Nanoparticle motion within glassy polymer melts

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.

Dynamics and yielding of binary self-suspended nanoparticle fluids

Yielding and flow transitions in bi-disperse suspensions of particles are studied using a model system comprised of self-suspended spherical nanoparticles. An important feature of the materials is that the nanoparticles are uniformly dispersed in the absence of a solvent. Addition of larger particles to a suspension of smaller ones is found to soften the suspensions, and in the limit of large size disparities, completely fluidizes the material. We show that these behaviors coincide with a speeding-up of de-correlation dynamics of all particles in the suspensions and are accompanied by a reduction in the energy dissipated at the yielding transition. We discuss our findings in terms of ligand-mediated jamming and un-jamming of hairy particle suspensions.

Simultaneous multiplexed materials characterization using a high-precision hard X-ray micro-slit array

The needs both for increased experimental throughput and for in operando characterization of functional materials under increasingly realistic experimental conditions have emerged as major challenges across the whole of crystallography. A novel measurement scheme that allows multiplexed simultaneous measurements from multiple nearby sample volumes is presented. This new approach enables better measurement statistics or direct probing of heterogeneous structure, dynamics or elemental composition. To illustrate, the submicrometer precision that optical lithography provides has been exploited to create a multiplexed form of ultra-small-angle scattering based X-ray photon correlation spectroscopy (USAXS-XPCS) using micro-slit arrays fabricated by photolithography. Multiplexed USAXS-XPCS is applied to follow the equilibrium dynamics of a simple colloidal suspension. While the dependence of the relaxation time on momentum transfer, and its relationship with the diffusion constant and the static structure factor, follow previous findings, this measurements-in-parallel approach reduces the statistical uncertainties of this photon-starved technique to below those associated with the instrument resolution. More importantly, we note the potential of the multiplexed scheme to elucidate the response of different components of a heterogeneous sample under identical experimental conditions in simultaneous measurements. In the context of the X-ray synchrotron community, this scheme is, in principle, applicable to all in-line synchrotron techniques. Indeed, it has the potential to open a new paradigm for in operando characterization of heterogeneous functional materials, a situation that will be even further enhanced by the ongoing development of multi-bend achromat storage ring designs as the next evolution of large-scale X-ray synchrotron facilities around the world.

Correlated heterogeneous dynamics in glass-forming polymers

We report x-ray photon correlation spectroscopy experiments on the dynamics of the glass-former polypropylene glycol covering a temperature range from room temperature to the glass transition at T(g)=205 K using silica tracer particles. Three temperature regimes are identified: At high temperatures, Brownian motion of the tracer particles is observed. Near T(g), the dynamics is hyperdiffusive and ballistic. Around 1.12T(g), we observe an intermediate regime. Here the stretching exponent of the Kohlrausch-Williams-Watts function becomes q dependent. By analyzing higher-order correlations in the scattering data, we find that dynamical heterogeneities dramatically increase in this intermediate-temperature regime. This leads to two effects: increasing heterogeneous dynamics and correlated motion at temperatures close to and below 1.12T(g).

Impact of small changes in particle surface chemistry for unentangled polymer nanocomposites

We report microstructural and rheological consequences of altering silica particle surface chemistry when the particles are suspended in unentangled polyethylene glycol with a molecular weight of 400. The particle surfaces are altered by reacting them with isobutyltrimethyoxysilane. Levels of silanization are chosen so that the particles remain dispersed in the polymer at all volume fractions studied. Our studies indicate that at the levels studied, silanization does not alter the hydrodynamic thickness of the absorbed polymer layer thickness. Rheological properties are not sensitive to levels of silanization up to particle volume fractions where the average particle separation h ∼ 6Rg (4.8 nm). At these volume fractions, composite microstructure undergoes changes associated with jamming of soft particles (decorrelations in the first peak of the particle structure factor and the onset of a non-diffusive mechanism that dominates particle density fluctuations at short times.) In the region of volume fractions where h/Rg < 6, the zero-shear rate viscosity of the composites is extremely sensitive to level of silanization with a decrease in the zero-shear rate viscosity by four orders of magnitude observed for the highest levels of silanization studied in comparison to the bare particles.

