Effect of Counterion Valence on Conformational Behavior of Spherical Polyelectrolyte Brushes Confined between Two Parallel Walls

We study the conformational behavior of spherical polyelectrolyte brushes in the presence of monovalent and trivalent counterions in a confined environment. The confinement is exerted by two parallel walls on the brushes. The enhancement of the confinement induces the extension of grafted chains. For the monovalent case, the increase of the charge fraction leads to extended brush conformation for different slit width (distance between two walls) but collapsed brush in the presence of trivalent counterions is observed. The confinement does not affect electrostatic correlation between trivalent counterions and charged monomers. However, it was found that narrow slit width contributes to stronger electrostatic correlation for the monovalent case. This is because more monovalent counterions are inside the brush at strong confinement, but almost all trivalent counterions are trapped into the brush independently of the slit width. The diffusion of counterions under the confinement is related to the electrostatic correlation. Our simulations also reveal that the brush thickness depends on the slit width nonlinearly.