refnx: neutron and X-ray reflectometry analysis in Python

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.

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.

Optimizing experimental design in neutron reflectometry

Using the Fisher information (FI), the design of neutron reflectometry experiments can be optimized, leading to greater confidence in parameters of interest and better use of experimental time [Durant, Wilkins, Butler & Cooper (2021). J. Appl. Cryst. 54, 1100-1110]. In this work, the FI is utilized in optimizing the design of a wide range of reflectometry experiments. Two lipid bilayer systems are investigated to determine the optimal choice of measurement angles and liquid contrasts, in addition to the ratio of the total counting time that should be spent measuring each condition. The reduction in parameter uncertainties with the addition of underlayers to these systems is then quantified, using the FI, and validated through the use of experiment simulation and Bayesian sampling methods. For a 'one-shot' measurement of a degrading lipid monolayer, it is shown that the common practice of measuring null-reflecting water is indeed optimal, but that the optimal measurement angle is dependent on the deuteration state of the monolayer. Finally, the framework is used to demonstrate the feasibility of measuring magnetic signals as small as 0.01 μB per atom in layers only 20 Å thick, given the appropriate experimental design, and that the time to reach a given level of confidence in the small magnetic moment is quantifiable.

GenX 3: the latest generation of an established tool

Improvements to the GenX program are discussed, including performance, model building and error analysis.

Since its publication more than 15 years ago the GenX software has been continuously developed and has established itself as a standard package for analyzing X-ray and neutron reflectometry data. The evolution of the software during the last two major revisions is reported here. This includes a simplified model builder for beginners, simple samples, additional sample models, statistical error analysis and the use of just-in-time compilation modules for the reflectometry kernel to achieve higher performance. In addition, the influence of experimental errors on the reflectivity curve is discussed, and new features are described that allow the user to include these in the error statistics to improve the fitting and uncertainty estimation.

Electro-polymerization rates of diazonium salts are dependent on the crystal orientation of the surface

Electro-polymerization of diazonium salts is widely used for modifying surfaces with thin organic films. Initially this method was primarily applied to carbon, then to metals, and more recently to semiconducting Si. Unlike on other surfaces, electrochemical reduction of diazonium salts on Si, which is one of the most industrially dominant material, is not well understood. Here, we report the electrochemical reduction of diazonium salts on a range of silicon electrodes of different crystal orientations (111, 211, 311, 411, and 100). We show that the kinetics of surface reaction and the reduction potential is Si crystal-facet dependent and is more favorable in the hierarchical order (111) > (211) > (311) > (411) > (100), a finding that offers control over the surface chemistry of diazonium salts on Si. The dependence of the surface reaction kinetics on the crystal orientation was found to be directly related to differences in the potential of zero charge (PZC) of each crystal orientation, which in turn controls the adsorption of the diazonium cations prior to reduction. Another consequence of the effect of PZC on the adsorption of diazonium cations, is that molecules terminated by distal diazonium moieties form a compact film in less time and requires less reduction potentials compared to that formed from diazonium molecules terminated by only one diazo moiety. In addition, at higher concentrations of diazonium cations, the mechanism of electrochemical polymerization on the surface becomes PZC-controlled adsorption-dominated inner-sphere electron transfer while at lower concentrations, diffusion-based outer-sphere electron transfer dominates. These findings help understanding the electro-polymerization reaction of diazonium salts on Si en route towards an integrated molecular and Si electronics technology.

Parameter estimation for X-ray scattering analysis with Hamiltonian Markov Chain Monte Carlo

Bayesian-inference-based approaches, in particular the random-walk Markov Chain Monte Carlo (MCMC) method, have received much attention recently for X-ray scattering analysis. Hamiltonian MCMC, a state-of-the-art development in the field of MCMC, has become popular in recent years. It utilizes Hamiltonian dynamics for indirect but much more efficient drawings of the model parameters. We described the principle of the Hamiltonian MCMC for inversion problems in X-ray scattering analysis by estimating high-dimensional models for several motivating scenarios in small-angle X-ray scattering, reflectivity, and X-ray fluorescence holography. Hamiltonian MCMC with appropriate preconditioning can deliver superior performance over the random-walk MCMC, and thus can be used as an efficient tool for the statistical analysis of the parameter distributions, as well as model predictions and confidence analysis.

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.

