Unraveling the Mechanism of Nanoscale Mechanical Reinforcement in Glassy Polymer Nanocomposites

Dynamics of poly(methyl acrylate)/poly(methyl methacrylate)-grafted-Fe3O4 nanocomposites

We investigated the dynamics of nanocomposites prepared through mixing poly(methyl methacrylate) grafted Fe3O4 nanoparticles (PMMA-g-Fe3O4) with poly(methyl acrylate) (PMA). A key feature here different from previous dynamics measurements of polymer nanocomposites is the different chemistry between the matrix polymer and the polymer grafts, which introduces chemical heterogeneity. Transmission electron microscopy shows clear evidence of nanoparticle clustering due to the poor miscibility between the bulk PMA and the bulk PMMA. At the same time, broadband dielectric spectroscopy measurements detect two leading relaxations, i.e. the α and α* processes, where the α process is associated with the bulk PMA and the α* process from the PMA interacting with the grafted PMMA in the nanoparticle clustering region. Interestingly, the characteristic time of α*, τα*, is slightly slower than that of the α, τα, at high temperatures, and exhibits near Arrhenius temperature dependence at low temperatures. As a result, τα* and τα cross each other in the activation plot upon cooling and τα* ≪ τα is observed at temperatures approaching the glass transition temperature of PMA. These observations suggest the presence of component dynamics and the dynamics confinement effect between PMA and PMMA in the nanoparticle clustering region, highlighting an active interaction between PMA and PMMA at the interface despite their poor miscibility. These results thus suggest new routes to control interface dynamics through immiscible polymer pairs.

GMXPolymer: a generated polymerization algorithm based on GROMACS

CONTEXT

This work introduces a method for generating generalized structures of amorphous polymers using simulated polymerization and molecular dynamics equilibration, with a particular focus on amorphous polymers. The techniques and algorithms used in this method are described in the main text, and example input scripts are provided for the GMXPolymer code, which is based on the GROMACS molecular dynamics package. To demonstrate the efficacy of our method, we apply it to different glassy polymers exhibiting varying degrees of functionality, polarity, and rigidity. The reliability of the method is validated by comparing simulation results with experimental data in various structural and thermal properties, both of which show excellent agreement.

METHODS

This work implements the GMXPolymer simulated polymerization algorithm on the GROMACS program. GMXPolymer code controls the main polymerization loop. The energy minimizations and molecular dynamics simulations use the GROMACS program called by the GMXPolymer code. A new ITP file is generated when a new bond is formed, and the necessary additions to the ITP file are made to include new bonds, angles, and dihedrals. In preparing the ITP file of the monomer, the charge of the reactive atom must be modified before the code runs so that it is a correct value after bonding.

Supramolecular Complexation Reinforced Polymer Frustrated Packing: Controllable Dual Porosity for Improved Permselectivity of Coordination Nanocage Mixed Matrix Membranes

The developments of mixed matrix membranes (MMMs) are severely hindered by the complex inter-phase interaction and the resulting poor utilization of inorganics' microporosity. Herein, a dual porosity framework is constructed in MMMs to enhance the accessibility of inorganics' microporosity to external gas molecules for the effective application of microporosity for gas separation. Nanocomposite organogels are first prepared from the supramolecular complexation of rigid polymers and 2 nm microporous coordination nanocages (CNCs). The network structures can be maintained with microporous features after solvent removal originated from the rigid nature of polymers, and the strong coordination and hydrogen bond between the two components. Moreover, the strong supramolecular attraction reinforces the frustrated packing of the rigid polymers on CNC surface, leading to polymer networks' extrinsic pores and the interconnection of CNCs' micro-cavities for the fast gas transportation. The gas permeabilities of the MMMs are 869 times for H2 and 1099 times for CO2 higher than those of pure polymers. The open metal sites from nanocage also contribute to the enhanced gas selectivity and the overall performance surpasses 2008 H2/CO2 Robeson upper bound. The supramolecular complexation reinforced packing frustration strategy offers a simple and practical solution to achieve improved gas permselectivity in MMMs.

