Effective Interactions, Structure, and Phase Behavior of Lightly Tethered Nanoparticles in Polymer Melts

Effect of shape anisotropy on the precipitation of dimeric nanoparticles

We use grand canonical transition matrix Monte Carlo simulations to study the precipitation of dimeric nanoparticles. The dimers are composed of two particles having different chemical features and separated by a fixed distance. The non-attractive and attractive parts of the dimer are modeled using hard-sphere and square-well potentials, respectively. The shape anisotropy is altered by changing the relative sizes of the two particles. We observe that the stability of the nanosuspension increases with the increase in the size of the non-attractive part of the dimer. The precipitates of dimers having larger non-attractive parts have lower packing densities, contain large cavities, and show evidence of self-assembly in the bulk and on the surface. We also use the results from our simulations and the classical nucleation theory to study the kinetics of precipitation. At a given temperature and relative supersaturation, the rate of homogeneous nucleation increases with the increase in the size of the non-attractive parts. Finally, we use an example to show how our results can guide the design of nanosuspensions containing chemically anisotropic dimers that are stable under particular conditions.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

A long chain-induced depletion effect for abnormal grafting in the preparation of bimodal bidisperse polymer-grafted nanoparticles

One of the challenging problems in the research field of polymer nanocomposites is how to prepare nanocomposites with high grafting density and strong ability of dispersion at the same time. For nanocomposites composed of bimodal bidisperse polymer chains and nanoparticles, the above requirements can be met by rationally adjusting the ratio of long and short polymer chains. In this study, the process of grafting bimodal bidisperse polymer chains onto the surface of nanoparticles in a grafting-to manner was investigated via computer simulation and theoretical methods. Three grafting strategies were designed: first short then long (SL) system, both short and long (Both) system and first long then short (LS) system. An abnormal phenomenon for the Both system was found by analyzing the grafting density of long and short polymer chains on the surface of nanoparticles. We speculate that the reason for this anomalous phenomenon is the "depletion effect" brought about by the long chains in the Both system. We employ the Polymer Reference Interaction Site Model (PRISM) theory to investigate this anomaly in-depth. By comparing the radial distribution function (RDF) predicted by the PRISM theory with the RDF results obtained by the molecular dynamics (MD) simulation, we found that with the increase of the number of long chains in the system, the grafting density of short polymer chains on the nanoparticle surface showed an obvious upward trend. The "depletion effect" brought by long chains was the main reason for higher short chains' grafting density of the Both system compared to the SL system. Our findings provide effective guidance for the design of nanoparticle-grafted bimodal bidisperse polymer chains and provide a theoretical basis for experimentation and production of polymer nanocomposites with better performance.

Deep learning potential of mean force between polymer grafted nanoparticles

Grafting polymer chains on the surfaces of nanoparticles is a well-known route to control their self-assembly and distribution in a polymer matrix. A wide variety of self-assembled structures are achieved by changing the grafting patterns on the surface of an individual nanoparticle. However, an accurate estimation of the effective potential of mean force between a pair of grafted nanoparticles that determines their assembly and distribution in a polymer matrix is an outstanding challenge in nanoscience. We address this problem via deep learning. As a proof of concept, here we report a deep learning framework that learns the interaction between a pair of single-chain grafted spherical nanoparticles from their molecular dynamics trajectory. Subsequently, we carry out the deep learning potential of mean force-based molecular simulation that predicts the self-assembly of a large number of single-chain grafted nanoparticles into various anisotropic superstructures, including percolating networks and bilayers depending on the nanoparticle concentration in three-dimensions. The deep learning potential of mean force-predicted self-assembled superstructures are consistent with the actual superstructures of single-chain polymer grafted spherical nanoparticles. This deep learning framework is very generic and extensible to more complex systems including multiple-chain grafted nanoparticles. We expect that this deep learning approach will accelerate the characterization and prediction of the self-assembly and phase behaviour of polymer-grafted and unfunctionalized nanoparticles in free space or a polymer matrix.

