Counterion localization in solutions of starlike polyelectrolytes and colloidal polyelectrolyte brushes: a self-consistent field theory

A quantitative analysis of the distribution of counterions in salt-free solutions of colloidal polyelectrolyte brushes and starlike polyelectrolytes is performed on the level of the Poisson-Boltzmann approximation. Exact numerical solutions are obtained for starlike polyelectrolyte molecules composed of f = 20, . . ., 50 arms with a fixed fractional charge alpha per segment by applying the self-consistent field method of Scheutjens and Fleer (SF-SCF). The Wigner-Seitz cell dimension defines the concentration of polyelectrolyte stars in the system. The numerical results are compared to predictions of an analytical mean field theory and related to experimental observations on the osmotic pressure in solutions of starlike polyelectrolytes and colloidal polyelectrolyte brushes.