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.     

Effect of Chain Stiffness on Nanoparticle Segregation in Polymer/Nanoparticle Blends Near a Substrate

Nanoparticles in a flexible polymer melt film often segregate to the substrate due to attractive depletion interactions between the nanoparticles and the substrate. Here, molecular dynamics simulations are performed to study the effect of chain stiffness on this segregation. The nanoparticles are modeled as spheres and the polymers as semi‐flexible bead‐spring chains. Both purely repulsive and attractive forces are considered, while assuming non‐selective interactions among all species. The nanoparticles are found to be well‐dispersed in the system having repulsive forces only and aggregate into clusters in the completely attractive system. For the repulsive system, adding chain stiffness substantially decreases the nanoparticles' segregation, and hence their concentration, at the substrate.

     

Mean‐field theoretical analysis of brush‐coated nanoparticle dispersion in polymer matrices

The equilibrium dispersion of nanoparticles with grafted polymer chains into polymer matrices, of the same chemical structure as the brush, is studied through the device of mean‐field theory. Our results show that the disperion of brush‐coated nanoparticles into a matrix polymer is improved with (i) decreasing particle radius and (ii) increasing brush chain length. Both of these aspects can be understood based on the fact that, unlike the case of planar surfaces, homopolymer chains end‐grafted to spherical nanoparticle surfaces tangentially spread away from the surface thus alleviating the packing frustration that is created by the relatively high grafting densities. This permits significant brush/matrix overlap, even at high grafting densities, a regime that has only recently become experimentally available due to advances in polymer synthesis (i.e., the “grafting‐to” methods). © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 351–358, 2008     

Multiple dynamic regimes in colloid‐polymer dispersions: New insight using X‐ray photon correlation spectroscopy

We present an X‐ray photon correlation spectroscopy (XPCS) study of dynamic transitions in an anisotropic colloid‐polymer dispersion with multiple arrested states. The results provide insight into the mechanism for formation of repulsive glasses, attractive glasses, and networked gels of colloids with weakly adsorbing polymer chains. In the presence of adsorbing polymer chains, we observe three distinct regimes: a state with slow dynamics consisting of finite particles and clusters, for which interparticle interactions are predominantly repulsive; a second dynamic regime occurring above the saturation concentration of added polymer, in which small clusters of nanoparticles form via a short‐range depletion attraction; and a third regime above the overlap concentration in which dynamics of clusters are independent of polymer chain length. The observed complex dynamic state diagram is primarily governed by the structural reorganization of a nanoparticle cluster and polymer chains at the nanoparticle‐polymer surface and in the concentrated medium, which in turn controls the dynamics of the dispersion. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 752–760     

Phase behavior of polymer/nanoparticle blends near a substrate

We use the recent fluids density functional theory of Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005); J. Chem. Phys. 122, 094506 (2005)] to investigate the phase behavior of athermal polymer/nanoparticle blends near a substrate. The blends are modeled as a mixture of hard spheres and freely jointed hard chains, near a hard wall. There is a first order phase transition present in these blends in which the nanoparticles expel the polymer from the surface to form a monolayer at a certain nanoparticle concentration. The nanoparticle transition density depends on the length of the polymer, the nanoparticle diameter, and the overall bulk density of the system. The phase transition is due to both packing entropy effects related to size asymmetry between the components and to the polymer configurational entropy, justifying the so-called "entropic push" observed in experiments. In addition, a layered state is found at higher densities which resembles that in colloidal crystals, in which the polymer and nanoparticles form alternating discrete layers. We show that this laminar state has nearly the same free energy as the homogeneously mixed fluid in the bulk and is nucleated by the surface.     

Polymer grafted nanoparticles: Effect of chemical and physical heterogeneity in polymer grafts on particle assembly and dispersion

Macroscopic properties of polymer nanocomposites depend on the microscopic composite morphology of the constituent nanoparticles and polymer matrix. One way to control the spatial arrangement of the nanoparticles in the polymer matrix is by grafting the nanoparticle surfaces with polymers that can tune the effective interparticle interactions in the polymer matrix. A fundamental understanding of how graft and matrix polymer chemistries and molecular weight, grafting density, and nanoparticle size, and chemistry affect interparticle interactions is needed to design the appropriate polymer ligands to achieve the target morphology. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level interactions to the morphology. In this feature article, we present our recent theory and simulation studies of polymer grafted nanoparticles with chemical and physical heterogeneity in grafts to calculate the effective interactions and morphology as a function of chemistry, molecular weights, grafting densities, and so forth. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

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     

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.     

