Fig. 3: Water and ion transport.

a, Macroscopic permeation and microscopic self-diffusion of water through membrane micropores. b, Analysis of QENS signal acquired with an energy resolution (E_res) of 32.8 µeV. Data points (open squares) were fitted globally, shown as red lines, with the instrument resolution function in green. Polymer relaxation resulted in a broad Lorentzian contribution (grey shaded area) and a fast contribution (solid black lines). Water dynamics produced the main Lorentzian contribution with a narrower line width (light blue shaded area). c, Nanometric water self-diffusion as determined by QENS. d, Temperature-dependent ionic conductivity measured in 1 M aqueous KCl with activation energy labelled. T represents temperature. e, Modelled n(r) of K⁺ ions with respect to water molecules. f, Hydration number of K⁺ ions in the first hydration shell. g, Linear coupling of cation and water self-diffusion. Open symbols represent molecular dynamics simulation data with a timescale of 20 ns for polymers hydrated with 1 M aqueous KCl, whereas solid symbols represent those measured for 1 M aqueous LiCl by ⁷Li and ¹H PFG-NMR, with observation times of 120 ms for Li⁺ ions and 30 ms for water. h, Relative percentages of each structural segment within 1 Å of the pore surface, calculated by atom count. i, K⁺ ion trajectory in cPIM-Ph over 1.25 ns of molecular dynamics simulation at 300 K, with K⁺ ions colour-coded by elapsed time. For clarity, some polymers, water molecules and ions are omitted (see Supplementary Fig. 26 for the original snapshot). j, Modelled n(r) between K⁺ ions and oxygen-containing components in cPIM-Ph.