Nanomaterials in 4D Printing: Expanding the Frontiers of Advanced Manufacturing

As an innovative technology, four-dimentional (4D) printing is built upon the principles of three-dimentional (3D) printing with an additional dimension: time. While traditional 3D printing creates static objects, 4D printing generates "responsive 3D printed structures", enabling them to transform or self-assemble in response to external stimuli. Due to the dynamic nature, 4D printing has demonstrated tremendous potential in a range of industries, encompassing aerospace, healthcare, and intelligent devices. Nanotechnology has gained considerable attention owing to the exceptional properties and functions of nanomaterials. Incorporating nanomaterials into an intelligent matrix enhances the physiochemical properties of 4D printed constructs, introducing novel functions. This review provides a comprehensive overview of current applications of nanomaterials in 4D printing, exploring their synergistic potential to create dynamic and responsive structures. Nanomaterials play diverse roles as rheology modifiers, mechanical enhancers, function introducers, and more. The overarching goal of this review is to inspire researchers to delve into the vast potential of nanomaterial-enabled 4D printing, propelling advancements in this rapidly evolving field.

Distribution of Mechanical Properties in Poly(ethylene oxide)/silica Nanocomposites via Atomistic Simulations: From the Glassy to the Liquid State

Polymer nanocomposites exhibit a heterogeneous mechanical behavior that is strongly dependent on the interaction between the polymer matrix and the nanofiller. Here, we provide a detailed investigation of the mechanical response of model polymer nanocomposites under deformation, across a range of temperatures, from the glassy regime to the liquid one, via atomistic molecular dynamics simulations. We study the poly(ethylene oxide) matrix with silica nanoparticles (PEO/SiO2) as a model polymer nanocomposite system with attractive polymer/nanofiller interactions. Probing the properties of polymer chains at the molecular level reveals that the effective mass density of the matrix and interphase regions changes during deformation. This decrease in density is much more pronounced in the glassy state. We focus on factors that govern the mechanical response of PEO/SiO2 systems by investigating the distribution of the (local) mechanical properties, focusing on the polymer/nanofiller interphase and matrix regions. As expected when heating the system, a decrease in Young's modulus is observed, accompanied by an increase in Poisson's ratio. The observed differences regarding the rigidity between the interphase and the matrix region decrease as the temperature rises; at temperatures well above the glass-transition temperature, the rigidity of the interphase approaches the matrix one. To describe the nonlinear viscoelastic behavior of polymer chains, the elastic modulus of the PEO/SiO2 systems is further calculated as a function of the strain for the entire nanocomposite, as well as the interphase and matrix regions. The elastic modulus drops dramatically with increasing strain for both the matrix and the interphase, especially in the small-deformation regime. We also shed light on characteristic structural and dynamic attributes during deformation. Specifically, we examine the rearrangement behavior as well as the segmental and center-of-mass dynamics of polymer chains during deformation by probing the mobility of polymer chains in both axial and radial motions under deformation. The behavior of the polymer motion in the axial direction is dominated by the deformation, particularly at the interphase, whereas a more pronounced effect of the temperature is observed in the radial directions for both the interphase and matrix regions.

Temperature Dependence of the Polar and Lewis Acid-Base Properties of Poly Methyl Methacrylate Adsorbed on Silica via Inverse Gas Chromatography

The adsorption of polymers on solid surfaces is common in many industrial applications, such as coatings, paints, catalysis, colloids, and adhesion processes. The properties of absorbed polymers commonly vary with temperature. In this paper, inverse gas chromatography at infinite dilution was used to determine the physicochemical characterization of PMMA adsorbed on silica. A new method based on the London dispersion equation was applied with a new parameter associating the deformation polarizability with the harmonic mean of the ionization energies of the solvent. More accurate values of the dispersive and polar interaction energies of the various organic solvents adsorbed on PMMA in bulk phase and PMMA/silica at different recovery fractions were obtained, as well as the Lewis acid-base parameters and the transition temperatures of the different composites. It was found that the temperature and the recovery fraction have important effects on the various physicochemical and thermodynamic properties. The variations in all the interaction parameters showed the presence of three transition temperatures for the different PMMA composites adsorbed on silica with various coverage rates, with a shift in these temperatures for a recovery fraction of 31%. An important variation in the polar enthalpy and entropy of adsorption, the Lewis acid-base parameters and the intermolecular separation distance was highlighted as a function of the temperature and the recovery fraction of PMMA on silica.

