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.     

Variations in molecular compactness and chain entanglement during the compression of grafted polymers

Characterizing the effect of geometrical confinement on mean polymer shape is an important step towards understanding and controlling molecular behaviour at interfaces. In this work, we study the configurational transitions and molecular shape changes that take place when a grafted polymer (or “mushroom”) is compressed by a hard plane. The polymer is modelled as a single, permanently‐grafted chain with a Lennard‐Jones interaction between monomer beads. For this model, we have monitored molecular size, asphericity, and chain entanglements as a function of compression, from the regime of self‐avoiding walks to the regime of collapsed polymers. With these tools, we show that strong confinement can produce chain compactization and disentanglement even in the presence of a mild attractive interaction. Our results provide limit values to the degree of compression and monomer attraction that is necessary to deform strongly collapsed polymer mushrooms.     

Structure and dynamics of short chain molecules in disordered porous materials: a molecular dynamics simulation study

The static and dynamic properties of short polymer chains in disordered materials are studied using discontinuous molecular dynamics simulations. The polymers are modeled as chains of hard spheres and the matrix is a collection of fixed hard spheres. The simulations show that the chain size is a nonmonotonic function of the matrix concentration for all polymer concentrations. The dependence of polymer diffusion D on the degree of polymerization N becomes stronger as the matrix concentration is increased. At high matrix concentrations we observe a decoupling between translational and rotational diffusion, i.e., the rotational relaxation time becomes very large but the translational diffusion is not affected significantly. We attribute this to the trapping of a small number of polymers. Under these conditions the polymer chains diffuse via a hopping mechanism.     

Dynamics of grafted star-branched polymers. A Monte Carlo study

Monte Carlo simulations of simple models of star-branched polymers were carried out. The model chains were confined to simple cubic lattice and consisted of f = 3 branches of equal length and the total number of polymer segments as well as the density of grafted chains on the surface were varied. The chains have had one arm end attached to an impenetrable plate. The simulations were performed by employing the set of local micromodifications of the chain conformations. The model chains were athermal, i.e. good solvent conditions were modeled, the excluded volume effect was present at the model. The density of grafted chains on the surface was varied from a single chain up to 0.3. The static and dynamic properties of the system were studied. The influence of polymer concentration as well as the polymer length on static and dynamic properties of the system studied was shown. The relation between the structure and short-time dynamics (relaxation times) was discussed.     

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.     

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.     

Temperature-dependent intermolecular force measurement of poly(N-isopropylacrylamide) grafted surface with protein

We have investigated the temperature dependence of the intermolecular force between poly(N-isopropylacrylamide) (PNiPAM) grafted surface and bovine serum albumin (BSA) in phosphate buffer (pH 7.4) using atomic force microscopy at the nanonewton scale. These observations show that the interaction force is nearly zero below the phase transition temperature of PNiPAM and that it increases steeply during the phase transition. Since the PNiPAM chains are grafted onto the aminosilane (gamma-aminopropyltriethoxysilane)-treated silicon wafer, we measured the force-distance curve of BSA-immobilized tips for the bare and the aminosilane-treated silicon wafer. These surfaces show no temperature dependence and their values are different from those of the PNiPAM-grafted surfaces at 30 degrees C. The results indicate that the measured adhesion force is between the PNiPAM-grafted surface and the BSA-immobilized tip. Our studies on the intermolecular force between other surfaces (CH(3)- and COOH-terminated self-assembled monolayers) and the BSA-immobilized tip indicate that the variation in the intermolecular force between the PNiPAM surface and BSA with temperature can be attributed to the changes in the properties of the PNiPAM chains. From consideration of the PNiPAM phase transition mechanism, it is speculated that the intermolecular force between the PNiPAM-grafted surface and BSA would be affected by changes in the arrangement of the bound water molecules around the PNiPAM chain and by changes in the conformation (i.e., in the chain mobility) of the PNiPAM chain during the phase transition.     

