Coarse-Grained Molecular Dynamics Simulation of Filled Polymer Nanocomposites under Uniaxial Elongation

Molecular Dynamics Analysis of Surface-Modified Carbon Nanoparticle Reinforced Epoxy Resin

Surface-modified carbon nanoparticles (CNPs) as reinforcement materials have attracted significant attention due to their potential for substantially enhancing mechanical properties. However, the development and application of CNP-enhanced polymeric materials are constrained by an incomplete understanding of their reinforcement mechanisms, impeding sustainable progress. In this study, we employed molecular dynamics simulations to investigate the mechanical properties of surface-modified CNP-reinforced epoxy resin composites at the microscopic scale. The simulations focused on the tensile process and the nanopinning effect of CNPs within the epoxy resin matrix. Our results indicate that surface-modified CNPs form stronger interfacial connections with the epoxy resin, leading to enhanced mechanical strength of the composites. Quantitative analysis revealed that these composites exhibit higher tensile strength compared to nonmodified counterparts, with a significant improvement in stability due to the robust noncovalent interactions between CNPs and the epoxy matrix. This study elucidates the reinforcement mechanisms of surface-modified CNPs in polymers, providing valuable insights for further optimization and sustainable development of CNP-reinforced polymeric materials.

All-atom molecular dynamics simulations of polymer and polyelectrolyte brushes

Densely grafted polymer and polyelectrolyte (PE) brushes, owing to their significant abilities to functionalize surfaces for a plethora of applications in sensing, diagnostics, current rectification, surface wettability modification, drug delivery, and oil recovery, have attracted significant attention over the past several decades. Unfortunately, most of the attention has primarily focused on understanding the properties of the grafted polymer and the PE chains with little attention devoted to studying the behavior of the brush-supported ions (counterions needed to screen the PE chains) and water molecules. Over the past few years, our group has been at the forefront of addressing this gap: we have employed all-atom molecular dynamics (MD) simulations for studying a wide variety of polymer and PE brush systems with specific attention to unraveling the properties and behavior of the brush-supported water molecules and ions. Our findings have revealed some of the most fascinating properties of such brush-supported ions and water molecules, including the most remarkable control of nanofluidic transport afforded by the specific ion and water responses induced by the PE brushes grafted on the inner walls of the nanochannel. This feature article aims to summarize some of our key contributions associated with such atomistic simulations of polymer and PE brushes and brush-supported water molecules and counterions.

Chain-Level Analysis of Reinforced Polyethylene through Stretch-Induced Crystallization

Herein, we propose a large-scale simulation approach to perform the stretch-induced crystallization of entangled polyethylene (PE) melts. Sufficiently long (1000 ns) united-atom molecular dynamics (UAMD) simulations for 16000 chains of 1000 consecutive CH2 united-atom particles under periodic boundary conditions were performed to achieve the crystallinity observed in experiments. Before the isothermal crystallization process, we applied uniaxial stretching as pre-elongation to the embedded strain memory on the entangled PE melts. We confirmed significant differences in the morphologies of crystal domains and scattering patterns for pre-elongation ratios of 400% and 800%. The obtained scattering patterns were consistent with the experimental results. Uniaxial stretching MD simulations revealed that the elastic modulus at 800% pre-elongation was stronger than that at 400% pre-elongation. From this observation, we can derive the structure-property relationship, wherein the magnitude of the pre-elongation governs the crystal domain structures and mechanical properties.

Glass Transition Temperatures and Thermal Conductivities of Polybutadiene Crosslinked with Randomly Distributed Sulfur Chains Using Molecular Dynamic Simulation

