Entanglement-controlled subdiffusion of nanoparticles within concentrated polymer solutions

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.

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.

Nanoparticle Motion in Entangled Melts of Linear and Nonconcatenated Ring Polymers

The motion of nanoparticles (NPs) in entangled melts of linear polymers and nonconcatenated ring polymers are compared by large-scale molecular dynamics simulations. The comparison provides a paradigm for the effects of polymer architecture on the dynamical coupling between NPs and polymers in nanocomposites. Strongly suppressed motion of NPs with diameter d larger than the entanglement spacing a is observed in a melt of linear polymers before the onset of Fickian NP diffusion. This strong suppression of NP motion occurs progressively as d exceeds a and is related to the hopping diffusion of NPs in the entanglement network. In contrast to the NP motion in linear polymers, the motion of NPs with d > a in ring polymers is not as strongly suppressed prior to Fickian diffusion. The diffusion coefficient D decreases with increasing d much slower in entangled rings than in entangled linear chains. NP motion in entangled nonconcatenated ring polymers is understood through a scaling analysis of the coupling between NP motion and the self-similar entangled dynamics of ring polymers.

Multiscale Molecular Simulations of Polymer-Matrix Nanocomposites: or What Molecular Simulations Have Taught us About the Fascinating Nanoworld

Following the substantial progress in molecular simulations of polymer-matrix nanocomposites, now is the time to reconsider this topic from a critical point of view. A comprehensive survey is reported herein providing an overview of classical molecular simulations, reviewing their major achievements in modeling polymer matrix nanocomposites, and identifying several open challenges. Molecular simulations at multiple length and time scales, working hand-in-hand with sensitive experiments, have enhanced our understanding of how nanofillers alter the structure, dynamics, thermodynamics, rheology and mechanical properties of the surrounding polymer matrices.

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.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

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.

2D dynamical arrest transition in a mixed nanoparticle-phospholipid layer studied in real and momentum spaces

We investigate the interfacial dynamics of a 2D self-organized mixed layer made of silica nanoparticles interacting with phospholipid (DPPC) monolayers at the air/water interface. This system has biological relevance, allowing investigation of toxicological effects of nanoparticles on model membranes and lung surfactants. It might also provide bio-inspired technological solutions, exploiting the self-organization of DPPC to produce a non-trivial 2D structuration of nanoparticles. The characterization of interfacial dynamics yields information on the effects of NPs on the mechanical properties, important to improve performances of systems such as colloidosomes, foams, creams. For this, we combine micro-tracking in real-space with measurement in momentum-space via x-ray photon-correlation spectroscopy and Digital Fourier Microscopy. Using these complementary techniques, we extend the spatial range of investigation beyond the limits of each one. We find a dynamical transition from Brownian diffusion to an arrested state driven by compression, characterized by intermittent rearrangements, compatible with a repulsive glass phase. The rearrangement and relaxation of the monolayer structure results dramatically hindered by the presence of NPs, which is relevant to explain some the mechanical features observed for the dynamic surface pressure response of these systems and which can be relevant for the respiratory physiology and for future drug-delivery composite systems.

Sequential Single Shot X-ray Photon Correlation Spectroscopy at the SACLA Free Electron Laser

Hard X-ray free electron lasers allow for the first time to access dynamics of condensed matter samples ranging from femtoseconds to several hundred seconds. In particular, the exceptional large transverse coherence of the X-ray pulses and the high time-averaged flux promises to reach time and length scales that have not been accessible up to now with storage ring based sources. However, due to the fluctuations originating from the stochastic nature of the self-amplified spontaneous emission (SASE) process the application of well established techniques such as X-ray photon correlation spectroscopy (XPCS) is challenging. Here we demonstrate a single-shot based sequential XPCS study on a colloidal suspension with a relaxation time comparable to the SACLA free-electron laser pulse repetition rate. High quality correlation functions could be extracted without any indications for sample damage. This opens the way for systematic sequential XPCS experiments at FEL sources.

