Tuneable ion selectivity in vermiculite membranes intercalated with unexchangeable ions

Membranes selective to ions of the same charge are increasingly sought for wastewater processing and valuable element recovery. However, while narrow channels are known to be essential, other membrane parameters remain difficult to identify and control. Here we show that Zr$^{4+}$, Sn$^{4+}$, Ir$^{4+}$, and La$^{3+}$ ions intercalated into vermiculite laminate membranes become effectively unexchangeable, creating stable channels, one to two water layers wide, that exhibit robust and tuneable ion selectivity. Ion permeability in these membranes spans five orders of magnitude, following a trend dictated by the ions' Gibbs free energy of hydration. Unexpectedly, different intercalated ions lead to two distinct monovalent ion selectivity sequences, despite producing channels of identical width. The selectivity instead correlates with the membranes' stiffness and the entropy of hydration of the intercalated ions. These results introduce a new ion selectivity mechanism driven by entropic and mechanical effects, beyond classical size and charge exclusion.