Theory of Brushes Formed by Ψ-Shaped Macromolecules at Solid-Liquid Interfaces

Polymer Brush in a Nanopore: Effects of Solvent Strength and Macromolecular Architecture Studied by Self-Consistent Field and Scaling Theory

To study conformational transition occuring upon inferior solvent strength in a brush formed by linear or dendritically branched macromolecules tethered to the inner surface of cylindrical or planar (slit-like) pore, a self-consistent field analytical approach is employed. Variations in the internal brush structure as a function of variable solvent strength and pore radius, and the onset of formation of a hollow channel in the pore center are analysed. The predictions of analytical theory are supported and complemented by numerical modelling by a self-consistent field Scheutjens–Fleer method. Scaling arguments are used to study microphase segregation under poor solvent conditions leading to formation of a laterally and longitudinally patterned structure in planar and cylindrical pores, respectively, and the effects of confinement on "octopus-like" clusters in the pores of different geometries.

Branched versus linear lactide chains for cellulose nanoparticle modification: an atomistic molecular dynamics study

We studied the structure of brushes consisting of branched oligolactide (OLA) chains grafted onto the surface of cellulose nanoparticles (CNPs) in polylactide (PLA) and compared the outcomes to the case of grafting linear OLA chains using atomistic molecular dynamics simulations. The systems were considered in a melt state. The branched model OLA chains comprised one branching point and three branches, while the linear OLA chains examined had a molecular weight similar to the branched chains. It was shown that free branches of the branched OLA chains tend to fold back toward the CNPs due to dipole-dipole interactions within the grafted layer, in contrast to the well-established behavior of the grafted uncharged branched chains. This result, however, is in qualitative agreement with the conformational behavior known for linear OLA chains. At the same time, no significant difference in the effectiveness of covering the filler surface with grafted branched or linear OLA chains was found. In terms of the expelling ability of the grafted chains and the interaction between PLA and CNP or OLA, the linear chains were broadly similar (sparse grafting) or better (intermediate or dense grafting) compared to the branched ones. Thus, the grafted lactide chains with a linear architecture, rather than their branched counterpart, may be preferable for the covalent modification of cellulose nanoparticles.

Brushes and lamellar mesophases of comb-shaped (co)polymers: a self-consistent field theory

Theory describing equilibrium structural properties of solvent-free brushes formed by comblike polymers tethered by end segment of backbone to planar surface is developed using strong-stretching self-consistent field (SS-SCF) analytical approach and supported by numerical self-consistent field calculations based on the Scheutjens-Fleer (SF-SCF) method. The explicit dependence of self-consistent molecular potential on architectural parameters of comblike polymers is analyzed. It is demonstrated that distribution of local tension in backbones of long comblike polymers approaches that for linear chains. The star-to-comblike transition in solvent-free lamellas which occurs upon increase of backbone length of graft-polymer is analyzed.

Simulations of 3-arm polyelectrolyte star brushes under external electric fields

Langevin dynamics (LD) simulations have been performed to study the conformations and stratification of grafted three-arm polyelectrolyte (PE) stars in response to external electric fields. The grafted chains with neutral stems and fully charged branches were immersed in a salt-free solution sandwiched between the grafting electrode and a second oppositely charged electrode. The branching points of neutral-stem PE brushes at low grafting densities exhibit a bimodal distribution normal to the grafting electrode. With increasing grafting density, the molecular conformations in the brush layer become more complex with the emergence of multi-mode distributions of the branching point monomers. Under strong electric fields, the fraction of grafted chains with either nearly completely stretched stems or collapsed branches onto the grafting electrode gradually decreases with increasing grafting density due to the stronger electrostatic screening from counterions and monomer charges at higher grafting densities. Simulation results revealed that a collapsing electric field promotes the stratification within the brush layer, leading to high degrees of charge overcompensation from charged monomers collapsed onto the oppositely charged grafting electrode. An approximate analytical self-consistent field model was developed to examine the stratification within the brush layer. Regarding the fraction of grafted chains with the free branches in the upper layer, the prediction of the analytical model qualitatively agrees with the simulation results.

Towards the description of adsorption of water in slit-like pores with walls covered by molecular brushes

The density profiles, adsorption isotherms, and phase behavior of a water model in a slit-like pore with walls modified by pre-adsorbed tethered chain molecules have been studied in the framework of a density functional theory. Each chain is bonded to the surface by its terminal segment, and the surface density of grafted chains is the same for each wall. The model for water taken from the work of Clark et al. [Mol. Phys. 104, 3561 (2006)] reproduces successfully a bulk equation of state. The mean field approach has been used to describe the effects of attractive interactions. The chemical association effects are taken into account by using the first-order thermodynamic perturbation theory of Wertheim. We have found that the presence of molecular brushes on the pore walls has important consequences for the adsorption and phase behavior of confined water. If the brush segments do not attract water molecules strongly, the vapor-liquid coexistence envelope shrinks upon increasing brush density, but the critical temperature is weakly affected. Alteration from capillary condensation to evaporation is observed with changes in the brush density, number of segments of tethered chains, and/or chemical identity of segments. The crossover temperature is affected by all these factors. Moreover, we have shown that affinity of water to segments of tethers is an important factor determining adsorption of water vapor and the entire phase diagram.

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.

Dendron and Hyperbranched Polymer Brushes in Good and Poor Solvents

We present a theory of conformational transition triggered by inferior solvent strength in brushes formed by dendritically branched macromolecules tethered to planar, concave, or convex cylindrical and spherical surfaces. In the regime of linear elasticity for brush-forming dendrons, an analytical strong stretching self-consistent field (SS-SCF) approach provides brush conformational properties as a function of solvent strength. A boxlike model is applied to describe the collapse transition in brushes formed by macromolecules with arbitrary treelike topology, including hyperbranched polymers. We demonstrate that an increase in the degree of branching, that is, an increase in the number of generations or/and functionality of branching points in tethered macromolecules, makes the swelling-to-collapse transition less sharp. A decrease in surface curvature has a similar effect. The numerical Scheutjens-Fleer self-consistent field approach is used to analyze the collapse transition in dendron brushes in the nonlinear stretching regime. It is demonstrated that inferior solvent strength suppresses stratification that is exhibited under good solvent conditions by densely grafted dendron brushes.

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.