Accounting for frame of reference and thermodynamic non-idealities when calculating salt diffusion coefficients in ion exchange membranes

Jovan Kamcev, Donald R. Paul, Gerald S. Manning, Benny D. Freeman

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Accurate evaluation of salt diffusion coefficients from transport rate data in ion exchange membranes requires accounting for frame of reference and non-ideal thermodynamic effects. Due to a lack of models and experimental data quantifying membrane ion activity coefficients, it has been impossible to evaluate the impact of non-ideal thermodynamic effects on observed salt diffusion coefficients. Here, a framework is presented that includes both frame of reference (i.e., convection) and non-ideal thermodynamic effects in calculating salt diffusion coefficients in ion exchange membranes. Effective concentration averaged NaCl diffusion coefficients were determined as a function of upstream NaCl concentration in commercial ion exchange membranes from NaCl permeability and sorption measurements via the solution-diffusion model. Frame of reference effects were evaluated using a version of Fick's law that accounts for convection. The factors necessary to account for non-ideal thermodynamic effects were developed using Manning's counter-ion condensation theory. At low upstream NaCl concentrations, frame of reference and non-ideal thermodynamic effects on diffusion coefficients were negligible. However, at higher upstream NaCl concentrations (e.g., >0.1 M), both effects contribute measurably to NaCl diffusion coefficients. Correcting for frame of reference effects increased apparent NaCl diffusion coefficients. However, correcting for thermodynamic non-idealities of the ions sorbed into the membranes reduced apparent NaCl diffusion coefficients. Fortuitously, for the materials considered in this study, frame of reference and non-ideal thermodynamic effects nearly cancel each other.

Original languageEnglish
Pages (from-to)396-406
Number of pages10
JournalJournal of Membrane Science
Publication statusPublished - 1 Sep 2017
Externally publishedYes


  • Frame of reference
  • Ion exchange membrane
  • Non-ideal
  • Salt diffusion
  • Salt sorption

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