Fig. 5: Transport mechanism of water molecules and sodium ions through crystalline and amorphous regions.

Equilibrium membrane structure with crystalline (aligned) regions (a) and the continuous water channel formed (b–d). Equilibrium membrane structure with amorphous (disordered) regions (e) and discontinuous water pathways constructed (f–h). During desalination, continuous water channel in crystalline regions results in continuous water transport; while the wetting-dewetting process occurs in amorphous phases due to the discontinuous water pathways, as shown in green dashed circles. Water molecules are depicted as transparent surfaces for clarity in (a) and (e), while the membranes are shown with transparent surfaces to highlight the water channel features in (b–d) and (f–h). i Number profiles of water molecules transferred across membranes with crystalline and amorphous structures during desalination. j Mean square displacement of water molecules in the crystalline and amorphous regions. k Distribution probability for water dipole angles in the crystalline and amorphous zones. l Potential of mean force profiles for sodium ion transporting from membrane centre to the membrane’s entrance. m Pore size distribution of equilibrium solvation structures in crystalline and amorphous regions. n Evolution of sodium ion solvation structures during transport across the crystalline and amorphous regions, respectively.