Mixed homopolymer brushes grafted onto a nanosphere

Microphase separation of mixed A∕B polymer brushes grafted onto a nanosphere with its radius comparable to the size of polymers is investigated by numerical implementation of the self-consistent field theory. The idea is to embed the sphere within a larger cubic computational cell and use a "masking" technique to treat the spherical boundary. The partial differential equations for the chain propagator on the sphere can thus be readily solved with an efficient and high-order accurate pseudospectral method involving fast Fourier transform on a cubic cell. This numerical technique can circumvent the "pole problem" due to the use of a spherical coordinate system in conventional finite difference or finite element grid. We systematically investigate the effect of the total grafting density, composition, chain length asymmetry between two grafted homopolymers as well as spherical radius, i.e., substrate curvature on the formation of island structure with specific arrangement in a regular lattice. A series of island structures with different island numbers representing specific structure symmetry ranging from 2 to 12 except for 11 are found, in contrast to conventional hexagonal arrangement for polymer brushes on a planar substrate. Among these parameters, the spherical radius plays a significant role in determining the type of island structures, i.e., the morphology formed on the sphere.     

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     

Brownian dynamics of grafted polymer chains: time dependent properties

Results of computer simulations of polymer layers consisting of chains grafted by one end on an unpenetrable plane are presented. Characteristics of translational and rotational motion of different chain segments and correlation functions of chain radii were calculated both for single layers at different grafting densities s and for two interacting layers at different distances D between parallel grafting planes. Two values of grafting density were used in the latter case. The behavior of different correlation times as function of s and D and the interplay between the interpenetration of the brushes and rotational and translational motion are discussed. Both relaxation functions and mean square displacements are discussed in terms of stretched exponentials, and the behavior of the resulting “Kohlrausch exponents” γ is presented in detail.     

Coherent elastic scattering of a reptating chain in a melt during transient relaxation

We calculate the elastic scattering of a long chain in a polymer melt during the process of relaxation after a sudden deformation, i.e., the return to equilibrium with time, while the deformed shape is maintained. The scattering thus depends on the duration t of the relaxation, as well as on the scattering vector, and is a physical quantity characteristic of the dynamics of long chains. The reptation model of de Gennes is used as developed for deformed melts by Doi and Edwards: the chain is confined by other chains in a tube, from which disengagement by the ends is the only way of renewing its configuration. The tube diameter is taken as a parameter. We give both an analytic form and numerical evaluations. On comparison with calculations based on the Rouse model, in which the chain is assumed to be free in a viscous medium, it is seen that the experimental data (given elsewhere) should enable one to distinguish between the two models.     

Dynamics of solvent-free grafted nanoparticles

The diffusivity and structural relaxation characteristics of oligomer-grafted nanoparticles have been investigated with simulations of a previously proposed coarse-grained model at atmospheric pressure. Solvent-free, polymer-grafted nanoparticles as well as grafted nanoparticles in a melt were compared to a reference system of bare (ungrafted) particles in a melt. Whereas longer chains lead to a larger hydrodynamic radius and lower relative diffusivity for grafted particles in a melt, bulk solvent-free nanoparticles with longer chains have higher relative diffusivities than their short chain counterparts. Solvent-free nanoparticles with short chains undergo a glass transition as indicated by a vanishing diffusivity, diverging structural relaxation time and the formation of body-centered-cubic-like order. Nanoparticles with longer chains exhibit a more gradual increase in the structural relaxation time with decreasing temperature and concomitantly increasing particle volume fraction. The diffusivity of the long chain nanoparticles exhibits a minimum at an intermediate temperature and volume fraction where the polymer brushes of neighboring particles overlap, but must stretch to fill the interparticle space.     

