Elucidating and tuning the strain-induced non-linear behavior of polymer nanocomposites: a detailed molecular dynamics simulation study

Percolation-Triggered Negative Permittivity in Nano Carbon Powder/Polyvinylidene Fluoride Composites

Percolating composites exhibiting negative permittivity have garnered considerable attention due to their promising applications in the realm of electromagnetic shielding, innovative capacitance devices, coil-less inductors, etc. Nano carbon powder/polyvinylidene fluoride (CP/PVDF) percolating composites were fabricated that exhibit Drude-type negative-permittivity behavior upon reaching the CP percolation threshold. This phenomenon is attributed to the formation of a plasmonic state within the interconnected CP network, enabling the delocalization of electrons under the alternating electric field. Furthermore, a significant (nearly two orders of magnitude) increase in the conductivity of sample is observed at a CP content of 12.5 wt%. This abrupt change coincides with the percolation phenomenon, suggesting a transition in the conduction mechanism. To elucidate this behavior, comprehensive analyses of the phase composition, microstructure, AC conductivity, and relative permittivity were performed. Additionally, the sample containing 5 wt% CP exhibits a remarkably high permittivity of 31.5, accompanied by a relatively low dielectric loss (tanδ < 0.2). The findings expand the potential applications of PVDF, while the fabricated percolating composites hold promise for electromagnetic shielding, antennas, and other electromagnetic devices.

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.

Structural and dynamical properties of thermoplastic polyurethane/fullerene nanocomposites: a molecular dynamics simulations study

In this work, the structural and dynamical properties of thermoplastic polyurethane (TPU)/fullerene (C60) nanocomposites are investigated using atomistic molecular dynamics simulations, focusing on the glass transition, thermal expansion, polymer mobility, polymer-C60 interactions, and diffusion behavior of C60. The results show a slight increase in the glass transition temperature (Tg) with increasing C60 weight fraction (wt%), attributed to hindered polymer dynamics, and a remarkable reduction in the coefficient of thermal expansion above Tg. Results of the mean squared displacement and the time decay of bond-reorientation autocorrelation indicate that the mobility of TPU hard segments is more restricted than that of soft segments, owing to the electrostatic attractions and the π-π stacking between isocyanate groups and C60 molecules. Analysis of TPU-C60 interaction energy reveals that the electrostatic interactions are weakened with an increase in the C60 wt%, while the van der Waals contributions become more significant due to the TPU-C60 interfacial characteristics. Further analysis shows that the translational and rotational diffusion of C60 are both increasingly suppressed with the increase of C60 wt%, indicating a violation of Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations, presumably due to the polymer chain-mediated hydrodynamic interactions arising from chain bridges between neighboring C60 particles. This is highlighted by a stronger decoupling of translational-rotational diffusion and a lower ratio of translational-rotational diffusion coefficient (DT/DR) with increasing C60 wt%. This work elucidates an atomistic understanding of the structure and properties of polymer/C60 nanocomposites.

Molecular dynamics simulations of the effects of carbon nanotube content on stretch-induced crystallization of polyethylene/carbon nanotube nanocomposites

In the present work, we used molecular dynamics simulations to study the effects of carbon nanotube (CNT) content on stretch-induced crystallization behaviors in CNT filled polyethylene systems. During high-temperature stretching,...

Fracture in Silica/Butadiene Rubber: A Molecular Dynamics View of Design-Property Relationships

Despite intense investigation, the mechanisms governing the mechanical reinforcement of polymers by dispersed nanoparticles have only been partially clarified. This is especially true for the ultimate properties of the nanocomposites, which depend on their resistance to fracture at large deformations. In this work, we adopt molecular dynamics simulations to investigate the mechanical properties of silica/polybutadiene rubber, using a quasi-atomistic model that allows a meaningful description of bond breaking and fracture over relatively large length scales. The behavior of large nanocomposite models is explored systematically by tuning the cross-linking, grafting densities, and nanoparticle concentration. The simulated stress-strain curves are interpreted by monitoring the breaking of chemical bonds and the formation of voids, up to complete rupture of the systems. We find that some chemical bonds, and particularly the S-S linkages at the rubber-nanoparticle interface, start breaking well before the appearance of macroscopic features of fracture and yield.

