Entanglement-controlled subdiffusion of nanoparticles within concentrated polymer solutions

Diffusion of Nanosheets in Unentangled Polymer Melts

Understanding the dynamics of nanosheets in polymer matrices is crucial for the processing of polymer nanocomposites and their applications in drug delivery. In this work, we investigate the diffusion of thin nanosheets in unentangled polymer melts using molecular dynamics simulations. We show that for nanosheets smaller than a characteristic size lc, which is a few times the polymer chain size, the continuum hydrodynamic theory based on macroscopic viscosity breaks down and significantly underestimates the diffusion coefficients. For nanosheets with sizes l < lc, we derive scaling relationships for both translational and rotational diffusion coefficients as functions of l and further reveal the dynamical coupling between nanosheet motion and the modes of the polymer melt. For l > lc, the continuum theory is recovered. Our findings reconcile the continuum and scaling theories for the diffusion of nanoparticles in polymer melts.

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 [Formula: see text], 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 [Formula: see text] 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.

Particle topology-regulated relaxation dynamics in cluster-ordering

The granular materials of soft particles (SPs) demonstrate unique viscoelasticity distinct from general colloidal and polymer systems. Exploiting dynamic light scattering measurements, together with molecular dynamics simulations, we study the diffusive dynamics of soft particle clusters (SPCs) with spherical and cylindrical brush topologies, respectively, in the melts of SPs. A topologically constrained relaxation theory is proposed by quantitatively correlating the relaxation time to the topologies of the SPCs, through the mean free space (Va) of tethered SPs in the cluster. The tethered SPs in SPCs are crowded by SPs of the melts to form the cage zones, and the cooperative diffusion of the tether SPs in the zones is required for the diffusive motion of SPCs. The cage zone serves as an entropic barrier for the diffusion of SP clusters, while its strength is determined by Va. Three characteristic modes can be confirmed: localized non-diffusive mode around critical Va, diffusive mode with Va deviating far from the critical value, and a sub-diffusive mode as an interlude between two limits. Our studies raise attention to the emergent physical properties of materials based on SPs via a topological design while opening new avenues for the design of soft structural 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.

Electro-optical Study of the Anomalous Rotational Diffusion in Polymer Solutions

Brownian diffusion of spherical nanoparticles is usually exploited to ascertain the rheological properties of complex media. However, the behavior of the tracer particles is affected by a number of phenomena linked to the interplay between the dynamics of the particles and polymer coils. For this reason, the characteristic lengths of the dispersed entities, depletion phenomena, and the presence of sticking conditions have been observed to affect the translational diffusion of the probes. On the other hand, the retardation effect of the host fluid on the rotational diffusion of nonspherical particles is less understood. We explore the possibility of studying this phenomenon by analyzing the electro-orientation of the particles in different scenarios in which we vary the ratio between the particle and polymer characteristic size, and the geometry of the particles, including both elongated and oblate shapes. We find that the Stokes-Einstein relation only applies if the radius of gyration of the polymer is much shorter than the particle size and when some repulsive interaction between both is present.

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

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

Crowding and confinement act in concert to slow DNA diffusion within cell-sized droplets

Dynamics of biological macromolecules, such as DNA, in crowded and confined environments are critical to understanding cellular processes such as transcription, infection, and replication. However, the combined effects of cellular confinement and crowding on macromolecular dynamics remain poorly understood. Here, we use differential dynamic microscopy to investigate the diffusion of large DNA molecules confined in cell-sized droplets and crowded by dextran polymers. We show that confined and crowded DNA molecules exhibit universal anomalous subdiffusion with scaling that is insensitive to the degree of confinement and crowding. However, effective DNA diffusion coefficients Deff decrease up to 2 orders of magnitude as droplet size decreases—an effect that is enhanced by increased crowding. We mathematically model the coupling of crowding and confinement by combining polymer scaling theories with confinement-induced depletion effects. The generality and tunability of our system and models render them applicable to elucidating wide-ranging crowded and confined systems.

