Structure of weakly charged polyelectrolyte brushes: Monomer density profiles

The internal structure (the monomer density profiles) of weakly charged polyelectrolyte brushes of different morphologies has been analyzed on the basis of the self-consistent-field approach. In contrast to previous studies based on the local electroneutrality approximation valid for sufficiently strongly charged or densely grafted (osmotic) brushes we consider the opposite limit of sparse brushes which are unable to retain the counterions inside the brush. We have shown that an exact analytical solution of the SCF-equations is available in the case of a planar brush. In contrast to Gaussian monomer density profile known for osmotic polyelectrolyte brushes we have found that weakly charged brushes are characterized by constant monomer density. At the same time free ends of grafted polyions are distributed throughout the brush. Thus, the structural cross-over between polyelectrolyte mushrooms and dense brush regimes is established.