Adsorption of Polyelectrolyte Solutions on Surfaces: A Debye-Hückel Theory

The adsorption onto a solid surface of a flexible polyelectrolyte solution in equilibrium with a reservoir is investigated. Both the electrostatic and the short-ranged interactions with the interface are taken into account. The polyelectrolyte chains are supposed to be infinitely long and to obey Gaussian statistics. We obtain analytical results for the concentration profiles within the framework of a mean-field theory and in the limit of weak adsorption (linear approximation). At high salt concentration, the polyelectrolyte chains behave as neutral polymers and electrostatic interactions are screened over the Debye-Hückel length. At low salt concentration, the profiles show damped oscillations. Similarly, the energy and the force between two interfaces mediated by the polyelectrolyte solution can show oscillations as a function of the separation between the interfaces. At the onset of the instability of the bulk polyelectrolyte solution, the structure factor diverges at the wavevector of the oscillations. We also consider the polymer surface excess and find a condition for which it shows a maximum at a given value of the fraction of charged monomers.