Capillary waves on the surface of simple liquids measured by x-ray reflectivity

Thermodynamics of Surfactant-Enriched Binary-Fluid Systems

Surface-active agents (surfactants) release potential energy as they migrate from one of two adjacent fluids onto their fluid-fluid interface, a process that profoundly impacts the system's energy and entropy householding. The continuum thermodynamics underlying such a surfactant-enriched binary-fluid system has not yet been explored comprehensively. In this article, we present a mathematical description of such a system, in terms of balance laws, equations of state, and permissible constitutive relations and interface conditions, that satisfies the first and second law of thermodynamics. The interface conditions and permissible constitutive relations are revealed through a Coleman-Noll analysis. We characterize the system's equilibrium by defining equilibrium equivalences and study an example system. With our work, we aim to provide a systematically derived framework that combines and links various elements of existing literature, and that can serve as a thermodynamically consistent foundation for the (numerical) modeling of full surfactant-enriched binary-fluid systems.

Revisiting the Thickness of the Air-Water Interface from Two Extremes of Interface Hydrogen Bond Dynamics

The air-water interface plays a crucial role in many aspects of science because of its unique properties, such as a two-dimensional hydrogen bond (HB) network and completely different HB dynamics compared to bulk water. However, accurately determining the boundary of interfacial and bulk water, that is, the thickness of the air-water interface, still challenges experimentalists. Various simulation-based methods have been developed to estimate the thickness, converging on a range of approximately 3-10 (Å). In this study, we introduce a novel approach, grounded in density functional theory-based molecular dynamics and deep potential molecular dynamics simulations, to measure the air-water interface thickness, offering a different perspective based on prior research. To capture realistic HB dynamics in the air-water interface, two extreme scenarios of the interface HB dynamics are obtained: one underestimates the interface HB dynamics, while the other overestimates it. Surprisingly, our results suggest that the interface HB dynamics in both scenarios converges as the thickness of the air-water interface increases to 4 (Å). This convergence point, indicative of the realistic interface thickness, is also validated by our calculation of anisotropic decay of OH stretch and the free OH dynamics at the air-water interface.

Reconstructing the reflectivity of liquid surfaces from grazing incidence X-ray off-specular scattering data

The capillary wave model of a liquid surface predicts both the X-ray specular reflection and the diffuse scattering around it. A quantitative method is presented to obtain the X-ray reflectivity (XRR) from a liquid surface through the diffuse scattering data around the specular reflection measured using a grazing incidence X-ray off-specular scattering (GIXOS) geometry at a fixed horizontal offset angle with respect to the plane of incidence. With this approach the entire Qz -dependent reflectivity profile can be obtained at a single, fixed incident angle. This permits a much faster acquisition of the profile than with conventional reflectometry, where the incident angle must be scanned point by point to obtain a Qz -dependent profile. The XRR derived from the GIXOS-measured diffuse scattering, referred to in this paper as pseudo-reflectivity, provides a larger Qz range compared with the reflectivity measured by conventional reflectometry. Transforming the GIXOS-measured diffuse scattering profile to pseudo-XRR opens up the GIXOS method to widely available specular XRR analysis software tools. Here the GIXOS-derived pseudo-XRR is compared with the XRR measured by specular reflectometry from two simple vapor-liquid interfaces at different surface tension, and from a hexadecyltri-methyl-ammonium bromide monolayer on a water surface. For the simple liquids, excellent agreement (beyond 11 orders of magnitude in signal) is found between the two methods, supporting the approach of using GIXOS-measured diffuse scattering to derive reflectivities. Pseudo-XRR obtained at different horizontal offset angles with respect to the plane of incidence yields indistinguishable results, and this supports the robustness of the GIXOS-XRR approach. The pseudo-XRR method can be extended to soft thin films on a liquid surface, and criteria are established for the applicability of the approach.

Intrinsic Stress Field for Liquid Surfaces

The microscopic stress field inhomogeneity in the interfacial region adjacent to the liquid surface is the fundamental origin of the liquid surface tension, but because of broadening due to capillary fluctuations, a detailed molecular level understanding of the stress field remains elusive. In this work, we deconvolute the capillary fluctuations to reveal the intrinsic stress field and show that the atomic-level contributions to the surface tension are similar in functional form across a variety of monatomic systems. These contributions are confined to an interfacial region approximately 1.5±0.1 times the particle diameter for all systems studied. In addition, the intrinsic density and stress profiles show a strong spatial correlation that should be useful in the development of a statistical mechanical theory for the prediction of surface stress and surface tension.

Neural network analysis of neutron and X-ray reflectivity data incorporating prior knowledge

Due to the ambiguity related to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This ambiguity poses limitations on standard neural networks, constraining the range and number of considered parameters in previous machine learning solutions. To overcome this challenge, a novel training procedure has been designed which incorporates dynamic prior boundaries for each physical parameter as additional inputs to the neural network. In this manner, the neural network can be trained simultaneously on all well-posed subintervals of a larger parameter space in which the inverse problem is underdetermined. During inference, users can flexibly input their own prior knowledge about the physical system to constrain the neural network prediction to distinct target subintervals in the parameter space. The effectiveness of the method is demonstrated in various scenarios, including multilayer structures with a box model parameterization and a physics-inspired special parameterization of the scattering length density profile for a multilayer structure. In contrast to previous methods, this approach scales favourably when increasing the complexity of the inverse problem, working properly even for a five-layer multilayer model and a periodic multilayer model with up to 17 open parameters.

