Skip to main content
Open Access Publications from the University of California

UC Berkeley

UC Berkeley Previously Published Works bannerUC Berkeley

Theory of Multicomponent Phenomena in Cation-Exchange Membranes: Part I. Thermodynamic Model and Validation


We present and validate a mathematical model for multicomponent thermodynamic activity in phase-separated cation-exchange membranes (e.g., perfluorinated sulfonic-acid ionomers). The model consists of an expression for the free energy of the membrane and of the surrounding electrolyte solution. A modified Stokes-Robinson ionic solvation framework treats the solution-like non-idealities resulting from hydration, electrostatics, ion association, and physical interactions in bulk solution and in ionomer hydrophilic domains. Inside the membrane, a mechanics-based composite approach accounts for the swelling of the hydrophobic matrix. Treating the membrane microstructure as a disordered system of domains calculates steric exclusion of ions. Electroneutrality guarantees that the charge of mobile ions in the membrane is equal to the charge on polymer groups. Osmotic coefficients for electrolytes from literature parameterize solution-like interactions while mechanical and X-ray scattering characterization gives most membrane-specific parameters. Model predictions compare favorably to measured membrane thermodynamics (i.e., water and ion uptake) in dilute and concentrated binary and ternary salt electrolytes and in water vapor. Interactions between ions in the membrane are similar to those present in bulk electrolytes. Our results reveal that water and ion uptake is dictated by a balance between solution-like energetics and membrane swelling.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View