Grafted polymers with annealed excluded volume: A model for surfactant association in brushes

Reduction of protein adsorption on well-characterized polymer brush layers with varying chemical structures

Using Monte Carlo simulations, we investigate the protein adsorption behaviors on polymer brushes in the presence of hydrogen bonding between proteins and polymer brushes. It is interesting to observe in simulation that as a function of grafting density, the amount of protein adsorbed passes through a minimum, that is, a critical grafting density with the minimum amount of adsorbed protein exists. The existence of a critical grafting density uncovers two different driving forces of protein adsorption. The driving force of protein adsorption is mainly the hydrogen bonding between proteins and polymer brushes when the grafting density is above the critical value, whereas the driving force is the attraction between proteins and the hydrophobic substrate when the grafting density is below the critical value. It is extraordinary that at the critical grafting density, increasing the hydrophilicity of the polymer brushes will lead to an increase in protein adsorption, even when the formation of hydrogen bonding between the proteins and polymer brushes is suppressed by the increasing hydrophilicity of the polymer brushes. This mainly results from the conformational transition of the polymer chains from collapsed to stretched when the hydrophilicity is increased. It is noteworthy that the relationship between protein adsorption and grafting density reported in this study is quite consistent with our previous experimental work. Beyond that, the simulation results also provide detailed information about protein adsorption location and grafting chain conformation, which helps us to better understand the protein adsorption behaviors on polymer brushes induced by hydrogen bonding.

We revise the classical Daoud-Cotton (DC) model to describe conformations of polymer and polyelectrolyte chains end-grafted to convex spherical and cylindrical surfaces. In the framework of the DC model, local stretching of chains in the brush does not depend on the degree of polymerization of grafted chains, and the polymer density profile follows a single-exponent power law. This model, however, does not correspond to a minimum in free energy of the curved brush. The nonlocal (NL) approximation exploited in the present paper implies the minimization of the overall free energy of the brush and predicts that the polymer density profile does not follow a single-exponent power law. In the limit of large surface curvature the NL approximation provides the same scaling laws for brush thickness and free energy as the local DC model. Numerical prefactors are however different. Extra extension of chains in the brush interior region leads to larger equilibrium brush thickness and lower free energy per chain. A significant difference between outcomes of the two models is found for brushes formed by ionic polymers, particularly for weakly dissociating (p H-sensitive) polyelectrolytes at low solution salinity.

Nanoparticles can be used to tune the properties of polyelectrolyte brushes, and polyelectrolyte brushes can be used to control the interaction between nanoparticles and substrates. In the present paper, we investigate the polyelectrolyte brushes immersed in a nanoparticle solution within the analytical strong-stretching theoretical framework. The theoretical model does not take the excluded volume interaction between any two components into account. When there is no nanoparticle loaded, the polyelectrolyte brush is assumed to be an osmotic brush. Local electroneutral approximation is assumed to be still valid after the nanoparticles have been loaded. The loaded nanoparticles are not big enough to deform the grafted polyelectrolyte chains laterally. Analytical formulae for density profiles of each component and brush thickness are derived. The loaded nanoparticles always compress the polyelectrolyte brush. By analyzing the limiting case, a scaling-type diagram for behaviors of the nanoparticle-loading polyelectrolyte brush is constructed. Two characteristic nanoparticle controlling regimes are shown. When the charge of the nanoparticle, <i>Z</i>, is not very large, charged nanoparticles penetrate into the brush and the brush thickness is scaled by <inline-formula><tex-math id="M5">\begin{document}$H \sim (Z\varPhi)^{-1/3}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M5.png"/></alternatives></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$\varPhi$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M6.png"/></alternatives></inline-formula> is the nanoparticle volume fraction. When the nanoparticle charge <i>Z</i> is large enough, nanoparticles are mainly distributed outside the brush and the brush thickness is scaled by <inline-formula><tex-math id="M7">\begin{document}$H \sim (Z\varPhi)^{-1}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="14-20200432_M7.png"/></alternatives></inline-formula>. In the former case, the Coulombic repulsion between the grafted polyelectrolyte chains is screened by the counterions and the nanoparticles, and the brush behavior is determined by the balance between the chain elasticity and the osmotic pressure of the counterions and the nanoparticles. In the latter case, the electrostatic screening is executed by the counterions, and the chain elasticity is balanced by the osmotic pressure of the counterions. The two regimes are divided into subregimes which are dominated respectively by electrostatic or non-electrostatic interaction. The effects of size polydispersity of the nanoparticles are also investigated. It is found that the behaviors of the grafted polyelectrolyte chains are mainly determined by the ratio between the first two moments of the nanoparticle size distribution function. The polyelectrolyte brush is compressed more by the polydispere nanoparticles than by the monodisperse ones. Possible improvement in the present theory is discussed in the conclusion section.