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DNA diffusion measured in cell-sized droplets with differential dynamic microscopy

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Combination of crowding and confinement leads to subdiffusion and slowing

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Diffusion coefficients of DNA decrease strongly with decreasing droplet size

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Polymer scaling theories and depletion effects predict observed dynamics

Resolving molecular diffusion and aggregation of antibody proteins with megahertz X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) with megahertz repetition rate can provide novel insights into structural dynamics of biological macromolecule solutions. However, very high dose rates can lead to beam-induced dynamics and structural changes due to radiation damage. Here, we probe the dynamics of dense antibody protein (Ig-PEG) solutions using megahertz X-ray photon correlation spectroscopy (MHz-XPCS) at the European XFEL. By varying the total dose and dose rate, we identify a regime for measuring the motion of proteins in their first coordination shell, quantify XFEL-induced effects such as driven motion, and map out the extent of agglomeration dynamics. The results indicate that for average dose rates below 1.06 kGy μs^-1 in a time window up to 10 μs, it is possible to capture the protein dynamics before the onset of beam induced aggregation. We refer to this approach as correlation before aggregation and demonstrate that MHz-XPCS bridges an important spatio-temporal gap in measurement techniques for biological samples.

Molecular Simulation of Hopping Mechanisms of Nanoparticles in Regular Cross-Linked Polymer Networks

We use coarse-grained simulations to explore the diffusion mechanism of nanoparticles with different sizes at various nanoparticle-polymer interactions in regular cross-linked polymer networks. The long time diffusivities of nanoparticles show a non-monotonic tendency at various nanoparticle-polymer interactions, due to the intermittent hopping of nanoparticles through network cells. The preferred locations of small nanoparticles switch from the cell centers to the corner of cells as they interact with network more strongly, which results in the hopping energy barrier between different cells switching from cell center localization to adsorption on networks. Steric hindrance seriously hampers large nanoparticles from hopping to neighboring network cells, the interactions between nanoparticle and network enhance the network deformability and also affect the hopping of nanoparticles. The multiple constraint mechanisms result in the non-monotonic diffusivities of nanoparticles with different interactions and non-Brownian motions at different time scales. Our work illustrates the hopping mechanisms of nanoparticles in polymer networks from thermodynamic and dynamic points of view.

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.

Electrostatic Repulsion Slows Relaxations of Polyelectrolytes in Semidilute Solutions

We investigate the structure and dynamics of unentangled semidilute solutions of sodium polystyrenesulfonate (NaPSS) using small-angle neutron scattering (SANS) and neutron spin-echo (NSE) spectroscopy. The effects of electrostatic interactions and chain structure are examined as a function of ionic strength and polymer concentration, respectively. The SANS profiles exhibit a characteristic structural peak, signature of polyelectrolyte solutions, that can be fit with a combination of a semiflexible chain with excluded volume interactions form factor and a polymer reference interaction site model (PRISM) structure factor. We confirm that electrostatic interactions vary with ionic strength across solutions with similar geometries. The segmental relaxations from NSE deviate from theoretical predictions from Zimm and exhibit two scaling behaviors, with the crossover between the two regimes taking place around the characteristic structural peak. The chain dynamics are suppressed across the length scale of the correlation blob, and inversely related to the structure factor. These observations suggest that the highly correlated nature of polyelectrolytes presents an additional energy barrier that leads to de Gennes narrowing behavior.

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.

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

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

Molecular Characterization of Polymer Networks

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

Two modes of cluster dynamics govern the viscoelasticity of colloidal gels

Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.

Local Confinement Controls Diffusive Nanoparticle Dynamics in Semidilute Polyelectrolyte Solutions

We investigate the mobility of polystyrene particles ranging from 100 to 790 nm in diameter in dilute and semidilute sodium polystyrene sulfonate (NaPSS) solutions using fluorescence microscopy. We tune the polymer conformations by varying the ionic strength of the solution. The nanoparticle mean-squared displacements evolve linearly with time at all time scales, indicating Fickian diffusive dynamics. In solutions of high ionic strength, chains adopt a random walk conformation and particle dynamics couple to the bulk zero-shear rate viscosity, according to the Stokes-Einstein picture. In solutions of low ionic strength, however, particle dynamics nonmonotonically deviate from bulk predictions as polymer concentration increases and are not accurately predicted by the available models. These nonmonotonic dynamics directly correlate with the non-Gaussianity in distributions of particle displacements, suggesting the emergence of a local confining length scale as polyelectrolyte concentration increases.

