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.     

Nanoparticle Dispersion and Glass Transition Behavior of Polyimide-grafted Silica Nanocomposites

How to control the spatial distribution of nanoparticles to meet different performance requirements is a constant challenge in the field of polymer nanocomposites.Current studies have been focused on the flexible polymer chain systems.In this study,the rigid polyimide(PI) chain grafted silica particles with different grafting chain lengths and grafting densities were prepared by "grafting to" method,and the influence of polymerization degree of grafted chains(N),matrix chains(P),and grafting density(a) on the spatial distribution of nanoparticles in the PI matrix was explored.The glass transition temperature(Tg) of PI composites was systematically investigated as well.The results show that silica particles are well dispersed in polyamic acid composite systems,while aggregation and small clusters appear in PI nanocomposites after thermal imidization.Besides,the particle size has no impact on the spatial distribution of nanoparticles.When σ·N0.5<<(N/P)2,the grafted and matrix chains interpenetrate,and the frictional resistance of the segment increases,resulting in restricted relaxation kinetics and Tg increase of the PI composite system.In addition,smaller particle size and longer grafted chains are beneficial to improving Tg of composites These results are all propitious to complete the microstructure control theory of nanocomposites and make a theoretical foundation for the high performance and multi-function of PI nanocomposites.     

受限状态聚合物熔体的分子动力学模拟

用粗粒化的分子动力学(MD)模拟方法从分子层次研究了受限于粗糙壁内的聚合物熔体的动力学性质. 结果表明, 对于链长较短的受限聚合物熔体体系, 随着膜厚的增加, 体系内部高分子链的松弛时间逐渐减少; 然而对于链长较长的受限体系, 聚合物链的松弛时间随着膜厚的增加先减少后增加. 推测这种由于链长的变化所引起的动力学性质的差异源自受限熔体内聚合物链聚集状态的改变, 并且通过考察交叠参数对这种改变进行了分析. 结果表明, 在膜厚增加的过程中, 决定受限状态高分子长链松弛机理的因素逐渐从受限效应转变成为链间的缠结效应.     

Dynamics in coarse-grained models for oligomer-grafted silica nanoparticles

Coarse-grained models of poly(ethylene oxide) oligomer-grafted nanoparticles are established by matching their structural distribution functions to atomistic simulation data. Coarse-grained force fields for bulk oligomer chains show excellent transferability with respect to chain lengths and temperature, but structure and dynamics of grafted nanoparticle systems exhibit a strong dependence on the core-core interactions. This leads to poor transferability of the core potential to conditions different from the state point at which the potential was optimized. Remarkably, coarse graining of grafted nanoparticles can either accelerate or slowdown the core motions, depending on the length of the grafted chains. This stands in sharp contrast to linear polymer systems, for which coarse graining always accelerates the dynamics. Diffusivity data suggest that the grafting topology is one cause of slower motions of the cores for short-chain oligomer-grafted nanoparticles; an estimation based on transition-state theory shows the coarse-grained core-core potential also has a slowing-down effect on the nanoparticle organic hybrid materials motions; both effects diminish as grafted chains become longer.     

Structure and transport properties of polymer grafted nanoparticles

We perform molecular dynamics simulations on a bead-spring model of pure polymer grafted nanoparticles (PGNs) and of a blend of PGNs with a polymer melt to investigate the correlation between PGN design parameters (such as particle core concentration, polymer grafting density, and polymer length) and properties, such as microstructure, particle mobility, and viscous response. Constant strain-rate simulations were carried out to calculate viscosities and a constant-stress ensemble was used to calculate yield stresses. The PGN systems are found to have less structural order, lower viscosity, and faster diffusivity with increasing length of the grafted chains for a given core concentration or grafting density. Decreasing grafting density causes depletion effects associated with the chains leading to close contacts between some particle cores. All systems were found to shear thin, with the pure PGN systems shear thinning more than the blend; also, the pure systems exhibited a clear yielding behavior that was absent in the blend. Regarding the mechanism of shear thinning at the high shear rates examined, it was found that the shear-induced decrease of Brownian stresses and increase in chain alignment, both correlate with the reduction of viscosity in the system with the latter being more dominant. A coupling between Brownian stresses and chain alignment was also observed wherein the non-equilibrium particle distribution itself promotes chain alignment in the direction of shear.     

