Semidilute Brush Research Articles

Softness- and Size-Dependent Packing Symmetries of Polymer-Grafted Nanoparticles.

Achieving ordered arrays of nanoparticles (NPs) with controlled packing symmetry and interparticle spacing is of great importance to design complex metamaterials. Herein, we report softness- and size-dependent self-assembly behavior of polystyrene-grafted Au NPs (Au@PS NPs). We varied the core size of Au NPs from 1.9 to 9.6 nm and the number-average molecular weight (Mn) of thiol-terminated polystyrene from 1.8 to 7.9 kg mol-1. The optimal packing model based on an "effective softness" parameter λeff that accounts for close-packed and semidilute brush regimes could predict the effective radius of Au@PS NPs (within ±9%) for a wide range of PS Mn, grafting density, and Au core size. With increasing λeff, the self-assembled Au@PS NP superlattices undergo a symmetry transition from hexagonal close packed (hcp) to body-centered tetragonal (bct) to body-centered cubic (bcc). This work demonstrates the effective softness model as a simple but robust tool for the design of NP superlattices with precisely controlled interparticle distance and packing symmetry, both of which are critical for the development of sophisticated materials through control of nanoscale structure.

Tuning the Properties of Nanogel Surfaces by Grafting Charged Alkylamine Brushes.

Nanogels are chemically crosslinked polymeric nanoparticles endowed with high encapsulation ability, tunable size, ease of preparation, and responsiveness to external stimuli. The presence of specific functional groups on their surfaces provides an opportunity to tune their surface properties and direct their behavior. In this work, we used mesoscale modeling to describe conformational and mechanical properties of nanogel surfaces formed by crosslinked polyethylene glycol and polyethyleneimine, and grafted by charged alkylamine brushes of different lengths. Simulations show that both number of chains per area and chain length can be used to tune the properties of the coating. Properly selecting these two parameters allows switching from a hydrated, responsive coating to a dried, highly charged layer. The results also suggest that the scaling behavior of alkylamine brushes, e.g., the transition from a mushroom to semi-dilute brush, is only weakly coupled with the shielding ability of the coating and much more with its compressibility.

Spontaneous Tilting Transition in Liquid-Crystalline Polymer Brushes

The equilibrium phase behavior of main-chain liquid-crystalline polymer brushes in good solvent is investigated using self-consistent field theory. The calculation assumes semidilute brushes, where the grafting density is sufficient to cause overlap among the polymers but low enough to allow the solvent to be treated implicitly. The polymers are modeled as semiflexible wormlike chains with Maier–Saupe interactions. Previous calculations based on freely jointed chains have predicted that extended brushes collapse into folded nematic brushes, as the liquid-crystalline interaction strength is increased. For the more sophisticated model of wormlike chains, which penalizes hairpin folds, we find that extended brushes become unstable with respect to tilting prior to the onset of folding. This implies that the brushes spontaneously collapse by a symmetry-breaking transition, where the chains tilt rather than fold.

Materials by Design for Stiff and Tough Hairy Nanoparticle Assemblies.

Matrix-free polymer-grafted nanocrystals, called assembled hairy nanoparticles (aHNPs), can significantly enhance the thermomechanical performance of nanocomposites by overcoming nanoparticle dispersion challenges and achieving stronger interfacial interactions through grafted polymer chains. However, effective strategies to improve both the mechanical stiffness and toughness of aHNPs are lacking given the general conflicting nature of these two properties and the large number of molecular parameters involved in the design of aHNPs. Here, we propose a computational framework that combines multiresponse Gaussian process metamodeling and coarse-grained molecular dynamics simulations to establish design strategies for achieving optimal mechanical properties of aHNPs within a parametric space. Taking poly(methyl methacrylate) grafted to high-aspect-ratio cellulose nanocrystals as a model nanocomposite, our multiobjective design optimization framework reveals that the polymer chain length and grafting density are the main influencing factors governing the mechanical properties of aHNPs, in comparison to the nanoparticle size and the polymer-nanoparticle interfacial interactions. In particular, the Pareto frontier, that marks the upper bound of mechanical properties within the design parameter space, can be achieved when the weight percentage of nanoparticles is above around 60% and the grafted chains exceed the critical length scale governing transition into the semidilute brush regime. We show that theoretical scaling relationships derived from the Daoud-Cotton model capture the dependence of the critical length scale on graft density and nanoparticle size. Our established modeling framework provides valuable insights into the mechanical behavior of these hairy nanoparticle assemblies at the molecular level and allows us to establish guidelines for nanocomposite design.

Scaling Theory for Compressed Polymer-Brush Bilayers.

We present a novel scaling theory to describe the interaction free energy within a compressed polymer-brush bilayer. For semidilute brushes at intermediate and strong compressions, we predict that the interaction free energy scales with distance, D, between the grafting surfaces as A(D) ∼ D-2.5; i.e., the repulsive force, f(D) ∼ D-3.5, measured at the surfaces increases more strongly upon compression than predicted by the classical theory of Milner, Witten, and Cates. We find good agreement with experimental data and excellent agreement with numerical results, which follow our analytical predictions over a wide range of surface separations. The theory is based on the assumption of a strong correlation of the repulsive force and the interpenetration between the brushes. Using our numerical data, we can demonstrate this correlation with great precision.

