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

In this study, 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.

36 MATERIALS SCIENCE↗

Microscopic Origins of the Nonlinear Behavior of Particle-Filled Rubber Probed with Dynamic Strain XPCS

The underlying microscopic response of filler networks in reinforced rubber to dynamic strain is not well understood due to the experimental difficulty of directly measuring filler network behavior in samples undergoing dynamic strain. This difficulty can be overcome with in situ X-ray photon correlation spectroscopy (XPCS) measurements. The contrast between the silica filler and the rubber matrix for X-ray scattering allows us to isolate the filler network behavior from the overall response of the rubber. This in situ XPCS technique probes the microscopic breakdown and reforming of the filler network structure, which are responsible for the nonlinear dependence of modulus on strain, known in the rubber science community as the Payne effect. These microscopic changes in the filler network structure have consequences for the macroscopic material performance, especially for the fuel efficiency of tire tread compounds. In this work, we elucidate the behavior with in situ dynamic strain XPCS experiments on industrially relevant, vulcanized rubbers filled (13 vol %) with novel air-milled silica of ultrahigh-surface area (UHSA) (250 m 2 /g). The addition of a silane coupling agent to rubber containing this silica causes an unexpected and counterintuitive increase in the Payne effect and decrease in energy dissipation. For this rubber, we observe a nearly two-fold enhancement of the storage modulus and virtually equivalent loss tangent compared to a rubber containing a coupling agent and conventional silica. Interpretation of our in situ XPCS results simultaneously with interpretation of traditional dynamic mechanical analysis (DMA) strain sweep experiments reveals that the debonding or yielding of bridged bound rubber layers is key to understanding the behavior of rubber formulations containing the silane coupling agent and high-surface area silica. These results demonstrate that the combination of XPCS and DMA is a powerful method for unraveling the microscale filler response to strain which dictates the dynamic mechanical properties of reinforced soft matter composites. With this combination of techniques, we have elucidated the great promise of UHSA silica when used in concert with a silane coupling agent in filled rubber. Such composites simultaneously exhibit large moduli and low hysteresis under dynamic strain.

36 MATERIALS SCIENCE↗

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. Finally, we are able to use XPCS to effectively probe the viscoelasticity and relaxation behavior within the material microenvironments.

36 MATERIALS SCIENCE↗

Direct measurement of Stokes–Einstein diffusion of Cowpea mosaic virus with 19 µs-resolved XPCS

Brownian motion of Cowpea mosaic virus (CPMV) in water was measured using small-angle X-ray photon correlation spectroscopy (SA-XPCS) at 19.2 µs time resolution. It was found that the decorrelation time τ(Q) = 1/DQ 2 up to Q = 0.091 nm -1 . The hydrodynamic radius R H determined from XPCS using Stokes–Einstein diffusion D = kT/(6πηR H ) is 43% larger than the geometric radius R 0 determined from SAXS in the 0.007 M K 3 PO 4 buffer solution, whereas it is 80% larger for CPMV in 0.5 M NaCl and 104% larger in 0.5 M (NH 4 ) 2 SO 4 , a possible effect of aggregation as well as slight variation of the structures of the capsid resulting from the salt–protein interactions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Robotic pendant drop: containerless liquid for μs-resolved, AI-executable XPCS

Abstract The dynamics and structure of mixed phases in a complex fluid can significantly impact its material properties, such as viscoelasticity. Small-angle X-ray Photon Correlation Spectroscopy (SA-XPCS) can probe the spontaneous spatial fluctuations of the mixed phases under various in situ environments over wide spatiotemporal ranges (10 −6 –10 3 s /10 −10 –10 −6 m). Tailored material design, however, requires searching through a massive number of sample compositions and experimental parameters, which is beyond the bandwidth of the current coherent X-ray beamline. Using 3.7-μs-resolved XPCS synchronized with the clock frequency at the Advanced Photon Source, we demonstrated the consistency between the Brownian dynamics of ~100 nm diameter colloidal silica nanoparticles measured from an enclosed pendant drop and a sealed capillary. The electronic pipette can also be mounted on a robotic arm to access different stock solutions and create complex fluids with highly-repeatable and precisely controlled composition profiles. This closed-loop, AI-executable protocol is applicable to light scattering techniques regardless of the light wavelength and optical coherence, and is a first step towards high-throughput, autonomous material discovery.

36 MATERIALS SCIENCE↗

Investigation of the yielding transition in concentrated colloidal systems via rheo-XPCS

We probe the microstructural yielding dynamics of a concentrated colloidal system by performing creep/recovery tests with simultaneous collection of coherent scattering data via X-ray Photon Correlation Spectroscopy (XPCS). This combination of rheology and scattering allows for time-resolved observations of the microstructural dynamics as yielding occurs, which can be linked back to the applied rheological deformation to form structure–property relations. Under sufficiently small applied creep stresses, examination of the correlation in the flow direction reveals that the scattering response recorrelates with its predeformed state, indicating nearly complete microstructural recovery, and the dynamics of the system under these conditions slows considerably. Conversely, larger creep stresses increase the speed of the dynamics under both applied creep and recovery. The data show a strong connection between the microstructural dynamics and the acquisition of unrecoverable strain. By comparing this relationship to that predicted from homogeneous, affine shearing, we find that the yielding transition in concentrated colloidal systems is highly heterogeneous on the microstructural level.