Characterization of the Interfacial Orientation and Molecular Conformation in a Glass-Forming Organic Semiconductor

The ability to control structure in molecular glasses has enabled them to play a key role in modern technology; in particular, they are ubiquitous in organic light-emitting diodes. While the interplay between bulk structure and optoelectronic properties has been extensively investigated, few studies have examined molecular orientation near buried interfaces despite its critical role in emergent functionality. Direct, quantitative measurements of buried molecular orientation are inherently challenging, and many methods are insensitive to orientation in amorphous soft matter or lack the necessary spatial resolution. To overcome these challenges, we use polarized resonant soft X-ray reflectivity (p-RSoXR) to measure nanometer-resolved, molecular orientation depth profiles of vapor-deposited thin films of an organic semiconductor Tris(4-carbazoyl-9-ylphenyl)amine (TCTA). Our depth profiling approach characterizes the vertical distribution of molecular orientation and reveals that molecules near the inorganic substrate and free surface have a different, nearly isotropic orientation compared to those of the anisotropic bulk. Comparison of p-RSoXR results with near-edge X-ray absorption fine structure spectroscopy and optical spectroscopies reveals that TCTA molecules away from the interfaces are predominantly planar, which may contribute to their attractive charge transport qualities. Buried interfaces are further investigated in a TCTA bilayer (each layer deposited under separate conditions resulting in different orientations) in which we find a narrow interface between orientationally distinct layers extending across ≈1 nm. Coupling this result with molecular dynamics simulations provides additional insight into the formation of interfacial structure. This study characterizes the local molecular orientation at various types of buried interfaces in vapor-deposited glasses and provides a foundation for future studies to develop critical structure-function relationships.

Spontaneous surface adsorption of aqueous graphene oxide by synergy with surfactants

The spontaneous adsorption of graphene oxide (GO) sheets at the air-water interface is explored using X-ray reflectivity (XRR) measurements. As a pure aqueous dispersion, GO sheets do not spontaneously adsorb at the air-water interface due to their high negative surface potential (-60 mV) and hydrophilic functionality. However, when incorporated with surfactant molecules at optimal ratios and loadings, GO sheets can spontaneously be driven to the surface. It is hypothesised that surfactant molecules experience favourable attractive interactions with the surfaces of GO sheets, resulting in co-assembly that serves to render the sheets surface active. The GO/surfactant composites then collectively adsorb at the air-water interface, with XRR analysis suggesting an interfacial structure comprising surfactant tailgroups in air and GO/surfactant headgroups in water for a combined thickness of 30-40 Å, depending on the surfactant used. Addition of too much surfactant appears to inhibit GO surface adsorption by saturating the interface, and low loadings of GO/surfactant composites (even at optimal ratios) do not show significant adsorption indicating a partitioning effect. Lastly, surfactant chemistry is also a key factor dictating adsorption capacity of GO. The zwitterionic surfactant oleyl amidopropyl betaine causes marked increases in GO surface activity even at very low concentrations (≤0.2 mM), whereas non-ionic surfactants such as Triton X-100 and hexaethyleneglycol monododecyl ether require higher concentrations (ca. 1 mM) in order to impart spontaneous adsorption of the sheets. Anionic surfactants do not enhance GO surface activity presumably due to like-charge repulsions that prevent co-assembly. This work provides useful insight into the synergy between GO sheets and molecular amphiphiles in aqueous systems for enhancing the surface activity of GO, and can be used to inform system formulation for developing water-friendly, surface active composites based around atomically thin materials.

Using refnx to Model Neutron Reflectometry Data from Phospholipid Bilayers

Neutron reflectometry has emerged as a powerful method for studying the structure of thin films in contact with solution at sub-molecular spatial resolution (Penfold and Thomas, J Phys Condens Matter 2:1369-1412, 1990). This type of experiment is undertaken at large international central facilities and experience in data analysis and interpretation is not always available "locally". Here, we describe the application of the refnx software suite (Nelson and Prescott, J Appl Crystallogr 52:193-200, 2019) to the analysis of a single phospholipid bilayer deposited at a silicon/buffer interface. The data is modeled such that the fitted parameters are readily interpretable by researchers working with lipid bilayers.

Multilayered Lamellar Materials and Thin Films by Instant Self-Assembly of Amphiphilic Random Copolymers

Making ordered nanostructures in polymers and their thin films is an important technique to produce functional materials. Herein, we report instant yet precise self-assembly systems of amphiphilic random copolymers to build multilayered lamellar structures in bulk materials and thin films. Random copolymers bearing octadecyl groups and hydroxyethyl groups induced crystallization-driven microphase separation via simple evaporation from the solutions to form lamellar structures in the solid state. The domain spacing was controlled in the range between 3.1 and 4.2 nm at the 0.1 nm level by tuning copolymer composition. Interestingly, just by spin-coating the polymer solutions onto silicon substrates, the copolymers autonomously formed thin films consisting of multilayered lamellar structures, where amorphous/hydrophilic parts and crystalline octadecyl domains are alternatingly layered from a silicon substrate to the air/polymer interface at regular intervals. The lamellar domain spacing was tunable by selecting hydrophilic pendants.