Dispersion and Diffusion Mechanism of Nanofillers with Different Geometries in Bottlebrush Polymers: Insights from Molecular Dynamics Simulation

The dispersion and diffusion mechanism of nanofillers in polymer nanocomposites (PNCs) are crucial for understanding the properties of PNCs, which is of great significance for the design of novel materials. Herein, we investigate the dispersion and diffusion behavior of two geometries of nanofillers, namely, spherical nanoparticles (SNPs) and nanorods (NRs), in bottlebrush polymers by utilizing coarse-grained molecular dynamics simulations. With the increase of the interaction strength between the nanofiller and polymer (ε_np), both the SNPs and NRs experience a typical "aggregated phase-dispersed phase-bridged phase" state transition in the bottlebrush polymer matrix. We evaluate the validity of the Stokes-Einstein (SE) equation for predicting the diffusion coefficient of nanofillers in bottlebrush polymers. The results demonstrate that the SE predictions are slightly larger than the simulated values for small SNP sizes because the local viscosity that is felt by small SNPs in the densely grafted bottlebrush polymer does not differ much from the macroscopic viscosity. The relative size of the length of the NRs (L) and the radius of gyration (R_g) of the bottlebrush polymer play a key role in the diffusion of NRs. In addition, we characterize the anisotropic diffusion of NRs to analyze their translational and rotational diffusion. The motion of NRs in the direction perpendicular to the end-to-end vector is more hindered, indicating that there is a strong coupling between the rotation of NRs and the motion of the polymer. The NR motion shows stronger anisotropic diffusion at short time scales because of the steric effects generated by side chains of the bottlebrush polymer. In general, our results provide a fundamental understanding of the dispersion of nanofillers and the microscopic mechanism of nanofiller diffusion in bottlebrush polymers.

Understanding asymmetry effects at low grafting density on the self-assembly of polyion grafted nanoparticles

Grafting of spherical nanoparticles (NPs) with polymeric ligands has been an effective way of controlling the dispersion state of NPs either in the matrix or in solution. Despite the fast evolving synthesis techniques, it is still experimentally difficult to precisely control the position of tethers on the surface of NPs. At low grafting density, due to the surface anisotropy, a wide range of assemblies could be achieved depending on the position of the tethers on the NP surface. This may pose a challenge in interpreting data from scattering and electron micrographs. In the current manuscript, we use coarse-grained molecular dynamics simulations to study the effect of graft angles (positions) on the self-assembly of NPs grafted with oppositely charged polyions at low grafting density driven by coulombic interactions. Our study shows that the NPs grafted with oppositely charged polyions self-assemble into a wide range of morphologies like dimers, rings, strings, coils, tetramers and aggregates depending on the angle between the grafts. Furthermore, the morphologies obtained in the case of semi-flexible and rigid-chains as tethers are more sensitive to the graft positions (angles) compared to that of flexible chains. Molecular dynamics studies carried out at low grafting densities of the system comprising an equimolar mixture of nanoparticles grafted with polyions at varying grafting angles showed that the polyions grafted at low/high grafting angles preferentially interacted with oppositely charged polyion grafts tethered at low/high graft angles.

Interactions between Sterically Stabilized Nanoparticles: The Effects of Brush Bidispersity and Chain Stiffness

Density Functional Theory is employed to study structural properties and interactions between solvent-free polymer-grafted nanoparticles. Both monodisperse and bidisperse polymer brushes with variable chain stiffness are considered. The three major control parameters are the grafting density, the grafted chain length, and its stiffness. The effect of these parameters on the brush-brush overlap and attractive interaction strength is analyzed. The Density Functional Theory results are compared with the available simulation data, and good quantitative agreement is found.

Long Rod-Like Liquid Crystal Containing Azobenzene and the Applications in Phase-Transition Regulation and Orientation of Nematic Liquid Crystal

Phase-transition and orientation of liquid crystal (LC) are two crucial factors for LC application. In this work, a long rod-like LC compound containing double azobenzene (M1) is successfully designed and synthesized. The combing technologies of nuclear magnetic resonance (1H NMR, 13C NMR) and Fourier transform infrared spectroscopy (FTIR) are used to identify the chemical structure of the molecule. Additionally, the polarized optical microscopy (POM), differential scanning calorimetry (DSC), and one-dimensional wide-angle X-ray diffraction (1D WAXD) experimental results show that M1 exhibits an ultrawide range of LC phases and a stable LC structure even at ultrahigh temperature, which indicates that this LC can be applied in some especial devices. Further, the compound M1 is used to tune the LC temperature range of the commercial LC 4-cyano-4′-pentylbiphenyl (5CB). A series of samples 1–7 are obtained through doping different contents of M1, which show different LC temperature ranges that are dependent on the composition ratio of M1 and 5CB. More interestingly, all resultant samples show spontaneous vertical orientation on the hydrophilic glass substrate. Meanwhile, due to the effect of azobenzene in the compound M1, a reversible transition between homeotropic to random orientation of the LC molecules is achieved when these LC cells are alternately exposed to UV irradiation and visible light, which implies that this material shows potential application in especial display and optical storage technologies.

