Polyelectrolyte brush interaction with multivalent ions

We present a scaling theory to describe the equilibrium structure of an annealed polyelectrolyte brush interacting with multivalent salt ions. We demonstrate that at low ionic strengths of the solution the polyelectrolyte brush swells with increases in the bulk concentration of salt, Phi(s). When multivalent counterions are added to the solution, the scaling exponents describing the dependences of the brush thickness H on Phi(s) become a function of the valency q of the counterion. We also find that, when such a brush is compressed, the shape of the force versus deformation profile depends on q. In the case of multivalent colons, the characteristics of the brush depend on the net concentration of charge, q Phi(s), of the added ions. As a result, the force versus deformation profile obeys a single scaling law as a function of q Phi(s). At high concentrations of salt, the features of the salt ions affect the properties of the annealed brush through the net ionic strength of the solution.