The thermal conductivities and glass transition temperatures of polybutadiene crosslinked with randomly distributed sulfur chains having different lengths from mono-sulfur (S1) to octa-sulfur (S8) were investigated. The thermal conductivities of the related models as a function of the heat flux autocorrelation function, applying an equilibrium molecular dynamic (EMD) simulation and the Green-Kubo method, were studied for a wide range of temperatures. The influence of the length of sulfur chains, degree of crosslinking, and molar mass of the crosslinker on the glass transition temperature and final values of thermal conductivities were studied. First, the degree of crosslinking is considered constant for the eight simulation models, from mono-sulfur (S1) to octa-sulfur (S8), while the molar mass of the sulfur is increases. The results show that the thermal conductivities of the crosslinked structure decrease with increasing temperature for each model. Moreover, by increasing the lengths of the sulfur chains and the molar weight of the crosslinker, thermal conductivity increases at a constant temperature. The MD simulation demonstrates that the glass transition temperature and density of the crosslinked structure enhance as the length of the sulfur chains and molar mass of the sulfur increase. Second, the molar weight of sulfur is considered constant in these eight models; therefore, the degree of crosslinking decreases with the increase in the lengths of the sulfur chains. The results show that the thermal conductivities of the crosslinked structure decrease with the increase in the temperature for each model. Moreover, by increasing the lengths of sulfur chains and thus decreasing the degree of crosslinking, the trend in changes in thermal conductivities are almost the same for all of these models, so thermal conductivity is constant for a specific temperature. In addition, the glass transition temperature and density of the crosslinked structure decrease.

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.

Nanoindentation Study of Calcium-Silicate-Hydrate Gel via Molecular Dynamics Simulations

The mechanical properties of calcium-silicate-hydrate (C-S-H) gels in cementitious materials are mainly realized by nanoindentation experiments. There is limited research on the dynamic response of the molecular structure of C-S-H under nanoindentation conditions. This study simulated the nanoindentation on the C-S-H gel samples by the molecular dynamics method considering the essential factors of modeling and loading process. The results demonstrate that the averaged elastic moduli we obtained had slight differences from those by experiments. In contrast to the experimental results, the gels showed bi-modulus and transverse isotropic with the material principal direction perpendicular to the C-S-H layers. The modulus in a direction increased with the loading speed, which indicates that C-S-H behaves viscous due to the water motion in the sample and the propagation of stress wave. The saturation of water influenced the moduli differently because more water in C-S-H will reduce the polymerization of silicon chains and then weaken the local stiffness. The conclusions provide a deeper understanding of the mechanism on the unique mechanical response of C-S-H gels.

Approaches and Perspective of Coarse-Grained Modeling and Simulation for Polymer-Nanoparticle Hybrid Systems

Molecular modeling and simulations have emerged as effective and indispensable tools to characterize polymeric systems. They provide fundamental and essential insights to design a product of the required properties and to improve the understanding of a phenomenon at the molecular level for a particular system. The polymer-nanoparticle hybrids are materials with outstanding properties and correspondingly large applications whose study has benefited from this new paradigm. However, despite the significant expansion of modern day computational powers, investigation of the long time and large length scale phenomenon in polymeric and polymer-nanoparticle systems is still a challenging task to complete through all-atom molecular dynamics (AA-MD) simulations. To circumvent this problem, a variety of coarse-grained (CG) models have been proposed, ranging from the generic CG models for qualitative properties predictions to more realistic chemically specific CG models for quantitative properties predictions. These CG models have already delivered some success stories in the study of several spatial and temporal evolutions of many processes. Some of these studies were beyond the feasibility of traditional atomistic resolution models due to either the size or the time constraints. This review captures the different types of popular CG approaches that are utilized in the investigation of the microscopic behavior of polymer-nanoparticle hybrid systems. The rationale of this article is to furnish an overview of the popular CG approaches and their applications, to review several important and most recent developments, and to delineate the perspectives on future directions in the field.

Improved Coarse-Grained Model for Nanoparticles Based on the Martini Force Field and Its Application in Molecular Dynamics Simulation on Gel Ink

Research on the dispersion and stability of nanoparticles in liquid media is one of the key subjects for nanomaterial utilization. In consideration of the preponderance of coarse-grained (CG) molecular dynamics (MD) simulation in following and understanding the structure and dynamics on the nanoscale, an improved CG model for nanoparticles based on the Martini force field is established to facilitate the more extensive applications of this simulation method and further studies on complex nanoparticle liquid systems. Gel ink is selected as the liquid system for nanoparticles to validate the improved CG model on the one hand and introduce the CGMD simulation method into the studies of this system on the other. The calculation shows that the improved model can provide relatively precise results and has good computational stability. The effect mechanisms of the thickener and disperser on the carbon black nanoparticle are similar, namely the result of a delicate balance between the interaction of the thickener/disperser with the carbon black nanoparticle and the interaction of the thickener and disperser with each other. Furthermore, the phase assimilating effect of disperser molecules is key for separating the agglomerated carbon black nanoparticles; thereafter, the space steric hindrance effect and the electrostatic hindrance effect play main roles in maintaining the dispersion of carbon black nanoparticles.

