Macromolecules, Vol.43, No.21, 9168-9180, 2010
On the Corrections to Strong-Stretching Theory for End-Confined, Charged Polymers in a Uniform Electric Field
We investigate the properties of a system of semidiluted polymers in the presence of charged groups and counterions 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 semidiluted, grafted polymer chains in the presence of charged 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.