Semiflexible polymers grafted to a solid planar substrate: Changing the structure from polymer brush to “polymer bristle”

Glass transition and dynamics of semiflexible polymer brushes

The glass transition and dynamics of densely grafted semiflexible polymer brushes are studied by molecular dynamics simulation. The glass transition temperature (T_g) increases with the polymer rigidity. The local glass transition temperature (T_g,local) is estimated from the temperature-dependent dynamics of individual segments including the lateral position fluctuation and lateral mean square displacement. Different from the flexible polymer brush, T_g,local of semiflexible polymer brushes is roughly independent of the segment height. Our simulation reveals that the glass transition is in synchronism with an abrupt change of the chain conformation in semiflexible polymer brushes. When the temperature drops to near T_g, the semiflexible polymer chains elongate, tilt, and become more ordered. Moreover, enhanced segmental dynamics is observed at temperatures just above T_g for the semiflexible polymer brushes.

A Local-Exchange Model of Folding Chain Surface of Polymer Crystal Based on Worm-Like Chain Model within Single-Chain in Mean-Field Theory

The structure of amorphous layer of folding surface controls the properties of the polymer lamellar crystal, which consists of chains with a loop conformation. The surface tension depends on the length and the distance between two injection points of the loop which involving the reptation motion and lateral exchange motion of the stems. In the present work, a local-exchange motion model based on the worm-like chain model is developed to investigate the effects of lateral motion of stems on the release the surface tension. The optimal distance between two injection points is determined by the balance of chain bending energy and conformational entropy. The numerical results provide evidences to the adjacent re-entry model for various loop lengths. A possible explanation involving density of injection points is proposed to interpret the mechanism.

Grafting-Induced Structural Ordering of Lactide Chains

The structure of a grafted layer of lactide chains in the “dry brush” regime immersed in a melt of chemically similar polymer was examined while varying graft lengths. To this end, microsecond atomistic molecular dynamics simulations were performed. Almost no influence of graft length on the fraction of the grafted chains backfolded to the grafting surface was found. However, a structural ordering was unexpectedly observed in the system when the length of the grafted lactide chains was close to approximately 10 Kuhn segments. This ordering of the grafts is characterized by the formation of helical fragments whose structure is in good agreement with the experimental data for the α crystal of the lactide chains. Both the backfolding and the structural ordering may be viewed as the initial stage of the crystallization of the layer of grafted lactide chains. In contrast to the known behavior for conventional polymer brushes in the “dry brush” regime, the structure of the grafted lactide chains can be either amorphous or ordered, depending on the graft length N and the grafting density σ when their product Nσ is fixed.

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

This topical review discusses the theoretical progress made in the field of polymer nanocomposites, i.e., hybrid materials created by mixing (typically inorganic) nanoparticles (NPs) with organic polymers. It primarily focuses on the outstanding issues in this field and is structured around five separate topics: (i) the synthesis of functionalized nanoparticles; (ii) their phase behavior when mixed with a homopolymer matrix and their assembly into well-defined superstructures; (iii) the role of processing on the structures realized by these hybrid materials and the role of the mobilities of the different constituents; (iv) the role of external fields (electric, magnetic) in the active assembly of the NPs; and (v) the engineering properties that result and the factors that control them. While the most is known about topic (ii), we believe that significant progress needs to be made in the other four topics before the practical promise offered by these materials can be realized. This review delineates the most pressing issues on these topics and poses specific questions that we believe need to be addressed in the immediate future.

Modeling individual and pairs of adsorbed polymer-grafted nanoparticles: structure and entanglements

We analyze the canopy structure and entanglement network of isolated polymer-grafted nanoparticles (PGNs) adsorbed on a surface. As expected, increasing the monomer-surface adsorption strength causes the polymer chains to spread out to increase contact with the surface, leading to a canopy shape that is in qualitative agreement with recent experimental results. We compare height profiles and other structural features of four PGN systems to show the separate and combined effects of increasing chain length and graft density. At moderate graft density and low surface attraction strength, nearby PGN canopies interpenetrate substantially and their combined shape is similar to that of a single PGN canopy. At high graft density or surface interaction, the interparticle spacing increases significantly. We use a geometrical primitive path analysis to calculate average entanglement properties including canopy-canopy entanglements between pairs of PGNs. The longer chain systems are well entangled at both graft densities considered, and we find that as the monomer-surface interaction strength is increased (and the interparticle distance increases), entanglements between the two PGNs are reduced. We find that the number of inter-PGN entanglements per chain is slightly larger at the lower graft density, likely because steric constraints at high graft density tend to reduce interparticle entanglements.