From fundamental insights to rational (bio)polymer nanocomposite design - Connecting the nanometer to meter scale

Nanoparticle addition has the potential to make bioplastic use mainstream, as the resultant nanocomposite shows improved mechanical, barrier, and thermal properties. It is well established that the architecture and dynamics of the nanoparticle-polymer interphasial region, ∼ 1.5-9 nm from the nanoparticle surface, are crucial for nanocomposite characteristics. Yet, how these molecular phenomena translate to the bulk is still largely unknown. A multi-disciplinary and multi-scale vision is required to capture the full picture and improve materials far beyond what is currently possible. In this review, a first step in bridging the apparent gap between fundamental insights toward observed material properties is made. At the molecular scale, the polymer chain density and dynamics at the nanoparticle surface are governed by a complex interplay between enthalpy and entropy. The resultant interphasial properties can only be propagated to the macroscopic scale effectively when the nanoparticles are well-distributed. This makes the dispersion state a key parameter for which thermodynamic and kinetic insights can be used to prevent nanoparticle aggregation. These insights are linked to material properties relevant to packaging. The outlook section elaborates on the remaining challenges and the steps required to further understand and better design nanocomposite systems.

Revealing the Role of Chain Conformations on the Origin of the Mechanical Reinforcement in Glassy Polymer Nanocomposites

Understanding the mechanism of mechanical reinforcement in glassy polymer nanocomposites is of paramount importance for their tailored design. Here, we present a detailed investigation, via atomistic simulation, of the coupling between density, structure, and conformations of polymer chains with respect to their role in mechanical reinforcement. Probing the properties at the molecular level reveals that the effective mass density as well as the rigidity of the matrix region changes with filler volume fraction, while that of the interphase remains constant. The origin of the mechanical reinforcement is attributed to the heterogeneous chain conformations in the vicinity of the nanoparticles, involving a 2-fold mechanism. In the low-loading regime, the reinforcement comes mainly from a thin, single-molecule, 2D-like layer of adsorbed polymer segments on the nanoparticle, whereas in the high-loading regime, the reinforcement is dominated by the coupling between train and bridge conformations; the latter involves segments connecting neighboring nanoparticles.

Intermediate Polymer Relaxation Explains the Anomalous Rheology of Nanocomposites with Ultrasmall Attractive POSS Nanoparticles

The rheological properties of entangled polymers loaded with very small, strongly attractive polyhedral oligomeric silsesquioxane (POSS) fillers differ from that of nanocomposites with larger fillers by (1) the shorter breadth of the entanglement plateau and (2) the relatively unchanged terminal viscosity with increasing POSS loading. Although such anomalous rheological properties can rewrite the property-processing map of materials (e.g., high glass transition temperature and low viscosity), their mechanism remains unclear. In this study, we report that polymer relaxations on intermediate time scales between α and entire-chain relaxation, so-called "slower processes", are responsible for this unusual rheological behavior of poly(2-vinylpyridine)/octa(aminophenyl)silsesquioxane (P2VP/OAPS) nanocomposites. To uncover the effects of entanglements on the nanocomposite dynamics, rheometry is used for variable matrix molecular weights. Results show a systematic change in the rheological response, which is independent of the molecular weight, and in turn, the presence of entanglements. This supports a physical interpretation that a slower process dominates the rheological response of the material at intermediate frequencies on length scales larger than the segment length or the OAPS diameter, while the underlying physical time scales associated with the entanglement relaxation remain unchanged. Such insights are anticipated to assist the future rational design of other highly attractive and ultrasmall nanoparticles that enable a fine-tuned rheological response of nanocomposites across multiple length scales.

