Comparing Solvophobic and Multivalent Induced Collapse in Polyelectrolyte Brushes

Coarse-grained molecular dynamics enhanced by free-energy sampling methods is used to examine the roles of solvophobicity and multivalent salts on polyelectrolyte brush collapse. Specifically, we demonstrate that while ostensibly similar, solvophobic collapsed brushes and multivalent-ion collapsed brushes exhibit distinct mechanistic and structural features. Notably, multivalent-induced heterogeneous brush collapse is observed under good solvent polymer backbone conditions, demonstrating that the mechanism of multivalent collapse is not contingent upon a solvophobic backbone. Umbrella sampling of the potential of mean-force (PMF) between two individual brush strands confirms this analysis, revealing starkly different PMFs under solvophobic and multivalent conditions, suggesting the role of multivalent "bridging" as the discriminating feature in trivalent collapse. Structurally, multivalent ions show a propensity for nucleating order within collapsed brushes, whereas poor-solvent collapsed brushes are more disordered; this difference is traced to the existence of a metastable PMF minimum for poor solvent conditions, and a global PMF minimum for trivalent systems, under experimentally relevant conditions.