X-ray Photon Correlation Spectroscopy Research Articles

Performance of the time-resolved ultra-small-angle X-ray scattering beamline with the Extremely Brilliant Source.

The new technical features and enhanced performance of the ID02 beamline with the Extremely Brilliant Source (EBS) at the ESRF are described. The beamline enables static and kinetic investigations of a broad range of systems from ångström to micrometre size scales and down to the sub-millisecond time range by combining different small-angle X-ray scattering techniques in a single instrument. In addition, a nearly coherent beam obtained in the high-resolution mode allows multispeckle X-ray photon correlation spectroscopy measurements down to the microsecond range over the ultra-small- and small-angle regions. While the scattering vector (of magnitude q) range covered is the same as before, 0.001 ≤ q ≤ 50 nm-1 for an X-ray wavelength of 1 Å, the EBS permits relaxation of the collimation conditions, thereby obtaining a higher flux throughput and lower background. In particular, a coherent photon flux in excess of 1012 photons s-1 can be routinely obtained, allowing dynamic studies of relatively dilute samples. The enhanced beam properties are complemented by advanced pixel-array detectors and high-throughput data reduction pipelines. All these developments together open new opportunities for structural, dynamic and kinetic investigations of out-of-equilibrium soft matter and biophysical systems.

X-ray free-electron laser heating of water at picosecond time scale

Split-pulse x-ray photon correlation spectroscopy using x-ray free-electron laser is a promising tool to probe atomic dynamics in liquid and soft-matter in picosecond time scale, which has been accessible only by spectroscopy. However, sample heating by x-ray beam is a major obstacle for this technique. Using molecular dynamics and the two-temperature model we examine the atomic level response of water to x-ray laser pulse at picosecond time scale and compare with observations from recent x-ray free-electron laser experiments. We investigate the effects of the heating due to x-ray laser pulses of different energies and the effects of the heat dissipation on the structure and dynamics of water through the atomic density correlation and the dynamic structure factor. Our results indicate, in agreement with experiment that in addition to the beam energy the time delay between the two pulses is a critical factor for obtaining reliable information on the atomic level dynamics of water.

Using coherent X-rays to follow dynamics in amorphous ices.

Amorphous solid water plays an important role in our overall understanding of water's phase diagram. X-ray scattering is an important tool for characterising the different states of water, and modern storage ring and XFEL facilities have opened up new pathways to simultaneously study structure and dynamics. Here, X-ray photon correlation spectroscopy (XPCS) was used to study the dynamics of high-density amorphous (HDA) ice upon heating. We follow the structural transition from HDA to low-density amorphous (LDA) ice, by using wide-angle X-ray scattering (WAXS), for different heating rates. We used a new type of sample preparation, which allowed us to study μm-sized ice layers rather than powdered bulk samples. The study focuses on the non-equilibrium dynamics during fast heating, spontaneous transformation and crystallization. Performing the XPCS study at ultra-small angle (USAXS) geometry allows us to characterize the transition dynamics at length scales ranging from 60 nm-800 nm. For the HDA-LDA transition we observe a clear separation in three dynamical regimes, which show different dynamical crossovers at different length scales. The crystallization from LDA, instead, is observed to appear homogenously throughout the studied length scales.

Real Space Imaging of Spin Stripe Domain Fluctuations in a Complex Oxide

Understanding the formation and dynamics of charge and spin-ordered states in low-dimensional transition metal oxide materials is crucial to understanding unconventional high-temperature superconductivity. La_{2-x}Sr_{x}NiO_{4+δ} (LSNO) has attracted much attention due to its interesting spin dynamics. Recent x-ray photon correlation spectroscopy studies have revealed slow dynamics of the spin order (SO) stripes in LSNO. Here, we applied resonant soft x-ray ptychography to map the spatial distribution of the SO stripe domain inhomogeneity in real space. The reconstructed images show the SO domains are spatially anisotropic, in agreement with previous diffraction studies. For the SO stripe domains, it is found that the correlation lengths along different directions are strongly coupled in space. Surprisingly, fluctuations were observed in the real space amplitude signal, rather than the phase or position. We attribute the observed slow dynamics of the stripe domains in LSNO to thermal fluctuations of the SO domain boundaries.