Evaluation of Microscopic Damage of PEEK Polymers under Cyclic Loadings Using Molecular Dynamics Simulations

Full-atomic molecular dynamics simulations were conducted to investigate the time evolution of microscopic damage in polyetheretherketone (PEEK) polymers under cyclic loading conditions. Three characteristics were used to quantify microscopic damage: entropy, distribution of the end-to-end distance of polymers, and the volume fraction of voids. Our results show that the degree of disentanglement of polymers and the volume fraction of voids increase with cyclic loading, which may lead to entropy generation. Uniaxial tensile strength simulations of the polymer system before and after cyclic loading were performed. The tensile strength after cyclic loading was lower than that before loading. Furthermore, two systems with the same entropy and different loading histories showed almost the same strength. These results imply that entropy generation is expressed as the total microscopic damage and can potentially be employed for effective evaluation of the degradation of material characteristics.

Atomistic-scale analysis of the deformation and failure of polypropylene composites reinforced by functionalized silica nanoparticles

Interfacial adhesion between polymer matrix and reinforcing silica nanoparticles plays an important role in strengthening polypropylene (PP) composite. To improve the adhesion strength, the surface of silica nanoparticles can be modified by grafted functional molecules. Using atomistic simulations, we examined the effect of functionalization of silica nanoparticles by hexamethyldisilazane (HMDS) and octyltriethoxysilane (OTES) molecules on the deformation and failure of silica-reinforced PP composite. We found that the ultimate tensile strength (UTS) of PP composite functionalized by OTES (28 MPa) is higher than that of HMDS (25 MPa), which is in turn higher than that passivated only by hydrogen (22 MPa). To understand the underlying mechanistic origin, we calculated the adhesive energy and interfacial strength of the interphase region, and found that both the adhesive energy and interfacial strength are the highest for the silica nanoparticles functionalized by OTES molecules, while both are the lowest by hydrogen. The ultimate failure of the polymer composite is initiated by the cavitation in the interphase region with the lowest mass density, and this cavitation failure mode is common for all the examined PP composites, but the cavitation position is dependent on the tail length of the functional molecules. The present work provides interesting insights into the deformation and cavitation failure mechanisms of the silica-reinforced PP composites, and the findings can be used as useful guidelines in selecting chemical agents for surface treatment of silica nanoparticles.

Ionic Polymer Nanocomposites Subjected to Uniaxial Extension: A Nonequilibrium Molecular Dynamics Study

We explore the behavior of coarse-grained ionic polymer nanocomposites (IPNCs) under uniaxial extension up to 800% strain by means of nonequilibrium molecular dynamics simulations. We observe a simultaneous increase of stiffness and toughness of the IPNCs upon increasing the engineering strain rate, in agreement with experimental observations. We reveal that the excellent toughness of the IPNCs originates from the electrostatic interaction between polymers and nanoparticles, and that it is not due to the mobility of the nanoparticles or the presence of polymer-polymer entanglements. During the extension, and depending on the nanoparticle volume fraction, polymer-nanoparticle ionic crosslinks are suppressed with the increase of strain rate and electrostatic strength, while the mean pore radius increases with strain rate and is altered by the nanoparticle volume fraction and electrostatic strength. At relatively low strain rates, IPNCs containing an entangled matrix exhibit self-strengthening behavior. We provide microscopic insight into the structural, conformational properties and crosslinks of IPNCs, also referred to as polymer nanocomposite electrolytes, accompanying their unusual mechanical behavior.

