Fig. 2: High K⁺/Li⁺ selectivity.

a–c Control experiments. a, b Concentration of K⁺ and Li⁺ in the permeate in response to permeation time, showing the low K⁺/Li⁺ selectivity of AAO substrate (a) and the LDH/AAO composite membrane (b). c To confirm the absence of contamination, we used DI water as the feed solution, and found trace amount of K⁺ contamination and no Li⁺ contamination. d Permeation of K⁺ through the r-TpPa-SO₃H membrane when the feed solution contains 0.1 M K⁺. e Permeation of Li⁺ through the r-TpPa-SO₃H membrane when the feed solution contains 0.1 M Li⁺, showing the completely blocked Li⁺ transport. f Comparison of the K⁺ and Li⁺ permeation rate, summarized from (d) and (e). g Permeation of K⁺ and Li⁺ through the r-TpPa-SO₃H membrane when the feed solution contains 0.1 M K⁺ + 0.1 M Li⁺, showing high K⁺/Li⁺ selectivity. h Permeation rate of the K⁺ and Li⁺ when the feed solution contains different concentrations of equimolar K⁺ and Li⁺. i Permeation rate of the K⁺ and Li⁺ for membranes with different thickness of COFs when the feed solution contains 0.1 M K⁺ + 0.1 M Li⁺. h and i suggest the robustly high K⁺/Li⁺ selectivity. Error bars in all cases represent standard deviation of the data from at least three individual experiments.