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.

anaklasis: a compact software package for model-based analysis of specular neutron and X-ray reflectometry data sets

A new software package (anaklasis) for model-based analysis of specular neutron and X-ray reflectivity is introduced. Key features include a user-friendly compact interfacial model definition scheme and a complete set of methods for co-refining data and estimating parameter uncertainty.

anaklasis constitutes a set of open-source Python scripts that facilitate a range of specular neutron and X-ray reflectivity calculations, involving the generation of theoretical curves and the comparison/fitting of interfacial model reflectivity against experimental data sets. The primary focus of the software is twofold: on one hand to offer a more natural framework for model definition, requiring minimum coding literacy, and on the other hand to include advanced analysis methods that have been proposed in recent work. Particular attention is given to the ability to co-refine reflectivity data and to the estimation of model-parameter uncertainty and covariance using bootstrap analysis and Markov chain Monte Carlo sampling. The compactness and simplicity of model definition together with the streamlined analysis do not present a steep learning curve for the user, an aspect that may accelerate the generation of reproducible, easily readable and statistically accurate reports in future neutron and X-ray reflectivity related literature.

Modular Assembly of Vibrationally and Electronically Coupled Rhenium Bipyridine Carbonyl Complexes on Silicon

Hybrid inorganic/organic heterointerfaces are promising systems for next-generation photocatalytic, photovoltaic, and chemical-sensing applications. Their performance relies strongly on the development of robust and reliable surface passivation and functionalization protocols with (sub)molecular control. The structure, stability, and chemistry of the semiconductor surface determine the functionality of the hybrid assembly. Generally, these modification schemes have to be laboriously developed to satisfy the specific chemical demands of the semiconductor surface. The implementation of a chemically independent, yet highly selective, standardized surface functionalization scheme, compatible with nanoelectronic device fabrication, is of utmost technological relevance. Here, we introduce a modular surface assembly (MSA) approach that allows the covalent anchoring of molecular transition-metal complexes with sub-nanometer precision on any solid material by combining atomic layer deposition (ALD) and selectively self-assembled monolayers of phosphonic acids. ALD, as an essential tool in semiconductor device fabrication, is used to grow conformal aluminum oxide activation coatings, down to sub-nanometer thicknesses, on silicon surfaces to enable a selective step-by-step layer assembly of rhenium(I) bipyridine tricarbonyl molecular complexes. The modular surface assembly of molecular complexes generates precisely structured spatial ensembles with strong intermolecular vibrational and electronic coupling, as demonstrated by infrared spectroscopy, photoluminescence, and X-ray photoelectron spectroscopy analysis. The structure of the MSA can be chosen to avoid electronic interactions with the semiconductor substrate to exclusively investigate the electronic interactions between the surface-immobilized molecular complexes.

Deep learning approach for an interface structure analysis with a large statistical noise in neutron reflectometry

Neutron reflectometry (NR) allows us to probe into the structure of the surfaces and interfaces of various materials such as soft matters and magnetic thin films with a contrast mechanism dependent on isotopic and magnetic states. The neutron beam flux is relatively low compared to that of other sources such as synchrotron radiation; therefore, there has been a strong limitation in the time-resolved measurement and further advanced experiments such as surface imaging. This study aims at the development of a methodology to enable the structural analysis by the NR data with a large statistical error acquired in a short measurement time. The neural network-based method predicts the true NR profile from the data with a 20-fold lower signal compared to that obtained under the conventional measurement condition. This indicates that the acquisition time in the NR measurement can be reduced by more than one order of magnitude. The current method will help achieve remarkable improvement in temporally and spatially resolved NR methods to gain further insight into the surface and interfaces of materials.

Distributions of Deuterated Polystyrene Chains in Perforated Layers of Blend Films of a Symmetric Polystyrene-block-poly(methyl methacrylate)

We have examined the spatial distributions of polymer chains in blend films of weakly segregated polystyrene-block-poly(methyl methacrylate) [P(S-b-MMA)] and deuterated polystyrene (dPS). By fine-tuning the composition (ϕ_PS+dPS = 63.8 vol %) of the total PS/dPS component and annealing temperature (230 and 270 °C), P(S-b-MMA)/dPS blend films mainly form perforated layers with a parallel orientation (hereafter PLs^//). The distributions of dPS in PLs^// were probed by grazing-incidence small-angle neutron scattering (GISANS) and time-of-flight neutron reflectivity (ToF-NR). GISANS and ToF-NR results offer evidence that dPS chains preferentially locate at the free surface and within the PS layers for blend films that were annealed at 230 °C. Upon annealing at 270 °C, dPS chains distribute within PS layers and perforated PMMA layers. Nevertheless, dPS chains still retain a surface preference for thin films. In contrast, such surface segregation of dPS chains is prohibited for thick films when annealed at 270 °C.

