  Charged polymer brushes are layers of surface-tethered chains. Experimental
systems are frequently strongly charged. Here we calculate phase diagrams for
such brushes in terms of salt concentration n_s, grafting density and polymer
backbone charge density. Electrostatic stiffening and counterion condensation
effects arise which are absent from weakly charged brushes. In various phases
chains are locally or globally fully stretched and brush height H has unique
scaling forms; at higher salt concentrations we find H ~ n_s^(-1/3), in good
agreement with experiment.
