Chain conformation in polymer nanocomposites with uniformly dispersed nanoparticles

Simulation study on the effect of polydisperse nanoparticles on polymer diffusion in crowded environments

The diffusion of polymer chains in a crowded environment with large and small immobile, attractive nanoparticles (NPs) is studied using Langevin dynamics simulations. For orderly distributed NPs on the simple cubic lattice, our results show that the diffusion of polymer chains is dependent on the NP-NP distance or lattice distance d. At low d where NPs are placed closely, subdiffusion occurs at a sufficiently high polydispersity of NPs, PD. Both the apparent diffusion coefficient and subdiffusion exponent of polymer chains decrease with increasing PD, attributed to the adsorption of polymers on NP clusters formed by larger NPs. At large d, normal diffusion is always observed, and the diffusion coefficient increases with increasing PD. The reason is that, at high PD, the difference between single large NP adsorption and double large NP adsorption is reduced, which increases the exchange of a polymer between the two adsorption states. Finally, the impact of size polydispersity of NPs on the diffusion of polymer chains in a crowded environment with randomly distributed NPs is also investigated. The results show that the position disorder of NPs enhances the subdiffusion of the system.

Dynamic Processes and Mechanical Properties of Lipid-Nanoparticle Mixtures

In this study, we investigate the dynamic processes and mechanical properties of lipid nanoparticle mixtures in a melt via dissipation particle dynamic simulation. By investigating the distribution of nanoparticles in lamellar and hexagonal lipid matrices in equilibrium state and dynamic processes, we observe that the morphology of such composites depends not only on the geometric features of the lipid matrix but also on the concentration of nanoparticles. The dynamic processes are also demonstrated by calculating the average radius of gyration, which indicates the isotropic conformation of lipid molecules in the x-y plane and that the lipid chains are stretched in the z direction with the addition of nanoparticles. Meanwhile, we predict the mechanical properties of lipid-nanoparticle mixtures in lamellar structures by analyzing the interfacial tensions. Results show that the interfacial tension decreased with the increase in nanoparticle concentration. These results provide molecular-level information for the rational and a priori design of new lipid nanocomposites with ad hoc tailored properties.

Relaxation dynamics of deformed polymer nanocomposites as revealed by small-angle scattering and rheology

The relaxation dynamics of polystyrene (PS)/silica nanocomposites after a large step deformation are studied by a combination of small-angle scattering techniques and rheology. Small-angle X-ray scattering measurements and rheology show clear signatures of nanoparticle aggregation that enhances the mechanical properties of the polymer nanocomposites (PNCs) in the linear viscoelastic regime and during the initial phase of stress relaxation along with accelerated relaxation dynamics. Small-angle neutron scattering experiments under the zero-average-contrast condition reveal, however, smaller structural anisotropy in the PNCs than that in the neat polymer matrix, as well as accelerated anisotropy relaxation. In addition, the degrees of anisotropy reduction and relaxation dynamics acceleration increase with increasing nanoparticle loading. These results are in sharp contrast to the prevailing viewpoint of enhanced molecular deformation as the main mechanism for the mechanical enhancement in PNCs. Furthermore, the observed acceleration of stress relaxation and reduction in structural anisotropy point to two types of nonlinear effects in the relaxation dynamics of PNCs at large deformation.

Polymer solution structure and dynamics within pores of hexagonally close-packed nanoparticles

