Efficient end-to-end simulation of time-dependent coherent X-ray scattering experiments.

Physical optics simulations for beamlines and experiments allow users to test experiment feasibility and optimize beamline settings ahead of beam time in order to optimize valuable beam time at synchrotron light sources like NSLS-II. Further, such simulations also help to develop and test experimental data processing methods and software in advance. The Synchrotron Radiation Workshop (SRW) software package supports such complex simulations. We demonstrate how recent developments in SRW significantly improve the efficiency of physical optics simulations, such as end-to-end simulations of time-dependent X-ray photon correlation spectroscopy experiments with partially coherent undulator radiation (UR). The molecular dynamics simulation code LAMMPS was chosen to model the sample: a solution of silica nanoparticles in water at room temperature. Real-space distributions of nanoparticles produced by LAMMPS were imported into SRW and used to simulate scattering patterns of partially coherent hard X-ray UR from such a sample at the detector. The partially coherent UR illuminating the sample can be represented by a set of orthogonal coherent modes obtained by simulation of emission and propagation of this radiation through the coherent hard X-ray (CHX) scattering beamline followed by a coherent-mode decomposition. GPU acceleration is added for several key functions of SRW used in propagation from sample to detector, further improving the speed of the calculations. The accuracy of this simulation is benchmarked by comparison with experimental data.

Coherent X-ray Spectroscopy Elucidates Nanoscale Dynamics of Plasma-Enhanced Thin-Film Growth.

Sophisticated thin film growth techniques increasingly rely on the addition of a plasma component to open or widen a processing window, particularly at low temperatures. Taking advantage of continued increases in accelerator-based X-ray source brilliance, this real-time study uses X-ray Photon Correlation Spectroscopy (XPCS) to elucidate the nanoscale surface dynamics during Plasma-Enhanced Atomic Layer Deposition (PE-ALD) of an epitaxial indium nitride film. Ultrathin films are synthesized from repeated cycles of alternating self-limited surface reactions induced by temporally separated pulses of the material precursor and plasma reactant, allowing the influence of each on the evolving morphology to be examined. During the heteroepitaxial 3D growth examined here, sudden changes in the surface structure during initial film growth, consistent with numerous overlapping stress-relief events, are observed. When the film becomes continuous, the nanoscale surface morphology abruptly becomes long-lived with a correlation time spanning the period of the experiment. Throughout the growth experiment, there is a consistent repeating pattern of correlations associated with the cyclic growth process, which is modeled as transitions between different surface states. The plasma exposure does not simply freeze in a structure that is then built upon in subsequent cycles, but rather, there is considerable surface evolution during all phases of the growth cycle.

Effects of the Grazing Incidence Geometry on X-ray Photon Correlation Spectroscopy Measurements.

X-ray photon correlation spectroscopy (XPCS) is a versatile tool to measure dynamics on the nanometer to micrometer scale in bulk samples. XPCS has also been applied in grazing incidence (GI) geometry to examine the dynamics of surface layers. However, considering GI scattering experiments more universally, the GI geometry leads to a superposition of signals due to reflection and refraction effects, also known from the distorted-wave Born approximation (DWBA). In this paper, the impact of these reflection and refraction effects on the correlation analysis is determined experimentally by measuring grazing incidence transmission XPCS (GT-XPCS) and grazing incidence XPCS (GI-XPCS) simultaneously for a thin film sample, showing non-equilibrium dynamics. The results of the GI and GT geometry comparisons are combined within the framework of the standardly applied, simplified DWBA. These calculations allow identifying the main contributions of the detected signal from the leading scattering terms along the out-of-plane direction qz, which dominate the measured intensity pattern on the detector. In combination with the calculation of the non-linear effect of refraction in GTSAXS and GISAXS, it is possible to identify experimental conditions that can be chosen to run experiments and data analysis as close as possible to transmission XPCS and to explain which limitations for data interpretations are observed. Consequently, the beam exposure can be significantly reduced by using GI geometry only. Calculations of experimental settings prior to experiments are detailed to determine suitable qz regions for a variety of material systems measured in bulk-sensitive GI-XPCS experiments, allowing us to determine the scaling behavior of typical decay times as a function of q that is comparable to the scaling behavior obtained in distortion-free GT-XPCS or transmission XPCS experiments.

Rheology and dynamics of a solvent segregation driven gel (SeedGel).

