Conformations of polyelectrolyte molecular brushes: A mean-field theory

We present a mean-field theory for the solution properties of polyelectrolyte molecular brushes, comprising multiple ionically charged side chains tethered to the main chain (backbone). The power-law dependences for local and large-scale conformational properties, i.e., the brush thickness, extension of spacers between the grafts, and end-to-end distance for the main chain macromolecule, are derived as a function of architectural parameters (the lengths of the main chain and of the grafts, grafting density). We demonstrate that at high grafting density or/and a large fraction of charged monomer units in the grafts, the localization of counterions in the intra-molecular volume occurs and we specify the onset of this transition. We prove that such localization of the counterions is accompanied by full extension of the main chain of the polyelectrolyte molecular brush in salt-free solution. This stretching of the main chain is relaxed upon an increase in the salt concentration. The dependence of the macromolecular dimensions of the polyelectrolyte molecular brush on the salt concentration is derived, and multiple power-law exponents valid in different salt concentration ranges are predicted.