XPCS: Nanoscale motion and rheology

Micro- and milli-fluidic sample environments for in situ X-ray analysis in the chemical and materials sciences

X-ray-based methods are powerful tools for structural and chemical studies of materials and processes, particularly for performing time-resolved measurements. In this critical review, we highlight progress in the development of X-ray compatible microfluidic and millifluidic platforms that enable high temporal and spatial resolution X-ray analysis across the chemical and materials sciences. With a focus on liquid samples and suspensions, we first present the origins of microfluidic sample environments for X-ray analysis by discussing some alternative liquid sample holder and manipulator technologies. The bulk of the review is then dedicated to micro- and milli-fluidic devices designed for use in the three main areas of X-ray analysis: (1) scattering/diffraction, (2) spectroscopy, and (3) imaging. While most research to date has been performed at synchrotron radiation facilities, the recent progress made using commercial and laboratory-based X-ray instruments is then reviewed here for the first time. This final section presents the exciting possibility of performing in situ and operando X-ray analysis in the 'home' laboratory and transforming microfluidic and millifluidic X-ray analysis into a routine method in physical chemistry and materials research.

Linking structural and rheological memory in disordered soft materials

Linking the macroscopic flow properties and nanoscopic structure is a fundamental challenge to understanding, predicting, and designing disordered soft materials. Under small stresses, these materials are soft solids, while larger loads can lead to yielding and the acquisition of plastic strain, which adds complexity to the task. In this work, we connect the transient structure and rheological memory of a colloidal gel under cyclic shearing across a range of amplitudes via a generalized memory function using rheo-X-ray photon correlation spectroscopy (rheo-XPCS). Our rheo-XPCS data show that the nanometer scale aggregate-level structure recorrelates whenever the change in recoverable strain over some interval is zero. The macroscopic recoverable strain is therefore a measure of the nano-scale structural memory. We further show that yielding in disordered colloidal materials is strongly heterogeneous and that memories of prior deformation can exist even after the material has been subjected to flow.

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.

Smectite phase separation is driven by hydration-mediated interfacial charge

Smectite clay minerals have an outsize impact on the response of clay-rich media to common stimuli, such as hydration and ion exchange, motivating extensive effort to understand behaviors resulting from these processes such as swelling and exfoliation. Smectites are common and historic systems for investigating colloidal and interfacial phenomena, with two swelling regimes commonly identified across myriad clays: osmotic swelling at high water activity and crystalline swelling at low water activity. However, no current swelling model seamlessly spans the full ranges of water, salt and clay content encountered in natural or engineered settings. Here, we show that structures previously rationalized as either osmotic or crystalline coexist as a rich array of distinct colloidal phases that differ by water content, layer stacking thickness, and curvature. We present an analytical model for intermolecular potentials among water, salt and clay in both mono- and divalent electrolytes that predicts swelling pressures across high and low water activities. Our results indicate that all clay swelling is osmotic swelling, but that the osmotic pressure of charged mineral interfaces becomes attractive and dominates that of the electrolyte at high clay activities. Global energy minima are often not reached on experimental timescales due to many local energy minima that promote long-lived intermediate states with vast differences in clay, ion, and water mobilities, leading to hyperdiffusive layer dynamics driven by variable hydration-mediated interfacial charge. Teaser Distinct colloidal phases of swelling clays emerge via ion (de)hydration at mineral interfaces that drives hyperdiffusive layer dynamics as metastable smectites approach equilibrium.

Leveraging the Polymer Glass Transition to Access Thermally Switchable Shear Jamming Suspensions

Suspensions of polymeric nano- and microparticles are fascinating stress-responsive material systems that, depending on their composition, can display a diverse range of flow properties under shear, such as drastic thinning, thickening, and even jamming (reversible solidification driven by shear). However, investigations to date have almost exclusively focused on nonresponsive particles, which do not allow in situ tuning of the flow properties. Polymeric materials possess rich phase transitions that can be directly tuned by their chemical structures, which has enabled researchers to engineer versatile adaptive materials that can respond to targeted external stimuli. Reported herein are suspensions of (readily prepared) micrometer-sized polymeric particles with accessible glass transition temperatures (T _g) designed to thermally control their non-Newtonian rheology. The underlying mechanical stiffness and interparticle friction between particles change dramatically near T _g. Capitalizing on these properties, it is shown that, in contrast to conventional systems, a dramatic and nonmonotonic change in shear thickening occurs as the suspensions transition through the particles' T _g. This straightforward strategy enables the in situ turning on (or off) of the system's ability to shear jam by varying the temperature relative to T _g and lays the groundwork for other types of stimuli-responsive jamming systems through polymer chemistry.

