Structural and Dynamical Properties of Polyethylene/Graphene Nanocomposites through Molecular Dynamics Simulations

Crystallisation Kinetics and Associated Electrical Conductivity Dynamics of Poly(Ethylene Vinyl Acetate) Nanocomposites in the Melt State

Nanocomposite systems comprised of a poly(ethylene vinyl acetate) (EVA) matrix and carbon black (CB) or graphene nanoplatelets (GNPs) were used to investigate conductivity and crystallisation dynamics using a commercially relevant melt-state mixing process. Crystallisation kinetics and morphology, as investigated by DSC and SEM, turn out to depend on the interplay of (i) the interphase interactions between matrix and filler, and (ii) the degree of filler agglomeration. For the GNP-based systems, an almost constant conductivity value was observed for all compositions upon cooling, something not observed for the CB-based compositions. These conductivity changes reflect structural and morphological changes that can be associated with positive and negative thermal expansion coefficients. GNP-based systems were observed to exhibit a percolation threshold of approximately 2.2 vol%, lower than the 4.4 vol% observed for the CB-based systems.

Dynamics of Polymer Chains in Poly(ethylene oxide)/Silica Nanocomposites via a Combined Computational and Experimental Approach

The dynamics of polymer chains in poly(ethylene oxide)/silica (PEO/SiO₂) nanoparticle nanohybrids have been investigated via a combined computational and experimental approach involving atomistic molecular dynamics simulations and dielectric relaxation spectroscopy (DRS) measurements. The complementarity of the approaches allows us to study systems with different polymer molecular weights, nanoparticle radii, and compositions across a broad range of temperatures. We study the effects of spatial confinement, which is induced by the nanoparticles, and chain adsorption on the polymer's structure and dynamics. The investigation of the static properties of the nanocomposites via detailed atomistic simulations revealed a heterogeneous polymer density layer at the vicinity of the PEO/SiO₂ interface that exhibited an intense maximum close to the inorganic surface, whereas the bulk density was reached for distances ∼1-1.2 nm away from the nanoparticle. For small volume fractions of nanoparticles, the polymer dynamics, probed by the atomistic simulations of low-molecular-weight chains at high temperatures, are consistent with the presence of a thin adsorbed layer that exhibits slow dynamics, with the dynamics far away from the nanoparticle being similar to those in the bulk. However, for high volume fractions of nanoparticles (strong confinement), the dynamics of all polymer chains were predicted slower than that in the bulk. On the other hand, similar dynamics were found experimentally for both the local β-process and the segmental dynamics for high-molecular-weight systems measured at temperatures below the melting temperature of the polymer, which were probed by DRS. These differences can be attributed to various parameters, including systems of different molecular weights and nanoparticle states of dispersion, the different temperature range studied by the different methods, the potential presence of a reduced-mobility PEO/SiO₂ interfacial layer that does not contribute to the dielectric spectrum, and the presence of amorphous-crystalline interfaces in the experimental samples that may lead to a different dynamical behaviors of the PEO chains.

Interface and Interphase in Polymer Nanocomposites with Bare and Core-Shell Gold Nanoparticles

Metal nanoparticles are used to modify/enhance the properties of a polymer matrix for a broad range of applications in bio-nanotechnology. Here, we study the properties of polymer/gold nanoparticle (NP) nanocomposites through atomistic molecular dynamics, MD, simulations. We probe the structural, conformational and dynamical properties of polymer chains at the vicinity of a gold (Au) NP and a functionalized (core/shell) Au NP, and compare them against the behavior of bulk polyethylene (PE). The bare Au NPs were constructed via a systematic methodology starting from ab-initio calculations and an atomistic Wulff construction algorithm resulting in the crystal shape with the minimum surface energy. For the functionalized NPs the interactions between gold atoms and chemically adsorbed functional groups change their shape. As a model polymer matrix we consider polyethylene of different molecular lengths, from the oligomer to unentangled Rouse like systems. The PE/Au interaction is parametrized via DFT calculations. By computing the different properties the concept of the interface, and the interphase as well, in polymer nanocomposites with metal NPs are critically examined. Results concerning polymer density profiles, bond order parameter, segmental and terminal dynamics show clearly that the size of the interface/interphase, depends on the actual property under study. In addition, the anchored polymeric chains change the behavior/properties, and especially the chain density profile and the dynamics, of the polymer chain at the vicinity of the Au NP.

