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Two Methods for Determination of Transport Numbers in Ion-Exchange Membranes

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Abstract

Chronopotentiometry and electromotive force methods were used to determine ion transport numbers in two homogeneous and highly selective cation- and anion-exchange membranes. NaCl aqueous solutions of different concentrations, varying from 1  mol·m−3 to 100 mol·m−3 were used to analyze the possible impact of the electrolyte concentration on the results obtained by both methods. Cation transport numbers close to unity for the cation exchange membrane and to zero for the anion-exchange membrane were found for both membrane types with both methods when the NaCl-concentration exceeded 10 mol·m−3. At the lowest concentrations, a systematic deviation from ideal behavior was seen, mainly in the electromotive force method, possibly due to a higher contribution from transport of water. The cation transport number estimated by the electromotive force method was systematically lower than the number obtained from chronopotentiometry, probably due to larger concentration polarization at low electrolyte concentration. We conclude that chronopotentiometry is a relatively rapid and precise technique for ion transport number determination at electrolyte concentrations for which membranes maintain a good selectivity for the measurement conditions used.

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Acknowledgements

Financial support from Banco de Santander and Universidad Complutense de Madrid under Project PR75/18-21589 is gratefully acknowledged. K.R.K. and S.K. are grateful to Research Council of Norway for project no 262644 PoreLab.

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Authors and Affiliations

  1. Department of Structure of Matter, Thermal Physics and Electronics, Faculty of Physics, Complutense University of Madrid, 28040, Madrid, Spain

    C. Tian & V. M. Barragán

  2. PoreLab, Department of Chemistry, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    K. R. Kristiansen & S. Kjelstrup

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  1. C. Tian
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Appendix

Appendix

The electric conductivity of the solutions used in the chronopotentiometry measurements was measured according to the method previously described. From the obtained values, the exact concentration of the prepared solutions can be determined from tabulated values of the electric conductivity \(\sigma\)(S·cm−1) versus concentration c (mol·L−1) for NaCl solutions at 25 ºC [58, 59]. Known the true concentration of each electrolyte solution, the diffusion coefficient D and the transport number of ion sodium in free solution t+ were estimated from tabulated data for the different electrolyte solutions [58, 59]. The results are showed in Table 3.

Table 3 Concentration, electric conductivity, diffusion coefficient and transport number of ion sodium in free solution, for the used electrolytes at 25ºC
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Tian, C., Kristiansen, K.R., Kjelstrup, S. et al. Two Methods for Determination of Transport Numbers in Ion-Exchange Membranes. Int J Thermophys 43, 14 (2022). https://doi.org/10.1007/s10765-021-02939-1

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