Graphenylene and inorganic graphenylene nanopores for gas-phase 4He/3He separation: kinetic and steady-state considerations

Selective membrane-based separation of light isotopes is considered to be possible based on the quantum phenomena. In this regard, the role of two mass-dependent effects, quantum tunneling and zero-point energy (ZPE), is realized to be consequential for selective separation of helium isotopes using appropriate membranes. In the present study, the efficiency of two analogous nanoporous membranes, graphenylene (GP) and inorganic graphenylene (IGP), for gas phase separation of 3He and 4He has been theoretically investigated. Since the performance of the studied membranes is extremely influenced by the close competition between both quantum tunneling and zero-point energy (ZPE) effects, high precision in the calculations is required to provide more realistic theoretical predictions. The current study attempts to provide such predictions by applying domain-based local pair natural orbital coupled cluster theory (DLPNO-CCSD) to obtain the accurate helium–pore interaction potential, based on which the tunneling rates, as well as the exact (anharmonic) bound levels for the vibration of helium in the pore plane, are calculated. From the analysis of the obtained results, the performance of the GP and IGP nanopores has been investigated in both kinetic competition and steady-state conditions in the temperature range of 10–200 K. The results of this study indicate that harmonic oscillator approximation significantly overestimates the efficiency of the studied nanopores for helium isotope separation. Based on our accurate calculations, both GP and IGP nanopores provide almost similar selectivities in kinetic competition conditions (Stot4/3 ≈ 3 at T = 50 K); however, the predicted permeance for GP (10−8 mol m−2 s−1 bar−1) is about 100 times higher than that predicted for IGP under the same conditions. Under steady-state conditions, IGP has been shown to be more efficient than GP, since it provides acceptable values of separation factor at higher temperatures.