Fig. 3: Charge density-dependent ion separation.

a Charge densities of MLM and MLM-EDTA-1.5 membranes at different pH, calculated by the membranes surface zeta potential (Eq. (2)). b Schematic diagram of the main sources of negative charges in MLM-EDTA. c pH-dependent K⁺/Mg²⁺ selectivity of MLM and MLM-EDTA-1.5. d Relationship between charge density and K⁺/Mⁿ⁺ selectivity for MLM-EDTA-1.5 membrane. e Relationship between K⁺, Mg²⁺ transport resistance (reciprocal of ion permeation rates, 1/P_i) and K⁺/Mg²⁺ selectivity with charge density as independent variable for MLM-EDTA-1.5 membrane. f The transport energy barrier (obtained from Arrhenius plots, Supplementary Fig. 27) for K⁺ and Mg²⁺ diffusion through MLM-EDTA-1.5 membrane in a 0.2 M mixed salt solution at different charge densities. g The DFT calculated adsorption energy for K⁺ and Mg²⁺ on EDTA molecules with different negatively charged oxygen atoms. h, Schematic illustration of the possible mechanism for charge density enhancing the K⁺/Mg²⁺ selectivity in intra-membrane diffusion process. Error bars represent the standard deviation of three measurements of a sample.