Millisecond X-ray reflectometry and neural network analysis: unveiling fast processes in spin coating

X-ray reflectometry (XRR) is a powerful tool for probing the structural characteristics of nanoscale films and layered structures, which is an important field of nanotechnology and is often used in semiconductor and optics manufacturing. This study introduces a novel approach for conducting quantitative high-resolution millisecond monochromatic XRR measurements. This is an order of magnitude faster than in previously published work. Quick XRR (qXRR) enables real time and in situ monitoring of nanoscale processes such as thin film formation during spin coating. A record qXRR acquisition time of 1.4 ms is demonstrated for a static gold thin film on a silicon sample. As a second example of this novel approach, dynamic in situ measurements are performed during PMMA spin coating onto silicon wafers and fast fitting of XRR curves using machine learning is demonstrated. This investigation primarily focuses on the evolution of film structure and surface morphology, resolving for the first time with qXRR the initial film thinning via mass transport and also shedding light on later thinning via solvent evaporation. This innovative millisecond qXRR technique is of significance for in situ studies of thin film deposition. It addresses the challenge of following intrinsically fast processes, such as thin film growth of high deposition rate or spin coating. Beyond thin film growth processes, millisecond XRR has implications for resolving fast structural changes such as photostriction or diffusion processes.

X-ray Reflectivity Study of Polylysine Adsorption on the Surface of DMPS Monolayers

The results of a systematic study on the adsorption of polylysine molecules of different lengths on the surface of a 1,2-dimyristoyl-sn-glycero-3-phospho-L-serine (DMPS) monolayer in the liquid (LE) and condensed (LC) states are presented. A compressibility diagram and the Volta potential were recorded with the Langmuir monolayer technique and further analyzed with the empirical approach. The structure of the monolayer films with adsorbed polypeptides was studied with synchrotron X-ray reflectometry. Two- and three-layer slab models describe the reflectivity data fairly well and reveal both the significant structural changes and the dehydration of the polar groups induced by all polylysines used at the maximal coverage of the monolayer interface in both the LE and LC states. On the one hand, in the LE phase of the monolayer (area per molecule A ≅ 70 Ǻ²), the integrated electron density of the lipid headgroup region is approximately half the density contained in the clean monolayer. This indicates both significant compaction and dehydration in the polar groups of the lipids, caused by the adsorption of polypeptides. On the other hand, in the LC state (A ≅ 40 Ǻ²), the degree of the hydration of the polar region is similar to that for the initial DMPS monolayer. However, both the electron density and the thickness of the head group region differ significantly from the values of these parameters for the clean monolayer in the LC state.

Counterions under a Surface-Adsorbed Cationic Surfactant Monolayer: Structure and Thermodynamics

The surface adsorption of ionic surfactants is fundamental for many widespread phenomena in life sciences and for a wide range of technological applications. However, direct atomic-resolution structural experimental studies of noncrystalline surface-adsorbed films are scarce. Thus, even the most central physical aspects of these films, such as their charge density, remain uncertain. Consequently, theoretical models based on contradicting assumptions as for the surface films' ionization are widely used for the description and prediction of surface thermodynamics. We employ X-ray reflectivity to obtain the Ångström-scale surface-normal structure of surface-adsorbed films of the cationic surfactant cetyltrimethylammonium bromide (CTAB) in aqueous solutions at several different temperatures and concentrations. In conjunction with published neutron reflectivity data, we determine the surface-normal charge distribution due to the dissociated surfactants' headgroups. The distribution appears to be inconsistent with the Gouy-Chapman model yet consistent with a compact Stern layer model of condensed counterions. The experimental surfactant adsorption thermodynamics conforms well to classical, Langmuir and Kralchevsky, adsorption models. Furthermore, the Kralchevsky model correctly reproduces the observed condensation of counterions, allowing the values of the adsorption parameters to be resolved, based on the combination of the present data and the published surface tension measurements.

Faster and lower-dose X-ray reflectivity measurements enabled by physics-informed modeling and artificial intelligence co-refinement

An approach is presented for analysis of real-time X-ray reflectivity (XRR) process data not just as a function of the magnitude of the reciprocal-space vector q, as is commonly done, but as a function of both q and time. The real-space structures extracted from the XRR curves are restricted to be solutions of a physics-informed growth model and use state-of-the-art convolutional neural networks (CNNs) and differential evolution fitting to co-refine multiple time-dependent XRR curves R(q, t) of a thin film growth experiment. Thereby it becomes possible to correctly analyze XRR data with a fidelity corresponding to standard fits of individual XRR curves, even if they are sparsely sampled, with a sevenfold reduction of XRR data points, or if the data are noisy due to a 200-fold reduction in counting times. The approach of using a CNN analysis and of including prior information through a kinetic model is not limited to growth studies but can be easily extended to other kinetic X-ray or neutron reflectivity data to enable faster measurements with less beam damage.

X-ray reflectivity from curved surfaces as illustrated by a graphene layer on molten copper

The X-ray reflectivity technique can provide out-of-plane electron-density profiles of surfaces, interfaces, and thin films, with atomic resolution accuracy. While current methodologies require high surface flatness, this becomes challenging for naturally curved surfaces, particularly for liquid metals, due to the very high surface tension. Here, the development of X-ray reflectivity measurements with beam sizes of a few tens of micrometres on highly curved liquid surfaces using a synchrotron diffractometer equipped with a double crystal beam deflector is presented. The proposed and developed method, which uses a standard reflectivity θ-2θ scan, is successfully applied to study in situ the bare surface of molten copper and molten copper covered by a graphene layer grown in situ by chemical vapor deposition. It was found that the roughness of the bare liquid surface of copper at 1400 K is 1.25 ± 0.10 Å, while the graphene layer is separated from the liquid surface by a distance of 1.55 ± 0.08 Å and has a roughness of 1.26 ± 0.09 Å.

