A numerical study of spherical polyelectrolyte brushes by the self-consistent field theory

Abstract

The self-consistent field theory (SCFT) is employed to numerically study the scaling laws of brush height and the amount of counter-ions trapped inside a spherical polyelectrolyte (PE) brush immersed in a good solvent with no added salt ions. In particular, the curvature effect of the grafting substrate on the brush height and the amount of counter-ions trapped inside the PE brush is carefully examined. It is found that the brush height shows a non-trivial dependence on the radius of the grafting substrate. The numerical result reveals that the brush height scales linearly with respect to the grafting density and the average degree of ionization of PE chains in the planar surface limit, but not in the opposite limit. The numerical results show that, in a salt-free solution, about 96% of the counter-ions are trapped within the range of extension of grafted PE chains in the planar surface limit, irrespective of other system parameters. On the contrary, for the grafting substrate with high curvature, i.e., the radius of the grafting substrate is much smaller than the brush height, the amount of counter-ions trapped inside the PE brush approaches zero in the large system size limit. The underlining mechanisms governing the curvature effect of the grafting substrate on the brush height and the amount of counter-ions trapped inside PE brushes are elucidated.