The Coordination Nanocages-Integrated Polymer Brush Networks for Flexible Microporous Membranes with Exceptional H2 /CO2 Separation Performance

The emergence of polymers with intrinsic microporosity provides solutions for flexible gas separation membranes with both high gas permeability and selectivity. However, their applications are significantly hindered by the costly synthetic efforts, limited availability of chemical systems, and narrow window of microporosity sizes. Herein, flexible mixed matrix membranes with tunable intrinsic microporosity can be facilely fabricated from the coordination assembly of polymer brushes and coordination nanocages. Polymer brushes bearing isophthalic acid side groups can coordinate with Cu2+ to assemble into polymer networks crosslinked by 2 nm nanocages. The semi-flexible feature of the polymer brush and the high crosslinking density of the network prevent the network from collapsing during solvent removal and the obtained aerogels demonstrate hierarchical structure with dual porosity from the crosslinked polymer network and coordination nanocage, respectively. The porosity can be facilely tuned via the amount of Cu2+ by regulating the network crosslinking density and nanocage loadings, and finally, optimized gas separation that surpasses Robeson upper bound for H2 /CO2 can be achieved. The coordination-driven assembly protocol paves a new avenue for the cost-effective synthesis of polymers with intrinsic microporosity and the fabrication of flexible gas separation membranes.

Reversible Change in Performances of Polymer Networks via Invertible Architecture-Transformation of Cross-Links

A polymer nanoparticle network using single-chain nanoparticles (SCNPs) as cross-links is designed. The experimental and theoretical study shows that incorporating SCNPs in polymer networks leads to smaller mesh size, faster terminal relaxation time, and reduced fluctuation among cross-links, resulting in a significant increase in shear storage modulus, and enhancement in tensile stress. Notably, the reversible single-chain collapse of SCNPs under thermal stimulation enables the polymer network to undergo coherent changes between two topological states, thereby exhibiting reversible transformations between soft and stiff states. This approach and finding can effectively tailor the mechanical properties of polymer networks, potentially leading to the development of intelligent, responsive materials.

Understanding creep suppression mechanisms in polymer nanocomposites through machine learning

While recent efforts have shown how local structure plays an essential role in the dynamic heterogeneity of homogeneous glass-forming materials, systems containing interfaces such as thin films or composite materials remain poorly understood. It is known that interfaces perturb the molecular packing nearby, however, numerous studies show the dynamics are modified over a much larger range. Here, we examine the dynamics in polymer nanocomposites (PNCs) using a combination of simulations and experiments and quantitatively separate the role of polymer packing from other effects on the dynamics, as a function of distance from the nanoparticle surfaces. After showing good qualitative agreement between the simulations and experiments in glassy structure and creep compliance, we use a machine-learned structure indicator, softness, to decompose polymer dynamics in our simulated PNCs into structure-dependent and structure-independent processes. With this decomposition, the free energy barrier for polymer rearrangement can be described as a combination of packing-dependent and packing-independent barriers. We find both barriers are higher near nanoparticles and decrease with applied stress, quantitatively demonstrating that the slow interfacial dynamics is not solely due to polymer packing differences, but also the change of structure-dynamics relationships. Finally, we present how this decomposition can be used to accurately predict strain-time creep curves for PNCs from their static configuration, providing additional insights into the effects of polymer-nanoparticle interfaces on creep suppression in PNCs.

Molecular Origin of the Reinforcement Effect and Its Strain-Rate Dependence in Polymer Nanocomposite Glass

We investigate the molecular origin of mechanical reinforcement in a polymer nanocomposite (PNC) under a glass state via molecular dynamics simulations. The strength of the PNC system is found to be reinforced mainly via reduced plastic deformations of the nanoparticle neighborhood (NN). Such a reinforcement effect is found to decay with an increase in the strain rate. The Arrhenius-Eyring relation is used to analyze its origin. The amplitude of the reinforcement is found to be determined by the difference between the energy barrier (ΔE) for the activation of NN and the work (W) done by the applied stress to conquer that barrier. A larger strain rate is found to result in a larger W and, hence, a weaker reinforcement effect. Such a strain-rate dependence is verified in the experimental tensile tests of a poly(vinyl alcohol)/SiO2 composite system. These results not only provide a new understanding of the molecular origin of the reinforcement effect in the PNC system, but also pave the way for a better design of the PNC material properties.