Kinetic viscoelasticity during early polymer-polymer spinodal dewetting

The dewetting kinetics of a supported polymer bilayer were measured in situ using coherent grazing-incidence x-ray scattering. X-ray photon correlation spectroscopy provides both the two-time correlation functions and the cross-correlation function which measures the average spatial shift of the speckles produced by the coherent x rays. The stress in the ultrathin top dewetting film can be directly observed due to the exquisite sensitivity to sample curvature changes provided by the x-ray speckle correlation functions. The hole-opening events in the film are found to be associated with significant changes to the stress. These results are interpreted through an analogy between viscoelastic spinodal dewetting and early-stage bulk viscoelastic phase separation. The frequency of hole-initiation events during dewetting decreases with time as a power law, and the power-law exponent can be linked to nonlinear viscoelastic effects, showing similarity in their stress relief dynamics to aftershock decays.

Nonlinear Architectures Can Alter the Dynamics of Polymer–Nanoparticle Composites

Polymer nanocomposites exhibit remarkable physical properties that are attractive for many applications. These systems have been so far investigated using linear polymer chains; the role of polymer matrix architecture in local dynamics, bulk rheology, and nanoparticle (NP) motion remains unexplored. Here, using quasi-elastic neutron scattering, bulk rheology, and X-ray photon correlation spectroscopy, we investigated nanocomposites with spherical silica nanoparticles well dispersed in poly(ethylene oxide) matrices having different architectures (specifically linear, stars, and hyperbranched). The results reveal that the mechanical reinforcement of the nanocomposites with the nonlinear polymers can be altered by orders of magnitude with respect to the conventional nanocomposite with the linear polymer. Polymer compactness and interpenetrability are found to play crucial roles in determining their bulk rheology. At the microscopic level, average segmental dynamics is remarkably slowed down by the attractive NPs in the matrices of high degree of branching, whereas no significant effect is observed in the linear polymer matrix at the same NP loading. In addition, the nanoscale dynamics of particles in the compact nonlinear matrices exhibits strong decoupling from the bulk viscoelasticity, allowing their fast relaxation even at ≈30% by volume. These results provide an experimental evidence that macromolecular architecture is a powerful new tool for tuning the bulk rheological properties as well as the nanoscale dynamics of polymer nanocomposites (PNCs) without the need for changing polymer molecular weight, nanoparticle size, shape, loading, or dispersion state.

Shape memory effect in metallic glasses

Shape memory effect in metallic glasses

Using low dose x-ray speckle visibility spectroscopy to study dynamics of soft matter samples

We demonstrate the successful application of x-ray speckle visibility spectroscopy (XSVS) experiments to study the dynamics of radiation sensitive, biological samples with unprecedented small x-ray doses of 45 Gy and below. Using XSVS, we track the dynamics of casein micelles in native, concentrated, and acidified solution conditions, while substantially reducing the deposited dose as compared to alternative techniques like sequential x-ray photon correlation spectroscopy. The Brownian motion in a skim milk sample yields the hydrodynamic radius of the casein micelles while deviations from Brownian motion with a characteristic q-dependent diffusion coefficient D(q) can be observed in more concentrated solution conditions. The low dose applied in our experiments allows the observation of static, frozen speckle patterns from gelled acidic milk. We show that the XSVS technique is especially suitable for tracking dynamics of radiation sensitive samples in combination with the improved coherent properties of new generation x-ray sources, emphasizing the great potential for further investigations of protein dynamics using fourth generation synchrotrons and free electron lasers.

Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients.

