Theoretical description of quantum mechanical permeation of graphene membranes by charged hydrogen isotopes

Abstract

It has been recently shown that in the presence of an applied voltage, hydrogen and deuterium nuclei can be separated from one another using graphene membranes as a nuclear sieve, resulting in a 10-fold enhancement in the concentration of the lighter isotope. While previous studies, both experimental and theoretical, have attributed this effect mostly to differences in vibrational zero point energy (ZPE) of the various isotopes near the membrane surface, we propose that multi-dimensional quantum mechanical tunneling of nuclei through the graphene membrane influences this proton permeation process in a fundamental way. We perform ring polymer molecular dynamics calculations in which we include both ZPE and tunneling effects of various hydrogen isotopes as they permeate the graphene membrane and compute rate constants across a range of temperatures near 300 K. While capturing the experimentally observed separation factor, our calculations indicate that the transverse motion of the various isotopes across the surface of the graphene membrane is an essential part of this sieving mechanism. An understanding of the multi-dimensional quantum mechanical nature of this process could serve to guide the design of other such isotopic enrichment processes for a variety of atomic and molecular species of interest.

Graphene multi-protonation: A cooperative mechanism for proton permeation

“…These discoveries were absolutely unexpected since graphene was believed to be completely impermeable to all atoms and molecules under ambient conditions [3,4]. A number of works have subsequently appeared -both experimental [5][6][7][8][9][10] and theoretical [11][12][13][14][15][16]-not only stimulated by the promise of important applications in hydrogen technology but also with the aim to uncover the microscopic mechanisms underlying these observations.…”

“…Despite much recent progress on the theoretical insight into the processes leading to such a facile permeation of protons through graphene [11][12][13][14][15][16], we consider that a complete and satisfactory understanding has not been achieved yet (e.g. see Refs.…”

Isotopic separation of helium through graphyne membranes: a ring polymer molecular dynamics study

“…Other processes at the gas-membrane interface do require an explicit treatment of the carbon atoms dynamics since they involve large deformations of the carbon framework, including rehybridization and formation of new bonds. 8,88…”

“…The RPMD method has recently been used to describe phenomena such as atom scattering or sticking on surfaces 74,75 and a related problem on permeation of H + and D + on pristine graphene. 8 Nonetheless, in all cases, the authors point out, again, the importance of considering both ZPE and tunneling for isotopic separation.…”

“…3,4 Some years ago, experiments by Lozada-Hidalgo et al 5,6 and recently by Creager et al 7 have shown that small charged particles such as the proton and its isotopes can penetrate through a monolayer of pristine graphene. There is no complete explanation despite many theoretical calculations, [8][9][10] although some kind of chemical interaction seems to be responsible for this process. Even more recently, it has also be found that hydrogen can permeate pristine graphene.…”