Brushes of Dendritically Branched Polyelectrolytes

We present an analytical theoretical framework to describe a polymer brush formed by dendritically branched polyions root-tethered to a planar inert surface. First, a mean-field boxlike model is used to obtain the average thickness of the dendron brush with arbitrary number of generations in branched macromolecules. Here, finite extensibility of dendrons with high degree of ionization is taken into account. Second, a more refined self-consistent field Poisson-Boltzmann formalism is developed to analyze the internal structure of the brushes formed by branched polyions with Gaussian elasticity. Brushes of first-generation ionic dendrons (arm-grafted starlike polymers) are considered in detail. Diagrams of states for such brushes are constructed in salt-free and salt-added solutions: The analytical dependences for the overall brush thickness in various regimes, the profiles of electrostatic potential, monomer units, and mobile ions are derived explicitly as a function of grafting density, branching functionality of macromolecules, and ionic strength in solution.