Influence of TMAO as co-solvent on the gelation of silica-PNIPAm core-shell nanogels at intermediate volume fractions

We study the structure and dynamics of poly(N-isopropylacrylamide) (PNIPAm) core-shell nanogels dispersed in aqueous trimethylamine N-oxide (TMAO) solutions by means of small-angle X-ray scattering and X-ray photon correlation spectroscopy (XPCS). Upon increasing the temperature above the lower critical solution temperature of PNIPAm at 33 °C, a colloidal gel is formed as identified by an increase of I(q) at small q as well as a slowing down of sample dynamics by various orders of magnitude. With increasing TMAO concentration the gelation transition shifts linearly to lower temperatures. Above a TMAO concentration of approximately 0.40 mol/L corresponding to a 1 : 1 ratio of TMAO and NIPAm groups, collapsed PNIPAm states are found for all temperatures without any gelation transition. This suggests that reduction of PNIPAm-water hydrogen bonds due to the presence of TMAO results in a stabilisation of the collapsed PNIPAm state and suppresses gelation of the nanogel.

Defect-targeted self-healing of multiscale damage in polymers

Self-healing materials capable of restoring functionality in response to damage are expected to gain prolonged service lifespan. Yet the ability to repair damage of diverse length scales which is demanded for the survival of highly capricious and uncontrolled damage modes has not been demonstrated with current self-healing approaches. Herein the repeatable self-healing of multiscale damage ranging from nanometer to millimeter is achieved in thermoplastic polymers through defect-targeted heating and welding. The key to the ability to deal with multiscale damage is the automatic and targeted transport and assembly of superparamagnetic nanoparticles toward the defect site. This allows the concentrated nanoparticles to deliver a high heating power under an oscillating magnetic field and locally fuse the matrix, whereas the overall dimensional integrity of the material is well preserved. Moreover, as the polymer melt drives progressively into the open volume of the crack, the nanoparticles keep migrating with the edge of the crack until the fractured portions are united. The cracking-healing cycle can be repeated 100 times with a constantly high healing efficiency above 95%. This work sheds light on the new design of self-healing materials where the ability to deal with complex damage modes represents a key merit to prompt real-world applications.

Three dimensional spatiotemporal nano-scale position retrieval of the confined diffusion of nano-objects inside optofluidic microstructured fibers

Understanding the dynamics of single nano-scale species at high spatiotemporal resolution is of utmost importance within fields such as bioanalytics or microrheology. Here we introduce the concept of axial position retrieval via scattered light at evanescent fields inside a corralled geometry using optofluidic microstructured optical fibers allowing to unlock information about diffusing nano-scale objects in all three spatial dimensions at kHz acquisition rate for several seconds. Our method yields the lateral positions by localizing the particle in a wide-field microscopy image. In addition, the axial position is retrieved via the scattered light intensity of the particle, as a result of the homogenized evanescent fields inside a microchannel running parallel to an optical core. This method yields spatial localization accuracies <3 nm along the transverse and <21 nm along the retrieved directions. Due to its unique properties such as three dimensional tracking, straightforward operation, mechanical flexibility, strong confinement, fast and efficient data recording, long observation times, low background scattering, and compatibility with microscopy and fiber circuitry, our concept represents a new paradigm in light-based nanoscale detection techniques, extending the capabilities of the field of nanoparticle tracking analysis and potentially allowing for the observation of so far inaccessible processes at the nanoscale level.

Nanoscale viscosity of confined polyethylene oxide

Complex fluids near interfaces or confined within nanoscale volumes can exhibit substantial shifts in physical properties compared to bulk, including glass transition temperature, phase separation, and crystallization. Because studies of these effects typically use thin film samples with one dimension of confinement, it is generally unclear how more extreme spatial confinement may influence these properties. In this work, we used x-ray photon correlation spectroscopy and gold nanoprobes to characterize polyethylene oxide confined by nanostructured gratings (<100nm width) and measured the viscosity in this nanoconfinement regime to be ∼500 times the bulk viscosity. This enhanced viscosity occurs even when the scale of confinement is several times the polymer's radius of gyration, consistent with previous reports of polymer viscosity near flat interfaces.