Self-assembly of diphenylalanine peptides on graphene via detailed atomistic simulations

The self-assembly of diphenylalanine peptides (FF) on a graphene layer, in aqueous solution, is investigated, through all atom molecular dynamics simulations. Two interfacial systems are studied, with different concentrations of dipeptides and the results are compared with an aqueous solution of FF at room temperature. Corresponding length and time scales of the formed structures are quantified providing important insight into the adsorption mechanism of FF onto the graphene surface. A hierarchical formation of FF structures is observed involving two sequential processes: first, a stabilized interfacial layer of dipeptides onto the graphene surface is formulated, which next is followed by the development of a structure of self-aggregated dipeptides on top of this layer. The whole procedure is completed in almost 200 ns, whereas self-assembly in the system without graphene is accomplished much faster; in less than 50 ns cylindrical structures, the microscopic signal of the macroscopic fibrillar ones, are formed. Strong π-π* interactions between FF and the graphene lead to a parallel orientation to the graphene layer of the phenyl rings within a characteristic time of 80 ns, similar to the one indicated by the time evolution of the number of adsorbed FF atoms at the surface. Reduction in the number of hydrogen bonds between FF peptides is observed because of the graphene layer, since it disturbs their self-assembly propensity. The self-assembly of dipeptides and their adsorption onto the graphene surface destruct the hydrogen bond network of water, in the vicinity of FF, however, the total number of hydrogen bonds in all systems increases, promoting the formed structures.

Viscoelasticity of Nanosheet-Filled Polymer Composites: Three Regimes in the Enhancement of Moduli

We employed nonequilibrium molecular dynamics simulations to elucidate the viscoelastic properties of nanosheet (NS)-filled polymer composites. The effects of NS loadings and NS-polymer interaction on viscoelasticity were examined. The simulation results show that the NS-filled polymer composites exhibit an enhanced storage modulus and loss modulus as the NSs are loaded. There are three regimes of the enhanced process based on the NS loadings. At lower NS loadings, the motion of polymers slows down owing to the interaction between NSs and polymers, and the polymer chains generally follow the Rouse dynamics. As the NS loadings increase, the polymer chains are confined between NSs, leading to a substantial increment in dynamic moduli. At higher NS loadings, a transient network is formed, which strengthens the dynamic moduli further. In addition, the attractive NS-polymer interaction can improve the dispersion of NSs and increase the storage and loss moduli. The present work could provide essential information for designing high-performance hybrid polymeric materials.

Performance of Coarse Graining in Estimating Polymer Properties: Comparison with the Atomistic Model

Combining atomistic and coarse-grained (CG) models is a promising approach for quantitative prediction of polymer properties. However, the gaps between the length and time scales of atomistic and CG models still need to be bridged. Here, the scale gaps of the atomistic model of polyethylene melts, the bead–spring Kremer–Grest model, and dissipative particle dynamics with the slip-spring model were investigated. A single set of spatial and temporal scaling factors was determined between the atomistic model and each CG model. The results of the CG models were rescaled using the set of scaling factors and compared with those of the atomistic model. For each polymer property, a threshold value indicating the onset of static or dynamic universality of polymers was obtained. The scaling factors also revealed the computational efficiency of each CG model with respect to the atomistic model. The performance of the CG models of polymers was systematically evaluated in terms of both the accuracy and computational efficiency.

Surface Modification Design for Improving the Strength and Water Vapor Permeability of Waterborne Polymer/SiO2 Composites: Molecular Simulation and Experimental Analyses

Polymer-based nanocomposites properties are greatly affected by interfacial interaction. Polyacrylate nanocomposites have been widely studied, but few studies have been conducted on their interface mechanism. Therefore, there was an urgent demand for providing a thorough understanding of the polymethyl acrylate/SiO₂ (PMA/SiO₂) nanocomposites to obtain the desired macro-performance. In this paper, a methodology, which combined molecular dynamics simulation with experimental researches, was established to expound the effect of the surface structure of SiO₂ particles which were treated with KH550, KH560 or KH570 (KH550-SiO₂, KH560-SiO₂ and KH570-SiO₂) on the mechanical characteristic and water vapor permeability of polymethyl acrylate/SiO₂ nanocomposites. The polymethyl acrylate/SiO₂ nanocomposites were analyzed in binding energy and mean square displacement. The results indicate that PMA/KH570-SiO₂ had the highest tensile strength, while PMA/KH550-SiO₂ had the highest elongation at break at the same filler content; KH550-SiO₂ spheres can significantly improve water vapor permeability of polyacrylate film.

