REVIEW
◥MEMBRANES
Subatomic species transport through atomically thin
membranes: Present and future applications
Piran R. Kidambi1,2,3,4*, Pavan Chaturvedi^1 , Nicole K. Moehring2,4
Atomically thin two-dimensional materials present opportunities for selective transport of subatomic
species. The pristine lattice of monolayer graphene and hexagonal boron nitride, although impermeable
to helium atoms, allows for transmission of electrons and permits transport of thermal protons and
its isotopes. We discuss advances in selective subatomic species transport through atomically thin
membranes and their potential for transformative advances in energy storage and conversion, isotope
separations, in situ electron microscopy and spectroscopy, and future electronic applications. We
outline technological challenges and opportunities for these applications and discuss early adoption in
imaging and spectroscopy that are starting to become commercially available, as well as emerging
applications in the nuclear industry and future application potential in grid storage, clean/green
transportation, environmental remediation, and others.
A
tomically thin two-dimensional (2D)
materials are crystalline solids with
constituent atoms bonded in a planar
2D sheet and exhibit distinctly different
properties compared to bulk materials
( 1 ). Graphene, a monolayer mesh of carbon
atoms arranged in a hexagonal lattice (~3.4 Å
thick), was initially isolated as a model 2D
material and can be considered as a building
block for other carbon materials such as graph-
ite (stack of graphene sheets held together
via van der Waals forces), carbon nanotubes
(seamless cylinders of graphene), and bucky-
balls (seamless spheres of graphene) ( 1 ). In-
terest in the properties of 2D materials have
since resulted in successful isolation of mono-
layers from other layered materials, e.g., mono-
layer hexagonal boron nitride (h-BN, isomorph
of graphene with alternating B and N atoms),
graphene oxide, 2D chalcogenides (about three
atoms thick), 2D oxides, 2D mica (~10 Å thick),
2D metal-organic frameworks, 2D covalent-
organic frameworks, and others ( 2 – 6 ), as well
as combinations in lateral (in-plane bonding
of different 2D materials) or vertical (stacking
different 2D materials) heterostructures ( 2 , 5 ).
Membranes are typically thin physical bar-
riers that allow for transport of certain species
while hindering others, and their ratio is com-
monly defined as selectivity ( 7 , 8 ). Monolayer
graphene and h-BN represent the thinnest
possible physical barrier and allow for selective
permeation of subatomic species (Fig. 1)—i.e.,
the pristine lattice of graphene and h-BN is
impermeable to small atoms such as helium at
room temperature ( 9 ) but allows for transport
of protons ( 10 ) and deuterons ( 11 ) and shows
energy-dependent transparency to electrons
( 12 ). Graphene exhibits excellent thermal
conductivity [(4.84 ± 0.44) ×10^3 to (5.30 ±
0.48) ×10^3 W/mK] ( 13 ) and electron mobility
(~3000 to 230,000 cm^2 V−^1 s−^1 )( 1 , 14 , 15 ), where-
as h-BN is an insulator (bandgap ~5.9 to 6 eV)
( 16 ) with high thermal conductivity (~751 W/mK
at room temperature) ( 17 ). The exceptional
mechanical strength of monolayer graphene
(Young’s modulus∼1 TPa, breaking strength
~42 N m–^1 )( 18 ) and h-BN (Young’s modulus
~0.86 TPa, fracture strength of ~70 GPa) ( 19 )
when suspended over micrometer-scale aper-
tures, coupled with the high adhesion energy
(graphene ~0.45 Jm−^2 )( 20 ), enables the fabri-
cation of functional atomically thin membranes.
