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

Experimental probing of dynamic self-organized columnar assemblies in colloidal liquid crystals

Self-organized supramolecular assemblies are widespread in nature and technology in the form of liquid crystals, colloids, and gels. The reversible nature of non-covalent bonding leads to dynamic functions such as stimuli-responsive switching and self-healing, which are unachievable from an isolated molecule. However, multiple intermolecular interactions generate diverse conformational and configurational molecular motions over various time scales in their self-assembled states, and their specific dynamics remains unclear. In the present study, we have experimentally unveiled the static structures and dynamical behaviors in columnar colloidal liquid crystals by a coherent X-ray scattering technique using refined model samples. We have found that controlling the size distribution of the colloidal nanoplates dramatically changed their static and dynamic properties. Furthermore, the resulting dynamical behaviors obtained by X-ray photon correlation spectroscopy have been successfully decomposed into multiple distinct modes, allowing us to explore the dynamical origin in the colloidal liquid-crystalline state. The present approaches using a columnar liquid crystal may contribute to a better understanding of the dynamic nature of molecular assemblies and dense colloidal systems and bring valuable insights into rational design of functional properties of self-assembled materials such as stimuli-responsive liquid crystals, self-healing gels, and colloidal crystals. For these materials, the motion of constituent particles and molecules in the self-assembled state is a key factor for structural formation and dynamically responsive performance.

Using coherent X-rays to follow dynamics in amorphous ices

Amorphous solid water plays an important role in our overall understanding of water's phase diagram. X-ray scattering is an important tool for characterising the different states of water, and modern storage ring and XFEL facilities have opened up new pathways to simultaneously study structure and dynamics. Here, X-ray photon correlation spectroscopy (XPCS) was used to study the dynamics of high-density amorphous (HDA) ice upon heating. We follow the structural transition from HDA to low-density amorphous (LDA) ice, by using wide-angle X-ray scattering (WAXS), for different heating rates. We used a new type of sample preparation, which allowed us to study μm-sized ice layers rather than powdered bulk samples. The study focuses on the non-equilibrium dynamics during fast heating, spontaneous transformation and crystallization. Performing the XPCS study at ultra-small angle (USAXS) geometry allows us to characterize the transition dynamics at length scales ranging from 60 nm-800 nm. For the HDA-LDA transition we observe a clear separation in three dynamical regimes, which show different dynamical crossovers at different length scales. The crystallization from LDA, instead, is observed to appear homogenously throughout the studied length scales.

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.

Interaction between Filler and Polymeric Matrix in Nanocomposites: Magnetic Approach and Applications

In recent years, polymer nanocomposites produced by combining nanofillers and a polymeric matrix are emerging as interesting materials. Polymeric composites have a wide range of applications due to the outstanding and enhanced properties that are obtained thanks to the introduction of nanoparticles. Therefore, understanding the filler-matrix relationship is an important factor in the continued growth of this scientific area and the development of new materials with desired properties and specific applications. Due to their performance in response to a magnetic field magnetic nanocomposites represent an important class of functional nanocomposites. Due to their properties, magnetic nanocomposites have found numerous applications in biomedical applications such as drug delivery, theranostics, etc. This article aims to provide an overview of the filler-polymeric matrix relationship, with a special focus on magnetic nanocomposites and their potential applications in the biomedical field.

Application of Synchrotron Radiation X-ray Scattering and Spectroscopy to Soft Matter

Light produced by synchrotron radiation (SR) is much brighter than that produced by conventional laboratory X-ray sources. The photon energy of SR X-ray ranges from soft and tender X-rays to hard X-rays. Moreover, X-rays become element sensitive with decreasing photon energy. By using a wide energy range and high-quality light of SR, different scattering and spectroscopic methods were applied to various soft matters. We present five of our recent studies performed using specific light properties of a synchrotron facility, which are as follows: (1) In situ USAXS study to understand the deformation behavior of colloidal crystals during uniaxial stretching; (2) structure characterization of semiconducting polymer thin films along the film thickness direction by grazing-incidence wide-angle X-ray scattering using tender X-rays; (3) X-ray absorption fine structure (XAFS) analysis of the formation mechanism of poly(3-hexylthiophene) (P3HT); (4) soft X-ray absorption and emission spectroscopic analysis of water structure in polyelectrolyte brushes; and (5) X-ray photon correlation spectroscopic analysis of the diffusion behavior of polystyrene-grafted nanoparticles dispersed in a polystyrene matrix.