Bicontinuous structures promise applications in a broad range of research fields, such as energy storage, membrane science, and biomaterials. Kinetically arrested spinodal decomposition is found responsible for stabilizing such structures in different types of materials. A recently developed solvent segregation driven gel (SeedGel) is demonstrated to realize bicontinuous channels thermoreversibly with tunable domain sizes by trapping nanoparticles in a particle domain. As the mechanical properties of SeedGel are very important for its future applications, a model system is characterized by temperature-dependent rheology. The storage modulus shows excellent thermo-reproducibility and interesting temperature dependence with the maximum storage modulus observed at an intermediate temperature range (around 28 °C). SANS measurements are conducted at different temperatures to identify the macroscopic solvent phase separation during the gelation transition, and solvent exchange between solvent and particle domains that is responsible for this behavior. The long-time dynamics of the gel is further studied by X-ray Photon Correlation Spectroscopy (XPCS). The results indicate that particles in the particle domain are in a glassy state and their long-time dynamics are strongly correlated with the temperature dependence of the storage modulus.

Noise reduction in X-ray photon correlation spectroscopy with convolutional neural networks encoder-decoder models.

Like other experimental techniques, X-ray photon correlation spectroscopy is subject to various kinds of noise. Random and correlated fluctuations and heterogeneities can be present in a two-time correlation function and obscure the information about the intrinsic dynamics of a sample. Simultaneously addressing the disparate origins of noise in the experimental data is challenging. We propose a computational approach for improving the signal-to-noise ratio in two-time correlation functions that is based on convolutional neural network encoder-decoder (CNN-ED) models. Such models extract features from an image via convolutional layers, project them to a low dimensional space and then reconstruct a clean image from this reduced representation via transposed convolutional layers. Not only are ED models a general tool for random noise removal, but their application to low signal-to-noise data can enhance the data's quantitative usage since they are able to learn the functional form of the signal. We demonstrate that the CNN-ED models trained on real-world experimental data help to effectively extract equilibrium dynamics' parameters from two-time correlation functions, containing statistical noise and dynamic heterogeneities. Strategies for optimizing the models' performance and their applicability limits are discussed.

Collective Nanoparticle Dynamics Associated with Bridging Network Formation in Model Polymer Nanocomposites.

The addition of nanoparticles (NPs) to polymers is a powerful method to improve the mechanical and other properties of macromolecular materials. Such hybrid polymer-particle systems are also rich in fundamental soft matter physics. Among several factors contributing to mechanical reinforcement, a polymer-mediated NP network is considered to be the most important in polymer nanocomposites (PNCs). Here, we present an integrated experimental-theoretical study of the collective NP dynamics in model PNCs using X-ray photon correlation spectroscopy and microscopic statistical mechanics theory. Silica NPs dispersed in unentangled or entangled poly(2-vinylpyridine) matrices over a range of NP loadings are used. Static collective structure factors of the NP subsystems at temperatures above the bulk glass transition temperature reveal the formation of a network-like microstructure via polymer-mediated bridges at high NP loadings above the percolation threshold. The NP collective relaxation times are up to 3 orders of magnitude longer than the self-diffusion limit of isolated NPs and display a rich dependence with observation wavevector and NP loading. A mode-coupling theory dynamical analysis that incorporates the static polymer-mediated bridging structure and collective motions of NPs is performed. It captures well both the observed scattering wavevector and NP loading dependences of the collective NP dynamics in the unentangled polymer matrix, with modest quantitative deviations emerging for the entangled PNC samples. Additionally, we identify an unusual and weak temperature dependence of collective NP dynamics, in qualitative contrast with the mechanical response. Hence, the present study has revealed key aspects of the collective motions of NPs connected by polymer bridges in contact with a viscous adsorbing polymer medium and identifies some outstanding remaining challenges for the theoretical understanding of these complex soft materials.

XPCS Microrheology and Rheology of Sterically Stabilized Nanoparticle Dispersions in Aprotic Solvents.

