Combining Manning's theory and the ionic conductivity experimental approach to characterize selectivity of cation exchange membranes

Abstract

The transport selectivity of different cations through cation exchange membranes (CEMs) could be estimated with the partition coefficient (𝐾 ! " ) and the cation mobility ratio in the membrane (𝑢 # " 𝑢 # ! ⁄ ), which in turn can be related to corresponding membrane conductivity and dimensional swelling degree data [Journal of Membrane Science, 2020, 597, 117645]. This method has been validated in two hydrocarbon-based CEMs, and the obtained K + /Na + selectivity equals to the one obtained with conventional electrodialysis (ED) method. However, the K + /Na + selectivity of perfluorosulfonic acid (PFSA) membranes, and the bi-/monovalent cation (Mg 2+ /Na + ) selectivity of all three types of CEMs estimated with this ionic conductivity experimental approach deviate noticeably from corresponding values obtained with ED. In this work, it is proved that this deviation is mostly due to the simplification of cation activity coefficients in the membrane. Here, the cation activity coefficients in three types of CEMs are calculated according to Manning`s counter-ion condensation model. In this model, the Manning parameter (𝜉) characterizing the dimensionless linear charge density is determined by the

Manning condensation in ion exchange membranes: A review on ion partitioning and diffusion models

“…The improved agreement between the Mg 2+ /Na + transport selectivity obtained by Luo et al after accounting for non‐idealities 118 may be a coincidence, since the agreement between the predicted and measured ED selectivity worsened for two of the three membranes when considering K + /Na + transport. Their application of Manning's model is only strictly valid for monovalent ions, so this result should be more representative of its analytic capabilities.…”

“…Luo et al studied the mobility ratios of Mg 2+ /Na + and K + /Na + counter-ions in CMX, SPEEK, and F9120 membranes. 118 The authors quantified the counter-ion transport selectivity of their mixed-salt equilibrated IEMs via two methods: (1) ionic conductivity measurements in the single salt limit and (2) ED experiments with both salts present. Ion activities, instead of concentrations, were notably employed in the calculation of ionic mobilities from ionic conductivity results through the classical Nernst-Einstein equation.…”

“…The latter case is observed in Luo et al's data. 118 The strictly preferred condensation of multivalent counter-ions complicates the comparison of ideal divalent/monovalent transport selectivities. Because this same problem is not present for ideal monovalent/ monovalent selectivities, the worsened agreement between the K + /Na + data should be a better representation of this data analysis technique.…”

“…Several researchers have utilized the Manning model to correct for nonideal effects toward the counter‐ion activity when predicting the counter‐ion transport selectivity of IEMs. Luo et al studied the mobility ratios of Mg 2+ /Na + and K + /Na + counter‐ions in CMX, SPEEK, and F9120 membranes 118 . The authors quantified the counter‐ion transport selectivity of their mixed‐salt equilibrated IEMs via two methods: (1) ionic conductivity measurements in the single salt limit and (2) ED experiments with both salts present.…”

Counterion Mobility in Ion-Exchange Membranes: Spatial Effect and Valency-Dependent Electrostatic Interaction

“…At the membrane matrix-scale, the electric field from the fixed point charges perturbs the smooth slope of the external voltage-induced potential, and the overall result is a downward sloping but “rough” electric potential (φ in Figure ). Mobile point charges of counterions moving down the net negative gradient experience local electrostatic interactions of Coulombic attraction at nanometer length scales (typical distance between IEM fixed charges is 0.2–2 nm ,− ). The roughness in the electric potential causes a friction-like loss in the macroscale effective ion mobility.…”