First principles study of the permeability of graphene to hydrogen atoms

Abstract

Using calculations from first principles and harmonic transition state theory, we investigated the permeability of a single graphene sheet to protons and hydrogen atoms. Our results show that while protons can readily pass through a graphene sheet with a low tunneling barrier, for hydrogen atoms the barriers are substantially higher. At the same time, the presence of defects in the membrane can significantly reduce the penetration barrier in a region that extends beyond the defect site itself.

Proton transport through one-atom-thick crystals

“…If perforated with atomic or nanometer accuracy, graphene may provide ultrafast and highly selective sieving of gases, liquids, ions, etc. 2,9-19 However, in its pristine state, graphene is absolutely impermeable for all atoms and molecules moving at thermal energies [1][2][3][4][5][6][7] . Theoretical estimates for the kinetic energy E required for an atom to penetrate through monolayer graphene vary significantly, depending on the employed model, but even the smallest literature value of 2.4 eV for atomic hydrogen 3-6 is 100 times larger than typical k B T which ensures essentially an impenetrable barrier (k B is the Boltzmann constant and T the temperature).…”

“…even the latter barrier is still prohibitively high to allow appreciable transport of thermal protons (E 1.2 eV is estimated 5 to result in permeation rates of 10 9 sec).…”

Hydrogenation Facilitates Proton Transfer through Two-Dimensional Honeycomb Crystals

“…Specifically, computed barriers of 3.5-4.0 eV have been reported for chemisorbed protons (i.e. protons that are covalently bonded to the 2D materials) to penetrate graphene [17,18,23]. If the protons do not chemisorb on the surface but rather penetrate the sheet via a metastable physisorption state, smaller barriers of 1.4-2.6 eV have been reported [17,18,23].…”

“…Considerable theoretical effort has been devoted towards understanding the microscopic details of how protons penetrate 2D materials [9,17,18,[20][21][22]. It has been established on the basis of density-functional theory (DFT) calculations that the barriers to proton penetration through pristine graphene and h-BN in vacuum can be excessively high.…”

“…Two-dimensional (2D) materials like graphene and hexagonal boron nitride (h-BN) offer potential as membrane materials since they are a single atom thick and have high mechanical stability and flexibility [1,2,4,5,[7][8][9][10]. For some time, it was believed that pristine graphene and h-BN were impermeable to ions due to high energy barriers for penetration [17,18]. Recent experiments, however, have suggested that protons can in fact penetrate pristine graphene and h-BN [1,2].…”