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

Molecular movies with X-ray photon correlation spectroscopy

Molecular movies with X-ray photon correlation spectroscopy

Grazing-incidence small-angle X-ray photoncorrelation spectroscopy: limitations and opportunities

Grazing-incidence small-angle X-ray photoncorrelation spectroscopy: limitations and opportunities

Microsecond hydrodynamic interactions in dense colloidal dispersions probed at the European XFEL.

Many soft-matter systems are composed of macromolecules or nanoparticles suspended in water. The characteristic times at intrinsic length scales of a few nanometres fall therefore in the microsecond and sub-microsecond time regimes. With the development of free-electron lasers (FELs) and fourth-generation synchrotron light-sources, time-resolved experiments in such time and length ranges will become routinely accessible in the near future. In the present work we report our findings on prototypical soft-matter systems, composed of charge-stabilized silica nanoparticles dispersed in water, with radii between 12 and 15 nm and volume fractions between 0.005 and 0.2. The sample dynamics were probed by means of X-ray photon correlation spectroscopy, employing the megahertz pulse repetition rate of the European XFEL and the Adaptive Gain Integrating Pixel Detector. We show that it is possible to correctly identify the dynamical properties that determine the diffusion constant, both for stationary samples and for systems driven by XFEL pulses. Remarkably, despite the high photon density the only observable induced effect is the heating of the scattering volume, meaning that all other X-ray induced effects do not influence the structure and the dynamics on the probed timescales. This work also illustrates the potential to control such induced heating and it can be predicted with thermodynamic models.

Measurement of Spin Dynamics in a Layered Nickelate Using X-Ray Photon Correlation Spectroscopy: Evidence for Intrinsic Destabilization of Incommensurate Stripes at Low Temperatures.

We study the temporal stability of stripe-type spin order in a layered nickelate with x-ray photon correlation spectroscopy and observe fluctuations on timescales of tens of minutes over a wide temperature range. These fluctuations show an anomalous temperature dependence: they slow down at intermediate temperatures and speed up on both heating and cooling. This behavior appears to be directly connected with spatial correlations: stripes fluctuate slowly when stripe correlation lengths are large and become faster when spatial correlations decrease. A low-temperature decay of nickelate stripe correlations, reminiscent of what occurs in cuprates as a result of a competition between stripes and superconductivity, hence occurs via loss of both spatial and temporal correlations.

Interplay between Kinetics and Dynamics of Liquid-Liquid Phase Separation in a Protein Solution Revealed by Coherent X-ray Spectroscopy.

Microscopic dynamics of complex fluids in the early stage of spinodal decomposition (SD) is strongly intertwined with the kinetics of structural evolution, which makes a quantitative characterization challenging. In this work, we use X-ray photon correlation spectroscopy to study the dynamics and kinetics of a protein solution undergoing liquid-liquid phase separation (LLPS). We demonstrate that in the early stage of SD, the kinetics relaxation is up to 40 times slower than the dynamics and thus can be decoupled. The microscopic dynamics can be well described by hyper-diffusive ballistic motions with a relaxation time exponentially growing with time in the early stage followed by a power-law increase with fluctuations. These experimental results are further supported by simulations based on the Cahn-Hilliard equation. The established framework is applicable to other condensed matter and biological systems undergoing phase transitions and may also inspire further theoretical work.

Noise reduction in X-ray photon correlation spectroscopy with convolutional neural networks encoder\u2013decoder 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.

Glass-liquid and glass-gel transitions of soft-shell particles.

We study the structure and dynamics of colloidal particles with a spherical hard core and a thermo-responsive soft shell over the whole phase diagram by means of small-angle x-ray scattering and x-ray photon correlation spectroscopy. By changing the effective volume fraction by temperature and particle concentration, liquid, repulsive glass. and attractive gel phases are observed. The dynamics slow down with increasing volume fraction in the liquid phase and reflect a Vogel-Fulcher-Tamann behavior known for fragile glass formers. We find a liquid-glass transition above 50 vol.% that is independent of the particles' concentration and temperature. In an overpacked state at effective volume fractions above 1, the dispersion does not show a liquid phase but undergoes a gel-glass transition at an effective volume fraction of 34 vol.%. At the same concentration, extrema of subdiffusive dynamics are found in the liquid phase at lower weight fractions. We interpret this as dynamic precursors of the glass-gel transition.