The effect of dynamically heterogeneous interphases on the particle dynamics of polymer nanocomposites

The entanglements of dynamically asymmetric polymer layers influence relaxations of nanoparticles in polymer nanocomposites. In this work, the dynamics of polymer-adsorbed and polymer-grafted nanoparticles in a poly(methyl acrylate) matrix polymer was investigated using X-ray photon correlation spectroscopy (XPCS) to understand the role of chain rigidity and chemical heterogeneities in particle dynamics. Locations of dynamic heterogeneities close to nanoparticles and away from particle surfaces were examined with the comparison of adsorbed and grafted nanoparticles. Our results show that the chemical heterogeneities around dispersed nanoparticles transitioned the particle dynamics from Brownian diffusion into hyperdiffusion, and moreover, the high rigidity of chains in the chemically heterogeneous interfacial layers slowed down the particle dynamics. The hyperdiffusion measured both in grafted particles and adsorbed particles was attributed to the dense interfacial mixing of dynamically heterogeneous chains.

Resolving Salt-Induced Agglomeration of Laponite Suspensions Using X-ray Photon Correlation Spectroscopy and Molecular Dynamics Simulations

Linking the physics of the relaxation behavior of viscoelastic fluids as they form arrested gel states to the underlying chemical changes is essential for developing predictive controls on the properties of the suspensions. In this study, 3 wt.% laponite suspensions are studied as model systems to probe the influence of salt-induced relaxation behavior arising from the assembly of laponite nanodisks. X-ray Photon Correlation Spectroscopy (XPCS) measurements show that laponite suspensions prepared in the presence of 5 mM concentrations of CaCl₂, MgCl₂ and CsCl salts accelerate the formation of arrested gel states, with CaCl₂ having a significant impact followed by CsCl and MgCl₂ salts. The competing effects of ion size and charge on relaxation behavior are noted. For example, the relaxation times of laponite suspensions in the presence of Mg²⁺ ions are slower compared to Cs+ ions despite the higher charge, suggesting that cation size dominates in this scenario. The faster relaxation behavior of laponite suspensions in the presence of Ca²⁺ ions compared to Cs⁺ ions shows that a higher charge dominates the size of the ion. The trends in relaxation behavior are consistent with the cluster formation behavior of laponite suspensions and the electrostatic interactions predicted from MD simulations. Charge balance is achieved by the intercalation of the cations at the negatively charged surfaces of laponite suspensions. These studies show that the arrested gel state of laponite suspensions is accelerated in the presence of salts, with ion sizes and charges having a competing effect on relaxation behavior.

X-Ray Photon Correlation Spectroscopy Towards Measuring Nanoparticle Diameters in Biological Environments Allowing for the In Situ Analysis of their Bio-Nano Interface

X-ray photon correlation spectroscopy (XPCS), a synchrotron source-based technique to measure sample dynamics, is used to determine hydrodynamic diameters of gold nanoparticles (Au NPs) of different sizes in biological environments. In situ determined hydrodynamic diameters are benchmarked with values obtained by dynamic light scattering. The technique is then applied to analyze the behavior of the Au NPs in a biological environment. First, a concentration-dependent agglomeration in the presence of NaCl is determined. Second, concentration-dependent increase in hydrodynamic diameter of the Au NPs upon the presence of proteins is determined. As X-rays in the used energy range are barely scattered by biological matter, dynamics of the Au NPs can be also detected in situ in complex biological environments, such as blood. These measurements demonstrate the possibility of XPCS for in situ analytics of nanoparticles (NPs) in biological environments where similar detection techniques based on visible light would severely suffer from scattering, absorption, and reflection effects.

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Spatially-Resolved Network Dynamics of Poly(vinyl alcohol) Gels Measured with Dynamic Small Angle Light Scattering

Hydrogels are cross-linked polymer networks swollen in water. The large solvent content enables hydrogels to have unique physical properties and allows them to be used in diverse applications such as tissue engineering, drug delivery, and absorbents. Gel properties are linked to internal dynamics. While bulk gel dynamics have been studied extensively, how gel networks respond locally to deformation has yet to be understood. Here, poly(vinyl alcohol) (PVA) gels have been stretched to study the effects of deformation on gel dynamics parallel and perpendicular to the stretching direction using dynamic small angle light scattering (DSALS). The implementation of DSALS is described and compared to traditional DLS for PVA gels with different crosslink densities, ranging from 0.75–2%. Despite the orders of magnitude difference in the scattering vector, q, range of the techniques, the dynamics match, and the apparent elastic diffusion coefficient, D_A increases linearly with the crosslink density for unstretched gels at a constant 2 wt% concentration. We observe that the elastic motion depends on the direction of stretch, decreasing perpendicular to stretching and increasing at parallel direction. Using DSALS can therefore be an effective tool to evaluate local hydrogel response to deformation.