Dynamical Heterogeneity near Glass Transition Temperature under Shear Conditions

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

Anomalous Dynamics of Concentrated Silica-PNIPAm Nanogels

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

Nanoscale Particle Motion Reveals Polymer Mobility Gradient in Nanocomposites

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

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.

Tuning the Relaxation of Nanopatterned Polymer Films with Polymer-Grafted Nanoparticles: Observation of Entropy-Enthalpy Compensation

Polymer films provide a versatile platform in which complex functional relief patterns can be thermally imprinted with a resolution down to few nanometers. However, a practical limitation of this method is the tendency for the imprinted patterns to relax ("slump"), leading to loss of pattern fidelity over time. While increasing temperature above glass transition temperature ( Tg) accelerates the slumping kinetics of neat films, we find that the addition of polymer-grafted nanoparticles (PGNP) can greatly enhance the thermal stability of these patterns. Specifically, increasing the concentration of poly(methyl methacrylate) (PMMA) grafted titanium dioxide (TiO2) nanoparticles in the composite films slows down film relaxation dynamics, leading to enhanced pattern stability for the temperature range that we investigated. Interestingly, slumping relaxation time is found to obey an entropy-enthalpy compensation (EEC) relationship with varying PGNP concentration, similar to recently observed relaxation of strain-induced wrinkling in glassy polymer films having variable film thickness. The compensation temperature,  Tcomp was found to be in the vicintity of the bulk  Tg of PMMA. Our results suggest a common origin of EEC relaxation in patterned polymer thin films and  nanocomposites.

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.

Grafted polymer chains suppress nanoparticle diffusion in athermal polymer melts

We measure the center-of-mass diffusion of poly(methyl methacrylate) (PMMA)-grafted nanoparticles (NPs) in unentangled to slightly entangled PMMA melts using Rutherford backscattering spectrometry. These grafted NPs diffuse ∼100 times slower than predicted by the Stokes-Einstein relation assuming a viscosity equal to bulk PMMA and a hydrodynamic NP size equal to the NP core diameter, 2R_core = 4.3 nm. This slow NP diffusion is consistent with an increased effective NP size, 2R_eff ≈ 20 nm, nominally independent of the range of grafting density and matrix molecular weights explored in this study. Comparing these experimental results to a modified Daoud-Cotton scaling estimate for the brush thickness as well as dynamic mean field simulations of polymer-grafted NPs in athermal polymer melts, we find that 2R_eff is in quantitative agreement with the size of the NP core plus the extended grafted chains. Our results suggest that grafted polymer chains of moderate molecular weight and grafting density may alter the NP diffusion mechanism in polymer melts, primarily by increasing the NP effective size.

Altering surface fluctuations by blending tethered and untethered chains

"Partially tethering" a thin film of a polymer melt by covalently attaching to the substrate a fraction of the chains in an unentangled melt dramatically increases the relaxation time of the surface height fluctuations. This phenomenon is observed even when the film thickness, h, is 20 times the unperturbed chain radius, R_g,tethered, of the tethered chains, indicating that partial tethering is more influential than any physical attraction with the substrate. Furthermore, a partially tethered layer of a low average molecular weight of 5k showed much slower surface fluctuations than did a reference layer of pure untethered chains of much greater molecular weight (48k), so the partial tethering effect is stronger than the effects of entanglement and increase in glass transition temperature, T_g, with molecular weight. Partial tethering offers a means of tailoring these fluctuations which influence wetting, adhesion, and tribology of the surface.

Particle localization and hyperuniformity of polymer-grafted nanoparticle materials

The properties of materials largely reflect the degree and character of the localization of the molecules comprising them so that the study and characterization of particle localization has central significance in both fundamental science and material design. Soft materials are often comprised of deformable molecules and many of their unique properties derive from the distinct nature of particle localization. We study localization in a model material composed of soft particles, hard nanoparticles with grafted layers of polymers, where the molecular characteristics of the grafted layers allow us to "tune" the softness of their interactions. Soft particles are particular interesting because spatial localization can occur such that density fluctuations on large length scales are suppressed, while the material is disordered at intermediate length scales; such materials are called "disordered hyperuniform". We use molecular dynamics simulation to study a liquid composed of polymer-grafted nanoparticles (GNP), which exhibit a reversible self-assembly into dynamic polymeric GNP structures below a temperature threshold, suggesting a liquid-gel transition. We calculate a number of spatial and temporal correlations and we find a significant suppression of density fluctuations upon cooling at large length scales, making these materials promising for the practical fabrication of "hyperuniform" materials.

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.

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).