Gases can permeate through 2D channels made from materials like graphene and boron nitride much faster than predicted by theory. The effect can be explained by “specular surface scattering”, which leads to frictionless flow, and it could be exploited in applications such as filtration and flow control.
“Gas permeation through nanoscale pores is ubiquitous in nature but it also plays an important role in many technologies,” explains Boya Radha of the University of Manchester in the UK who led this research effort together with Nobel laureate Sir Andre Geim. “Since the size of the pores is usually smaller than the mean free diffusion path of gas molecules, we can describe this flow by conventional Knudsen theory. Here, the diffusing molecules randomly bounce back (or scatter) from confining channel walls, which reduces their flow.
“In channels with atomically-flat walls, however, such as those made from graphene (a 2D carbon sheet) and boron nitride (BN), which are flat at scales of 1 ångström (10-10 m) this theory breaks down. This is because the diffusing molecules only rarely scatter from the walls and so essentially permeate through the channel as if it weren’t there.”
Graphene is flattest
Geim, Radha and their colleagues obtained their results by measuring the rate at which helium gas diffuses through ångström-scale slit-like channels with walls made from cleaved graphite, hexagonal BN and molybdenum sulphide (MoS2). All these materials can be exfoliated, or thinned down, to monolayer thicknesses and have atomically flat surfaces. In the experiments, the researchers made channels using two thin (roughly 10–100 nm thick) crystals of each of the materials and used these as the bottom and top walls of a channel. They plasma etched a third thinner crystal so that it contained long narrow trenches. This crystal plays the role of a spacer between the top and bottom walls.
“We assembled the three crystals, which are held together by van der Waals forces, on top of each other,” explains Ashok Keerthi, who is first author of the study. “We could choose the spacing between them to be just one atomic layer thick or up to as many layers as we required.
“We found that the rate of helium transport is fastest through graphene and slowest in MoS2. Although all the 2D materials we studied are atomically flat, the minute differences in the atomic “corrugations” of graphene, hBN and MoS2 can be ‘felt’ by the scattered helium molecules. This can only be explained by quantum effects, that is the wave-like nature of matter (helium).”
In fact, when the (de Broglie) wavelength of helium is much larger than the atomic-scale roughness of the wall surface, as is the situation for a wall made of graphene, it is specularly scattered. Such scattering leads to frictionless gas flow and ballistic transport. In contrast, helium permeates through MoS2 at a rate predicted by Knudsen theory because it is rougher at atomic scales than graphite (and hBN). This roughness in fact comes from sulphur atoms protruding in between Mo atoms. These corrugations are almost an ångström tall, which is around the same diameter as the wavelength of helium molecules.
Confirming the matter-wave effect
The Manchester team backed up this matter-wave effect by measuring the rate at which deuterium (hydrogen’s heavier isotope) permeates through 2D channels made from graphene and hBN. “We found that hydrogen permeates faster than deuterium, even though it should be the opposite according to the classical Knudsen description,” says Geim. “While the size of both hydrogen and deuterium molecules are the same, their de Broglie wavelengths are not. The de Broglie wavelength of hydrogen is bigger than deuterium’s, and this leads to increased specular reflection of hydrogen from the channel walls and thus faster diffusion.”
These results back up previous findings from experiments on gas transport in various atomically smooth nanochannels, such as carbon nanotubes, nanoporous films made from graphene, graphene oxide and other 2D materials, adds Radha.
The researchers, reporting their work in Nature 558 420, say that they would now like to study size-selective separation of gases in even thinner channels. “While small molecules pass through these channels at high speed thanks to specular rather than diffusive scattering, the larger ones should be excluded due to steric effects,” she explains. “This could come in useful in filtration technologies since we would have fast flow and size exclusion at the same time in one system.”