Quantum Effects on H₂ Diffusion in Zeolite RHO: Inverse Kinetic Isotope Effect for Sieving

Abstract

We use canonical variational theory (CVT) with small-curvature tunneling (SCT) contributions to investigate quantum effects on the H 2 diffusion process in the pure-silica zeolite RHO. At low temperature we find an inverse kinetic isotopic sieving effect in that the heavier isotopic species diffuses faster than the lighter one. Three quantum effects contribute to this kinetic isotope effect (KIE). The first one is quantum mechanical tunneling; thison its ownwould lead to a normal kinetic isotopic sieving effect, in which lighter diprotium diffuses faster than dideuterium. The second factor, which we find to dominate in the present case, is zero-point energy (ZPE). Deuterium has a lower ZPE, which leads to a smaller effective barrier for tunneling because the transition state has a larger ZPE than the precursor stable state; this results in an inverse KIE. The third factor, the thermal vibrational energy (computed from the quantized vibrational partition function), also favors a normal KIE, but it is outweighed by the ZPE effect. The vibrations of the zeolite host framework are found to play an important role at low temperatures, and our calculations consider up to 7296 degrees of freedom at the equilibrium structure and the saddle point and up to 221 degrees of freedom along the reaction path. The importance of quantum considerations on the dynamics is elucidated by comparison to a purely classical treatment.

Molecular hydrogen isotope separation by a graphdiyne membrane: a quantum-mechanical study

“…In the insets of Fig. 3 we present the low-energy behavior of some of the transmission probabilities, specifically, the probabilities for (l x ,l y ) = (0,0), (0,4) and (12,4), for H 2 , and (0,0), (12,0) and (18,8), for D 2 . For these energies, tunneling effects play an important role in the behavior of the probabilities.…”

“…Based on these ideas, there has been an impressive progress in the use of nanoporous materials for isotope separation. [2][3][4] An issue-also occurring in the separation of gases in general-is that large selectivities for separation are often accompanied by low permeances (thermal molecular flux per unit pressure) and vice versa. 5 As permeance is usually inversely proportional to the membrane thickness, new one-atomic-thick, two-dimensional (2D) nanoporous membranes offer great prospect for large selectivities without compromising the permeability.…”

“…28 A good agreement was found for the dependence of the 4 He/ 3 He selectivity with temperature when the separation membrane is GDY. However, for a holey graphene model, tunn-TST overestimates considerably the 4 He/ 3 He selectivity because it is unable to account for the extent of tunneling as well as other quantum features (resonances) found in the accurate treatment. 30 Helium isotopes quantum sieving through a graphtriyne membrane was also studied by means of the 3D-TDWP calculations, 31 which have served as benchmarks for ring polymer molecular dynamics calculations.…”

H2/D2 Kinetic Isotope Effects in Methanol Synthesis on an In2O3 Catalyst

“…In this study, 1:1 ratio at a higher temperature range around 260 °C suggests that the normal KIE is probably superimposed with an additional weak inverse effect. The reason of the inverse KIE has many other quantum theory explanations, of which the tunneling effect and zero point energy (ZPE) 64 are mostly considered. In this case, the ZPE is more likely related since it is correlated with a very small scale inverse KIE.…”

Rapid diffusion of H2 and strong adsorption of D2 in Ni-4PyC realized the efficient separation of H2/D2 by gas chromatography

“…8 However, Pd and Pd alloys are expensive and have high energy consumption, which limits their further application. The other type is porous material based on physical adsorption, such as carbon material, 9,10 zeolite, [11][12][13][14] organic cage, 15 and alumina. 16 However, these materials have problems such as non-adjustable pore size, the need for relatively low temperature during separation and poor selectivity.…”