Theoretically computed proton diffusion coefficients in hydrated PEEKK membranes

Abstract

A recently derived molecular structure–function model based on non-equilibrium statistical mechanics has been used to compute proton friction and diffusion coefficients in 65% sulfonated PEEKK membranes at various degrees of hydration. Morphological parameters, taken from recent SAXS measurements, including pore radius and average separation distance of the sulfonate fixed sites within the pore, along with results from electronic structure explicit water calculations for para-toluene sulfonic acid, were used as input parameters in the model. For membranes where the hydration levels (λ) were 15, 23, and 30 H₂O's/SO₃⁻, the model predicted proton diffusion coefficients of 4.13 × 10⁻¹⁰, 1.23 × 10⁻⁹, and 1.54 × 10⁻⁹ m² s⁻¹, respectively. These values were obtained without any attempt at fitting to the results obtained from pulsed-field gradient NMR experiments. These computed diffusion coefficients are all within approximately 15% of the measured values; demonstrating the substantial predictive capability of the model. Furthermore, this investigation has shown that at the lower water content (λ = 15) the transport of the proton may be adequately described as vehicular in nature, while at the two higher water contents (λ = 23, 30) there is a contribution via structural diffusion.