Ion complexation waves emerge at the curved interfaces of layered minerals

Visualizing hydrated interfaces is of widespread interest across the physical sciences and is a particularly acute need for layered minerals, whose properties are governed by the structure of the electric double layer (EDL) where mineral and solution meet. Here, we show that cryo electron microscopy and tomography enable direct imaging of the EDL at montmorillonite interfaces in monovalent electrolytes with ångstrom resolution over micron length scales. A learning-based multiple-scattering reconstruction method for cryo electron tomography reveals ions bound asymmetrically on opposite sides of curved, exfoliated layers. We observe conserved ion-density asymmetry across stacks of interacting layers in cryo electron microscopy that is associated with configurations of inner- and outer-sphere ion-water-mineral complexes that we term complexation waves. Coherent X-ray scattering confirms that complexation waves propagate at room-temperature via a competition between ion dehydration and charge interactions that are coupled across opposing sides of a layer, driving dynamic transitions between stacked and aggregated states via layer exfoliation.

The structure of hydrated interfaces is essential for understanding of geochemical processes and behavior of layered minerals. The authors show that waves of hydrated ions emerge at curved aqueous interfaces and couple mineral deformation to the chemistry of the solution.

Microscopic Dynamics of Inverse Wormlike Micelles Probed Using X-ray Photon Correlation Spectroscopy

Wormlike micelles (WLMs) are ubiquitous viscoelastic modifiers that share properties with polymer solutions. While their macroscopic rheology is well-understood, their microscopic dynamics remain difficult to measure because they span a large range of time and length scales. In this work, we demonstrate the use of X-ray photon correlation spectroscopy to interrogate the segmental dynamics of inverse WLM solutions swollen with a rubidium chloride solution. We observe a diffusive scaling of the dynamics and extract a temperature-dependent diffusion coefficient, which we associate with the thermal interactions of the slow segmental dynamics near entanglement points. We probe this relaxation process across the unbranched to branched topological transition and find no microstructural evidence of branch formation in the slow mode. Instead, we observe that the dynamics become more homogeneous and prominent as the temperature is reduced and water content increases.

Spatially-resolved nanometer-scale measurement of cartilage extracellular matrix mobility

OBJECTIVE

Tissues have complex structures, comprised of solid and fluid phases. Improved understanding of interactions between joint fluid and extracellular matrix (ECM) is required in models of cartilage mechanics. X-ray photon correlation spectroscopy (XPCS) directly measures nanometer-scale dynamics and can provide insight into biofluid-biosolid interactions in cartilage. This study applies XPCS to evaluate dynamic interactions between intact cartilage and biofluids.

DESIGN

Cartilage biopsies were collected from bovine femoral condyles. During XPCS measurements, cartilage samples were exposed to different fluids: deionized water, PBS, synovial fluid, or sonicated synovial fluid. ECM-biofluid interactions were also assessed at different length scales and different depths from the cartilage surface.

RESULTS

Using XPCS, cartilage ECM mobility was detected at length scales from 50 to 207 nm. As length scale decreased, time scale for autocorrelation decay decreased, suggesting smaller ECM components are more mobile. ECM dynamics were slowed by dehydrating the sample, demonstrating XPCS assesses matrix mobility in hydrated environments. At all length scales, the matrix was more mobile in deionized water and slowest in synovial fluid. Using the 207 nm length scale assessment, ECM dynamics in synovial fluid were fastest at the cartilage surface and progressively slowed as depth into the sample increased, demonstrating XPCS can assess spatial distribution of ECM dynamics. Finally, ECM mobility increased for degraded synovial fluid.

CONCLUSIONS

This study demonstrates the potential of XPCS to provide unique insights into nanometer-scale cartilage ECM mobility in a spatially resolved manner and illustrates the importance of biosolid-biofluid interactions in dictating ECM dynamics.

Melittin exerts opposing effects on short- and long-range dynamics in bicontinuous microemulsions