Nanoscale Structure-Property Relations in Self-Regulated Polymer-Grafted Nanoparticle Composite Structures

Using a model system of poly(methyl methacrylate)-grafted silica nanoparticles (PMMA-NP) and poly(styrene-ran-acrylonitrile) (SAN), we generate unique polymer nanocomposite (PNC) morphologies by balancing the degree of surface enrichment, phase separation, and wetting within the films. Depending on the annealing temperature and time, thin films undergo different stages of phase evolution, resulting in homogeneously dispersed systems at low temperatures, enriched PMMA-NP layers at the PNC interfaces at intermediate temperatures, and three-dimensional bicontinuous structures of PMMA-NP pillars sandwiched between two PMMA-NP wetting layers at high temperatures. Using a combination of atomic force microscopy (AFM), AFM nanoindentation, contact angle goniometry, and optical microscopy, we show that these self-regulated structures lead to nanocomposites with increased elastic modulus, hardness, and thermal stability compared to analogous PMMA/SAN blends. These studies demonstrate the ability to reliably control the size and spatial correlations of both the surface-enriched and phase-separated nanocomposite microstructures, which have attractive technological applications where properties such as wettability, toughness, and wear resistance are important. In addition, these morphologies lend themselves to substantially broader applications, including: (1) structural color applications, (2) tuning optical adsorption, and (3) barrier coatings.

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 Nanocomposite Dielectrics: Understanding the Matrix/Particle Interface

Polymer nanocomposite dielectrics possess exceptional electric properties that are absent in the pristine dielectric polymers. The matrix/particle interface in polymer nanocomposite dielectrics is suggested to play decisive roles on the bulk material performance. Herein, we present a critical overview of recent research advances and important insights in understanding the matrix/particle interfacial characteristics in polymer nanocomposite dielectrics. The primary experimental strategies and state-of-the-art characterization techniques for resolving the local property-structure correlation of the matrix/particle interface are dissected in depth, with a focus on the characterization capabilities of each strategy or technique that other approaches cannot compete with. Limitations to each of the experimental strategy are evaluated as well. In the last section of this Review, we summarize and compare the three experimental strategies from multiple aspects and point out their advantages and disadvantages, critical issues, and possible experimental schemes to be established. Finally, the authors' personal viewpoints regarding the challenges of the existing experimental strategies are presented, and potential directions for the interface study are proposed for future research.

Unraveling Nanoscale Elastic and Adhesive Properties at the Nanoparticle/Epoxy Interface Using Bimodal Atomic Force Microscopy

The addition of a small fraction of solid nanoparticles to thermosetting polymers can substantially improve their fracture toughness, while maintaining various intrinsic thermomechanical properties. The underlying mechanism is largely related to the debonding process and subsequent formation of nanovoids at a nanoscale nanoparticle/epoxy interface, which is thought to be associated with a change in the structural and mechanical properties of the formed epoxy network at the interface compared with the matrix region. However, a direct characterization of the local physical properties at this nanoscale interface remains significantly challenging. Here, we employ a recently developed bimodal atomic force microscopy technique for the direct mapping of nanoscale elastic and adhesive responses of an amine-cured epoxy resin filled with ∼50 nm diameter silica nanoparticles. The obtained elastic modulus and dissipated energy maps with high spatial resolution evidence the existence of a ∼20-nm-thick interfacial epoxy layer surrounding the nanoparticles, which exhibits a reduced modulus and weaker adhesive response in comparison with the matrix properties. While the presence of such a soft and weak-adhesive interfacial layer is found not to affect the architecture of structural heterogeneities in the epoxy matrix, it conceivably supports the toughening mechanism related to the debonding and plastic nanovoid growth at the silica/epoxy interface. The incorporation of this soft interfacial layer into the Halpin-Tsai model also provides a good explanation for the effect of the silica fraction on the tensile modulus of cured epoxy nanocomposites.

Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies

We rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes. While gas permeabilities depend specifically on the chemistry of the polymers considered, we focus here on permeabilities relative to the corresponding pure polymer which show interesting, "universal" behavior. For a given NP radius, R_c, and for large enough areal grafting densities, σ, to be in the dense brush regime we find that gas permeability enhancements display a maximum as a function of the graft chain molecular weight, M_n. Based on a recently proposed theory for the structure of a spherical brush in a melt of GNPs, we conjecture that this peak permeability occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The corresponding brush thickness is predicted to be h max = 3 R c , independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕ_NP, ϕ_NP,max = [R_c/(R_c + h_max)]³ ≈ 0.049. Motivated by this conclusion, we measured CO_-2 and CH₄ permeability enhancements across a variety of R_c, M_n and σ, and find that they behave in a similar manner when considered as a function of ϕ_NP, with a peak in the near vicinity of the predicted ϕ_NP,max. Thus, the chain length dependent extension free energy appears to be the critical variable in determining the gas permeability for these hybrid materials. The emerging picture is that these curved polymer brushes, at high enough σ behave akin to a two-layer transport medium - the region in the near vicinity of the NP surface is comprised of extended polymer chains which speed-up gas transport relative to the unperturbed melt. The chain extension free energy increases with increasing chain length, up to a maximum, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that is akin to an unperturbed melt with slow gas transport. The permeability maximum and decreasing permeability with increasing chain length then follow naturally.

Direct Visualization of Interfacial Regions between Fillers and Matrix in Rubber Composites Observed by Atomic Force Microscopy-Based Nanomechanics Assisted by Electron Tomography

In order to explain or predict the macroscopic mechanical properties of polymer composites with complex nanostructures, atomic force microscopy (AFM)-based nanomechanics is one of the most appropriate tools because the local mechanical properties can be obtained by it. However, automatic force curve analysis based on contact mechanics would mislead us to the wrong conclusion. The purpose of this study is to elucidate this point by applying AFM nanomechanics on a carbon black (CB)-reinforced isoprene rubber (IR). The CB aggregates underneath the rubber surface prevent us from quantitatively evaluating the ratio of CB and interfacial polymer region (IPR), which is an important parameter to determine the macroscopic mechanical properties. In order to overcome this problem, transmission electron microtomography was incorporated to investigate the 3D structure in the same field of view as AFM nanomechanics. As a result, it was found that there are buried structures that do not appear in the AFM topographic image. In addition, we were able to reveal the existence of a force curve with an inflection point, which is characteristic of such "false" IPRs. To put it another way, we evidenced the existence of true IPRs for the first time by combining these state-of-the-art techniques.

Rationalizing the Composition Dependence of Glass Transition Temperatures in Amorphous Polymer/POSS Composites

We report that the fractions of "bonded" or "unbonded" monomers at a filler interface dictate the composition dependence of the glass transition temperatures (T_g) of polyhedral oligomeric silsesquioxane (POSS)-containing nanocomposites. T_g is arguably the single most important material property; however, predicting T_g in nanocomposites is often challenging because of confounding interfacial effects. To this end, we design a model nanocomposite to systematically study T_g of nanocomposites by leveraging the "all-interfacial" nature of ultrasmall POSS fillers loaded into random copolymers of styrene and 2-vinylpyridine (2VP). The amine-functionalized POSS forms hydrogen bonds only with 2VP, which behaves as a "bonded" monomer. The influence of copolymer composition and POSS loading on the T_g of this model composite is successfully explained by a Fox equation framework. This model also captures the T_g increase of other POSS-based polymer composites and potentially directs the future design of nanocomposite materials with tailored T_g.

