Abstract
Ionic diffusion coefficients in the membrane are needed for the modelling of ion transport in ion-exchange membranes (IEMs) with the Nernst-Planck equation. We have determined the ionic diffusion coefficients of Na +, OH −, H +, Cl −, SO 4 2−, NaSO 4 −, and HSO 4 − from the diffusion experiments of dilute NaCl, NaOH, HCl, Na 2SO 4, and H 2SO 4 solutions through IEMs and the membrane conductivity measured in these solutions, using electrochemical impedance spectroscopy. The order of diffusion fluxes across the anion-exchange membrane is found to be as H 2SO 4>HCl>NaCl>Na 2SO 4>NaOH, whereas for the cation-exchange membrane it was NaOH>NaCl>Na 2SO 4≥H 2SO 4. Special attention is given to sulfates because of the partial dissociation of bisulfate and NaSO 4 −, which makes the use of the Nernst-Hartley equation, that is, splitting the electrolyte diffusion coefficient into its ionic contributions, impossible. The expression of the diffusion coefficient of sulfates taking into account the dissociation equilibrium has been derived and the corresponding Fick equation has been integrated. In addition, for sulfates, finite element simulations with COMSOL Multiphysics, applying a homogeneous membrane model, were done to give estimates of their ionic diffusion coefficients. This work offers a convenient approach to finding diffusion coefficients of various ions inside IEMs.
Original language | English |
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Article number | e202200403 |
Journal | ChemElectroChem |
Volume | 9 |
Issue number | 11 |
DOIs | |
Publication status | Published - 14 Jun 2022 |
MoE publication type | A1 Journal article-refereed |
Funding
This work has received funding from the European Union, EIT Raw Materials project Credit-18243. SUEZ Water Technologies and Solutions is acknowledged for the supply of the membranes. J.A.M acknowledges the funding from project PID2021-126109-NB−I00, Ministry of Science and Innovation (Spain), and FEDER.
Keywords
- COMSOL Multiphysics
- diffusion coefficients
- ion-exchange membranes
- ionic diffusion
- ionic transport