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

We present a theoretical analysis targeted to describe the structural properties of brushes formed by Psi-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 Psi-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.