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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↗

Extremely Slow Diffusion of Gold Nanoparticles under Confinement in Mesoporous Silica

Here, we report an X-ray photon correlation spectroscopy (XPCS) study of the mobility of colloidal gold nanoparticles with a diameter of approximately 4 nm in glycerol under confinement within the channels of SBA-15 mesoporous silica with pore diameters of approximately 6 and 12 nm. The XPCS correlation functions result from an effective heterodyne signal due to the mixing of the coherent scattering from the nanoparticles and the mesoporous silica. Over the range of wave vectors and hence length scales probed, the nanoparticle dynamics are well described by one-dimensional diffusion. The nanoparticle diffusivity varies with temperature in a manner expected based on the temperature-dependent viscosity of glycerol; however, the magnitudes of the diffusion coefficients are several orders of magnitude smaller than those of the nanoparticles in bulk glycerol. We consider mechanisms that might contribute to this reduction in diffusivity including enhancement in hydrodynamic drag under confinement, effects of nanoparticle adsorption to the pore walls, and slowing structural dynamics in glycerol due to the combination of the nanometer-scale confinement and the presence of the nanoparticles.

36 MATERIALS SCIENCE↗

Structure of Complex Liquid–Liquid Extraction Organic Phases for Rare Earth Separations

Complex, multicomponent liquids with hierarchical structure and phase transitions are encountered in many natural and industrial processes, including in chemical separations. One notable example is aggregation and organic phase splitting in liquid–liquid extraction (LLE) of metal ions. While these two phenomena that have long been closely associated, a mechanistic link between mesoscale structure and the capacity-limiting organic phase splitting remains elusive due to complexity of these systems. Here, in this study, we combine small-angle X-ray scattering (SAXS), X-ray photon correlation spectroscopy (XPCS), and molecular dynamics simulation to reveal a comprehensive picture of structure at the nano- and mesoscale in these complex solutions. For the representative case of rare earth extraction from an acidic aqueous phase by a malonamide extractant in dodecane, we investigate a wide range of process-relevant extractant and acid concentrations to provide a complete picture of how aggregation depends on composition. We decompose organic phase structure from SAXS into two contributions, which together can capture the scattering at all compositions: composition fluctuations described by the Ornstein–Zernike equation at low wavenumber Q, and nanostructure modeled by a “pre-peak” at intermediate Q. The former contains information about the thermodynamics of demixing, while the latter reflects nanoscopic self-assembly of the extractant and extracted solutes. While fluctuations have typically not been considered in the literature, we find they in fact dominate the total structure for nearly all practical conditions. As only the fluctuations have a strong temperature response, we confirm this attribution with temperature-dependent SAXS measurements, including for extracted europium nitrate complexes. SAXS and XPCS measurements near the critical point find static and dynamic scaling consistent with theory. Overall, this new paradigm for understanding LLE organic phases connects composition, nanoscale, and mesoscale structuring to phase behavior, providing both a comprehensive picture of solution structure and a quantitative link between aggregation and third phase formation.

Peroutka, Allison A. [Argonne National Laboratory ↗

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 by using linear polymer chains; the role of polymer matrix architecture on local dynamics, bulk rheology and nanoparticle motion remains unexplored. Here, using quasielastic 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. Additionally, the polymer compactness and inter-penetrability are found to play crucial roles in determining their bulk rheology. At 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 linear polymer matrix at the same NP loading. In addition, the nanoscale dynamics of particles in the compact nonlinear matrices exhibit 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 PNCs without the need for changing polymer molecular weight, nanoparticle size, shape, loading or dispersion state.

36 MATERIALS SCIENCE↗

Nanoparticle Diffusion in Miscible Polymer Nanocomposite Melts

X-ray photon correlation spectroscopy measurements were used to quantify the dynamics of bare and bimodal grafted silica nanoparticles mixed with PEO melts of different molecular weights. In dilute polymer nanocomposite (PNC) samples, we find diffusive NP behavior as described by the Stokes–Einstein relationship so long as the adsorbed PEO polymer layer is taken into account in determining both the effective NP size and its role on composite viscosity. The size of this bound layer was found to be approximately 2R g , where R g is the chain radius of gyration. We also expanded our system to investigate how the dynamics of grafted NPs differ from bare NPs with an adsorbed layer. We showed that the dynamics again can be determined by an effective NP radius at a scale smaller than the effective interparticle spacing; however, at larger length scales, the morphology and grafting parameters play a major role in the system dynamics. These results allow us to quantify NP ordering driven by polymer crystallization. It has previously been speculated that behavior is controlled by the relative ratio of time scale of crystal growth and the diffusive time scale of the NPs, a Peclet number. When the former time scale is longer, then the NPs are expected to be segregated into the interlamellar amorphous zones, while the NPs are too slow to be reorganized in the opposite case. We show here that this conjecture is quantitatively correct and the demarcation in behavior occurs for Pe = 1. Thus, we provide a way to estimate a critical spherulite growth rate for any semicrystalline PNC, at which a given NP can be ordered. Together, the results of this study permit us to tunably design PNCs through directed dispersion of NPs in a polymer matrix.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Structural and Dynamical Insights into the Formation Process of a Cross-Linked Polymer Network in Acrylic Adhesives During Thermal Curing

