Theoretical study of cooperativity in multivalent polymers for colloidal stabilization

Multivalent polymers, i.e., copolymers with multiple binding sites, have been proposed recently for stabilization of fusogentic liposomes and other liposomal colloids useful for drug delivery. The performance of such polymers critically depends on their molecular architecture, in particular the strength and frequency of surface anchoring sites along the backbone of a highly soluble polymer. In this work, we investigate the adsorption and surface forces due to multivalent polymers based on coarse-grained polymer models. We find that for W-type polymers that form dangling tails when all anchoring segments are attached to a surface, increasing the chain length at fixed polymer composition leads to a stronger repulsive barrier in the polymer-mediated surface forces thereby increasing the ability of the polymer to stabilize colloidal particles. This prediction conforms to an earlier experiment indicating that increasing the number of hydrophobic anchors along poly(ethylene glycol) polymers results in the cooperative behavior for both surface adsorption and steric stabilization. For M-type multivalent polymers that have weakly anchoring sites placed at the ends, however, addition of binding sites at fixed polymer composition could lead to negative cooperativity, i.e., the more binding sites, the less the amount of adsorption or the weaker the ability of surface protection. The theory also predicts that polymers with two anchoring sites (e.g., telechelic copolymers) are most efficient for colloidal stabilization.