Using coarse-grained molecular dynamics simulations, we examine structure and dynamics of polymer solutions under confinement within the pores of a hexagonally close-packed (HCP) nanoparticle system with nanoparticle diameter fifty times that of the polymer Kuhn segment size. We model a condition where the polymer chain is in a good solvent (i.e., polymer-polymer interaction is purely repulsive and polymer-solvent and solvent-solvent interactions are attractive) and the polymer-nanoparticle and solvent-nanoparticle interactions are purely repulsive. We probe three polymer lengths (N = 10, 114, and 228 Kuhn segments) and three solution concentrations (1, 10, and 25%v) to understand how the polymer chain conformations and chain center-of-mass diffusion change under confinement within the pores of the HCP nanoparticle structure from those seen in bulk. The known trend of bulk polymer R_g² decreasing with increasing concentration no longer holds when confined in the pores of HCP nanoparticle structure; for example, for the 114-mer, the HCP 〈R_g²〉 at 1%v concentration is lower than HCP 〈R_g²〉 at 10%v concentration. The 〈R_g²〉 of the 114-mer and 228-mer exhibit the largest percent decline going from bulk to HCP at the 1%v concentration and the smallest percent decline at the 25%v concentration. We also provide insight into how the confinement ratio (CR) of polymer chain size to pore size within tetrahedral and octahedral pores in the HCP arrangement of nanoparticles affects the chain conformation and diffusion at various concentrations. At the same concentration, the N = 114 has significantly more movement between pores than the N = 228 chains. For the N = 114 polymer, the diffusion between pores (i.e., inter-pore diffusion) accelerates the overall diffusion rate for the confined HCP system while for the N = 228 polymer, the polymer diffusion in the entire HCP is dominated by the diffusion within the tetrahedral or octahedral pores with minor contributions from inter-pore diffusion. These findings augment the fundamental understanding of macromolecular diffusion through large, densely packed nanoparticle assemblies and are relevant to research focused on fabrication of polymer composite materials for chemical separations, storage, optics, and photonics. We perform coarse-grained molecular dynamics simulations to understand structure and dynamics of polymer solutions under confinement within hexagonal close packed nanoparticles with radii much larger than the polymer chain's bulk radius of gyration.

Ionic poly(dimethylsiloxane)-silica nanocomposites: Dispersion and self-healing

ABSTRACT

Poly(dimethylsiloxane) (PDMS)-based nanocomposites have attracted increasing attention due to their inherent outstanding properties. Nevertheless, the realization of high levels of dispersion of nanosilicas in PDMS represents a challenge arising from the poor compatibility between the two components. Herein, we explore the use of ionic interactions located at the interface between silica and a PDMS matrix by combining anionic sulfonate-functionalized silica and cationic ammonium-functionalized PDMS. A library of ionic PDMS nanocomposites was synthesized and characterized to highlight the impact of charge location, density, and molecular weight of ionic PDMS polymers on the dispersion of nanosilicas and the resulting mechanical reinforcement. The use of reversible ionic interactions at the interface of nanoparticles-polymer matrix enables the healing of scratches applied to the surface of the nanocomposites. Molecular dynamics simulations were used to estimate the survival probability of ionic cross-links between nanoparticles and the polymer matrix, revealing a dependence on polymer charge density.

IMPACT STATEMENT

Poly(dimethylsiloxane) (PDMS) has been widely used in diverse applications due to its inherent attractive and multifunctional properties including optical transparency, high flexibility, and biocompatibility. The combination of such properties in a single polymer matrix has paved the way toward a wide range of applications in sensors, electronics, and biomedical devices. As a liquid at room temperature, the cross-linking of the PDMS turns the system into a mechanically stable elastomer for several applications. Nanofillers have served as a reinforcing agent to design PDMS nanocomposites. However, due to significant incompatibility between silica and the PDMS matrix, the dispersion of nanosilica fillers has been challenging. One of the existing strategies to improve nanoparticle dispersion consists of grafting oppositely charged ionic functional groups to the nanoparticle surface and the polymer matrix, respectively, creating nanoparticle ionic materials. Here, this approach has been explored further to improve the dispersion of nanosilicas in a PDMS matrix. The designed ionic PDMS nanocomposites exhibit self-healing properties due to the reversible nature of ionic interactions. The developed synthetic approach can be transferred to other kinds of inorganic nanoparticles dispersed in a PDMS matrix, where dispersion at the nanometer scale is a prerequisite for specific applications such as encapsulants for light-emitting diodes (LEDs).