Structural and Dynamical Coupling in Solvent-Free Polymer Brushes Elucidated by Molecular Dynamics Simulations

We investigate the chain configuration and segmental dynamics in interacting solvent-free polymer brushes using molecular dynamics simulations. The brush systems are designed to mimic the interstitial space between a pair of neighboring polymer-grafted nanoparticles in solvent-free nanoparticle-organic hybrid materials. Each brush consists of uniformly grafted chains formed by a given number of monomer beads. In monodisperse systems, two opposing brushes have the same chain length and grafting density. In mixed conditions, we consider binary systems with two surfaces being separately grafted with polymers of distinct chain lengths at different grafting densities as well as bidisperse systems with polymers of two different lengths being tethered to the surfaces at a fixed grafting density. We demonstrate that the brush configuration and interpenetration are both governed by the need that monomer beads have to uniformly fill the space. For systems with longer chain lengths and/or higher grafting densities, the larger interwall separation yields more stretched brush conformations and reduced extents of interbrush mixing. As a result, the polymer configurational entropy is generally decreased and the segment-to-segment relaxation dynamics is slowed down accordingly. The grafting of chains at a high density not only makes the relaxation dynamics deviate from the standard Rouse prediction but also leads to distinct relaxation times for the free and tethered segments. The more slowly relaxing tethered segments play a more important role in determining the overall end-to-end fluctuations. Moreover, the two distinct relaxation processes are consistent with the two-stage decay in the Rouse mode fluctuation autocorrelation function. In the presence of brush bidispersity, the collaboration between polymers of different lengths is evidently observed in the brush profiles. The variations of the chain configuration for the two polymers are complementary, and the associated relaxation dynamics of the two species are significantly coupled.

Assembly of Polymer-Grafted Nanoparticles in Polymer Matrices

Leibler pioneered the idea that long enough matrix polymers of length P will spontaneously dewet a chemically identical polymer layer, comprising chains of length N, densely end-grafted to a flat surface ("brush"). This entropically driven idea is routinely used to explain experiments in which 10-20 nm diameter nanoparticles (NPs) densely grafted with polymer chains are found to phase separate from chemically identical melts for P/N ≳4. At lower grafting densities, these effects are also thought to underpin the self-assembly of grafted NPs into a variety of structures. To explore the validity of this picture, we conducted large-scale molecular dynamics simulations of grafted NPs in a chemically identical polymer melt. For the NPs we consider, in the ≈5 nm diameter range, we find no phase separation even for P/N = 10 in the absence of attractions. Instead, we find behavior that more closely parallels experiments when all of the chain monomers are equally attractive to each other but repel the NPs. Our results thus imply that experimental situations investigated to date are dominated by the surfactancy of the NPs, which is driven by the chemical mismatch between the inorganic core and the organic ligands (the graft and free chains are chemically identical). Entropic effects, that is, the translational entropy of the NPs and the matrix, the entropy of mixing of the grafts and the matrix, and the conformational entropy of the chains appear to thus have a second-order effect even in the context of these model systems.

Entropic Effects in Solvent-Free Bidisperse Polymer Brushes Investigated Using Density Functional Theories

Solvent-free polymer-functionalized nanoparticles form a special type of colloid composed of inorganic cores self-suspended by their grafted coronas. In the absence of intervening solvent molecules, the fluidity of the system is provided by these tethered polymers as they fill the space. Here, we study the structure and interaction of neighboring polymer-grafted surfaces in the solvent-free condition using mean-field density functional theories. For opposing flat surfaces, the brush configuration and the associated energy landscape are semianalytically investigated given the incompressibility of the tethered entropic chains. The effect of brush polydispersity (including variations in both chain length and surface grafting density) is considered by two bidisperse models corresponding to different physical scenarios: one for opposing brushes uniformly mixed with two species at a fixed grafting density, and the other for opposing brushes with distinct chain lengths and grafting densities. The space-filling capabilities of the neighboring coronas differ not only by their ratio of radii of gyration for the composing polymers but also by their ratio of grafting densities. We show that the system energy depicts a steric repulsion as the brushes are compressed, which is typical for hairy particles in a solvent. However, as the interwall separation increases, the cooperative stretching of the chains leads to an entropic attraction between them, a unique characteristic of solventless systems. The corresponding brush profiles change from a bell-like shape to a more step-function-like feature as the interwall spacing increases significantly. The interwall separation associated with the overall free energy minimum therefore characterizes the favorable interparticle spacing for solvent-free polymer-functionalized particles. The limiting accessible parameter space of polymer sizes and grafting densities subjected to the space-filling constraint is comprehensively explored for representative interparticle spacing characterizing the compressed, relaxed, and stretched regimes for a given polymer species, respectively. Such information would be useful for guiding the design of experimental solvent-free polymer-functionalized nanoparticles.

