Extending the capillary wave model to include the effect of bending rigidity: X-ray reflectivity and diffuse scattering

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 hexadecyltrimethylammonium 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.

The microscopic structure of Langmuir films of derivatized gold nanoparticles has been studied as a function of area/particle on the water surface. The molecules (AuSHDA) consist of gold particles of mean core diameter D approximately 22 angstroms that have been stabilized by attachment of carboxylic acid terminated alkylthiols, HS-(CH2)15-COOH. Compression of the film results in a broad plateau of finite pressure in the surface pressure versus area/particle isotherm that is consistent with a first-order monolayer/bilayer transition. X-ray specular reflectivity (XR) and grazing incidence diffraction show that when first spread at large area/particle, AuSHDA particles aggregate two dimensionally to form hexagonally packed monolayer domains at a nearest-neighbor distance of a = 34 angstroms. The lateral positional correlations associated with the two-dimensional (2D) hexagonal order are of short range and extend over only a few interparticle distances; this appears to be a result of the polydispersity in particle size. Subsequent compression of the film increases the surface coverage by the monolayer but has little effect on the interparticle distance in the close-packed domains. The XR and off-specular diffuse scattering (XOSDS) results near the onset of the monolayer/bilayer coexistence plateau are consistent with complete surface coverage by a laterally homogeneous monolayer of AuSHDA particles. On the high-density side of the plateau, the electron-density profile extracted from XR clearly shows the formation of a bilayer in which the newly formed second layer on top is slightly less dense than the first layer. In contrast to the case of the homogeneous monolayer, the XOSDS intensities observed from the bilayer are higher than the prediction based on the capillary wave model and the assumption of homogeneity, indicating the presence of lateral density inhomogeneities in the bilayer. According to the results of Bragg rod measurements, the 2D hexagonal order in the two layers of the bilayer are only partially correlated.

We fabricated a new class of supported membranes based on monolayers of artificial bola (transmembrane) lipids. The lipids used in this study are symmetric bola lipids with two phosphocholine head groups, which resemble natural archaea lipids. To prevent bending of the hydrocarbon chains, stiff triple bonds are inserted in the middle of the hydrocarbon cores. The formation of homogeneous "monolayers" of transmembrane lipids over macroscopic areas can be monitored with fluorescence microscopy. Structures of such supported monolayers in bulk water were characterized with specular X-ray reflectivity using high energy X-ray radiation, which guarantees a high transmission through bulk water. Here, the vertical structure of single monolayers could be resolved from reconstructed electron density profiles. To verify the structural model suggested by the specular reflectivity, we also performed small- and wide-angle X-ray scattering of transmembrane lipid suspensions. The wide-angle patterns reflect a distorted chain-chain correlation, while the small-angle scattering allowed us to model an electron density profile which is consistent with the profile calculated from specular reflectivity.

The phase problem for specular x-ray and neutron reflectivity from liquid surfaces and thin films on liquid surfaces can be solved in the distorted-wave Born approximation. The gradient of the scattering-length density (SLD) profile normal to the plane of the surface is bounded in these cases. This provides a powerful constraint allowing the phase problem to be solved with no a priori assumptions via an iterative Fourier refinement procedure applied to the Fresnel-normalized reflectivity. The critical boundary condition can be determined experimentally from the autocorrelation of the gradient profile obtained via an inverse Fourier transform of the Fresnel-normalized reflectivity without phase information. The phase solution and the resulting gradient SLD profile can be shown to be unique, and therefore unambiguously determined, when all of phase space is systematically explored for particular cases, especially for thin films on liquid surfaces. This gradient SLD profile can then be integrated either numerically, or better, analytically to provide the scattering-length density profile itself on an absolute scale.

We review the use of specular X-ray reflectivity (XRR) for the characterization of thin-film and surface structures. Specular X-ray scattering at small scattering vectors allows characterization of electron density profiles perpendicular to the surface on the length scale of 0.1 to 100 nm. This allows measurement of surface morphology, thin films, multilayer structures, and buried interfaces. The technique is nondestructive and can be applied in situ in a variety of processing environments. In the first half of the article, we review the theory and methods of XRR, including analysis of XRR spectra by a multilayer optical approach and a discussion of surface roughness measurements by XRR and other techniques. In the second half, we present a wide range of examples of XRR applications in thin-film structures, dynamic processes, liquid surfaces, and macromolecular structures.

The purpose of this study is to investigate conformations of antibodies immobilized on three kinds of solid surfaces modified with APTES, AEAPTES or GA and their antigen-binding affinities. In the recent developments in biosensors, although the geometric structure of antibodies determines their sensitivity, few studies have focused on their conformations and its effect on their antigen-binding capacity due to a lack of applicable analysis techniques. In this work, specular and off-specular X-ray reflectivity measurement were employed, which enables us to analyze vertical and lateral multilayer structure. The results showed that the antigen-binding affinity on GA was highest among antibodies immobilized on three modified surfaces, although their conformations were almost the same as 'flat-on' analyzed by specular X-ray reflectivity. In contrast, lateral layer structure analysis by off-specular reflection revealed that protein layer on GA before antigen-binding had a relatively-long lateral correlation length and a low fractal dimension which would cause the reduction of steric hindrance for antigens' access to binding sites of antibodies.