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1557/s43577-022-00346-x.

Direct Structural Evidence for Interfacial Gradients in Asymmetric Polymer Nanocomposite Blends

Understanding the complex structure of polymer blends filled with nanoparticles (NPs) is key to design their macroscopic properties. Here, the spatial distribution of hydrogenated (H) and deuterated (D) polymer chains asymmetric in mass is studied by small-angle neutron scattering. Depending on the chain mass, a qualitatively new large-scale organization of poly(vinyl acetate) chains beyond the random-phase approximation is evidenced in nanocomposites with attractive polymer-silica interactions. The silica is found to systematically induce bulk segregation. Only with long H-chains, a strong scattering signature is observed in the q range of the NP size: it is the sign of interfacial isotopic enrichment, that is, of contrasted polymer shells close to the NP surface. A quantitative model describing both the bulk segregation and the interfacial gradient (over ca. 10-20 nm depending on the NP size) is developed, showing that both are of comparable strength. In all cases, NP surfaces trap the polymer blend in a non-equilibrium state, with preferential adsorption around NPs only if the chain length and isotopic preference toward the surface combine their entropic and enthalpic driving forces. This structural evidence for interfacial polymer gradients will open the road for quantitative understanding of the dynamics of many-chain nanocomposite systems.

Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites

Conformations, entanglements and dynamics in attractive polymer nanocomposites are investigated in this work by means of coarse-grained molecular dynamics simulation, for both weak and strong confinements, in the presence of nanoparticles (NPs) at NP volume fractions φ up to 60%. We show that the behavior of the apparent tube diameter dapp in such nanocomposites can be greatly different from nanocomposites with nonattractive interactions. We find that this effect originates, based on a mean field argument, from the geometric confinement length dgeo at strong confinement (large φ) and not from the bound polymer layer on NPs (interparticle distance ID <2Rg) as proposed recently based on experimental measurements. Close to the NP surface, the entangled polymer mobility is reduced in attractive nanocomposites but still faster than the NP mobility for volume fractions beyond 20%. Furthermore, entangled polymer dynamics is hindered dramatically by the strong confinement created by NPs. For the first time using simulations, we show that the entangled polymer conformation, characterized by the polymer radius of gyration Rg and form factor, remains basically unperturbed by the presence of NPs up to the highest volume fractions studied, in agreement with various experiments on attractive nanocomposites. As a side-result we demonstrate that the loose concept of ID can be made a microscopically well defined quantity using the mean pore size of the NP arrangement.

Molecular Modeling and Simulation of Polymer Nanocomposites with Nanorod Fillers

We present a coarse-grained (CG) molecular dynamics (MD) simulation study of polymer nanocomposites (PNCs) containing nanorods with homogeneous and patchy surface chemistry/functionalization, modeled with isotropic and directional nanorod-nanorod attraction, respectively. We show how the PNC morphology is impacted by the nanorod design (i.e., aspect ratio, homogeneous or patchy surface chemistry/functionalization) for nanorods with a diameter equal to the Kuhn length of the polymer in the matrix. For PNCs with 10 vol % nanorods that have an aspect ratio ≤5, we observe percolated morphology with directional nanorod-nanorod attraction and phase-separated (i.e., nanorod aggregation) morphology with isotropic nanorod-nanorod attraction. In contrast, for nanorods with higher aspect ratios, both types of attractions result in aggregated nanorods morphology due to the dominance of entropic driving forces that cause long nanorods to form orientationally ordered aggregates. For most PNCs with isotropic or directional nanorod-nanorod attractions, the average matrix polymer conformation is not perturbed by the inclusion of up to 20 vol % nanorods. The polymer chains in contact with nanorods (i.e., interfacial chains) are on average extended and statistically different from the conformations the matrix chains adopt in the pure melt state (with no nanorods); in contrast, the polymer chains far from nanorods (i.e., bulk chains) adopt the same conformations as the matrix chains adopt in the pure melt state. We also study the effect of other parameters, such as attraction strength, nanorod volume fraction, and matrix chain length, for PNCs with isotropic or directional nanorod-nanorod attractions. Collectively, our results provide valuable design rules to achieve specific PNC morphologies (i.e., dispersed, aggregated, percolated, and orientationally aligned nanorods) for various potential applications.

