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

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

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.     

Simple model for grafted polymer brushes

The first theories of grafted polymer brushes assumed a step profile for the monomer density. Later, the real density profile was obtained from Monte Carlo or molecular dynamics simulations and calculated numerically using a self-consistent field theory. The analytical approximations of the solutions of the self-consistent field equations provided a parabolic dependence of the self-consistent field, which in turn led to a parabolic distribution for the monomer density in neutral brushes. As shown by numerical simulations, this model is not accurate for dense polymer brushes, with highly stretched polymers. In addition, the scaling laws obtained from the analytical approximations of the self-consistent field theory are identical to those derived from the earlier step-profile-approximation and predict a vanishing thickness of the brush at low graft densities, and a thickness exceeding the length of the polymer chains at high graft densities. Here a simple model is suggested to calculate the monomer density and the interaction between surfaces with grafted polymer brushes, based on an approximate calculation of the partition function of the polymer chains. The present model can be employed for both good and poor solvents, is compatible with a parabolic-like profile at moderate graft densities, and leads to an almost steplike density for highly stretched brushes. While the thickness of the brush depends strongly on solvent quality, it is a continuous function in the vicinity of the temperature. In good and moderately poor solvents, the interactions between surfaces with grafted polymer brushes are always repulsive, whereas in poor solvents the interactions are repulsive at small separations and become attractive at intermediate separation distances, in agreement with experiment. At large separations, a very weak repulsion is predicted.     

Evaluation of an atomic force microscopy pull-off method for measuring molecular weight and polydispersity of polymer brushes: effect of grafting density

The accuracy of the molecular weights Mn and polydispersities of polymer brushes, determined by stretching the grafted chains using atomic force microscopy (AFM) and measuring the contour length distribution, was evaluated as a function of grafting density sigma. Poly(N,N-dimethylacrylamide) brushes were prepared by surface initiated atom transfer radical polymerization on latex particles with sigma ranging between 0.17 and 0.0059 chains/nm2 and constant Mn. The polymer, which could be cleaved from the grafting surface by hydrolysis and characterized by gel permeation chromatography (GPC), had a Mn of 30,600 and polydispersity (PDI) of 1.35. The Mn determined by the AFM technique for the higher density brushes agreed quite well with the GPC results but was significantly underestimated for the lower sigma. At high grafting density in good solvent, the extended structure of the brush increases the probability of forming segment-tip contacts located at the chain end. When the distance between chains approached twice the radius of gyration of the polymer, the transition from brush to mushroom structure presumably enabled the formation of a larger number of segment-tip contacts having separations smaller than the contour length, which explains the discrepancy between the two methods at low sigma. The PDI was typically higher than that obtained by GPC, suggesting that sampling of chains with above average contour length occurs at a frequency that is greater than their spatial distribution.     

Effect of grafting on nanoparticle segregation in polymer/nanoparticle blends near a substrate

Nanoparticles in polymer films have shown the tendency to migrate to the substrate due to an entropic-based attractive depletion interaction between the particles and the substrate. It is also known that polymer-grafted nanoparticles show better dispersion in a polymer matrix. Here, molecular dynamics simulations are employed to study the effect of grafting on the nanoparticle segregation to the substrate. The nanoparticles were modeled as spheres and the polymers as bead-spring chains. The polymers of the grafts and the matrix are identical in nature. For a purely repulsive system, the nanoparticle density near the surface was found to decrease as the length of grafted chains and the number of grafts increased and in the bulk, the nanoparticles are well-dispersed. Whereas, in case of attractive systems with interparticle interactions on the order of thermal energy, the nanoparticles segregated to the substrate even more strongly, essentially forming clusters on the wall and in the bulk. However, due to the presence of grafted chains on the nanoparticles, the clusters formed in the bulk are structurally anisotropic. The effect of grafts on nanoparticle segregation to the surface was found to be qualitatively similar to the purely repulsive case.     

Inhibitory effect of hydrophilic polymer brushes on surface-induced platelet activation and adhesion

