Accurate measurement of gas permeation through sub-nanopores of two-dimensional materials by mass spectrometry

Mass transport at the sub-nanometre scale plays a key role in systems such as catalysis, energy generation and storage, chemical sensing, and molecular separation. Highly efficient biological channels in living organisms have inspired the design of artificial channels with similar or even higher mass transport efficiency. The membranes function by forming a barrier between the two phases, restricting the movement of some molecules while letting others through. The mass transport rate of the membrane is inversely proportional to thickness, and theoretically, the membrane with atomic layer thickness can produce the maximum flux with the minimum energy cost. Meanwhile, the pore size can be precisely manipulated within sub-nanometer size for molecular separation, such as gas separation. So, sub-nanopores in graphene and other atomically thin two-dimensional materials are regarded as highly promising membrane materials for high-performance substance separation due to their atomic thickness, large-scale synthesizability, excellent mechanical strength, and chemical stability. Sub-nanopores membranes base on two-dimensional (2D) materials with atomic-scale thickness are expected to break the trade-off between selectivity and permeation of conventional separation membranes, resulting in efficient separation. The mass transport mechanism of sub-nanopores in 2D materials is different from that predicted by classical theories, and the mechanism is yet to be understood to design efficient separation membranes. The gas permeation reflects the permeability of membrane materials and is an important parameter describing gas transport characteristics. Studying the gas permeation of membrane materials can not only provide basic information about the materials, such as pore size and distribution, but also further understand the influence of gas adsorption and diffusion on the mechanism of gas transport. Although some theoretical studies have predicted the molecular transport properties of single-layer sub-nanopores, experimental research is still scarce, and there is a gap between theory and experiment due to the lack of accurate measurement methods and unclear understanding of the transport mechanism. Although planar nanomaterials are often fabricated on a centimeter-scale, the use of standard methods (such as gas flowmeters) for studying mass transport properties of the free-standing layers is complicated. And the measurement of the minimum gas permeation is greatly affected by the measurement method and the working state of the measuring instrument. The permeation of the same material reported in the literature varies greatly and is far beyond the range of experimental error. So, accurate measurement of the gas permeation through sub-nanopores in two-dimensional materials is a prerequisite for studying the unique mass transport properties. We developed a method based on ultra-high vacuum technology and mass spectrometry to measure extremely low gas permeation, achieving highly sensitive and real-time measurement of gas permeation through sub-nanopores in 2D materials. The usage of ultra-high vacuum reduces the background of the measurement effectively. By optimizing the detection sensitivity of the mass spectrometry, the measurement limit for the permeation reaches as low as 9x10(8) molecules/s, which is two orders better than those of the reported methods. We measured the permeation of He, Ne, and Ar through sub-nanometer pores in monolayer MoS2 and observed the molecular sieving characteristics. The method provides an effective means for studying the transport mechanism of gas through sub-nanopores in 2D materials.