Multiscale modelling of strain-resistance behaviour for graphene rubber composites under large deformation

The electrical conductivity of graphene rubber nanocomposites under large deformation is studied based on multiscale modeling with effective medium theory and molecular dynamics simulations. The effects of graphene filling volume fractions, graphene dispersion patterns and interfacial interaction strengths of graphene/rubber are investigated on the electrical properties of the composites. The results show that the strain-resistance sensitivity of the composites is determined by graphene volume fractions and the relationship between the average spacing of graphene sheets and the strain, which might take a nonlinear form for the system with large initial spacing ratios of graphene. Detailed analysis of graphene clusters and system energy reveals that too high or too low interfacial interaction might decrease the strain-resistance sensitivity by preventing the decomposition of large graphene clusters while moderate interfacial interaction can help maintain the structure of graphene conductive networks with high strain-resistance sensitivity.

Investigation of the properties of nanographene in polymer nanocomposites through molecular simulations: dynamics and anisotropic Brownian motion

The dynamical behavior of nanographene sheets dispersed in polymer matrices is investigated through united-atom molecular dynamics simulations. The Brownian motion of the sheet and the anisotropy in its translational and orientational diffusion are the topics of the current study. Different polymer matrices and pristine and functionalized graphene constitute various nanocomposite systems. Interactions between the nanographene flake and the matrix determine the dynamics of the systems. The dynamics is reduced in polyethylene oxide compared to polyethylene matrix, whereas carboxylated sheets move considerably slower than the pristine nanographene in any matrix. Diffusion is anisotropic for short times, while it becomes isotropic in the long time limit. The in-plane motion of the nanographene sheet is faster than the out-of-plane component, in agreement with the diffusion of perfectly oblate ellipsoids. In functionalized graphene, the anisotropy is suppressed. By exploring the temperature effect on both the nanographene sheet and polymer close to the surface, indications for coupling in the motion of the two components are revealed. The strong effect of edge functional groups on the dynamics can be used as a way to control the Brownian motion of nanographene sheets in polymer nanocomposites and consequently tailor the properties of the materials.

Nano-Level Damage Characterization of Graphene/Polymer Cohesive Interface under Tensile Separation

The mechanical behavior of graphene/polymer interfaces in the graphene-reinforced epoxy nanocomposite is one of the factors that dictates the deformation and damage response of the nanocomposites. In this study, hybrid molecular dynamic (MD) and finite element (FE) simulations of a graphene/polymer nanocomposite are developed to characterize the elastic-damage behavior of graphene/polymer interfaces under a tensile separation condition. The MD results show that the graphene/epoxy interface behaves in the form of elastic-softening exponential regressive law. The FE results verify the adequacy of the cohesive zone model in accurate prediction of the interface damage behavior. The graphene/epoxy cohesive interface is characterized by normal stiffness, tensile strength, and fracture energy of 5 × 10⁻⁸ (aPa·nm⁻¹), 9.75 × 10⁻¹⁰ (nm), 2.1 × 10⁻¹⁰ (N·nm⁻¹) respectively, that is followed by an exponential regressive law with the exponent, α = 7.74. It is shown that the commonly assumed bilinear softening law of the cohesive interface could lead up to 55% error in the predicted separation of the interface.

