Interaction between polyelectrolyte brushes in poor solvents

This study examines the structure of planar polyelectrolyte brushes and the disjoining pressure between such brushes in a poor solvent. The self-consistent field theory is used in this work in contrast with the earlier studies that used a step-density model. We predict that upon the reduction in solvent quality the brush collapses continuously whereas the step-density model predicts a first-order collapse. In a sufficiently poor solvent the brush shows a discontinuous density profile: (i) between the grafting surface and the discontinuity the density is dominated by the solvent translational entropy and (ii) beyond the discontinuity the density is determined by the counterion translational entropy. The force-distance profiles are also always continuous unlike the prediction of the step-density model, which predicts discontinuous collapse under constant external pressure.