Thermodynamics of Ion Partitioning in Polyamide Membranes: Donnan and Non-Donnan Contributions

Ion partitioning is a key step influencing ion selectivity in nanoporous membranes, yet its thermodynamic origin remains insufficiently understood because Donnan and non-Donnan effects are often coupled. Here, we develop a thermodynamic framework to operationally decompose and quantify non-Donnan and Donnan contributions to ion partitioning for both co-ions and counterions. Using quartz crystal microbalance measurements combined with temperature-dependent analysis, we estimate non-Donnan partition coefficients and associated enthalpic and entropic changes. Non-Donnan partitioning is closely associated with ion dehydration and ion–membrane interactions and exhibits enthalpy–entropy compensation with additional ion–membrane interactions for divalent ions. We further evaluate the thermodynamic contribution of Donnan partitioning and show that electrostatic interactions affect co-ions and counterions differently. We infer that those electrostatic interactions may be associated with cation dehydration or hydration-shell reorganization. This work provides a thermodynamic basis for understanding ion-specific selectivity in polyamide membranes.