Construction of a Different Polymer Chain Structure to Study π-π Interaction between Polymer and Reduced Graphene Oxide

In this work, a different polymer chain structure was synthesized to study π-π interactions between polymer and reduced graphene oxide (RGO). Polymers with different chain structures were obtained from free radical copolymerization of styrene with 4-cyanostyrene (containing substituted phenyl rings) and 2-vinylnaphthalene (containing naphthalene rings). In this work, the polystyrene, poly(styrene-co-4-cyanostyrene) and poly(styrene-co-2-vinylnaphthalene) were named as PS, PSCN and PSNP, respectively. RGO was prepared through modified Hummers' method and further thermal reduction, and nanocomposites were prepared by solution blending. Thus, different π-π interactions were formed between polymers and RGO. Raman and thermal gravimetric analysis (TGA) were used to characterize the interfacial interaction, showing that the trend of the interfacial interaction should be in the order of RGO/PSCN, RGO/PS, and RGO/PSNP. The differential scanning calorimetry (DSC) measurement showed that, compared with polymer matrix, the glass transition temperature (Tg) of RGO/PS, RGO/PSCN and RGO/PSNP nanocomposites with the addition of 4.0 wt% RGO are increased by 14.3 °C, 25.2 °C and 4.4 °C, respectively. Compared with π-π interaction only formed through aromatic rings, substituent groups changed the densities of electron clouds on the phenyl rings. This change resulted in the formation of donor-acceptor interaction and reinforcement of the π-π interaction at the interface, which leads to increased value of Tg. This comparative study can be useful for selecting appropriate interaction groups, as well as suitable monomers, to prepare high performance nanocomposites.

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.

Enhanced Computational Sampling of Perylene and Perylothiophene Packing with Rigid-Body Models

Molecular simulations have the potential to advance the understanding of how the structure of organic materials can be engineered through the choice of chemical components but are limited by computational costs. The computational costs can be significantly lowered through the use of modeling approximations that capture the relevant features of a system, while lowering algorithmic complexity or by decreasing the degrees of freedom that must be integrated. Such methods include coarse-graining techniques, approximating long-range electrostatics with short-range potentials, and the use of rigid bodies to replace flexible bonded constraints between atoms. To understand whether and to what degree these techniques can be leveraged to enhance the understanding of planar organic molecules, we investigate the morphologies predicted by molecular dynamic simulations using simplified molecular models of perylene and perylothiophene. Approximately, 10 000 wall-clock hours of graphics processing unit-accelerated simulations are performed using both rigid and flexible models to test their efficiency and predictive capability with the two chemistries. We characterize the 1191 resulting morphologies using simulated X-ray diffraction and cluster analysis to distinguish structural transitions, summarized by four phase diagrams. We find that the morphologies generated by the rigid model of perylene and perylothiophene match with those generated by the flexible model. We find that ordered, hexagonally packed columnar phases are thermodynamically favored over a wide range of densities and temperatures for both molecules, in qualitative agreement with experiments. Furthermore, we find the rigid model to be more computationally efficient for both molecules, providing more samples per second and shorter times to equilibrium. Owing to the structural accuracy and improved computational efficiency of modeling polyaromatic groups as rigid bodies, we recommend this modeling choice for enhancing the sampling in polyaromatic molecular simulations.

Molecular Dynamics Simulations for Resolving Scaling Laws of Polyethylene Melts

Long-timescale molecular dynamics simulations were performed to estimate the actual physical nature of a united-atom model of polyethylene (PE). Several scaling laws for representative polymer properties are compared to theoretical predictions. Internal structure results indicate a clear departure from theoretical predictions that assume ideal chain statics. Chain motion deviates from predictions that assume ideal motion of short chains. With regard to linear viscoelasticity, the presence or absence of entanglements strongly affects the duration of the theoretical behavior. Overall, the results indicate that Gaussian statics and dynamics are not necessarily established for real atomistic models of PE. Moreover, the actual physical nature should be carefully considered when using atomistic models for applications that expect typical polymer behaviors.