Kinetics of dispersion of nanoparticles in thin polymer films at high temperature

We report the first detailed study of the kinetics of dispersion of nanoparticles in thin polymer films using temperature dependent in situ X-ray scattering measurements. We show a comparably enhanced dispersion at higher temperatures for systems which are otherwise phase segregated at room temperature. Detailed analysis of the time dependent X-ray reflectivity and diffuse scattering data allows us to explore the out-of-plane and in-plane mobility of the nanoparticles in the polymer films. While the out-of-plane motion is diffusive with a diffusion coefficient almost two orders of magnitude lower than that expected in bulk polymer, the in-plane one is found to be super-diffusive resulting in significantly larger in-plane displacement at similar time scales. We discuss the origin of the observed highly anisotropic motion of nanoparticles due to their slaved motion with respect to the anisotropic chain orientation and consequent diffusivity anisotropy of matrix chains. We also suggest strategies to utilize these observations to kinetically improve dispersion in otherwise thermodynamically segregated polymer nanocomposite films.

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.

Structural and microscopic relaxations in a colloidal glass

The aging dynamics of a colloidal glass has been studied by multiangle dynamic light scattering, neutron spin echo, X-ray photon correlation spectroscopy and molecular dynamics simulations. The two relaxation processes, microscopic (fast) and structural (slow), have been investigated in an unprecedentedly wide range of time and length scales covering both ergodic and nonergodic regimes. The microscopic relaxation time remains diffusive at all length scales across the glass transition scaling with wavevector Q as Q(-2). The length-scale dependence of structural relaxation time changes from diffusive, characterized by a Q(-2)-dependence in the early stages of aging, to a Q(-1)-dependence in the full aging regime which marks a discontinuous hopping dynamics. Both regimes are associated with a stretched behaviour of the correlation functions. We expect these findings to provide a general description of both relaxations across the glass transition.

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.

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.

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.

Cobalt nanoparticles growth on a block copolymer thin film: a time-resolved GISAXS study

Cobalt sputter deposition on a nanostructured polystyrene-block-poly(ethylene oxide), P(S-b-EO), template is followed in real time with grazing incidence small-angle X-ray scattering (GISAXS). The polymer template consists of highly oriented parallel crystalline poly(ethylene oxide) (PEO) domains that are sandwiched between two polystyrene (PS) domains. In-situ GISAXS shows that cobalt atoms selectively decorate the PS domains of the microphase-separated polymer film and then aggregate to form surface metal nanopatterns. The polymer template is acting as a directing agent where cobalt metal nanowires are formed. At high metal load, the characteristic selectivity of the template is lost, and a uniform metal layer forms on the polymer surface. During the early stage of cobalt metal deposition, a highly asymmetric nanoparticles agglomeration is dominating structure formation. The cobalt nanoparticles mobility in combination with the high tendency of the nanoparticles to coalescence and to form immobile large-sized particles at the PS domains are discussed as mechanisms of structure formation.

Jamming behavior of domains in a spiral antiferromagnetic system

Using resonant magnetic x-ray photon correlation spectroscopy, we show that the domains of a spiral antiferromagnet enter a jammed state at the onset of long-range order. We find that the slow thermal fluctuations of the domain walls exhibit a compressed exponential relaxation with an exponent of 1.5 found in a wide variety of solidlike jammed systems and can be qualitatively explained in terms of stress release in a stressed network. As the temperature decreases, the energy barrier for fluctuations becomes large enough to arrest further domain wall fluctuations, and the domains freeze into a spatial configuration within 10 K of the Néel temperature. The relaxation times can be fitted with the Vogel-Fulcher law as observed in polymers, glasses, and colloids, thereby indicating that the dynamics of domain walls in an ordered antiferromagnet exhibit some of the universal features associated with jamming behavior.

Structure and transport anomalies in soft colloids

Anomalous trends in nanoparticle correlation and motion are reported in soft nanoparticle suspensions using static and dynamic x-ray scattering measurements. Contrary to normal expectations, we find that particle-particle correlations decrease and particle dynamics become faster as volume fraction rises above a critical particle loading associated with overlap. Our observations bear many similarities to the cascade of structural and transport anomalies reported for complex, network forming molecular fluids such as water, and are argued to share similar physical origins.