Size-Dependent Dynamics of Nanoparticles in Unentangled Polyelectrolyte Solutions

The mobility of polystyrene nanoparticles ranging in diameter from 300 nm to 2 μm was measured in dilute and semidilute solutions of partially hydrolyzed polyacrylamide. In this model system, the ratio of particle to polymer size controls the long-time diffusivity of nanoparticles. The particle dynamics transition from subdiffusive on short time scales to Fickian on long time scales, qualitatively similar to predictions for polymer dynamics using a Rouse model. The diffusivities extracted from the long-time Fickian regime, however, are larger than those predicted by the Stokes-Einstein equation and the bulk zero-shear viscosity and moreover do not collapse according to hydrodynamic models. The size-dependent deviations of the long-time particle diffusivities derive instead from the coupling between the dynamics of the particle and the polymer over the length scale of the particle. Although the long-time diffusivities collapse according to predictions, deviations of the short-time scaling exponents and the crossover time between subdiffusive and Fickian dynamics indicate that the particles are only partially coupled to the relaxation modes of the polymer.

Active one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation

We present molecular dynamics simulations for active one-particle microrheology of an unentangled polymer melt. The tracer particle is forced to oscillate by an oscillating harmonic potential, which models an experiment using optical tweezers. The amplitude and phase shift of this oscillation are related to the complex shear modulus of the polymer melt. In the linear response regime at low frequencies, the active microrheology gives the same result as the passive microrheology, where the thermal motion of a tracer particle is related to the complex modulus. We expand the analysis to include full hydrodynamic effects instead of stationary Stokes friction only, and show that different approaches suggested in the literature lead to completely different results, and that none of them improves on the description using the stationary Stokes friction.

Hopping Diffusion of Nanoparticles in Polymer Matrices

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size ax of unentangled polymer networks or tube diameter ae of entangled polymer liquids are trapped by the network or entanglement cells. At long time scales, however, these particles can diffuse by overcoming free energy barrier between neighboring confinement cells. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size moderately larger than the network mesh size ax or tube diameter ae . Much larger particles in polymer solids will be permanently trapped by local network cells, whereas they can still move in polymer liquids by waiting for entanglement cells to rearrange on the relaxation time scales of these liquids. Hopping diffusion in entangled polymer liquids and networks has a weaker dependence on particle size than that in unentangled networks as entanglements can slide along chains under polymer deformation. The proposed novel hopping model enables understanding the motion of large nanoparticles in polymeric nanocomposites and the transport of nano drug carriers in complex biological gels such as mucus.

X-ray photon correlation spectroscopy

In recent years, X-ray photon correlation spectroscopy (XPCS) has emerged as one of the key probes of slow nanoscale fluctuations, applicable to a wide range of condensed matter and materials systems. This article briefly reviews the basic principles of XPCS as well as some of its recent applications, and discusses some novel approaches to XPCS analysis. It concludes with a discussion of the future impact of diffraction-limited storage rings on new types of XPCS experiments, pushing the temporal resolution to nanosecond and possibly even picosecond time scales.

Passive one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation

We present a molecular dynamics simulation study of the possibility of performing a microrheological analysis of a polymer melt by following the Brownian motion of a dispersed nanoparticle. We study the influence of the size of the nanoparticle, taken to be comparable to the radius of gyration of the chains, and of the strength of the interaction between the nanoparticle and the repeat units of the polymer chains. The influence of the presence of the nanoparticle on the melt mechanical behavior is analyzed, and the importance of effects of different levels of hydrodynamic analysis on the frequency-dependent dynamic shear modulus derived from the particle motion is worked out.

Silica nanoparticles as tracers of the gelation dynamics of a natural biopolymer physical gel

The gelation of methylcellulose in water has been studied by X-ray photon correlation spectroscopy, electrophoresis and rheological measurements by looking into the dynamics of silica nanoparticles as tracers in the polymer matrix. The temperature and scattering vector dependence of the structural relaxation time is investigated at the nanometric length scale during the formation of the strong gel state. We find a stress-dominated dynamics on approaching the gel state, characterized by a hyper-diffusive motion of the silica particles. These results support the idea of a unifying scenario for the dynamics of complex out of equilibrium soft materials.