Towards automated analysis for neutron reflectivity

We describe a neural network-based tool for the automatic estimation of thin film thicknesses and scattering length densities from neutron reflectivity curves. The neural network sits within a data pipeline, that takes raw data from a neutron reflectometer, and outputs data and parameter estimates into a fitting program for end user analysis. Our tool deals with simple cases, predicting the number of layers and layer parameters up to three layers on a bulk substrate. This provides good accuracy in parameter estimation, while covering a large portion of the use case. By automating steps in data analysis that only require semi-expert knowledge, we lower the barrier to on-experiment data analysis, allowing better utility to be made from large scale facility experiments. Transfer learning showed that our tool works for x-ray reflectivity, and all code is freely available on GitHub (neutron-net 2020, available at: https://github.com/xmironov/neutron-net) (Accessed: 25 June 2020).

Machine learning for neutron reflectometry data analysis of two-layer thin films *

Neutron reflectometry (NR) is a powerful tool for probing thin films at length scales down to nanometers. We investigated the use of a neural network to predict a two-layer thin film structure to model a given measured reflectivity curve. Application of this neural network to predict a thin film structure revealed that it was accurate and could provide an excellent starting point for traditional fitting methods. Employing prediction-guided fitting has considerable potential for more rapidly producing a result compared to the labor-intensive but commonly-used approach of trial and error searches prior to refinement. A deeper look at the stability of the predictive power of the neural network against statistical fluctuations of measured reflectivity profiles showed that the predictions are stable. We conclude that the approach presented here can provide valuable assistance to users of NR and should be further extended for use in studies of more complex n-layer thin film systems. This result also opens up the possibility of developing adaptive measurement systems in the future.

Increasing Antibiotic Susceptibility: The Use of Cationic Gold Nanoparticles in Gram-Negative Bacterial Membrane Models

Antibiotic resistance will be one of the most prominent challenges to health-care systems in the coming decades, with the OECD predicting that up to 2.4 million deaths will be caused between 2015 and 2050 by drug-resistant bacterial infections in first-world countries alone, with infections costing health-care systems billions of dollars each year. Developing new methods to increase bacterial susceptibility toward drugs is an important step in treating resistant infections. Here, the synergistic effects of gold nanoparticles and the antibiotic drug colistin sulfate have been examined. A tethered lipid bilayer membrane was used to mimic a Gram-negative bacterial cell membrane. Exposing the membrane to gold nanoparticles prior to adding the antibiotic significantly increased the effect of the antibiotic on the membrane. Cationic gold nanoparticles could thus be used to enhance bacterial susceptibility to antibiotics, leading to a more potent treatment.

Nanostructural Characterization of Cardiolipin-Containing Tethered Lipid Bilayers Adsorbed on Gold and Silicon Substrates for Protein Incorporation

A key to the development of lipid membrane-based devices is a fundamental understanding of how the molecular structure of the lipid bilayer membrane is influenced by the type of lipids used to build the membrane. This is particularly important when membrane proteins are included in these devices since the precise lipid environment affects the ability to incorporate membrane proteins and their functionality. Here, we used neutron reflectometry to investigate the structure of tethered bilayer lipid membranes and to characterize the incorporation of the NhaA sodium proton exchanger in the bilayer. The lipid membranes were composed of two lipids, dioleoyl phosphatidylcholine and cardiolipin, and were adsorbed on gold and silicon substrates using two different tethering architectures based on functionalized oligoethylene glycol molecules of different lengths. In all of the investigated samples, the addition of cardiolipin caused distinct structural rearrangement including crowding of ethylene glycol groups of the tethering molecules in the inner head region and a thinning of the lipid tail region. The incorporation of NhaA in the tethered bilayers following two different protocols is quantified, and the way protein incorporation modulates the structural properties of these membranes is detailed.

Determining the maximum information gain and optimizing experimental design in neutron reflectometry using the Fisher information

An approach based on the Fisher information (FI) is developed to quantify the maximum information gain and optimal experimental design in neutron reflectometry experiments. In these experiments, the FI can be calculated analytically and used to provide sub-second predictions of parameter uncertainties. This approach can be used to influence real-time decisions about measurement angle, measurement time, contrast choice and other experimental conditions based on parameters of interest. The FI provides a lower bound on parameter estimation uncertainties, and these are shown to decrease with the square root of the measurement time, providing useful information for the planning and scheduling of experimental work. As the FI is computationally inexpensive to calculate, it can be computed repeatedly during the course of an experiment, saving costly beam time by signalling that sufficient data have been obtained or saving experimental data sets by signalling that an experiment needs to continue. The approach's predictions are validated through the introduction of an experiment simulation framework that incorporates instrument-specific incident flux profiles, and through the investigation of measuring the structural properties of a phospholipid bilayer.

