Dispersion, Depletion, and Bridging of Athermal and Attractive Nanorods in Polymer Melt

Tailoring the Mechanical Properties of Polymer/Nanorod Nanocomposites through Polymer Functionalization

The rational design of polymers to improve nanorod dispersion and strengthen polymer-nanorod interfacial interactions is crucial for designing nanorod-filled polymer nanocomposites (PNCs). Herein, using coarse-grained molecular dynamics simulations, we studied the effect of polymer chain functionalization on the dispersion state of nanorods, the diffusion/relaxation of polymer matrix chains, and the mechanical properties of the corresponding PNCs. The simulation results showed that the nanorod dispersion state could be adjusted by functionalizing the polymer chain. Enhancing the functionalized bead-nanorod interactions or increasing the polymer chain functionalization degree improved the dispersion state of nanorods. The optimized nanorod dispersion state offered a much larger surface that could interact with the polymer matrix, resulting in an enhanced polymer-nanorod adsorption network. The simulation results indicated that the mechanical properties of the polymer nanocomposites (PNCs) improved progressively with an increase in interactions between functionalized beads and nanorods. However, the improvement was not monotonic with respect to the degree of functionalization, suggesting the existence of an optimal functionalization degree. The underlying mechanism of this was that a higher polymer chain functionalization degree optimized the polymer-nanorod adsorption network but hindered the polymer chain orientation during deformation. This work provides evidence theoretical guidance to design and fabricate nanorod-filled nanocomposites with tailored mechanical properties.

Unusual Electrical Conductivity Enhancement in Stable n-Type Carbon Nanotube Networks

Organic molecule-doped n-type single-walled carbon nanotube (SWCNT) networks are promising candidates for advanced energy applications, such as flexible thermoelectrics and photovoltaics. Yet charge transport in n-type SWCNTs is limited by two factors: i) charge localization impeding inter-tube transport caused by disordered mesostructure of randomly oriented SWCNTs and ii) reduction of charge carrier concentration driven by oxidation. Herein, studied the relationship between the mesostructure and thermoelectric properties of n-type SWCNTs obtained by surfactant-functionalization and polymer-dopant grafting. Surprisingly, the electrical conductivity of the polymer-doped SWCNTs keeps increasing with increasing polymer content, even after the saturation of carrier concentration, resulting in 12x higher conductivity on polymer-doping compared to surfactant-functionalization. While hopping transport typically dominates in disordered systems, it is shown that a bridging effect from the polymer causes unusual band-like conduction in polymer-doped SWCNTs. Additionally, since surfactants are essential to prevent oxidation and retain n-type over a long duration, shows that SWCNTs obtained through a dual-functionalization strategy using both polymer-dopant and surfactant, demonstrates a long-term stable high n-type thermoelectric power factor, when the surfactant amount is carefully controlled. Besides thermoelectrics, the findings are of general interest to developing stable and conductive n-type SWCNTs for various energy and electronic applications.

Does pervasive interconnected network of cellulose nanocrystals in nanocomposite membranes address simultaneous mechanical strength/water permeability/salt rejection improvement?

In this research work, we investigated the effect of two cellulose nanocrystal (CNC)-related parameters, namely aspect ratio and loading content on the mechanical and desalination performance of a cellulose diacetate (CDA) model membrane system. Dispersion of high aspect ratio (HAR) CNCs in the CDA resulted in different types of nanoassembly, represented by evaluating the mechanical efficacy coefficient (CFE), viscoelastic responses and separation performance of the nanocomposite membranes. Accordingly, 0.15 and 0.25 wt% showed random isolated dispersion and tight polymer-nanorod network, while 0.50 and 0.75 wt% conformed to nanorods' pervasive interconnected network (PIN) through side-by-side aggregation and intensive bundle alignment, respectively. Specifically, the nanocomposite membrane containing 0.50 wt% HAR-CNCs simultaneously demonstrated improved mechanical strength along with mitigated water permeability/salt rejection tradeoff for brackish water desalination. This concurrent boosting was attributed to the effective mechanical reinforcement mechanism induced by the percolating network along with its partial aggregation-caused bi-continuous and electrostatically-controlled nano-pathways, orchestrating the separation tradeoff. It confirmed our hypothesis that a nanocomposite membrane with metamaterial characteristic could be obtained via manipulating the dispersion state of CNC rods in the CDA, triggering coincided optimization of mechanical strength and desalination performance.