Monolayer graphene in particular can with-
stand ~100 bar of applied pressure ( 21 ) and
several orders of magnitude pressure differ-
ential ( 22 ). The pressure tolerance, however,
depends on the area over which graphene is
suspended ( 21 ), and calculations indicate that
aperture diameters <1mm are ideal for extreme
pressures(upto~570bar)( 23 ). This review will
focus on selective transport of electrons, pro-
tons, and deuterons through atomically thin
membranes and discuss the most promising
present and future applications.Impermeability to atoms, gases, and molecules
Graphene and h-BN were initially shown to
be impermeable to helium and other gases
(Fig. 1C, inset) ( 9 , 20 ). Atomically thin balloons
formed by sealing micrometer-sized gas-filled
cavities with mechanically exfoliated mono-
layer graphene or h-BN flakes exhibited neg-
ligible leakage (transport of gas through the2D lattice) rates, indicating that their lattice
is impermeable to helium and larger atoms or
molecules at room temperature ( 9 , 24 , 25 ).
Monolayer molybdenum disulfide (MoS 2 ) is
also impermeable to H 2 at ~50°C (1 bar and
over 3 days) ( 26 ). By contrast, high gas leakage
rates were observed for even nanoscale defects
( 24 , 25 , 27 ). Theoretical calculations were in
agreement with experimental observations of
gas impermeability and predicted large energy
barriers (EB) for the permeation of atoms
through the hexagonal rings (radius ~1.42 to
1.45Å) in the pristine lattice of graphene (H
atoms,EB~2.86 to 4.61 eV; He atoms,EB~3.5
to 18.77 eV; O atoms,EB~5.5 eV; and N atoms,
EB~3.2 eV) and h-BN (H atoms,EB~6.38 eV)
( 9 , 28 – 31 ).
The impermeability of graphene and h-BN
to even small gas atoms at room tempera-
ture offers routes to creating atomically thin
barriers or atomically sharp interfaces that
separate two distinct reservoirs of atoms or
molecules. However, observations of anoma-
lous H 2 permeation through monolayer gra-
phene, while maintaining impermeability to
the smaller He atoms as well as the absence
of molecular deuterium (D 2 ) permeation ( 26 ),
taken together with the stochastic switching
behavior of leakage rates observed in some
atomically thin balloon experiments ( 24 , 27 , 32 ),
raise fundamentally interesting questions on
the absolute limits of gas impermeability, as
well as the transport mechanisms (and asso-
ciatedEB) for selective H 2 permeation ( 26 ).
By contrast, the transmission of energetic
He ions or alpha particles and other larger
ions through graphene, h-BN, and other 2D
materials depends on the ion energy, size, and
incident angle wherein collisions with the 2D
lattice can also result in the formation of de-
fects with varying yields ( 33 , 34 ). Irradiation
with energetic ions and protons, as well as
with alpha, beta, and gamma particles, is
typically used to assess the reliability of elec-
tronic devices incorporating 2D materials for
space applications ( 35 , 36 ). Finally, selective
transport of atoms, molecules, and ions through
defects in 2D materials presents the potential
for advancing separation processes ( 7 , 8 ).Transmission of electrons
Electron transmission through 2D materials
entails combinations of electron-electron and
electron-phonon interactions in the lattice, via
elastic and inelastic collisions with the nuclei
of the atoms in the lattice ( 37 ). Electrons tunnel
through the lattice of monolayer graphene
( 38 – 40 ) and h-BN (tunnel-barrier height
~3.07 eV, dielectric strength ~7.94 MV/cm)
( 41 , 42 ), and the in-plane electron conduc-
tivity of graphene can be used to modulate
tunneling via changes to the potential or charge
distribution, which the tunneling electrons en-
counter during transport in the normal directionRESEARCH
Kidambiet al.,Science 374 , eabd7687 (2021) 5 November 2021 1 of 12
(^1) Department of Chemical and Bimolecular Engineering,
Vanderbilt University, Nashville, TN, USA.^2 Vanderbilt
Institute of Nanoscale Sciences and Engineering, Vanderbilt
University, Nashville, TN, USA.^3 Department of Mechanical
Engineering, Vanderbilt University, Nashville, TN, USA.
(^4) Interdisciplinary Graduate Program in Material Science,
Vanderbilt University, Nashville, TN, USA.
*Corresponding author. Email: [email protected]