Nanoparticles In Polymer Melts Research Articles

Solvation Free Energy of Dilute Grafted (Nano)Particles in Polymer Melts via the Self-Consistent Field Theory.

Predicting the distribution of a chemical species across multiple phases is of critical importance to environmental protection, pharmaceuticals, and high added-value chemicals. Computationally, this problem is addressed by determining the free energy of solvation of the species in the different phases using a well-established thermodynamic formulation. Following recent developments in sterically stabilized colloids and nanocomposite materials, the solvation of polymer-grafted nanoparticles in different solvents or polymer melts has become relevant. We develop a Self-Consistent Field theoretical framework to determine the solvation free energy of grafted particles inside a molten polymer matrix phase at low concentrations. The solvation free energy is calculated based on the notion of a pseudochemical potential introduced by Ben-Naim. Grafted and matrix chains are taken to be of the same chemical constitution, but their lengths are varied systematically, as are the particle radius and the areal density of grafted chains. In addition, different affinities between the nanoparticle core and the polymer (contact angles) are considered. At very low or very high amounts of grafted material, solvation depends on the adhesion tension between the bare particle and the matrix or on the surface tension of the grafted polymer, respectively. The dependence of the solvation free energy on molecular characteristics is more complicated at intermediate grafting densities and high curvatures, where the contribution of the entropy of grafted chains becomes significant. In general, solvation is less favored in cases where the matrix chains are much shorter than the grafted ones. The former tend to penetrate and swell the brush, thus generating conformational and translational entropy penalties. This effect becomes more pronounced when considering large particles since the grafted chains have less available space and extend more. For extremely low amounts of grafted material, we observe the opposite trend, albeit weak. Based on our calculations, we propose a generic model for estimating the solvation free energies of grafted nanoparticles in polymer melts from their molecular characteristics. The model and associated SCF formulation, illustrated here for chemically identical grafted and matrix chains, can be extended to obtain partition coefficients of grafted nanoparticles between different polymer melts.

Single-Particle Tracking of Nonsticky and Sticky Nanoparticles in Polymer Melts

We use single-particle tracking (SPT) to explore the role of nanoparticles/polymer interactions and polymer molecular weight on nanoparticle (NP) diffusion in unentangled polymer melts. The very di...

Diffusion of Nanoparticles in Polymer Systems

The state-of-the-art in research of the mobility of nanoparticles in polymer melts is presented. It is important to determine the mechanisms of diffusion processes in these systems and factors affecting the diffusion of nanoparticles of different sizes when developing methods for controlling the distribution of nanoparticles in polymer nanocomposites that play an increasingly important role in various industries. The modern theoretical concepts of the diffusion of small particles in solutions and polymer melts, as well as results of computer simulation and experimental studies, are discussed. It is shown that the key factor determining the nature of the motion of nanoparticles is the ratio of the particle size to the characteristic dimensions of the polymer, which explains the strong relationship between the mobility of nanoparticles and the local structure of polymer molecules.

Diffusion of Sticky Nanoparticles in a Polymer Melt: Crossover from Suppressed to Enhanced Transport

The self-diffusion of a single large particle in a fluid is usually described by the classic Stokes–Einstein (SE) hydrodynamic relation. However, there are many fluids where the SE prediction for nanoparticles diffusion fails. These systems include diffusion of nanoparticles in porous media, in entangled and unentangled polymer melts and solutions, and protein diffusion in biological environments. A fundamental understanding of the microscopic parameters that govern nanoparticle diffusion is relevant to a wide range of applications. In this work, we present experimental measurements of the tracer diffusion coefficient of small and large nanoparticles that experience strong attractions with unentangled and entangled polymer melt matrices. For the small nanoparticle system, a crossover from suppressed to enhanced diffusion is observed with increasing polymer molecular weight. We interpret these observations based on our theoretical and simulation insights of the preceding article (paper 1) as a result of a ...

