Differential Permeability of Proton Isotopes through Graphene and Graphene Analogue Monolayer

Two-dimensional (2D) monolayer nanomaterials can be exploited as the thinnest membrane with distinct differential sieving properties for proton isotopes. Motivated from the experimental evidence of differential sieving proton isotopes through graphene and hexagonal boron nitrate (h-BN) monolayer, we compute the kinetic barrier of isotope H(+) and D(+) permeation through model graphene and h-BN fragments at the MP2/6-31++G(d,p) level of theory. On the basis of the ratio of tunneling reaction rate constant, the isotope separation ratio of H(+)/D(+) and H(+)/T(+) is predicted to be ∼12 and 37, respectively. The tunneling reaction rate constant can be estimated from the zero-point-energy computed at the transition state for the proton isotope permeation though the 2D model systems. We show that the presence of Stone-Wales (55-77) defect in the model graphene fragment can significantly lower the proton permeation barrier by 0.55 eV. With the defect, the ratio of tunneling reaction rate constant of H(+)/D(+) is increased to ∼25. In addition to model graphene and h-BN, we have examined proton permeation capability of α-boron monolayer. We compute the tunneling reaction pathway for H(+) through α-boron monolayer using both the climbing nudged elastic band (c-NEB) method and the scanning-path method. Both methods suggest that α-boron monolayer entails a relatively low barrier of ∼0.20 eV for H(+) permeation, much lower than that of the model graphene and h-BN fragments. Our studies provide molecular-level insights into the differential permeation of proton isotopes through 2D materials. The methods can be extended to examine isotope separation capability of other 2D materials as well.