Brushes of Linear and Dendritically Branched Polyelectrolytes

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.