Gas permeation through graphdiyne-based nanoporous membranes

The study addresses how quasi-2D nanoporous membranes based on multilayer graphdiyne transport gases, aiming to reconcile high permeance with selectivity. Prior work established that atomically thin membranes with pores larger than the kinetic diameter yield Knudsen-type flows with modest selectivity, while angstrom-scale pores near the kinetic diameter increase selectivity at the cost of exponentially reduced flow rates. Bottom-up synthesized quasi-2D membranes may retain high permeance due to thickness comparable to molecular mean free paths, but the dominant transport mechanisms can deviate from simple Knudsen or activated models. Graphdiyne, a carbon allotrope with intrinsic angstrom-scale pores and a larger unit cell, has been theoretically proposed as a promising gas separation material. This work experimentally investigates gas permeation through graphdiyne-based films, probing whether transport follows Knudsen behavior, exhibits molecular sieving, or involves additional mechanisms such as adsorption within nanoscale channels.

The paper builds on studies demonstrating rapid permeation and tunable selectivity in atomically thin porous graphene and related 2D materials (e.g., Celebi et al., Thiruraman et al., Zhao et al.), and the general permeability–selectivity trade-off in membranes (Park et al.). Quasi-2D laminates and thin films of MOFs, COFs, and zeolites offer high flux but with varied porosity and selectivity (Li et al., Shen et al., Peng et al., Fan et al., Dakhchoune et al.). Carbon nanotubes exemplify fast transport in sub-2-nm pores (Holt et al.). For graphdiyne and graphyne, theoretical predictions suggest intrinsic pores enable gas and isotope separation, including possible quantum effects for helium isotopes (Jiao et al., Bartolomei et al., Hernández et al., Qiu et al.). However, experimental validation of gas separation performance in graphdiyne films has been lacking, and the role of quasi-2D film microstructure in transport remained unclear.

Graphdiyne-based films were synthesized via cross-coupling of 1,2,3,4,5,6-hexaethynylbenzene (HEB) on copper foils under argon at 110 °C for 64 h, followed by solvent rinsing and drying under argon. Films exhibit a quasi-2D basal layer (~90 nm thick) and a vertically oriented scaffold forming merged microwells. Morphology was characterized by SEM (including tilted and cross-sectional FIB-SEM) and TEM; electron diffraction confirmed ABC-stacked graphdiyne. Films were transferred using PMMA-assisted wet transfer onto silicon nitride membranes containing micrometer apertures to create suspended membranes. Gas permeation devices were mounted between two He-leak-tight chambers: a feed chamber with test gas or binary mixtures up to 1 bar and a vacuum chamber coupled to a mass spectrometer or helium leak detector. Flow rate I was measured versus pressure P to extract permeance (I/P). Controls included multilayer graphene-capped apertures and metal-coated graphdiyne, which showed no measurable He flow. Calibration used bare-hole devices (apertures without graphdiyne) to quantify open-hole permeance and estimate graphdiyne film porosity. Temperature-dependent measurements from 300 K down to 10 K (He) and 30 K (H2 isotopes) used a custom constant-flow cryogenic cooling setup, enabling assessment of T-dependence and transition regimes. Binary mixture experiments involved varying helium partial pressure in the presence of Ne, Ar, Kr, or Xe at fixed total pressure (1 × 10^5 Pa) to probe interactions between species. Pore size constraints were inferred from Knudsen scaling with T and P, absence of quantum diffraction/isotope effects at low T, porosity estimates from bare-hole comparison, TEM-observed thinnest regions, and DFT considerations of barrier heights for intrinsic graphdiyne pores. DFT simulations (details in Supplementary) assessed energy barriers for noble gas translocation through intrinsic graphdiyne meshes.

