Humidity effect on temperature behavior of proton diffusion coefficient in sulfonated co-polynaphthoyleneimide membranes measured by ¹H NMR diffusometry

Proton diffusion in the co-PNIS85/15 membrane was investigated in the temperature range from 200 to 363 K at different water contents (4 ≤ λ ≤ 21) using ¹H SFG NMR diffusometry. At high hydration values, above the threshold value λ₀ = 10.5, the ln(DNMR(1/T)) dependences show two different activation modes, separated by a crossover point Tcr ≈ 250–260 K. At temperatures above Tcr, the activation energy is Ea ~ 0.20 eV, which is close to the value for bulk water (Ea ~ 0.17 eV). At temperatures below the crossover point, the ln(DNMR(1/T)) dependences for different water contents merge together into one straight line characterized by a much higher Ea = 0.46 eV. At low hydration values λ < λ₀, the activation energies for the high-temperature and low-temperature modes converge, so that at λ = 4, the dependence ln(DNMR(1/T)) is described by one straight line throughout the studied temperature range with Ea = 0.38 eV. A model is proposed that phenomenologically describes the diffusion in the co-PNIS membrane at different moisture contents λ.