Many modern adhesives, sealants, and coatings rely on the controlled transition from a liquid to a solid state by forming a three-dimensional cross-linked polymer network, often referred to as curing. The curing process, which is initiated by the mixing of reactive components or an external trigger, defines the structure of a network and further controls the final mechanical properties of cured materials. However, the curing mechanism is not fully understood yet due to the lack of experimental tools capable of directly probing the structure and dynamics of a network over relevant time- and length scales. Here, in this paper, we report the curing process of a commercial two-component methyl methacrylate (MMA) adhesive using in operando X-ray photon correlation spectroscopy (XPCS), a method that closely simulates the target manufacturing environment of the adhesive. The results are then integrated with those obtained by rheology, differential scanning calorimetry (DSC), and transmission electron microscopy to establish the structure–dynamics–process–property relationship. The XPCS results identify four distinct stages in the curing process after the mixing, extrusion, and deposition of the acrylic adhesive: (i) At a cure time (or “aging time”, t age ) of less than 1 min, nanodomains of polymerized MMA are formed within a liquid monomeric MMA matrix. The average size is several nm and remains constant over t age , while the dynamics of the nanodomains are slowed down with t age due to an increase in the viscosity of the MMA matrix. (ii) After t age > 1 min, the size of the nanodomains increases with t age until the gel point (= 6.3 min after mixing as determined by rheology). The dynamics of the nanodomains also increase due to the heat generated by the exothermic reaction. (iii) At the gel point, the nanodomains begin to interconnect each other, resulting in a network structure with a characteristic length of about 100 nm. This characteristic network size does not change for the rest of the curing process up to t age = 500 min. The dynamics of the network structure, however, show a rapid slowing down with t age up to t age ≈ 12 min, corresponding to the onset of vitrification (as determined by rheology). (iv) At t age > 12 min, when the DSC and rheology data can no longer provide meaningful information, the XPCS data show a further slowing down of the network dynamics associated with vitrification. Our results provide rich and complex insights into the physics and material design of thermosets in commercially relevant processes, which are essential for future industrial applications.

36 MATERIALS SCIENCE↗

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↗

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

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

36 MATERIALS SCIENCE↗

Bridging length scales in organic mixed ionic–electronic conductors through internal strain and mesoscale dynamics

Understanding the structural and dynamic properties of disordered systems at the mesoscale is crucial. This is particularly important in organic mixed ionic-electronic conductors (OMIECs), which undergo significant and complex structural changes when operated in an electrolyte. Here, in this study, we investigate the mesoscale strain, reversibility and dynamics of a model OMIEC material under external electrochemical potential using operando X-ray photon correlation spectroscopy. Our results reveal that strain and structural hysteresis depend on the sample's cycling history, establishing a comprehensive kinetic sequence bridging the macroscopic and microscopic behaviours of OMIECs. Furthermore, we uncover the equilibrium and non-equilibrium dynamics of charge carriers and material-doping states, highlighting the unexpected coupling between charge carrier dynamics and mesoscale order. These findings advance our understanding of the structure-dynamics-function relationships in OMIECs, opening pathways for designing and engineering materials with improved performance and functionality in non-equilibrium states during device operation. Understanding mesoscale structure and dynamics in organic mixed ionic-electronic conductors is crucial. Mesoscale strain kinetics and structural hysteresis have been studied, and they uncover the coupling between charge carrier dynamics and mesoscale order in organic mixed ionic-electronic conductors.

36 MATERIALS SCIENCE↗

Dynamics at the crystal-melt interface in a supercooled chalcogenide liquid near the glass transition

Direct quantitative measurements of nanoscale dynamical processes associated with structural relaxation and crystallization near the glass transition are a major experimental challenge. These type of processes have been primarily treated as macroscopic phenomena within the framework of phenomenological models and bulk experiments. Here, we report x-ray photon correlation spectroscopy measurements of dynamics at the crystal-melt interface during the radiation induced formation of Se nano-crystallites in pure Se and in binary AsSe 4 glass-forming liquids near their glass transition temperature. We observe a heterogeneous dynamical behaviour where the intensity correlation functions g 2 (q, t) exhibits either a compressed or a stretched exponential decay, depending on the size of the Se nano-crystallites. The corresponding relaxation timescale for the AsSe 4 liquid increases as the temperature is raised, which can be attributed to changes in the chemical composition of the melt at the crystal-melt interface with the growth of the Se nano-crystallites.

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↗

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.