A Review of Multiscale Computational Methods in Polymeric Materials

Polymeric materials display distinguished characteristics which stem from the interplay of phenomena at various length and time scales. Further development of polymer systems critically relies on a comprehensive understanding of the fundamentals of their hierarchical structure and behaviors. As such, the inherent multiscale nature of polymer systems is only reflected by a multiscale analysis which accounts for all important mechanisms. Since multiscale modelling is a rapidly growing multidisciplinary field, the emerging possibilities and challenges can be of a truly diverse nature. The present review attempts to provide a rather comprehensive overview of the recent developments in the field of multiscale modelling and simulation of polymeric materials. In order to understand the characteristics of the building blocks of multiscale methods, first a brief review of some significant computational methods at individual length and time scales is provided. These methods cover quantum mechanical scale, atomistic domain (Monte Carlo and molecular dynamics), mesoscopic scale (Brownian dynamics, dissipative particle dynamics, and lattice Boltzmann method), and finally macroscopic realm (finite element and volume methods). Afterwards, different prescriptions to envelope these methods in a multiscale strategy are discussed in details. Sequential, concurrent, and adaptive resolution schemes are presented along with the latest updates and ongoing challenges in research. In sequential methods, various systematic coarse-graining and backmapping approaches are addressed. For the concurrent strategy, we aimed to introduce the fundamentals and significant methods including the handshaking concept, energy-based, and force-based coupling approaches. Although such methods are very popular in metals and carbon nanomaterials, their use in polymeric materials is still limited. We have illustrated their applications in polymer science by several examples hoping for raising attention towards the existing possibilities. The relatively new adaptive resolution schemes are then covered including their advantages and shortcomings. Finally, some novel ideas in order to extend the reaches of atomistic techniques are reviewed. We conclude the review by outlining the existing challenges and possibilities for future research.

Molecular insights into the effect of graphene packing on mechanical behaviors of graphene reinforced cis-1,4-polybutadiene polymer nanocomposites

We adopt molecular dynamics simulation to study the graphene packing patterns on chain structure, dynamics, uniaxial tension and visco-elastic behaviors.

Atomistic Modelling of Confined Polypropylene Chains between Ferric Oxide Substrates at Melt Temperature

The interactions and conformational characteristics of confined molten polypropylene (PP) chains between ferric oxide (Fe₂O₃) substrates were investigated by molecular dynamics (MD) simulations. A comparative analysis of the adsorbed amount shows strong adsorption of the chains on the high-energy surface of Fe₂O₃. Local structures formed in the polymer film were studied utilizing density profiles, orientation of bonds, and end-to-end distance of chains. At interfacial regions, the backbone carbon-carbon bonds of the chains preferably orient in the direction parallel to the surface while the carbon-carbon bonds with the side groups show a slight tendency to orient normal to the surface. Based on the conformation tensor data, the chains are compressed in the normal direction to the substrates in the interfacial regions while they tend to flatten in parallel planes with respect to the surfaces. The orientation of the bonds as well as the overall flattening of the chains in planes parallel to the solid surfaces are almost identical to that of the unconfined PP chains. Also, the local pressure tensor is anisotropic closer to the solid surfaces of Fe₂O₃ indicating the influence of the confinement on the buildup imbalance of normal and tangential pressures.

Adsorption of poly(ethylene succinate) chain onto graphene nanosheets: A molecular simulation

Understanding the interaction between single polymer chain and graphene nanosheets at local and global length scales is essential for it underlies the mesoscopic properties of polymer nanocomposites. A computational attempt was then performed using atomistic molecular dynamics simulation to gain physical insights into behavior of a model aliphatic polyester, poly(ethylene succinate), single chain near graphene nanosheets, where the effects of the polymer chain length, graphene functionalization, and temperature on conformational properties of the polymer were studied comparatively. Graphene functionalization was carried out through extending the parameters set of an all-atom force field. The results showed a significant conformational transition of the polymer chain from three-dimensional statistical coil, in initial state, to two-dimensional fold, in final state, during adsorption on graphene. The conformational order, overall shape, end-to-end separation statistics, and mobility of the polymer chain were found to be influenced by the graphene functionalization, temperature, and polymer chain length. Furthermore, the polymer chain dynamics mode during adsorption on graphene was observed to transit from normal diffusive to slow subdiffusive mode. The findings from this computational study could shed light on the physics of the early stages of aliphatic polyester chain organization induced by graphene.