Poly(N,N-dimethylacrylamide) (PDMA) brushes are successfully grown from unplasticized poly(vinyl chloride) (uPVC) by well-controlled surface-initiated atom transfer radical polymerization (SI-ATRP). Molecular weights of the grafted PDMA brushes vary from ≈ 35,000 to 2,170000 Da, while the graft density ranges from 0.08 to 1.13 chains · nm(-2). The polydispersity of the grafted PDMA brushes is controlled within 1.20 to 1.80. Platelet activation (expression of CD62) and adhesion studies reveal that the graft densities of the PDMA brushes play an important role in controlling interfacial properties. PDMA brushes with graft densities between 0.35 and 0.50 chains · nm(-2) induce a significantly reduced platelet activation compared to unmodified uPVC. Moreover, the surface adhesion of platelets on uPVC is significantly reduced by the densely grafted PDMA brushes. PDMA brushes that have high molecular weights lead to a relatively lower platelet activation compared to low-molecular-weight brushes. However, the graft density of the brush is more important than molecular weight in controlling platelet interactions with PVC. PDMA brushes do not produce any significant platelet consumption in platelet rich plasma. Up to a seven-fold decrease in the number of platelets adhered on high graft density brushes is observed compared to the bare PVC surface. Unlike the bare PVC, platelets do not form pseudopodes or change morphology on PDMA brush-coated surfaces.     

Grafting acrylic polymers from flat nickel and copper surfaces by surface-initiated atom transfer radical polymerization

Acrylic polymers, including poly(methyl methacrylate), poly(2,2,2-trifluoroethyl methacrylate), poly( N,N'-dimethyaminoethyl methacrylate), and poly(2-hydroxyethyl methacrylate) were grafted from flat nickel and copper surfaces through surface-initiated atom transfer radical polymerization (ATRP). For the nickel system, there was a linear relationship between polymer layer thickness and monomer conversion or molecular weight of "free" polymers. The thickness of the polymer brush films was greater than 80 nm after 6 h of reaction time. The grafting density was estimated to be 0.40 chains/nm2. The "living" chain ends of grafted polymers were still active and initiated the growth of a second block of polymer. Block copolymer brushes with different block sequences were successfully prepared. The experimental surface chemical compositions as measured by X-ray photoelectron spectroscopy agreed very well with their theoretical values. Water contact angle measurements further confirmed the successful grafting of polymers from nickel and copper surfaces. The surface morphologies of all samples were studied by atomic force microscopy. This study provided a novel approach to prepare stable functional polymer coatings on reactive metal surfaces.     

Unique molecular orientation in a smectic liquid crystalline polymer film attained by surface-initiated graft polymerization

Liquid crystalline (LC) polymer brushes containing a mesogenic azobenzene (Az) moiety are synthesized on a quartz or silicon substrate by surface-initiated atom transfer radical polymerization. The molecular orientation of the Az units and the LC properties in the grafted chains are evaluated by UV-vis spectroscopy, polarized optical microscopy, and grazing incidence X-ray diffraction measurements. The Az side chains of the grafted chains exhibited a smectic LC phase in which the smectic layers are oriented perpendicular to the substrate with a parallel orientation of the mesogens. In contrast, a spincast film of the identical LC polymer without grafting to the surface shows layer structures parallel to the substrate. A drastic effect of tethering one end to the substrate on the LC orientation is demonstrated.     

Stochastic dynamics simulation of grafted polymer brushes under shear deformation

We present results of computer simulations of polymer brushes (layers of polymer chains attached at one end onto an impermeable planar surface) under shear deformation at constant shear rate. As the first stage of calculations the behavior of a single brush was studied. The monomer density profile, the distribution of the chain ends, the positions and orientations of different monomers along the chain were calculated. Dimensions of the polymer chains as functions of the shear rate were obtained for different grafting densities. An increase in the brush thickness over the grafting plane with an increase in the shear rate as predicted by the theory of Barrat was observed. However, the magnitude of the effect appears to be small. We explain this by finite extensibility of the grafted chains.     

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.     

Tethered polymer chains: surface chemistry and their impact on colloidal and surface properties

In this review the grafting of polymer chains to solid supports or interfaces and the subsequent impact on colloidal properties is examined. We start by examining theoretical models for densely grafted polymers (brushes), experimental techniques for their preparation and the properties of the ensuing structures. Our aim is to present a broad overview of the state of the art in this field, rather than an in-depth study. In the second section the interactions of surfaces with tethered polymers with the surrounding environment and the impact on colloidal properties are considered. Various theoretical models for such interactions are discussed. We then review the properties of colloids with tethered polymer chains, interactions between planar brushes and nanocolloids, interactions between brushes and biocolloids and the impact of grafted polymers on wetting properties of surfaces, using the ideas presented in the first section. The review closes with an outlook to possible new directions of research.     