Polymer Conformations, Entanglements and Dynamics in Ionic Nanocomposites: A Molecular Dynamics Study

We investigate nanoparticle (NP) dispersion, polymer conformations, entanglements and dynamics in ionic nanocomposites. To this end, we study nanocomposite systems with various spherical NP loadings, three different molecular weights, two different Bjerrum lengths, and two types of charge-sequenced polymers by means of molecular dynamics simulations. NP dispersion can be achieved in either oligomeric or entangled polymeric matrices due to the presence of electrostatic interactions. We show that the overall conformations of ionic oligomer chains, as characterized by their radii of gyration, are affected by the presence and the amount of charged NPs, while the dimensions of charged entangled polymers remain unperturbed. Both the dynamical behavior of polymers and NPs, and the lifetime and amount of temporary crosslinks, are found to depend on the ratio between the Bjerrum length and characteristic distance between charged monomers. Polymer-polymer entanglements start to decrease beyond a certain NP loading. The dynamics of ionic NPs and polymers is very different compared with their non-ionic counterparts. Specifically, ionic NP dynamics is getting enhanced in entangled matrices and also accelerates with the increase of NP loading.

Study on the interfacial properties of polymers around a nanoparticle

The interfacial properties of polymer chains on spherical nanoparticles are investigated using off-lattice Monte Carlo simulations.

Tailoring the mechanical properties of polymer nanocomposites via interfacial engineering

The improvement of mechanical properties of polymer nanocomposites (PNCs) has been studied for many years, with the main focus on the structure of the nanofillers. Much less effort has been devoted to unraveling the factors controlling the structure of the grafted chains. Herein, through coarse-grained molecular-dynamics simulations, we have successfully fabricated an ideal, mechanically-interlocked composite structure composed of end-functionalized chains grafted to the nanoparticle surface forming rings and making the matrix chains thread through these rings. Depending on the details of the grafting, the reinforcement effect can be remarkable, improving the tensile stress of the system significantly up to 700%. Meanwhile, anisotropy of the system's mechanical response is also observed. Furthermore, the influence of the grafted chain distribution on the mechanical properties of the system has been investigated as well. We observe that the mechanical properties of the system are closely related to the total number of the beads in the grafted chains or the synergistic effect between the length and density of the grafted chains leads to no significant difference in the performance of systems. At constant grafting density, the mechanical properties of the systems correlate negatively to the grafted chain length. In general, our study should help to design and fabricate high-performance PNCs with excellent mechanical properties.

Miscibility and Nanoparticle Diffusion in Ionic Nanocomposites

We investigate the effect of various spherical nanoparticles in a polymer matrix on dispersion, chain dimensions and entanglements for ionic nanocomposites at dilute and high nanoparticle loading by means of molecular dynamics simulations. The nanoparticle dispersion can be achieved in oligomer matrices due to the presence of electrostatic interactions. We show that the overall configuration of ionic oligomer chains, as characterized by their radii of gyration, can be perturbed at dilute nanoparticle loading by the presence of charged nanoparticles. In addition, the nanoparticle's diffusivity is reduced due to the electrostatic interactions, in comparison to conventional nanocomposites where the electrostatic interaction is absent. The charged nanoparticles are found to move by a hopping mechanism.