Percolated Network of Mixed Nanoparticles with Different Sizes in Polymer Nanocomposites: A Coarse-Grained Molecular Dynamics Simulation

The size of real nanoparticles (NPs) is polydisperse which can influence the electrical property of polymer nanocomposites (PNCs). Here, we explored the percolated network of mixed NPs with different sizes (small NPs and big NPs) by adopting a molecular dynamics simulation. The simulated results reveal that the big NPs are adverse to building the percolated network compared to the small NPs. Thus, the percolation threshold becomes higher along with increasing the mixing ratio, which denotes the concentration ratio of big NPs to the total NPs. For a better understanding of it, the dispersion state and the number and the size of clusters are employed to analyze the percolated network, which can explain the percolation threshold well. Furthermore, by adopting the Sun’s theory (Macromolecules, 2009, 42, 459–463), small and big NPs exhibit a weak antagonistic effect in the simulation if their total concentration is fixed. On the one hand, the number of small NPs is larger than that of big NPs at the same concentration. In addition, one big NP can connect to more others than one small NP. These two contrast effects are responsible for it. Interestingly, the shear flow leads to more contact aggregation structure of NPs which is beneficial to build the new percolated networks. Especially, the big NPs play a more important role in forming the percolated network than small NPs. Consequently, the percolation threshold is reduced at a higher shear rate. In total, our research work provides a further understanding of how the mixed NPs with different sizes form the percolated network in polymer matrix.

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.

Phase manipulation of topologically engineered AB-type multi-block copolymers

Recent advances in the fundamental understanding of the ordered phases of multi-block copolymers (MBCPs) at the molecular level have attracted considerable scientific interest in recent years. Herein, by employing molecular dynamics simulation, we focus on the four typical systems: linear alternating, branch-like, star-like AB-type MBCPs and linear copolymers filled with nanoparticles (NPs). First, we establish the phase diagram for the linear tetrablock copolymers (ABAB) as a function of the composition ratio between A- and B-block, exhibiting six typical phase states. Furthermore, increasing the mutual repulsive interaction strength, the temperature and the periodic dynamic shearing cycle result in the merging of spheres, presenting a clear beginning of the order-to-order transition (OOT) behavior. Second, we examine the branch-like and star-like copolymers and find that increasing branch density significantly leads to the occurrence of phase transition. Particularly, we illustrate that the sphere configurations of the MBCPs can be described in terms of tail, loop and bridge conformations. Increasing the number of distinct blocks in linear alternating copolymers results in an enhancement of the bridge conformation, in which case some spheres are separated to smaller ones. Furthermore, for the tail conformation, we present a unified theoretical framework to rationalize the topological state of the chain arrangements of spheres and infer that the entanglements within the internal reaction layer between different A-blocks result in the inhomogeneous distribution of the spheres sizes even with controlled molecular weight and composition ratio between each block. Finally, we find that the ABAB tetrablock copolymers filled with moderate spherical NPs exhibit a clear OOT from spheres to double gyroid or cylinders. We infer that the maximum amount of the B-block within the second and/or third layers for the filled spherical NPs connects different NPs effectively, leading to the complicated OOT behavior. Generally, this fundamental study could provide some guidelines for designing and fabricating high performance BCPs by manipulating the formation of the ordered phases.

Preparation and Performance of Silica/ESBR Nanocomposites Modified by Bio-Based Dibutyl Itaconate

Ester-functionalized styrene-butadiene rubber (dibutyl itaconate-styrene-butadiene rubber) (D-ESBR) was synthesized by low-temperature emulsion polymerization using dibutyl itaconate (DBI) as a modified monomer containing ester groups. Nonpetroleum-based silica with hydroxy groups was used as a filler to enhance the D-ESBR, which can provide excellent mechanical properties, low rolling resistance, and high wet skid resistance. During the preparation of the silica/D-ESBR nanocomposites, a hydrogen-bonding interface was formed between the hydroxy groups on the surface of silica and the ester groups in the D-ESBR macromolecules. As the content of ester groups in the D-ESBR increases, the dispersion of silica in the nanocomposites is gradually improved, which was verified by rubber process analyzer (RPA) and scanning electron microscopy (SEM). Overall mechanical properties of the silica/D-ESBR modified with 5 wt % DBI were improved and became superior to that of the non-modified nanocomposite. Compared with the non-modified silica/D-ESBR, the DBI modified silica/D-ESBR exhibited a lower tan δ value at 60 °C and comparable tan δ value at 0 °C, indicating that the DBI modified silica/D-ESBR had lower rolling resistance without sacrificing wet skid resistance.

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.

