Fig. 5: K⁺-selective transport mechanism.

a Schematic diagram of ion transport process. The interaction energy (c) and schematic diagram (b) obtained from density functional theory (DFT) calculations. d Simulation snapshots visually depict the transmembrane behavior of Na⁺ (yellow) and K⁺ ions (pink) (C, O, N, H, and Cu are depicted in gray, red, blue, white and orange respectively). e PMF profiles for K⁺, Na⁺, Li⁺ and Mg²⁺ ions across the CMOF membrane. f Transmembrane ion permeation kinetics across the CMOF membrane in single-ion and binary-ion systems.