Divalent cation-mediated polyanion attraction in an aqueous solution

Polyelectrolytes are known to passivate/delay limescale (CaCO₃) crystallization from aqueous suspension. Negatively charged functional groups along the polymer backbone chelate cations and form both intrachain and interchain ion bridges. At sufficiently high ionic strengths, these ion bridges lead to attractive interactions between the polyanions and precipitate polymer-ion complexes out of suspension. Polyelectrolyte effectiveness in preventing scale formation depends on its ability to chelate more Ca²⁺ ions before precipitation. The critical Ca²⁺ concentration is known as the Ca-tolerance of the polyelectrolyte. Our objective is to design polyelectrolytes with higher Ca-tolerance. We use the thermodynamic stability criterion and relate the Ca-tolerance of a polyelectrolyte to the potential of mean force (PMF) between two polyelectrolyte chains in an aqueous Ca²⁺ salt solution. We employ well-tempered metadynamics and Hamiltonian replica exchange protocols to calculate the two-chain PMF from molecular simulations. We systematically characterize the effect of solution ionic strength, temperature, functional groups, and molecular weight of the polyelectrolyte on the two-chain PMF. We will clarify the mechanism through which multi-valent ions result in the precipitation of the polyelectrolyte and present design principles for polyelectrolytes with higher Ca-tolerance values.