Nanoparticle motion within glassy polymer melts

Lipid vesicle pools studied by passive X-ray microrheology

Vesicle pools can form by attractive interaction in a solution, mediated by proteins or divalent ions such as calcium. The pools, which are alternatively also denoted as vesicle clusters, form by liquid-liquid phase separation (LLPS) from an initially homogeneous solution. Due to the short range liquid-like order of vesicles in the pool or cluster, the vesicle-rich phase can also be regarded as a condensate, and one would like to better understand not only the structure of these systems, but also their dynamics. The diffusion of vesicles, in particular, is expected to change when vesicles are arrested in a pool. Here we investigate whether passive microrheology based on X-ray photon correlation spectroscopy (XPCS) is a suitable tool to study model systems of artificial lipid vesicles exhibiting LLPS, and more generally also other heterogeneous biomolecular fluids. We show that by adding highly scattering tracer particles to the solution, valuable information on the single vesicle as well as collective dynamics can be inferred. While the correlation functions reveal freely diffusing tracer particles in solutions at low CaCl[Formula: see text] concentrations, the relaxation rate [Formula: see text] shows a nonlinear dependence on [Formula: see text] at a higher concentration of around 8 mM CaCl[Formula: see text], characterised by two linear regimes with a broad cross-over. We explain this finding based on arrested diffusion in percolating vesicle clusters.

Coherent X-ray Scattering Reveals Nanoscale Fluctuations in Hydrated Proteins

Hydrated proteins undergo a transition in the deeply supercooled regime, which is attributed to rapid changes in hydration water and protein structural dynamics. Here, we investigate the nanoscale stress-relaxation in hydrated lysozyme proteins stimulated and probed by X-ray Photon Correlation Spectroscopy (XPCS). This approach allows us to access the nanoscale dynamics in the deeply supercooled regime (T = 180 K), which is typically not accessible through equilibrium methods. The observed stimulated dynamic response is attributed to collective stress-relaxation as the system transitions from a jammed granular state to an elastically driven regime. The relaxation time constants exhibit Arrhenius temperature dependence upon cooling with a minimum in the Kohlrausch-Williams-Watts exponent at T = 227 K. The observed minimum is attributed to an increase in dynamical heterogeneity, which coincides with enhanced fluctuations observed in the two-time correlation functions and a maximum in the dynamic susceptibility quantified by the normalized variance χ_T. The amplification of fluctuations is consistent with previous studies of hydrated proteins, which indicate the key role of density and enthalpy fluctuations in hydration water. Our study provides new insights into X-ray stimulated stress-relaxation and the underlying mechanisms behind spatiotemporal fluctuations in biological granular materials.

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.

Diffusion of polymer-grafted nanoparticles with dynamical fluctuations in unentangled polymer melts

The dynamics of polymer-grafted nanoparticles (PGNPs) in melts of unentangled linear chains were investigated by means of coarse-grained molecular dynamics simulations. The results demonstrated that the graft monomers closer to the particle surface relax more slowly than those farther away due to the constraint of the grafted surface and the confinement of the neighboring chains. Such heterogeneous relaxations of the surrounding environment would perturb the particle motion, making them fluctuating around their centers before they can diffuse through the melt. During such intermediate-time stage, the dynamics is subdiffusive while the distribution of particle displacements is Gaussian, which can be described by the popular fractional Brownian motion model. For the long-time Fickian diffusion, we found that the diffusivity D decreases with increasing grafting density Σ_g, grafted chain length N_g, and matrix chain length N_m. This is due to the fact that the diffusivity is controlled by the viscous drag of an effective core, consisting of the NP and the non-draining layer of graft segments, and that of the free-draining graft layer outside the "core". With increasing Σ_g, the PGNPs become harder with greater effective size and thinner free draining layer, resulting in a reduction in D. At extremely high Σ_g, the diffusivity can even be estimated by the diameter-renormalized Stokes-Einstein (SE) relation. With increasing N_g, both the effective core size and the thickness of the free-draining layer increase, leading to a reduction in diffusivity by D ∼ N-γg with 0.5 < γ < 1. Increasing N_m would lead to the enlargement of the effective core size but meanwhile result in the reduction of the free-draining layer thickness due to autophobic dewetting. The counteraction between these two opposite effects leads to only a slight reduction in the diffusivity, significantly different from the typical SE behavior where D ∼ N_m^-1. These findings bear significance in unraveling the fundamental physics of the anomalous dynamics of PGNPs in various polymers, including biological and synthetic.