Dynamics of matrix-free nanocomposites consisting of block copolymer-grafted silica nanoparticles under elongation evaluated through X-ray photon correlation spectroscopy

X-ray photon correlation spectroscopy (XPCS) is a powerful tool for investigating the dynamics of polymer nanocomposites. In this study, XPCS was utilized to analyze the dynamics of a matrix-free nanocomposite consisting of poly(methyl methacrylate)-b-poly(butyl acrylate)-g-silica nanoparticles (PMMA-b-PBA-g-SiNPs) during uniaxial elongation and stress relaxation. The effect of the microphase-separated state of PMMA-b-PBA on the dynamics of the SiNP core in the PMMA-b-PBA-g-SiNPs was confirmed at the initial state with temperature-dependence. The SiNPs exhibited a hyperdiffusive and ballistic-like motion in the temperature range of 298–423 K, including at temperatures above and below the glass transition temperature (Tg) of the outer PMMA layer. The SiNPs velocity increased rapidly when the temperature approached the Tg of PMMA. During uniaxial elongation, the PMMA-b-PBA-g-SiNPs exhibited anisotropic dynamics between two directions, namely parallel and perpendicular to elongation. The SiNPs velocity in the direction perpendicular to elongation was faster than those parallel to elongation, despite the small strain, high weight ratio of SiNP, and the large size of SiNP in the PMMA-b-PBA-g-SiNPs. A decrease in the relaxation rate of the SiNPs was also observed by XPCS during stress relaxation at strain = 0.2, which is in the plastic deformation region.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

X-ray photon correlation spectroscopy (XPCS) enables the study of sample dynamics between micrometer and atomic length scales. As a coherent scattering technique, it benefits from the increased brilliance of the next-generation synchrotron radiation and Free-Electron Laser (FEL) sources. In this article, we will introduce the XPCS concepts and review the latest developments of XPCS with special attention on the extension of accessible time scales to sub-μs and the application of XPCS at FELs. Furthermore, we will discuss future opportunities of XPCS and the related technique X-ray speckle visibility spectroscopy (XSVS) at new X-ray sources. Due to its particular signal-to-noise ratio, the time scales accessible by XPCS scale with the square of the coherent flux, allowing to dramatically extend its applications. This will soon enable studies over more than 18 orders of magnitude in time by XPCS and XSVS.

Structure and dynamics of dense colloidal ellipsoids at the nearest-neighbor length scale

Anisotropic particles are known to exhibit a richer and more complex phase behavior in comparison to their spherical counterpart. While the majority of the existing studies address structural properties, the dynamic behavior of anisotropic particles is a relatively lesser explored avenue. Using multispeckle ultra-small-angle x-ray photon correlation spectroscopy (USA-XPCS), we have carried out a systematic investigation of the structural and dynamic properties of colloidal ellipsoids at the nearest-neighbor length scale. The USA-XPCS measurements have allowed us to probe, as a function of the volume fraction, the q-dependent effective structure factor, Seff(q), along with the effective long time diffusion coefficient, Deff(q), for this anisotropic system. Our results indicate a scaling behavior of Deff(q) with 1/Seff(q) from which we have estimated the effective amplitude function Aeff(q), which can be directly related to the effective hydrodynamic function Heff(q). Aeff(q) shows a similar q dependence to that of S(q). Our investigation also allows for the precise determination of the volume fraction corresponding to the arrest transition.

Dynamics of Polymerization and Gelation in Epoxy Nanocomposites via X-ray Photon Correlation Spectroscopy

Dynamics of Polymerization and Gelation in Epoxy Nanocomposites <i>via</i> X-ray Photon Correlation Spectroscopy