Polyelectrolyte Solutions between Charged Surfaces

The effect of electrostatic interactions on the distribution of polymers in a good solvent is investigated for semi-dilute solutions containing charged polymers (polyelectrolytes) and small ions. A mean field approach is used to derive two coupled differential equations: a modified Poisson-Boltzmann equation for the electrostatic potential, and a self-consistent field equation for the polymer order parameter. We compare several monomer charge distributions; smeared, annealed and quenched. The polymers are confined between two charged surfaces, and are in contact with a reservoir of polymers and electrolyte. This makes the annealed and quenched cases equivalent. Non-monotonous profiles are obtained for the case of competing surface interactions: electrostatic adsorption vs. short-range desorption.