Molecular dynamics simulation of thermo-mechanical behaviour of elastomer cross-linked via multifunctional zwitterions

Coarse-grained (CG) molecular dynamics simulations have been employed to study the thermo-mechanical response of a physically cross-linked network composed of zwitterionic moieties and fully flexible elastomeric polymer chains.

Interfacial interaction modes construction of various functional SSBR–silica towards high filler dispersion and excellent composites performances

The impacts of the interfacial interaction modes and their strength on the filler dispersion and composites performances were clearly clarified.

Designing the Slide-Ring Polymer Network with both Good Mechanical and Damping Properties via Molecular Dynamics Simulation

Through coarse-grained molecular dynamics simulation, we have successfully designed the chemically cross-linked (fixed junction) and the slide-ring (SR) systems. Firstly, we examine the dynamic properties such as the mean-square displacement, the bond, and the end-to-end autocorrelation functions as a function of the cross-linking density, consistently pointing out that the SR system exhibits much lower mobility compared with the fixed junction one at the same cross-linking density. This is further validated by a relatively higher glass transition temperature for the SR system compared with that of the fixed junction one. Then, we calculated the effect of the cross-linking density on the stretch-recovery behavior for the SR and fixed junction systems. Although the chain orientation of the SR system is higher than that of the fixed-junction system, the tensile stress is smaller than the latter. We infer that much greater chain sliding can occur during the stretch, because the movable ring structure homogeneously sustains the external force of the SR system, which, therefore, leads to much larger permanent set and higher hysteresis during the recovery process compared with the fixed-junction one. Based on the stretch-recovery behavior for various cross-linking densities, we obtain the change of the hysteresis loss, which is larger for the SR system than that of the fixed junction system. Lastly, we note that the relatively bigger compressive stress for the SR system results from the aggregation of the rigid rings compared with the fixed junction system. In general, compared with the traditionally cross-linked system, a deep molecular-level insight into the slide-ring polymer network is offered and thus is believed to provide some guidance to the design and preparation of the slide-ring polymer network with both good mechanical and damping properties.

Tailoring the mechanical properties by molecular integration of flexible and stiff polymer networks

Designing a multiple-network structure at the molecular level to tailor the mechanical properties of polymeric materials is of great scientific and technological importance. Through the coarse-grained molecular dynamics simulation, we successfully construct an interpenetrating polymer network (IPN) composed of a flexible polymer network and a stiff polymer network. First, we find that there is an optimal chain stiffness for a single network (SN) to achieve the best stress-strain behavior. Then we turn to study the mechanical behaviors of IPNs. The result shows that the stress-strain behaviors of the IPNs appreciably exceed the sum of that of the corresponding single flexible and stiff network, which highlights the advantage of the IPN structure. By systematically varying the stiffness of the stiff polymer network of the IPNs, optimal stiffness also exists to achieve the best performance. We attribute this to a much larger contribution of the non-bonded interaction energy. Last, the effect of the component concentration ratio is probed. With the increase of the concentration of the flexible network, the stress-strain behavior of the IPNs is gradually enhanced, while an optimized concentration (around 60% molar ration) of the stiff network occurs, which could result from the dominant role of the enthalpy rather than the entropy. In general, our work is expected to provide some guidelines to better tailor the mechanical properties of the IPNs made of a flexible network and a stiff network, by manipulating the stiffness of the stiff polymer network and the component concentration ratio.

Formation mechanism of bound rubber in elastomer nanocomposites: a molecular dynamics simulation study

The formation mechanism of the bound rubber in elastomer nanocomposites using the coarse-grained molecular-dynamics simulations.

Mechanisms of reinforcement in polymer nanocomposites

Qualitatively different stress–strain responses of polymer nanocomposites are shown to result from the dynamical evolution of three principal molecular structural motifs in the polymer–filler network.

Simulational insights into the mechanical response of prestretched double network filled elastomers

This paper deals with molecular-dynamics simulations of the mechanical properties of prestretched double network filled elastomers. To this end, we firstly validated the accuracy of this method, and affirmed that the produced stress-strain characteristics were qualitatively consistent with Lesser's experimental results on the prestretched tri-block copolymers with a competitive double network. Secondly, we investigated the effect of the crosslinking network ratio on the mechanical properties of the prestretched double network homopolymers under uniaxial tension. We found that the prestretched double network contributes greatly to the enhanced tensile stress and ultimate strength at fracture, as well as to the lower permanent set (the residual strain) and dynamic hysteresis loss, both parallel and perpendicular to the prestretching direction. Notably, though, an anisotropic behavior was observed: in the parallel direction, both the first and the second crosslinked networks bore the external force; whereas in the perpendicular direction, only the second crosslinked network was relevantly effective. Finally, the polymer nanocomposites with a prestretched double network exhibited tensile mechanical properties similar to those of the studied homopolymers with prestretched double networks. Summing up the results, it can be concluded that the incorporation of prestretched double networks with a specified crosslinking network ratio seems to be a promising method for manipulating the mechanical properties of elastomers and their nanocomposites, as well as for introducing anisotropy in their mechanical response.

