The theory of a polyelectrolyte brush immersed in a solution of mobile polyelectrolyte

The self-consistent-field analytical theory of polymer brushes is utilized to consider the equilibrium behaviour of a polyelectrolyte brush immersed in a solution of mobile polyelectrolyte. It is shown that under the conditions of the solution-dominance regime, when the mobile chains penetrate into the brush, the characteristics of the system are determined by the effective second virial coefficient upsilon _eff, dependent on the degrees of charging of grafted and mobile chains, the length of mobile chains and their concentration in the bulk of the solution. In concentrated solutions and melts of mobile polyelectrolytes the brush thickness exhibits non-monotonic behaviour upon increasing the difference between the degrees of charging of grafted and mobile chains. At equal degrees of charging the system exhibits quasineutral behaviour.