Kamani, Krutarth M. [Univ. of Illinois at Urbana-C↗

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.

36 MATERIALS SCIENCE↗

Transport coefficient approach for characterizing nonequilibrium dynamics in soft matter

Nonequilibrium states in soft condensed matter require a systematic approach to characterize and model materials, enhancing predictability and applications. Among the tools, X-ray photon correlation spectroscopy (XPCS) provides exceptional temporal and spatial resolution to extract dynamic insight into the properties of the material. However, existing models might overlook intricate details. We introduce an approach for extracting the transport coefficient, denoted as $J(t)$, from the XPCS studies. This coefficient is a fundamental parameter in nonequilibrium statistical mechanics and is crucial for characterizing transport processes within a system. Our method unifies the Green–Kubo formulas associated with various transport coefficients, including gradient flows, particle–particle interactions, friction matrices, and continuous noise. We achieve this by integrating the collective influence of random and systematic forces acting on the particles within the framework of a Markov chain. We initially validated this method using molecular dynamics simulations of a system subjected to changes in temperatures over time. Subsequently, we conducted further verification using experimental systems reported in the literature and known for their complex nonequilibrium characteristics. The results, including the derived $J(t)$ and other relevant physical parameters, align with the previous observations and reveal detailed dynamical information in nonequilibrium states. This approach represents an advancement in XPCS analysis, addressing the growing demand to extract intricate nonequilibrium dynamics. Further, the methods presented are agnostic to the nature of the material system and can be potentially expanded to hard condensed matter systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Developments in SRW Code and Sirepo Framework Supporting Simulation of Time-Dependent Coherent X-ray Scattering Experiments

Physical optics simulations for beamlines and experiments are essential for the effective use of synchrotron light source facilities such as NSLS-II at BNL. The SRW software package supports such source-to-detector simulations for coherent X-ray scattering and imaging experiments through its Python interface and Sirepo browser-based graphical user interface. This allows one to define custom sample models, assess the feasibility of an experiment, and estimate most appropriate beamline settings before using valuable beamtime. We discuss the recent use of general-purpose GPU resources and coherent mode decomposition algorithms in SRW to accelerate physical optics simulations with partially coherent X-rays. To illustrate these new capabilities, we describe simulations of typical time series of partially coherent scattering images used in X-ray Photon Correlation Spectroscopy (XPCS) experiments; aiming to characterize the nanoscale dynamics of a disordered sample, representing a solution of nanoparticles undergoing Brownian diffusion.

36 MATERIALS SCIENCE↗

Anomalous lattice relaxation dynamics in optimally doped La 2−𝑥⁢ Sr 𝑥 ⁢CuO 4

The atomic lattice plays a critical role in the emergence of high-𝑇 𝑐 superconductivity in cuprates. While the dynamics associated with electron-lattice coupling typically unfold on picosecond-to-femtosecond timescales, we present an x-ray photon correlation spectroscopy investigation on an optimally doped La-based cuprate that reveals a strong response of kilosecond-scale lattice relaxation dynamics to the superconducting state. Notably, an anomaly emerges around 𝑇 𝑐 : upon cooling into the superconducting state, the average atomic relaxation lifetime decreases, i.e., dynamics accelerate. This indicates a significant change in the local disorder-induced strain field dynamics at the superconducting transition, highlighting a remarkable coupling between superconductivity and the lattice on quasistatic timescales.

Petsch, A. N. [SLAC National Accelerator Laborator↗

Nanoscale dynamics during self-organized ion beam patterning of Si. II. Kr + bombardment

Understanding the self-organized ion beam nanopatterning of elemental semiconductors, particularly silicon, is of intrinsic scientific and technological interest. This is the second component of a two-part coherent x-ray scattering and x-ray photon correlation spectroscopy (XPCS) investigation of the kinetics and fluctuation dynamics of nanoscale ripple development on silicon during 1 keV Ar + (part I) and Kr + bombardment at 65° polar angle. Here it is found that the ion-enhanced viscous flow relaxation is essentially equal for Kr + -induced patterning as previously found for Ar + patterning despite the difference in ion masses. However, the magnitude of the surface curvature-dependent roughening rate in the early-stage kinetics is larger for Kr + than for Ar + , consistent with expectations that the heavier ion gives an increased mass redistributive contribution to the initial surface instability. As with the Ar + case, fluctuation dynamics in the late stage show a peak in correlation times at the length scale corresponding to the dominant structural feature on the surface—the ripples. Finally, it is shown that speckle motion during the surface evolution can be analyzed to determine spatial inhomogeneities in erosion rate and ripple velocity. This allows the direction and speed of ripple motion to be measured in a real time experiment. In the present case, ripple motion is found to be into the projected direction of the ion source, in contrast to expectations from an existing sputter erosion driven model with parameters derived from binary collision approximation simulations.

36 MATERIALS SCIENCE↗