42 ENGINEERING↗

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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. Here 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 q z , 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 q z 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.

36 MATERIALS SCIENCE↗

Multitiered computational methodology for extracting three-dimensional rotational diffusion coefficients from x-ray photon correlation spectroscopy data without structural information

X-ray photon correlation spectroscopy (XPCS) is a powerful technique for analyzing particle systems by investigating their dynamics in suspensions across a broad range of temporal and spatial scales. This is done by illuminating samples with coherent x-ray beams and calculating the correlation function of the obtained x-ray scattering images. XPCS is uniquely suited for studying Brownian dynamics, consisting of translational and rotational diffusion. While traditional XPCS image analysis techniques can extract translational diffusion components, they are unable to estimate rotational diffusion coefficients. Here, we introduce a methodology that combines the angular-temporal cross-correlation analysis and a algorithmic framework called Multi-Tiered Estimation for Correlation Spectroscopy in 3D for estimating three-dimensional rotational diffusion coefficients from XPCS images of three-dimensional particle systems. We demonstrate our methodology for extracting rotational diffusion coefficients from XPCS data by applying it to simulated noisy x-ray images of systems of crossing nanotubes and proteins that evolve under translational and rotational Brownian motion for different diffusion rates. Furthermore, our results show that our approach determines rotational diffusion coefficients within a few percent error.

97 MATHEMATICS AND COMPUTING↗

pyXPCSviewer : an open-source interactive tool for X-ray photon correlation spectroscopy visualization and analysis

pyXPCSviewer , a Python-based graphical user interface that is deployed at beamline 8-ID-I of the Advanced Photon Source for interactive visualization of XPCS results, is introduced. pyXPCSviewer parses rich X-ray photon correlation spectroscopy (XPCS) results into independent PyQt widgets that are both interactive and easy to maintain. pyXPCSviewer is open-source and is open to customization by the XPCS community for ingestion of diversified data structures and inclusion of novel XPCS techniques, both of which are growing demands particularly with the dawn of near-diffraction-limited synchrotron sources and their dedicated XPCS beamlines.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Microscale dynamics in thermoreversible hydrogels: Impact of probe size and concentration

Passive microrheology techniques using dynamic light scattering (DLS) and X-ray photon correlation spectroscopy (XPCS) have emerged as important techniques for characterizing the dynamics and viscoelastic properties of soft polymeric biomaterials. However, the impact of probe particle type, size, and concentration are important considerations in interpretation of results and comparison to properties obtained from bulk rheology measurements. In this work, we investigate a model thermoreversible polymeric hydrogel and compare results from DLS-microrheology with different size and concentrations of polystyrene probe particles and XPCS-microrheology with inorganic nanoparticles. We obtained trends that aligned most closely with the macroscopic rheology with probe particles that are slightly larger than the characteristic length scale of the gel structure, but within the same order of magnitude. By contrast, larger probe particles yielded microrheology data that are more dominated by elastic behavior than what we might expect from bulk rheology experiments, while use of small inorganic nanoparticles in XPCS-microrheology resulted in a more a more viscous response than would be expected based on the bulk rheology. Finally, this study demonstrates the utility of passive DLS- and XPCS-based microrheology in characterizing the rheological properties of complex polymeric biomaterials, while also highlighting important considerations in experimental design and choice of type, size, and concentration of probe particles used.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Probing the Self-Assembly dynamics of cellulose nanocrystals by X-ray photon correlation spectroscopy

Charge-stabilized colloidal cellulose nanocrystals (CNCs) can self-assemble into higher-ordered chiral nematic structures by varying the volume fraction. The assembly process exhibits distinct dynamics during the isotropic to liquid crystal phase transition, which can be elucidated using X-ray photon correlation spectroscopy (XPCS). Anionic CNCs were dispersed in propylene glycol (PG) and water spanning a range of volume fractions, encompassing several phase transitions. Coupled with traditional characterization techniques, XPCS was conducted to monitor the dynamic evolution of the different phases. Additionally, simulated XPCS results were obtained using colloidal rods and compared with the experimental data, offering additional insights into the dynamic behavior of the system. The results indicate that the particle dynamics of CNCs undergo a stepped decay in three stages during the self-assembly process in PG, coinciding with the observed phases. The phase transitions are associated with a total drop of Brownian diffusion rates by four orders of magnitude, a decrease of more than a thousand times slower than expected in an ideal system of repulsive Brownian rods. Given the similarity in the phase behaviors in CNCs dispersed in PG and in water, we hypothesize that these dynamic behaviors can be extrapolated to other polar solvent environments. Importantly, these findings represent the direct measurement of CNC dynamics using XPCS, underscoring the feasibility of directly assessing the dynamic behavior of other rod-like colloidal suspensions.