Nanoparticle stability in semidilute and concentrated polymer solutions

The wetting of PDMS-grafted silica spheres (PDMS- g-silica) is connected to their depletion restabilization in semidilute and concentrated PDMS/cyohexane polymer solutions. Specifically, we found that a wetting diagram of chemically identical graft and free homopolymers predicts stability of hard, semisoft, and soft spheres as a function of the bulk free polymer volume fraction, graft density, and the graft and free polymer chain lengths. The transition between stable and aggregated regions is determined optically and with dynamic light scattering. The point of demarcation between the regions occurs when the graft and free polymer chains are equal in length. When graft chains are longer than free chains, the particles are stable; in contrast, the particles are unstable when the opposite is true. The regions of particle stability and instability are corroborated with theoretical self-consistent mean-field calculations, which not only show that the grafted brush is responsible for particle dispersion in the complete wetting region but also aggregation in the incomplete wetting region. Ultimately, our results indicate that depletion restabilization depends on the interfacial properties of the nanoparticles in semidilute and concentrated polymer solutions.     

Physical aging and glass transition of hairy nanoparticle assemblies

Matrix free assemblies of polymer-grafted, “hairy” nanoparticles (aHNP) exhibit novel morphology, dielectric, and mechanical properties, as well as providing means to overcome dispersion challenges ubiquitous to conventional polymer-inorganic nanocomposite blends. Physical aging of the amorphous polymer glass between the close-packed nanoparticles (NPs) will dominate long-term stability; however, the energetics of volume recovery within the aHNPs is unknown. Herein, we compare glass transition temperature (T_g) and enthalpy recovery of aHNPs to NP-polymer blends, across different nano-silica loadings (0–50 v/v%) and canopy architecture of polystyrene (PS) grafted silica. For aHNPs, the grafting of PS to silica imposes an additional design constraint between silica volume fraction, graft density, and graft molecular weight. At low and intermediate silica volume fraction, the T_g of blended nanocomposites is independent of silica content, reflecting a neutral polymer-NP interface. For aHNPs, the T_g decreases with silica content, implying that chain tethering decreases local segment density more than the effect of molecular weight or polymer-NP interactions. Additionally, the T_g of the aHNPs is higher than a linear matrix of comparable molecular weight, implying a complementary effect to local segment density that constrains cooperativity. In contrast, enthalpy recovery rate in the blend or aHNP glass is retarded comparably. In addition, a cross-over temperature, T_x, emerges deep within the glass where the enthalpy recovery process of all nanocomposites becomes similar to linear unfilled matrices. Differences between structural recovery in aHNP and blended nanocomposites occur only at the highest silica loadings (∼ 50 v/v%), where enthalpy recovery for aHNPs is substantially suppressed relative to the blended counterparts. The absence of physical aging at these loadings is independent of brush architecture (graft density or molecular weight of tethered chains) and indicates that the impact of chain tethering on effective bulk structural relaxation starts to appear at particle-particle surface separations on the order of the Kuhn length. Overall, these observations can be understood within the context of how three separate structural characteristics impact local segment density and relaxation processes: the dimension and architecture of the tethered polymer chains, the separation between NP surfaces, and the confinement imposed by chain tethering and space filling within the aHNP. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 319–330     

Interactions between polymer brush-coated spherical nanoparticles: the good solvent case

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of the grafted chains, etc.). When the nanoparticles approach very closely, some chains need to be squeezed out into the tangent plane in between the particles, causing a very steep rise of the repulsive interaction energy between the particles. We consider as a complementary method the density functional theory approach. We find that the quantitative accuracy of the density functional theory is limited to large nanoparticle separation and short chain length. A brief comparison to Flory theory and related work on other models also is presented.     