Gas Transport in Interacting Planar Brushes

Recent experiments on melts of spherical nanoparticles (NPs) densely grafted with polymer chains show enhanced gas transport relative to the neat polymer (without NPs). As a means of understanding this unexpected behavior, we consider here the simpler case of two interacting planar brushes, under conditions representing a polymer melt far below its critical point (i.e., where the "free volume" or holes act akin to a poor solvent). Computer simulations illustrate, in agreement with mean-field ideas, that the density profile far away from the walls is flat but with a value that is marginally larger than the corresponding polymer melt under identical state conditions. We find that tracer particles, which represent the gas of interest, segregate preferentially to the grafting surface, with this result being relatively insensitive to the nature of polymer-surface interactions. These brush layers therefore correspond to heterogeneous transport media: the gas molecules near the grafting surface have accelerated dynamics (presumably parallel to the wall) relative to the corresponding polymer melt, but they have slower dynamics in the central region of the brush. We therefore find that gas molecules perform hop-like motions - they spend a significant part of their time in the regions of fast transport, separated by motions where they "hop" from one surface to the other. These phenomena in combination lead to an overall speedup in gas dynamics in these brush layers relative to a polymer melt, in good agreement with the experimental data.

Collective Nanoparticle Dynamics Associated with Bridging Network Formation in Model Polymer Nanocomposites

The addition of nanoparticles (NPs) to polymers is a powerful method to improve the mechanical and other properties of macromolecular materials. Such hybrid polymer-particle systems are also rich in fundamental soft matter physics. Among several factors contributing to mechanical reinforcement, a polymer-mediated NP network is considered to be the most important in polymer nanocomposites (PNCs). Here, we present an integrated experimental-theoretical study of the collective NP dynamics in model PNCs using X-ray photon correlation spectroscopy and microscopic statistical mechanics theory. Silica NPs dispersed in unentangled or entangled poly(2-vinylpyridine) matrices over a range of NP loadings are used. Static collective structure factors of the NP subsystems at temperatures above the bulk glass transition temperature reveal the formation of a network-like microstructure via polymer-mediated bridges at high NP loadings above the percolation threshold. The NP collective relaxation times are up to 3 orders of magnitude longer than the self-diffusion limit of isolated NPs and display a rich dependence with observation wavevector and NP loading. A mode-coupling theory dynamical analysis that incorporates the static polymer-mediated bridging structure and collective motions of NPs is performed. It captures well both the observed scattering wavevector and NP loading dependences of the collective NP dynamics in the unentangled polymer matrix, with modest quantitative deviations emerging for the entangled PNC samples. Additionally, we identify an unusual and weak temperature dependence of collective NP dynamics, in qualitative contrast with the mechanical response. Hence, the present study has revealed key aspects of the collective motions of NPs connected by polymer bridges in contact with a viscous adsorbing polymer medium and identifies some outstanding remaining challenges for the theoretical understanding of these complex soft materials.

Molecular View on Mechanical Reinforcement in Polymer Nanocomposites

The microscopic origin of mechanical enhancement in polymer nanocomposite (PNC) melts is investigated through the combination of rheology and small-angle neutron scattering. It is shown that in the absence of an extensive particle network, the molecular deformation of polymer chains dominates the stress response on intermediate time scales. Quantitative analyses of small-angle neutron scattering spectra, however, reveal no enhanced structural anisotropy in the PNCs, compared with the pristine polymers under the same deformation conditions. These results demonstrate that the mechanical reinforcement of PNCs is not due to molecular overstraining, but instead a redistribution of strain field in the polymer matrix, akin to the classical picture of hydrodynamic effect of nanoparticles.

Turning Rubber into a Glass: Mechanical Reinforcement by Microphase Separation

Supramolecular associations provide a promising route to functional materials with properties such as self-healing, easy recyclability or extraordinary mechanical strength and toughness. The latter benefit especially from the transient character of the formed network, which enables dissipation of energy as well as regeneration of the internal structures. However, recent investigations revealed intrinsic limitations in the achievable mechanical enhancement. This manuscript presents studies of a set of telechelic polymers with hydrogen-bonding chain ends exhibiting an extraordinarily high, almost glass-like, rubbery plateau. This is ascribed to the segregation of the associative ends into clusters and formation of an interfacial layer surrounding these clusters. An approach adopted from the field of polymer nanocomposites provides a quantitative description of the data and reveals the strongly altered mechanical properties of the polymer in the interfacial layer. These results demonstrate how employing phase separating dynamic bonds can lead to the creation of high-performance materials.