Neural network analysis of neutron and X-ray reflectivity data: automated analysis using mlreflect, experimental errors and feature engineering

A Python-based analysis pipeline for the fast analysis of X-ray and neutron reflectivity data using neural networks is presented.

The Python package mlreflect is demonstrated, which implements an optimized pipeline for the automated analysis of reflectometry data using machine learning. The package combines several training and data treatment techniques discussed in previous publications. The predictions made by the neural network are accurate and robust enough to serve as good starting parameters for an optional subsequent least-mean-squares (LMS) fit of the data. For a large data set of 242 reflectivity curves of various thin films on silicon substrates, the pipeline reliably finds an LMS minimum very close to a fit produced by a human researcher with the application of physical knowledge and carefully chosen boundary conditions. The differences between simulated and experimental data and their implications for the training and performance of neural networks are discussed. The experimental test set is used to determine the optimal noise level during training. The extremely fast prediction times of the neural network are leveraged to compensate for systematic errors by sampling slight variations in the data.

Assessment of nanoparticle immersion depth at liquid interfaces from chemically equivalent macroscopic surfaces

HYPOTHESIS

We test whether the wettability of nanoparticles (NPs) straddling at an air/water surface or oil/water interface can be extrapolated from sessile drop-derived macroscopic contact angles (mCAs) on planar substrates, assuming that both the nanoparticles and the macroscopic substrates are chemically equivalent and feature the same electrokinetic potential.

EXPERIMENTS

Pure silica (SiO₂) and amino-terminated silica (APTES-SiO₂) NPs are compared to macroscopic surfaces with extremely low roughness (root mean square [RMS] roughness ≤ 2 nm) or a roughness determined by a close-packed layer of NPs (RMS roughness ∼ 35 nm). Equivalence of the surface chemistry is assessed by comparing the electrokinetic potentials of the NPs via electrophoretic light scattering and of the macroscopic substrates via streaming current analysis. The wettability of the macroscopic substrates is obtained from advancing (ACAs) and receding contact angles (RCAs) and in situ synchrotron X-ray reflectivity (XRR) provided by the NP wettability at the liquid interfaces.

FINDINGS

Generally, the RCA on smooth surfaces provides a good estimate of NP wetting properties. However, mCAs alone cannot predict adsorption barriers that prevent NP segregation to the interface, as is the case with the pure SiO₂ nanoparticles. This strategy greatly facilitates assessing the wetting properties of NPs for applications such as emulsion formulation, flotation, or water remediation.

Neural network analysis of neutron and x-ray reflectivity data: pathological cases, performance and perspectives

Neutron and x-ray reflectometry (NR and XRR) are powerful techniques to investigate the structural, morphological and even magnetic properties of solid and liquid thin films. While neutrons and x-rays behave similarly in many ways and can be described by the same general theory, they fundamentally differ in certain specific aspects. These aspects can be exploited to investigate different properties of a system, depending on which particular questions need to be answered. Having demonstrated the general applicability of neural networks to analyze XRR and NR data before (Greco et al 2019 J. Appl. Cryst. 52 1342), this study discusses challenges arising from certain pathological cases as well as performance issues and perspectives. These cases include a low signal-to-noise ratio, a high background signal (e.g. from incoherent scattering), as well as a potential lack of a total reflection edge (TRE). By dynamically modifying the training data after every mini batch, a fully-connected neural network was trained to determine thin film parameters from reflectivity curves. We show that noise and background intensity pose no significant problem as long as they do not affect the TRE. However, for curves without strong features the prediction accuracy is diminished. Furthermore, we compare the prediction accuracy for different scattering length density combinations. The results are demonstrated using simulated data of a single-layer system while also discussing challenges for multi-component systems.

Water cavitation from ambient to high temperatures

Predicting cavitation has proved a formidable task, particularly for water. Despite the experimental difficulty of controlling the sample purity, there is nowadays substantial consensus on the remarkable tensile strength of water, on the order of -120 MPa at ambient conditions. Recent progress significantly advanced our predictive capability which, however, still considerably depends on elaborate fitting procedures based on the input of external data. Here a self-contained model is discussed which is shown able to accurately reproduce cavitation data for water over the most extended range of temperatures for which accurate experiments are available. The computations are based on a diffuse interface model which, as only inputs, requires a reliable equation of state for the bulk free energy and the interfacial tension. A rare event technique, namely the string method, is used to evaluate the free-energy barrier as the base for determining the nucleation rate and the cavitation pressure. The data allow discussing the role of the Tolman length in determining the nucleation barrier, confirming that, when the size of the cavitation nuclei exceed the thickness of the interfacial layer, the Tolman correction effectively improves the predictions of the plain Classical Nucleation Theory.

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.

Synergistic and Competitive Adsorption of Hydrophilic Nanoparticles and Oil-Soluble Surfactants at the Oil-Water Interface

Fundamental insights into the interplay and self-assembly of nanoparticles and surface-active agents at the liquid-liquid interface play a pivotal role in understanding the ubiquitous colloidal systems present in our natural surroundings, including foods and aquatic life, and in the industry for emulsion stabilization, drug delivery, or enhanced oil recovery. Moreover, well-controlled model systems for mixed interfacial adsorption of nanoparticles and surfactants allow unprecedented insights into nonideal or contaminated particle-stabilized emulsions. Here, we investigate such a model system composed of hydrophilic, negatively, and positively charged silica nanoparticles and the oil-soluble cationic lipid octadecyl amine with in situ synchrotron-based X-ray reflectometry, which is analyzed and discussed jointly with dynamic interfacial tensiometry. Our results indicate that negatively charged silica nanoparticles only adsorb if the oil-water interface is covered with the positively charged lipid, indicating synergistic adsorption. Conversely, the positively charged nanoparticles readily adsorb on their own, but compete with octadecyl amine and reversibly desorb with increasing concentrations of the lipid. These results further indicate that with competitive adsorption, an electrostatic exclusion zone exists around the adsorbed particles. This prevents the adsorption of lipid molecules in this area, leading to a decreased surface excess concentration of surfactants and unexpectedly high interfacial tension.