Bicontinuous microemulsions (BμEs) are a promising biomembrane mimetic system for investigating the behavior of antimicrobial peptides (AMPs) and their delivery to open wounds to combat antibiotic-resistant microorganisms. The properties of the BμE host are in turn affected by the guest AMP and can deviate from those of the unperturbed BμEs, especially at higher AMP concentrations. Here we report the effect of an archetypal AMP, melittin, over a wide range of concentrations, on the nanoscopic dynamics of BμEs formed by water/sodium dodecyl sulfate (SDS)/1-pentanol/dodecane, investigated using quasi-elastic neutron scattering (QENS). Two distinct motions are observed, namely, (i) the lateral motion of the surfactant on the surface of the oil channels and (ii) the internal motion of the surfactants. It is found that melittin restricts both the lateral and the internal motion, thereby acting as a stiffening agent. The lateral motion is more strongly affected, at low concentration of melittin. The lateral diffusion coefficient decreased sharply, approaching a constant value at higher melittin concentration. These results are in sharp contrast with the recent dynamic light scattering and neutron spin echo results which showed that at the length and time scales longer than those probed in the current work, melittin enhanced the long-range collective and local undulation motions of BμEs. Considered together, our results indicate that incorporation of melittin modulates the dynamics differently depending on the spatial and temporal regimes, in which the dynamics are being probed. The addition of melittin at low concentrations increased the magnitude of the zeta potential, but further increase of the melittin concentration decreased it. This suggests that addition of melittin at low concentrations led to increase in the surfactant concentration, but did not affect the negative charge per surfactant molecule, while further addition of melittin led to ion pairing of melittin with the oppositely charged surfactant. This study therefore demonstrates how the addition of melittin hinders the lateral motion of surfactants as a result of the strong association between melittin and SDS, suggesting that the release of AMPs from BμE-based delivery vehicles may be hindered.

Molecular Characterization of Polymer Networks

Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

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.

Large T g Shift in Hybrid Bragg Stacks through Interfacial Slowdown

Studies of glass transition under confinement frequently employ supported polymer thin films, which are known to exhibit different transition temperature T g close to and far from the interface. Various techniques can selectively probe interfaces, however, often at the expense of sample designs very specific to a single experiment. Here, we show how to translate results on confined thin film T g to a "nacre-mimetic" clay/polymer Bragg stack, where periodicity allows to limit and tune the number of polymer layers to either one or two. Exceptional lattice coherence multiplies signal manifold, allowing for interface studies with both standard T g and broadband dynamic measurements. For the monolayer, we not only observe a dramatic increase in T g (∼ 100 K) but also use X-ray photon correlation spectroscopy (XPCS) to probe platelet dynamics, originating from interfacial slowdown. This is confirmed from the bilayer, which comprises both "bulk-like" and clay/polymer interface contributions, as manifested in two distinct T g processes. Because the platelet dynamics of monolayers and bilayers are similar, while the segmental dynamics of the latter are found to be much faster, we conclude that XPCS is sensitive to the clay/polymer interface. Thus, large T g shifts can be engineered and studied once lattice spacing approaches interfacial layer dimensions.

Use of continuous sample translation to reduce radiation damage for XPCS studies of protein diffusion

An experimental setup to measure X-ray photon correlation spectroscopy during continuous sample translation is presented and its effectiveness as a means to avoid sample damage in dynamics studies of protein diffusion is evaluated. X-ray damage from focused coherent synchrotron radiation remains below tolerable levels as long as the sample is translated through the beam sufficiently quickly. Here it is shown that it is possible to separate sample dynamics from the effects associated with the transit of the sample through the beam. By varying the sample translation rate, the damage threshold level, D_thresh = 1.8 kGy, for when beam damage begins to modify the dynamics under the conditions used, is also determined. Signal-to-noise ratios, R_sn ≥ 20, are obtained down to the shortest delay times of 20 µs. The applicability of this method of data collection to the next generation of multi-bend achromat synchrotron sources is discussed and it is shown that sub-microsecond dynamics should be obtainable on protein samples.

Techniques to characterize dynamics in biomaterials microenvironments: XPCS and microrheology of alginate/PEO-PPO-PEO hydrogels

Many recent studies have highlighted the timescale for stress relaxation of biomaterials on the microscale as an important factor in regulating a number of cell-material interactions, including cell spreading, proliferation, and differentiation. Relevant timescales on the order of 0.1-100 s have been suggested by several studies. While such timescales are accessible through conventional mechanical rheology, several biomaterials have heterogeneous structures, and stress relaxation mechanisms of the bulk material may not correspond to that experienced in the cellular microenvironment. Here we employ X-ray photon correlation spectroscopy (XPCS) to explore the temperature-dependent dynamics, relaxation time, and microrheology of multicomponent hydrogels comprising of commercial poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer F127 and alginate. Previous studies on this system have shown thermoreversible behavior in the bulk oscillatory shear rheology. At physiological temperatures, bulk rheology of these samples shows behavior characteristic of a soft solid, with G' > G'' and no crossover between G' and G'' over the measurable frequency range, indicating a relaxation time >125 s. By contrast, XPCS-based microrheology shows viscoelastic behavior at low frequencies, and XPCS-derived correlation functions show relaxation times ranging from 10-45 s on smaller length scales. Thus, we are able to use XPCS to effectively probe the viscoelasticity and relaxation behavior within the material microenvironments.