Dispersion and orientation patterns in nanorod-infused polymer melts

Introducing nanorods into a polymeric matrix can enhance the physical and mechanical properties of the resulting material. In this paper, we focus on understanding the dispersion and orientation patterns of nanorods in an unentangled polymer melt, particularly as a function of nanorod concentration, using molecular dynamics simulations. The system is comprised of flexible polymer chains and multi-thread nanorods that are equilibrated in the NPT ensemble. All interactions are purely repulsive except for those between polymers and rods. Results with attractive vs repulsive polymer-rod interactions are compared and contrasted. The concentration of rods has a direct impact on the phase behavior of the system. At lower concentrations, rods phase separate into nematic clusters, whereas at higher concentrations more isotropic and less structured rod configurations are observed. A detailed examination of the conformation of the polymer chains near the rod surface shows extension of the chains along the director of the rods (especially within clusters). The dispersion and orientation of the nanorods are a result of the competition between depletion entropic forces responsible for the formation of rod clusters, the enthalpic effects that improve mixing of rods and polymer, and entropic losses of polymers interpenetrating rod clusters.

Polymer-mediated self-assembly, dispersion, and phase separation of Janus nanorods

The challenge of stabilizing polymer nanocomposites lies in the fact that nanoparticles tend to phase separate from the polymer melt due to an entropic 'depletion attraction' between nanoparticles. Additionally, composites of polymer and nanorods show a decrease in miscibility with increasing nanorod aspect ratio [U. K. Sankar and M. Tripathy, Macromolecules, 2015, 48, 432-442; U. Erigi, U. Dhumal and M. Tripathy, J. Chem. Phys., 2021, 154, 124903]. In this work, we have studied the structure and phase behaviour of polymer-Janus nanorod mixtures using Polymer Reference Interaction Site Model (PRISM) theory and molecular dynamics simulations. The composite system of polymer and Janus nanorods of two different thicknesses, at various Janus nanorod densities, and for different interaction strengths between polymer and attractive sites of Janus nanorods (ε_pa), is investigated for their miscibility and self-assembly. At low Janus nanorod density, PRISM theory predicts transitions from the entropic depletion-driven contact aggregation of Janus nanorods to a well-dispersed phase to the bridging-driven phase separation of Janus nanorods, with increasing ε_pa. This behaviour is similar to earlier predictions for homogeneous nanorods. However, molecular dynamics simulations do not confirm the bridging-driven phase separation at high ε_pa predicted by PRISM theory. We find that both PRISM theory and molecular dynamics simulations are in agreement in the intermediate and high Janus nanorod density regimes. PRISM theory predicts, and simulations confirm, that at high Janus nanorod densities, the system undergoes a transition from depletion-driven macrophase separation to dispersion to chemical anisotropy-driven self-assembly with increasing ε_pa. The self-assembly at high ε_pa is mediated by the polymer. At intermediate Janus nanorod densities, the usual transition from an entropic depletion-driven macrophase separation to dispersion is predicted at low ε_pa. At high ε_pa, both PRISM theory and molecular dynamics simulations show transition to a state that is simultaneously macrophase separated and microphase separated (self-assembled).

Effect of softness on glass melting and re-entrant solidification in mixtures of soft and hard colloids

We present a systematic investigation of the structure and dynamic properties of model soft-hard colloidal mixtures. Results of a coarse-grained theoretical model are contrasted with rheological data, where the soft and hard colloids are mimicked by large star polymers with high functionality as the soft component and smaller stars with ultrahigh functionality as the hard one. Previous work by us revealed the recovery of the ergodicity of glassy soft star solutions and subsequent arrested phase separation and re-entrant solid transition upon progressive addition of small hard depletants. Here, we use different components to show that a small variation in softness has a significant impact on the state diagram of such mixtures. In particular, we establish that rendering the soft component more penetrable and modifying the size ratio bring about a remarkable shift in both the phase separation region and the glass-melting line so that the region of restored ergodicity can be notably enhanced and extended to much higher star polymer concentrations than for pure systems. We further rationalize our findings by analyzing the features of the depletion interaction induced by the smaller component that result from the interplay between the size ratio and the softness of the large component. These results demonstrate the great sensitivity of the phase behavior of entropic mixtures to small changes in the molecular architecture of the soft stars and point to the importance of accounting for details of the internal microstructure of soft colloidal particles for tailoring the flow properties of soft composites.