Effect of Nanoparticles Surface Bonding and Aspect Ratio on Mechanical Properties of Highly Cross-Linked Epoxy Nanocomposites: Mesoscopic Simulations

The paper aims to study the mechanical properties of epoxy resin filled with clay nanoparticles (NPs), depending on their shapes and content on the surface of a modifying agent capable of forming covalent bonds with a polymer. The cylindrical clay nanoparticles with equal volume and different aspects ratios (disks, barrel, and stick) are addressed. The NPs' bonding ratio with the polymer (RGC) is determined by the fraction of reactive groups and conversion time and varies from RGC = 0 (non-bonded nanoparticles) to RGC = 0.65 (more than half of the surface groups are linked with the polymer matrix). The performed simulations show the so-called load-bearing chains (LBCs) of chemically cross-linked monomers and modified nanoparticles to determine the mechanical properties of the simulated composites. The introduction of nanoparticles leads to the breaking of such chains, and the chemical cross-linking of NPs with the polymer matrix restores the LBCs and strengthens the composite. At small values of RGC, the largest value of the elastic modulus is found for systems filled with nanoparticles having the smallest surface area, and at high values of RGC, on the contrary, the systems containing disk-shaped particles with the largest surface area have a larger elastic modulus than the others. All calculations are performed within the framework of a mesoscopic model based on accurate mapping of the atomistic structures of the polymer matrix and nanoparticles into coarse-grained representations, which, if necessary, allow reverse data mapping and quantitative assessment of the state of the filled epoxy resin. On the other hand, the obtained data can be used to design the functional materials with specified mechanical properties based on other practically significant polymer matrices and nanofillers.

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.

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.

Towards realistic simulations of polymer networks: tuning vulcanisation and mechanical properties

Simulations of coarse-grained network models have long been used to test theoretical predictions about rubber elasticity, while atomistic models are still largely unexplored. Here we devise a novel algorithm for the vulcanisation of united-atom poly(cis-1,4-butadiene), characterize the topology of the resulting networks and test their mechanical properties. We observe clear changes in the network structure when using slower vulcanisation, contrary to the traditional view that cross-linking simply freezes the melt configuration. Non-ideality of our networks reverberates on the distribution of strand length and on the strands deformation, which is highly non-affine, especially for short strands. Nevertheless, we do recover some of the trends observed on ideal bead-and-spring networks and controlled laboratory experiments, such as the linear relationships linking the degree of cross-linking and the density. We also compare different deformation methods and find step-equilibrium protocols to be more reliable. Regardless of the adopted method, it is advisable to precede the deformation by a pre-stretching cycle in order to release internal stresses accumulated during the vulcanisation.

Microscopic insight into nanodiamond polymer composites: reinforcement, structural, and interaction properties

Nanodiamond (ND)-reinforced polymer composites attract a great deal of attention; however, insufficient understanding of their reinforced behavior is greatly limiting their further design and application. In this paper, a microscopic investigation of the stretched processes of aminated ND and resin composites is undertaken to elucidate the reinforcement mechanism of ND in the polymer matrix by employing molecular dynamics and semi-empirical quantum chemistry simulations. The stretching process and reinforcement behavior are observed on the nanoscale, and the nano-pinning effect of ND on the resin matrix is clarified. Further analyses indicate that due to the increase of system volume, the interactions between the ND and resin molecules increase with stretching; this facilitates the combination of ND and resin molecules and thus recovers the breakage of the resin matrix. This recovery process is regarded as the origin of the ND reinforcement of the polymer. The strong interaction between the ND and resin molecules is quantitatively assessed by the interpenetration of the van der Waals surface and the reduced density gradient analysis of electrons using quantum chemistry calculations. The high stability of their noncovalent combination is also revealed. This investigation provides an excellent approach for revealing the origin of ND reinforcement behavior and thus facilitates further optimization of the performance of the ND-polymer composites.

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

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

Synthesis of computer simulation and machine learning for achieving the best material properties of filled rubber

Molecular dynamics (MD) simulation is used to analyze the mechanical properties of polymerized and nanoscale filled rubber. Unfortunately, the computation time for a simulation can require several months’ computing power, because the interactions of thousands of filler particles must be calculated. To alleviate this problem, we introduce a surrogate convolutional neural network model to achieve faster and more accurate predictions. The major difficulty when employing machine-learning-based surrogate models is the shortage of training data, contributing to the huge simulation costs. To derive a highly accurate surrogate model using only a small amount of training data, we increase the number of training instances by dividing the large-scale simulation results into 3D images of middle-scale filler morphologies and corresponding regional stresses. The images include fringe regions to reflect the influence of the filler constituents outside the core regions. The resultant surrogate model provides higher prediction accuracy than that trained only by images of the entire region. Afterwards, we extract the fillers that dominate the mechanical properties using the surrogate model and we confirm their validity using MD.