Adsorption Behavior of Polymer Chain with Different Topology Structure at the Polymer-Nanoparticle Interface

The effect of the polymer chain topology structure on the adsorption behavior in the polymer-nanoparticle (NP) interface is investigated by employing coarse-grained molecular dynamics simulations in various polymer-NP interaction and chain stiffness. At a weak polymer-NP interaction, ring chain with a closed topology structure has a slight priority to occupy the interfacial region than linear chain. At a strong polymer-NP interaction, the “middle” adsorption mechanism dominates the polymer local packing in the interface. As the increase of chain stiffness, an interesting transition from ring to linear chain preferential adsorption behavior occurs. The semiflexible linear chain squeezes ring chain out of the interfacial region by forming a helical structure and wrapping tightly the surface of NP. In particular, this selective adsorption behavior becomes more dramatic for the case of rigid-like chain, in which 3D tangent conformation of linear chain is absolutely prior to the 2D plane orbital structure of ring chain. The local packing and competitive adsorption behavior of bidisperse matrix in polymer-NP interface can be explained based on the adsorption mechanism of monodisperse (pure ring or linear) case. These investigations may provide some insights into polymer-NP interfacial adsorption behavior and guide the design of high-performance nanocomposites.

Static and dynamic properties of a semiflexible polymer in a crowded environment with randomly distributed immobile nanoparticles

The dimensions, diffusivity, and relaxation of a polymer are dependent on the attraction strength and concentration of nanoparticles.

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.

A study on the diffusivity of polymers in crowded environments with periodically distributed nanoparticles

Two novel diffusion behaviors of polymers at low temperature: a minimum at an intermediate inter-particle distance and oscillation with polymer length.

The effect of size and concentration of nanoparticles on the glass transition temperature of polymer nanocomposites

Here we use model nanocomposites based on polystyrene and polyphenylene dendrimers to show both theoretically and experimentally that inclusion of rigid nanoparticles of 2.3–5 nm size into the polymer leads to a negligible glass transition temperature (T_g) increase.

Intra- and Interchain Correlations in Polymer Nanocomposites: A Small-Angle Neutron Scattering Extrapolation Method

In this Letter we applied for the first time a small-angle neutron scattering (SANS) extrapolation method to study the influence of nanoparticles (NPs) on polymer chain conformation in polymer nanocomposites (PNCs). This new approach is based on a perfect NP matching thanks to a statistical hydrogenated (H)/ deuterated (D) polymer matrix in which a certain amount of labeled chain (H) is added. The extrapolation to zero H content gives the intrachain structure factor, S₁(q), and the interchain correlations, S₂(q), the latter not being accessible under the zero average contrast (ZAC) condition preferentially used in the previous studies. We validate the method on well-known silica/polystyrene (PS) PNCs and compare the results with our previous ZAC measurements. The analysis of both S₁(q) and S₂(q) shows (i) no significant modifications of the radius of gyration R_g of the chain and of the interchain interaction induced by the presence of NPs and more interestingly (ii) the existence of chain domains with lower densities included inside NP clusters as the result of excluded volume effects that create an extra scattering at low q. The extrapolation method unambiguously shows that the unexpected behavior observed at low q comes from the chains and not from the unmatched NPs.

Temperature-Dependent Suppression of Polymer Diffusion in Polymer Nanocomposites

The polymer center-of-mass tracer diffusion coefficient in athermal polymer nanocomposites (PNCs) composed of polystyrene and phenyl-capped, spherical silica nanoparticles was measured over a range of temperatures and nanoparticle concentrations using elastic recoil detection. The polymer tracer diffusion coefficient in the PNC relative to the bulk decreases with increasing nanoparticle concentration and is unexpectedly more strongly reduced at higher temperatures. This unusual temperature dependence of polymer diffusion in PNCs cannot be explained by the reptation model or a modified version incorporating an effective tube diameter. Instead we show that our results are consistent with a mechanism based on nanoparticle-imposed configurational entropy barriers.