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.

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.

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

The kinetics of heat-induced gelation and the microscopic dynamics of a hen egg white gel are probed using x-ray photon correlation spectroscopy along with ultrasmall-angle x-ray scattering. The kinetics of structural growth reveals a reaction-limited aggregation process with a gel fractal dimension of ≈2 and an average network mesh size of ca. 400 nm. The dynamics probed at these length scales reveals an exponential growth of the characteristic relaxation times followed by an intriguing steady state in combination with a compressed exponential correlation function and a temporal heterogeneity. The degree of heterogeneity increases with decreasing length scale. We discuss our results in the broader context of experiments and models describing attractive colloidal gels.

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

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

Ion-Mediated Cross-linking of Biopolymers Confined at Liquid/Liquid Interfaces Probed by In Situ High-Energy Grazing Incidence X-ray Photon Correlation Spectroscopy

As manifested in biological cell membranes, the confinement of chemical reactions at the 2D interfaces significantly improves the reaction efficacy. The interface between two liquid phases is used in various key processes in industries, such as in food emulsification and floatation. However, monitoring the changes in the mechanics and dynamics of molecules confined at the liquid/liquid interfaces still remains a scientific challenge because it is nontrivial to access the interface buried under a liquid phase. Herein, we report the in situ monitoring of the cross-linking of polyalginate mediated by Ca²⁺ ions at the oil/water interface by grazing incidence X-ray photon correlation spectroscopy (GIXPCS). We first optimized the reaction conditions with the aid of interfacial shear rheology and then performed GIXPCS using a high-energy synchrotron X-ray beam (22 keV) that guarantees sufficiently high transmittance through the oil phase. The intensity autocorrelation functions implied that the formation of a percolated network of polyalginate is accompanied by increasing relaxation time. Moreover, the relaxation rate scales linearly with the momentum transfer parallel to the interface, suggesting that the process is driven by hyperdiffusive propagation but not by Brownian diffusion. Our data indicated that high-energy GIXPCS has potential for in situ monitoring of changes in the dynamics of polymers confined between two liquid phases.

Wave-Vector Dependence of the Dynamics in Supercooled Metallic Liquids

We present a detailed investigation of the wave-vector dependence of collective atomic motion in Au_{49}Cu_{26.9}Si_{16.3}Ag_{5.5}Pd_{2.3} and Pd_{42.5}Cu_{27}Ni_{9.5}P_{21} supercooled liquids close to the glass transition temperature. Using x-ray photon correlation spectroscopy in a previously uncovered spatial range of only a few interatomic distances, we show that the microscopic structural relaxation process mimics the structure and presents a marked slowing down at the main average interparticle distance. This behavior is accompanied by dramatic changes in the shape of the intermediate scattering functions, which suggest the presence of large dynamical heterogeneities at length scales corresponding to a few particle diameters. A ballisticlike mechanism of particle motion seems to govern the structural relaxation of the two systems in the highly viscous phase, likely associated with hopping of caged particles in agreement with theoretical studies.

Anisotropic and heterogeneous dynamics in an aging colloidal gel

We investigate the out-of-equilibrium dynamics of a colloidal gel obtained by quenching a suspension of soft polymer-coated gold nanoparticles close to and below its gelation point using X-ray Photon Correlation Spectroscopy (XPCS). A faster relaxation process emergent from the localized motions of the nanoparticles reveals a dynamically-arrested network at the nanoscale as a key signature of the gelation process. We find that the slower network dynamics is hyperdiffusive with a compressed exponential form, consistent with stress-driven relaxation processes. Specifically, we use direction-dependent correlation functions to characterize the anisotropy in dynamics. We show that the anisotropy is greater for the gel close to its gelation point than at lower temperatures, and the anisotropy decreases as the gel ages. We quantify the anisotropic dynamical heterogeneities emergent in such a stress-driven dynamical system using higher order intensity correlations, and demonstrate that the aging phenomenon contributes significantly to the properties evaluated by the fluctuations in the intensity correlations. Our results provide important insights into the structural origin of the emergent anisotropic and cooperative heterogeneous dynamics, and we discuss analogies with previous work on other soft disordered systems.