Brownian dynamics of a compressed polymer brush model. Off-equilibrium response as a function of surface coverage and compression rate

We study the compressive behaviour of a polymer-covered surface (i.e., a "polymer brush") using Brownian dynamics simulations. The model consists of grafted chains with variable flexibility, variable intra- and inter-chain interactions, as well as different surface coverage. We discuss the polymer brush response to confinement by considering variable rates of compression under a hard plane. Our results show a small degree of inter-chain entanglement, regardless of whether the interaction is attractive or merely excluded volume. We observe that the molecular shape depends strongly on the surface coverage. Dense brushes exhibit a limited degree of lateral deformation under compression; instead, chains undergo a transition that produces a local patch with near-solid packing. This effect due to surface density can be undone partially by increasing the attractive nature of the chain interaction, by modulating the rate of compression, or by allowing "soft anchoring", i.e., the possible Brownian drift of the grafting bead on the surface. We have also studied the polymer brush relaxation while maintaining the compressing plane, as well as after its sudden removal. We find evidence that also the relaxation depends on surface density; dense brushes appear to be configurationally frustrated at high compression and are unable to undergo swelling, regardless of the pressure applied.     

Functionalization of hydrogen-terminated silicon via surface-initiated atom-transfer radical polymerization and derivatization of the polymer brushes

Surface-initiated atom-transfer radical polymerization (ATRP) of poly(ethylene glycol) monomethacrylate (PEGMA) was carried out on the hydrogen-terminated Si(100) substrates with surface-tethered alpha-bromoester initiator. Kinetic studies confirmed an approximately linear increase in polymer film thickness with reaction time, indicating that chain growth from the surface was a controlled "living" process. The "living" character of the surface-grafted PEGMA chains was further ascertained by the subsequent extension of these graft chains, and thus the graft layer. Well-defined polymer brushes of near 100 nm in thickness were grafted on the Si(100) surface in 8 h under ambient temperature in an aqueous medium. The hydroxyl end groups of the poly(ethylene glycol) (PEG) side chains of the grafted PEGMA polymer were derivatized into various functional groups, including chloride, amine, aldehyde, and carboxylic acid groups. The surface-functionalized silicon substrates were characterized by reflectance FT-IR spectroscopy and X-ray photoelectron spectroscopy (XPS). Covalent attachment and derivatization of the well-defined PEGMA polymer brushes can broaden considerably the functionality of single-crystal silicon surfaces.     

Control of surface properties using fluorinated polymer brushes produced by surface-initiated controlled radical polymerization

Surface-grafted styrene-based homopolymer and diblock copolymer brushes bearing semifluorinated alkyl side groups were synthesized by nitroxide-mediated controlled radical polymerization on planar silicon oxide surfaces. The polymer brushes were characterized by X-ray photoelectron spectroscopy (XPS), near-edge X-ray absorption fine structure (NEXAFS), and time-dependent water contact angle measurements. Angle-resolved XPS studies and water contact angle measurements showed that, in the case of the diblock copolymer brushes, the second block to be added was always exposed at the polymer-air interface regardless of its surface energy. Values of z*/Rg were estimated based on the radius of gyration, Rg, of the grafted homopolymer or block copolymer chains for the grafted brushes and thickness of the brush, z*. The fact that z*/Rg > 1 suggests that all these brushes are stretched. These results support the idea that after grafting the first block onto the surface the nitroxide-end capped polymer chains were able to polymerize the second block in a "living" fashion and the stretched brush so formed was dense enough that the outermost block in all cases completely covers the surface. NEXAFS analysis showed a relationship between the surface orientation of the fluorinated side chains and brush thickness with thicker brushes having more oriented side chains. Time-dependent water contact angle measurements revealed that the orientation of the side chains of the brush improved the surface stability toward reconstruction upon prolonged exposure to water.     

Attractive bridging interactions in dense polymer brushes in good solvent measured by atomic force microscopy

Using an atomic force microscope (AFM), we have investigated the interaction forces exerted by latex particles bearing densely grafted polymer brushes consisting of poly(N,N-dimethylacrylamide) (PDMA), poly(methoxyethylacrylamide) (PMEA), poly(N-isopropylacrylamide) (PNIPAM), and PMEA-b-PNIPAM in aqueous media (good solvent). The brushes were prepared by controlled surface-initiated atom transfer radical polymerization, and the hydrodynamic thicknesses were measured by dynamic light scattering. The molecular weight (Mn), grafting density (sigma), and polydispersity (PDI) of the brushes were determined by gel permeation chromatography and multiangle laser light scattering after cleaving the polymer from the latex surface by hydrolysis. Force profiles of PDMA (0.017 nm(-2) < or = sigma < or = 0.17 nm-2) and PMEA (sigma = 0.054 nm-2) brushes were purely repulsive upon compression, with forces increasing with Mn and a, as expected, due to excluded volume interactions. At a sufficiently low grafting density (sigma = 0.012 nm-2), PDMA exhibited a long-range exponentially increasing attractive force followed by repulsion upon further compression. The long-range attractive force is believed to be due to bridging between the free chain ends and the AFM tip. The PNIPAM brush exhibited a bridging force at a grafting density of 0.037 nm(-2), a value lower than the sigma needed to induce bridging in the PDMA brush. Bridging was therefore found to depend on grafting density as well as on the nature of the monomer. The grafting densities of these polymers were larger than those typically associated with bridging. Bridging interactions were used to confirm the presence of PNIPAM in a block copolymer PMEA-b-PNIPAMA brush given that the original PMEA homopolymer brush produced a purely repulsive force. The attractive force was first detected in the block copolymer brush at a separation that increased with the length of the PNIPAM block.     