Structure and dynamics studies of concentrated micrometer-sized colloidal suspensions

We present an experimental study of the structural and dynamical properties of concentrated suspensions of different sized polystyrene microspheres dispersed in glycerol for volume fraction concentrations between 10% and 20%. The static structure, probed with ultrasmall-angle X-ray scattering, shows a behavior very similar to that of hard spheres. The equilibrium dynamics is probed with ultrasmall-angle X-ray scattering-X-ray photon correlation spectroscopy, a new technique that overcomes the limits of visible light-scattering techniques imposed by multiple scattering and is suitable for studies of optically opaque materials containing micrometer-sized structures. We found that the intensity autocorrelation functions are better described by a stretched exponential function and microspheres in a concentrated suspension move collectively. We also found that the inverse of the effective diffusion coefficients displays a peak with respect to the scattering vector that resembles the peaks in the static structure factors, which indicates that a long-lived, low free-energy state exists. The relaxation time is approximately inversely related to scattering vector, a behavior consistent with models that describe the dynamics in terms of random, local structural arrangements in disordered media.

Atomic-scale relaxation dynamics and aging in a metallic glass probed by x-ray photon correlation spectroscopy

We use x-ray photon correlation spectroscopy to investigate the structural relaxation process in a metallic glass on the atomic length scale. We report evidence for a dynamical crossover between the supercooled liquid phase and the metastable glassy state, suggesting different origins of the relaxation process across the transition. Furthermore, using different cooling rates, we observe a complex hierarchy of dynamic processes characterized by distinct aging regimes. Strong analogies with the aging dynamics of soft glassy materials, such as gels and concentrated colloidal suspensions, point at stress relaxation as a universal mechanism driving the relaxation dynamics of out-of-equilibrium systems.

Entanglement-controlled subdiffusion of nanoparticles within concentrated polymer solutions

We describe x-ray photon correlation spectroscopy (XPCS) experiments tracking the motion of gold nanoparticles within solutions of high-molecular-weight polystyrene. Over displacements from nanometers to tens of nanometers, the particles undergo subdiffusive motion that is dictated by the temporal evolution of the entangled polymer mesh in the immediate vicinity of the particles. The results thus provide a novel microscopic dynamical characterization of this key structural property of polymers and more broadly demonstrate the capability of XPCS-based microrheology to interrogate heterogeneous mechanical environments in nanostructured soft materials.

Mobility of Nonsticky Nanoparticles in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr2〉 of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr2 (t)〉 ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (〈Δr2 (t)〉 ~ t1/2) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ e of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ e ) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τrep. At longer times t > τrep, the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.

Direct measurement of microstructural avalanches during the martensitic transition of cobalt using coherent x-ray scattering

Heterogeneous microscale dynamics in the martensitic phase transition of cobalt is investigated with real-time x-ray scattering. During the transformation of the high-temperature face-centered cubic phase to the low-temperature hexagonal close-packed phase, the structure factor evolution suggests that an initial rapid local transformation is followed by a slower period during which strain relaxes. Coherent x-ray scattering measurements performed during the latter part of the transformation show that the kinetics is dominated by discontinuous sudden changes-avalanches. The spatial size of observed avalanches varies widely, from 100 nm to 10 μm, the size of the x-ray beam. An empirical avalanche amplitude quantifies this behavior, exhibiting a power-law distribution. The avalanche rate decreases with inverse time since the onset of the transformation.

Slow dynamics of a colloidal lamellar phase

We used x-ray photon correlation spectroscopy to study the dynamics in the lamellar phase of a platelet suspension as a function of the particle concentration. We measured the collective diffusion coefficient along the director of the phase, over length scales down to the interparticle distance, and quantified the hydrodynamic interaction between the particles. This interaction sets in with increasing concentration and can be described qualitatively by a simplified model. No change in the microscopic structure or dynamics is observed at the transition between the fluid and the gel-like lamellar phases.