Particle-particle interactions and chain dynamics of fluorocarbon and hydrocarbon functionalized ZrO2 nanoparticles

The chain conformation and dynamics of hydrocarbon and perfluorocarbon fatty acids adsorbed on 4 nm ZrO2 particles were characterized by solid-state 13C chemical shift and 19F NMR relaxation measurements, respectively, and compared to those from previous studies on lower surface area fumed metal oxide powders. The interdigitation of chains between neighboring particles, which increases with chain length, can be detected from the splitting of the 13C NMR and 19F NMR signals of the CH3 and CF3 groups, respectively. Similar to the case of alkanethiol self-assembled monolayers (SAMs) on gold nanoparticles, this interdigitation allows for efficient chain packing despite the high surface curvature. The hydrocarbon chains on the ZrO2 nanoparticles are more ordered, and the reversible chain length dependent order-disorder transition temperatures are elevated relative to those of the same fatty acids adsorbed on fumed ZrO2 powder. Likewise, the 19F spin lattice relaxation times of the fluorocarbon chains approach those of the bulk acids with increasing chain length and interdigitation, indicating densely packed chains.     

Molecular dynamics simulations of monodisperse/bidisperse polymer melt crystallization

We use large scale coarse‐grained molecular dynamics simulations to study the kinetics of polymer melt crystallization. For monodisperse polymer melts of several chain lengths under various cooling protocols, we show that short chains have a higher terminal crystallinity value compared to longer ones. They align at the early stages and then cease evolving. Long chains, however, align, fold into lamella structures and then slowly optimize their dangling ends for the remaining simulation time. We then identify the mechanism behind bidisperse blend crystallization. To this end, we introduce a new algorithm (called Individual Chain Crystallinity) that allows the calculation of the crystallinity separately for short and long chains in the blend. We find that, in general, bidispersity hinders crystallization significantly. At first the crystallinity of the long chain components exceeds that of the monodisperse melt, but subsequently falls below the corresponding monodisperse melt curve after a certain “crossover time.” The time of the crossover can be attributed to the time required for the full crystallization of the short chains. This indicates that at the early stages the short chains are helping long chains to crystallize. However, after all short chains have crystallized they start to hinder the crystallization of the long chains by obstructing their motion. Lastly, polymer crystallization upon various thermodynamic protocols is studied. Slower cooling is found to increase the crystallinity value. Upon an instantaneous deep quench and subsequent isothermal relaxation, the crystallinity grows rapidly with time at early stages and subsequently saturates. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2318–2326     

Chain confinement in polymer nanocomposites and its effect on polymer bulk properties

The issue of chain confinement in nanocomposites remains largely unanswered because experimental systems are plagued by additional complicating variables such as particle–polymer interactions and free volume increases brought upon by the addition of the particles. Using computer simulation of high length chain polymers, we show that simple excluded volume interactions between polymer and nanoparticles lead to a wealth of changes in the diffusion coefficient and entanglement density of the chains. This opens up the possibility of using nanoparticles for tuning polymer properties, such as toughness, melt viscosity, and transient rubberlike behavior. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 687–692, 2010     

Interfacial properties of statistical copolymer brushes in contact with homopolymer melts

We use polymer self-consistent field theory to quantify the interfacial properties of random copolymer brushes (AB) in contact with a homopolymer melt chemically identical to one of the blocks (A). We calculate the interfacial widths and interfacial energies between the melt and the brush as a function of the relative chain sizes, grafting densities, compositions of the random copolymer in the brush, and degree of chemical incompatibility between the A and B species. Our results indicate that the interfacial energies between the melt and the brush increase (signifying expulsion of the free chains from the brush) with increasing grafting density, chemical incompatibility between A and B components, and size of the free chains relative to the grafted chains. We also compare the interfacial energies of random copolymers of different sequence characteristics and find that, except for the case of very blocky or proteinlike chains, blockiness of the copolymer has only little effect on interfacial properties. Our results for interfacial energies are rationalized based on the concept of an "effective volume fraction" of the brush copolymers, f(eff), which quantifies the chemical composition of the brush segments in the interfacial zone between the brush and melt copolymers. Using this concept, we modify the strong-stretching theory of brush-melt interfaces to arrive at a simple model whose results qualitatively agree with our results from self-consistent field theory. We discuss the ramifications of our results for the design of neutral surfaces.     

