Fig. 2: Molecular sieving performance of cyclodextrin membranes for Li⁺/Mg²⁺ separation.

a Selectivity comparison between amino-cyclodextrin membranes with 6, 7, and 8 (LiOH-AmCD-0.1 TMC) glucose subunits; Feed solutions contain 2000 ppm MgCl₂ and 100 ppm LiCl. b Selectivity and flux of LiOH-Am7CD-TMC membranes with various thicknesses; Feed solutions contain 2000 ppm MgCl₂ and 100 ppm LiCl. c Schematic diagram illustrating the ion transport through the nanofilms with the CD-stacked channel structure. d Comparison of separation factor (right) and flux (left) between LiOH-Am7CD-0.01 TMC and HAc-Am7CD-0.3 TMC membranes with binary salt feed compositions. Feed solutions contain 2000 ppm MgCl₂ and 100 ppm LiCl. e Rejection of neutral solutes with different Stokes radius by LiOH-Am7CD-0.01 TMC and HAc-Am7CD-0.3 TMC membranes. The dashed lines indicate the sugar molecules that were rejected with a rate of 90% or higher. f Schematic diagram illustrating the tortuous transport through the nanofilms without the CD-stacked channel structure. g Comparison of Li⁺/Mg²⁺ selectivity and Li⁺ permeation rate between LiOH-Am7CD-0.05/0.01/0.005 TMC membranes and other reported membranes containing COFs, MOFs, and other 2D materials. h Permeance and Li⁺/Mg²⁺ separation factor of LiOH-Am7CD-0.05/0.01/0.005 TMC membranes, commercial NF 90 membranes, and other reported pressure-driven nanofiltration membranes. (Note: selected membranes are given in Supplementary Tables 6 and 7). i Ionic rejection and corresponding Li⁺/Mg²⁺ separation factor of LiOH-Am7CD-0.05 TMC membranes using a series of feeds with different Mg²⁺ /Li⁺ mass ratios and Mg²⁺ mass concentration. (Note: all tests were conducted at 5 bar, except for the final one with a Mg²⁺ mass concentration of 1700 ppm, which was conducted at 10 bar to overcome the osmotic pressure). Error bar standard deviation.