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 cb, 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.