Interactions between calcium ion and functional groups of organic scale inhibitors in aqueous solutions: an <i>ab initio</i> study

The anti-scaling performance of organic inhibitors is closely related to the Ca-trapping capacity of functional groups in polymer frameworks. In this study, we performed static density functional theory calculations and <i>ab initio</i> metadynamics simulations to systematically investigate the association behaviors of Ca²⁺ with carbonate species (CO₃^2- and HCO₃^-) and representative functional groups of organic inhibitors (carboxylate, phosphonate, and sulfonate) in aqueous solutions. By calculating the binding free energies and activation barriers for separating contact ion pairs, we propose a new strategy for predicting the Ca-trapping capacity of organic additives. Simulation results revealed that carboxylate and phosphonate groups possess potential calcium sequestration abilities, while the formation of the calcium-sulfonate pair is almost impossible in aqueous solutions. For the carboxylate group, which possesses a planar structure akin to that of the carbonate species, its presence has less impact on the solvation structure of Ca²⁺. The monodentate and bidentate configurations have similar stabilities for the contact ion pair. However, for the phosphonate and sulfonate groups that possess a trigonal pyramid structure, their association with Ca²⁺ disrupts the symmetry of the coordination structure to a greater extent. The monodentate state is clearly favored over the more tightly coordinated bidentate state. Moreover, since CO₃^2- exhibits the strongest affinity for Ca²⁺, a rising CO₃^2- concentration at a high pH diminishes the anti-scaling efficiency of all inhibitors. Overall, we offer new insights into the inhibiting effects of organic additives on the initial stage of CaCO₃ formation by analyzing calcium-organic compound interactions. These findings provide theoretical support for the development of more effective scale inhibitors in the industry.