Molecular dynamics simulations of polymer transport in nanocomposites

Molecular dynamics simulations on the Kremer-Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration R(g) away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.     

Simulation of interaction forces between nanoparticles in the presence of Lennard-Jones polymers: freely adsorbing homopolymer modifiers

The force between two nanoscale colloidal particles dispersed in a solution of freely adsorbing Lennard-Jones homopolymer modifiers is calculated using the expanded grand canonical Monte Carlo simulation method. We investigate the effect of polymer chain length (N), nanoparticle diameter (sigma(c)), and colloid-polymer interaction energy (epsilon(cp)) on polymer adsorption (Gamma) and polymer-induced forces (F(P)(r)) between nanoparticles in the full thermodynamic equilibrium condition. There is a strong correlation between polymer adsorption and the polymer-mediated nanoparticle forces. When the polymer adsorption is weak, as in the case of smaller diameters and short polymer chain lengths (sigma(c) = 5, N = 10), the polymers do not have any significant effect on the bare nanoparticle interactions. The adsorbed amount increases with increasing particle diameter, polymer chain length, and colloid-polymer interaction energy. In general, for strong polymer-particle adsorption the polymer-governed force profiles between nanoparticles show short-range repulsion and long-ranged attraction, suggesting that homopolymers would not be ideal for achieving stabilization in nanoparticle dispersions. The attraction is likely due to bridging, as well as polymer segment-segment interactions. The location and magnitude of attractive minimum in the force profile can be controlled by varying N and epsilon(cp). The results show partial agreement and some marked differences with previous theoretical and experimental studies of forces in the limit of flat walls in an adsorbing polymer solution. The difference could be attributed to incorporation of long-ranged colloid-polymer potential in our simulations and the influence of the curvature of the nanoparticles.     

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.     

Influence of added particles on the phase behavior of polymer solutions. Analysis by mean-field lattice theory

The influence of added colloidal particles on the phase stability of polymer solutions is investigated theoretically. The polymer has an affinity to the particle surface. A mean-field lattice theory based on the Flory-Huggins theory is used to calculate the phase behavior in solutions containing a single polymer component and particles. The particles are described in two different ways. The first approach considers the surface free energy associated with added solid particles and the mixing entropy of the particles. In the second approach, the particles are simply modeled as large polymers. Both ways of describing the added particles show that the added particles decrease the stability of the polymer solution when the polymer-particle attraction is strong. A higher particle concentration enhances the effect. Experiments where polystyrene latex particles are added at different concentrations to aqueous dispersions of ethyl(hydroxyethyl)cellulose (EHEC) support the theoretical findings.     

Density functional theory for a primitive model of nanoparticle-block copolymer mixtures

Amphiphilic block copolymers provide useful templates for fabrication of nanostructured materials that are appealing for a wide variety of applications. The preparation of polymer-particle hybrid materials requires a good understanding of the chemical nature and topology of the amphiphilic molecules as well as their interactions with the embedded nanoparticles. This article reports a density functional theory (DFT) for a coarse-grained model of block copolymer-nanoparticle mixtures that is able to account for the properties of particles and copolymers within a self-consistent framework. It predicts various well-organized structures that can be effectively controlled by adjusting the polymer chain length and polymer-particle interactions. Illustrative examples based on relatively short chains suggest that, in qualitative agreement with experiments, large particles tend to be excluded from a polymer brush near a solid substrate, whereas smaller particles may be dissolved. The DFT is able to capture the dispersion of large particles in the microdomain of block copolymer that is energetically favorable, but localization of smaller particles at the microdomain interfaces.     