Towards molecular movies with X-ray photon correlation spectroscopy

In this perspective article we highlight research opportunities and challenges in probing structural dynamics of molecular systems using X-ray Photon Correlation Spectroscopy (XPCS). The development of new X-ray sources, such as 4th generation storage rings and X-ray free-electron lasers (XFELs), provides promising new insights into molecular motion. Employing XPCS at these sources allows to capture a very broad range of timescales and lengthscales, spanning from femtoseconds to minutes and atomic scales to the mesoscale. Here, we discuss the scientific questions that can be addressed with these novel tools for two prominent examples: the dynamics of proteins in biomolecular condensates and the dynamics of supercooled water. Finally, we provide practical tips for designing and estimating feasibility of XPCS experiments as well as on detecting and mitigating radiation damage.

20 µs-resolved high-throughput X-ray photon correlation spectroscopy on a 500k pixel detector enabled by data-management workflow

The performance of the new 52 kHz frame rate Rigaku XSPA-500k detector was characterized on beamline 8-ID-I at the Advanced Photon Source at Argonne for X-ray photon correlation spectroscopy (XPCS) applications. Due to the large data flow produced by this detector (0.2 PB of data per 24 h of continuous operation), a workflow system was deployed that uses the Advanced Photon Source data-management (DM) system and high-performance software to rapidly reduce area-detector data to multi-tau and two-time correlation functions in near real time, providing human-in-the-loop feedback to experimenters. The utility and performance of the workflow system are demonstrated via its application to a variety of small-angle XPCS measurements acquired from different detectors in different XPCS measurement modalities. The XSPA-500k detector, the software and the DM workflow system allow for the efficient acquisition and reduction of up to ∼10⁹ area-detector data frames per day, facilitating the application of XPCS to measuring samples with weak scattering and fast dynamics.

Nanoscale Critical Phenomena in a Complex Fluid Studied by X-Ray Photon Correlation Spectroscopy

The advent of high-speed x-ray photon correlation spectroscopy now allows the study of critical phenomena in fluids to much smaller length scales and over a wider range of temperatures than is possible with dynamic light scattering. We present an x-ray photon correlation spectroscopy study of critical fluctuation dynamics in a complex fluid typical of those used in liquid-liquid extraction (LLE) of ions, dodecane-DMDBTDMA with extracted aqueous Ce(NO_{3})_{3}. We observe good agreement with both static and dynamic scaling without the need for significant noncritical background corrections. Critical exponents agree with 3D Ising values, and the fluctuation dynamics are described by simple exponential relaxation. The form of the dynamic master curve deviates somewhat from the Kawasaki result, with a more abrupt transition between the critical and noncritical asymptotic behavior. The concepts of critical phenomena thus provide a quantitative framework for understanding the structure and dynamics of LLE systems and a path forward to new LLE processes.

X-Ray Photon Correlation Spectroscopy with Coherent Nanobeams: A Numerical Study

X-ray photon correlation spectroscopy accesses a wide variety of dynamic phenomena at the nanoscale by studying the temporal correlations among photons that are scattered by a material in dynamical equilibrium when it is illuminated with a coherent X-ray beam. The information that is obtained is averaged over the illuminated area, which is generally of the order of several square microns. We propose here that more local information can be obtained by using nanobeams with great potential for the study of heterogeneous systems and show the feasibility of this approach with the support of numerical simulations.

Advances in Kriging-Based Autonomous X-Ray Scattering Experiments

Autonomous experimentation is an emerging paradigm for scientific discovery, wherein measurement instruments are augmented with decision-making algorithms, allowing them to autonomously explore parameter spaces of interest. We have recently demonstrated a generalized approach to autonomous experimental control, based on generating a surrogate model to interpolate experimental data, and a corresponding uncertainty model, which are computed using a Gaussian process regression known as ordinary Kriging (OK). We demonstrated the successful application of this method to exploring materials science problems using x-ray scattering measurements at a synchrotron beamline. Here, we report several improvements to this methodology that overcome limitations of traditional Kriging methods. The variogram underlying OK is global and thus insensitive to local data variation. We augment the Kriging variance with model-based measures, for instance providing local sensitivity by including the gradient of the surrogate model. As with most statistical regression methods, OK minimizes the number of measurements required to achieve a particular model quality. However, in practice this may not be the most stringent experimental constraint; e.g. the goal may instead be to minimize experiment duration or material usage. We define an adaptive cost function, allowing the autonomous method to balance information gain against measured experimental cost. We provide synthetic and experimental demonstrations, validating that this improved algorithm yields more efficient autonomous data collection.