A purely kinetic description of the evaporation of water droplets

The process of water evaporation, although deeply studied, does not enjoy a kinetic description that captures known physics and can be integrated with other detailed processes such as drying of catalytic membranes embedded in vapor-fed devices and chemical reactions in aerosol whose volumes are changing dynamically. In this work, we present a simple, three-step kinetic model for water evaporation that is based on theory and validated by using well-established thermodynamic models of droplet size as a function of time, temperature, and relative humidity as well as data from time-resolved measurements of evaporating droplet size. The kinetic mechanism for evaporation is a combination of two limiting processes occurring in the highly dynamic liquid-vapor interfacial region: direct first order desorption of a single water molecule and desorption resulting from a local fluctuation, described using third order kinetics. The model reproduces data over a range of relative humidities and temperatures only if the interface that separates bulk water from gas phase water has a finite width, consistent with previous experimental and theoretical studies. The influence of droplet cooling during rapid evaporation on the kinetics is discussed; discrepancies between the various models point to the need for additional experimental data to identify their origin.

Tuneable interfacial surfactant aggregates mimic lyotropic phases and facilitate large scale nanopatterning

It is shown that the air-liquid interface can be made to display the same rich curvature phenomena as common lyotropic liquid crystal systems. Through mixing an insoluble, naturally occurring, branched fatty acid, with an unbranched fatty acid of the same length, systematic variation in the packing constraints at the air-water interface could be obtained. The combination of atomic force microscopy and neutron reflectometry is used to demonstrate that the water surface exhibits significant tuneable topography. By systematic variation of the two fatty acid proportions, ordered arrays of monodisperse spherical caps, cylindrical sections, and a mesh phase are all observed, as well as the expected lamellar structure. The tuneable deformability of the air-water interface permits this hitherto unexplored topological diversity, which is analogous to the phase elaboration displayed by amphiphiles in solution. It offers a wealth of novel possibilities for the tailoring of nanostructure.

Structural Changes in Films of Pulmonary Surfactant Induced by Surfactant Vesicles

When compressed by the shrinking alveolar surface area during exhalation, films of pulmonary surfactant in situ reduce surface tension to levels at which surfactant monolayers collapse from the surface in vitro. Vesicles of pulmonary surfactant added below these monolayers slow collapse. X-ray scattering here determined the structural changes induced by the added vesicles. Grazing incidence X-ray diffraction on monolayers of extracted calf surfactant detected an ordered phase. Mixtures of dipalmitoyl phosphatidylcholine and cholesterol, but not the phospholipid alone, mimic that structure. At concentrations that stabilize the monolayers, vesicles in the subphase had no effect on the unit cell, and X-ray reflection showed that the film remained monomolecular. The added vesicles, however, produced a concentration-dependent increase in the diffracted intensity. These results suggest that the enhanced resistance to collapse results from enlargement by the additional material of the ordered phase.

Evolution and Reversible Polarity of Multilayering at the Ionic Liquid/Water Interface

Highly correlated positioning of ions underlies Coulomb interactions between ions and electrified interfaces within dense ionic fluids such as biological cells and ionic liquids. Recent work has shown that highly correlated ionic systems behave differently than dilute electrolyte solutions, and interest is focused upon characterizing the electrical and structural properties of the dense electrical double layers (EDLs) formed at internal interfaces. It has been a challenge for experiments to characterize the progressive development of the EDL on the nanoscale as the interfacial electric potential is varied over a range of positive and negative values. Here we address this challenge by measuring X-ray reflectivity from the interface between an ionic liquid (IL) and a dilute aqueous electrolyte solution over a range of interfacial potentials from -450 to 350 mV. The growth of alternately charged cation-rich and anion-rich layers was observed along with a polarity reversal of the layers as the potential changed sign. These data show that the structural development of an ionic multilayer-like EDL with increasing potential is similar to that suggested by phenomenological theories and MD simulations, although our data also reveal that the excess charge beyond the first ionic layer decays more rapidly than predicted.

Solution chemistry in the surface region of aqueous solutions

Solution chemistry is commonly regarded as the physical chemistry of reactions and chemical equilibria taking place in the bulk of a solvent, and between solutes in solution, and solids or gases in contact with the solution. Our knowledge about such reactions and equilibria in aqueous solution is very detailed such as their physico–chemical constants at varying temperature, pressure, ionic medium and strength. In this paper the solution chemistry in the surface region of aqueous solutions, down to ca. 10 Å below the water–air interface, will be discussed. In this region, the density and relative permittivity are significantly smaller than in the aqueous bulk strongly affecting the chemical behaviour of solutes. Surface sensitive X-ray spectroscopic methods have recently been applicable on liquids and solutions by use of liquid jets. This allows the investigation of the speciation of compounds present in the water–air interface and the surface region, a region hardly studied before. Speciation studies show overwhelmingly that neutral molecules are accumulated in the surface region, while charged species are depleted from it. It has been shown that the equilibria between aqueous bulk, surface region, solids and/or air are very fast allowing effective transport of chemicals over the aqueous surface region.