Spatial Dependence of Non-Gaussian Diffusion of Nanoparticles in Free-Standing Thin Polymer Films

The addition of nanoparticles (NPs) to a free-standing polymer film affects the properties of the film such as viscosity and glass transition temperature. Recent experiments, for example, showed that the glass transition temperature of thin polymer films was dependent on how NPs were distributed within the polymer films. However, the spatial arrangement of NPs in free-standing polymer films and its effect on the diffusion of NPs and polymers remain elusive at a molecular level. In this study, we employ generic coarse-grained models for polymers and NPs and perform extensive molecular dynamics simulations to investigate the diffusion of polymers and NPs in free-standing thin polymer films. We find that small NPs are likely to stay at the interfacial region of the polymer film, while large NPs tend to stay at the center of the film. On the other hand, as the interaction between a NP and a monomer becomes more attractive, the NP is more likely to be placed at the film center. The diffusion of monomers slows down slightly as more NPs are added to the film. Interestingly, the NP diffusion is dependent strongly on the spatial arrangement of the NPs: NPs at the interfacial region diffuse faster and undergo more non-Gaussian diffusion than NPs at the film center, which implies that the interfacial region would be more mobile and dynamically heterogeneous than the film center. We also find that the mechanism for non-Gaussian diffusion of NPs at the film center differs from that at the interfacial region and that the NP diffusion would reflect the local viscosity of the polymer films.

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.

Soft Interactions Modify the Diffusive Dynamics of Polymer-Grafted Nanoparticles in Solutions of Free Polymer

We examine the dynamics of silica particles grafted with high molecular weight polystyrene suspended in semidilute solutions of chemically similar linear polymer using X-ray photon correlation spectroscopy. The particle dynamics decouple from the bulk viscosity despite their large hydrodynamic size and instead experience an effective viscosity that depends on the molecular weight of the free polymer chains. Unlike for hard-sphere nanoparticles in semidilute polymer solutions, the diffusivities of the polymer-grafted nanoparticles do not collapse onto a master curve solely as a function of normalized length scales. Instead, the diffusivities can be collapsed across two orders of magnitude in free polymer molecular weight and concentration and one order of magnitude in grafted molecular weight by incorporating the ratio of free to grafted polymer molecular weights. These results suggest that the soft interaction potential between polymer-grafted nanoparticles and free polymer allows polymer-grafted nanoparticles to diffuse faster than predicted based on bulk rheology and modifies the coupling between grafted particle dynamics and the relaxations of the surrounding free polymer.

Driven spheres, ellipsoids and rods in explicitly modeled polymer solutions

Understanding the transport of driven nano- and micro-particles in complex fluids is of relevance for many biological and technological applications. Here we perform hydrodynamic multiparticle collision dynamics simulations of spherical and elongated particles driven through polymeric fluids containing different concentrations of polymers. We determine the mean particle velocities which are larger than expected from Stokes law for all particle shapes and polymer densities. Furthermore we measure the fluid flow fields and local polymer density and polymer conformation around the particles. We find that polymer-depleted regions close to the particles are responsible for an apparent tangential slip velocity which accounts for the measured flow fields and transport velocities. A simple two-layer fluid model gives a good match to the simulation results.

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.

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.

Dynamics of soft nanoparticle suspensions at hard X-ray FEL sources below the radiation-damage threshold

The application of X-ray photon correlation spectroscopy (XPCS) at free-electron laser (FEL) facilities enables, for the first time, the study of dynamics on a (sub-)nanometre scale in an unreached time range between femtoseconds and seconds. For soft-matter materials, radiation damage is a major limitation when going beyond single-shot applications. Here, an XPCS study is presented at a hard X-ray FEL on radiation-sensitive polymeric poly(N-isopropylacrylamide) (PNIPAM) nanoparticles. The dynamics of aqueous suspensions of densely packed silica-PNIPAM core-shell particles and a PNIPAM nanogel below the radiation-damage threshold are determined. The XPCS data indicate non-diffusive behaviour, suggesting ballistic and stress-dominated heterogeneous particle motions. These results demonstrate the feasibility of XPCS experiments on radiation-sensitive soft-matter materials at FEL sources and pave the way for future applications at MHz repetition rates as well as ultrafast modes using split-pulse devices.

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.