Cellular interactions with polystyrene nanoplastics-The role of particle size and protein corona

Plastic waste is ubiquitously spread across the world and its smaller analogs-microplastics and nanoplastics-raise particular health concerns. While biological impacts of microplastics and nanoplastics have been actively studied, the chemical and biological bases for the adverse effects are sought after. This work explores contributory factors by combining results from in vitro and model mammalian membrane experimentation to assess the outcome of cell/nanoplastic interactions in molecular detail, inspecting the individual contribution of nanoplastics and different types of protein coronae. The in vitro study showed mild cytotoxicity and cellular uptake of polystyrene (PS) nanoplastics, with no clear trend based on nanoplastic size (20 and 200 nm) or surface charge. In contrast, a nanoplastic size-dependency on bilayer disruption was observed in the model system. This suggests that membrane disruption resulting from direct interaction with PS nanoplastics has little correlation with cytotoxicity. Furthermore, the level of bilayer disruption was found to be limited to the hydrophilic headgroup, indicating that transmembrane diffusion was an unlikely pathway for cellular uptake-endocytosis is the viable mechanism. In rare cases, small PS nanoplastics (20 nm) were found in the vicinity of chromosomes without a nuclear membrane surrounding them; however, this was not observed for larger PS nanoplastics (200 nm). We hypothesize that the nanoplastics can interact with chromosomes prior to nuclear membrane formation. Overall, precoating PS particles with protein coronae reduced the cytotoxicity, irrespective of the corona type. When comparing the two types, the extent of reduction was more apparent with soft than hard corona.

Effect of nonionic and amphoteric surfactants on salivary pellicles reconstituted in vitro

Surfactants are important components of oral care products. Sodium dodecyl sulfate (SDS) is the most common because of its foaming properties, taste and low cost. However, the use of ionic surfactants, especially SDS, is related to several oral mucosa conditions. Thus, there is a high interest in using non-ionic and amphoteric surfactants as they are less irritant. To better understand the performance of these surfactants in oral care products, we investigated their interaction with salivary pellicles i.e., the proteinaceous films that cover surfaces exposed to saliva. Specifically, we focused on pentaethylene glycol monododecyl ether (C12E5) and cocamidopropyl betaine (CAPB) as model nonionic and amphoteric surfactants respectively, and investigated their interaction with reconstituted salivary pellicles with various surface techniques: Quartz Crystal Microbalance with Dissipation, Ellipsometry, Force Spectroscopy and Neutron Reflectometry. Both C12E5 and CAPB were gentler on pellicles than SDS, removing a lower amount. However, their interaction with pellicles differed. Our work indicates that CAPB would mainly interact with the mucin components of pellicles, leading to collapse and dehydration. In contrast, exposure to C12E5 had a minimal effect on the pellicles, mainly resulting in the replacement/solubilisation of some of the components anchoring pellicles to their substrate.

Towards reflectivity profile inversion through artificial neural networks

The goal of specular neutron and x-ray reflectometry is to infer a material’s scattering length density (SLD) profile from its experimental reflectivity curves. This paper focuses on the investigation of an original approach to the ill-posed non-invertible problem which involves the use of artificial neural networks (ANNs). In particular, the numerical experiments described here deal with large data sets of simulated reflectivity curves and SLD profiles, and aim to assess the applicability of data science and machine learning technology to the analysis of data generated at large-scale neutron scattering facilities. It is demonstrated that, under certain circumstances, properly trained deep neural networks are capable of correctly recovering plausible SLD profiles when presented with previously unseen simulated reflectivity curves. When the necessary conditions are met, a proper implementation of the described approach would offer two main advantages over traditional fitting methods when dealing with real experiments, namely (1) sample physical models are described under a new paradigm: detailed layer-by-layer descriptions (SLDs, thicknesses, roughnesses) are replaced by parameter-free curves ρ(z), allowing a priori assumptions to be used in terms of the sample family to which a given sample belongs (e.g. ‘thin film,’ ‘lamellar structure’,etc.); (2) the time required to reach a solution is shrunk by orders of magnitude, enabling faster batch analysis for large datasets.

Solid Electrolyte Interphase Layer Formation during Lithiation of Single-Crystal Silicon Electrodes with a Protective Aluminum Oxide Coating

The lithiation of crystalline silicon was studied over several cycles using operando neutron reflectometry over six cycles. A thin layer of aluminum oxide was employed as an artificial coating on the silicon to suppress the solid electrolyte interphase (SEI) layer-related aging effects. Initially, the artificial SEI prevented side effects but led to increased lithium trapping. This layer degraded after two cycles, followed by side reactions, which decrease the coulombic efficiency. No hint for electrode fracturization was found even though the lithiation depth exceeded 1 μm. Two distinct zones with high and low lithium concentrations were found, initially separated by a sharp interface, which broadens with cycling. The correlation of the reflectometry results with the electrochemical current showed the lithium fraction that is lithiated in the silicon and the lithium consumed in side reactions. Also, neutron reflectometry was used to quantify the amount of lithium that remained inside of the silicon. Additional electrochemical impedance spectroscopy was used to gain insights into the electrical properties of the sample via fitting to an equivalent circuit.