3D texturing of the air-water interface by biomimetic self-assembly

A simple, insoluble monolayer of fatty acid is shown to induce 3D nanotexturing of the air-water interface. This advance has been achieved through the study of monolayers of a methyl-branched long chain fatty acid, analogous to those found on the surface of hair and wool, directly at the air-water interface. Specular neutron reflectometry combined with AFM probing of deposited monolayers shows pronounced 3D surface domains, which are absent for unbranched analogues and are attributed to hydrocarbon packing constraints. The resulting surface topographies of the water far exceed the height perturbation that can be explained by the presence of capillary waves of a free liquid surface. These have hitherto been considered the only source of perturbation of the flatness of a planar water interface under gravity in the absence of topographical features from the presence of extended, globular or particulate matter. This amounts to a paradigm shift in the study of interfacial films and opens the possibility of 3D texturing of the air-water interface.

Fast fitting of reflectivity data of growing thin films using neural networks

X-ray reflectivity (XRR) is a powerful and popular scattering technique that can give valuable insight into the growth behavior of thin films. This study shows how a simple artificial neural network model can be used to determine the thickness, roughness and density of thin films of different organic semiconductors [diindenoperylene, copper(II) phthalocyanine and α-sexithiophene] on silica from their XRR data with millisecond computation time and with minimal user input or a priori knowledge. For a large experimental data set of 372 XRR curves, it is shown that a simple fully connected model can provide good results with a mean absolute percentage error of 8-18% when compared with the results obtained by a genetic least mean squares fit using the classical Parratt formalism. Furthermore, current drawbacks and prospects for improvement are discussed.

Surface Ordering in Molecular Clusters by Interactions of Well-Defined Parity Multipoles

The spontaneous alignment of dipoles in patterns tangential or transversal to the interface of molecular clusters is studied by molecular dynamics simulations throughout the entire aggregation process. Tangential ordering (TANGO) is found to rely on dispersion forces driven by dipolar fluctuations. Transversal ordering (TRANSO) results from the interplay of two conditions: the broken translational invariance at the cluster interface and the interactions of multipoles of opposite parity. In this case, the orientational order parameter at the interface follows a universal scaling law behavior. In the limiting case of strongly interacting particles, a sharp structural transition from a disordered into an ordered state is observed at a critical distance inside the cluster and at a critical magnitude of the dipole moment.

Structure of Langmuir Monolayers of Perfluorinated Fatty Acids: Evidence of a New 2D Smectic C Phase

Due to the characteristic chain rigidity and weak intermolecular interactions of perfluorinated substances, the phase diagram of Langmuir monolayer formed by perfluorinated molecules has been interpreted so far as displaying only two phases, a 2D gas (G) and a liquid condensed (LC). However, in this work, we presented Grazing Incidence X-ray Diffraction measurements, which exhibit two diffraction peaks on the transition plateau: One is the signature of the hexagonal structure of the LC phase, the second one is associated to the low-density fluid phase and is thus more ordered than expected for a 2D gas or a typical fluid phase. Atomistic molecular dynamics simulations, performed on the transition plateau, revealed the existence of clusters in which domains of vertical molecules organized in a hexagonal lattice coexist with domains of parallel lines formed by tilted molecules, a new structure that could be described as a “2D smectic C” phase. Moreover, the diffraction spectrum calculated from the simulation trajectories compared favorably with the experimental spectra, fully validating the simulations and the proposed interpretation. The results were also in agreement with the thermodynamic analysis of the fluid phase and X-ray Reflectivity experiments performed before and after the transition between these two phases.

Comprehensive Study of the Liquid Expanded-Liquid Condensed Phase Transition in 1,2-Dimyristoyl-sn-glycero-3-phospho-l-serine Monolayers: Surface Pressure, Volta Potential, X-ray Reflectivity, and Molecular Dynamics Modeling

An integrated approach is applied to reveal fine changes in the surface-normal structure of 1,2-dimyristoyl-sn-glycero-3-phospho-l-serine (DMPS) monolayers at the air-lipid-water interface occurring in a liquid expanded (LE)-liquid condensed (LC) transition. The combination of the Langmuir monolayer technique, X-ray reflectometry, and molecular dynamics (MD) modeling provides new insight into the molecular nature of electrostatic phenomena in different stages of lipid compression. A homemade setup with a laboratory X-ray source (λ = 1.54 Å) offers a nondestructive way to reveal the structural difference between the LE and LC phases of the lipid. The electron density profile in the direction normal to the interface is recovered from the X-ray reflectivity data with the use of both model-independent and model-based approaches. MD simulations of the DMPS monolayer are performed for several areas per lipid using the all-atom force field. Using the conventional theory of capillary waves, a comparison is made between the electron density profiles reconstructed from the X-ray data and those calculated directly from MD modeling, which demonstrates remarkable agreement between the experiment and simulations for all selected lipid densities. This confirms the validity of the simulations and allows an analysis of the contributions of the hydrophobic tails and hydrated polar groups to the electron density profile and to the dipole component of the electric field at the interface. According to the MD data, the dependence of the Volta potential on the area per lipid in the monolayer has a different molecular nature below and above the phase transition. In the LE state of the monolayer, the potential is determined mostly by the oriented water molecules in the polar region of the lipid. In the LE-LC transition, these molecules are displaced to the bulk, and their effect on the Volta potential becomes insignificant compared with the contribution of the hydrophobic tails. The hydrophobic tails are highly ordered in the state of the liquid crystal so that their dipole moments entirely determine the growth of the potential upon compression up to the monolayer collapse.