Molecular dynamics in thin (grafted) polymer layers

Broadband dielectric spectroscopy is employed to study the molecular dynamics in thin polymer layers of (spin-coated) cis-1, 4-polyisoprene (PI) and of (grafted and spin-coated) polydimethylsiloxane (PDMS). For the former, besides the segmental and the normal mode relaxation, a confinement-induced mode is observed, which is assigned to fluctuations of terminal subchains. It turns out that the uptake of water has a strong influence on the dynamics of this relaxation, which takes place in the immediate vicinity of the interface. Between grafted and spin-coated PDMS a pronounced difference in the dynamics is observed for layers that are comparable in thickness to the radius of gyration of the confined chain. This is attributed to the different conformation of grafted and spin-coated polymer layers.     

Free Energy of a Non‐Gaussian Polymer Brush

An analytical theory describing layers of polymer chains grafted to a planar surface (i.e. polymer brush) is developed. We consider a brush of chains with finite extensibility (or non‐Gaussian brush) within the framework of molecular field theory. An analytical solution for free energy of the brush and a few other brush characteristics are obtained and studied. Comparison with other known models of a brush is also made.

Chain extensibility E(x, y) for Gaussian model (dashed lines) and BCC model (solid lines) for a few chain end positions y (numbers near curves).     

Dynamic mechanical properties of poly-α-olefins containing ring structures in side chains

Dynamic loss modulus curves have been determined over a temperature range beginning at liquid nitrogen temperature for poly-α-olefin polymers containing various ring structures, i.e., phenyl, cyclohexyl, cyclopentyl, and naphthyl, in the side chain. Glass transition and appropriate secondary relaxation temperatures were observed for each polymer. Separation of each pendant ring structure from the main backbone chain by successive additions of methylene units results in lower glass-transition temperatures. Comparison of polymers with similar side chains and different ring structures shows that the respective glass-transition temperatures decrease in the order naphthyl > cyclohexyl > phenyl > cyclopentyl. Secondary relaxation peaks were obtained at about ?150°C for polymers containing the cyclohexyl and cyclopentyl rings. A similar peak was observed for the polymer possessing a phenyl ring separated from the main chain backbone by two methylene units. The comparable polymer containing the naphthyl ring structure exhibited a broad secondary relaxation peak centered at ?20°C. The polymers possessing cyclohexyl rings separated from the main chain backbone by one or two methylene units had an additional low temperature peak at ?80°C. The molecular mechanism associated with this relaxation may be related to intramolecular transformations of the cyclohexyl ring between its “chair–chair” conformations.     

粒子-聚合物相互作用与粒子-粒子相互作用对聚合物基纳米复合物力学性能的影响

聚合物基纳米复合物(PNCs)具有比传统高分子材料更加优异的光学、力学、热力学等性能,广泛应用于各个工程领域.而纳米粒子(NPs)对材料性能提高的机理则是当前聚合物纳米复合物领域研究的重要问题,聚合物纳米复合体系相互作用的影响因素众多,至今尚未明确并完整建立复合体系相互作用与性能增强之间的关系.本文总结了近年来关于纳米粒子填充聚合物基体力学性能的研究,从粒子-聚合物相互作用和粒子-粒子相互作用角度阐述了聚合物纳米复合体系力学性能的增强机理,并根据体系中不同的结构关系分别总结了聚合物/未改性纳米粒子复合体系和聚合物/聚合物接枝纳米粒子复合体系中影响力学性能的因素.该部分内容具有重要的理论和实践意义,有助于构建复合体系微观结构与宏观性能之间的关系,进而对微观层面调控PNCs的力学性能提供指导.     

Molecular dynamics simulations of grafted polyelectrolytes on two apposing walls

Molecular dynamics simulations of polyelectrolytes grafted to two apposing surfaces were performed. Bead-spring polymer models are used to treat flexible chains [e.g., sodium poly(styrene sulfonate)] and stiff chains (double-stranded DNA). The counterions are explicitly treated. The effect of the surface density of the grafted polymer, the chain length, and the gap width on the structure and the pressure were studied. Results are compared to experimental measurements and to simulations of polyelectrolyte brushes on a single surface. The density profiles exhibit a maximum not found in single surface data. The maximum is due to the brushes shrinking to avoid interpenetration.