• Graphdiyne-based membranes exhibit direct porosity of approximately 0.1%, inferred from bare-hole calibration showing about 1000× higher flow than with graphdiyne, while withstanding pressures up to 1 × 10^5 Pa.
• For light gases (3He, 4He, D2, HD, Ne), permeance follows Knudsen scaling I ∝ m^(-1/2) and T-dependence ∝ T^(-1/2) from 300 K down to 10–30 K, indicating free molecular flow through nanoscale pores.
• Heavy noble gases deviate from Knudsen behavior: Kr and Xe permeances are suppressed by ~2.5× and ~4×, respectively, relative to Knudsen expectations; resulting selectivity S(4He/Xe) ≈ 20 (vs ≈5 for pure Knudsen).
• Hydrogen isotopes (D2, HD) show permeances similar to same-mass helium isotopes, despite larger kinetic diameters, contradicting steric sieving through intrinsic graphdiyne meshes.
• Pore size is constrained to approximately 1–5 nm: upper bound from sustaining Knudsen regime at 10 K and 1 × 10^5 Pa; lower bound from absence of diffraction/isotope effects (He de Broglie wavelength ~4 Å at 10 K), porosity–spacing arguments (~3 nm opening within ~10 nm thinnest regions spaced ~100 nm apart), and lack of activated transport (barriers < few meV). DFT indicates intrinsic mesh would impose ~1 eV barriers and is thus not the active pathway.
• Binary mixtures reveal non-additive, interacting flows: presence of heavier noble gases (e.g., Xe) suppresses helium flux beyond partial-pressure scaling (e.g., 0.2 × 10^5 Pa He + 0.8 × 10^5 Pa Xe reduces He flow by >2× vs pure He at same partial pressure). The suppression weakens progressively from Xe to Kr to Ar to Ne and diminishes at elevated temperature for He/Ne, consistent with reduced adsorption at higher T.
• Mechanism: adsorption of heavier atoms on inner walls of nanometer-scale straight-through holes partially blocks or narrows channels, reducing effective pore diameter and slowing translocation, thereby suppressing both heavy-gas flows and even helium in mixtures.
• Overall, membranes combine high permeance (due to pore density ~10^10 cm^-2 and Knudsen transport) with enhanced selectivity from adsorption-mediated suppression of heavier species, outperforming typical permeability–selectivity trade-offs.

The investigation resolves the apparent contradiction between Knudsen-like transport for light gases and suppressed flow for heavier noble gases by identifying adsorption within quasi-2D, few-nanometer straight-through holes as the key mechanism. The pore network comprises nanoscopic thinning regions that act as short channels where free molecular (Knudsen) flow dominates for small, light species across broad T and P ranges. Heavier atoms experience stronger dispersion interactions and adsorb on channel walls, effectively reducing the available cross-section and slowing traversal, which lowers permeance below Knudsen predictions. This adsorption further leads to unprecedented interaction between flows in binary mixtures, where heavy species present in the pores attenuate helium flux, violating additive behavior typical for inert gas mixtures. The absence of activated transport signatures and isotope effects excludes intrinsic angstrom-scale graphdiyne meshes or quantum sieving as dominant pathways; DFT supports the high barriers for intrinsic pores and multilayer ABC stacking misalignment that would block such routes. These findings clarify that in quasi-2D nanoporous films, adsorption within short nanometer channels can impart selectivity without sacrificing high throughput associated with Knudsen flow, offering a route to membranes that surpass conventional permeability–selectivity bounds.

Multilayer graphdiyne-based nanoporous membranes exhibit fast Knudsen-type gas transport for light species alongside significant suppression of heavier noble gases, yielding selectivity such as S(He/Xe) ~ 20 while maintaining high permeance enabled by a direct porosity of ~0.1% and pore sizes of ~1–5 nm. Temperature dependence and isotope tests confirm free molecular flow without activated barriers, while binary mixture measurements reveal adsorption-driven interactions between gas flows, where heavier species partially block pores and reduce helium permeation. Transport does not occur through intrinsic graphdiyne meshes but through straight-through nanometer-scale holes formed in the quasi-2D film microstructure. These insights highlight adsorption within nanoscale channels as a powerful lever to enhance selectivity in quasi-2D membranes without incurring drastic flux penalties. Future work should focus on tailoring pore size and length, controlling wall chemistry to modulate adsorption, exploring carbon allotropes with larger unit cells for aligned intrinsic porosity, improving mechanical stability for scalable applications, and systematic multi-component separation studies across wider temperature and pressure ranges.

Direct imaging of the active nanometer-scale holes at high resolution was limited by electron-beam-induced instability, preventing conclusive identification of their origin (intrinsic vs beam-induced defects). Low-temperature permeation could not be measured for gases with m > 4 due to setup constraints (e.g., condensation), and H2 was excluded at room temperature because of high mass spectrometry background. Pore size estimates are indirect, inferred from transport scaling, porosity comparisons, and morphology rather than direct metrology. The adsorption-based mechanism is supported by mixture and temperature trends but adsorption energies and kinetics were not measured directly. Intrinsic graphdiyne mesh transport was not observed, potentially due to small effective pore size and multilayer misalignment; thus, conclusions about intrinsic meshes are based on DFT and structural considerations.