Designing polymer nanocomposites with a semi-interpenetrating or interpenetrating network structure: toward enhanced mechanical properties

Semi-interpenetrating and interpenetrating network structures for the uniform dispersion of NPs and the reinforced mechanical properties of polymer nanocomposites.

Revealing the three-dimensional filler structure in a rubber matrix based on fluorescein modified layered double hydroxides

A facile fluorescent labeling method was developed to track the filler structural evolution in a rubber matrix, which could be helpful in understanding the Payne effect in the filled compounds.

Filler reinforcement in cross-linked elastomer nanocomposites: insights from fully atomistic molecular dynamics simulation

Using a fully atomistic model, we perform large-scale molecular dynamics simulations of sulfur-cured polybutadiene (PB) and nanosilica-filled PB composites. A well-integrated network without sol fraction is built dynamically by cross-linking the coarse-grained precursor chains in the presence of embedded silica nanoparticles. Initial configurations for subsequent atomistic simulations are obtained by reverse mapping of the well-equilibrated coarse-grained systems. Based on the concept of "maximally inflated knot" introduced by Grosberg et al., we show that the networks simulated in this study behave as mechanically isotropic systems. Analysis of the network topology in terms of graph theory reveals that mechanically inactive tree-like structures are the dominant structural components of the weakly cross-linked elastomer, while cycles are mainly responsible for the transmission of mechanical forces through the network. We demonstrate that quantities such as the system density, thermal expansion coefficient, glass transition temperature and initial Young's modulus can be predicted in qualitative and sometimes even in quantitative agreement with experiments. The nano-filled system demonstrates a notable increase in the glass transition temperature and an approximately two-fold increase in the nearly equilibrium value of elastic modulus relative to the unfilled elastomer even at relatively small amounts of filler particles. We also examine the structural rearrangement of the nanocomposite subjected to tensile deformation. Under high strain-rate loading, the formation of structural defects (microcavities) within the polymer bulk is observed. The nucleation and growth of cavities in the post-yielding strain hardening regime mainly take place at the elastomer/nanoparticle interfaces. As a result, the cavities are concentrated just near the embedded nanoparticles. Therefore, while the silica nanofiller increases the elastic modulus of the elastomer, it also creates a more defective structure of higher energy in comparison with the unfilled network.

Molecular dynamics simulations of the structural, mechanical and visco-elastic properties of polymer nanocomposites filled with grafted nanoparticles

Through coarse-grained molecular dynamics simulations, we have studied the effects of grafting density (Σ) and grafted chain length (Lg) on the structural, mechanical and visco-elastic properties of end-grafted nanoparticles (NPs) filled polymer nanocomposites (PNCs). It is found that increasing the grafting density and grafted chain length both enhance the brush/matrix interface thickness and improve the dispersion of NPs, but there seems to exist an optimum grafting density, above which the end-grafted NPs tend to aggregate. The uniaxial stress-strain behavior of PNCs is also examined, showing that the tensile stress is more enhanced by increasing Lg compared to increasing Σ. The tensile modulus as a function of the strain is fitted following our previous work (Soft Matter, 2014, 10, 5099), exhibiting a gradually reduced non-linearity with the increase of Σ and Lg. Meanwhile, by imposing a sinusoidal external shear strain, for the first time we probe the effects of Σ and Lg on the visco-elastic properties such as the storage modulus G', loss modulus G'' and loss factor tan δ of end-grafted NPs filled PNCs. It is shown that the non-linear relation of G' and G'' as a function of shear strain amplitude decreases with the increase of Σ and Lg, which is consistent with experimental observations. We infer that the increased mechanical and reduced non-linear visco-elastic properties are correlated with the enhanced brush/matrix interface and therefore better dispersion of NPs and stronger physical cross-linking. This work may provide some rational means to tune the mechanical and visco-elastic properties of end-grafted NPs filled polymer nanocomposites.