A small-angle scattering chamber for x-ray photon correlation spectroscopy at low temperatures

A low temperature sample environment for x-ray photon correlation spectroscopy measurements in small-angle scattering geometry is presented. The chamber has been designed to allow investigations of dynamical phenomena in supercooled liquids and the typical working temperature range is 110-330 K with a thermal stability ΔT/T down to 10(-4). A variable external magnetic field up to 0.12 T can be applied, which is of interest in studies of, e.g., ferrofluids and liquid crystalline materials. Here, technical details about the sample environment are given together with examples of recent applications.

Slow dynamics in an azopolymer molecular layer studied by x-ray photon correlation spectroscopy

We report the results of x-ray photon correlation spectroscopy (XPCS) experiments on multilayers of a photosensitive azo-polymer which can be softened by photoisomerization. Time correlation functions have been measured at different temperatures and momentum transfers (q) and under different illumination conditions (dark, UV or visible). The correlation functions are well described by the Kohlrausch-Williams-Watts (KWW) form with relaxation times that are proportional to q(-1). The characteristic relaxation times follow the same Vogel-Fulcher-Tammann law describing the bulk viscosity of this polymer. The out-of-equilibrium relaxation dynamics following a UV photoperturbation are accelerated, which is in agreement with a fluidification effect previously measured by rheology. The transient dynamics are characterized by two times correlation function, and dynamical heterogeneity is evidenced by calculating the variance χ of the degree of correlation as a function of ageing time. A clear peak in χ appears at a well defined time τ(C) which scales with q(-1) and with the ageing time, in a similar fashion as previously reported in colloidal suspensions [O. Dauchot, Phys. Rev. Lett. 95, 265701 (2005)]. From an accurate analysis of the correlation functions we could demonstrate a temperature and light dependent cross-over from compressed KWW to simple exponential behavior.

Subdiffusion and intermittent dynamic fluctuations in the aging regime of concentrated hard spheres

We study the nonequilibrium aging dynamics in a system of quasihard spheres at large density by means of computer simulations. We find that, after a sudden quench to large density, the relaxation time initially increases exponentially with the age of the system. After a surprisingly large crossover time, the system enters the asymptotic aging regime characterized by a nearly linear increase in the relaxation time with age. In this aging regime, single-particle motion is strongly non-fickian, with a mean-squared displacement increasing subdiffusively, associated with broad non-gaussian tails in the distribution of particle displacements. We find that the system ages through temporally intermittent relaxation events, and a detailed finite-size analysis of these collective dynamic fluctuations reveals that these events are not spanning the entire system, but remain spatially localized.

Anomalous chain diffusion in polymer nanocomposites for varying polymer-filler interaction strengths

Anomalous diffusion of polymer chains in a polymer nanocomposite melt is investigated for different polymer-nanoparticle interaction strengths using stochastic molecular dynamics simulations. For spherical nanoparticles dispersed in a polymer matrix the results indicate that the chain motion exhibits three distinct regions of diffusion, the Rouse-like motion, an intermediate subdiffusive regime followed by a normal Fickian diffusion. The motion of the chain end monomers shows a scaling that can be attributed to the formation of strong "networklike" structures, which have been seen in a variety of polymer nanocomposite systems. Irrespective of the polymer-particle interaction strengths, these three regimes seem to be present with small deviations. Further investigation on dynamic structure factor shows that the deviations simply exist due to the presence of strong enthalpic interactions between the monomers with the nanoparticles, albeit preserving the anomaly in the chain diffusion. The time-temperature superposition principle is also tested for this system and shows a striking resemblance with systems near glass transition and biological systems with molecular crowding. The universality class of the problem can be enormously important in understanding materials with strong affinity to form either a glass, a gel or networklike structures.

Two-dimensional heterogeneous dynamics at the surface of a colloidal suspension

We report on an x-ray photon correlation spectroscopy experiment investigating the surface structure and dynamics of colloidal particles suspended in a supercooled viscous liquid. The static structure factor in the direction parallel and perpendicular to the surface reveals a more disordered structure at the surface as compared to the bulk. The particles display heterogeneous ballistic dynamics parallel to the surface. The particle dynamics in the direction perpendicular to the surface is much slower and does not show the hallmarks of ballistic motion.