Adsorption of polyelectrolytes and inter-colloidal forces

The effect of charged polymers on the interactions between charged surfaces in solution is investigated theoretically. We use mean-field theory to derive a self-consistent field equation for the polymer order parameter, and a modified Poisson-Boltzmann equation for the electrostatic potential. The two differential equations together with the appropriate boundary conditions are solved numerically. We use simple scaling arguments to investigate the adsorption characteristics to a single surface in the strong electrostatic regime. We obtain simple expressions for the dependence of the adsorbed amount Γ on the charge fraction p and the salt concentration c_b, in good agreement with experiments. The forces between two charged surfaces in the presence of polyelectrolytes are calculated using a generalized contact theorem. We obtain repulsion as well as attraction between equally charged surfaces.