Surface-Initiated Controlled Radical Polymerization: State-of-the-Art, Opportunities, and Challenges in Surface and Interface Engineering with Polymer Brushes

The generation of polymer brushes by surface-initiated controlled radical polymerization (SI-CRP) techniques has become a powerful approach to tailor the chemical and physical properties of interfaces and has given rise to great advances in surface and interface engineering. Polymer brushes are defined as thin polymer films in which the individual polymer chains are tethered by one chain end to a solid interface. Significant advances have been made over the past years in the field of polymer brushes. This includes novel developments in SI-CRP, as well as the emergence of novel applications such as catalysis, electronics, nanomaterial synthesis and biosensing. Additionally, polymer brushes prepared via SI-CRP have been utilized to modify the surface of novel substrates such as natural fibers, polymer nanofibers, mesoporous materials, graphene, viruses and protein nanoparticles. The last years have also seen exciting advances in the chemical and physical characterization of polymer brushes, as well as an ever increasing set of computational and simulation tools that allow understanding and predictions of these surface-grafted polymer architectures. The aim of this contribution is to provide a comprehensive review that critically assesses recent advances in the field and highlights the opportunities and challenges for future work.

Polyelectrolyte brushes: theory, modelling, synthesis and applications

Polyelectrolyte (PE) brushes are a special class of polymer brushes (PBs) containing charges. Polymer chains attain "brush"-like configuration when they are grafted or get localized at an interface (solid-fluid or liquid-fluid) with sufficiently close proximity between two-adjacent grafted polymer chains - such a proximity triggers a particular nature of interaction between the adjacent polymer molecules forcing them to stretch orthogonally to the grafting interface, instead of random-coil arrangement. In this review, we discuss the theory, synthesis, and applications of PE brushes. The theoretical discussion starts with the standard scaling concepts for polymer and PE brushes; following that, we shed light on the state of the art in continuum modelling approaches for polymer and PE brushes directed towards analysis beyond the scaling calculations. A special emphasis is laid in pinpointing the cases for which the PE electrostatic effects can be de-coupled from the PE entropic and excluded volume effects; such de-coupling is necessary to appropriately probe the complicated electrostatic effects arising from pH-dependent charging of the PE brushes and the use of these effects for driving liquid and ion transport at the interfaces covered with PE brushes. We also discuss the atomistic simulation approaches for polymer and PE brushes. Next we provide a detailed review of the existing approaches for the synthesis of polymer and PE brushes on interfaces, nanoparticles, and nanochannels, including mixed brushes and patterned brushes. Finally, we discuss some of the possible applications and future developments of polymer and PE brushes grafted on a variety of interfaces.

Brushes of semiflexible polymers in equilibrium and under flow in a super-hydrophobic regime

We performed molecular dynamics simulations to study the equilibrium and flow properties of a liquid in a nano-channel with confining surfaces coated with a layer of grafted semiflexible polymers. The coverage spans a wide range of grafting densities from essentially isolated chains to dense brushes. The end-grafted polymers were described by a bead spring model with a harmonic potential to include the bond stiffness of the chains. We varied the rigidity of the chains, from fully flexible polymers to rigid rods, in which the configurational entropy of the chains is negligible. The brush-liquid interaction was tuned to obtain a super-hydrophobic channel, in which the liquid did not penetrate the polymer brush, giving rise to a Cassie-Baxter state. Equilibrium properties such as brush height and bending energy were measured, varying the grafting density and the stiffness of the polymers. We also studied the characteristics of the brush-liquid interface and the morphology of the polymer chains supporting the liquid for different bending rigidities. Non-equilibrium simulations were performed, moving the walls of the channel in opposite directions at constant speed, obtaining a Couette velocity profile in the bulk liquid. The molecular degrees of freedom of the polymers were studied as a function of the Weissenberg number. Also, the violation of the no-slip boundary condition and the slip properties were analyzed as a function of the shear rate, grafting density and bending stiffness. At high grafting densities, a finite slip length independent of the shear rate or bending constant was found, while at low grafting densities a very interesting non-monotonic dependence on the bending constant is observed.

