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

Abstract

We present a theoretical analysis targeted to describe the structural properties of brushes formed by Ψ-shaped macromolecules tethered by terminal segment of stem to planar surface while exposing multiple free branches to the surrounding solution. We use an analytical self-consistent field approach based on the strong stretching approximation, and the assumption of Gaussian elasticity for linear chain fragments of the tethered macromolecules. The effect of weak and strong polydispersity of branches is analyzed. In the case of weakly polydisperse macromolecules, variations in length of branches lead to a more uniform polymer density distribution with slight increase in the brush thickness compared to the case of monodisperse chains with the same degree of polymerization. We demonstrate that in contrast to linear chains, strong polydispersity of Ψ-shaped macromolecules does not necessarily lead to strong perturbations in polymer density distribution. In particular, mixed brushes of the so-called "mirror" dendrons (in which number of stem monomers in one component coincides with number of monomers in a branch of the other component, and vice versa) give rise to a unified polymer density distribution with shape independent of the brush composition. The predictions of analytical theory are systematically compared to the results of numerical self-consistent field modeling based on the Scheutjens-Fleer approach.

The structure of brushes made of dendrimers: Recent advances

“…Dendritically branched polyelectrolytes have been analyzed using meanfield and SCF theory in a recent study [59], and the properties of mixed brushes, made in parts of dendrimers and in parts of linear polymers, has been analyzed, too [1]. The analytical SCF model of dendrimer brushes is meanwhile generalized to polydisperse molecules [30], and brushes made of comblike polymers have been studied in scaling theory [22] and in numerical SCF simulations [7]. It should be added that (linear) brushes at high densities have also been successfully treated with density functional theory [60,61].…”

“…A first analytical SCF model of branched polymer brushes has been presented by Pickett [28] and subsequently been generalized by Polotsky et al [29] and Zhulina et al [30][31][32]. Assuming a low stretching and thus Gaussian elasticity of the molecules, this approach arrives at a parabolic self-consistent potential of the form…”

“…in which z denotes the vertical brush coordinate, while the factor α depends on the architecture of the dendrimer. With symmetric stars this model yields [30] α(g = 1)…”

Theoretical approaches to starlike polymer brushes in Θ-solvent

“…Self-consistent-field (SCF) theories have been designed to obtain vertical monomer density profiles of the brushes [22,[24][25][26][27]. A common feature of these approaches is that every single molecule of the brush is treated equally, but it has been suspected early on that this might not reflect reality: Inside a dense brush, branched polymers have to segregate into several populations of molecules, each of which featuring different degrees of vertical elongation, in order to assume a homogeneous monomer density [24].…”

Towards the description of water adsorption in slit-like nanochannels with grafted molecular brushes. Density functional theory

“…At high grafting densities, polymer chains become stretched due to an increased mutual confinement that creates a rather concentrated polymer brush layer [10,14].From theoretical perspective, computer simulation methods, see e.g., [15][16][17][18][19][20][21][22][23] and [24] for a quite recent review, and entirely theoretical approaches have been applied to describe systems involving tethered brushes. The latter include the self-consistent field approaches [25][26][27][28][29], and density functional (DF) theories [30]. The DF approaches represent versatile tools to describe an ample variety of brush-fluid models and have been applied in the studies of lipids, co-polymers, grafted polymers, polymer/colloid, and polymer/nanoparticle systems [31][32][33][34][35].…”