Tethered chains in good solvent conditions: An experimental study involving Langmuir diblock copolymer monolayers

Structure of Self-Initiated Photopolymerized Films: A Comparison of Models

Self-initiated photografting and photopolymerization (SI-PGP) uses UV illumination to graft polymers to surfaces without additional photoinitiators using the monomers as initiators, "inimers". A wider use of this method is obstructed by a lack of understanding of the resulting, presumably heterogeneous, polymer structure and of the parallel degradation under continuous UV illumination. We have used neutron reflectometry to investigate the structure of hydrated SI-PGP-prepared poly(HEMA-co-PEG₁₀MA) (poly(2-hydroxyethyl methacrylate-co-(ethylene glycol)₁₀ methacrylate)) films and compared parabolic, sigmoidal, and Gaussian models for the polymer volume fraction distributions. Results from fitting these models to the data suggest that either model can be used to approximate the volume fraction profile to similar accuracy. In addition, a second layer of deuterated poly(methacrylic acid) (poly(dMAA)) was grafted over the existing poly(HEMA-co-PEG₁₀MA) layer, and the resulting double-grafted films were also studied by neutron reflectometry to shed light on the UV-polymerization process and the inevitable UV-induced degradation which competes with the grafting.

Structural and Dynamical Coupling in Solvent-Free Polymer Brushes Elucidated by Molecular Dynamics Simulations

We investigate the chain configuration and segmental dynamics in interacting solvent-free polymer brushes using molecular dynamics simulations. The brush systems are designed to mimic the interstitial space between a pair of neighboring polymer-grafted nanoparticles in solvent-free nanoparticle-organic hybrid materials. Each brush consists of uniformly grafted chains formed by a given number of monomer beads. In monodisperse systems, two opposing brushes have the same chain length and grafting density. In mixed conditions, we consider binary systems with two surfaces being separately grafted with polymers of distinct chain lengths at different grafting densities as well as bidisperse systems with polymers of two different lengths being tethered to the surfaces at a fixed grafting density. We demonstrate that the brush configuration and interpenetration are both governed by the need that monomer beads have to uniformly fill the space. For systems with longer chain lengths and/or higher grafting densities, the larger interwall separation yields more stretched brush conformations and reduced extents of interbrush mixing. As a result, the polymer configurational entropy is generally decreased and the segment-to-segment relaxation dynamics is slowed down accordingly. The grafting of chains at a high density not only makes the relaxation dynamics deviate from the standard Rouse prediction but also leads to distinct relaxation times for the free and tethered segments. The more slowly relaxing tethered segments play a more important role in determining the overall end-to-end fluctuations. Moreover, the two distinct relaxation processes are consistent with the two-stage decay in the Rouse mode fluctuation autocorrelation function. In the presence of brush bidispersity, the collaboration between polymers of different lengths is evidently observed in the brush profiles. The variations of the chain configuration for the two polymers are complementary, and the associated relaxation dynamics of the two species are significantly coupled.

End-anchored polymers in good solvents from the single chain limit to high anchoring densities

An increasing number of applications utilize grafted polymer layers to alter the interfacial properties of solid substrates, motivating refinement in our theoretical understanding of such layers. To assess existing theoretical models of them, we have investigated end-anchored polymer layers over a wide range of grafting densities, σ, ranging from a single chain to high anchoring density limits, chain lengths ranging over two orders of magnitude, for very good and marginally good solvent conditions. We compare Monte Carlo and molecular dynamics simulations, numerical self-consistent field calculations, and experimental measurements of the average layer thickness, h, with renormalization group theory, the Alexander-de Gennes mushroom theory, and the classical brush theory. Our simulations clearly indicate that appreciable inter-chain interactions exist at all simulated areal anchoring densities so that there is no mushroom regime in which the layer thickness is independent of σ. Moreover, we find that there is no high coverage regime in which h follows the predicted scaling, h ∼ Nσ^1/3, for classical polymer brushes either. Given that no completely adequate analytic theory seems to exist that spans wide ranges of N and σ, we applied scaling arguments for h as a function of a suitably defined reduced anchoring density, defined in terms of the solution radius of gyration of the polymer chains and N. We find that such a scaling approach enables a smooth, unified description of h in very good solvents over the full range of anchoring density and chain lengths, although this type of data reduction does not apply to marginal solvent quality conditions.