Quantifying the robustness of the neutron reflectometry technique for structural characterization of polymer brushes

Neutron reflectometry is the foremost technique for in situ determination of the volume fraction profiles of polymer brushes at planar interfaces. However, the subtle features in the reflectometry data produced by these diffuse interfaces challenge data interpretation. Historically, data analyses have used least-squares approaches that do not adequately quantify the uncertainty of the modeled profile and ignore the possibility of other structures that also match the collected data (multimodality). Here, a Bayesian statistical approach is used that permits the structural uncertainty and multimodality to be quantified for polymer brush systems. A free-form model is used to describe the volume fraction profile, minimizing assumptions regarding brush structure, while only allowing physically reasonable profiles to be produced. The model allows the total volume of polymer and the profile monotonicity to be constrained. The rigor of the approach is demonstrated via a round-trip analysis of a simulated system, before it is applied to real data examining the well characterized collapse of a thermoresponsive brush. It is shown that, while failure to constrain the interfacial volume and consider multimodality may result in erroneous structures being derived, carefully constraining the model allows for robust determination of polymer brush compositional profiles. This work highlights that an appropriate combination of flexibility and constraint must be used with polymer brush systems to ensure the veracity of the analysis. The code used in this analysis is provided, enabling the reproduction of the results and the application of the method to similar problems.

Neutron Reflectometry Tomography for Imaging and Depth Structure Analysis of Thin Films with In-Plane Inhomogeneity

Neutron reflectometry (NR) has been used for the depth structure analysis of materials at the surface and interface with a sub-nanometric resolution. Conventional NR provides averaged information for an area larger than several square centimeters; therefore, it cannot be applied to an interface with an in-plane inhomogeneity. In this study, the NR imaging of the in-plane structure of polymer thin films was achieved. The tomographic reconstruction of the spatially resolved NR profiles obtained by a sheet-shaped neutron beam provided a two-dimensional image of the in-plane interface morphology. The depth distribution of the neutron scattering length density was obtained by analyzing the position-dependent NR profile at a local area less than 0.1 mm². The current NR tomography method enables NR measurements for an interface with an inhomogeneous structure. It also provides information on the three-dimensional distribution of the atomic composition near the surface and interfaces for various materials.

Structure and Hydration of Asymmetric Polyelectrolyte Multilayers as Studied by Neutron Reflectometry: Connecting Multilayer Structure to Superior Membrane Performance

Porous membranes coated with so-called asymmetric polyelectrolyte multilayers (PEMs) have recently been shown to outperform commercial membranes for micropollutant removal. They consist of open support layers of poly(styrene sulfonate) (PSS)/poly(allylamine) (PAH) capped by denser and more selective layers of either PAH/poly(acrylic acid) (PAA) or PAH/Nafion. Unfortunately, the structure of these asymmetric PEMs, and thus their superior membrane performance, is poorly understood. In this work, neutron reflectometry (NR) is employed to elucidate the multilayered structure and hydration of these asymmetric PEMs. NR reveals that the multilayers are indeed asymmetric in structure, with distinct bottom and top multilayers when air-dried and when solvated. The low hydration of the top [PAH/Nafion] multilayer, together with the low water permeance of comparable [PAH/Nafion]-capped PEM membranes, demonstrate that it is a reduction in hydration that makes these separation layers denser and more selective. In contrast, the [PAH/PAA] capping multilayers are more hydrated than the support [PSS/PAH] layers, signifying that, here, densification of the separation layer occurs through a decrease in the mesh size (or effective pore size) of the top layer due to the higher charge density of the PAH/PAA couple compared to the PSS/PAH couple. The [PAH/PAA] and [PAH/Nafion] separation layers are extremely thin (∼4.5 and ∼7 nm, respectively), confirming that these asymmetric PEM membranes have some of the thinnest separation layers ever achieved.

A comparison between the structures of reconstituted salivary pellicles and oral mucin (MUC5B) films

HYPOTHESIS

Salivary pellicles i.e., thin films formed upon selective adsorption of saliva, protect oral surfaces against chemical and mechanical insults. Pellicles are also excellent aqueous lubricants. It is generally accepted that reconstituted pellicles have a two-layer structure, where the outer layer is mainly composed of MUC5B mucins. We hypothesized that by comparing the effect of ionic strength on reconstituted pellicles and MUC5B films we could gain further insight into the pellicle structure.

EXPERIMENTS

Salivary pellicles and MUC5B films reconstituted on solid surfaces were investigated at different ionic strengths by Force Spectroscopy, Quartz Crystal Microbalance with Dissipation, Null Ellipsometry and Neutron Reflectometry.

