Semiflexible polymer brushes and the brush-mushroom crossover

Interactions between Sterically Stabilized Nanoparticles: The Effects of Brush Bidispersity and Chain Stiffness

Density Functional Theory is employed to study structural properties and interactions between solvent-free polymer-grafted nanoparticles. Both monodisperse and bidisperse polymer brushes with variable chain stiffness are considered. The three major control parameters are the grafting density, the grafted chain length, and its stiffness. The effect of these parameters on the brush-brush overlap and attractive interaction strength is analyzed. The Density Functional Theory results are compared with the available simulation data, and good quantitative agreement is found.

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.

Insight into the Mechanisms Driving the Self-Assembly of Functional Interfaces: Moving from Lipids to Charged Amphiphilic Oligomers

Polymer-stabilized liquid/liquid interfaces are an important and growing class of bioinspired materials that combine the structural and functional capabilities of advanced synthetic materials with naturally evolved biophysical systems. These platforms have the potential to serve as selective membranes for chemical separations and molecular sequencers and to even mimic neuromorphic computing elements. Despite the diversity in function, basic insight into the assembly of well-defined amphiphilic polymers to form functional structures remains elusive, which hinders the continued development of these technologies. In this work, we provide new mechanistic insight into the assembly of an amphiphilic polymer-stabilized oil/aqueous interface, in which the headgroups consist of positively charged methylimidazolium ionic liquids, and the tails are short, monodisperse oligodimethylsiloxanes covalently attached to the headgroups. We demonstrate using vibrational sum frequency generation spectroscopy and pendant drop tensiometery that the composition of the bulk aqueous phase, particularly the ionic strength, dictates the kinetics and structures of the amphiphiles in the organic phase as they decorate the interface. These results show that H-bonding and electrostatic interactions taking place in the aqueous phase bias the grafted oligomer conformations that are adopted in the neighboring oil phase. The kinetics of self-assembly were ionic strength dependent and found to be surprisingly slow, being composed of distinct regimes where molecules adsorb and reorient on relatively fast time scales, but where conformational sampling and frustrated packing takes place over longer time scales. These results set the stage for understanding related chemical phenomena of bioinspired materials in diverse technological and fundamental scientific fields and provide a solid physical foundation on which to design new functional interfaces.

Synthetic Semiflexible and Bioactive Brushes

Polymer brushes are extensively used for the preparation of bioactive surfaces. They form a platform to attach functional (bio)molecules and control the physicochemical properties of the surface. These brushes are nearly exclusively prepared from flexible polymers, even though much stiffer brushes from semiflexible polymers are frequently found in nature, which exert bioactive functions that are out of reach for flexible brushes. Synthetic semiflexible polymers, however, are very rare. Here, we use polyisocyanopeptides (PICs) to prepare high-density semiflexible brushes on different substrate geometries. For bioconjugation, we developed routes with two orthogonal click reactions, based on the strain-promoted azide-alkyne cycloaddition reaction and the (photoactivated) tetrazole-ene cycloaddition reaction. We found that for high brush densities, multiple bonds between the polymer and the substrate are necessary, which was achieved in a block copolymer strategy. Whether the desired biomolecules are conjugated to the PIC polymer before or after brush formation depends on the dimensions and required densities of the biomolecules and the curvature of the substrate. In either case, we provide mild, aqueous, and highly modular reaction strategies, which make PICs a versatile addition to the toolbox for generating semiflexible bioactive polymer brush surfaces.

Ionic Strength-Dependent Interactions and Dimensions of Adsorbed Zwitterionic Copolymers

We report direct measurements of ionic strength-dependent interactions between different molecular weights of zwitterionic triblock copolymers adsorbed to hydrophobic colloids and surfaces. The zwitterionic copolymers investigated include phosphorylcholine [poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC)] and sulfopropylbetaine [poly(3-( N-2-methacryloyloxyethyl- N, N-dimethyl)ammonatopropanesulfonate) (PMAPS)] end blocks separated by poly(propylene oxide) center blocks. The range of repulsion between adsorbed PMAPS copolymer layers increases with increasing NaCl from 0.01 to 3 M, and layer thicknesses range from ∼50 to 100% of the PMAPS block contour length. In contrast, repulsion between PMPC layers does not change for 0.01-3 M NaCl, and layers remain near full extension at their contour length. NaCl-dependent interactions and inferred layer dimensions correlate with hydrodynamic layer thickness and polymer second virial coefficients. These results suggest that the interaction range and layer thickness of adsorbed zwitterionic copolymers arise from a balance of intramolecular dipolar attraction and repulsion possibly mediated by water solvation. The balance between these competing effects and resulting ionic strength dependence is determined by specific zwitterionic moieties.

