Fig. 2: Cooperative ion transport.

a Summary of the sequential permeation test results of K⁺, Pb²⁺, and K⁺/Pb²⁺ mixtures across one MoS₂-COOH membrane. b, c The fluxes of K⁺ and Pb²⁺ versus concentration of Pb²⁺ in the feed for the series of tests across the MoS₂-COOH membrane and PTFE membrane, respectively. In the panel, both the ion fluxes and osmotic pressure are normalized to values corresponding to the initial K⁺ test. Data: mean ± standard error. d Systematic XRD measurements for the MoS₂-COOH membrane. The effective height of the Pb²⁺-locked channel is ~11.4 Å−6.2 Å=5.2 Å, where 6.2 Å corresponds to the intrinsic thickness of monolayer MoS₂. The annotation “solution 1 to solution 2” in the legend of (d) indicates that the MoS₂-COOH membrane was first saturated in solution 1 and then switched to solution 2 for uptake, and finally the MoS₂-COOH membrane was taken out of solution 2 for XRD measurements. The pink triangle indicates the PTFE peak. a.u. is arbitrary unit. The salts used are nitrate-based.