Adsorption of molecular brushes with polyelectrolyte backbones onto oppositely charged surfaces: A self-consistent field theory

The two-gradient version of the Scheutjens-Fleer self-consistent field (SF-SCF) theory is employed to model the interaction between a molecular bottle brush with a polyelectrolyte backbone and neutral hydrophilic side chains and an oppositely charged surface. Our system mimics graft-copolymers with a cationic main chain (among which poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG) or poly(L-lysine)-graft-polyoxazoline are well-known examples) interacting with negatively charged (metal oxide) solid surfaces. We aim to analyze the copolymer-surface interaction patterns as a function of the molecular architecture parameters. Two regimes are investigated: First, we compute the effective interaction potential versus the distance from the surface for individual bottle brush macromolecules. Here, depending on the grafting ratio and the degree of polymerization of the side chains, the interplay of electrostatic attractions of the main chain to the surface and the steric repulsion of the grafts results in different patterns in the interaction potential and, therefore, in qualitatively different adsorption behavior. In particular, we demonstrate that, at high side chain grafting density and short grafts, the molecular brushes are strongly adsorbed electrostatically onto negatively charged substrates, whereas, in the opposite case of low grafting ratio and high molecular weight of grafts, the steric repulsion of the side chains from the surface dominates the polymer-surface interaction. At inter-mediate grafting ratios, the adsorption/depletion scenario depends essentially on the ratio between the electrostatic screening length and the thickness of the molecular bottle brush. We further have analyzed the equilibrium adsorbed amount as a function of the macromolecular architecture. Our results are based on a detailed account of attractive and repulsive (including intermolecular in-plane) interactions, and suggest a nonmonotonic dependence of the adsorbed amount on the grafting ratio, in good agreement with the experimental studies for PLL-g-PEG adsorption onto Nb2O5 surfaces. The results of the theoretical modeling are discussed in the context of the optimization of the PLL-g-PEG molecular design parameters in order to create protein-resistant surfaces.