Polymers on nanoparticles: structure & dynamics

Grafting polymers to nanoparticle surfaces influences properties from the conformation of the polymer chains to the dispersion and assembly of nanoparticles within a polymeric material. Recently, a small body of work has begun to address the question of how grafting polymers to a nanoparticle surface impacts chain dynamics, and the resulting physical properties of a material. This Review discusses recent work that characterizes the structure and dynamics of polymers that are grafted to nanoparticles and opportunities for future research. Starting from the case of a single polymer chain attached to a nanoparticle core, this Review follows the structure of the chains as grafting density increases, and how this structure slows relaxation of polymer chains and affects macroscopic material properties.

Different bending models predict different dynamics of sedimenting elastic trumbbells

The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at low-Reynolds-number. We use the bead-spring approximation of a filament and the Rotne-Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or - alternatively - by the 'cosine' (also called the Kratky-Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic long-lasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky-Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky-Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads well-separated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own.

Polymer on Top: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting

Well-defined polymer strands covalently tethered onto solid substrates determine the properties of the resulting functional interface. Herein, the current approaches to determine quantitative grafting densities are assessed. Based on a brief introduction into the key theories describing polymer brush regimes, a user's guide is provided to estimating maximum chain coverage and-importantly-examine the most frequently employed approaches for determining grafting densities, i.e., dry thickness measurements, gravimetric assessment, and swelling experiments. An estimation of the reliability of these determination methods is provided via carefully evaluating their assumptions and assessing the stability of the underpinning equations. A practical access guide for comparatively and quantitatively evaluating the reliability of a given approach is thus provided, enabling the field to critically judge experimentally determined grafting densities and to avoid the reporting of grafting densities that fall outside the physically realistic parameter space. The assessment is concluded with a perspective on the development of advanced approaches for determination of grafting density, in particular, on single-chain methodologies.

Droplet Transport in a Nanochannel Coated by Hydrophobic Semiflexible Polymer Brushes: The Effect of Chain Stiffness

We study the influence of chain stiffness on droplet flow in a nanochannel, coated with semiflexible hydrophobic polymers by means of nonequilibrium molecular dynamics simulations. The studied system is then a moving droplet in the slit channel, coexisting with its vapor and subjected to periodic boundary conditions in the flow direction. The polymer chains, grafted by the terminal bead to the confining walls, are described by a coarse-grained model that accounts for chain connectivity, excluded volume interactions and local chain stiffness. The rheological, frictional and dynamical properties of the brush are explored over a wide range of persistence lengths. We find a rich behavior of polymer conformations and concomitant changes in the friction properties over the wide range of studied polymer stiffnesses. A rapid decrease in the droplet velocity was observed as the rigidity of the chains is increased for polymers whose persistence length is smaller than their contour length. We find a strong relation between the internal dynamics of the brush and the droplet transport properties, which could be used to tailor flow properties by surface functionalization. The monomers of the brush layer, under the droplet, present a collective "treadmill belt" like dynamics which can only be present due the existence of grafted chains. We describe its changes in spatial extension upon variations of polymer stiffness, with bidimensional velocity and density profiles. The deformation of the polymer brushes due to the presence of the droplet is analyzed in detail. Lastly, the droplet-gas interaction is studied by varying the liquid to gas ratio, observing a 16% speed increase for droplets that flow close to each other, compared to a train of droplets that present a large gap between consecutive droplets.

Molecular dynamics simulations of oligoester brushes: the origin of unusual conformations

We present results from all-atom molecular dynamics simulations for the structural properties of oligomeric lactic acid chains (OLA) grafted to the surface of cellulose nanocrystals (CNCs) and immersed in the melt of polylactic acid (PLA). Earlier, we have found that the distribution of free ends of OLA molecules is bimodal [Glova et al., Polym. Int., 2016, 65(8), 892]. The results cannot be explained within the standard picture of uncharged polymer brushes exposed to the melt of a chemically identical polymer. Although the oligomeric brushes of the OLA chains are uncharged, they have partial polarization charges producing a non-zero dipole moment of the monomeric chain unit. We study the influence of partial charges on the structure of the layer of OLA chains grafted to the CNC surface. A detailed analysis of the conformations of the grafted chains shows that interaction of partial charges in the models causes bending of the OLA molecules toward the cellulose surface, forming a hairpin structure. The observed separation of the grafted chains into two populations increases with grafting density. We demonstrate that hydrogen bonds can be formed between the free ends of the grafted chains and the CNC surface, but they do not affect the brush structure significantly. Thus, dipole-dipole interactions turn out to be the key factor governing the unusual conformations of grafts.

