Modeling ionomer swelling dynamics of a sulfonated polyphenylene, pentablock copolymers, and nafion

Donghui Wang, Chris J. Cornelius

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The water swelling behavior of Nafion, sulfonated poly(phenylene) (sPP), and poly[t-butyl styrene-b-hydrogenated isoprene-b-sulfonated styrene-b-hydrogenated isoprene-b-t-butyl styrene) was studied in order to understand microscopic molecular interactions. Ionomer swelling was modeled using the Flory-Rehner relationship to predict solvent-ionomer interaction parameter (χ12) and effective number of elastically active chains (n). Water swollen PBC had a decreasing χ12 from 1.146 to 0.516 when its ion-exchange capacity (IEC) increased from 1.0 to 2.0. Nafion 117 and sPP χ12 values were 0.93 and 0.807 at an IEC of 0.91 and 1.8. Polymer water uptake was inversely dependent upon n and IEC or sulfonic acid-group concentration. The following trend was noted for ionomer type, n, and water uptake: PBC-2.0 (159 wt % and 7.89e-4 mol/cm3) > sPP (48.6 wt % and 1.40e-3 mol/cm3) > Nafion 117 (23 wt % and 1.24e-3 mol/cm3). The ionomer's Gibb's total free change (ΔGTot) due to water swelling for Nafion 117 was −15.3 J, sPP was −28.5 J, and PBC-2.0 was −53.2 J. An empirical equation was created to estimate a material's total solubility parameter (δ); and dispersion (δd), dipolar (δp,), and hydrogen bonding (δh) forces. The δ values for Nafion 117, sPP, and PBC-2.0 were 19.9 (J/cm3)1/2, 21.3 (J/cm3)1/2, and 21.0 (J/cm3)1/2. Idealized swelling within an ionomer due to solvent. Ion domains are comprised of fixed sulfonated acid groups (SO3H) along the polymer's backbone. These functional groups provide interaction sites for molecules to diffusion and swell chains. The total change in free energy ΔG is dominated by ΔGmix that is attributed to hydrogen bonding and the concentration of elastically active chains n, which directly impacts its chemical potential Δμ.

Original languageEnglish (US)
Pages (from-to)435-443
Number of pages9
JournalJournal of Polymer Science, Part B: Polymer Physics
Issue number5
StatePublished - Mar 1 2017


  • Flory-Huggins
  • Flory-Rehner
  • Hildebrand solubility parameter
  • ionomer
  • swelling

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Polymers and Plastics
  • Materials Chemistry


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