FINDINGS

Our results support the two-layer structure for reconstituted salivary pellicles. The outer layer swelled when ionic strength decreased, indicating a weak polyelectrolyte behavior. While initially the MUC5B films exhibited a similar tendency, this was followed by a drastic collapse indicating an interaction between exposed hydrophobic domains. This suggests that mucins in the pellicle outer layer form complexes with other salivary components that prevent this interaction. Lowering ionic strength below physiological values also led to a partial removal of the pellicle inner layer. Overall, our results highlight the importance that the interactions of mucins with other pellicle components play on their structure.

Enrichment of Charged Monomers Explains Non-monotonic Polymer Volume Fraction Profiles of Multi-stimulus Responsive Copolymer Brushes

Multi-stimulus responsive poly(2-(2-methoxyethoxy)ethyl methacrylate-co-2-(diethylamino)ethyl methacrylate) [P(MEO₂MA-co-DEA)] 80:20 mol % copolymer brushes were synthesized on planar silica substrates via surface-initiated activators continuously regenerated via electron transfer atom transfer radical polymerization. Brush thickness was sensitive to changes in pH and temperature as monitored with ellipsometry. At low pH, the brush is charged and swollen, while at high pH, the brush is uncharged and more collapsed. Clear thermoresponsive behavior is also observed with the brush more swollen at low temperatures compared to high temperatures at both high and low pH. Neutron reflectometry was used to determine the polymer volume fraction profiles (VFPs) at various pH values and temperatures. A region of lower polymer content, or a depletion region, near the substrate is present in all of the experimental polymer VFPs, and it is more pronounced at low pH (high charge) and less so at high pH (low charge). Polymer VFPs calculated through numerical self-consistent field theory suggest that enrichment of DEA monomers near the substrate results in the experimentally observed non-monotonic VFPs. Adsorption of DEA monomers to the substrate prior to initiation of polymerization could give rise to DEA segment-enriched region proximal to the substrate.

Competitive specific ion effects in mixed salt solutions on a thermoresponsive polymer brush

HYPOTHESIS

Grafted poly(ethylene glycol) methyl ether methacrylate (POEGMA) copolymer brushes change conformation in response to temperature ('thermoresponse'). In the presence of different ions the thermoresponse of these coatings is dramatically altered. These effects are complex and poorly understood with no all-inclusive predictive theory of specific ion effects. As natural environments are composed of mixed electrolytes, it is imperative we understand the interplay of different ions for future applications. We hypothesise anion mixtures from the same end of the Hofmeister series (same-type anions) will exhibit non-additive and competitive behaviour.

EXPERIMENTS

The behaviour of POEGMA brushes, synthesised via surface-initiated ARGET-ATRP, in both single and mixed aqueous electrolyte solutions was characterised with ellipsometry and neutron reflectometry as a function of temperature.

FINDINGS

In mixed fluoride and chloride aqueous electrolytes (salting-out ions), or mixed thiocyanate and iodide aqueous electrolytes (salting-in ions), a non-monotonic concentration-dependent influence of the two anions on the thermoresponse of the brush was observed. A new term, δ, has been defined to quantitively describe synergistic or antagonistic behaviour. This study determined the specific ion effects imparted by salting-out ions are dependent on available solvent molecules, whereas the influence of salting-in ions is dependent on the interactions of the anions and polymer chains.

Solid-supported lipid bilayers - A versatile tool for the structural and functional characterization of membrane proteins

The cellular membrane is central to the development of single-and multicellular life, as it separates the delicate cellular interior from the hostile environment. It exerts tight control over entry and exit of substances, is responsible for signaling with other cells in multicellular organisms and prevents pathogens from entering the cell. In the case of bacteria and viruses, the cellular membrane also hosts the proteins enabling invasion of the host organism. In a very real sense therefore, the cellular membrane is central to all life. The study of the cell membrane and membrane proteins in particular has therefore attracted significant attention. Due to the enormous variety of tasks performed by the membrane, it is a highly complex and challenging structure to study. Ideally, membrane components would be studied in isolation from this environment, but unlike water soluble proteins, the amphiphilic environment provided by the cellular membrane is key to the structure and function of the cell membrane. Therefore, model membranes have been developed to provide an environment in which a membrane protein can be studied. This review presents a set of tools that enable the comprehensive characterization of membrane proteins: electrochemical tools, surface plasmon resonance, neutron scattering, the surface forces apparatus and atomic force microscopy are discussed, with a particular focus on experimental technique and data evaluation.

A general approach to maximise information density in neutron reflectometry analysis

Neutron and x-ray reflectometry are powerful techniques facilitating the study of the structure of interfacial materials. The analysis of these techniques is ill-posed in nature requiring the application of model-dependent methods. This can lead to the over- and under- analysis of experimental data when too many or too few parameters are allowed to vary in the model. In this work, we outline a robust and generic framework for the determination of the set of free parameters that are capable of maximising the information density of the model. This framework involves the determination of the Bayesian evidence for each permutation of free parameters; and is applied to a simple phospholipid monolayer. We believe this framework should become an important component in reflectometry data analysis and hope others more regularly consider the relative evidence for their analytical models.