Surfactant-Induced Patterns in Polymer Brushes

The properties of surfaces with grafted macromolecules are determined by a fine structure of the macromolecular layer, whereas the mixtures of macromolecules with surfactants are very rich in structure types. Using the scaling mean-field theory, we consider the self-assembly in polymer brushes into various patterns induced by interactions with low-molecular surfactants. The interaction energies of the parts of a surfactant molecule with the polymer units are assumed to be greatly different. With increasing the grafting density, the formation of lamellae perpendicular to the grafting plane, a continuous layer with oblong or round pores, or a homogeneous brush is predicted. The driving force of the pattern formation is a gain in the interaction energy of surfactant molecules oriented at the lateral surfaces of lamellae or pores. The process of pore formation in a homogeneous brush caused by a temperature change at definite grafting densities is described as the first-order phase transition. It is accompanied by a stepwise extension of the brush and by orientational ordering of surfactant molecules. The transitions between the other patterns are of the second order. The thickness of lamellae and the distance between pores are approximately twice the surfactant molecule size except for the extremely high grafting densities. The diagrams of brush patterns are presented and discussed.

Optimal Reactivity and Improved Self-Healing Capability of Structurally Dynamic Polymers Grafted on Janus Nanoparticles Governed by Chain Stiffness and Spatial Organization

Structurally dynamic polymers are recognized as a key potential to revolutionize technologies ranging from design of self-healing materials to numerous biomedical applications. Despite intense research in this area, optimizing reactivity and thereby improving self-healing ability at the most fundamental level pose urgent issue for wider applications of such emerging materials. Here, the authors report the first mechanistic investigation of the fundamental principle for the dependence of reactivity and self-healing capabilities on the properties inherent to dynamic polymers by combining large-scale computer simulation, theoretical analysis, and experimental discussion. The results allow to reveal how chain stiffness and spatial organization regulate reactivity of dynamic polymers grafted on Janus nanoparticles and mechanically mediated reaction in their reverse chemistry, and, particularly, identify that semiflexible dynamic polymers possess the optimal reactivity and self-healing ability. The authors also develop an analytical model of blob theory of polymer chains to complement the simulation results and reveal essential scaling laws for optimal reactivity. The findings offer new insights into the physical mechanism in various systems involving reverse/dynamic chemistry. These studies highlight molecular engineering of polymer architecture and intrinsic property as a versatile strategy in control over the structural responses and functionalities of emerging materials with optimized self-healing capabilities.

Scaling features of the tribology of polymer brushes of increasing grafting density around the mushroom-to-brush transition

Nonequilibrium coarse-grained, dissipative particle dynamics simulations of complex fluids, made up of polymer brushes tethered to planar surfaces immersed in a solvent yield nonmonotonic behavior of the friction coefficient as a function of the polymer grating density on the substrates, Γ, while the viscosity shows a monotonically increasing dependence on Γ. This effect is shown to be independent of the degree of polymerization, N, and the size of the system. It arises from the composition and the structure of the first particle layer adjacent to each surface that results from the confinement of the fluid. Whenever such layers are made up of as close a proportion of polymer beads to solvent particles as there are in the fluid, the friction coefficient shows a minimum, while for disparate proportions the friction coefficient grows. At the mushroom-to-brush transition (MBT) the viscosity scales with an exponent that depends on the characteristic exponent of the MBT (6/5) and the solvent quality exponent (ν=0.5, for θsolvent), but it is independent of the polymerization degree (N). On the other hand, the friction coefficient at the MBT scales as μ∼N^{6/5}, while the grafting density at the MBT scales as Γ∼N^{-6/5} when friction is minimal, in agreement with previous scaling theories. We argue these aspects are the result of cooperative phenomena that have important implications for the understanding of biological brushes and the design of microfluidics devices, among other applications of current academic and industrial interest.