Interfacial Properties and Hopping Diffusion of Small Nanoparticle in Polymer/Nanoparticle Composite with Attractive Interaction on Side Group

The diffusion dynamics of fullerene (C 60 ) in unentangled linear atactic polystyrene (PS) and polypropylene (PP) melts and the structure and dynamic properties of polymers in interface area are investigated by performing all-atom molecular dynamics simulations. The comparison of the results in two systems emphasises the influence of local interactions exerted by polymer side group on the diffusion dynamics of the nanoparticle. In the normal diffusive regime at long time scales, the displacement distribution function (DDF) follows a Gaussian distribution in PP system, indicating a normal diffusion of C 60 . However, we observe multiple peaks in the DDF curve for C 60 diffusing in PS melt, which indicates a diffusion mechanism of hopping of C 60 . The attractive interaction between C 60 and phenyl ring side groups are found to be responsible for the observed hopping diffusion. In addition, we find that the C 60 is dynamically coupled with a subsection of a tetramer on PS chain, which has a similar size with C 60 . The phenyl ring on PS chain backbone tends to have a parallel configuration in the vicinity of C 60 surface, therefore neighbouring phenyl rings can form chelation effect on the C 60 surface. Consequently, the rotational dynamics of phenyl ring and the translational diffusion of styrene monomers are found to be slowed down in this interface area. We hope our results can be helpful for understanding of the influence of the local interactions on the nanoparticle diffusion dynamics and interfacial properties in polymer/nanoparticle composites.

Nanorheology of Entangled Polymer Melts

We use molecular simulations to probe the local viscoelasticity of an entangled polymer melt by tracking the motion of embedded nonsticky nanoparticles (NPs). As in conventional microrheology, the generalized Stokes-Einstein relation is employed to extract an effective stress relaxation function G_{GSE}(t) from the mean square displacement of NPs. G_{GSE}(t) for different NP diameters d are compared with the stress relaxation function G(t) of a pure polymer melt. The deviation of G_{GSE}(t) from G(t) reflects the incomplete coupling between NPs and the dynamic modes of the melt. For linear polymers, a plateau in G_{GSE}(t) emerges as d exceeds the entanglement mesh size a and approaches the entanglement plateau in G(t) for a pure melt with increasing d. For ring polymers, as d increases towards the spanning size R of ring polymers, G_{GSE}(t) approaches G(t) of the ring melt with no entanglement plateau.

Transient anomalous diffusion regimes in reversible adsorbing systems

A solvable, minimal model of diffusion in the presence of a reversible adsorption site is investigated. We show that the diffusive particles are influenced by the adsorbing site on transient times when they have anomalous subdiffusive behavior. However, the particle dispersion law crosses over to the normal diffusive regime on asymptotically long times. The subdiffusive regime is characterized by a t^{1/4} transient scaling with the same exponent as for the irreversible adsorption. On this transient time scale dominated by particle adsorption, there is a depletion of particles near the adsorbing site, and the typical width of the depletion zone grows in time as t^{1/4} with the same exponent as the subdiffusive dispersion. We show that having a nonzero desorption probability for the adsorbed particles produces a crossover towards normal diffusion on time scales larger than a characteristic reactive time, which we show scales with diffusivity and the adsorption site reactivity.

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.

The effect of hydrodynamic interactions on nanoparticle diffusion in polymer solutions: a multiparticle collision dynamics study

The diffusion of nanoparticles (NPs) in polymer solutions is studied by a combination of a mesoscale simulation method, multiparticle collision dynamics (MPCD), and molecular dynamics (MD) simulations. We investigate the long-time diffusion coefficient D as well as the subdiffusive behavior in the intermediate time region. The dependencies of both D and subdiffusion factor α on NP size and polymer concentration, respectively, are explicitly calculated. Particular attention is paid to the role of hydrodynamic interaction (HI) in the NP diffusion dynamics. Our simulation results show that the long-time diffusion coefficients satisfy perfectly the scaling relation found by experimental observations. Meanwhile, the subdiffusive factor decreases with the increase in polymer concentration but is of little relevance to the NP size. By parallel simulations with and without HI, we reveal that HI will generally enhance D, while the enhancement effect is non-monotonous with increasing polymer concentration, and it becomes most pronounced at semidilute concentrations. With the aid of a scaling law based on the diffusive activation energy model, we understand that HI affects diffusion through decreasing the diffusive activation energy on the one hand while increasing the effective diffusion size on the other. In addition, HI will certainly influence the subdiffusive behavior of the NP, leading to a larger subdiffusion exponent.