Self-assembly and structural manipulation of diblock-copolymer grafted nanoparticles in a homopolymer matrix

Detailed coarse-grained molecular dynamics simulations are performed to investigate the structural and mechanical properties of nanoparticles (NPs) grafted with an amphiphilic AB diblock copolymer, with the A-block being compatible with NPs and the B-block being miscible with a homopolymer matrix.

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

This topical review discusses the theoretical progress made in the field of polymer nanocomposites, i.e., hybrid materials created by mixing (typically inorganic) nanoparticles (NPs) with organic polymers. It primarily focuses on the outstanding issues in this field and is structured around five separate topics: (i) the synthesis of functionalized nanoparticles; (ii) their phase behavior when mixed with a homopolymer matrix and their assembly into well-defined superstructures; (iii) the role of processing on the structures realized by these hybrid materials and the role of the mobilities of the different constituents; (iv) the role of external fields (electric, magnetic) in the active assembly of the NPs; and (v) the engineering properties that result and the factors that control them. While the most is known about topic (ii), we believe that significant progress needs to be made in the other four topics before the practical promise offered by these materials can be realized. This review delineates the most pressing issues on these topics and poses specific questions that we believe need to be addressed in the immediate future.

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.

Computationally Guided Assembly of Oriented Nanocubes by Modulating Grafted Polymer-Surface Interactions

The bottom-up fabrication of ordered and oriented colloidal nanoparticle assemblies is critical for engineering functional nanomaterials beyond conventional polymer-particle composites. Here, we probe the influence of polymer surface ligands on the self-orientation of shaped metal nanoparticles for the formation of nanojunctions. We examine how polymer graft-surface interactions dictate Ag nanocube orientation into either edge-edge or face-face nanojunctions. Specifically, we investigate the effect of end-functionalized polymer grafts on nanocube assembly outcomes, such as interparticle angle and interparticle distance. Our assembly results can be directly mapped onto our theoretical phase diagrams for nanocube orientation, enabling correlation of experimental variables (such as graft length and metal binding strength) with computational parameters. These results represent an important step toward unifying modeling and experimental approaches to understanding nanoparticle-polymer self-assembly.

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.

Controlling the localization of nanoparticles in assemblies of amphiphilic diblock copolymers

We performed a dissipative particle dynamics (DPD) approach to study the self-assembly of AB diblock copolymer tethered nanoparticles (P) in dilute solutions. Different morphological aggregates, including spherical micelles, vesicles, disk-like micelles and rod-like micelles, were found by varying the interaction between block copolymers and nanoparticles. Most importantly, the nanoparticles can selectively localize in the different domains within the aggregates. When the repulsive interaction between block copolymers and nanoparticles aPA = aPB = 25, the nanoparticles are evenly distributed within the spherical micelles. While aPA or aPB increases, the nanoparticles gradually aggregate and separate from copolymers and then localize in the central portion of vesicular wall or disk-like and rod-like micelles. The degree of stretching of the tethered copolymer chains gradually grows with the increase of aPA or aPB, while the degree of stretching of solvophobic block B decreases when the morphologies change from spherical to disk-like micelles and further to rod-like micelles. This work illustrates that tuning the miscibility of copolymers and nanoparticles could be used to project the selective localization of nanoparticles within the aggregates self-assembled by diblock copolymer tethered nanoparticles in dilute solutions.

Integral equation theory for atactic polystyrene nanocomposite melts with a multi-site model

In this work, a multi-site chain model was incorporated into the polymer reference interaction site model to investigate the structure and properties of atactic polystyrene (aPS) melt and the structural correlations of dilute spherical nanoparticles dissolved in aPS melt. The theoretically calculated X-ray scattering intensities, solubility parameters and intermolecular correlation functions of aPS and its nanocomposites are found to be in agreement with the corresponding molecular simulation and experimental data. The theory was further employed to investigate the distribution functions of different size effects of aPS-nanoparticle system with consideration of the potential of mean force and depletion force. The aggregation of large nanoparticles increases with the increase of the nanoparticle-site size ratio in the infinitely dilute limit. The results show that the present theory can be used to investigate the structure of aPS melt and its nanocomposite, and give a further understanding of the filler dispersion and aggregation. All the observations indicate molecular-level details of the underlying mechanisms, providing useful information for the future design control of new aPS-nanocomposite materials with tailored properties.

