Salt dependence of compression normal forces of quenched polyelectrolyte brushes

Abstract

We obtained mean-field expressions for the compression normal forces between two identical opposing quenched polyelectrolyte brushes in the presence of monovalent salt. The brush elasticity is modeled using the entropy of ideal Gaussian chains, while the entropy of the microions and the electrostatic contribution to the grand potential is obtained by solving the nonlinear Poisson–Boltzmann equation for the system in contact with a salt reservoir. The interplay between these distinct contributions upon variations of the ionic strength determines the brush thickness. For the polyelectrolyte brush we considered both an isotropic charged slab as well as a longitudinally heterogeneous charge profile obtained using a self-consistent field theory. Using the Derjaguin approximation, we related the planar-geometry results to the realistic two-crossed cylinders experimental setup. Theoretical predictions are compared to experimental measurements of the salt dependence of the compression normal forces between two quenched polyelectrolyte brushes formed by the adsorption of diblock copolymers poly(tert-butyl styrene)-sodium poly(styrene sulfonate) onto an octadecyltriethoxysilane hydrophobically modified mica surface.