Structure and Swelling of Grafted Polyelectrolytes: Predictions from a Nonlocal Density Functional Theory

The properties of polyelectrolytes anchored on surfaces depend on a broad range of parameters including the characteristics of the polyions, salt concentration, ion valence, and solvent conditions. While these systems have been subjected to extensive theoretical and experimental investigations in particular in the brush limit, a number of important questions remain to be addressed concerning the electrostatic correlations and excluded-volume effects beyond typical mean-field approximations. In this work, we applied a nonlocal density functional theory (DFT) to tethered polyelectrolytes within a primitive model and examined the effects of salt concentration, polymer grafting density, and chain length on the polyion configurations, the mean electrostatic potential, and the distributions of both counterions and co-ions. Whereas the theoretical framework is directly applicable to arbitrary solution conditions, this work is focused on systems containing only monovalent ions so that the comparison can be made with the established results. Given the polyion chain length and grafting density, we predicted a smooth transition from the osmotic brush to the salted brush in response to the increase of the salt concentration. In the osmotic regime, the brush thickness is invariant with the salt concentration but grows with the grafting density. In the salted regime, the brush thickness follows the classical scaling relation H ∝ Cs-1/3 for long polyelectrolytes but noticeably, the magnitude of the fractional exponent declines as the polyion chain length falls. Linear relations between the polyelectrolyte chain length and the brush thickness were identified for both osmotic and salted brushes. Qualitatively, all these predictions were found in good agreement with experiments or with simulations.