In the conventional X-ray reflectivity (XRR) analysis, the reflectivity is calculated based on the Parratt formalism, incorporating the effect of the interface roughness according to Nevot and Croce. However, the results of calculations of the XRR have shown strange outcomes, where interference effects increase at a rough surface because of a lack of consideration of diffuse scattering within the Parratt formalism. Therefore, we have developed a new improved formalism in which the effects of the surface and interface roughness are included correctly. In this study, for deriving a more accurate formalism of XRR, we tried to compare the measurements of surface roughness of the same sample by atomic force microscopy (AFM) and XRR. It is found that the AFM result could not be completely reproduced even with the improved XRR formalism. By careful study of the AFM results, we determined the need for an additional effective roughness term within the XRR simulation that depends on the angle of incidence of the beam.

Specular x-ray reflectivity (XRR) measurements were used to study the density and surface roughness of ultrathin hydrogen-free amorphous carbon films deposited by sputtering, of thickness varying from 25 to 325 Å. The film thickness and surface roughness obtained from XRR measurements are in good agreement with that found by spectroscopic ellipsometry (SE) and atomic force microscopy. The results for the film composition obtained from SE and XRR are supported by stress measurements. Films (especially those with thickness below 100 Å) deposited with positive substrate bias voltage were found to exhibit a reduction in density, sp3 C–C bonding, and internal compressive stresses and an increase in surface roughness by increasing film thickness.

Investigation of structure, thermal and oxygen plasma stability of mesoporous methylsilsesquioxane films by X-ray reflectivity and small angle scattering

Nondestructive evaluation (NDE) method reliability can be determined by a statistical flaw detection study called probability of detection (POD) study. In many instances, the NDE flaw detectability is given as a flaw size such as crack length. An alternate approach is to use a more complex flaw size parameter. Earlier models by the author did not include scattering effects in detection of cracks. X-ray flaw size parameter model, given here, investigates one of scattering effects namely specular reflectivity of low energy x-rays impinging on crack faces at grazing angle. Reflectivity of x-rays at low grazing angle to crack faces is almost 100%. If crack faces are smooth and flat, the grazing angle x-rays channel between the crack faces. The paper models the specular reflection to study its effect on contrast of x-ray image. The channeling of x-rays can improve x-ray image contrast significantly. Normalized exposure and image width are used to calculate the flaw size parameter. Reflectivity of grazing angle x-rays can be used to improve x-ray crack detectability in thin low density materials.

Specular neutron and X-ray reflection have been used to investigate the penetration of water into silica gel films. The effect on water penetration of incorporating fluoroalkysilane (FAS) into the gel has also been measured. Gel films were deposited onto float glass substrates and exposed to either liquid water or an atmosphere of known relative humidity (between 0% and 100%). It was shown that, irrespective of FAS content, water penetrates throughout the gel film, and deeper into the glass substrate if the sample has prolonged contact with water. The X-ray reflection measurements have shown there are no changes in the structure of the gel film on glass on exposure to a humid atmosphere. This result is verified by the neutron reflection data and suggests that as water penetrates into the surface it occupies in the gel network. These voids can be filled or emptied by changing the relative humidity. The neutron reflectivity measurements have also revealed additional information about the distribution of the water. For the pure silica gel, with no added FAS, there is a water-rich layer (∼30 A thick) at the gel surface and a significant amount of water (volume fraction up to 18%) penetrated throughout the gel film. Gel films made with moderate amounts of FAS show no evidence for a water-rich layer on the surface. In fact, the water density is effectively zero within ∼20 A of the gel's surface. This suggests that the fluorinated materialformed a hydrophobic monolayer near the surface of the gel. For gels with much higher levels of FAS, the film surface becomes very rough and a detailed interpretation is not possible.

In the conventional X-ray reflectivity (XRR) analysis for the estimation of multilayer surface, the reflectivity is calculated based on the Parratt formalism, accounting for the effect of roughness by the theory of Nevot-Croce. However, the calculated results have shown often strange behaviour due to the fact that the diffuse scattering at the rough interface was not taken into account in the equation. Then we developed new improved formalism to correct this mistake. In this study, we show applying of new improved formalism using a transmission electron microscope (TEM) observation result. The result of interfacial roughness by using the conventional XRR formulae showed large difference with the TEM result, and derived wrong structure of surface. While, the result by new improved formalism reproduce the TEM result well, but need appropriate parameters in transmission coefficient. It shows that new improved XRR formalism derives more accurate analysis of the XRR, but the reduced Fresnel coefficients with physical grounds in the reflectivity equation are need in further research.