Non-biofouling property of well-defined concentrated poly(2-hydroxyethyl methacrylate) brush

We comprehensively studied protein adsorption and human umbilical vein endothelial cell adhesion on poly(2-hydroxyethyl methacrylate) brushes by varying different graft densities and thicknesses. Concentrated brushes were prepared by surface-initiated atom transfer radical polymerization, and semi-dilute brushes were prepared by a “grafting-to” method on a silicon wafer or a quartz crystal microbalance sensor. The concentrated brushes notably prevented protein adsorption and HUVEC adhesion compared with the corresponding semi-dilute brushes. The results suggest that the physical structure, namely the concentrated brush structure plays an important role in non-biofouling property.

Compression of polyelectrolyte brushes in a salt-free theta solvent

This paper examines the normal force between two opposing polyelectrolyte brushes and the interpenetration of their chains that is responsible for sliding friction. It focuses on the special case of semi-dilute brushes in a salt-free theta solvent, for which Zhulina and Borisov (J. Chem. Phys. 107, 5952 (1997)) have derived analytical predictions using the classical strong-stretching theory (SST). Interestingly, SST predicts that the brushes contract as they are compressed together maintaining a polymer-free gap, which provides an explanation for the ultra-low frictional forces observed in experiment. We examine the degree to which the SST predictions are affected by chain fluctuations by employing self-consistent field theory (SCFT). While the normal force is relatively unaffected, fluctuations are found to have a strong impact on brush interpenetration. Even still, the contraction of the brushes does significantly prolong the onset of interpenetration, implying that a sizeable normal force can be achieved before the sliding friction becomes significant.

Flexible Particle Array Structures by Controlling Polymer Graft Architecture

Surface-initiated atom-transfer radical polymerization is used to synthesize particle brushes with controlled fraction of extended and relaxed conformations of surface-grafted chains. In the semidilute brush limit, the grafting of polymeric ligands is shown to facilitate the formation of ordered yet plastic-compliant particle array structures in which chain entanglements give rise to fracture through a polymer-like crazing process that dramatically increases the toughness and flexibility of the particle assembly.

Protein Repellency of Well-Defined, Concentrated Poly(2-hydroxyethyl methacrylate) Brushes by the Size-Exclusion Effect

The adsorption of proteins on poly(2-hydroxyethyl methacrylate) (PHEMA) brushes was systematically studied by quartz crystal microbalance (QCM) and fluorescence microscopy as a function of graft density and protein size. The graft density σ (chains/nm2) ranged from 0.007 (dilute or semidilute brush regime) to 0.7 (concentrated brush regime), and the protein size ranged from 2 to 13 nm in an effective diameter. The lowest-density brush (σ = 0.007) adsorbed all the tested four proteins, while the highest-density brush (σ = 0.7) adsorbed none of them. The middle-density brush (σ = 0.06) showed an intermediate behavior, adsorbing the smallest two proteins but effectively repelling the largest two. PHEMA cast films adsorbed a probe protein with the adsorbed amount increasing approximately proportionally to the film thickness, indicating that the adsorption mainly occurred in the bulk of the film. The noted results for the brushes support the idea of size-exclusion effect, an effect characteristic of concentrat...

Elasticity of ``Fuzzy'' Biomembranes

Sensitive micropipet methods have been used to measure the elastic stretch modulus and bending rigidity of biomembranes studded with water-soluble polymers. The fully extended lengths of the chemically grafted chains ranged from $10--50\ifmmode\times\else\texttimes\fi{}$ the length of the embedding membrane lipid. Concentrations of the polymer were varied from $1--10\ifmmode\times\else\texttimes\fi{}$ the surface density needed for isolated chains to touch, nominally satisfying the scaling theory requirement for semidilute brushes. Over this range, the membrane stretch modulus was unchanged by the polymer layers, but the bending rigidity increased by as much as ${10k}_{B}T$. Surprisingly, the increase in rigidity deviated significantly from scaling theory predictions, revealing a large marginal brush regime between dilute mushrooms and a semidilute brush.

Conformations of Block Copolymers Terminally Adsorbed at the Solid-Liquid Interface

Abstract The conformations of end-adsorbed diblock and mblock copolymers of polystyrene (PS) and polyethylene oxide (PEO) adsorbed onto mica from toluene have been studied by the surface force method. The PS-PEO diblock copolymer system forms a semi-dilute brush with the non-adsorbing PS chains adopting an extended configuration away from the surface. Neutron reflectometry indicates that the volume fraction profile of such a system has a broadly parabolic shape, in agreement with theory. In contrast to PS-PEO diblock copolymers which adsorb only in a “tail” conformation, PEO-PS-PEO triblock chains form “loops” as well as “tails” on the mica substrate. Attractive forces are observed when an adsorbed layer of PEO-PS-PEO triblock copolymer is allowed to interact with a bare mica wall, due to the formation of polymer bridges between the two opposing surfaces.