Fig. 5: Mechanistic insights into the facilitated water permeation through DP-M.

a Schematic representation of the advanced structure of an ultrapermeable PA membrane with precise co-cation sieving capability. b DFT atomistic calculations of polarity differences between DP-M and P-M molecular fragments. c ESP distributions of van der Waals surfaces of the water molecules obtained by DFT calculations. d Three representative PA molecular fragments of DP-M and P-M (left) and the schematic illustration of water cluster distribution in each fragment (right). e The radial distribution functions (RDFs) between water and the three PA fragments. f Binding energy (BE) and the number of water molecules (NW) around the three PA fragments. All the information and data described in (d–f) were obtained from MD simulations. g Schematic illustration of the working principle of the semipermeable DP-M for ultrafast co-cation nanofiltration (yellow and blue spheres represent monovalent and divalent cations, respectively).