Semiflexible Polymers in the Bulk and Confined by Planar Walls

Semiflexible polymers in solution under good solvent conditions can undergo an isotropic-nematic transition. This transition is reminiscent of the well-known entropically-driven transition of hard rods described by Onsager's theory, but the flexibility of the macromolecules causes specific differences in behavior, such as anomalous long wavelength fluctuations in the ordered phase, which can be understood by the concept of the deflection length. A brief review of the recent progress in the understanding of these problems is given, summarizing results obtained by large-scale molecular dynamics simulations and density functional theory. These results include also the interaction of semiflexible polymers with hard walls and the wall-induced nematic order, which can give rise to capillary nematization in thin film geometry. Various earlier theoretical approaches to these problems are briefly mentioned, and an outlook on the status of experiments is given. It is argued that in many cases of interest, it is not possible to describe the scaled densities at the isotropic-nematic transition as functions of the ratio of the contour length and the persistence length alone, but the dependence on the ratio of chain diameter and persistence length also needs to be considered.

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are discussed for the well-known worm-like-chain (WLC) model. There is mounting evidence that biofilaments (except stable d-DNA) are not fully described by the WLC model. A number of augmented models, like the (super) helical WLC model, the polymorphic model of microtubules (MT) and a model with (strongly) nonlinear flexural elasticity are presented, and some aspects of their surface behavior are analyzed. In many cases, we use approaches different from those in our previous work, give additional results and try to adopt a more general point of view with the hope to shed some light on this complex field.

Self-Assembly into Strands in Amphiphilic Polymer Brushes

The self-assembly of amphiphilic macromolecules end-grafted to a plane surface is studied using mean-field theory and computer simulations. Chain backbones are built from hydrophobic groups, whereas side groups are hydrophilic. The brush is immersed in a solvent, which can be good or poor, but on average is not far from θ conditions. It is demonstrated that the strong amphiphilicity of macromolecules at a monomer unit level leads to their self-assembly into a system of strands with a 2D hexagonal order in a cross-section parallel to the grafting plane. The structure period is determined by the length of side groups. In theory, this effect is explained by the orientation of strongly amphiphilic monomer units at a strand/solvent boundary that leads to an effective negative contribution to the surface tension. Computer simulations with molecular dynamics (MD) are used for a detailed study of the local brush structure. The aggregation number of strands grows with the increase of the grafting density and side group length.

A new insight into the isotropic-nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecular dynamics

Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter in comparison with the DFT prediction. It is also found that DFT becomes unreliable for rather flexible polymers in predicting that the transition from the isotropic (I)-phase to the nematic (N)-phase still exists at very high monomer concentrations (which in reality does not occur). However, under conditions when DFT is accurate, it provides reliable predictions also for the width of the I-N two-phase coexistence region, which are difficult to obtain from MD in spite of the use of very large systems (up to 500 000 monomers) by means of graphics processing units (GPU). For short and not very stiff chains, a pre-transitional chain stretching is found in the isotropic phase near the I-N-transition, not predicted by theories. A comparison with theoretical predictions by Khokhlov-Semenov, Odijk, and Chen reveals that the scaled transition densities are not simply functions of L/lp only, as these theories predict, but depend on d/lp (where d is the chain diameter) as well. Chain properties in the nematically ordered phase are compared to those of chains confined in tubes, and the deflection length concept is tested. Eventually, some consequences for the interpretation of experiments are spelled out.

Chain stiffness regulates entropy-templated perfect mixing at single-nanoparticle level

The mixing on a single-particle level of chemically incompatible nanoparticles is an outstanding challenge for many applications. Burgeoning research activity suggests that entropic templating is a potential strategy to address this issue. Herein, using systematic computer simulations of model nanoparticle systems, we show that the entropy-templated interfacial organization of nanoparticles significantly depends on the stiffness of tethered chains. Unexpectedly, the optimal chain stiffness can be identified wherein a system exhibits the most perfect mixing for a certain compression ratio. Our simulations demonstrate that entropic templating regulated by chain stiffness precisely reflects various entropic repulsion states that arise from typical conformation regimes of semiflexible chains. The physical mechanism of the chain stiffness effect is revealed by analyzing the entropic repulsion states of tethered chains and quantitatively estimating the resulting entropy penalties, which provides direct evidence that supports the key role of entropic transition in the entropic templating strategy, as suggested in experiments. Moreover, the model nanoparticle systems are found to evolve into binary nanoparticle superlattices by remixing at extremely high stiffness. The findings facilitate the wide application of the entropic templating strategy in creating interfacially reactive nanomaterials with ordered structures on the single-nanoparticle level as well as mechanomutable responses.

Synthesis and in vitro properties of iron oxide nanoparticles grafted with brushed phosphorylcholine and polyethylene glycol

A new and facile strategy for grafting IONPs by phosphonic acic terminated PC brushes has been demonstrated and characterized in vitro.

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.