Density Functional Theory For Polyelectrolyte Adsorption On Uniformly Charged Planar Surface

Electrostatic interactions may promote or abate polyelectrolyte adsorption onto a charged surface depending on a number of inter-related factors including the surface and polymer charge densities, the salt concentration, and non-electrostatic interactions such as van der Waals and hydrophobic forces. Even without the non-electrostatic interactions, the electrostatic behavior of polyelectrolyte systems are often counterintuitive and cannot be explained with conventional theories of polymers or simple electrolytes.In this work, a non-local density functional theory (NLDFT) and Monte Carlo simulations are used together to investigate polyelectrolyte adsorption at both oppositely-charged and like-charged surfaces (one due to the direct electrostatic attraction and the other due to counterion correlations). The simulation results provide a stringent test of the numerical performance of the NLDFT, in particular for systems containing multivalent counterions where electrostatic correlations are important. A systematic study of the effects of ion valence, salt concentration, and polyion chain length reveals that polyelectrolyte attraction to an oppositely-charged surface is nearly a neutralization effect, little influenced by the polyion chain length and counterion valence. Both the surface mean electrostatic potential and the integrated local charge density show no significant sign of charge inversion. Both theory and simulation predict polyelectrolyte adsorption onto a like-charged surface when the system contains multivalent counterions. In that case, the surface excess is sensitive to the surface charge density, the counterion valence and the salt concentration. The surface mean electrostatic potential shows a clear evidence of charge inversion when two layers of like charges are mediated by multivalent counterions.The theoretical investigations indicate that most likely, the electrostatic correlation mediated by multivalent counterions is responsible for the layer-by-layer assembly of oppositely-charged polyelectrolyte films. To furtherly investigate the effect of the electrostatic correlation on the layer-by-layer adsorption of polyelectrolytes, we continue utilizing the NLDFT for investigating the interfacial behavior of different polyelectrolytes in the system with polyions as counterions and with the same primitive model. The density profiles of oppositely charged polyelectrolytes are solved respectively, at varied surface charge densities and at different counterion valences, then the surface excesses of different polyeletrolyte species and the integrated charge distribution function are calculated. Unfortunately, little charge inversion occurs except when the polyions existing as counterions bear 2 unit charges per segment. Ultimately, the results reveal that, with the existence of polyions as counterions in the system, distinguished adsorption behaviors absolutely appear, in particular when the polyelectrolyte chains are depleted from the surface. In that case, the density profiles of the polyions firstly exhibit a trend of accumulating near the charged surface with increased surface charge density, and afterward deplete from the surface when the surface charge density is higher than a critical value. In addition, the effect of the electrostatic correlation mediated by polyions is indeed higher than that mediated by small ions, as a result, the charge inversion phenomena here is much more significant. However, by comparison with the integrated charge distribution functions in small counterion systems, it is indicated that, the degree of the enhancement of electrostatic correlation by chain connectivity of polyions locates merely between the effect of the di- and tri- counterion valences. And after addition of small ions, there display no distinctive phenomena in the system, but the screening effect of small ions on polyions adsorption. Although obvious layer-by-layer adsorption is almost absent in our investigation process, the electrostatic correlations are indispensable in the multilayer building of polyeletrolytes, which is implied in our results.