CNTs in polymer melt: The influence on dispersion by sonication

Nanocomposites have become more important as the implementation of nanoparticles in polymer allows additional functions in common industrial parts. Especially in the fabrication of filaments or fibres nanomodification is crucial, as only very small fillers can be added to the very fine fibres (common fibre diameter is 20 μm, fine filaments are 1 μm). [1,2]Discharging fibres, conductive fibres and many other functional fibres raise in their importance nowadays, as the need for highly functional but flexible surfaces, such as textiles rises. Especially the dispersion quality is essential for the final enhancement of the filament properties. Homogeneously distributed particles serve function throughout the full fibre giving equal mechanical and functional properties over the length of the fibre and of the manufactured textile [3,4]. Counteracting this requirement nanoparticles tend to form agglomerates due to their high specific surface area during the manufacturing of those nanocomposites [5].In this paper the distribution and dispersion methods are introduced. The homogenization of carbon nanoparticles in polymer melt is enhanced by a novel sonication unit of ITA and BANDELIN electronic GmbH & Co. KG. The first development steps of the semi-industrial unit fabrication as well as the first experimental results in the lab scale of the modification of the dispersion will be shown. Special focus will be laid on the sealing of the new sonication unit as well as the positioning and equipment size when being implemented in an existing melt spinning unit.The paper will show the status of the project as well as the next steps, to show other participants the potential of the newly developed unit.

Temperature induced transition from acceleration to deceleration of the diffusion of polymers by soft nanoparticles in their composite

It is well known that the presence of nanoparticles in polymer melt can dramatically influence the dynamics of the polymers. Here from a molecular dynamics simulation study, we find that such influences can be largely temperature dependent in a polymer/single chain nanoparticle composite. At high temperature, the translational diffusion of polymers can be accelerated due to large deformability of nanoparticle surface. While when temperature decreases, nanoparticle surface deformability decreases dramatically and therefore nanoparticles can impose large excess free energy barrier on polymer diffusion. As a consequence, the diffusion of polymers at low temperature can be largely decelerated.

Breakdown of the Stokes–Einstein Relation for the Rotational Diffusivity of Polymer Grafted Nanoparticles in Polymer Melts

We report observations of breakdown of the Stokes-Einstein relation for the rotational diffusivity of polymer-grafted spherical nanoparticles in polymer melts. The rotational diffusivity of magnetic nanoparticles coated with poly(ethylene glycol) dispersed in poly(ethylene glycol) melts was determined through dynamic magnetic susceptibility measurements of the collective rotation of the magnetic nanoparticles due to imposed time-varying magnetic torques. These measurements clearly demonstrate the existence of a critical molecular weight for the melt polymer, below which the Stokes-Einstein relation accurately describes the rotational diffusivity of the polymer-grafted nanoparticles and above which the Stokes-Einstein relation ceases to apply. This critical molecular weight was found to correspond to a chain contour length that approximates the hydrodynamic diameter of the nanoparticles.

Theoretical Insight into Dispersion of Silica Nanoparticles in Polymer Melts.

Silica nanoparticles dispersed in polystyrene, poly(methyl methacrylate), and poly(ethylene oxide) melts have been investigated using a density functional approach. The polymers are regarded as coarse-grained semiflexible chains, and the segment sizes are represented by their Kuhn lengths. The particle-particle and particle-polymer interactions are calculated with the Hamaker theory to reflect the relationship between particles and polymer melts. The effects of particle volume fraction and size on the particle dispersion have been quantitatively determined to evaluate their dispersion/aggregation behavior in these polymer melts. It is shown that theoretical predictions are generally in good agreement with the corresponding experimental results, providing the reasonable verification of particle dispersion/agglomeration and polymer depletion.

Assessing magnetic nanoparticle aggregation in polymer melts by dynamic magnetic susceptibility measurements

Abstract Aggregation of magnetic nanoparticles in polymer melts was assessed using dynamic magnetic susceptibility measurements. Magnetic nanocomposites consisting of polybutadiene/CoFe2O4 and polystyrene/CoFe2O4 mixtures were prepared using different techniques and characterized using dynamic magnetic susceptibility measurements. The presence of nanoparticle aggregates determined using magnetic measurements was confirmed with transmission electron microscopy examinations. The results were in good agreement with predictions from the Flory–Huggins interaction parameters.