Molecular-Scale Deformation of Polypropylene/Silica Composites Probed by Rheo-Optical Fourier-Transform Infrared (FTIR) Imaging Analysis Combined with Disrelation Mapping

We have developed a novel rheo-optical Fourier-transform infrared (FTIR) imaging technique that can probe the molecular-scale deformation behavior of a polymer matrix in composite materials. This rheo-optical FTIR imaging is based on in situ-polarized FTIR imaging of a polymer sample while it is being deformed by mechanical force. This imaging technique readily captures the orientation of the polymer molecules resulting from the applied strain. Analysis of the resulting FTIR imaging data by disrelation mapping makes it possible to further elucidate subtle but pertinent spectral variations arising from changes in the state of molecules within the spectroscopic images. In this study, the rheo-optical FTIR imaging is applied to analysis of the deformation behaviors of a composite composed of polypropylene containing hydroxyl groups (PPOH) and silica spheres (SS) to investigate matrix-filler adhesion of the composite. Our rheo-optical FTIR imaging analysis revealed selective inhibition of PPOH orientation at the matrix-filler interface during tensile deformation due to high matrix-filler adhesion via hydrogen bonding. The strong link between the PPOH matrix and SS filler efficiently restricts mobility of the matrix, resulting in the reinforcement of PPOH by addition of SS. Rheo-optical FTIR imaging is an effective tool for probing localized deformation behavior at the matrix-filler interface as well as achieving a better understanding of the correlation between matrix-filler adhesion and the effective reinforcement of composites.

Tunable interaction potentials and morphology of polymer-nanoparticle blends

We present the results of molecular dynamics simulations of a family of polymer nanocomposite systems. The polymer is described by a generic bead-and-spring model, while the polymer chains and the nanoparticles (NPs) interact by Hamaker-style potentials. The potential describing NP-NP interactions is modified by a tuning parameter f, which can be changed continuously between f = 0 (for fully developed van der Waals attractions between the NPs) and f = 1 (for completely repulsive interparticle interactions). We explore systematically the effect of the f parameter on the blend morphologies, for two representative NP sizes. When the polymer-NP attractions are decreased, the systems undergo a transition from dispersed to aggregated morphologies. The sharpness of the transition gradually increases with the interparticle attractions (i.e., decreasing f).

Rod-coil block copolymer aggregates via polymerization-induced self-assembly

Polymerization-induced self-assembly (PISA), incorporating the polymerization with in situ self-assembly, can achieve nano-objects efficiently. However, the cooperative polymerization and self-assembly lead to unclear polymerization kinetics and aggregation behavior, especially for the systems forming rigid chains. Here, we used dissipative particle dynamics simulations with a probability-based reaction model to explore the PISA behavior of rod-coil block copolymer systems. The impact of the length of macromolecular initiators, the targeted length of rigid chains, and the reaction probability on the PISA behavior, including polymerization kinetics and self-assembly, were examined. The difference between PISA and traditional self-assembly was revealed. A comparison with experimental observations shows that the simulation can capture the essential feature of the PISA. The present work provides a comprehensive understanding of rod-coil PISA systems and may provide meaningful information for future experimental research.

Modeling the Full Time-Dependent Phenomenology of Filled Rubber for Use in Anti-Vibration Design

Component design of rubber-based anti-vibration devices remains a challenge, since there is a lack of predictive models in the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). An approach is proposed that demonstrates all non-linear viscoelastic effects such as hysteresis and cyclic stress softening. As it is based on a free-energy, it is fast and easily implementable. The fitting parameters behave meaningfully when changing the filler volume fraction. The model was implemented for use in the commercial finite element software ABAQUS. Examples of how to fit experimental data and simulations for a variety of carbon black filled natural rubber compounds are presented.

Self-assembly of amphiphilic alternating copolymers with stimuli-responsive rigid pendant groups

Amphiphilic alternating copolymers (AACs) possess unique self-assembly behaviours owing to their unique regular architecture.

