Semianalytical continuum model for nondilute neutral and charged brushes including finite stretching

A semianalytical theory for neutral and charged monodisperse brushes under the strong-stretching limit of the self-consistent-field equation including corrections for finite stretching and nondilute conditions. The strong-stretching limit of the SCF equation is based on assuming at each position in the brush, that is above the grafting interface, and a mean-field approach in the lateral direction, the validity of the equation is V(h) - V(x)=μ(ø(x))-μ(ø(h)). V is the stretching or SCF potential which is a function of distance from the interface, x, with h the brush height. An approach based on the Carnahan-Starling equations-of-state from liquid-state theory for hard sphere mixtures was undertaken. It was observed that charged brushes's increasing charge and decreasing ionic strength have very different effects on the end-density distribution, the maximum of which moves toward the edge of the brush with increasing charge.