A new method for enhancing the Fourier transforms of x-ray reflectivity data is presented. This enhanced Fourier analysis, which employs differentiation of the scattered intensity signal, is shown to be extremely effective in extracting layer thicknesses from specular x-ray reflectivity scans from single and multi-layer structures. This is a powerful technique that complements simulations of x-ray scattering patterns that employ dynamical diffraction models. Examples of the procedure, data analysis, and comparison of the results with methods that have been described previously will be presented. A Fourier Transform (FT) power spectrum peak represents the frequency or period length of an interference oscillation. X-ray scattering measurements provide information in the reciprocal space domain. Therefore, the FT of an x-ray scattering measurement would be expected to provide information concerning layer properties, especially the layer thicknesses which establish the interference fringes in scattering measurements including reflectivity measurements and higher angle diffraction measurements. Indeed, the intensity modulations that are observed in specular x-ray reflectivity measurements are related to the layer thicknesses and to the difference in refractive index between one layer and the next. At x-ray wavelengths, the refractive index is determined by the material density. Discrete Fourier transforms and their application to x-ray reflectivity data will be discussed subsequently in terms of the mathematics, challenges inherent to x-ray scatter FTs, and enhancement techniques that have already been discussed in the literature. The key to the enhancement method described here is based around differentiating the specular intensity with respect to vertical reciprocal space coordinate QZ. This differentiation retains the important and useful components of the x-ray reflectivity measurements while minimizing the impact of features of the measurements that obscure the transformation of the interference pattern. The reflectivity data is transformed according to

The thicknesses and densities of coatings prepared by atomic layer deposition (ALD) and by other deposition techniques are important to understand their optical, electrical and mechanical properties. Specular X-ray reflectivity (XRR) is a powerful tool that is capable of nondestructively extracting layer thicknesses with angstrom resolution, and what is distinct, determining the layer densities through modeling structures with simulation programs. Unfortunately, problem with modeling usually arises when other layers form at the surface or interfaces, and it is also common to other nondestructive techniques such as ellipsometry. A recent development1 has shown that with differentiating the specular XRR intensity with respect to vertical reciprocal space coordinate, a Fourier transform (FT) approach can provide straightforward information about the layer thicknesses in multilayer systems, which will make it easier to build the XRR simulation model. Therefore, a novel combination of FT and specular XRR simulation would be quite efficient in layer thickness extraction compared with other conventional techniques (e.g. transmission electron microscope (TEM) and ellipsometry). In this study, the novel XRR approach, together with other techniques including optical microscope (OR), spectroscopic ellipsometry (SE), TEM, energy dispersive X-ray spectroscopy and glancing incidence X-ray diffraction, was utilized to characterize the effect of annealing on optical properties of Al2O3/TiO2/Al2O3 multilayer antireflection stack. The films were deposited on (0 0 1) Si wafers using ALD which is a good candidate for multilayer antireflection coatings, due to the self-limiting nature of chemical reactions resulting in the precise control of film thickness and large-area uniformity. The thickness values of the as-deposited layers determined by XRR agree quite well with those obtained from OR, SE and TEM, with the difference below uncertainty levels. This, together with the good correlation between layer densities extracted from XRR and refractive indices measured by OR and SE, demonstrates the validity of the XRR approach. On the other hand, it is revealed that air annealing at 400 °Ϲ for 10 min induces the densification of the TiO2 layer as well as the initiation of crystallization. Meanwhile, both Al2O3 layers keep amorphous after annealing, with the thickness of top Al2O3 layer decreased that is likely due to interdiffusion of Al and Ti atoms between the top two layers, while the thickness of bottom Al2O3 layer increased accompanied with a decrease in density, which is probably attributed to the diffusion of Si atoms from the substrate into layers. Reference 1B. Poust, R. Sandhu, and M. Goorsky, Phys. Status Solidi A. 206, 1780 (2009).

Interactions of the antimicrobial peptide protegrin-1 (PG-1) with phospholipid monolayers have been investigated by using grazing incidence X-ray diffraction (GIXD) and specular X-ray reflectivity (XR). The structure of a PG-1 film at the air-aqueous interface was also investigated by XR for the first time. Lipid A, dipalmitoyl-phosphatidylglycerol (DPPG) and dipalmitoyl-phosphatidylcholine (DPPC) monolayers were formed at the air-aqueous interface to mimic the surface of the bacterial cell wall and the outer leaflet of the erythrocyte cell membrane, respectively. Experiments were carried out under constant area conditions where the pressure changes upon insertion of peptide into the monolayer. GIXD data suggest that the greatest monolayer disruption produced by PG-1 is seen with the DPPG system at 20 mN/m since the Bragg peaks completely disappear after introduction of PG-1 to the system. PG-1 shows greater insertion into the lipid A system compared to the DPPC system when both films are held at the same initial surface pressure of 20 mN/m. The degree of insertion lessens at 30 mN/m with both DPPC and DPPG monolayer systems. XR data further reveal that PG-1 inserts primarily in the head group region of lipid monolayers. However, only the XR data of the anionic lipids suggest the existence of an additional adsorbed peptide layer below the head group of the monolayer. Overall the data show that the extent of peptide/lipid interaction and lipid monolayer disruption depends not only on the lipid composition of the monolayer, but the packing density of the lipids in the monolayer prior to the introduction of peptide to the subphase.