Understanding Vanadium Ion Diffusion in Nafion Using an Atomistic Study and Microscopic Concentration Profiles

The functionality of ionomeric membranes is influenced by small changes of several parameters. Aqueous network formation by phase separation between the hydrophilic andhydrophobic parts of the polymer is one critical factor for water and ion transport. In particular, the transport of highly charged ions like V³⁺ is not well understood. The unsteady diffusion in Nafion, a sulfonic acid based cation exchange polymer, using V³⁺ profiles obtained with micro X-ray fluorescence (0.5 μm spot over a 180 μm scan) yields a diffusion coefficient of 4× 10⁻¹³ m²s⁻¹ at λH₂ O/SO₃ = 12 and at ca. 20 ∘C. It is confirmed that the concentration profile can be described by an error function formalism. The diffusivity, determined from the entire profile, represents mainly the transport into a vanadium free environment with very low ionic strength as the membrane was conditioned in ultra-pure water. The macroscopic ion transport is influenced by local molecular interactions, interconnection of water pockets and long range ionic interactions. The local interactions of V³⁺ were studied using molecular dynamics (MDs) simulations. The MD simulation studies diffusion at a constant ion concentration and short length scale (ca. 30 nm). It gives insights on the effects of dissolved V3+ ions on the local structure. Radial distribution functions reveal that at low hydration, the vanadium ions have an ordering effect on water molecules. The diffusion coefficient of V3+ is determined on a molecular level from the mean-square displacement yielding 2.5 × 10⁻¹⁰ m²s⁻¹ for V³⁺ ions {at} a membrane water content of λH₂ O/SO₃ = 6. The phenomenon in which the diffusivity decreases over longer length scales was documented before for water and H⁺ in Nafion; however, this was by only about one order of magnitude. The experimental microscopic approach described by us is universally applicable, e.g., to environments of higher ionic strength, ions with different charges, and different types of ion-exchange membranes. Longer diffusion times allow us to distinguish between different concentration regimes.