Dynamical Heterogeneity near Glass Transition Temperature under Shear Conditions

We experimentally studied the shear effect on dynamical heterogeneity near glass transition temperature. X-ray photon correlation spectroscopy was utilized to study the dynamics of polyvinyl acetate with tracer particles near its glass transition temperature, to determine the local shear rate from the anisotropic behavior of the time autocorrelation function and to calculate the dynamical heterogeneity using higher-order correlation function. The obtained results show a decrease in the dynamical heterogeneity and faster dynamics with increasing shear rate. This is the first experimental result that proved the predictions of previous molecular dynamics simulations.

Microscopic pathways for stress relaxation in repulsive colloidal glasses

Residual stresses are well-known companions of all glassy materials. They affect and, in many cases, even strongly modify important material properties like the mechanical response and the optical transparency. The mechanisms through which stresses affect such properties are, in many cases, still under study, and their full understanding can pave the way to a full exploitation of stress as a primary control parameter. It is, for example, known that stresses promote particle mobility at small length scales, e.g., in colloidal glasses, gels, and metallic glasses, but this connection still remains essentially qualitative. Exploiting a preparation protocol that leads to colloidal glasses with an exceptionally directional built-in stress field, we characterize the stress-induced dynamics and show that it can be visualized as a collection of "flickering," mobile regions with linear sizes of the order of ≈20 particle diameters (≈2 μm here) that move cooperatively, displaying an overall stationary but locally ballistic dynamics.

Spontaneous Magnetic Superdomain Wall Fluctuations in an Artificial Antiferromagnet

Collective dynamics often play an important role in determining the stability of ground states for both naturally occurring materials and metamaterials. We studied the temperature dependent dynamics of antiferromagnetically ordered superdomains in a square artificial spin lattice using soft x-ray photon correlation spectroscopy. We observed an exponential slowing down of superdomain wall motion below the antiferromagnetic onset temperature, similar to the behavior of typical bulk antiferromagnets. Using a continuous time random walk model we show that these superdomain walls undergo low-temperature ballistic and high-temperature diffusive motions.

Anomalous Dynamics of Concentrated Silica-PNIPAm Nanogels

We present the structure and dynamics of highly concentrated core-shell nanoparticles composed of a silica core and a poly(N-isoproylacrylamide) (PNIPAm) shell suspended in water. With X-ray photon correlation spectroscopy, we are able to follow dynamical changes over the volume phase transition of PNIPAm at LCST = 32 °C. On raising the temperature beyond LCST, the structural relaxation times continue to decrease. The effect is accompanied by a transition from stretched to compressed exponential shape of the intensity autocorrelation function. Upon further heating, we find a sudden slowing down for the particles in their collapsed state. The q dependence of the relaxation time shows an anomalous change from τ_c ∝ q^-3 to τ_c ∝ q^-1. Small angle X-ray scattering data evidence a temperature-induced transition from repulsive to attractive forces. Our results indicate a temperature-induced phase transition from a colloidal liquid with polymer-driven dynamics toward a colloidal gel.

Nanoscale Particle Motion Reveals Polymer Mobility Gradient in Nanocomposites

Polymer mobility near nanoparticle surfaces has been extensively discussed; however, direct experimental observation in the nanocomposite melts has been a difficult task. Here, by taking advantage of large dynamical asymmetry between the miscible matrix and surface-bound polymers, we highlighted their interphases and studied the resulting effect on the nanoparticle relaxation using X-ray photon correlation spectroscopy. The local mobility gradient is signified by an unprecedented increase in the relaxation time at length scales on the order of polymer radius of gyration. The effect is accompanied by a transition from simple diffusive to subdiffusive behavior in accord with viscous and entangled dynamics of polymers in the matrix and in the interphase, respectively. Our results demonstrate that the nanoparticle-induced polymer mobility changes in the interphases of nanocomposite melts can be extracted from the length-scale-dependent slow particle motion.