Synthesis,characterization and cleavage of linear polymers attached to silica nanoparticles formed using thiol‐acrylate conjugate addition reactions

This study investigates the formation of linear polymer grafts using thiol‐acrylate conjugate addition reactions on nanoparticle surfaces. Silica nanoparticles were first modified with an amine functionality, followed by the attachment of a photocleavable acrylate. Dithiol‐diacrylate films were attached to the particles through the surface acrylate groups at various stoichiometric ratios of thiol to acrylate by conducting amine‐catalyzed conjugate addition polymerizations. The particles were then exposed to UV light to release the grafted polymer by photocleavage. The cleaved, grafted polymers were analyzed using infrared spectroscopy and gel permeation chromatography and compared to polymers formed in the bulk, which remained unattached to the particles. The measured number and weight average molecular weights were similar for both polymer types within experimental error and increased from 2000 to 5000 g/mol and 4000 to 10,000 g/mol, respectively, as the ratio of limiting to excess functionality increased from 0.8 to 1. Both number and weight average molecular weights followed the trend of step growth polymers with the highest molecular weight achieved for stoichiometric monomeric mixtures. Surface coverage of the nanoparticles was estimated using the molecular weight and thermogravimetric data and was found to be uniform (～0.15 chains/nm²) irrespective of the stoichiometry of the reacting monomers. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6896–6906, 2008     

Controlled nanoparticle assembly by dewetting of charged polymer solutions

In this paper, we present an alternative approach for controlled nanoparticle organization on a solid substrate by applying dewetting patterns of charged polymer solutions as a templating system. Thin films of charged polymer solutions dewet a solid substrate to form complex dewetting patterns that depend on the polymer charge density. These patterns, ranging from polygonal networks to elongated structures that are stabilized by viscous forces during dewetting, serve as potential templates for two-dimensional nanoparticle organization on a solid substrate. Thus, while nanoparticles dried in pure water undergo self-assembly to form close-packed arrays, addition of charged polymer in the dispersion leads to the formation of open structures that are directed by the dewetting patterns of the polymer solution. In this study, we focus on the application of elongated structures resulting from dewetting of high-charge-density polymer solutions to align nanoparticles of silica and gold into long chains that are several micrometers in length. The particle ordering process is a two-step mechanism: an initial confinement of the nanoparticles in the dewetting structures and self-assembly of the particles within these structures upon further drying by lateral capillary attractions.     

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.     

Interactions between nanocolloidal particles in polymer solutions: effect of attractive interactions

We present a density-functional theory study of nanoparticle interactions in a concentrated polymer solution. The polymers are modeled as freely jointed tangent chains; all nonbonded interactions between polymer segments and nanoparticles are described by Lennard-Jones potentials. We test several recently proposed methods of treating attractive interactions within the density-functional theory framework by comparing theoretical results with recent simulation data. We find that the simple van der Waals approach provides the most accurate results for the polymer-mediated potential of mean force between two dilute nanoparticles. We employ this approach to study nanoparticle interactions as a function of nanoparticle-segment interaction strength and polymer solution density and temperature.     

Surface-induced phase behavior of polymer/nanoparticle blends with attractions

In an athermal blend of nanoparticles and homopolymer near a hard wall, there is a first order phase transition in which the nanoparticles segregate to the wall and form a densely packed monolayer above a certain nanoparticle density. Previous investigations of this phase transition employed a fluids density functional theory (DFT) at constant packing fraction. Here we report further DFT calculations to probe the robustness of this phase transition. We find that the phase transition also occurs in athermal systems at constant pressure, the more natural experimental condition than constant packing fraction. Adding nanoparticle-polymer attractions increases the nanoparticle transition density, while sufficiently strong attractions suppress the first-order transition entirely. In this case the systems display a continuous transition to a bulk layered state. Adding attractions between the polymers and the wall has a similar effect of delaying and then suppressing the first-order nanoparticle segregation transition, but does not lead to any continuous phase transitions.     

AFM colloidal forces measured between microscopic probes and flat substrates in nanoparticle suspensions

Colloidal forces between atomic force microscopy probes of 0.12 and 0.58 N/m spring constant and flat substrates in nanoparticle suspensions were measured. Silicon nitride tips and glass spheres with a diameter of 5 and 15 mum were used as the probes whereas mica and silicon wafer were used as substrates. Aqueous suspensions were made of 5-80 nm alumina and 10 nm silica particles. Oscillatory force profiles were obtained using atomic force microscope. This finding indicates that the nanoparticles remain to be stratified in the intervening liquid films between the probe and substrate during the force measurements. Such structural effects were manifested for systems featuring attractive and weak repulsive interactions of nanoparticles with the probe and substrate. Oscillation of the structural forces shows a periodicity close to the size of nanoparticles in the suspension. When the nanoparticles are oppositely charged to the probes, they tend to coat the probes and hinder probe-substrate contact.     