Scaling Behavior and Segment Concentration Profile of Densely Grafted Polymer Brushes Swollen in Vapor

The scaling of the thickness, hs, of a densely grafted polymer brush of chain length N and grafting density σ swollen in vapor agrees quantitatively with the scaling reported by Kuhl et al. for densely grafted brushes swollen in liquid. Deep in the brush, next to the substrate, the shape of the segment concentration profile is the same whether the brush is swollen by liquid or by vapor. Differences in the segment concentration profile are manifested primarily in the swollen brush interface with the surrounding fluid. The interface of the polymer brush swollen in vapor is much more abrupt than that of the same brush swollen in liquid. This has implications for the compressibility of the swollen brush surface and for fluctuations at that surface.

Adsorption energies of poly(ethylene oxide)-based surfactants and nanoparticles on an air-water surface

The self-assembly of polymer-based surfactants and nanoparticles on fluid-fluid interfaces is central to many applications, including dispersion stabilization, creation of novel 2D materials, and surface patterning. Very often these processes involve compressing interfacial monolayers of particles or polymers to obtain a desired material microstructure. At high surface pressures, however, even highly interfacially active objects can desorb from the interface. Methods of directly measuring the energy which keeps the polymer or particles bound to the interface (adsorption/desorption energies) are therefore of high interest for these processes. Moreover, though a geometric description linking adsorption energy and wetting properties through the definition of a contact angle can be established for rigid nano- or microparticles, such a description breaks down for deformable or aggregating objects. Here, we demonstrate a technique to quantify desorption energies directly, by comparing surface pressure-density compression measurements using a Wilhelmy plate and a custom-microfabricated deflection tensiometer. We focus on poly(ethylene oxide)-based polymers and nanoparticles. For PEO-based homo- and copolymers, the adsorption energy of PEO chains scales linearly with molecular weight and can be tuned by changing the subphase composition. Moreover, the desorption surface pressure of PEO-stabilized nanoparticles corresponds to the saturation surface pressure for spontaneously adsorbed monolayers, yielding trapping energies of ∼10(3) k(B)T.

Observing the mushroom-to-brush transition for kinesin proteins

The height of polymers grafted to a surface is predicted to be constant at low densities ("mushroom" regime) and increase with the third root of the polymer surface density at high densities ("brush" regime). This mushroom-to-brush transition is explored with kinesin-1 proteins adhered to a surface at controlled densities. The kinesin height is measured by attaching fluorescently labeled microtubules to the kinesins and determining their elevation using fluorescence interference contrast microscopy. Our measurements are consistent with a mushroom regime and a brush regime and a transition near the theoretically predicted density. The mushroom-to-brush transition may play a role in protein behavior in crowded cellular environments and may be exploited as a signal in intracellular regulation and mechanotransduction.

Simulation and modelling of slip flow over surfaces grafted with polymer brushes and glycocalyx fibres

Fabrication of functionalized surfaces using polymer brushes is a relatively simple process and parallels the presence of glycocalyx filaments coating the luminal surface of our vasculature. In this paper, we perform atomistic-like simulations based on dissipative particle dynamics (DPD) to study both polymer brushes and glycocalyx filaments subject to shear flow, and we apply mean-field theory to extract useful scaling arguments on their response. For polymer brushes, a weak shear flow has no effect on the brush density profile or its height, while the slip length is independent of the shear rate and is of the order of the brush mesh size as a result of screening by hydrodynamic interactions. However, for strong shear flow, the polymer brush is penetrated deeper and is deformed, with a corresponding decrease of the brush height and an increase of the slip length. The transition from the weak to the strong shear regime can be described by a simple 'blob' argument, leading to the scaling γ̇₀ ∝ σ^3/2, where γ̇₀ is the critical transition shear rate and σ is the grafting density. Furthermore, in the strong shear regime, we observe a cyclic dynamic motion of individual polymers, causing a reversal in the direction of surface flow. To study the glycocalyx layer, we first assume a homogeneous flow that ignores the discrete effects of blood cells, and we simulate microchannel flows at different flow rates. Surprisingly, we find that, at low Reynolds number, the slip length decreases with the mean flow velocity, unlike the behaviour of polymer brushes, for which the slip length remains constant under similar conditions. (The slip length and brush height are measured with respect to polymer mesh size and polymer contour length, respectively.) We also performed additional DPD simulations of blood flow in a tube with walls having a glycocalyx layer and with the deformable red blood cells modelled accurately at the spectrin level. In this case, a plasma cell-free layer is formed, with thickness more than three times the glycocalyx layer. We then find our scaling arguments based on the homogeneous flow assumption to be valid for this physiologically correct case as well. Taken together, our findings point to the opposing roles of conformational entropy and bending rigidity - dominant effects for the brush and glycocalyx, respectively - which, in turn, lead to different flow characteristics, despite the apparent similarity of the two systems.

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.