Chemical equilibria of aqueous ammonium-carboxylate systems in aqueous bulk, close to and at the water-air interface

Previous studies have shown that the water-air interface and a number of water molecule layers just below it, the surface region, have significantly different physico-chemical properties, such as lower relative permittivity and density, than bulk water. The properties in the surface region of water favor weakly hydrated species as neutral molecules, while ions requiring strong hydration and shielding of their charge are disfavored. In this study the equilibria NH₄⁺(aq) + RCOO^-(aq) ⇌ NH₃(aq) + RCOOH(aq) are investigated for R = C_nH_2n+1, n = 0-8, as open systems, where ammonia and small carboxylic acids in the gas phase above the water surface are removed from the system by a gentle controlled flow of nitrogen to mimic the transport of volatile compounds from water droplets into air. It is shown that this non-equilibrium transport of chemicals can be sufficiently large to cause a change of the chemical content of the aqueous bulk. Furthermore, X-ray photoelectron spectroscopy (XPS) has been used to determine the relative concentration of alkyl carboxylic acids and their conjugated alkyl carboxylates in aqueous surfaces using a micro-jet. These studies confirm that neutral alkyl carboxylic acids are accumulated in the surface region, while charged species, as alkyl carboxylates, are depleted. The XPS studies show also that the hydrophobic alkyl chains are oriented upwards into regions with lower relative permittivity and density, thus perpendicular to the aqueous surface. These combined results show that there are several chemical equilibria between the aqueous bulk and the surface region. The analytical studies show that the release of mainly ammonia is dependent on its concentration in the surface region, as long as the solubility of the carboxylic acid in the surface region is sufficiently high to avoid a precipitation in/on the water-air interface. However, for n-octyl- and n-nonylcarboxylic acid the solubility is sufficiently low to cause precipitation. The combined analytical and surface speciation studies in this work show that the equilibria involving the surface region are fast. The results from this study increase the knowledge about the distribution of chemical species in the surface region at and close to the water-air interface, and the transport of chemicals from water to air in open systems.

Structure and Conformation of Wild-Type Bacterial Lipopolysaccharide Layers at Air-Water Interfaces

The outer membrane of Gram-negative bacteria is of great scientific interest because it mediates the action of antimicrobial agents. The membrane surface is composed of lipopolysaccharide (LPS) molecules with negatively charged oligosaccharide headgroups. To a certain fraction, LPSs additionally display linear polysaccharides termed O-side chains (OSCs). Structural studies on bacterial outer surfaces models, based on LPS monolayers at air-water interfaces, have so far dealt only with rough mutant LPSs lacking these OSCs. Here, we characterize monolayers of wild-type LPS from Escherichia coli O55:B5 featuring strain-specific OSCs in the presence of defined concentrations of monovalent and divalent ions. Pressure-area isotherms yield insight into in-plane molecular interactions and monolayer elastic moduli. Structural investigations by x-ray and neutron reflectometry reveal the saccharide conformation and allow quantifying the area per molecule and the fraction of LPS molecules carrying OSCs. The OSC conformation is satisfactorily described by the self-consistent field theory for end-grafted polymer brushes. The monolayers exhibit a significant structural response to divalent cations, which goes beyond generic electrostatic screening.

REFLEX: a program for the analysis of specular X-ray and neutron reflectivity data

The use of X-ray and neutron reflectivity has been generalized worldwide for scientists who want to determine specific physical properties (such as electron-density profile, scattering-length density, roughness and thickness) of films less than 200 nm thick deposited on a substrate. This paper describes a freeware program named REFLEX, which is a standalone program dedicated to the simulation and analysis of X-ray and neutron reflectivity from multilayers. This program was first written two decades ago and has been constantly improved since, but never published until now. The latest version of REFLEX covers generalized types of calculation of reflectivity curves including both neutron and X-ray reflectivity. In the case of X-rays, the program can deal with both s and p polarization, which is quite important in the soft X-ray region where the two polarizations can yield different results. Neutron reflectivity is calculated within the framework of non-spin-polarized neutrons. REFLEX has also been designed to include any type of fluid (such as supercritical CO2) on top of the analysed film and includes corrections of the footprint effect for analysis on an absolute scale.

X-ray reflectivity from curved liquid interfaces

X-ray reflectivity studies of the structure of liquid-vapour and liquid-liquid interfaces at modern sources, such as free-electron lasers, are currently impeded by the lack of dedicated liquid surface diffractometers. It is shown that this obstacle can be overcome by an alternative experimental approach that uses the natural curvature of a liquid drop for variation of the angle of incidence. Two modes of operation are shown: (i) sequential reflectivity measurements by a nanometre beam and (ii) parallel acquisition of large ranges of a reflectivity curve by micrometre beams. The feasibility of the two methods is demonstrated by studies of the Hg/vapour, H₂O/vapour and Hg/0.1 M NaF interface. The obtained reflectivity curves match the data obtained by conventional techniques up to 5α_c in micro-beam mode and up to 35α_c in nano-beam mode, allowing observation of the Hg layering peak.

Surface induced smectic order in ionic liquids - an X-ray reflectivity study of [C22C1im]+[NTf2]. Phys Chem Chem Phys 2018;19:26651-26661. [PMID: 28960006 DOI: 10.1039/c7cp04852a]

Surface induced smectic order was found for the ionic liquid 1-methyl-3-docosylimidazolium bis(trifluoromethlysulfonyl)imide by X-ray reflectivity and grazing incidence scattering experiments. Near the free liquid surface, an ordered structure of alternating layers composed of polar and non-polar moieties is observed. This leads to an oscillatory interfacial profile perpendicular to the liquid surface with a periodicity of 3.7 nm. Small angle X-ray scattering and polarized light microscopy measurements suggest that the observed surface structure is related to fluctuations into a metastable liquid crystalline SmA₂ phase that was found by supercooling the bulk liquid. The observed surface ordering persists up to 157 °C, i.e. more than 88 K above the bulk melting temperature of 68.1 °C. Close to the bulk melting point, we find a thickness of the ordered layer of L = 30 nm. The dependency of L(τ) = Λ ln(τ/τ₁) vs. reduced temperature τ follows a logarithmic growth law. In agreement with theory, the pre-factor Λ is governed by the correlation length of the isotropic bulk phase.