X-ray photon correlation spectroscopy (XPCS) microrheology and conventional bulk rheology were performed on silica nanoparticle dispersions associated with battery electrolyte applications to probe the properties of these specific complex materials and to explore the utility of XPCS microrheology in characterizing nanoparticle dispersions. Sterically stabilized shear-thickening electrolytes were synthesized by grafting poly(methyl methacrylate) chains onto silica nanoparticles. Coated silica dispersions containing 5-30 wt % nanoparticles dispersed in propylene carbonate were studied. In general, both XPCS microrheology and conventional rheology showed that coated silica dispersions were more viscous at higher concentrations, as expected. The complex viscosity of coated silica dispersions showed shear-thinning behavior over the frequency range probed by XPCS measurements. However, measurements using conventional mechanical rheometry yielded a shear viscosity with weak shear-thickening behavior for dispersions with the highest concentration of 30% particles. Our results indicate that there is a critical concentration needed for shear-thickening behavior, as well as appropriate particle size and surface polymer chain length, for this class of nanoparticle-based electrolytes. The results of this study can provide insights for comparing XPCS microrheology and bulk rheology for related complex fluids and whether XPCS microrheology can capture expected macroscopic rheological properties by probing small-scale particle dynamics.

de Gennes Narrowing and Relationship between Structure and Dynamics in Self-Organized Ion-Beam Nanopatterning.

Investigating the relationship between structure and dynamical processes is a central goal in condensed matter physics. Perhaps the most noted relationship between the two is the phenomenon of de Gennes narrowing, in which relaxation times in liquids are proportional to the scattering structure factor. Here, a similar relationship is discovered during the self-organized ion-beam nanopatterning of silicon using coherent x-ray scattering. However, in contrast to the exponential relaxation of fluctuations in classic de Gennes narrowing, the dynamic surface exhibits a wide range of behaviors as a function of the length scale, with a compressed exponential relaxation at lengths corresponding to the dominant structural motif-self-organized nanoscale ripples. These behaviors are reproduced in simulations of a nonlinear model describing the surface evolution. We suggest that the compressed exponential behavior observed here is due to the morphological persistence of the self-organized surface ripple patterns which form and evolve during ion-beam nanopatterning.

In-Operando Study of Shape Retention and Microstructure Development in a Hydrolyzing Sol-Gel Ink during 3D-Printing.

3D printing of amorphous and crystalline ceramics is of paramount importance for the fabrication of a wide range of devices with applications across different technology fields. Printed ceramics are remarkably enabled by the sol-gel synthesis method in conjunction with continuous filament direct ink writing. During printing, multiple processes contribute to the evolution of inks including shape retention, chemical conversion, solidification, and microstructure formation. Traditionally, depending on the ink composition and printing environment, several mechanisms have been associated with the shape retention and solidification of 3D printed structures: gelation, rapid solvent evaporation, energy-driven phase transformation, and chemical-driven phase transformation. Understanding the fundamental differences between these mechanisms becomes key since they strongly influence the spatiotemporal evolution of the materials, as the out-of-equilibrium processes inherent to the extrusion, relaxation, and solidification of printed materials have significant effects on the materials properties. In this work, we investigate the shape retention mechanism and the hydrolysis-induced material conversion and microstructure formation during the 3D printing of a water reactive sol-gel ink that transforms into titanium dioxide-based ceramic. This study aims at identifying characteristic mechanisms associated with the material transformation, establishing connections between the microstructure development and the timescales associated with solidification under operando 3D-printing conditions. The investigation of this material's out-of-equilibrium pathways under processing conditions is enabled by time-resolved coherent X-ray scattering, providing simultaneous access to temporospatially resolved microstructural and dynamics information. Furthermore, we explore X-ray speckle tracking as a tool to resolve deformations of the microstructure in a printed filament associated with the deposition of consecutive filaments. Through this work, we aim at providing a fundamental understanding of the relationships behind these transformative processes in 3D printing and their timescales as the basis for achieving unprecedented control over printed materials microstructure.

Fluctuation X-ray scattering from nanorods in solution reveals weak temperature-dependent orientational ordering.

Higher-order statistical analysis of X-ray scattering from dilute solutions of polydisperse goethite nanorods was performed and revealed structural information which is inaccessible by conventional small-angle scattering. For instance, a pronounced temperature dependence of the correlated scattering from suspension was observed. The higher-order scattering terms deviate from those expected for a perfectly isotropic distribution of particle orientations, demonstrating that the method can reveal faint orientational order in apparently disordered systems. The observation of correlated scattering from polydisperse particle solutions is also encouraging for future free-electron laser experiments aimed at extracting high-resolution structural information from systems with low particle heterogeneity.

In Operando Monitoring of Dynamic Recovery in 3D-Printed Thermoset Nanocomposites by XPCS.