A new numerical approach to dense polymer brushes and surface instabilities

We present a numerical self-consistent field (SCF) method which describes freely jointed chains of spherical monomers applied to densely grafted polymer brushes. We discuss both the Flory-Huggins model and the Carnahan-Starling equation of state and show the latter being preferable within our model at polymer volume fractions above 10%. We compare the results of our numerical method with data from molecular dynamics (MD) simulations [G.-L. He, H. Merlitz, J.-U. Sommer, and C.-X. Wu, Macromolecules 40, 6721 (2007)] and analytical SCF calculations [P. M. Biesheuvel, W. M. de Vos, and V. M. Amoskov, Macromolecules 41, 6254 (2008)] and obtain close agreement between the density profiles up to high grafting densities. In contrast to prior numerical and analytical studies of densely grafted polymer brushes our method provides detailed information about chain configurations including fluctuation, depletion, and packing effects. Using our model we could study the recently discovered instability of densely grafted polymer brushes with respect to slight variations of individual chain lengths, driven by fluctuation effects [H. Merlitz, G.-L. He, C.-X. Wu, and J.-U. Sommer, Macromolecules 41, 5070 (2008)]. The obtained results are in very close agreement with corresponding MD simulations.     

Nanowear on polymer films of different architecture

In this paper, we describe atomic force microscope (AFM) friction experiments on different polymers. The aim was to analyze the influence of the physical architecture of the polymer on the degree and mode of wear and on the wear mode. Experiments were carried out with (1) linear polystyrene (PS) and cycloolefinic copolymers of ethylene and norbornene, which are stabilized by entanglements, (2) mechanically stretched PS, (3) polyisoprene-b-polystyrene diblock copolymers, with varying composition, (4) brush polymers consisting of a poly(methyl methacrylate) (PMMA) backbone and PS side chains, (5) PMMA and PS brushes grafted from a silicon wafer, (6) plasma-polymerized PS, and (7) chemically cross-linked polycarbonate. For linear polymers, wear depends critically on the orientation of the chains with respect to the scan direction. With increasing cross-link density, wear was reduced and ripple formation was suppressed. The cross-linking density was the dominating material parameter characterizing wear.     

Interfacial friction and adhesion of polymer brushes

A bead-probe lateral force microscopy (LFM) technique is used to characterize the interfacial friction and adhesion properties of polymer brushes. Our measurements attempt to relate the physical structure and chemical characteristics of the brush to their properties as thin-film, tethered lubricants. Brushes are synthesized at several chain lengths and surface coverages from polymer chains of polydimethylsiloxane (PDMS), polystyrene (PS), and a poly(propylene glycol)-poly(ethylene glycol) block copolymer (PPG/PEG). At high surface coverage, PDMS brushes manifest friction coefficients (COFs) that are among the lowest recorded for a dry lubricant film (μ ≈ 0.0024) and close to 1 order of magnitude lower than the COF of a bare silicon surface. Brushes synthesized from higher molar mass chains exhibit higher friction forces than those created using lower molar mass polymers. Increased grafting density of chains in the brush significantly reduces the COF by creating a uniform surface of stretched chains with a decreased surface viscosity. Brushes with lower surface tension and interfacial shear stresses manifest the lowest COF. In particular, PDMS chains exhibit COFs lower than PS by a factor of 3.7 and lower than PPG/PEG by a factor of 4.7. A scaling analysis conducted on the surface coverage (σ) in relation to the fraction (ε) of the friction force developing from adhesion predicts a universal relation ε ~ σ(4/3), which is supported by our experimental data.     

Controlled swelling of polymer brushes

Very long chains with molecular weights up to 600000 can be grafted on a solid surface. We discuss here some specific features of these grafted systems: a) the climbing of a liquid along a vertical plane covered with long grafted polymer chains: because of a minute difference in chemical potential, the brushes can show color variations over an altitude ∼ 1 cm! b) swelling of brushes by elongated solvent molecules: this type of solvent can induce swelling in the isotropic phase, but when they become cooperatively ordered (nematic) we usually expect a collapse of the brush.     

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.