Anisotropic Superattenuation of Capillary Waves on Driven Glass Interfaces

Metrological atomic force microscopy measurements are performed on the silica glass interfaces of photonic band-gap fibers and hollow capillaries. The freezing of attenuated out-of-equilibrium capillary waves during the drawing process is shown to result in a reduced surface roughness. The roughness attenuation with respect to the expected thermodynamical limit is determined to vary with the drawing stress following a power law. A striking anisotropic character of the height correlation is observed: glass surfaces thus retain a structural record of the direction of the flow to which the liquid was submitted.

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.

Structural and Dynamic Heterogeneity of Capillary Wave Fronts at Aqueous Interfaces

Using a unique combination of slab-layering analyses and identification of truly interfacial molecules, this work examines water/vapor and water/n-hexane interfaces, specifically the structural and dynamic perturbations of the interfacial water molecules at different locations within the surface capillary waves. From both the structural and dynamic properties analyzed, it is found that these interfacial water molecules dominate the perturbations within the interfacial region, which can extend deep into the water phase relative to the Gibbs dividing surface. Of more importance is the demonstration of structural and dynamic heterogeneity of the interfacial water molecules at the capillary wave front, as indicated by the dipole orientation and the structural and dynamic behavior of hydrogen bonds and their networks.

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.

Angle-resolved molecular beam scattering of NO at the gas-liquid interface

This study presents first results on angle-resolved, inelastic collision dynamics of thermal and hyperthermal molecular beams of NO at gas-liquid interfaces. Specifically, a collimated incident beam of supersonically cooled NO (²Π_1/2, J = 0.5) is directed toward a series of low vapor pressure liquid surfaces ([bmim][Tf₂N], squalane, and PFPE) at θ_inc = 45(1)°, with the scattered molecules detected with quantum state resolution over a series of final angles (θ_s = -60°, -30°, 0°, 30°, 45°, and 60°) via spatially filtered laser induced fluorescence. At low collision energies [E_inc = 2.7(9) kcal/mol], the angle-resolved quantum state distributions reveal (i) cos(θ_s) probabilities for the scattered NO and (ii) electronic/rotational temperatures independent of final angle (θ_s), in support of a simple physical picture of angle independent sticking coefficients and all incident NO thermally accommodating on the surface. However, the observed electronic/rotational temperatures for NO scattering reveal cooling below the surface temperature (T_elec < T_rot < T_S) for all three liquids, indicating a significant dependence of the sticking coefficient on NO internal quantum state. Angle-resolved scattering at high collision energies [E_inc = 20(2) kcal/mol] has also been explored, for which the NO scattering populations reveal angle-dependent dynamical branching between thermal desorption and impulsive scattering (IS) pathways that depend strongly on θ_s. Characterization of the data in terms of the final angle, rotational state, spin-orbit electronic state, collision energy, and liquid permit new correlations to be revealed and investigated in detail. For example, the IS rotational distributions reveal an enhanced propensity for higher J/spin-orbit excited states scattered into near specular angles and thus hotter rotational/electronic distributions measured in the forward scattering direction. Even more surprisingly, the average NO scattering angle (⟨θ_s⟩) exhibits a remarkably strong correlation with final angular momentum, N, which implies a linear scaling between net forward scattering propensity and torque delivered to the NO projectile by the gas-liquid interface.

Perfect Composition Depth Profiling of Ionic Liquid Surfaces Using High-resolution RBS/ERDA

In order to reveal the surface structures of large molecular ionic liquids (ILs), the near-surface elemental depth distributions of 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C_nC₁Im][Tf₂N], n = 2, 6, 10) were studied using high-resolution Rutherford backscattering spectroscopy (HRBS) in combination with high-resolution elastic recoil detection analysis (HR-ERDA). The elemental depth profiles of all constituent elements, including hydrogen, were derived from HR-ERDA/HRBS measurements, so that the profiles would reproduce both HR-ERDA and HRBS spectra simultaneously. The derived elemental depth profiles agree with state-of-the-art molecular dynamics simulations, indicating the feasibility of this method. A controversy concerning the preferential orientation of [C₂C₁Im] at the surface has been resolved by this new combination analysis; namely, the [C₂C₁Im] cation has a preferential orientation with the ethyl chain pointing towards the vacuum in the topmost molecular layer.

Relative adsorption excess of ions in binary solvents determined by grazing-incidence X-ray fluorescence

We demonstrate a model-independent method for experimental determination of the relative surface excess of inorganic ions in binary liquid mixtures, based on grazing-incidence X-ray fluorescence. For this purpose, we probe the ion density profiles in a mixture of water and 2,6-dimethylpyridine containing a hydrophilic salt, potassium chloride. Thereby we demonstrate that the proposed method quantifies in a direct manner the difference between cation and anion excess adsorption in binary solvents with a resolution of one excess ion per 200nm² or better.