Theoretical study on tethered polymers with explicit grafting points in Θ-solvent

Systematic studies on the polymers chemically grafted onto a solid substrate with various grafting densities are presented based on the self-consistent mean-field theory (SCMFT). The distribution of the grafting points is explicitly included and all the three coordinates of each grafting point are fixed during the calculations. The existence of solvent molecules is also explicitly considered in the model and the case of Θ-solvent is investigated. The structure of the system is derived by solving the SCMFT equations in three-dimensional space. For the cases of low grafting density, the system is highly inhomogeneous and typical mushroom-like structures are derived. On the other hand, when the grafting density is high enough, the system is nearly homogeneous along the substrate and the polymer concentration profile is consistent with the numerical results of one dimensional SCMFT calculations. The crossover between "mushroom" regime and polymer brush is obtained by tuning the grafting density. In addition, in brush limit, while the root-mean-squared thickness of the brush is linearly dependent on the degree of polymerization, its dependency on the grafting density is in general more complicated than a simple power law.

Manipulating protein adsorption using a patchy protein-resistant brush

Toward the development of surfaces for the precise manipulation of proteins, this study explores the fabrication and protein-interactive behavior of a new type of surface containing extremely small (on the order of 10 nm or less) flat adhesive "patches" or islands embedded in and partially concealed by a protein-repellant PEG (poly(ethylene glycol)) brush. The adsorption of fibrinogen, the model protein chosen to probe the biomaterial interactions of these surfaces, is very sensitive to the surface density of the adhesive patches, occurring only above a threshold. This suggests that two or more adhesive patches are needed to capture each protein. When the average spacing of the adhesive patches exceeds the fibrinogen length, no adsorption occurs because individual patches are too weakly binding for protein capture, as a result of being at least partially obstructed by the brush. The small size of the adhesive patches relative to the 47 nm fibrinogen length thus defines a limiting regime of surface design, distinct from surfaces where larger features can adhere single isolated proteins or multiple proteins together. The restricted protein-surface contact may comprise a means of preserving protein structure and function in the adsorbed state. This article demonstrates several additional interesting features of PEG brushes relevant to biomaterial design. First a moderate amount of adhesive material can be buried at the base of a brush without a measurable impact on the corona density. Second, a different amount of material at the base of a brush can be rendered ineffective to capturing adhesive proteins, despite a modest compromise of the brush corona. From this will follow insight into the design of patterned biomaterial surfaces, the bioactivity of the edges of patterned features, and an understanding of how flaws in brushes compromise protein resistance or allow access to small adhesive sites.

Adsorption of copolymers aggregates: from kinetics to adsorbed layer structure

We examined the adsorption, on hydrophobic and hydrophilic surfaces, of 4 rake-type poly(dimethyl siloxane) (PDMS) copolymers varying the amount of poly(ethylene glycol) (PEG) graft arms from 41 to 72%. The copolymers formed large aggregates in solution, complicating their adsorption kinetics and layer structures. We found the adsorption process always to be dominated by the adsorption of large aggregates, with strongly bound layers resistant to rinsing in adsorbing buffer. Adsorbed amounts were nearly independent of the substrate. However, subtleties in the adsorption kinetics suggested different layer structures for the different systems. On hydrophilic silica, aggregates adsorbed at the transport limited rate until surface saturation, and associated interfacial structures were likely retained. On the hydrophobic surface, a subset of the copolymers exhibited retarded late stage adsorption kinetics suggestive of brush formation. This work demonstrates how subtle differences in adsorption kinetics provide insight into potential interfacial layer structures.

Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes

This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance mu proportional to L(-1) from the substrate, where L is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance xi proportional to L(-1/3). The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.

Concentration and saturation effects of tethered polymer chains on adsorbing surfaces

We consider end-grafted chains at an adsorbing surface under good solvent conditions using Monte Carlo simulations and scaling arguments. Grafting of chains allows us to fix the surface concentration and to study a wide range of surface concentrations from the undersaturated state of the surface up to the brushlike regime. The average extension of single chains in the direction parallel and perpendicular to the surface is analyzed using scaling arguments for the two-dimensional semidilute surface state according to Bouchaud and Daoud [J. Phys. (Paris) 48, 1991 (1987)]. We find good agreement with the scaling predictions for the scaling in the direction parallel to the surface and for surface concentrations much below the saturation concentration (dense packing of adsorption blobs). Increasing the grafting density we study the saturation effects and the oversaturation of the adsorption layer. In order to account for the effect of excluded volume on the adsorption free energy we introduce a new scaling variable related with the saturation concentration of the adsorption layer (saturation scaling). We show that the decrease of the single chain order parameter (the fraction of adsorbed monomers on the surface) with increasing concentration, being constant in the ideal semidilute surface state, is properly described by saturation scaling only. Furthermore, the simulation results for the chains' extension from higher surface concentrations up to the oversaturated state support the new scaling approach. The oversaturated state can be understood using a geometrical model which assumes a brushlike layer on top of a saturated adsorption layer. We provide evidence that adsorbed polymer layers are very sensitive to saturation effects, which start to influence the semidilute surface scaling even much below the saturation threshold.