Applications of neutron reflectometry in biology

Over the last 10 years, neutron reflectometry (NR) has emerged as a powerful technique for the investigation of biologically relevant thin films. The great advantage of NR with respect to many other surface-sensitive techniques is its sub-nanometer resolution that enables structural characterizations at the molecular level. In the case of bio-relevant samples, NR is non-destructive and can be used to probe thin films at buried interfaces or enclosed in bulky sample environment equipment. Moreover, recent advances in biomolecular deutera-tion enabled new labeling strategies to highlight certain structural features and to resolve with better accuracy the location of chemically similar molecules within a thin film.

In this chapter I will describe some applications of NR to bio-relevant samples and discuss some of the data analysis approaches available for biological thin films. In particular, examples on the structural characterization of biomembranes, protein films and protein-lipid interactions will be described.

BornAgain: software for simulating and fitting grazing-incidence small-angle scattering

BornAgain is a free and open-source multi-platform software framework for simulating and fitting X-ray and neutron reflectometry, off-specular scattering, and grazing-incidence small-angle scattering (GISAS). This paper concentrates on GISAS. Support for reflectometry and off-specular scattering has been added more recently, is still under intense development and will be described in a later publication. BornAgain supports neutron polarization and magnetic scattering. Users can define sample and instrument models through Python scripting. A large subset of the functionality is also available through a graphical user interface. This paper describes the software in terms of the realized non-functional and functional requirements. The web site https://www.bornagainproject.org/ provides further documentation.

Structural Properties and Magnetic Ordering in 2D Polymer Nanocomposites: Existence of Long Magnetic Dipolar Chains in Zero Field

The existence of magnetic dipolar nanoparticle chains at zero field has been predicted theoretically for decades, but these structures are rarely observed experimentally. A prerequisite is a permanent magnetic moment on the particles forming the chain. Here we report on the observation of magnetic dipolar chains of spherical iron oxide nanoparticles with a diameter of 12.8 nm. The nanoparticles are embedded in an ultrathin polymer film. Due to the high viscosity of the polymer matrix, the dominating aggregation mechanism is driven by dipolar interactions. Smaller iron oxide nanoparticles (8 nm) show no permanent magnetic moment and do not form chains but compact aggregates. Mixed monolayers of iron oxide nanoparticles and polymer at the air-water interface are characterized by Langmuir isotherms and in situ X-ray reflectometry (XRR). The combination of the particles with a polymer leads to a stable polymer nanocomposite film at the air-water interface. XRR experiments show that nanoparticles are immersed in a thin polymer matrix of 2 nm. Using atomic force microscopy (AFM) on Langmuir-Blodgett films, we measure the lateral distribution of particles in the film. An analysis of single structures within transferred films results in fractal dimensions that are in excellent agreement with 2D simulations.

refnx: neutron and X-ray reflectometry analysis in Python

refnx is a model-based neutron and X-ray reflectometry data analysis package written in Python. It is cross platform and has been tested on Linux, macOS and Windows. Its graphical user interface is browser based, through a Jupyter notebook. Model construction is modular, being composed from a series of components that each describe a subset of the interface, parameterized in terms of physically relevant parameters (volume fraction of a polymer, lipid area per molecule etc.). The model and data are used to create an objective, which is used to calculate the residuals, log-likelihood and log-prior probabilities of the system. Objectives are combined to perform co-refinement of multiple data sets and mixed-area models. Prior knowledge of parameter values is encoded as probability distribution functions or bounds on all parameters in the system. Additional prior probability terms can be defined for sets of components, over and above those available from the parameters alone. Algebraic parameter constraints are available. The software offers a choice of fitting approaches, including least-squares (global and gradient-based optimizers) and a Bayesian approach using a Markov-chain Monte Carlo algorithm to investigate the posterior distribution of the model parameters. The Bayesian approach is useful for examining parameter covariances, model selection and variability in the resulting scattering length density profiles. The package is designed to facilitate reproducible research; its use in Jupyter notebooks, and subsequent distribution of those notebooks as supporting information, permits straightforward reproduction of analyses.

Bayesian determination of the effect of a deep eutectic solvent on the structure of lipid monolayers

A novel reflectometry analysis method reveals the structure of lipid monolayers at the air-DES interface.

Temperature dependent specific ion effects in mixed salt environments on a thermoresponsive poly(oligoethylene glycol methacrylate) brush

The temperature induced swelling/collapse transition of poly(oligoethylene glycol methacrylate) (POEGMA) brushes has been investigated in electrolyte solutions comprised of multiple anions.