Accelerated brush growth on nanoparticle surfaces by reversible addition‐fragmentation chain transfer polymerization

It is now well established that controlling the grafted chain lengths and densities on nanoparticle surfaces determines the effective interactions between particles, and their assembly. Here, we present unusual kinetic results for achieving grafted chain lengths longer than the free chains using reversible addition‐fragmentation chain transfer (RAFT) polymerization and discuss the limitations to obtaining polymer grafting density higher than ～0.06 chains/nm². We observe that surface initiated polymerization grows faster than the free chains in solution with high RAFT agent coverage (1.95 agents/nm²) on nanoparticles. The time‐dependence of graft density suggests that activation of the anchored chain transfer agent (CTA) is limited by the diffusion of macro‐radicals within growing grafts. Thus, radical transfer and exchange reactions become inefficient between grafts and free polymer, and convert the surface‐initiated RAFT mechanism to a free radical polymerization. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1700–1705     

Reinforcement effect of carbon nanofillers in an epoxy resin system: Rheology,molecular dynamics,and mechanical studies

The reinforcing effect of carbon nanoparticles in an epoxy resin has been estimated with different approaches based on rheology, molecular dynamics (evaluated by differential scanning calorimetry, dielectric relaxation spectroscopy, and thermally stimulated depolarization current), and dynamic mechanical analysis. Carbon particles aggregate as the volume increases and form a fractal structure in the matrix polymer. The dispersion microstructure has been characterized by its viscoelastic properties and relaxation time spectrum. The scaling of the storage modulus and yield stress with the volume fraction of carbon shows two distinct exponents and has thus been used to determine the critical carbon volume fraction of the network formation (Φ*) for the carbon/epoxy dispersions. At nanofiller concentrations greater than Φ*, the overall mobility of the polymer chains is restricted in both dispersions and solid nanocomposites. Therefore, (1) the relaxation spectrum of the dispersions is strongly shifted toward longer times, (2) the glass‐transition temperature is increased and (3) the relaxation strength of both the secondary (β) and primary (α) relaxations increases in the nanocomposites, with respect to the pure polymer matrix. The dispersion microstructure, consisting of fractal flocs and formed above Φ*, is proposed to play the main role in the reinforcement of nanocomposites. Moreover, the network structure and the interface polymer layer (bond layer), surrounding nanoparticles, increases the relaxation strength and slows the cooperative α relaxation, and this results in an improvement of the mechanical properties. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 522–533, 2005     

Communication: Unusual dynamics of hybrid nanoparticles and their binary mixtures

We present the results on the evolution of microscopic dynamics of hybrid nanoparticles and their binary mixtures as a function of temperature and wave vector. We find unexpectedly a nonmonotonic dependence of the structural relaxation time of the nanoparticles as a function of the morphology. In binary mixtures of two of the largest nanoparticles studied, we observe re-entrant vitrification as a function of the volume fraction of the smaller nanoparticle, which is unusual for such high diameter ratio. Possible explanation for the observed behavior is provided.     

Dynamics of star branched polymers in a matrix of linear chains — a Monte Carlo study

A simple cubic lattice model of the melt of 3-arm star-branched polymers of various length dissolved in a matrix of long linear chains (n₁ = 800 beads) is studied using a dynamic Monte Carlo method. The total polymer volume fraction is equal to 0,5, while the volume fraction of the star polymers is about ten times smaller. The static and dynamic properties of these systems are compared with the corresponding model systems of isolated star-branched polymers and with the melt of linear chains. It has been found that the number of dynamic entanglements for the star polymers with arm length up to 400 segments is too small for the onset of the arm retraction mechanism of polymer relaxation. In this regime dynamics of star-branched polymers is close to the dynamics of linear polymers at corresponding concentration and with equivalent chain length. The entanglement length for star polymers appears to be somewhat larger compared with linear chains.     

