Fig. 3: Narrow channel induced by random orientation is crucial for the high selectivity.

a We measured the K⁺ and Li⁺ content inside the membrane after permeation experiments. Li⁺ content was much lower than the K⁺ content, confirming that the blocked Li⁺ transport is due to the rejection by narrow channels instead of Li⁺ adsorption inside the membrane. b, c To confirm the importance of narrow channels, we used horizontally aligned TpPa-SO₃H membrane, termed h-TpPa-SO₃H membrane for the K⁺/Li⁺ separation test (b). The membrane had nanometer-sized pores and showed low selectivity (c). d–f We also used vertically aligned TpPa-SO₃H membrane, termed v-TpPa-SO₃H membrane for the K⁺/Li⁺ separation test. d Schematic illustration of the membrane preparation and the test device. e Schematic illustration of the ion transport direction. f The v-TpPa-SO₃H membrane is impermeable to any ion. g Permeability comparison of the tested COF materials, suggesting that the importance of the narrow channels induced by the random orientation for the high selectivity. Error bars in all cases represent standard deviation of the data from at least three individual experiments.