Polymer-bridged gels of nanoparticles in solutions of adsorbing polymers

We use a combination of polymer mean field theory and Monte Carlo simulations to study the polymer-bridged gelation, clustering behavior, and elastic moduli of polymer-nanoparticle mixtures. Polymer self-consistent field theory is first numerically implemented to quantify both the polymer induced interparticle interaction potentials and the conformational statistics of polymer chains between two spherical particles. Subsequently, the formation and structure of polymer-bridged nanoparticle gels are examined using Monte Carlo simulations. Our results indicate a universality in the fractal structure for the polymer-bridged networks over a wide range of parametric conditions. Explicitly, near the gelation transition, the fractal dimension d(f) ranges between 2.2 and 2.5, and above the gelation thresholds, the elastic moduli are found to follow a universal power law G(') proportional, variant(eta-eta(c))(nu(eta) ) with a critical exponent nu(eta) approximately 1.82. The latter suggests strong similarities between polymer-bridging induced percolation and classical elastic resistor network percolation. Our results show a very good agreement with the experimental results for polymer-particle mixtures and suggest a possible framework for experimentally distinguishing the origins of gelation phenomena observed in polymer-particle mixtures.     

Effect of bidispersity in grafted chain length on grafted chain conformations and potential of mean force between polymer grafted nanoparticles in a homopolymer matrix

In efforts to produce polymeric materials with tailored physical properties, significant interest has grown around the ability to control the spatial organization of nanoparticles in polymer nanocomposites. One way to achieve controlled particle arrangement is by grafting the nanoparticle surface with polymers that are compatible with the matrix, thus manipulating the interfacial interactions between the nanoparticles and the polymer matrix. Previous work has shown that the molecular weight of the grafted polymer, both at high grafting density and low grafting density, plays a key role in dictating the effective inter-particle interactions in a polymer matrix. At high grafting density nanoparticles disperse (aggregate) if the graft molecular weight is higher (lower) than the matrix molecular weight. At low grafting density the longer grafts can better shield the nanoparticle surface from direct particle-particle contacts than the shorter grafts and lead to the dispersion of the grafted particles in the matrix. Despite the importance of graft molecular weight, and evidence of non-trivial effects of polydispersity of chains grafted on flat surfaces, most theoretical work on polymer grafted nanoparticles has only focused on monodisperse grafted chains. In this paper, we focus on how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in an implicit solvent and in a dense homopolymer polymer matrix. We first present the effects of bidispersity on grafted chain conformations in a single polymer grafted particle using purely Monte Carlo (MC) simulations. This is followed by calculations of the potential of mean force (PMF) between two grafted particles in a polymer matrix using a self-consistent Polymer Reference Interaction Site Model theory-Monte Carlo simulation approach. Monte Carlo simulations of a single polymer grafted particle in an implicit solvent show that in the bidisperse polymer grafted particles with an equal number of short and long grafts at low to medium grafting density, the short grafts are in a more coiled up conformation (lower radius of gyration) than their monodisperse counterparts to provide a larger free volume to the longer grafts so they can gain conformational entropy. The longer grafts do not show much difference in conformation from their monodisperse counterparts at low grafting density, but at medium grafting density the longer grafts exhibit less stretched conformations (lower radius of gyration) as compared to their monodisperse counterparts. In the presence of an explicit homopolymer matrix, the longer grafts are more compressed by the matrix homopolymer chains than the short grafts. We observe that the potential of mean force between bidisperse grafted particles has features of the PMF of monodisperse grafted particles with short grafts and monodisperse grafted particles with long grafts. The value of the PMF at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Further comparison of the PMF for bidisperse and monodisperse polymer grafted particles in a homopolymer matrix at varying parameters shows that the effects of matrix chain length, matrix packing fraction, grafting density, and particle curvature on the PMF between bidisperse polymer grafted particles are similar to those seen between monodisperse polymer grafted particles.     

The Correlation Functions of a Suspension of Large Particles in Amorphous Polybutadiene: A Molecular Dynamics Simulation Study

The correlation functions of a suspension of Lennard-Jones large particles in a model 1,4-cis-polybutadiene solvent have been investigated by molecular dynamics simulations. We present the effects of temperature, the degree of polymerization, and the solvent/large particle density on the effective interactions between the large particles and the solvent. It is found that as the temperature increases, the structure between solvent-solvent, solvent-large particle, and large-large particle decreases. Additionally, as the bulk density or the chain length is increased, the attractive part of the large-large interaction becomes weaker and small. We believe that in part, this is due to the polymer having collapsed onto itself and entangling the large particles and lessening their interaction until they are actually in contact. Increasing the length of the polymer also entangles the large particles. However, we believe that this may be a general feature that is a characteristic of a polymer solvent containing macroscopically large colloidal particles even though entanglement should be of less significance. Copyright 2000 Academic Press.     