A Kriging-Based Approach to Autonomous Experimentation with Applications to X-Ray Scattering

Modern scientific instruments are acquiring data at ever-increasing rates, leading to an exponential increase in the size of data sets. Taking full advantage of these acquisition rates will require corresponding advancements in the speed and efficiency of data analytics and experimental control. A significant step forward would come from automatic decision-making methods that enable scientific instruments to autonomously explore scientific problems—that is, to intelligently explore parameter spaces without human intervention, selecting high-value measurements to perform based on the continually growing experimental data set. Here, we develop such an autonomous decision-making algorithm that is physics-agnostic, generalizable, and operates in an abstract multi-dimensional parameter space. Our approach relies on constructing a surrogate model that fits and interpolates the available experimental data, and is continuously refined as more data is gathered. The distribution and correlation of the data is used to generate a corresponding uncertainty across the surrogate model. By suggesting follow-up measurements in regions of greatest uncertainty, the algorithm maximally increases knowledge with each added measurement. This procedure is applied repeatedly, with the algorithm iteratively reducing model error and thus efficiently sampling the parameter space with each new measurement that it requests. We validate the method using synthetic data, demonstrating that it converges to faithful replica of test functions more rapidly than competing methods, and demonstrate the viability of the approach in an experimental context by using it to direct autonomous small-angle (SAXS) and grazing-incidence small-angle (GISAXS) x-ray scattering experiments.

Refractive index matched, nearly hard polymer colloids

Refractive index matched particles serve as essential model systems for colloid scientists, providing nearly hard spheres to explore structure and dynamics. The poly(methyl methacrylate) latexes typically used are often refractive index matched by dispersing them in binary solvent mixtures, but this can lead to undesirable changes, such as particle charging or swelling. To avoid these shortcomings, we have synthesized refractive index matched colloids using polymerization-induced self-assembly (PISA) rather than as polymer latexes. The crucial difference is that these diblock copolymer nanoparticles consist of a single core-forming polymer in a single non-ionizable solvent. The diblock copolymer chosen was poly(stearyl methacrylate)-poly(2,2,2-trifluoroethyl methacrylate) (PSMA-PTFEMA), which self-assembles to form PTFEMA core spheres in n-alkanes. By monitoring scattered light intensity, n-tetradecane was found to be the optimal solvent for matching the refractive index of such nanoparticles. As expected for PISA syntheses, the diameter of the colloids can be controlled by varying the PTFEMA degree of polymerization. Concentrated dispersions were prepared, and the diffusion of the PSMA-PTFEMA nanoparticles as a function of volume fraction was measured. These diblock copolymer nanoparticles are a promising new system of transparent spheres for future colloidal studies.

Dynamics of proteins in solution

The dynamics of proteins in solution includes a variety of processes, such as backbone and side-chain fluctuations, interdomain motions, as well as global rotational and translational (i.e. center of mass) diffusion. Since protein dynamics is related to protein function and essential transport processes, a detailed mechanistic understanding and monitoring of protein dynamics in solution is highly desirable. The hierarchical character of protein dynamics requires experimental tools addressing a broad range of time- and length scales. We discuss how different techniques contribute to a comprehensive picture of protein dynamics, and focus in particular on results from neutron spectroscopy. We outline the underlying principles and review available instrumentation as well as related analysis frameworks.

Anisotropic and heterogeneous dynamics in stretched elastomer nanocomposites

We use X-ray photon correlation spectroscopy (XPCS) to investigate the dynamics of a stretched elastomer by means of probe particles. The particles dispersed in the elastomer were carbon black or silica aggregates classically used for elastomer reinforcement but their volume fraction is very low (φ < 10-2). We show that their dynamics is slower in the direction of the tensile strain than in the perpendicular one. For hydroxylated silica which is poorly wetted by the elastomer, there is no anisotropy. Two-time correlation functions confirm anisotropic dynamics and suggest dynamical heterogeneity already expected from the q-1 behavior of the relaxation times. The height χ* of the peak of the dynamical susceptibility, determined by the normalized variance of the instantaneous correlation function, is larger in the direction parallel to the strain than in the perpendicular one. It also appears that its q dependence changes with the morphology of the probe particle. Therefore, the heterogeneous dynamic probed by the particles is not related only to that of the strained elastomer matrix. In fact, it results from modification of the dynamics of the polymer chains near the surface of the particles and within the aggregate porosity (bound polymer). It is concluded that XPCS is a powerful method for investigating the dynamics, at a given strain, of the bound polymer-particle units which are responsible, at large volume fractions, for the reinforcement.