Polymer Chain Behavior in Polymer Nanocomposites with Attractive Interactions

Chain behavior has been determined in polymer nanocomposites (PNCs) comprised of well-dispersed 12 nm diameter silica nanoparticles (NPs) in poly(methyl methacrylate) (PMMA) matrices by Small-Angle Neutron Scattering (SANS) measurements under the Zero Average Contrast (ZAC) condition. In particular, we directly characterize the bound polymer layer surrounding the NPs, revealing the bound layer profile. The SANS spectra in the high-q region also show no significant change in the bulk polymer radius of gyration on the addition of the NPs. We thus suggest that the bulk polymer conformation in PNCs should generally be determined using the high q region of SANS data.

Distortion of Chain Conformation and Reduced Entanglement in Polymer-Graphene Oxide Nanocomposites

We study the conformations of polymer chains in polymer-graphene oxide nanocomposites. We show that the chains have a reduced radius of gyration that is consistent with confinement at a solid interface in the melt, as is expected for well-dispersed, high aspect ratio nanoparticles that are much larger than the polymer coil size. We show that confinement of the polymer chains causes a corresponding reduction in interchain entanglements, and we calculate a contribution to the plateau modulus from the distorted polymer network via a simple scaling argument. Our results are a significant step forward in understanding how two-dimensional nanoparticles affect global material properties at low loadings.

Density Functional Theory of Polymer Structure and Conformations

We present a density functional approach to quantitatively evaluate the microscopic conformations of polymer chains with consideration of the effects of chain stiffness, polymer concentration, and short chain molecules. For polystyrene (PS), poly(ethylene oxide) (PEO), and poly(methyl methacrylate) (PMMA) melts with low-polymerization degree, as chain length increases, they display different stretching ratios and show non-universal scaling exponents due to their different chain stiffnesses. In good solvent, increase of PS concentration induces the decline of gyration radius. For PS blends containing short (m1=1−100) and long (m=100) chains, the expansion of long chains becomes unobvious once m1 is larger than 40, which is also different to the scaling properties of ideal chain blends.

Entanglements in polymer nanocomposites containing spherical nanoparticles

We investigate the polymer packing around nanoparticles and polymer/nanoparticle topological constraints (entanglements) in nanocomposites containing spherical nanoparticles in comparison to pure polymer melts using molecular dynamics (MD) simulations. The polymer-nanoparticle attraction leads to good dispersion of nanoparticles. We observe an increase in the number of topological constraints (decrease of total entanglement length Ne with nanoparticle loading in the polymer matrix) in nanocomposites due to nanoparticles, as evidenced by larger contour lengths of the primitive paths. An increase of the nanoparticle radius reduces the polymer-particle entanglements. These studies demonstrate that the interaction between polymers and nanoparticles does not affect the total entanglement length because in nanocomposites with small nanoparticles, the polymer-nanoparticles topological constraints dominate.

Interplay between polymer chain conformation and nanoparticle assembly in model industrial silica/rubber nanocomposites

The question of the influence of nanoparticles (NPs) on chain dimensions in polymer nanocomposites (PNCs) has been treated mainly through the fundamental way using theoretical or simulation tools and experiments on well-defined model PNCs. Here we present the first experimental study on the influence of NPs on the polymer chain conformation for PNCs designed to be as close as possible to industrial systems employed in the tire industry. PNCs are silica nanoparticles dispersed in a styrene-butadiene-rubber (SBR) matrix whose NP dispersion can be managed by NP loading with interfacial coatings or coupling additives usually employed in the manufacturing mixing process. We associated specific chain (d) labeling, and the so-called zero average contrast (ZAC) method, with SANS, in situ SANS and SAXS/TEM experiments to extract the polymer chain scattering signal at rest for non-cross linked and under stretching for cross-linked PNCs. NP loading, individual clusters or connected networks, as well as the influence of the type, the quantity of interfacial agent and the influence of the elongation rate have been evaluated on the chain conformation and on its related deformation. We clearly distinguish the situations where the silica is perfectly matched from those with unperfected matching by direct comparison of SANS and SAXS structure factors. Whatever the silica matching situation, the additive type and quantity and the filler content, there is no significant change in the polymer dimension for NP loading up to 15% v/v within a range of 5%. One can see an extra scattering contribution at low Q, as often encountered, enhanced for non-perfect silica matching but also visible for perfect filler matching. This contribution can be qualitatively attributed to specific h or d chain adsorption on the NP surface inside the NP cluster that modifies the average scattering neutron contrast of the silica cluster. Under elongation, NPs act as additional cross-linking junctions preventing chain relaxation and giving a deformation of the chain with the NP closer to a theoretical phantom network prediction than a pure matrix.