A single particle model to simulate the dynamics of entangled polymer melts

We present a computer simulation model of polymer melts representing each chain as one single particle. Besides the position coordinate of each particle, we introduce a parameter n(ij) for each pair of particles i and j within a specified distance from each other. These numbers, called entanglement numbers, describe the deviation of the system of ignored coordinates from its equilibrium state for the given configuration of the centers of mass of the polymers. The deviations of the entanglement numbers from their equilibrium values give rise to transient forces, which, together with the conservative forces derived from the potential of mean force, govern the displacements of the particles. We have applied our model to a melt of C(800)H(1602) chains at 450 K and have found good agreement with experiments and more detailed simulations. Properties addressed in this paper are radial distribution functions, dynamic structure factors, and linear as well as nonlinear rheological properties.     

Nonequilibrium simulations of filled polymer networks: searching for the origins of reinforcement and nonlinearity

We present nonequilibrium dissipative particle dynamics (DPD) simulations of cross-linked elastomers containing solid filler particles at 30% volume fraction. We study systematically the effect of the morphology (dispersed or aggregated particles) and of the effective particle-particle interactions. In addition, we have experimented by replacing the standard harmonic DPD bonds with other potential functions, conceived to deal with the finite extensibility of the polymer chains and the possibility of a slow equilibrium between strongly and weakly adsorbed chains at the rubber-filler interface. The simulation results shed some light on the basic mechanisms of rubber reinforcement, including the nonlinearity and history dependence commonly known as "Payne effect" and "Mullins effect."     

Mineralization of monodispersed CdS nanoparticles on polyelectrolyte superstructure forming an electroluminescent "necklace-of-beads"

We report a nonmicellar method to synthesize monodisperse semiconducting nanoparticles templated on polymer chains dissolved in solution at high yield. The monodispersity is achieved due to the beaded necklace morphology of the polyelectrolyte chains in solution where the beads are nanometer-scale nodules in the polymer chain. The resultant structure is a nanoparticles studded necklace where the particles are imbedded in the beads. Multiple cycles of synthesis on the polymer template yield nanoparticles of identical size, resulting in a nanocomposite with high particle fraction. The resultant nanocomposite has beaded-fibrilar morphology with imbedded nanoparticles and can be solution-casted to make electroluminescent thin film device.     

Structure and effective interactions in polymer nanocomposite melts: an integral equation theory study

The polymer reference interaction site model from integral equation theory is used to investigate the structure and effective interactions in polymer nanocomposite melts where strong nanoparticle-monomer interactions are principally considered in this work. For finite particle volume fraction, the compromise for the interference between polymers and nanoparticles results in an optimum particle volume fraction for nanoparticle dispersion in polymer melts. At constant particle volume fraction, the effects of degree of polymerization become insignificant when it reaches a threshold value, below which quantitative effects on the organization states of polymer nanocomposite melts are found and help nanoparticles to well disperse in polymer. The aggregation of large nanoparticles decreases with the increase of the nanoparticle-monomer attraction strength. These observations may provide useful information for the development of new polymer materials.     

Mesoscale simulation of polymer reaction equilibrium: combining dissipative particle dynamics with reaction ensemble Monte Carlo. I. Polydispersed polymer systems

We present a mesoscale simulation technique, called the reaction ensemble dissipative particle dynamics (RxDPD) method, for studying reaction equilibrium of polymer systems. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), allowing for the determination of both static and dynamical properties of a polymer system. The RxDPD method is demonstrated by considering several simple polydispersed homopolymer systems. RxDPD can be used to predict the polydispersity due to various effects, including solvents, additives, temperature, pressure, shear, and confinement. Extensions of the method to other polymer systems are straightforward, including grafted, cross-linked polymers, and block copolymers. To simulate polydispersity, the system contains full polymer chains and a single fractional polymer chain, i.e., a polymer chain with a single fractional DPD particle. The fractional particle is coupled to the system via a coupling parameter that varies between zero (no interaction between the fractional particle and the other particles in the system) and one (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the DPD equations of motion, accompanied by changes in the coupling parameter. The coupling-parameter changes are either accepted with a probability derived from the grand canonical partition function or governed by an equation of motion derived from the extended Lagrangian. The coupling-parameter changes mimic forward and reverse reaction steps, as in RxMC simulations.     

