  We investigate the properties of a system of semi-diluted polymers in the
presence of charged groups and counter-ions, by means of self-consistent field
theory. We study a system of polyelectrolyte chains grafted to a similarly, as
well as an oppositely charged surface, solving a set of saddle-point equations
that couple the modified diffusion equation for the polymer partition function
to the Poisson-Boltzmann equation describing the charge distribution in the
system. A numerical study of this set of equations is presented and comparison
is made with previous studies. We then consider the case of semi-diluted,
grafted polymer chains in the presence of charge-end-groups. We study the
problem with self-consistent field as well as strong-stretching theory. We
derive the corrections to the Milner-Witten-Cates (MWC) theory for weakly
charged chains and show that the monomer-density deviates from the parabolic
profile expected in the uncharged case. The corresponding corrections are shown
to be dictated by an Abel-Volterra integral equation of the second kind. The
validity of our theoretical findings is confirmed comparing the predictions
with the results obtained within numerical self-consistent field theory.
