Polyelectrolyte brushes in monovalent and multivalent salt solutions

Langevin dynamics simulations are performed to study polyelectrolyte brushes by varying the chain grafting density σg, the added salt valence Z, and concentration Cs. The brush thickness H follows a scaling relation in monovalent salt solutions as C s − 0.15 , decreasing more slowly than the scaling prediction. In divalent and trivalent salt solutions, H acquires a minimum value at the stoichiometric point, and then levels off and slightly increases, respectively. The shape and orientation of the chains change with Cs accordingly. An electric double layer is formed around the brush rim, revealed by the calculation of vertical charge distribution. Increasing σg, Z, Cs reduces the width of the layer. Side-view density study further shows how the three parameters transform the brush profile from an individual-chain distribution to a homogeneous one. Finally, about 90% of chain charges are neutralized by the ions trapped in the brushes. It is found that ion condensation on the chains can be described by Manningʹs theory in sparse grafting and dilute salt conditions.