Abstract
The transport selectivity of different cations through cation exchange membranes (CEMs) could be estimated with the partitioning selectivity factor (Kji) and the cation mobility ratio in the membrane (uim/ujm), which in turn can be related to corresponding membrane conductivity and dimensional swelling ratio data [Journal of Membrane Science, 2020, 597, 117645]. This method has been validated in two hydrocarbon polymer-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 (Mg2+/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 partly 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 average distance between two adjacent fixed sulfonate groups (b) and the permittivity of hydrated membranes (ε). In hydrocarbon polymer-based CEMs, the average distance between fixed sulfonate groups can be estimated by assuming homogeneous distribution of the fixed groups, while in PFSA membranes three representative structure models are employed to estimate this average distance. After accounting for the cation activity coefficients in the membrane, the Mg2+/Na+ cation transport selectivity obtained with the ionic conductivity experimental approach gets closer to, but is still smaller than the selectivity obtained with the ED method. This work shows the importance of cation activity coefficients in the membrane phase in interpreting the membrane transport properties, and complements the proposed conductivity approach to characterize the counter-ion selectivity of ion exchange membranes.
Highlights
The transport characteristics of ions in ionomers and/or polyelectrolyte systems is interesting and important [1]
The ion transport selectivity values obtained by the conventional ED method and the ionic conductivity experimental approach we proposed before are illustrated in Figure 4, and numerical values are provided in the Supporting Information (Table S3)
The Mg2+/Na+ and K+/Na+ transport selectivity through three types of cation exchange membranes (CEMs) obtained from our newly proposed ionic conductivity experimental approach, after accounting for the cation activity coefficients in CEMs with Mannings counter-ion condensation theory, is compared to the results obtained via conventional electrodialysis (ED) method
Summary
The transport characteristics of ions in ionomers and/or polyelectrolyte systems is interesting and important [1]. While the former part, the partition selectivity, can be obtained from the ionic membrane conductivity when the membrane is in equilibrium with a solution of two different types of counter-ions with a known equivalence ratio Though this new method has been validated in two hydrocarbon-based cation exchange membranes (CEMs) for K+/Na+ transport, it is observed that the. Mannings counter-ion condensation theory could predict both the magnitude and variation trend of ion activity coefficients as a function of the salt concentration in external solutions [26] This approach has been applied in several hydrocarbon-based CEMs and anion exchange membranes (AEMs) for interpreting the ion partition [33], ion (especially co-ion) transport nicely [27, 28, 31, 34, 35]. With the Mannings theoretical framework as a predictive model, it is meaningful to explore the potential of this model for the applications in PFSA membranes
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