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