Structure of Polymer-Grafted Nanoparticle Melts

The structure of neat melts of polymer-grafted nanoparticles (GNPs) is studied via coarse-grained molecular dynamics simulations. We systematically vary the degree of polymerization and grafting density at fixed nanoparticle (NP) radius and study in detail the shape and size of the GNP coronas. For sufficiently high grafting density, chain sections close to the NP core are extended and form a dry layer. Further away from the NP, there is an interpenetration layer, where the polymer coronas of neighboring GNPs overlap and the chain sections have almost unperturbed conformations. To better understand this partitioning, we develop a two-layer model, representing the grafted polymer around an NP by spherical dry and interpenetration layers. This model quantitatively predicts that the thicknesses of the two layers depend on one universal parameter, x, the degree of overcrowding of grafted chains relative to chains in the melt. Both simulations and theory show that the chain extension free energy is nonmonotonic with increasing chain length at a fixed grafting density, with a well-defined maximum. This maximum is indicative of the crossover from the dry layer-dominated to interpenetration layer-dominated regime, and it could have profound consequences on our understanding of a variety of anomalous transport properties of these GNPs. Our theoretical approach therefore provides a facile means for understanding and designing solvent-free GNP-based materials.

Effect of polymer-nanoparticle interaction on strain localization in polymer nanopillars

Polymer nanocomposites (PNCs), a class of composites consisting of typically inorganic nanoparticles (NPs) embedded in a polymer matrix, have become an emerging class of materials due to their significant potential to combine the functionality of NPs with the toughness of polymers. However, many applications are limited by their mechanical properties, and a fundamental understanding of NPs' effect on the nonlinear mechanical properties is lacking. In this study, we used molecular dynamics simulations to investigate the influence of NPs on the tendency of a polymer nanopillar to form a shear band. Even though we restrict ourselves to sufficiently low NP loadings that the elastic and yield behaviors are unaffected compared to the pure polymer, the polymer-NP interactions have a surprisingly strong effect on the location of a shear band in the sample. Different polymer-NP interactions have been used to explore their effect on the local structure of materials which is described using a recently developed machine-learned quantity, softness. Our calculations reveal a strong correlation between the strain localization pattern and the local structural signatures. Lastly, we show that weak interactions between NP and polymer matrix can form a soft region near the NP, and this leads to an attraction of the shear band to the NP surface.

Revisiting stress-strain behavior and mechanical reinforcement of polymer nanocomposites from molecular dynamics simulations

Through coarse-grained molecular dynamics simulations, the effects of nanoparticle properties, polymer-nanoparticle interactions, chain crosslinks and temperature on the stress-strain behavior and mechanical reinforcement of polymer nanocomposites (PNCs) are comprehensively investigated. By regulating the filler-polymer interaction (miscibility) in a wide range, an optimal dispersion state of nanoparticles is found at moderate interaction strength, while the mechanical properties of PNCs are improved monotonically with the increase of the particle-polymer interaction due to the tele-bridge structures of nanoparticles via polymer chains. Although smaller-sized fillers more easily build interconnected structures, the elastic moduli of PNCs at the percolation threshold concentration where a three-dimensional filler network forms are almost independent of nanoparticle size. Compared with spherical nanoparticles, anisotropic rod-like ones, especially with larger aspect ratio and rod stiffness, contribute exceptional reinforcement towards polymer materials. In addition, the elastic modulus with the strain, derived from the stress-strain curve, shows an analogous nonlinear behavior to the amplitude-dependence of the storage modulus (Payne effect). Such a behavior originates essentially from the failure/breakup of the microstructures contributing to the mechanical reinforcement, such as bound polymer layers around nanoparticles or nanoparticle networking structures. The Young's modulus as a function of the nanoparticle volume fraction greatly exceeds that predicted by the Einstein-Smallwood model and Guth-Gold model, which arises primarily from the contribution of the local/global filler network. The temperature dependence of the Young's modulus is further examined by mode coupling theory (MCT) and the Vogel-Fulcher-Tammann (VFT) equation, and the results indicate that the time-temperature superposition principle holds modestly above the critical temperature on the short-time (small-length) scale of elastic response. This work is expected to provide some guidance on controlling and improving the mechanical properties and nonlinear behavior of PNCs.