This work aims to experimentally clarify how the single chain conformation evolves as a function of grafting density for model comb-like chains in dilute solution in the whole density regime. Via a combination of rational design, precise synthesis and accurate characterization, we obtained four sets of PPANb-g-PS30-σ comb-like samples with well-defined architectures and accurately extracted their molecular parameters by triple detection size exclusion chromatography (TD-SEC). With these samples in hand, we quantified how the excluded volume interaction and chain conformation evolve with the grafting density (σ) in the whole density regime. Three main findings are reported: (i) the graft-graft excluded volume interaction is not ignorable even in the low σ-regime; (ii) contrary to theoretical predictions, both the excluded volume interaction and the chain conformation are found to be Nb-dependent; (iii) both Rg ∼ σ1/3 and [η] ∼ σ0 are experimentally confirmed for comb-like chains from different σ and Nb, signifying a unique 3D mass-size growth pattern and a quasi-3D fractal feature. The obtained results help clarify some long-existed controversial issues in the field.

Three-dimensional Monte Carlo simulations of flexible and semiflexible polymer brushes at various grafting densities are carried out to study their equilibrium structure and attendant properties by using the bond fluctuation model. Our simulation results of long flexible polymer brushes are, in general, consistent with predictions of the self-consistent field theory. However, a depletion layer near the substrate is only observed at small grafting densities but not at medium densities. We have also measured the brush height and end-to-end distance of various polymer brushes, and their dependence on grafting density, chain length, and chain stiffness are obtained. The distribution of bending angles at various temperatures are calculated for four different forms of bending energy and our simulation results agree with theoretical predictions very well. Moreover, we study the isotropic-to-nematic transition of polymer brushes, which is found to be a continuous phase transition from our simulation results. Finally, we discuss the effects of local grafting density fluctuation on the monomer and end density distributions.

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.

Taking into account the well known correspondence between the field theoretical ϕ(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.

We fabricated ultrathin poly[styrene-b-butadiene-b-styrene] copolymer (SBS) films deposited on polystyrene brushes. The thickness of the films was kept constant, while the grafting density and molar mass of the grafted polymer layers were varied to reveal the influence of the brush interface on the structure of the films. We examined the surface morphology of the films formed and found a strong effect of the underlying brushes on the formation of the SBS films. The development of a zeroth layer (layer without internal microphase separated structure) of SBS on the top of the grafted layer was observed. Both polystyrene and polybutadiene blocks were present inside the zeroth layer. The first block copolymer layer formed on top of the zeroth layer possessed the surface microstructure typical for the block copolymer in the bulk state. The polymer brushes were actively involved in the formation of the zeroth layer, and the structure of the block copolymer films was influenced by the grafting density and degree of polymerization of the underlying grafted polymer layer. We observed significantly distinct morphologies for the copolymer films of the same thickness deposited on the different polymer brushes. Morphology of isolated islands, holes of different size, and intermediates between islands and holes as well as uniform zeroth layer developed during annealing. Our studies demonstrate that the morphology of ultrathin block copolymer film can be manipulated by the grafting density and molecular mass of the underlying brush.

Using molecular dynamics simulations in combination with scaling analysis, we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformations of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in one of four conformations: (1) a star-like conformation, (2) a "star of bundles" conformation in which the polyelectrolyte chains self-assemble into pinned cylindrical micelles, (3) a micelle-like conformation with a dense core and charged corona, or (4) a conformation in which there is a thin polymeric layer uniformly covering the particle surface. These different brush conformations appear as a result of the fine interplay between electrostatic and monomer-monomer interactions. The brush thickness depends nonmonotonically on the value of the Bjerrum length. This dependence of the brush thickness is due to counterion condensation inside the brush volume. We have also established that bundle formation in poor solvent conditions for the polymer backbone can also occur in a planar polyelectrolyte brush. In this case, the grafted polyelectrolyte chains form hemispherical aggregates at low polymer grafting densities, cylindrical aggregates at an intermediate range of the grafting densities, and vertically oriented ribbon-like aggregates at high grafting densities.

