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

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 (ΔG_Tot) 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 (δ_d), dipolar (δ_p,), and hydrogen bonding (δ_h) 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 ΔG_mix that is attributed to hydrogen bonding and the concentration of elastically active chains n, which directly impacts its chemical potential Δμ.