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.

One-Dimensional Anomalous Diffusion of Gold Nanoparticles in a Polymer Melt

We investigated the dynamics of polymer-grafted gold nanoparticles loaded into polymer melts using x-ray photon correlation spectroscopy. For low molecular weight host matrix polymer chains, normal isotropic diffusion of the gold nanoparticles is observed. For larger molecular weights, anomalous diffusion of the nanoparticles is observed that can be described by ballistic motion and generalized Lévy walks, similar to those often used to discuss the dynamics of jammed systems. Under certain annealing conditions, the diffusion is one-dimensional and related to the direction of heat flow during annealing and is associated with an dynamic alignment of the host polymer chains. Molecular dynamics simulations of a single gold nanoparticle diffusing in a partially aligned polymer network semiquantitatively reproduce the experimental results to a remarkable degree. The results help to showcase how nanoparticles can under certain circumstances move rapidly in polymer networks.

Physical aging and compressed exponential behaviors in a model soft colloidal system

Diffusing wave spectroscopy (DWS)-based micro-rheology has been used in different optical geometries (backscattering and transmission) as well as different sample thicknesses in order to probe system dynamics at different length scales [D. J. Pine, D. A. Weitz, J. X. Zhu, E. Herbolzheimer. J. Phys., 1990, 51(18), 2101-2127]. Previous study from this lab [Q. Li, X. Peng, G. B. McKenna. Soft Matter, 2017, 13(7), 1396-1404] indicates the DWS-based micro-rheology observes the system non-equilibrium behaviors differently from macro-rheology. The object of the present work was to further explore the non-equilibrium dynamics and to address the range of utility of DWS as a micro-rheological method. A thermo-sensitive core-shell colloidal system was investigated both during aging and subsequent to aging into a metastable equilibrium state using temperature-jump induced volume fraction-jump experiments. We find that in the non-equilibrium state, significant differences in the measured dynamics are observed for the different geometries and length scales. Compressed exponential relaxations for the autocorrelation function g2(t) were observed for large length scales. However, upon converting the g2(t) data to the mean square displacement (MSD), such differences with length scale diminished and the long-time MSD behavior was consistent with diffusive behavior. These observations in the non-equilibrium behaviors for different length scales leads to questioning of some interpretations in the current field of light scattering-based micro-rheology and provides a possibility to interrogate the aging mechanisms in colloidal glasses from a broader perspective than normally considered in measurements of g2(t) using DWS-based micro-rheology.

Mobility of Polymer-Tethered Nanoparticles in Unentangled Polymer Melts

A scaling theory is developed for the motion of a polymer-tethered nanoparticle (NP) in an unentangled polymer melt. We identify two types of scaling regimes depending on the NP diameter d and the size of a grafted polymer chain (tail) R tail . In one type of regimes, the tethered NP motion is dominated by the bare NP, as the friction coefficient of the tails is lower than that of the less mobile particle. The time dependence of the mean square displacement (MSD) of the tethered NP ⟨Δr 2(t)⟩ in the particle-dominated regime can be approximated by ⟨Δr 2(t)⟩ bare for the bare NP. In the other type of regimes, the tethered NP motion is dominated by the tails when the friction coefficient of the tails surpasses that of the particle at times longer than the crossover time τ ∗. In a tail-dominated regime, the MSD ⟨Δr 2(t)⟩ ≈ ⟨Δr 2(t)⟩ bare only for t < τ ∗. ⟨Δr 2(t)⟩ of a single-tail NP for t > τ ∗ is approximated as the MSD ⟨Δr 2(t)⟩ tail of monomers in a free tail, whereas ⟨Δr 2(t)⟩ of a multi-tail NP for t > τ ∗ is approximated as the MSD ⟨Δr 2(t)⟩ star of the branch point of a star polymer. The time dependence of ⟨Δr 2(t)⟩ in a tail-dominated regime exhibits two qualitatively different sub-diffusive regimes. The first sub-diffusive regime for t < τ ∗ arises from the dynamical coupling between the particle and the melt chains. The second sub-diffusive regime for t > τ ∗ occurs as the particle participates in the dynamics of the tails. For NPs with loosely grafted chains, there is a Gaussian brush region surrounding the NP, where the chain strands in Gaussian conformations undergo Rouse dynamics with no hydrodynamic coupling. The crossover time τ ∗ for loosely grafted multi-tail NPs in a tail-dominated regime decreases as the number of tails increases. For NPs with densely grafted chains, the tails are hydrodynamically coupled to each other. The hydrodynamic radii for the diffusion of densely grafted multi-tail NPs are approximated by the sum of the particle and tail sizes.