A Comparison of the Elastic Properties of Graphene- and Fullerene-Reinforced Polymer Composites: The Role of Filler Morphology and Size

Nanoscale carbon-based fillers are known to significantly alter the mechanical and electrical properties of polymers even at relatively low loadings. We report results from extensive molecular-dynamics simulations of mechanical testing of model polymer (high-density polyethylene) nanocomposites reinforced by nanocarbon fillers consisting of graphene flakes and fullerenes. By systematically varying filler concentration, morphology, and size, we identify clear trends in composite stiffness with reinforcement. To within statistical error, spherical fullerenes provide a nearly size-independent level of reinforcement. In contrast, two-dimensional graphene flakes induce a strongly size-dependent response: we find that flakes with radii in the 2–4 nm range provide appreciable enhancement in stiffness, which scales linearly with flake radius. Thus, with flakes approaching typical experimental sizes (~0.1–1 μm), we expect graphene fillers to provide substantial reinforcement, which also is much greater than what could be achieved with fullerene fillers. We identify the atomic-scale features responsible for this size- and morphology-dependent response, notably, ordering and densification of polymer chains at the filler–matrix interface, thereby providing insights into avenues for further control and enhancement of the mechanical properties of polymer nanocomposites.

Characterization of a graphene oxide/poly(acrylic acid) nanocomposite by means of molecular dynamics simulations

Graphene oxide/poly(acrylic acid) nanocomposite: static, dynamic, thermal properties and hydrogen bonding, as studied by molecular dynamics simulations.

Translational and rotational diffusion of a single nanorod in unentangled polymer melts

Polymer nanocomposites have been an issue of both academic and industrial interest due to promising electrical, mechanical, optical, and magnetic properties. The dynamics of nanoparticles in polymer nanocomposites is a key to understanding those properties of polymer nanocomposites and is important for applications such as self-healing nanocomposites. In this article we investigate the translational and the rotational dynamics of a single nanorod in unentangled polymer melts by employing extensive molecular dynamics simulations. A nanorod and polymers are modeled as semiflexible tangent chains of spherical beads. The stiffness of a nanorod is tuned by changing the bending potential between chemical bonds. When polymers are sufficiently long and the nanorod is stiff, the nanorod translates in an anisotropic fashion along the nanorod axis within time scales of translational relaxation times even in unentangled polymer melts. The rotational diffusion is suppressed more significantly than the translational diffusion as the polymer chain length is increased, thus the translational and rotational diffusion of the nanorod are decoupled. We also estimate the winding numbers of polymers, i.e., how many times a polymer winds the nanorod. The winding number increases with longer polymers but is relatively insensitive to the nanorod stiffness.

Revealing the toughening mechanism of graphene-polymer nanocomposite through molecular dynamics simulation

By employing united atom molecular dynamics simulation, we have investigated the effects of polymer-graphene interaction ε(np) volume fraction of grapheme φ thermodynamics of polymer matrix (rubbery versus glassy), interfacial interaction in the case of the same dispersion state, shape of nanoparticles (NPs) such as C60 CNT and graphene at the same loading on the toughening efficiency of polymer nanocomposites. By beginning with the pure polymer, we observe that a plateau stress occurs at long chain length because entangled polymer chains in fibrils cannot become broken. We find that the work needed to dissipate during the failure increases with the increase of ε(np) and φ and the yield point in the stress-strain behavior occurs at a smaller strain for an attractive NPs filled system compared to the pure case, attributed to the more mechanically heterogeneous environment. The thermodynamics of the polymer matrix (below and above Tg) seems to have a significant effect on the toughening efficiency of graphene sheets. In the case of the same dispersion state, stronger interfacial interaction always induces long and highly orientated polymer fibrils along the deformation direction, with graphene sheets being encapsulated in these fiber-like bundles. By characterizing the interaction energy between polymer-polymer and polymer-graphene as a function of the strain, we find that the separation of polymer chains from the graphene sheets cease immediately after the yield point, followed by the continuous propagation of the cavities by excluding surrounded polymer chains and graphene sheets together. We also find that at the same attractive interfacial interaction and same loading, the toughening efficiency exhibits the following order: graphene > CNT > C60 Generally, the toughening mechanism of graphene sheets results from the formation of long and highly orientated polymer fibrils to prevent the occurrence of the rupture, which can be greatly improved by the strong interfacial interaction and the large surface area compared to CNT and C60 This also indicates that polymer matrices with high flexibility and mobility of polymer chains tend to be better toughened. It is hoped that this simulation work will provide rational guidance for fabricating high performance of polymer nanocomposites with excellent toughness.