Anisotropic Polymer Conformations in Aligned SWCNT/PS Nanocomposites

Polymer radii of gyration in isotropic single-walled carbon nanotube (SWCNT)/polymer nanocomposites were previously found to increase with increasing SWCNT concentration. Here, the SWCNTs in nanocomposites were aligned by melt fiber spinning, and the polymer chain conformations were found to be anisotropic. Using SAXS and SANS, the anisotropic SWCNT meshes were found to have smaller mesh sizes in the direction perpendicular to the alignment direction than along the alignment direction. At fixed SWCNT orientation, the radius of gyration was probed parallel and perpendicular to the alignment direction, R_g^par and R_g^per, respectively, using SANS. With increasing SWCNT concentration, R_g^per increases significantly more than R_g^par, such that the extent of anisotropy increases with SWCNT concentration. The anisotropic polymer conformation is larger in the direction perpendicular to the alignment direction, which corresponds to a smaller SWCNT mesh size. Thus, when the SWCNT concentration and alignment combine to produce a SWCNT mesh size that is smaller than the unperturbed R_g, the polymer conformation circumvents the SWCNTs by adopting a larger R_g. Changes in the polymer conformation in nanocomposites with rod-like nanoparticles has important ramifications for entanglement density, polymer dynamics, and mechanical properties.

How the flow affects the phase behaviour and microstructure of polymer nanocomposites

We address the issue of flow effects on the phase behaviour of polymer nanocomposite melts by making use of a recently reported Hamiltonian set of evolution equations developed on principles of non-equilibrium thermodynamics. To this end, we calculate the spinodal curve, by computing values for the nanoparticle radius as a function of the polymer radius-of-gyration for which the second derivative of the generalized free energy of the system becomes zero. Under equilibrium conditions, we recover the phase diagram predicted by Mackay et al. [Science 311, 1740 (2006)]. Under non-equilibrium conditions, we account for the extra terms in the free energy due to changes in the conformations of polymer chains by the shear flow. Overall, our model predicts that flow enhances miscibility, since the corresponding miscibility window opens up for non-zero shear rate values.

Rouse mode analysis of chain relaxation in polymer nanocomposites

Large-scale molecular dynamics simulations are used to study the internal relaxations of chains in nanoparticle (NP)/polymer composites. We examine the Rouse modes of the chains, a quantity that is closest in spirit to the self-intermediate scattering function, typically determined in an (incoherent) inelastic neutron scattering experiment. Our simulations show that for weakly interacting mixtures of NPs and polymers, the effective monomeric relaxation rates are faster than in a neat melt when the NPs are smaller than the entanglement mesh size. In this case, the NPs serve to reduce both the monomeric friction and the entanglements in the polymer melt, as in the case of a polymer-solvent system. However, for NPs larger than half the entanglement mesh size, the effective monomer relaxation is essentially unaffected for low NP concentrations. Even in this case, we observe a strong reduction in chain entanglements for larger NP loadings. Thus, the role of NPs is to always reduce the number of entanglements, with this effect only becoming pronounced for small NPs or for high concentrations of large NPs. Our studies of the relaxation of single chains resonate with recent neutron spin echo (NSE) experiments, which deduce a similar entanglement dilution effect.