Phase behavior of polymer-nanorod composites: A comparative study using PRISM theory and molecular dynamics simulations

Well-dispersed composites of polymer and nanorods have many emerging applications and, therefore, are an important area of research. Polymer reference interaction site model (PRISM) theory and molecular dynamics simulations have become powerful tools in the study of the structure and phase behavior of polymer nanocomposites. In this work, we employ both PRISM theory and molecular dynamics simulations to determine the structure and spinodal phase diagram of 1% volume fraction of nanorods in a polymer melt. We make quantitative comparisons between the phase diagrams, which are reported as a function of nanorod aspect ratio and polymer-nanorod interactions. We find that both PRISM theory and molecular dynamics simulations predict the formation of contact aggregates at low polymer-nanorod attraction strength (γ) and bridged aggregates at high polymer-nanorod attraction strength. They predict an entropic depletion-driven phase separation at low γ and a bridging-driven spinodal phase separation at high γ. The polymer and nanorods are found to form stable composites at intermediate values of the polymer-nanorod attraction strength. The fall of the bridging boundary and the gradual rise of the depletion boundary with the nanorod aspect ratio are predicted by both PRISM theory and molecular dynamics simulations. Hence, the miscible region narrows with increasing aspect ratio. The depletion boundaries predicted by theory and simulation are quite close. However, the respective bridging boundaries present a significant quantitative difference. Therefore, we find that theory and simulations qualitatively complement each other and display quantitative differences.

Molecular Modeling and Simulation of Polymer Nanocomposites with Nanorod Fillers

We present a coarse-grained (CG) molecular dynamics (MD) simulation study of polymer nanocomposites (PNCs) containing nanorods with homogeneous and patchy surface chemistry/functionalization, modeled with isotropic and directional nanorod-nanorod attraction, respectively. We show how the PNC morphology is impacted by the nanorod design (i.e., aspect ratio, homogeneous or patchy surface chemistry/functionalization) for nanorods with a diameter equal to the Kuhn length of the polymer in the matrix. For PNCs with 10 vol % nanorods that have an aspect ratio ≤5, we observe percolated morphology with directional nanorod-nanorod attraction and phase-separated (i.e., nanorod aggregation) morphology with isotropic nanorod-nanorod attraction. In contrast, for nanorods with higher aspect ratios, both types of attractions result in aggregated nanorods morphology due to the dominance of entropic driving forces that cause long nanorods to form orientationally ordered aggregates. For most PNCs with isotropic or directional nanorod-nanorod attractions, the average matrix polymer conformation is not perturbed by the inclusion of up to 20 vol % nanorods. The polymer chains in contact with nanorods (i.e., interfacial chains) are on average extended and statistically different from the conformations the matrix chains adopt in the pure melt state (with no nanorods); in contrast, the polymer chains far from nanorods (i.e., bulk chains) adopt the same conformations as the matrix chains adopt in the pure melt state. We also study the effect of other parameters, such as attraction strength, nanorod volume fraction, and matrix chain length, for PNCs with isotropic or directional nanorod-nanorod attractions. Collectively, our results provide valuable design rules to achieve specific PNC morphologies (i.e., dispersed, aggregated, percolated, and orientationally aligned nanorods) for various potential applications.

Nanoparticle assembly modulated by polymer chain conformation in composite materials

Mixing nanoparticles into a strategically selected polymer matrix yields nanocomposites with well-controlled microstructures and unique properties and functions. The modulation of nanoparticle assembly by polymer chain conformation can play a dominant role in determining nanocomposite structures, yet such a physical mechanism remains largely unexplored. We hypothesize that highly ordered microdomains of rigid linear polymers provide a template for nanoparticle assembly into open fractal structures. We conducted mesoscopic computer simulations and physical experiments to elucidate how polymer chain conformation regulates the dynamic evolution of nanoparticle structures during the drying processing of polymer nanocomposite films. The evaporation of polymer-nanoparticle mixtures with varying chain stiffnesses was simulated using dissipative particle dynamics. The formation of distinguished nanoparticle assemblies as a result of matrix selection was further corroborated by probing nanoparticle aggregation in different polymer nanocomposite coatings. The results show that polymer conformation not only influences the dispersion states of individual particles (dispersed vs. aggregated), but also modulates the morphologies of large-scale assembly (globular vs. fractal). The emergence of nematically ordered polymer clusters when the chain rigidity is increased creates local solvent-rich "voids" that promote anisotropic particle aggregates, which then percolate into open fractal structures upon solvent evaporation. The nanoparticle dynamics also exhibits an intriguing non-monotonic behavior attributed to the transitions between the coupling and decoupling with polymer dynamics. The nanoparticle assembly morphologies obtained in simulations match well with the electron microscopy images taken in physical experiments.