Stretched and compressed exponentials in the relaxation dynamics of a metallic glass-forming melt

The dynamics of glass-forming systems shows a multitude of features that are absent in normal liquids, such as non-exponential relaxation and a strong temperature-dependence of the relaxation time. Connecting these dynamic properties to the microscopic structure of the system is challenging because of the presence of the structural disorder. Here we use computer simulations of a metallic glass-former to establish such a connection. By probing the temperature and wave-vector dependence of the intermediate scattering function we find that the relaxation dynamics of the glassy melt is directly related to the local arrangement of icosahedral structures: Isolated icosahedra give rise to a liquid-like stretched exponential relaxation whereas clusters of icosahedra lead to a compressed exponential relaxation that is reminiscent to the one found in a solid. Our results show that in metallic glass-formers these two types of relaxation processes can coexist and give rise to a dynamics that is surprisingly complex.

Glasses show peculiar relaxation dynamics below glass transition temperature, yet a deeper understanding of this phenomenon is still lacking. Wu et al. show the coexistence of stretched and compressed relaxation in a metallic glass system and attribute their origins to different local cluster structures.

Anomalous Dynamics of Magnetic Anisotropic Colloids Studied by XPCS

The influence of an applied magnetic field on the collective dynamics of novel anisotropic colloidal particles whose shape resembles peanuts is reported. Being made up of hematite cores and silica shells, these micrometer-sized particles align in a direction perpendicular to the applied external magnetic field, and assemble into chains along the field direction. The anisotropic dynamics of these particles is investigated using multispeckle ultrasmall-angle X-ray photon correlation spectroscopy (USA-XPCS). The results indicate that along the direction of the magnetic field, the particle dynamics strongly depends on the length scale probed. Here, the relaxation of the intermediate scattering function follows a compressed exponential behavior at large distances, while it appears diffusive at distances comparable or smaller than the particle size. Perpendicular to the applied field (and along the direction of gravity), the experimental data can be quantitatively reproduced by a combination of an advective term originating from sedimentation and a purely diffusive one that describes the thermal diffusion of the assembled chains and individual particles.

Chemical heterogeneity in interfacial layers of polymer nanocomposites

It is well-known that particle-polymer interactions strongly control the adsorption and conformations of adsorbed chains. Interfacial layers around nanoparticles consisting of adsorbed and free matrix chains have been extensively studied to reveal their rheological contribution to the behavior of nanocomposites. This work focuses on how chemical heterogeneity of the interfacial layers around the particles governs the microscopic mechanical properties of polymer nanocomposites. Low glass-transition temperature composites consisting of poly(vinyl acetate) coated silica nanoparticles in poly(ethylene oxide) and poly(methyl acrylate) matrices, and of poly(methyl methacrylate) silica nanoparticles in a poly(methyl acrylate) matrix are examined using rheology and X-ray photon correlation spectroscopy. We demonstrate that miscibility between the adsorbed and matrix chains in the interfacial layers led to the observed unusual reinforcement. We suggest that packing of chains in the interfacial regions may also contribute to the reinforcement in the polymer nanocomposites. These features may be used in designing mechanically adaptive composites operating at varying temperature.