Martini Coarse-Grained Model for Clay-Polymer Nanocomposites

We have developed a coarse-grained (CG) model of a polymer-clay system consisting of organically modified montmorillonite (oMMT) nanoclay as the nanoparticle in accordance with the MARTINI force field. We have used mechanical properties and cleavage free energy of the clay particle to respectively parameterize bonded and nonbonded interaction parameters for an oMMT clay particle, where intergallery Na⁺ ions are replaced by tetramethylammonium (TMA) ions. The mechanical properties were determined from the slope of the stress-strain curve and cleavage free energy was determined by allowing for full surface reconstruction corresponding to a slow equilibrium cleavage process. Individual dispersive and polar contributions to oMMT cleavage energy were used for determination of appropriate MARTINI bead types for the CG oMMT sheet. The self-consistency of the developed MARTINIFF parameters for the TMA-montmorillonite-polymer system was verified by comparing estimates for select structural, thermodynamic, and dynamic properties obtained in all-atomistic simulations with that obtained in CG simulations. We have determined the influence of clay particles on properties of three polymer melts (polyethylene, polypropylene, and polystyrene) at two temperatures to establish transferability of the developed parameters. We have also shown that the effect of clay-polymer interactions on structure-property relationships in the polymer-clay nanocomposite system is well captured by Rosenfeld's excess entropy scaling.

Particle-mesh two-dimensional pattern reverse Monte Carlo analysis on filled-gels during uniaxial expansion

A particle-mesh-based two-dimensional pattern reverse Monte Carlo (RMC) analysis method (PM-2DpRMC) is proposed for analyzing two-dimensional small-angle-scattering (2D-SAS) patterns. The results of analyzing such patterns in expanded gel networks filled with spherical nano-particles during uniaxial elongation are provided. Previously, characteristic 2D-SAS patterns, such as the two-point bar plate and figure-8 patterns, were observed to possess high stretching ratios in a coarse-grained molecular dynamics (CGMD) simulation, and the patterns were found to depend on the properties of the networks, such as whether they were topologically percolated or not. To establish real-space visualizations of the changes in the particle-configurations corresponding to the 2D-SAS patterns, the on-the-fly PM-2DpRMC method was employed to model the morphology changes of the filler particles during stretching in a series of 2D-SAS patterns. The use of quasi-dynamics to express deformation was validated by evaluating the accuracy of the elongation speed and the number of RMC trials predicted from the behavior of the converged χ2. The results confirm that the obtained sequences of 3D configurations were similar to the original configurations obtained in the CGMD simulations. Further, a demonstrative test using actual experimental data was conducted to verify the completeness of the confirmation.

Scattering patterns and stress-strain relations on phase-separated ABA block copolymers under uniaxial elongating simulations

To develop molecularly based interpretations of the two-dimensional scattering patterns (2DSPs) of phase-separated block copolymers (BCPs), we performed coarse-grained molecular dynamics simulations of ABA tri-BCPs under uniaxial stretching for block-fractions where the A-segment (glassy domain) is smaller than the B-segment (rubbery domain), and estimated the behaviour of their 2DSPs. In BCP stretching experiments, mechanical properties are generally evaluated using a stress-strain curve. We obtained 2DSPs with different contrasts for the A- and B-segments, which are indicative of the differences between X-ray and neutron scattering experiments. The small- and wide-angle behaviours of the 2DSPs originate from the morphologies of the phase-separated domains and local bond orientations, respectively. When the block-fractions are changed for a constant stress value on the stress-strain (SS) curve, the brightness of the spots in the wide-angle region of the A- and B-segment-dominant 2DSPs decreases and increases with increasing strain, respectively. We can regard the systematic changes in the small-angle 2DSPs of the glassy domain and the wide-angle 2DSPs of the rubbery domain with changes in the SS-curve as a structure-property relationship.

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.

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.

Modelling Filler Dispersion in Elastomers: Relating Filler Morphology to Interface Free Energies via SAXS and TEM Simulation Studies

The properties of rubber are strongly influenced by the distribution of filler within the polymer matrix. Here, we introduce a Monte Carlo-based morphology generator. The basic elements of our model are cubic cells, which, in the current version, can be either silica filler particles or rubber volume elements in adjustable proportion. The model allows the assignment of surface free energies to the particles according to whether a surface represents, for instance, ‘naked’ silica or silanised silica. The amount of silanisation is variable. We use a nearest-neighbour site-exchange Monte Carlo algorithm to generate filler morphologies, mimicking flocculation. Transmission electron micrographs (TEM) as well as small angle scattering (SAS) intensities can be calculated along the Monte Carlo trajectory. In this work, we demonstrate the application of our morphology generator in terms of selected examples. We illustrate its potential as a tool for screening studies, relating interface tensions between the components to filler network structure as characterised by TEM and SAS.