Modeling of Particle Migration inside Vibration Bubbles in Bubble-Stretching Dispersion Method

Bubble-stretching based dispersion method can be used to prevent the agglomeration of nanoparticles during the process of preparing nanocomposites, whereas its effectiveness is restricted by the practically low migration ratio of particles onto the bubble wall. Theoretical models for bubble vibration and particle migration have been presented, followed by numerically study on effects of different parameters on migration ratio of particles on to the bubble wall. The numerical results have shown that bubble initial radius, bubble initial pressure and particle diameters impact the particle migration ratio obviously and it is found that the particle migration ratio can be improved effectively through the optimal control of the vibration parameters of the bubble happed in the dispersion process. Therefore, this article provides a theoretical basis for the efforts on increasing the particles migration ratio and thus the dispersion effectiveness of nanoparticles in polymer melt.

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equation is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode-coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

Entropy-driven segregation of nanoparticles in polymer melts

We present a Monte Carlo study of the dispersibility of nanoparticles in polymer melts based on the relative entropic contributions of particles and polymer chains. Our model predictions are in terms of the particle diameter d and the chain statistical segment length ℓ. In the limit of small (d=ℓ) particles, a good dispersion is predicted, as the high entropy contribution of the small particles largely offsets the loss in polymer chain entropy. This is not the case, however, at larger d ≈ 3ℓ and particle segregation at the surfaces of thin polymer films is observed. That model prediction is in good agreement with experimental observation for systems with little or no enthalpic interaction between polymer and particles.

X-ray photon correlation spectroscopy using a fast pixel array detector with a grid mask resolution enhancer.

The performance of a fast pixel array detector with a grid mask resolution enhancer has been demonstrated for X-ray photon correlation spectroscopy (XPCS) measurements to investigate fast dynamics on a microscopic scale. A detecting system, in which each pixel of a single-photon-counting pixel array detector, PILATUS, is covered by grid mask apertures, was constructed for XPCS measurements of silica nanoparticles in polymer melts. The experimental results are confirmed to be consistent by comparison with other independent experiments. By applying this method, XPCS measurements can be carried out by customizing the hole size of the grid mask to suit the experimental conditions, such as beam size, detector size and sample-to-detector distance.

Assembly of Polymer-Grafted Magnetic Nanoparticles in Polymer Melts

Hydrophobic iron oxide nanoparticles grafted with hydrophobic polymer chains of varying molecular weights and graft densities are synthesized to underpin the role of brush entanglement and dipolar forces on creating nanostructures. Grafting density on magnetic nanoparticles is controlled in grafting-to method by changing the concentration of functionalized polymer in solution. The grafting density and brush length have varied systemically to observe the changes in nanostructures. Bridging between grafted chains and dipolar forces become effective only at low grafting density and result in long chains of particles. We demonstrate experimentally that structural transition of magnetic nanoparticles is controlled with the balance between grafted chain entanglements and dipolar forces.

Nanoparticle Dispersion and Aggregation in Polymer Nanocomposites: Insights from Molecular Dynamics Simulation

It is a great challenge to fully understand the microscopic dispersion and aggregation of nanoparticles (NPs) in polymer nanocomposites (PNCs) through experimental techniques. Here, coarse-grained molecular dynamics is adopted to study the dispersion and aggregation mechanisms of spherical NPs in polymer melts. By tuning the polymer-filler interaction in a wide range at both low and high filler loadings, we qualitatively sketch the phase behavior of the PNCs and structural spatial organization of the fillers mediated by the polymers, which emphasize that a homogeneous filler dispersion exists just at the intermediate interfacial interaction, in contrast with traditional viewpoints. The conclusion is in good agreement with the theoretically predicted results from Schweizer et al. Besides, to mimick the experimental coarsening process of NPs in polymer matrixes (ACS Nano 2008, 2, 1305), by grafting polymer chains on the filler surface, we obtain a good filler dispersion with a large interparticle distance. Considering the PNC system without the presence of chemical bonding between the NPs and the grafted polymer chains, the resulting good dispersion state is further used to investigate the effects of the temperature, polymer-filler interaction, and filler size on the filler aggregation process. It is found that the coarsening or aggregation process of the NPs is sensitive to the temperature, and the aggregation extent reaches the minimum in the case of moderate polymer-filler interaction, because in this case a good dispersion is obtained. That is to say, once the filler achieves a good dispersion in a polymer matrix, the properties of the PNCs will be improved significantly, because the coarsening process of the NPs will be delayed and the aging of the PNCs will be slowed.

Anomalous nanoparticle diffusion in polymer solutions and melts: A mode-coupling theory study

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.