Ultra-small-angle X-ray photon correlation spectroscopy using the Eiger detector

Successful implementation of the single-photon-counting Eiger 500k pixel array detector for sub-millisecond X-ray photon correlation spectroscopy (XPCS) measurements in the ultra-small-angle scattering region is reported. The performance is demonstrated by measuring the dynamics of dilute silica colloids in aqueous solvents when the detector is operated at different counter depths, 4, 8 and 12 bit. In the fastest mode involving 4 bit parallel readout, a stable frame rate of 22 kHz is obtained that enabled measurement of intensity-intensity autocorrelation functions with good statistics down to the 50 µs range for a sample with sufficient scattering power. The high frame rate and spatial resolution together with large number of pixels of the detector facilitate the investigation of sub-millisecond dynamics over a broad length scale by multispeckle XPCS. This is illustrated by an example involving phoretic motion of colloids during the phase separation of the solvent.

In situ coherent X-ray diffraction imaging of radiation-induced mass loss in metal-polymer composite spheres

A major limitation to the use of coherent X-ray diffraction imaging (CXDI) for imaging soft materials like polymers and biological tissue is that the radiation can cause extensive damage to the sample under investigation. In this study, CXDI has been used to monitor radiation-induced structural changes in metal-coated poly(methyl methacrylate) microspheres. Using a coherent undulator X-ray beam with 8.10 keV photon energy, 14 tomograms at a resolution of ∼30 nm were measured consecutively, which resulted in an accumulated dose of 30 GGy. The three-dimensional images confirmed that the polymer core was strongly affected by the absorbed dose, giving pronounced mass loss. Specifically, as the metal-polymer composite was exposed to the X-ray beam, a bubble-like region of reduced density grew within the composite, almost filling the entire volume within the thin metallic shell in the last tomogram. The bubble seemed to have its initiation point at a hole in the metal coating, emphasizing that the free polymer surface plays an important role in the degradation process. The irradiation of an uncoated polystyrene microsphere gave further evidence for mass loss at the free surface as the radius decreased with increased dose. The CXDI study was complemented by X-ray photon correlation spectroscopy, which proved efficient in establishing exposure dose limits. Our results demonstrate that radiation-induced structural changes at the tens of nanometer scale in soft materials can be followed as a function of dose, which is important for the further development of soft-matter technology.

SAXS on a chip: from dynamics of phase transitions to alignment phenomena at interfaces studied with microfluidic devices

The field of microfluidics offers attractive possibilities to perform novel experiments that are difficult (or even impossible) to perform using conventional bulk and surface-based methods. Such attractiveness comes from several important aspects inherent to these miniaturized devices. First, the flow of fluids under submillimeter confinement typically leads to a drop of inertial forces, meaning that turbulence is practically suppressed. This leads to predictable and controllable flow profiles, along with well-defined chemical gradients and stress fields that can be used for controlled mixing and actuation on the micro and nanoscale. Secondly, intricate microfluidic device designs can be fabricated using cleanroom standard procedures. Such intricate geometries can take diverse forms, designed by researchers to perform complex tasks, that require exquisite control of flow of several components and gradients, or to mimic real world examples, facilitating the establishment of more realistic models. Thirdly, microfluidic devices are usually compatible with in situ or integrated characterization methods that allow constant real-time monitoring of the processes occurring inside the microchannels. This is very different from typical bulk-based methods, where usually one can only observe the final result, or otherwise, take quick snapshots of the evolving process or take aliquots to be analyzed separately. Altogether, these characteristics inherent to microfluidic devices provide researchers with a set of tools that allow not only exquisite control and manipulation of materials at the micro and nanoscale, but also observation of these effects. In this review, we will focus on the use and prospects of combining microfluidic devices with in situ small-angle X-ray scattering (and related techniques such as small-angle neutron scattering and X-ray photon correlation spectroscopy), and their enormous potential for physical-chemical research, mainly in self-assembly and phase-transitions, and surface characterization.

Nanoscale Particle Motion in Attractive Polymer Nanocomposites

Using x-ray photon correlation spectroscopy, we examined the slow nanoscale motion of silica nanoparticles individually dispersed in an entangled poly (ethylene oxide) melt at particle volume fractions up to 42%. The nanoparticles, therefore, serve as both fillers for the resulting attractive polymer nanocomposites and probes for the network dynamics therein. The results show that the particle relaxation closely follows the mechanical reinforcement in the nanocomposites only at the intermediate concentrations below the critical value for the chain confinement. Quite unexpectedly, the relaxation time of the particles does not further slow down at higher volume fractions-when all chains are practically on the nanoparticle interface-and decouples from the elastic modulus of the nanocomposites that further increases orders of magnitude.