Extrusion-based additive manufacturing methods, such as direct-write of carbon fiber-reinforced epoxy inks, have become an attractive route toward development of structural composites in recent years, because of emerging techniques such as big area additive manufacturing. The development of improved materials for these methods has been a major focus area; however, an understanding of the effects of the printing process on the structural and dynamic recovery in printed materials remains largely unexplored. The goal of this work is to capture multiscale and temporal morphology and dynamics within thermosetting composite inks to determine the parameters during the printing process that influence the recovery of the printed material. Herein, we use X-ray photon correlation spectroscopy in small-angle scattering geometry to reveal both morphology and recovery dynamics of a nanoparticle (layered-silicate Cloisite 30B) in a thermoset epoxy resin (EPON 826) during the printing process in real time. Our results show that the dynamics of the layered silicate particles during recovery are anisotropic and slow down to behavior which is characteristic of aging in colloidal clay suspensions around  tage ≈ 12 s. The dynamics and alignment of the particles during recovery were tempo-spatially mapped, and the recovery post printing was shown to be strongly influenced by the deposition onto the build plate in addition to the extrusion through the print head. Our in operando results provide insight into the parameters that must be considered when optimizing materials and methods for precisely tailored local properties during 3D printing.

Coherent X-ray measurement of step-flow propagation during growth on polycrystalline thin film surfaces.

The properties of artificially grown thin films are strongly affected by surface processes during growth. Coherent X-rays provide an approach to better understand such processes and fluctuations far from equilibrium. Here we report results for vacuum deposition of C60 on a graphene-coated surface investigated with X-ray Photon Correlation Spectroscopy in surface-sensitive conditions. Step-flow is observed through measurement of the step-edge velocity in the late stages of growth after crystalline mounds have formed. We show that the step-edge velocity is coupled to the terrace length, and that there is a variation in the velocity from larger step spacing at the center of crystalline mounds to closely-spaced, more slowly propagating steps at their edges. The results extend theories of surface growth, since the behavior is consistent with surface evolution driven by processes that include surface diffusion, the motion of step-edges, and attachment at step edges with significant step-edge barriers.

Nanoscale viscosity of confined polyethylene oxide.

Complex fluids near interfaces or confined within nanoscale volumes can exhibit substantial shifts in physical properties compared to bulk, including glass transition temperature, phase separation, and crystallization. Because studies of these effects typically use thin film samples with one dimension of confinement, it is generally unclear how more extreme spatial confinement may influence these properties. In this work, we used x-ray photon correlation spectroscopy and gold nanoprobes to characterize polyethylene oxide confined by nanostructured gratings (<100nm width) and measured the viscosity in this nanoconfinement regime to be ∼500 times the bulk viscosity. This enhanced viscosity occurs even when the scale of confinement is several times the polymer's radius of gyration, consistent with previous reports of polymer viscosity near flat interfaces.

Coherent amplification of X-ray scattering from meso-structures.

Small-angle X-ray scattering (SAXS) often includes an unwanted background, which increases the required measurement time to resolve the sample structure. This is undesirable in all experiments, and may make measurement of dynamic or radiation-sensitive samples impossible. Here, we demonstrate a new technique, applicable when the scattering signal is background-dominated, which reduces the requisite exposure time. Our method consists of exploiting coherent interference between a sample with a designed strongly scattering 'amplifier'. A modified angular correlation function is used to extract the symmetry of the interference term; that is, the scattering arising from the interference between the amplifier and the sample. This enables reconstruction of the sample's symmetry, despite the sample scattering itself being well below the intensity of background scattering. Thus, coherent amplification is used to generate a strong scattering term (well above background), from which sample scattering is inferred. We validate this method using lithographically defined test samples.

Three-dimensional coherent X-ray diffractive imaging of whole frozen-hydrated cells.

A structural understanding of whole cells in three dimensions at high spatial resolution remains a significant challenge and, in the case of X-rays, has been limited by radiation damage. By alleviating this limitation, cryogenic coherent diffractive imaging (cryo-CDI) can in principle be used to bridge the important resolution gap between optical and electron microscopy in bio-imaging. Here, the first experimental demonstration of cryo-CDI for quantitative three-dimensional imaging of whole frozen-hydrated cells using 8 keV X-rays is reported. As a proof of principle, a tilt series of 72 diffraction patterns was collected from a frozen-hydrated Neospora caninum cell and the three-dimensional mass density of the cell was reconstructed and quantified based on its natural contrast. This three-dimensional reconstruction reveals the surface and internal morphology of the cell, including its complex polarized sub-cellular structure. It is believed that this work represents an experimental milestone towards routine quantitative three-dimensional imaging of whole cells in their natural state with spatial resolutions in the tens of nanometres.