Polypyrrole-palladium nanocomposite coating of micrometer-sized polymer particles toward a recyclable catalyst

A range of near-monodisperse, multimicrometer-sized polymer particles has been coated with ultrathin overlayers of polypyrrole-palladium (PPy-Pd) nanocomposite by chemical oxidative polymerization of pyrrole using PdCl(2) as an oxidant in aqueous media. Good control over the targeted PPy-Pd nanocomposite loading is achieved for 5.2 μm diameter polystyrene (PS) particles, and PS particles of up to 84 μm diameter can also be efficiently coated with the PPy-Pd nanocomposite. The seed polymer particles and resulting composite particles were extensively characterized with respect to particle size and size distribution, morphology, surface/bulk chemical compositions, and conductivity. Laser diffraction studies of dilute aqueous suspensions indicate that the polymer particles disperse stably before and after nanocoating with the PPy-Pd nanocomposite. The Fourier transform infrared (FT-IR) spectrum of the PS particles coated with the PPy-Pd nanocomposite overlayer is dominated by the underlying particle, since this is the major component (>96% by mass). Thermogravimetric and elemental analysis indicated that PPy-Pd nanocomposite loadings were below 6 wt %. The conductivity of pressed pellets prepared with the nanocomposite-coated particles increased with a decrease of particle diameter because of higher PPy-Pd nanocomposite loading. "Flattened ball" morphologies were observed by scanning/transmission electron microscopy after extraction of the PS component from the composite particles, which confirmed a PS core and a PPy-Pd nanocomposite shell morphology. X-ray diffraction confirmed the production of elemental Pd and X-ray photoelectron spectroscopy studies indicated the existence of elemental Pd on the surface of the composite particles. Transmission electron microscopy confirmed that nanometer-sized Pd particles were distributed in the shell. Near-monodisperse poly(methyl methacrylate) particles with diameters ranging between 10 and 19 μm have been also successfully coated with PPy-Pd nanocomposite, and stable aqueous dispersions were obtained. The nanocomposite particles functioned as an efficient catalyst for the aerobic oxidative homocoupling reaction of 4-carboxyphenylboronic acid in aqueous media for the formation of carbon-carbon bonds. The composite particles sediment in a short time (相似文献   

Noncontinuum effects in nanoparticle dynamics in polymers

We propose a continuum model for the dynamics of particles in polymer matrices which encompasses arbitrary size ratios of the polymer and particle. We present analytical and computer simulation results for the mobility of the particles and the viscosity of the suspension for the case of unentangled polymer melts. Our results indicate strong dependencies of the particle mobility upon the polymer-particle size ratios and much reduced intrinsic viscosities for the suspensions. These predictions rationalize some recent experimental observations on the dynamics of nanoparticles in polymer melts.     

Characterization of polymer-silica nanocomposite particles with core-shell morphologies using Monte Carlo simulations and small angle X-ray scattering