Theory and simulation studies of effective interactions, phase behavior and morphology in polymer nanocomposites

Polymer nanocomposites are a class of materials that consist of a polymer matrix filled with inorganic/organic nanoscale additives that enhance the inherent macroscopic (mechanical, optical and electronic) properties of the polymer matrix. Over the past few decades such materials have received tremendous attention from experimentalists, theoreticians, and computational scientists. These studies have revealed that the macroscopic properties of polymer nanocomposites depend strongly on the (microscopic) morphology of the constituent nanoscale additives in the polymer matrix. As a consequence, intense research efforts have been directed to understand the relationships between interactions, morphology, and the phase behavior of polymer nanocomposites. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level features of the polymer and nanoparticle additives to the resulting morphology within the composite. In this article we review recent theory and simulation studies, presenting briefly the methodological developments underlying PRISM theories, density functional theory, self-consistent field theory approaches, and atomistic and coarse-grained molecular simulations. We first discuss the studies on polymer nanocomposites with bare or un-functionalized nanoparticles as additives, followed by a review of recent work on composites containing polymer grafted or functionalized nanoparticles as additives. We conclude each section with a brief outlook on some potential future directions.

Distinct mechanical properties of nanoparticle-tethering polymers

Nanoparticle-tethering polymers exhibit enhanced mechanical properties relative to neat polymers and nanoparticle/polymer blends.

Computational study of nanoparticle dispersion and spatial distribution in polymer matrix under oscillatory shear flow

In this work, nonequilibrium molecular dynamics simulations were performed to investigate the dispersion and spatial distribution of spherical nanoparticles (NPs) in polymer matrix under oscillatory shear flow. We systematically analyzed the influences of four important factors that consist of NP-polymer interfacial strength, volume fraction of NPs, shear conditions, and polymer chain length. The simulation results showed that the oscillatory shear can greatly improve the dispersion of NPs, especially for the polymer nanocomposites (PNCs) with high NP-polymer interfacial strength. Under specific shear conditions, the NPs can exhibit three different spatial distribution states with increasing the NP-polymer interfacial strength. Interestingly, at high interfacial strength, we observed that the NPs can be distributed on several layers in the polymer matrix, forming the PNCs with sandwich-like structures. Such well-ordered nanocomposites can exhibit a higher tensile strength than those with the NPs dispersed randomly. It may be expected that the information derived in present study provides a useful foundation for guiding the design and preparation of high-performance PNCs.

Effect of nanoparticle polydispersity on the self-assembly of polymer tethered nanospheres

Recent simulations predict that aggregating nanospheres functionalized with polymer "tethers" can self-assemble to form a cylinder, perforated lamellae, lamellae, and even the double gyroid phase, which are phases also seen in block copolymer and surfactant systems. Nanoparticle size polydispersity is likely to be a characteristic of these systems. If too high, polydispersity may destabilize a phase. Using multiple thermodynamic paths to explore the phase diagram as a function of temperature and polydispersity, we explore the effect of nanosphere size polydispersity on the phase diagram. We show that in the portions of the phase diagram characterized by an icosahedral local nanoparticle packing motif, a low amount of polydispersity lowers the energy and a large amount of polydispersity raises the energy of the system by disrupting the icosahedral packing. In general, regions of the phase diagram characterized by liquid-like icosahedral packing have high terminal polydispersities from 15% to more than 30%. In the regions of the phase diagram characterized by crystalline local packing, polydispersity raises the energy of the system and induces a phase transition from crystalline to liquid-like ordering within the nanosphere rich regions of the microphase. We find the bilayer crystalline lamellae phase has a terminal polydispersity of 6%, but may still be partially crystalline up to 12%.

