Molecular-level theoretical model for electrostatic interactions within polyelectrolyte brushes: Applications to charged glycosaminoglycans

In this paper, we set forth a general theoretical framework to predict the nanoelectromechanical behavior of polyelectrolyte brushes and then apply it to a model system of negatively charged chondroitin sulfate glycosaminoglycan (CS-GAG) chains. We used a Poisson-Boltzmann (PB) based approach to calculate the electrostatic component of the interaction forces between polyelectrolyte molecules in a brush and to better understand how changes in polyelectrolyte fixed charge distribution affect these forces. The applicability and accuracy of three increasingly refined models were examined via a quantitative comparison with high-resolution force spectroscopy experimental data on a model CS-GAG brush system. In the first model, the polyelectrolyte brush was represented as a uniform, flat constant surface charge density. The second model approximated the polyelectrolyte brush as a uniform volume charge density. The third model represented the time-average space occupied by individual polyelectrolyte macromolecules in the brush as cylindrical rods of uniform volume charge density and finite height. This rod model approximates additional aspects of polymer molecular geometry and nonuniform molecular charge distribution inside the brush. Although the total polyelectrolyte charge was the same in all three models, both the rod and volume charge models, which accounted for the height of the brush, predicted much higher forces than the surface charge model at any given separation distance. The comparison between measured and theoretically predicted forces showed that the rod model gave better agreement with the force data over the widest range of separation distance D and for reasonable best-fit values of the brush height and rod radius. Therefore, in the framework of the PB theory, it appears that molecular-level changes in the charge distribution inside polyelectrolyte brush layers as manifested in the rod model can significantly change the magnitude and the shape of the resulting force profile.