Nanostructure and mechanical properties of polybutylacrylate filled with grafted silica particles

We investigate the nanostructure and the linear rheological properties of polybutylacrylate (PBA) filled with St?ber silica particles grafted with PBA chains. The silica volume fractions range from 1.8 to 4.7%. The nanostructure of these suspensions is investigated by small-angle neutron scattering (SANS), and we determine their spectromechanical behavior in the linear region. SANS measurements performed on low volume fraction composites show that the grafted silica particles are spherical, slightly polydisperse, and do not form aggregates during the synthesis process. These composites thus constitute model filled polymers. The rheological results show that introducing grafted silica particles in a polymer matrix results in the appearance of a secondary process at low frequency: for the lowest volume fractions, we observe a secondary relaxation that we attribute to the diffusion of the particles in the polymeric matrix. By increasing the silica volume fraction up to a critical value, we obtain gellike behavior at low frequency as well as the appearance of a structure factor on the scattering intensity curves obtained by SANS. Further increasing the silica particle concentration leads to composites exhibiting solidlike low-frequency behavior and to an enhanced structure peak on the SANS diagrams. This quantitative correlation between the progressive appearance of a solidlike rheological behavior, on one hand, and a structure factor, on the other hand, supports the idea that the viscoelastic behavior of filled polymers is governed by the spatial organization of the fillers in the matrix.     

The dynamics of single chains within a model polymer melt

Discontinuous molecular dynamics simulations are performed on a system containing 32 hard chains of length 192 at a volume fraction of phi = 0.45 to explore the idea that localized entanglements have a significant effect on the dynamics of the individual chains within an entangled polymer melt. Anomalous behavior can still be observed when studying the dynamics of the individual chains, although increased time averaging causes the anomalous relaxation-memory-release behavior that was observed previously in the system to smooth out. First, the individual chain mean squared displacements and apparent diffusion coefficients are calculated, and a wide distribution of diffusive behavior is found. Although the apparent diffusion coefficient curve averaged over all chains displays the predicted long-time diffusive behavior, the curves for the individual chains differ both qualitatively and quantitatively. They display superdiffusive, diffusive, and subdiffusive behavior, with the largest percentage of chains exhibiting superdiffusive behavior and the smallest percentage exhibiting the predicted diffusive behavior. Next, the individual chain end-to-end vector autocorrelation functions and relaxation times are determined, and a wide distribution of stress relaxation behavior is found. The times when the end-to-end vector autocorrelation functions relax completely span almost an order of magnitude in reduced time. For some chains, the end-to-end vector autocorrelation function relaxes smoothly toward zero similar to the system average; however, for other chains the relaxation is slowed greatly, indicating the presence of additional entanglements. Almost half of the chains exhibit the anomalous behavior in the end-to-end vector autocorrelation function. Finally, the dynamic properties are displayed for a single chain exhibiting anomalous relaxation-memory-release behavior, supporting the idea that the relaxation-memory-release behavior is a single-chain property.     

Glassy dynamics and mechanical response in dense fluids of soft repulsive spheres. I. Activated relaxation, kinetic vitrification, and fragility

The microscopic nonlinear Langevin equation theory of activated glassy dynamics is applied to dense fluids of spherical particles that interact via a finite range Hertzian contact soft repulsion. The activation barrier and mean alpha relaxation time are predicted to be rich functions of volume fraction and particle stiffness, exhibiting a non-monotonic variation with concentration at high volume fractions. The latter is due to a structural "soft jamming" crossover where the real space local cage order weakens when soft particles significantly overlap. The highly variable dependences of the relaxation time on temperature and volume fraction are reasonably well collapsed onto two distinct master curves that are qualitatively consistent with a recent scaling ansatz and computer simulation study. A kinetic vitrification diagram is constructed and compared to its dynamic crossover analog. Intersection of the dynamic crossover and soft jamming threshold boundaries occurs for particles that are sufficiently soft, implying the nonexistence of a clear activated dynamics regime or kinetic arrest transition for such particles. The isothermal dynamic fragility is predicted to vary over a wide range as a function of particle stiffness, and soft particles behave as strong glasses. Qualitative comparisons with simulations and microgel experiments reveal good agreement.