Integral Equation Prediction of the Structure of Alternating Copolymer Nanocomposites near a Substrate

The packing structure and phase behavior of polymer-nanoparticle mixtures under confinement play an important role in developing strategies for rational design of nanomaterials. However, understanding the microscopic dispersion and aggregation mechanism of polymer nanocomposites is a great challenge through experimental techniques. In this work, the microscopic structure of alternating copolymer nanocomposites (ACNs) near a substrate is investigated systematically through extension of the inhomogeneous polymer reference interaction site model (PRISM) theory. In order to characterize the flexibility and internal chain stiffness of copolymers, a semiflexible chain model is introduced to describe the intramolecular correlations between different monomers. Based on the bridge functionals derived from the fluids density functional theory, the modified hypernetted chain closure is integrated with the PRISM equation to form a full theoretical framework to capture the density distributions of ACNs. The influence of the particle volume fraction, nanoparticle diameter, and adsorption strengths between different interaction sites on the packing structure of ACNs under confinement is analyzed and discussed in detail. With the increase of the particle volume fraction, the size asymmetry between nanoparticles and copolymer monomers can greatly influence the density profiles of ACNs near a substrate. Increasing the nanoparticle diameter, the density distribution of nanoparticles experiences a process from absorbing onto the solid surface to segregating from the wall to larger distances. With increasing the adsorption strength between copolymers and nanoparticles, the density distribution of nanoparticles decreases, which is similar to the case of nanoparticles containing attractive interactions. All these characteristics of ACNs show that the current inhomogeneous PRISM theory can give a detailed description of the packing behavior of different segments. Predictive approaches could be desired and developed for design control of alternating copolymer nanocomposites under confinement.

Coarse-graining simulation approaches for polymer melts: the effect of potential range on computational efficiency

The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical consistencies with the related atomistic simulations. When compared to the atomistic description, the procedure of coarse-graining results in smoother free energy surfaces, longer-ranged potentials, a decrease in the number of interaction sites for a given polymer, and more. Because these changes have competing effects on the computational efficiency of the CG model, care needs to be taken when studying the effect of coarse-graining on the computational speed-up in CG molecular dynamics simulations. For instance, treatment of long-range CG interactions requires the selection of cutoff distances that include the attractive part of the effective CG potential and force. In particular, we show how the complex nature of the range and curvature of the effective CG potential, the selection of a suitable CG timestep, the choice of the cutoff distance, the molecular dynamics algorithms, and the smoothness of the CG free energy surface affect the efficiency of IECG simulations. By direct comparison with the atomistic simulations of relatively short chain polymer melts, we find that the overall computational efficiency is highest for the highest level of CG (soft spheres), with an overall improvement of the computational efficiency being about 106-108 for various CG levels/resolutions. Therefore, the IECG method can have important applications in molecular dynamics simulations of polymeric systems. Finally, making use of the standard spatial decomposition algorithm, the parallel scalability of the IECG simulations for various levels of CG is presented. Optimal parallel scaling is observed for a reasonably large number of processors. Although this study is performed using the IECG approach, its results on the relation between the level of CG and the computational efficiency are general and apply to any properly-constructed CG model.

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.

Self-assembly of polymer-linked nanoparticles and scaling behavior in the assembled phase