Controlling the dynamics of a bidimensional gel above and below its percolation transition

The morphology and the microscopic internal dynamics of a bidimensional gel formed by spontaneous aggregation of gold nanoparticles confined at the water surface are investigated by a suite of techniques, including grazing-incidence x-ray photon correlation spectroscopy (GI-XPCS). The range of concentrations studied spans across the percolation transition for the formation of the gel. The dynamical features observed by GI-XPCS are interpreted in view of the results of microscopic imaging; an intrinsic link between the mechanical modulus and internal dynamics is demonstrated for all the concentrations. Our work presents an example of a transition from a stretched to a compressed correlation function actively controlled by quasistatically varying the relevant thermodynamic variable. Moreover, by applying a model proposed some time ago by Duri and Cipelletti [Europhys. Lett. 76, 972 (2006)] we are able to build a master curve for the shape parameter, whose scaling factor allows us to quantify a "long-time displacement length." This characteristic length is shown to converge, as the concentration is increased, to the "short-time localization length" determined by pseudo-Debye-Waller analysis of the initial contrast. Finally, the intrinsic dynamics of the system is then compared with that induced by means of a delicate mechanical perturbation applied to the interface.

Nanoparticle diffusion in polymer nanocomposites

Large-scale molecular dynamics simulations show that nanoparticle (NP) diffusivity in weakly interacting mixtures of NPs and polymer melts has two very different classes of behavior depending on their size. NP relaxation times and their diffusivities are completely described by the local, Rouse dynamics of the polymer chains for NPs smaller than the polymer entanglement mesh size. The motion of larger NPs, which are comparable to the entanglement mesh size, is significantly slowed by chain entanglements, and is not describable by the Stokes-Einstein relationship. Our results are in essentially quantitative agreement with a force-level generalized Langevin equation theory for all the NP sizes and chain lengths explored, and imply that for these lightly entangled systems, activated NP hopping is not important.

Dynamical crossover between hyperdiffusion and subdiffusion of polymer-grafted nanoparticles in a polymer matrix

The dynamical behavior of polystyrene-grafted silica nanoparticles dispersed in an atactic polystyrene matrix was studied using x-ray photon correlation spectroscopy. The time-autocorrelation functions were subjected to fitting analyses based on continuous-time random walk models. The nanoparticles exhibited non-Brownian behavior, and as the temperature increased, the crossover from hyperdiffusion to subdiffusion occurred at 1.25T_{g}, where T_{g} is the glass transition temperature of the matrix polystyrene. Hyperdiffusive behavior is caused by the dynamical heterogeneity of the polymer matrix associated with the glass transition. When the temperature was higher than 1.25T_{g}, the interaction of the grafted polymers with the polymer matrix became relatively significant, and caused a dramatic change in the dynamical behavior of the nanoparticles.

Direction dependent diffusion of aligned magnetic rods by means of x-ray photon correlation spectroscopy

Rodlike hematite particles in suspension align perpendicular to an external magnetic field due to a negative anisotropy of their magnetic susceptibility Δχ. The diffusion tensor consists of two principal constants D(∥) and D(⊥) for the diffusion parallel and perpendicular to the long particle axis. X-ray photon correlation spectroscopy is capable of probing the diffusive motion in optically opaque suspensions of rodlike hematite particles parallel to the direction of the scattering vector Q. Choosing Q parallel or perpendicular to the direction of an external magnetic field H the direction dependent intermediate scattering function is measured by means of x-ray photon correlation spectroscopy. From the intermediate scattering function in both directions the principal diffusion constants D(∥) and D(⊥) are determined. The ratio D(∥)/D(⊥) increases with increasing aspect ratio of the particles and can be described via a rescaled theoretical approach for prolate ellipsoids of revolution.