A two-population model based on standard small-angle X-ray scattering (SAXS) equations is verified for the analysis of core-shell structures comprising spherical colloidal particles with particulate shells. First, Monte Carlo simulations of core-shell structures are performed to demonstrate the applicability of the model. Three possible shell packings are considered: ordered silica shells due to either charge-dependent repulsive or size-dependent Lennard-Jones interactions or randomly arranged silica particles. In most cases, the two-population model produces an excellent fit to calculated SAXS patterns for the simulated core-shell structures, together with a good correlation between the fitting parameters and structural parameters used for the simulation. The limits of application are discussed, and then, this two-population model is applied to the analysis of well-defined core-shell vinyl polymer/silica nanocomposite particles, where the shell comprises a monolayer of spherical silica nanoparticles. Comprehensive SAXS analysis of a series of poly(styrene-co-n-butyl acrylate)/silica colloidal nanocomposite particles (prepared by the in situ emulsion copolymerization of styrene and n-butyl acrylate in the presence of a glycerol-functionalized silica sol) allows the overall core-shell particle diameter, the copolymer latex core diameter and polydispersity, the mean silica shell thickness, the mean silica diameter and polydispersity, the volume fractions of the two components, the silica packing density, and the silica shell structure to be obtained. These experimental SAXS results are consistent with electron microscopy, dynamic light scattering, thermogravimetry, helium pycnometry, and BET surface area studies. The high electron density contrast between the (co)polymer and the silica components, together with the relatively low polydispersity of these core-shell nanocomposite particles, makes SAXS ideally suited for the characterization of this system. Moreover, these results can be generalized for other types of core-shell colloidal particles.     

Rheological Modeling of Dispersion System of Nano/Microsized Polymer Particles Considering Swelling Behavior

Rheological behavior of dispersion system containing nano/microsized cross-linked polymer particle was studied considering particle hydration and swelling. Viscosity of the dispersion system depends on swelling kinetics of polymer particles. Under shear flow, dispersion of swollen polymer particles is shear thinning. According to experimental results, kinetics of particle swelling and hydration was described well by second-order kinetic equation. Relational expression between equilibrium particle size and influencing factors of swelling such as salt concentration and temperature was presented. Assume that swollen polymer particles are uniform and have a simple core-shell structure, interacting through a repulsive steric potential. The rheological modeling of such dispersion system at low shear rate was presented using the concept of effective volume fraction, which depends on swelling kinetics and interparticle potential. Cross model was introduced to describe shear-thinning behavior. The viscosity equation allows correlation of experimental data of relative viscosity versus shear rate or hydration time; accounting for effect of temperature and salt concentration on viscosity. Predictions of the model have a good agreement with experimental results.     

Simulation of the latex particle morphology

A model is presented for the simulation of the structuration of polymer particles under conditions in which the new polymer chains are compatible with the polymer previously formed. The model involves the calculation of the monomer concentration gradients within the particles due to discrepancies in thermodynamic interactions between the monomer and the different polymers present in each part of the polymer particle. In addition, the distribution of free radicals in the latex particle is taken into account. This distribution results from the anchoring of the hydrophilic end-group of the growing polymer chain on the surface of the particle. The model was applied to the simulation of the polymerization of vinyl acetate on a butyl acrylate–vinyl acetate copolymer seed. It was found that the development of the particle morphology was mainly due to the profile of concentration of radicals in the particle. On the other hand, the effect of the monomer–polymer thermodynamic interactions on the particle morphology was found to be negligible. However, it has to be pointed out that this is because, for the system studied, the interaction parameters of vinyl acetate with polyvinyl acetate and polybutyl acrylate are nearly identical.     

Effect of highly filled ferrites on non-isothermal crystallization behavior of polyamide 6 bonded ferrites

The aim of this study is to characterize the non-isothermal crystallization of polyamide 6 bonded highly filled ferrites which were prepared by the melt extrusion. Especially, the effect of ferrite concentration and its surface property on the non-isothermal crystallization were investigated by means of differential scanning calorimetry. The highly filled ferrite particles acting as obstacles could severely hinder the motion of surrounding chain segments, which were irrespective of surface nature. The ferrite could be modified by silane and obtain a visually enhanced interaction with polymer matrix which evoked the heterogeneous nucleation. Increasing this enhanced interfacial area between polymer-particle can promote the heterogeneous nucleation. However, a strong interaction can slow the motion of surrounding chain segments of particles, thereby producing a competitive effect on the crystallization rate and crystallinity. The plot of crystallization activation energy against concentration also can evaluate dispersion performance of hydrophilic fillers within hydrophobic polymer.