Molecular-level understanding of ion–membrane interactions in polyamide nanofiltration systems

Polyamide thin-film composite (PA-TFC) membranes, particularly those based on poly (piperazine amide), are widely employed in nanofiltration due to their high separation efficiency and intrinsic negative charge. However, the molecular-scale origins of ion selectivity in these charged polymeric membranes remain insufficiently understood. In this work, Density Functional Theory (DFT) calculations were performed to investigate the interactions between a representative polyamide membrane fragment and common inorganic ions (Mg2⁺, Ca2⁺, Na⁺, and K⁺), considering both chloride and sulfate counterions. All calculations were carried out at the M06-2X/6–311 + G** level of theory to evaluate adsorption energies and elucidate the role of ionic charge density in ion–membrane interactions. The results demonstrate a strong correlation between cation–membrane interaction energies and cationic charge potential, highlighting electrostatic interactions as the dominant driving force for cation adsorption. In contrast, anion interactions (Cl⁻ and SO₄2⁻) are primarily governed by hydrogen bonding with functional groups within the polyamide matrix. Moreover, in systems containing both cations and anions, a cooperative interaction energy parameter (E_coop) was introduced to quantify ion-pair effects. Negative E_coop​ values indicate a synergistic enhancement of ion–membrane interactions arising from coupled cation–anion binding. Overall, this quantum chemical study provides molecular-level insights into ion–polymer interactions and establishes a theoretical framework linking membrane chemistry to ion selectivity, offering guidance for the rational design of advanced nanofiltration membranes.