COMPUTATIONAL SIMULATION OF ELASTOMER NANOCOMPOSITES: CURRENT PROGRESS AND FUTURE CHALLENGES

In the field of elastomer nanocomposites (ENCs), computational simulation technique is becoming more and more essential, as a result of its ability to provide important and clear information at the molecular level, which is always difficult to obtain or not accessible through experimental investigations. We focus on summarizing the progress achieved in the simulation research of three critical topics of ENCs, namely, (i) the dispersion mechanism (particularly polymer-mediated interparticle interaction, the “many-body” effect at high filler loading), (ii) the characterization of the nanoscale/microscale structure and dynamics [the modified chain configuration in the presence of nanoparticles (NPs), the interfacial binding strength determining the efficiency of the stress transfer, the possibly altered interfacial chain structure, interfacial segmental dynamics leading to the shift of the glass transition temperature Tg, the formation of the filler network and its structure, the chemical cross-linking process], and (iii) the macroscopic viscoelasticity (the Payne effect), mechanical reinforcement, and physical property (thermal conductivity). Since recently only limited simulation work has been carried out pertaining to ENCs, we discuss these three topics in light of the simulation and theoretical achievements of polymer nanocomposites (mainly polymer melts filled with NPs). Meanwhile, some relevant experimental studies are also included for better illustration. Furthermore, for each topic, three typically different reinforcing fillers, such as three-dimensional spherical, two-dimensional sheet, and one-dimensional rod NPs, separately corresponding to carbon black or silica, clay sheets, and carbon nanotubes intensively used in the practical applications of ENCs, are illustrated in order. In order to realize a comprehensive understanding of the structure–property relation and in the meantime to provide more practical guidelines for the engineering applications of ENCs, we investigate future simulation opportunities and difficulties.

Revisiting the dispersion mechanism of grafted nanoparticles in polymer matrix: a detailed molecular dynamics simulation

By focusing on the grafted nanoparticles (NPs) embedded in polymer melts, a detailed coarse-grained molecular dynamics simulation is adopted to investigate the effects of the grafting density, the length of the matrix and grafted chains on the dispersion of the NPs. We have employed visualization snapshots, radial distribution functions (RDFs), the interaction energy between NPs, the number of neighbor NPs, and the conformation of the brush chains to clearly analyze the dispersion state of the grafted NPs. Our simulated results generally indicate that the dispersion of the NPs is controlled by both the excluded volume of the grafted NPs and the interface between the brushes and the matrix. It is found that increasing grafting density or grafted chain length leads to better dispersion, owing to larger excluded volume; however, increasing the length of the matrix chains leads to aggregation of NPs, attributed to both a progressive loss of the interface between the brushes and the matrix and the overlap between brushes of different NPs, intrinsically driven by entropy. Meanwhile, it is found that there exists an optimum grafting density (σ(c)) for the dispersion of the NPs, which roughly obeys the following mathematical relation: σ(c) is proportional to N(m)(K)/N(g)(L), where K, L > 0 and N(m) and N(g) represent the length of the matrix and grafted chain length, respectively. Considering the practical situation that the grafted brushes and the matrix polymer are mostly not chemically identical, we also studied the effect of the compatibility between the brushes and the matrix polymer by taking into account the attraction between the grafted chains and the matrix chains. In general, our comprehensive simulation results are believed to guide the design and preparation of high-performance polymer nanocomposites with good or even tailored dispersion of NPs.

Nanoparticle dispersion and aggregation in polymer nanocomposites: insights from molecular dynamics simulation

It is a great challenge to fully understand the microscopic dispersion and aggregation of nanoparticles (NPs) in polymer nanocomposites (PNCs) through experimental techniques. Here, coarse-grained molecular dynamics is adopted to study the dispersion and aggregation mechanisms of spherical NPs in polymer melts. By tuning the polymer-filler interaction in a wide range at both low and high filler loadings, we qualitatively sketch the phase behavior of the PNCs and structural spatial organization of the fillers mediated by the polymers, which emphasize that a homogeneous filler dispersion exists just at the intermediate interfacial interaction, in contrast with traditional viewpoints. The conclusion is in good agreement with the theoretically predicted results from Schweizer et al. Besides, to mimick the experimental coarsening process of NPs in polymer matrixes (ACS Nano 2008, 2, 1305), by grafting polymer chains on the filler surface, we obtain a good filler dispersion with a large interparticle distance. Considering the PNC system without the presence of chemical bonding between the NPs and the grafted polymer chains, the resulting good dispersion state is further used to investigate the effects of the temperature, polymer-filler interaction, and filler size on the filler aggregation process. It is found that the coarsening or aggregation process of the NPs is sensitive to the temperature, and the aggregation extent reaches the minimum in the case of moderate polymer-filler interaction, because in this case a good dispersion is obtained. That is to say, once the filler achieves a good dispersion in a polymer matrix, the properties of the PNCs will be improved significantly, because the coarsening process of the NPs will be delayed and the aging of the PNCs will be slowed.