Effects of chemically heterogeneous nanoparticles on polymer dynamics: insights from molecular dynamics simulations

The dispersion of solid nanoparticles within polymeric materials is widely used to enhance their performance. Many scientific and technological aspects of the resulting polymer nanocomposites have been studied, but the role of the structural and chemical heterogeneity of the nanoparticles has just started to be appreciated. For example, simulations of polymer films on planar heterogeneous surfaces revealed unexpected, non-monotonic activation energy to diffusion on varying the surface composition. Motivated by these intriguing results, here we simulate via molecular dynamics a different, fully three-dimensional system, in which the heterogeneous nanoparticles are incorporated in a polymer melt. The nanoparticles are roughly spherical assemblies of strongly and weakly attractive sites, in fractions of f and 1 - f, respectively. We show that the polymer diffusion is still characterized by a non-monotonic dependence of the activation energy on f. The comparison with the case of homogeneous nanoparticles clarifies that the effect of the heterogeneity increases on approaching the polymer glass transition.

Modeling the Effect of Polymer Chain Stiffness on the Behavior of Polymer Nanocomposites

Due to their central role in industrial formulations spanning from food packaging to smart coatings, polymer nanocomposites have been the object of remarkable attention over the last two decades. Incorporating nanoparticles (NPs) into a polymer matrix modifies the conformation and mobility of the polymer chains at the NP-polymer interface and can potentially provide materials with enhanced properties as compared to pristine polymers. To this end, it is crucial to predict and control the ability of NPs to diffuse and achieve a good dispersion in the polymer matrix. Understanding how to control the NPs' dispersion is a challenging task controlled by the delicate balance between enthalpic and entropic contributions, such as NP-polymer interaction, NP size and shape, and polymer chain conformation. By performing molecular dynamics (MD) simulations, we investigate the effect of polymer chains' stiffness on the mobility of spherical NPs that establish weak or strong interactions with the polymer. Our results show a sound dependence of the NPs' diffusivity on the long-range order of the polymer melt, which undergoes an isotropic-to-nematic phase transition upon increasing chain stiffness. This phase transition induces a dynamical anisotropy in the nematic phase, with the NPs preferentially diffusing along the nematic director rather than in the directions perpendicular to it. Not only does this tendency determine the NPs' mobility and degree of dispersion in the polymer matrix, but it also influences the resistance to flow of the polymer nanocomposite when a shear is applied. In particular, to assess the role of the chains' conformation on the macroscopic response of our model PNC, we employ reverse nonequilibrium MD to calculate the zero-shear viscosity in both the isotropic and nematic phases, and unveil a plasticizing effect at increasing chain stiffness when the shear is applied along the nematic axis.

HORIZONS FOR DESIGN OF FILLED RUBBER INFORMED BY MOLECULAR DYNAMICS SIMULATION

Fillers such as carbon black provide a long-standing and essential strategy for the mechanical reinforcement of rubber in tires and other load-bearing applications. Despite their technological importance, however, the microscopic mechanism of this reinforcement remains a matter of considerable debate. A predictive understanding of filler-based reinforcement could catalyze the design of new rubber-filler composites with enhanced performance. Molecular dynamics simulations of rubber mechanical response in the presence of structured fillers offer a new strategy for resolving the origins of filler-based reinforcement and guiding filler design. Results of for ideal rubber-filler dispersions over a range of filler structures suggest that neither hydrodynamic effects nor non-deformable “bound rubber domains” are necessary to achieve high reinforcement. Moreover, simulations show that particle surface area is a poor predictor of reinforcement. Instead, simulated reinforcement correlates strongly with filler structure, with more rarified filler structure predicting much greater reinforcement at fixed loading. Simulation results are consistent with a scenario in which reinforcement at industrially relevant loadings is dominated by formation of a jammed network of filler particles, suggesting that reinforced rubber can be understood as a superposition of two materials: a rubbery solid, and a jammed granular solid. This perspective points to an opportunity to improve filler-reinforced rubber design by leveraging concepts and expertise developed over many decades in the fields of jamming and granular media.