal complexity, approximate methods for calculating scattering intensities are developed to take into account the subtleties of thermal diffuse scattering from layered liquid surfaces. With these methods, the calculations of XR/XDS intensities are reduced to a single numerical integration of simple functions in real space. In addition, an analytic expression is derived for small-angle XR that contains Debye-Waller-like factors with effective capillary roughness and takes into account the partial correlations of the two interfaces. The expression for the XR is quantitatively accurate so long as the reflection angle is small enough that the scattering from interfaces is distinguishable from bulk scattering. The results of the XR and XDS data analysis indicate that the capillary fluctuations at the two interfaces of the wetting films are partially correlated and their coupling is consistent with the van der Waals interactions. The relatively large intrinsic width (4 approximately 6A) of the liquid-liquid interface observed for thicker films (D greater than or similar to 50 A) is comparable to the value expected for the bulk liquid-liquid interface (D-->infinity), determined by either the radius of gyration (5.3 A) or the bulk correlation length (4.8 A) of the alkane C20. The intrinsic liquid-vapor interfacial width is sharper (approximately 2 A) and remains essentially constant over the entire probed range of D .

The intrinsic structure of the water surface

An operational procedure to obtain the intrinsic structure of liquid surfaces is applied here to a molecular dynamics simulation of water, with a model of point charges for the molecular interactions. The method, which had been recently proposed and used for simple fluids, is successfully extended to a molecular liquid with the complex bond structure of water. The elimination of the capillary wave fluctuations, in the intrinsic density and orientation profiles, gives a new overall view of the water surface, at the sharpest molecular level, and without the size-dependent broadening observed in the mean profiles. The molecules belonging to the outer liquid layer are clearly identified, and we find that only these molecules exhibit a clear preferential orientation to lie flat on the surface. Moreover, there is a strong correlation between the dipolar structure and the local curvatures of the intrinsic surface, so that at the extrusions of the intrinsic surface the molecular dipoles point preferentially toward the vapor side of the interface. Finally, we have found an intrinsic density layering structure, although the inner structure is strongly damped beyond the second layer.

X-ray reflectivity study of ultrathin liquid films of diphenylsiloxane-dimethylsiloxane copolymers

Using X-ray reflectivity, we observe drastic differences in the interfacial structure and molecular ordering of diphenylsiloxane-dimethylsiloxane copolymer thin films deposited on hydroxylated versus H-terminated (etched) silicon wafers. We find that substrate type and comonomer ratio determine the conformational arrangements in these liquid films. High-energy bonding between the substrate and the molecules and an increase in rigidity of the molecules due to replacement of methyl groups by phenyl groups leads to a specific molecular ordering at the liquid/solid interface and pronounced density oscillations in this region. The observed structural reorganizations are explained by the interplay and the established balance between the chain flexibility and the polymer-substrate interactions.

Characterization of molecular linkages placed between zeolite microcrystal monolayers and a substrate with X-ray reflectivity

We prepared silicalite-1 microcrystal (MC) monolayers on a Si wafer using two different types of molecular linkages, namely, through chloropropyl (CP) groups and through CP/polyethylene imine/CP groups. Whereas the scanning electron microscope images of the two MC monolayers look very much alike but hardly give any information on the nature of molecular linkage between the monolayers and the substrate, their reflectivity curves are distinctively different, despite the fact that the thicknesses of the molecular linkage layers ( approximately 10-20 A) are negligibly small compared to the thicknesses of MC monolayers, ( approximately 3200 A). On the basis of the atomic force microscopic images of the MC surfaces, a rough surface layer with the thickness of approximately 160 A was introduced onto the surface of each MC to conduct a meaningful simulation of the curves with the recursive Parratt formalism. The obtained thickness, roughness, and density of each layer were reasonable, indicating that X-ray reflectivity is a very useful tool for the characterization of very thin layers of molecular linkages existing between much thicker MC monolayers and the substrate.

Observation of surface layering in a nonmetallic liquid

Oscillatory density profiles (layers) have previously been observed at the free surfaces of liquid metals but not in other isotropic liquids. We have used x-ray reflectivity to study a molecular liquid, tetrakis(2-ethylhexoxy)silane. When cooled to T/Tc approximately 0.25 (well above the freezing point for this liquid), density oscillations appear at the surface. Lateral order within the layers is liquidlike. Our results confirm theoretical predictions that a surface-layered state will appear even in dielectric liquids at sufficiently low temperatures, if not preempted by freezing.

Surface roughness and adsorption isotherms of molecularly thin liquid films: an x-ray reflectivity study

We present an x-ray reflectivity study of molecularly thin films of liquid isobutane adsorbed on liquid glycerol. The glycerol-isobutane interface serves as a model system to investigate the influence of the substrate adsorbate interactions on both adsorption isotherms and capillary wave fluctuations. The measured surface roughness is smaller than expected from the harmonic approximation of the interaction potential. Expressions for the surface roughness in slightly anharmonic potentials are given and compared to the experimental data. A good agreement between data and theory is achieved.

Faraday instability in a surface-frozen liquid

Faraday surface instability measurements of the critical acceleration, a(c), and wave number, k(c), for standing surface waves on a tetracosanol (C24H50) melt exhibit abrupt changes at T(s)=54 degrees C, approximately 4 degrees C above the bulk freezing temperature. The measured variations of a(c) and k(c) vs temperature and driving frequency are accounted for quantitatively by a hydrodynamic model, revealing a change from a free-slip surface flow, generic for a free liquid surface (T>T(s)), to a surface-pinned, no-slip flow, characteristic of a flow near a wetted solid wall (T<T(s)). The change at T(s) is traced to the onset of surface freezing, where the steep velocity gradient in the surface-pinned flow significantly increases the viscous dissipation near the surface.

Deviations from liquidlike behavior in molten polymer films at interfaces

We have performed x-ray specular and diffuse scattering on liquid polymer films and analyzed the spectra as a function of film thickness and molecular weight. The results show that films whose molecular weight is close to the entanglement length behave as simple liquids except that the shortest wavelength is determined by the radius of gyration (R(g)) rather than the monomer-monomer distance. When the molecular weight is higher than the entanglement length, the strong deviations from liquidlike behavior are observed. We find that the long wavelength cutoff vector, q(l,c), scales with film thickness, d as d(-1.1+/-0.1) rather than the usual d(-2) expected for simple liquids. If we assume that these deviations are due to surface pinning of the polymer chains, then our results are consistent with the formalism developed by Fredrickson et al. to explain the capillary wave spectrum that can propagate in a polymer brush.