Adsorption Isotherm and Mechanism of Ca²⁺ Binding to Polyelectrolyte

Polyelectrolytes, such as poly(acrylic acid) (PAA), can effectively mitigate CaCO₃ scale formation. Despite their success as antiscalants, the underlying mechanism of binding of Ca²⁺ to polyelectrolyte chains remains unresolved. Through all-atom molecular dynamics simulations, we constructed an adsorption isotherm of Ca²⁺ binding to sodium polyacrylate (NaPAA) and investigated the associated binding mechanism. We find that the number of calcium ions adsorbed [Ca²⁺]_ads to the polymer saturates at moderately high concentrations of free calcium ions [Ca²⁺]_aq in the solution. This saturation value is intricately connected with the binding modes accessible to Ca²⁺ ions when they bind to the polyelectrolyte chain. We identify two dominant binding modes: the first involves binding to at most two carboxylate oxygens on a polyacrylate chain, and the second, termed the high binding mode, involves binding to four or more carboxylate oxygens. As the concentration of free calcium ions [Ca²⁺]_aq increases from low to moderate levels, the polyelectrolyte chain undergoes a conformational transition from an extended coil to a hairpin-like structure, enhancing the accessibility to the high binding mode. At moderate concentrations of [Ca²⁺]_aq, the high binding mode accounts for at least one-third of all binding events. The chain's conformational change and its consequent access to the high binding mode are found to increase the overall Ca²⁺ ion binding capacity of the polyelectrolyte chain.