Transition in Dynamics as Nanoparticles Jam at the Liquid/Liquid Interface

Nanoparticles (NPs) segregated to the liquid/liquid interface form disordered or liquid-like assemblies that show diffusive motions in the plane of the interface. As the areal density of NPs at the interface increases, the available interfacial area decreases, and the interfacial dynamics of the NP assemblies change when the NPs jam. Dynamics associated with jamming was investigated by X-ray photon correlation spectroscopy. Water-in-toluene emulsions, formed by a self-emulsification at the liquid/liquid interface and stabilized by ligand-capped CdSe-ZnS NPs, provided a simple, yet powerful platform, to investigate NP dynamics. In contrast to a single planar interface, these emulsions increased the number of NPs in the incident beam and decreased the absorption of X-rays in comparison to the same path length in pure water. A transition from diffusive to confined dynamics was manifested by intermittent dynamics, indicating a transition from a liquid-like to a jammed state.

Phoretic motion of colloids in a phase separating medium

The enhanced motion of dispersed particles driven by a concentration gradient is the basis for diffusiophoresis. Here we present the dynamics of colloids in a phase separating medium probed by X-Ray Photon Correlation Spectroscopy (XPCS) in the ultra-small angle scattering range. Charge stabilized silica colloids suspended in a binary mixture of 3-methylpyridine and water/heavy water are preferentially wetted by 3-methylpyridine and consequently display a phoretic motion towards that phase upon demixing. This activity lasts for hundreds of seconds before the phase separation is complete and the enhanced motion is arrested as the colloids return to normal diffusive dynamics.

Small Particle Driven Chain Disentanglements in Polymer Nanocomposites

Using neutron spin-echo spectroscopy, x-ray photon correlation spectroscopy, and bulk rheology, we studied the effect of particle size on the single-chain dynamics, particle mobility, and bulk viscosity in athermal polyethylene oxide-gold nanoparticle composites. The results reveal a ≈25% increase in the reptation tube diameter with the addition of nanoparticles smaller than the entanglement mesh size (≈5  nm), at a volume fraction of 20%. The tube diameter remains unchanged in the composite with larger (20 nm) nanoparticles at the same loading. In both cases, the Rouse dynamics is insensitive to particle size. These results provide a direct experimental observation of particle-size-driven disentanglements that can cause non-Einstein-like viscosity trends often observed in polymer nanocomposites.

Exploring the relationship between nanoscale dynamics and macroscopic rheology in natural polymer gums

We report a study connecting the nanoscale and macroscale structure and dynamics of Acacia mearnsii gum as probed by small-angle X-ray scattering (SAXS), X-ray photon correlation spectroscopy (XPCS) and rheology. Acacia gum, in general, is a complex polysaccharide used extensively in industry. Over the analyzed concentration range (15 to 30 wt%) the A. mearnsii gum is found to have a gel-like linear rheology and to exhibit shear thinning flow behavior under steady shear. The gum solutions exhibited a steadily increasing elastic modulus with increasing time after they were prepared and also the emergence of shear thickening events within the shear thinning behavior, characteristic of associative polymers. XPCS measurements using gold nanoparticles as tracers were used to explore the microscopic dynamics within the biopolymer gels and revealed a two-step relaxation process with a partial decay at inaccessibly short times, suggesting caged motion of the nanoparticles, followed by a slow decay at later delay times. Non-diffusive motion evidenced by a compressed exponential line shape and an inverse relationship between relaxation time and wave vector characterizes the slow dynamics of A. mearnsii gum gels. Surprisingly, we have determined that the nanometer-scale mean square displacement of the nanoparticles showed a close relationship to the values predicted from the macroscopic elastic properties of the material, obtained through the rheology experiments. Our results demonstrate the potential applicability of the XPCS technique in the natural polymers field to connect their macroscale properties with their nanoscale structure and dynamics.

Brownian and advective dynamics in microflow studied by coherent X-ray scattering experiments

Combining microfluidics with coherent X-ray illumination offers the possibility to not only measure the structure but also the dynamics of flowing samples in a single-scattering experiment. Here, the power of this combination is demonstrated by studying the advective and Brownian dynamics of colloidal suspensions in microflow of different geometries. Using an experimental setup with a fast two-dimensional detector and performing X-ray correlation spectroscopy by calculating two-dimensional maps of the intensity auto-correlation functions, it was possible to evaluate the sample structure and furthermore to characterize the detailed flow behavior, including flow geometry, main flow directions, advective flow velocities and diffusive dynamics. By scanning a microfocused X-ray beam over a microfluidic device, the anisotropic auto-correlation functions of driven colloidal suspensions in straight, curved and constricted microchannels were mapped with the spatial resolution of the X-ray beam. This method has not only a huge potential for studying flow patterns in complex fluids but also to generally characterize anisotropic dynamics in materials.