Surface structure of imidazolium-based ionic liquids: Quantitative comparison between simulations and high-resolution RBS measurements

Elemental depth profiles of 1-alkyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([CnMIM][TFSI], n = 4, 6, 8) are measured using high-resolution Rutherford backscattering spectroscopy (HRBS). The profiles are compared with the results of molecular dynamics (MD) simulations. Both MD simulations and HRBS measurements show that the depth profiles deviate from the uniform stoichiometric composition in the surface region, showing preferential orientations of ions at the surface. The MD simulations qualitatively reproduce the observed HRBS profiles but the agreement is not satisfactory. The observed discrepancy is ascribed to the capillary waves. By taking account of the surface roughness induced by the capillary waves, the agreement becomes almost perfect.

The Atomic scale structure of liquid metal-electrolyte interfaces

Electrochemical interfaces between immiscible liquids have lately received renewed interest, both for gaining fundamental insight as well as for applications in nanomaterial synthesis. In this feature article we demonstrate that the atomic scale structure of these previously inaccessible interfaces nowadays can be explored by in situ synchrotron based X-ray scattering techniques. Exemplary studies of a prototypical electrochemical system - a liquid mercury electrode in pure NaCl solution - reveal that the liquid metal is terminated by a well-defined atomic layer. This layering decays on length scales of 0.5 nm into the Hg bulk and displays a potential and temperature dependent behaviour that can be explained by electrocapillary effects and contributions of the electronic charge distribution on the electrode. In similar studies of nanomaterial growth, performed for the electrochemical deposition of PbFBr, a complex nucleation and growth behaviour is found, involving a crystalline precursor layer prior to the 3D crystal growth. Operando X-ray scattering measurements provide detailed data on the processes of nanoscale film formation.

Surfactant Behavior of Sodium Dodecylsulfate in Deep Eutectic Solvent Choline Chloride/Urea

Deep eutectic solvents (DES) resemble ionic liquids but are formed from an ionic mixture instead of being a single ionic compound. Here we present some results that demonstrate that surfactant sodium dodecyl sulfate (SDS) remains surface-active and shows self-assembly phenomena in the most commonly studied DES, choline chloride/urea. X-ray reflectivity (XRR) and small angle neutron scattering (SANS) suggest that the behavior is significantly different from that in water. Our SANS data supports our determination of the critical micelle concentration using surface-tension measurements and suggests that the micelles formed in DES do not have the same shape and size as those seen in water. Reflectivity measurements have also demonstrated that the surfactants remain surface-active below this concentration.

Ti-Sb-Te alloy: a candidate for fast and long-life phase-change memory

Phase-change memory (PCM) has great potential for numerous attractive applications on the premise of its high-device performances, which still need to be improved by employing a material with good overall phase-change properties. In respect to fast speed and high endurance, the Ti-Sb-Te alloy seems to be a promising candidate. Here, Ti-doped Sb2Te3 (TST) materials with different Ti concentrations have been systematically studied with the goal of finding the most suitable composition for PCM applications. The thermal stability of TST is improved dramatically with increasing Ti content. The small density change of T0.32Sb2Te3 (2.24%), further reduced to 1.37% for T0.56Sb2Te3, would greatly avoid the voids generated at phase-change layer/electrode interface in a PCM device. Meanwhile, the exponentially diminished grain size (from ∼200 nm to ∼12 nm), resulting from doping more and more Ti, enhances the adhesion between phase-change film and substrate. Tests of TST-based PCM cells have demonstrated a fast switching rate of ∼10 ns. Furthermore, because of the lower thermal conductivities of TST materials, compared with Sb2Te3-based PCM cells, T0.32Sb2Te3-based ones exhibit lower required pulse voltages for Reset operation, which largely decreases by ∼50% for T0.43Sb2Te3-based ones. Nevertheless, the operation voltages for T0.56Sb2Te3-based cells dramatically increase, which may be due to the phase separation after doping excessive Ti. Finally, considering the decreased resistance ratio, TixSb2Te3 alloy with x around 0.43 is proved to be a highly promising candidate for fast and long-life PCM applications.

Interaction of a patterned amphiphilic polyphenylene dendrimer with a lipid monolayer: electrostatic interactions dominate

Dendrimeric macromolecules with defined shape and size are promising candidates for delivering drug or DNA molecules into cells. In this work we study the influence of an amphiphilic polyphenylene dendrimer on a model cell membrane consisting of a condensed 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid monolayer. A small surface pressure decrease is observed when the dendrimer solution is injected into the aqueous phase below the monolayer. X-ray reflectivity measurements show that the surface monolayer remains intact. The molecular-scale picture is obtained with sum-frequency generation spectroscopy. With this technique, we observe that the tails of the surfactant molecules become less ordered upon interaction with the amphiphilic polyphenylene dendrimer. In contrast, the water molecules below the DPPC layer become more ordered. Our observations suggest that electrostatic interactions between the negative charge of the dendrimer and the positively charged part of the DPPC headgroup keep the dendrimer located below the headgroup. No evidence of dendrimer insertion into the membrane has been observed. Apparently before entering the cell membrane the dendrimer can stick at the hydrophilic part of the lipids.

About the role of surfactants on the magnetic control over liquid interfaces

The behavior of magnetically responsive aqueous Fe(III) surfactant solutions at liquid interfaces is analyzed. Such surfactants attracted much attention, because of the ability to manipulate interfaces by magnetic fields without any use of magnetic nanoparticles. A detailed analysis of the surface properties proves that the mixing of paramagnetic electrolyte solution with anionic, cationic and nonionic surfactants yields the similar magnetic response and no effect of the surfactant charge can be observed. We conclude that the observed magnetic shiftability of interfaces is caused by a combination of the paramagnetic behavior of the bulk liquid and a reduction of the surface tension. Thus, this work gives an alternative interpretation of the properties of "magnetic surfactants" compared to the ones claimed in the literature.