36 MATERIALS SCIENCE↗

Revealing nanoscale dynamics during an epoxy curing reaction with x-ray photon correlation spectroscopy

In this work the evolution of nanoscale properties is measured during the thermally triggered curing of an industrial epoxy adhesive. We use x-ray photon correlation spectroscopy (XPCS) to track the progression of the curing reaction through the local dynamics of filler particles that reflect the formation of a thermoset network. Out-of-equilibrium dynamics are resolved through identification and analysis of the intensity– intensity autocorrelation functions obtained from XPCS. The characteristic time scale and local velocity of the filler is calculated as functions of time and temperature. We find that the dynamics speed up when approaching the curing temperature (T cure ), and decay rapidly once T cure is reached. We compare the results from XPCS to conventional macroscale characterization by differential scanning calorimetry (DSC). The demonstration and implementation of nanoscale characterization of curing reactions by XPCS proves useful for future development and optimization of epoxy thermoset materials and other industrial adhesive systems.

36 MATERIALS SCIENCE↗

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.

97 MATHEMATICS AND COMPUTING↗

Computational approaches to model X-ray photon correlation spectroscopy from molecular dynamics

X-ray photon correlation spectroscopy (XPCS) allows for the resolution of dynamic processes within a material across a wide range of length and time scales. X-ray speckle visibility spectroscopy (XSVS) is a related method that uses a single diffraction pattern to probe ultrafast dynamics. Interpretation of the XPCS and XSVS data in terms of underlying physical processes is necessary to establish the connection between the macroscopic responses and the microstructural dynamics. To aid the interpretation of the XPCS and XSVS data, we present a computational framework to model these experiments by computing the X-ray scattering intensity directly from the atomic positions obtained from molecular dynamics simulations. We compare the efficiency and accuracy of two alternative computational methods: the direct method computing the intensity at each diffraction vector separately, and a method based on fast Fourier transform that computes the intensities at all diffraction vectors at once. Furthermore, the computed X-ray speckle patterns capture the density fluctuations over a range of length and time scales and are shown to reproduce the known properties and relations of experimental XPCS and XSVS for liquids.

36 MATERIALS SCIENCE↗

Theory of x-ray photon correlation spectroscopy for multiscale flows

Complex multiscale flows associated with instabilities and turbulence are commonly induced under high-energy density (HED) conditions, but accurate measurement of their transport properties has been challenging. X-ray photon correlation spectroscopy (XPCS) with coherent x-ray sources can, in principle, probe material dynamics to infer transport properties using time autocorrelation of density fluctuations. Here we develop a theoretical framework for utilizing XPCS to study material diffusivity in multiscale flows. We extend single-scale shear flow theories to broadband flows using a multiscale analysis that captures shear and diffusion dynamics. Our theory is validated with simulated XPCS for Brownian particles advected in multiscale flows. We demonstrate the versatility of the method over several orders of magnitude in timescale using sequential-pulse XPCS, single-pulse x-ray speckle visibility spectroscopy (XSVS), and double-pulse XSVS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The Effect of Intensity Fluctuations on Sequential X-ray Photon Correlation Spectroscopy at the X-ray Free Electron Laser Facilities

How materials evolve at thermal equilibrium and under external excitations at small length and time scales is crucial to the understanding and control of material properties. X-ray photon correlation spectroscopy (XPCS) at X-ray free electron laser (XFEL) facilities can in principle capture dynamics of materials that are substantially faster than a millisecond. However, the analysis and interpretation of XPCS data is hindered by the strongly fluctuating X-ray intensity from XFELs. Here we examine the impact of pulse-to-pulse intensity fluctuations on sequential XPCS analysis. We show that the conventional XPCS analysis can still faithfully capture the characteristic time scales, but with substantial decrease in the signal-to-noise ratio of the g2 function and increase in the uncertainties of the extracted time constants. We also demonstrate protocols for improving the signal-to-noise ratio and reducing the uncertainties.

36 MATERIALS SCIENCE↗

Multi-Tiered Estimation for Correlation Spectroscopy in 3D (MTECS3D) v0.1

This innovative software estimates rotational diffusion coefficients of particles from X-ray photon correlation spectroscopy (XPCS) data of monodispersed particle systems. It is the first method capable of extracting rotational diffusion information from three-dimensional particle systems using XPCS. Using the angular-temporal cross-correlation of the XPCS images, this software is able to estimate the rotational diffusion coefficients with only a few percent relative errors while requiring minimal prior knowledge of particle structures. This software enhances XPCS analysis capabilities, allowing researchers to study translational and rotational Brownian dynamics of particles in suspension across various temporal and spatial scales.

Hu, Zixi↗