Solid phase DNA amplification: a Brownian dynamics study of crowding effects

Solid phase amplification (SPA), a new method to amplify DNA, is characterized by the use of surface-bound primers. This limits the amplification to two-dimensional surfaces and therefore allows the easy parallelization of DNA amplification in a single system. SPA leads to the formation of small but dense DNA brushes, called DNA colonies. For a molecule to successfully duplicate itself, it needs to bend so that its free end can find a matching primer, located on the surface. We used Brownian dynamics simulations (with a united-atom model) to model the basic kinetics of an SPA experiment. The simulations mimic the temperature cycles and the molecule duplication process found in SPA. Our results indicate that the steric interaction between molecules leads to a decreased duplication probability for molecules in the center of a colony and to an outward leaning for the molecules on the perimeter. These effects result in slower amplification (compared to solution PCR) and indicate that steric interaction alone can explain the loss of the exponential growth (characteristic of solution PCR) of the number of molecules in an SPA experiment. Furthermore, the growth of the colony as a function of the number of thermal cycles is found to be similar to the one obtained with a simple Monte Carlo simulation.

Nanostructure of a "carpet"-like dense layer/polyelectrolyte brush layer in a block copolymer monolayer at the air-water interface

The "carpet"/brush double layer structure in the polyelectrolyte layer in the amphiphilic diblock copolymer monolayer at the air-water interface was quantitatively studied by in situ neutron reflectometry in addition to X-ray reflectivity measurements. As a result of the higher contrast between polyelectrolyte [poly(methacrylic acid)] and solvent (D(2)O) for the neutron, the brush structure could be estimated more accurately as a function of surface pressure, that is, brush density. The thickness of the carpet layer, which is thought to be formed to reduce the interfacial free energy between water and the hydrophobic layer, was almost constant at 10-20 A at any surface pressure studied. Growth was clearly observed in the whole brush length with increasing surface pressure, and it was estimated to be almost 60% of the full-stretch length of the ionic polymer chain. Furthermore, by the comparison of density profiles by neutron and X-ray reflectometry, an anomalous hydration was suggested.

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.

Dynamic Properties of Poly(styrene)–Poly(ethylene oxide) Diblock Copolymer Films at the Air–Water Interface

The complex dynamic elasticity of monolayers of the diblock copolymer poly(styrene)-poly(ethylene oxide) at the air-water interface in the pancake, quasi-brush, and brush regimes has been studied by means of three experimental techniques--the surface transverse and longitudinal waves and the oscillating barrier method. In the pancake regime the surface viscoelastic properties in the frequency range under investigation (0.01-520 Hz) prove to be indistinguishable from the surface properties of the homopolymer PEO. Transition to the quasi-brush regime is accompanied by rather abrupt changes in both components of the surface viscoelasticity. The surface viscosity in the brush regime exceeds significantly the results calculated from the theory of D. M. A. Buzza et al. (J. Chem. Phys.109, 5008 (1998)), which takes into account the dissipation arising from the flow of solvent through the brush phase. Possible reasons of this discrepancy are discussed.

Block copolymer micelle coronas as quasi-two-dimensional dilute or semidilute polymer solutions

Chain-chain interactions in a corona of polymers tethered to a spherical core under good solvent conditions are studied using Monte Carlo simulations. The total scattering function of the corona as well as different partial contributions are sampled. By combining the different contributions in a self-consistent approach, it is demonstrated that the corona can be regarded as a quasi-two-dimensional polymer solution, with a concentration dependence analogous to that of an ordinary polymer solution. Scattering due to the corona profile and density fluctuation correlations are separated in this approach. The osmotic compressibility is extracted from the latter, and it is shown to be a universal function of surface coverage, with some deviations at high coverage due to surface curvature effects.

Polyelectrolyte brushes: counterion distribution and complexation properties

The structure of dense grafted polyelectrolyte layers has been studied with a combination of neutron reflectivity and infrared spectroscopy techniques. The polyelectrolyte brushes were made of poly(styrene sulfonate) neutralized by different counterions. Small counterions are distributed throughout the brush in order to ensure a highly local electroneutrality. In addition, they can be readily exchanged with other small ions. On the other hand, macromolecular counterions (as well as some proteins) are irreversibly trapped by the brush, but are located outside the grafted layer and cannot reach the surface.