Polymer Chain Conformation on Deuterated Polystyrene Nanoparticles Investigated by SANS

We previously reported that grafted polystyrene (PS) chains on silica nanoparticles at a low grafting density show similar conformations to free PS chains in the same solvent, THF (diameter ?50 nm, Colloid.poly.Sci. (2013), 291, 9, 2087–2099). As an extension of our previous study we choose an organic nanoparticle (deuterated polystyrene, dPS) instead of inorganic nanoparticle to see the impact of the substrate material on chain conformation. Additionally, a wider range of molecular weights were prepared to investigate the conformation feature of grafted PS chains more in detail. Small angle neutron scattering (SANS) experiments were performed to characterize PS grafted dPS particles in good solvent condition, with deuterated toluene and deuterated THF as solvent. To get insight into the conformation of the grafted PS layer we apply a scaling law describing the dimension of free PS polymer in good solvent condition to the obtained thickness of the grafted PS layer. We find an overall agreement with the scaling law where the thickness of the grafted PS layer is slightly larger than 2R_g of the free polymer chains in the respective solvent giving hint for semi dilute polymer brush (SDPB) situation.     

Tethered nanoparticle-polymer composites: phase stability and curvature

Phase behavior of poly(ethylene glycol) (PEG) tethered silica nanoparticles dispersed in PEG hosts is investigated using small-angle X-ray scattering. Phase separation in dispersions of densely grafted nanoparticles is found to display strikingly different small-angle X-ray scattering signatures in comparison to phase-separated composites comprised of bare or sparsely grafted nanoparticles. A general diagram for the dispersion state and phase stability of polymer tethered nanoparticle-polymer composites incorporating results from this as well as various other contemporary studies is presented. We show that in the range of moderate to high grafting densities the dispersion state of nanoparticles in composites is largely insensitive to the grafting density of the tethered chains and chemistry of the polymer host. Instead, the ratio of the particle diameter to the size of the tethered chain and the ratio of the molecular weights of the host and tethered polymer chains (P/N) are shown to play a dominant role. Additionally, we find that well-functionalized nanoparticles form stable dispersions in their polymer host beyond the P/N limit that demarcates the wetting/dewetting transition in polymer brushes on flat substrates interacting with polymer melts. A general strategy for achieving uniform nanoparticle dispersion in polymers is proposed.     

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.     

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.     

Forces between nanorods with end-adsorbed chains in a homopolymer melt

Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant. To investigate this effect for the case of cylindrical symmetry, I use a classical fluids density functional theory applied to a coarse-grained model to study the polymer-mediated interactions between two nanorods. The rods are coated with end-adsorbing chains and immersed in a polymer melt of chemically identical, nonadsorbing chains. The force between the nanorods is found to be nonmonotonic, with an attractive well when the two brushes come into contact with each other, followed by a steep repulsion at shorter distances. The attraction is due to the entropic phenomenon of autophobic dewetting, in which there is a surface tension between the brush and the matrix chains. These results are similar to previous results for planar and spherical polymer brushes in melts of the same polymer. The depth of the attractive well increases with matrix chain molecular weight and with the surface coverage. The attraction is very weak when the matrix chain molecular weight is similar to or smaller than the brush molecular weight, but for longer matrix chains the magnitude of the attraction can become large enough to cause aggregation of the nanorods.     

高分子/单链高分子纳米粒子复合体系中的界面性质

高分子与纳米粒子复合是改善高分子材料性能的有效途径.近20年来关于高分子/纳米粒子复合物的研究引起了学术界广泛的兴趣.然而由于此类体系中的影响因素复杂,虽然学者们在相关材料性能的研究方面取得了重要进展,但是相关理论的发展却相对滞后,其中一个重要原因是实验上表征手段的缺失,导致对体系中纳米粒子与本体高分子链相互作用规律的认识(尤其是两者界面性质的认识)不够.本文总结和阐述了我们近几年利用分子动力学模拟技术研究高分子/单链高分子纳米粒子复合体系的主要结果,并围绕此类复合体系中的界面结构及动力学性质,讨论并总结了纳米粒子对本体高分子链的作用范围及影响规律,指出单链纳米粒子对熔体链的作用范围与纳米粒子的自身尺寸相当,而与熔体高分子链的分子量没有直接的关系.该结论将为纳米复合体系高分子理论的发展提供重要参考.