An entropic depletion-driven phase separation is known to be observed for mixtures of polymers and nanoparticles. While polymer-linked nanoparticles have been synthesized, their phase behavior has only been predicted for chemically specific interactions. We use integral equation theory to determine the structure and phase behavior of chemically isotropic polymer-linked nanoparticles at high densities. When each end of a linear polymer is grafted to a nanoparticle, we predict an entropy-driven microphase separation of locally segregated polymer-rich and nanoparticle-rich domains. The formation of these self-assembled structures is purely a consequence of the shape of the polymer-linked particle species. The depletion-driven demixing of ungrafted polymer-nanoparticle composites (with small amounts of nanoparticles) is enhanced as particle diameter (D) grows compared to the polymer radius of gyration (R_g). However, this study shows that for polymer-linked nanoparticle systems, the transition from a liquid to microphase separated state shifts to higher densities (i.e. is inhibited) as D/R_g increases. The transition volume fractions attain a unique value (of ∼0.69) at D/R_g ∼ 1.13. The repeating length scale (L*) is 1.4-2.2 times the size of the entire species (D + R_g). Surprisingly, L*/(D + R_g) is a non-monotonic function of the polymer radius of gyration. The repeating length scale also displays a remarkable scaling behavior, as a function of the particle diameter and the polymer density. Additionally, our study implies that two different mechanisms of transitioning to the microphase separated state are possible for these systems, which has important implications for the transition density and the kinds of structures formed.

Influence of Morphology on the Mechanical Properties of Polymer Nanocomposites Filled with Uniform or Patchy Nanoparticles

In this work we perform molecular-dynamics simulations, both on the coarse-grained and the chemistry-specific levels, to study the influence of morphology on the mechanical properties of polymer nanocomposites (PNCs) filled with uniform spherical nanoparticles (which means without chemical modification) and patchy spherical nanoparticles (with discrete, attractive interaction sites at prescribed locations on the particle surface). Through the coarse-grained model, the nonlinear decrease of the elastic modulus (G') and the maximum of the viscous modulus (G″) around the shear strain of 10% is clearly reproduced. By turning to the polybutadiene model, we examine the effect of the shear amplitude and the interaction strength among uniform NPs on the aggregation kinetics. Interestingly, the change of the G' as a function of the aggregation time exhibited a maximum value at intermediate time attributed to the formation of a polymer-bridged filler network in the case of strong interaction between NPs. By imposing a dynamic periodic shear, we probe the change of the G' as a function of the strain amplitude while varying the interaction strength between uniform NPs and its weight fraction. A continuous filler network is developed at a moderate shear amplitude, which is critically related to the interaction strength between NPs and the weight fraction of the fillers. In addition, we study the self-assembly of the patchy NPs, which form the typical chain-like and sheet-like structures. For the first time, the effect of these self-assembled structures on the viscoelastic and stress-strain behavior of PNCs is compared. In general, in the coarse-grained model we focus on the size effect of the rough NPs on the Payne effect, while some other parameters such as the dynamic shear flow, the interaction strength between NPs, the weight fraction, and the chemically heterogeneous surface of the NPs are explored for the chemistry-specific model.

Phase separation of comb polymer nanocomposite melts

In this work, the spinodal phase demixing of branched comb polymer nanocomposite (PNC) melts is systematically investigated using the polymer reference interaction site model (PRISM) theory. To verify the reliability of the present method in characterizing the phase behavior of comb PNCs, the intermolecular correlation functions of the system for nonzero particle volume fractions are compared with our molecular dynamics simulation data. After verifying the model and discussing the structure of the comb PNCs in the dilute nanoparticle limit, the interference among the side chain number, side chain length, nanoparticle-monomer size ratio and attractive interactions between the comb polymer and nanoparticles in spinodal demixing curves is analyzed and discussed in detail. The results predict two kinds of distinct phase separation behaviors. One is called classic fluid phase boundary, which is mediated by the entropic depletion attraction and contact aggregation of nanoparticles at relatively low nanoparticle-monomer attraction strength. The second demixing transition occurs at relatively high attraction strength and involves the formation of an equilibrium physical network phase with local bridging of nanoparticles. The phase boundaries are found to be sensitive to the side chain number, side chain length, nanoparticle-monomer size ratio and attractive interactions. As the side chain length is fixed, the side chain number has a large effect on the phase behavior of comb PNCs; with increasing side chain number, the miscibility window first widens and then shrinks. When the side chain number is lower than a threshold value, the phase boundaries undergo a process from enlarging the miscibility window to narrowing as side chain length increases. Once the side chain number overtakes this threshold value, the phase boundary shifts towards less miscibility. With increasing nanoparticle-monomer size ratio, a crossover of particle size occurs, above which the phase separation is consistent with that of chain PNCs. The miscibility window for this condition gradually narrows while the other parameters of the PNCs system are held constant. These results indicate that the present PRISM theory can give molecular-level details of the underlying mechanisms of the comb PNCs. It is hoped that the results can be used to provide useful guidance for the future design control of novel, thermodynamically stable comb PNCs.