Semiflexible polymer brushes and the brush-mushroom crossover

Semiflexible polymers end-grafted to a repulsive planar substrate under good solvent conditions are studied by scaling arguments, computer simulations, and self-consistent field theory. Varying the chain length N, persistence length lp, and grafting density σg, the chain linear dimensions and distribution functions of all monomers and of the free chain ends are studied. Particular attention is paid to the limit of very small σg, where the grafted chains behave as "mushrooms" no longer interacting with each other. Unlike a flexible mushroom, which has a self-similar structure from the size (a) of an effective monomer up to the mushroom height (h/a ∝ N(v), ν ≈ 3/5), a semiflexible mushroom (like a free semiflexible chain) exhibits three different scaling regimes, h/a ∝ N for contour length L = Na < lp, a Gaussian regime, h/a ∝ (Llp)(1/2)/a for lp ≪ L ≪ R* ∝ (lp(2)/a), and a regime controlled by excluded volume, h/a ∝ (lp/a)(1/5)N(ν). The semiflexible brush is predicted to scale as h/a ∝ (lpaσg)(1/3)N in the excluded volume regime, and h/a ∝ (lpa(3)σ(2))(1/4)N in the Gaussian regime. Since in the volume taken by a semiflexible mushroom excluded-volume interactions are much weaker in comparison to a flexible mushroom, there occurs an additional regime where semiflexible mushrooms overlap without significant chain stretching. Moreover, since the size of a semiflexible mushroom is much larger than the size of a flexible mushroom with the same N, the crossover from mushroom to brush behavior is predicted to take place at much smaller densities than for fully flexible chains. The numerical results, however, confirm the scaling predictions only qualitatively; for chain lengths that are relevant for experiments, often intermediate effective exponents are observed due to extended crossovers.

Critical adsorption of a single macromolecule in polymer brushes

The adsorption of long flexible macromolecules by polymer brush-coated surfaces is studied by molecular dynamics simulations and by calculations using density functional and self-consistent field theories. The case of repulsive interactions between the substrate surface and the monomers of both the brush polymers and the extra chains that can get absorbed into the brush is considered. Under good solvent conditions, critical absorption can occur, if the interaction between the monomers of the brush polymers and the extra chain is (weakly) attractive. It is shown that it is possible to map out the details of the critical absorption transition, if the chain length and/or the grafting density of the brush polymers are varied. In this way both the strength and the range of the effective adsorption potential of the substrate surface can be controlled. However, it is found that in the general case there is no straightforward mapping of the present problem to the simpler problem of polymer adsorption in a square well potential, in contrast to suggestions in the literature. In particular, it is found that the fraction of monomers of the long free chain that is absorbed in the brush shows a nonmonotonic variation with the grafting density; i.e. from dense brushes free chains are again expelled from their interior. For strong attraction the free chain then gets adsorbed at the brush-solution interface.

Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression

Using a coarse-grained bead-spring model for semi-flexible macromolecules which form a polymer brush, the structure and dynamics of the polymers were investigated, varying the chain stiffness and the grafting density. The anchoring conditions for the grafted chains were chosen such that their first bonds were oriented along the normal to the substrate plane. The compression of such a semi-flexible brush by a planar piston was observed to be a two-stage process: for a small compression the chains were shown to contract by "buckling" deformation whereas for a larger compression the chains exhibited a collective (almost uniform) bending deformation. Thus, the stiff polymer brush underwent a 2nd order phase transition of collective bond reorientation. The pressure, required to keep the stiff brush at a given degree of compression, was thereby significantly smaller than for an otherwise identical brush made of entirely flexible polymer chains! While both the brush height and the chain linear dimensions in the z-direction perpendicular to the substrate increased monotonically with an increase in the chain stiffness, the lateral (xy) chain linear dimensions exhibited a maximum at an intermediate chain stiffness. Increasing the grafting density led to a strong decrease of these lateral dimensions which is compatible with an exponential decay. Also the recovery kinetics after removal of the compressing piston were studied, and were found to follow a power-law/exponential decay with time. A simple mean-field theoretical consideration, accounting for the buckling/bending behavior of semi-flexible polymer brushes under compression was suggested.

Ligand engineering of polymer nanocomposites: from the simple to the complex

One key to optimizing the performance of polymer nanocomposites for high-tech applications is surface ligand engineering of the nanofiller, which has been used to either tune the nanofiller morphology or introduce additional functionalities. Ligand engineering can be relatively simple such as a single population of short molecules on the nanoparticle surface designed for matrix compatibility. It can also have complexity that includes bimodal (or multimodal) populations of ligands that enable relatively independent control of enthalpic and entropic interactions between the nanofiller and matrix as well as introduce additional functionality and dynamic control. In this Spotlight on Applications, we provide a brief review into the use of brush ligands to tune the thermodynamic interactions between nanofiller and matrix and then focus on the potential for surface ligand engineering to create exciting nanocomposites properties for optoelectronic and dielectric applications.