Dynamics of Nanoparticles in Entangled Polymer Solutions

The mean square displacement ⟨r²⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (R_g), are investigated. In simple fluids and for polymer solutions in which d ≫ R_g, long-time particle dynamics obey random-walk statistics ⟨r²⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < R_g, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

Translational and rotational dynamics of an ultra-thin nanorod probe particle in linear polymer melts

Translational and rotational dynamics of a single rigid ultra-thin nanorod probe particle in linear polymer melts are investigated using coarse-grained molecular dynamics (CG-MD) simulations.

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.

Chain dynamics and nanoparticle motion in attractive polymer nanocomposites subjected to large deformations

The effect of large deformation on the chain dynamics in attractive polymer nanocomposites was investigated using neutron scattering techniques. Quasi-elastic neutron backscattering measurements reveal a substantial reduction of polymer mobility in the presence of attractive, well-dispersed nanoparticles. In addition, large deformations are observed to cause a further slowing down of the Rouse rates at high particle loadings, where the interparticle spacings are slightly smaller than the chain dimensions, i.e. in the strongly confined state. No noticeable change, however, was observed for a lightly confined system. The reptation tube diameter, measured by neutron spin echo, remained unchanged after shear, suggesting that the level of chain-chain entanglements is not significantly affected. The shear-induced changes in the interparticle bridging reflect the slow nanoparticle motion measured by X-ray photon correlation spectroscopy. These results provide a first step for understanding how large shear can significantly affect the segmental motion in nanocomposites and open up new opportunities for designing mechanically responsive soft materials.

Ultra-long-range dynamic correlations in a microscopic model for aging gels

We use large-scale computer simulations to explore the nonequilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically arrested phase separation is accompanied by "anomalous" particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatiotemporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is a microscopically resolved model reproducing all features of the spontaneous aging dynamics observed experimentally in soft materials.

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.

Structure and Dynamics of Bimodal Colloidal Dispersions in a Low-Molecular-Weight Polymer Solution

We present an experimental study of the structural and dynamical properties of bimodal, micrometer-sized colloidal dispersions (size ratio ≈ 2) in an aqueous solution of low-molecular-weight polymer (polyethylene glycol 2000) using synchrotron ultra-small angle X-ray scattering (USAXS) and USAXS-based X-ray photon correlation spectroscopy. We fixed the volume fraction of the large particles at 5% and systematically increased the volume fraction of the small particles from 0 to 5% to evaluate their effects on the structure and dynamics. The bimodal dispersions were homogenous through the investigated parameter space. We found that the partial structure factors can be satisfactorily retrieved for the bimodal colloidal dispersions using a Percus-Yevick hard-sphere potential when the size distributions of the particles were taken into account. We also found that the partial structure factor between the large particles did not exhibit a significant variation with increasing volume fraction of the small particles, whereas the isothermal compressibility of the binary mixture was found to decrease with increasing volume fraction of the small particles. The dynamics of single-component large-particle dispersion obey the principles of de Gennes narrowing, where the wave vector dependence of the interparticle diffusion coefficient is inversely proportional to the interparticle structure factor. The dynamics of the bimodal dispersions demonstrate a strong dependence on the fraction of small particles. We also made a comparison between the experimental effective dynamic viscosity of the bimodal dispersion with the theoretical predictions, which suggest that the complex mutual interactions between the large and small particles have a strong effect on the dynamic behaviors of bimodal dispersions.

Analytical Description of Degradation-Relaxation Transformations in Nanoinhomogeneous Spinel Ceramics

Mathematical models of degradation-relaxation kinetics are considered for jammed thick-film systems composed of screen-printed spinel Cu_0.1Ni_0.1Co_1.6Mn_1.2O₄ and conductive Ag or Ag-Pd alloys. Structurally intrinsic nanoinhomogeneous ceramics due to Ag and Ag-Pd diffusing agents embedded in a spinel phase environment are shown to define governing kinetics of thermally induced degradation under 170 °C obeying an obvious non-exponential behavior in a negative relative resistance drift. The characteristic stretched-to-compressed exponential crossover is detected for degradation-relaxation kinetics in thick-film systems with conductive contacts made of Ag-Pd and Ag alloys. Under essential migration of a conductive phase, Ag penetrates thick-film spinel ceramics via a considerable two-step diffusing process.