Photon statistics and speckle visibility spectroscopy with partially coherent X-rays.

A new approach is proposed for measuring structural dynamics in materials from multi-speckle scattering patterns obtained with partially coherent X-rays. Coherent X-ray scattering is already widely used at high-brightness synchrotron lightsources to measure dynamics using X-ray photon correlation spectroscopy, but in many situations this experimental approach based on recording long series of images (i.e. movies) is either not adequate or not practical. Following the development of visible-light speckle visibility spectroscopy, the dynamic information is obtained instead by analyzing the photon statistics and calculating the speckle contrast in single scattering patterns. This quantity, also referred to as the speckle visibility, is determined by the properties of the partially coherent beam and other experimental parameters, as well as the internal motions in the sample (dynamics). As a case study, Brownian dynamics in a low-density colloidal suspension is measured and an excellent agreement is found between correlation functions measured by X-ray photon correlation spectroscopy and the decay in speckle visibility with integration time obtained from the analysis presented here.

Salt effects in the formation of self-assembled lithocholate helical ribbons and tubes.

The formation of self-assembled nanotubes is usually accounted for by anisotropic elastic properties of membranelike precursors. We present experimental data as evidence of the role played by electrostatics in the formation of self-assembled tubes in alkaline aqueous suspensions of lithocholic acid (LCA). Striking salt effects are characterized by comparing the rheological, dynamical, and scattering properties of systems prepared either in stoichiometric neutralization conditions (SC) of LCA or in a large excess of sodium hydroxide (EOC, experimentally optimized conditions) and finally, in two steps: stoichiometric neutralization followed by an appropriate addition of NaCl (AISC). The SC liquid system is originally made up of loose helical ribbons (previous transmission electron microscopy data), and upon aging they exhibit both intra- and interordering processes. Initially, the helical ribbons are loose and progressively wind around a cylinder (R = 330 Å) with their edges exposed to the solvent. They can be temporarily organized in a centered rectangular two-dimensional lattice (pgg, a = 224 Å, b = 687 Å). Upon further aging, the ribbons wind into more compact helical ribbons (or tubes with helical grooves): their edges are less-exposed and their ordering vanishes. Upon addition of NaCl salt (as in the AISC systems), the specific screening of the intra-aggregate electrostatic repulsions induces the closure of the ribbons into tubes (R(ext) = 260 Å, R(int) = 245 Å as in the EOC systems). Simultaneously with the closure of the ribbons into plain tubes, a drastic enhancement of their interconnectivity through van der Waals attractions develops. Eventually, gels are obtained with networks having hexagonal bundles of tubes.

From specular reflectivity to time-resolved grazing incidence X-ray scattering out of the specular plane (GISAXS): equilibrium and nonequilibrium states of organic/inorganic monolayers at liquid surfaces.

The grazing incidence diffuse X-ray scattering out of the specular plane technique (GISAXS) is presented, and its capabilities are compared to the more classical X-ray specular reflectivity technique (XSR). Three experimental illustrations are given to prove the efficiency of GISAXS. First, the structure of a DPPC phospholipid monolayer is analyzed. Second, the time-resolved kinetics of lipid desorption from a monolayer interacting with a mineral gel subphase is studied. Third, the structural evolution of biomembranes at extremely low temperatures is illustrated. The GISAXS technique appears to compete efficiently with neutron reflection techniques by taking advantage of remarkably short acquisition times crucial in kinetics experiments.

Self-assembly of organic monolayers below the freezing threshold.

One measure that arctic fish and amphibians use to minimize damage to cellular membranes during cooling and freezing processes is the production of cryo-protective substances. We have mimicked this biological "trick" by using the surface of a cryo-protectant as a liquid subphase for the preparation of organic membranes. Following this innovative approach, quasi two-dimensional amphiphilic monolayers were cooled to -40 degrees C at a liquid/gas interface. To date, the low temperature region of the generic phase diagram for alkane chain molecules has been only "virtually" accessible by tuning the molecular chain length. By extending the temperature range well below the freezing point of water, we gained new insights into membrane stability, morphology, and reorganization at low temperatures. Upon cooling relaxed monolayers at a surface pressure of 4.5 mN/m, we find a transition from a mesophase with tilted chains at ambient temperature toward a crystalline phase with upright chains at low temperatures. Structure factor calculations reveal that the chain alignment in the crystalline phase differs from the classical herringbone configuration.