Mechanical reinforcement of polymer nanocomposites: theory and ultra-small angle X-ray scattering (USAXS) studies

The microstructure of polymer-grafted nanoparticles in polymer melts that are chemically identical to the brush was investigated using ultra-small angle X-ray scattering (USAXS). The dispersions were thermodynamically stable. Particle size and melt molecular weight were varied such that the particle softness, L*, or the ratio of the brush thickness to the particle radius ranged from L* = 0.02–0.29. The experimentally extracted structure factors and radial distribution functions from USAXS show stronger particle interactions in lower molecular weight melts due to brush stretching corresponding to an enhancement in bulk properties at particle concentrations above the jamming transition. Good agreement was found between the measured structure factors and those predicted using the Percus–Yevick closure. Further, enhancement in the storage modulus, previously observed with rheology, was predicted through the Zwanzig–Mountain relation and Monte Carlo simulations. Overall, the use of USAXS and rheology enables the connection between experiment and theory to predict, and ultimately control the interactions of polymer-grafted nanoparticles in polymer melts.

Rheological impacts of particle softness on wetted polymer-grafted silica nanoparticles in polymer melts

Well-characterized dispersions of silica nanoparticles, stabilized by end-tethered poly(dimethylsiloxane) (PDMS) chains in PDMS melts have been investigated to better understand the impact of the graft layer on bulk properties. The relative “softness” of completely wet, dispersed particles is examined by varying the melt molecular weight (P = 2–13 kg/mol) and particle core radius (ac = 16–600 nm). As P decreases at constant graft molecular weight (N = 25 kg/mol) and graft density (Σ ≈ 0.17 chains/nm2), enhanced stretching of the brush is supported by polymer scaling theory predictions. Using rheology, particle interactions for systems of varying particle volume fraction (i.e., interparticle separation distance) have been studied. Through steady shear and oscillatory rheological experiments, we have observed a liquid–solid transition that depends on particle softness, or the ratio of the brush height to particle core radius. At particle volume fractions above the liquid–solid transition, an increase in mechanical properties, namely storage modulus and relative viscosity, in lower molecular weight melts occurs due to higher interparticle repulsions from greater stretching of the brush. Moreover, plateau moduli, G′∞, for particle concentrations above the liquid–solid transition, scale with the interparticle separation distance with a dependence corresponding to a repulsive interaction potential. Ultimately, elucidation of the role of the graft layer on nanoparticles dispersed in polymer melts will aid in the formulation of nanomaterials in applications such as coatings, optics, catalysis, and plastics.

Effective Interactions, Structure, and Phase Behavior of Lightly Tethered Nanoparticles in Polymer Melts

We have generalized the microscopic polymer reference interaction site model (PRISM) theory to study the structure and phase behavior of polymer-tethered spherical nanoparticles in a dense homopolymer melt. In the absence of a polymer matrix, fluids of such hybrid nanoparticles show strong concentration fluctuations indicative of aggregate formation and/or a tendency for microphase separation as the total packing fraction and/or nanoparticle attraction strength increase. In the presence of a polymer matrix, there is a competition between tether-mediated microphase separation and matrix-induced macrophase separation. For a single tether of eight segments on a nanoparticle twice the diameter of a segment, the apparent microphase spinodal curve exhibits both dilution-like and depletion-like features and a nonmonotonic dependence of the spinodal temperature on matrix chain length. As the particle size and tether length are both increased, such that the total space filling volume of the tether continues to equ...

Dispersing hairy nanoparticles in polymer melts

The dispersion of hairy nanoparticles in polymer melts of chemically identical chains was investigated as a function of both molecular weight and volume fraction. Here we provide conclusive evidence that the shape of the phase diagram is determined primarily by the ratio of the chain length of the polymer melt to the chain length of the polymeric shell structure (or hair) of the core/shell nanoparticles, and that the phase behavior of different hairy particles in various polymer melts can be superimposed into one universal graph. Other factors, including the hair density and the particle diameter, are not nearly as significant as the above-noted ratio in this phase separation. In addition, we show that there is a strong connection between the rheological dynamics of the particle-filled system and the thermodynamics of the phase separation behavior. The shear-induced nonlinearity in the particle-filled system appears to display features of a singularity near the phase transition point.