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.

Nanoscale Motion of Soft Nanoparticles in Unentangled and Entangled Polymer Matrices

We have studied the motion of polyhedral oligomeric silsesquioxane (POSS) nanoparticles modified with poly(ethylene glycol) (PEG) arms immersed in PEG matrices of different molecular weight. Employing neutron spin echo spectroscopy in combination with pulsed field gradient (PFG) NMR we found the following. (i) For entangled matrices the center of mass mean square displacement (MSD) of the PEG-POSS particles is subdiffusive following a t^{0.56} power law. (ii) The diffusion coefficient as well as the crossover to Fickian diffusion is independent of the matrix molecular weight and takes place as soon as the center of mass has moved a distance corresponding to the particle radius-this holds also for unentangled hosts. (iii) For the entangled matrices Rubinstein's scaling theory is validated; however, the numbers indicate that beyond Rouse friction the entanglement constraints appear to strongly increase the effective friction even on the nanoparticle length scale imposing a caveat on the interpretation of microrheological experiments. (iv) The oligomer decorated PEG-POSS particles exhibit the dynamics of a Gaussian star with an internal viscosity that rises with an increase of the host molecular weight.

Applications and limitations of electron correlation microscopy to study relaxation dynamics in supercooled liquids

Electron correlation microscopy (ECM) is a way to measure structural relaxation times, τ, of liquids with nanometer-scale spatial resolution using coherent electron scattering equivalent of photon correlation spectroscopy. We have applied ECM with a 3.5nm diameter probe to Pt_57.5Cu_14.7Ni_5.3P_22.5 amorphous nanorods and Pd₄₀Ni₄₀P₂₀ bulk metallic glass (BMG) heated inside the STEM into the supercooled liquid region. These data demonstrate that the ECM technique is limited by the characteristics of the time series, which must be at least 40τ to obtain a well-converged correlation function g₂(t), and the time per frame, which must be less than 0.1τ to obtain sufficient sampling. A high-speed direct electron camera enables fast acquisition and affords reliable g₂(t) data even with low signal per frame.

Structure and Entanglement Factors on Dynamics of Polymer-Grafted Nanoparticles

Nanoparticles functionalized with long polymer chains at low graft density are interesting systems to study structure-dynamic relationships in polymer nanocomposites since they are shown to aggregate into strings in both solution and melts and also into spheres and branched aggregates in the presence of free polymer chains. This work investigates structure and entanglement effects in composites of polystyrene-grafted iron oxide nanoparticles by measuring particle relaxations using X-ray photon correlation spectroscopy. Particles within highly ordered strings and aggregated systems experience a dynamically heterogeneous environment displaying hyperdiffusive relaxation commonly observed in jammed soft glassy systems. Furthermore, particle dynamics is diffusive for branched aggregated structures which could be caused by less penetration of long matrix chains into brushes. These results suggest that particle motion is dictated by the strong interactions of chains grafted at low density with the host matrix polymer.

Hyperdiffusive Dynamics in Newtonian Nanoparticle Fluids

Hyperdiffusive relaxations in soft glassy materials are typically associated with out-of-equilibrium states, and nonequilibrium physics and aging are often invoked in explaining their origins. Here, we report on hyperdiffusive motion in model soft materials comprised of single-component polymer-tethered nanoparticles, which exhibit a readily accessible Newtonian flow regime. In these materials, polymer-mediated interactions lead to strong nanoparticle correlations, hyperdiffusive relaxations, and unusual variations of properties with temperature. We propose that hyperdiffusive relaxations in such materials can arise naturally from nonequilibrium or non-Brownian volume fluctuations forced by equilibrium thermal rearrangements of the particle pair orientations corresponding to equilibrated shear modes.