We present an analytical self‐consistent field model of planar brushes formed by linear or regularly branched charged macromolecules (dendrons with long flexible polyelectrolyte spacers). The macromolecules are tethered by a terminal root monomer to an impermeable surface at grafting densities at which intermolecular interactions dominate over intramolecular ones and lead to the elastic stretching of dendrons normally to the surface. Under the conditions of linear (Gaussian) elasticity for tethered chains, the architecture of polyion can be explicitly accounted for through the so‐called topological coefficient k. The topological coefficient k does not depend on the system parameters such as a fraction of ionized monomers, chain‐grafting density, salt concentration in solution, and thermodynamic quality of the solvent and provides a unified description of dendron brushes with various architectures. We focus here on symmetric polyelectrolyte dendrons with a number of generations, g = 1, 2, and 3, short comb‐like polymers, and also include for comparison linear polyions with g = 0. The analytical theory is complemented with the numerical Scheutjens‐Fleer self‐consistent field (SF‐SCF) calculations of electrostatic potential, polymer density profile, and end‐point distribution in brushes with selected architectures of dendrons. It is shown that both models are in good agreement under the conditions of linear (Gaussian) elasticity for the tethered polyions. An onset of nonlinear elasticity leads to noticeable deviations between the analytical and numerical results.

The structural features of polystyrene brushes grafted on spherical silica\nnanoparticles immersed in polystyrene are investigated by means of a Monte\nCarlo methodology based on polymer mean field theory. The nanoparticle radii\n(either 8 nm or 13 nm) are held constant, while the grafting density and the\nlengths of grafted and matrix chains are varied systematically in a series of\nsimulations. The primary objective of this work is to simulate realistic\nnanocomposite systems of specific chemistry at experimentally accessible length\nscales and study the structure and scaling of the grafted brush. The profiles\nof polymer density around the particles are examined; based on them, the brush\nthickness of grafted chains is estimated and its scaling behavior is compared\nagainst theoretical models and experimental findings. Then, neutron scattering\nspectra are predicted both from single grafted chains and from the entire\ngrafted corona. It is found that increasing both the grafting density and the\ngrafted chain molar mass drastically alters the brush dimensions, affecting the\nwetting behavior of the polymeric brush. On the contrary, especially for\nparticles dispersed in high molecular weight matrix, variation of the matrix\nchain length causes an almost imperceptible change of the density around the\nparticle surface.\n

Surface grafting of polymer brushes drastically modifies surface properties, including wettability, compatibility, responsiveness, etc. A broad variety of functionalities can be introduced to the surface via different types of polymers. Bringing together properties of two or more types of polymer brushes to one surface opens up even more possibilities in brush-modified materials. However, while it is generally feasible to introduce several chemical compositions along the brushes via copolymerization, it is challenging to vary the types of polymer brushes along a surface. Although previous studies have demonstrated binary brushes via orthogonal polymerization techniques or partial deactivation/regrafting, they commonly limit the number of polymer types to two. Here, we propose a strategy to introduce dynamic covalent diketoenamine linkages at the root of polymer brushes. The grafting density could be precisely tuned during surface functionalization. The surface-anchored polymer brushes were cleaved by the addition of small molecule amines. New polymer brushes can be regrafted from the surface following refunctionalization of exposed sites. The maneuverability allows tuning of the types and densities of the polymer brushes, pointing the way to the preparation of a new generation of well-defined brush-modified materials with mixed grafts, with potential applications in the design of smart materials and surfaces.

Silica particles with immobilized protein molecules and polymer brushes

While polymer brushes in contact with liquids have been researched intensively, the characteristics of brushes in equilibrium with vapors have been largely unexplored, despite their relevance for many applications, including sensors and smart adhesives. Here, we use molecular dynamics simulations to show that solvent and polymer density distributions for brushes exposed to vapors are qualitatively different from those of brushes exposed to liquids. Polymer density profiles for vapor-solvated brushes decay more sharply than for liquid-solvated brushes. Moreover, adsorption layers of enhanced solvent density are formed at the brush–vapor interface. Interestingly and despite all of these effects, we find that solvent sorption in the brush is described rather well with a simple mean-field Flory–Huggins model that incorporates an entropic penalty for stretching of the brush polymers, provided that parameters such as the polymer–solvent interaction parameter, grafting density, and relative vapor pressure are varied individually.