An ångström-scale Janus aperture as a gas flow rectifier

Nature Materials (2026)Cite this article Directional mass transport in confined space is crucial to life and the water–energy–environment nexus. Despite progress in understanding biological and designing artificial ionic diodes at the atomic scale, rectifying charge-neutral molecular flow remains a challenge. Here we explore gas transport through an ångström-sized Janus aperture in graphene, which is created by feedback-controlled ozone etching and features oxygen-containing functional groups asymmetrically distributed around the edge. Ten representative gases with molecules of varying compositions, shapes and sizes were measured. The permeation coefficients indicate energy barrier-controlled transport. Rectified flow was consistently observed for seven different species including krypton, xenon, hydrogen, oxygen, nitrogen, carbon dioxide and nitrous oxide, with rectification ratios of up to two orders of magnitude for oxygen. We also performed high-throughput density functional theory calculations, obtaining energy barriers that vary distinctly as the flow direction is flipped, in agreement with experimental measurements and ab initio molecular dynamics simulations. We reveal the impact of the molecular polarizability on the rectified gas flow, while the important role of dipole and higher-order moments remains to be elucidated.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data supporting the findings of this study are available in the Article and its Supplementary Information. Source data are provided with this paper.Alberts, B. et al. Molecular Biology of the Cell 7th edn (W. W. Norton & Company, 2022).Motohiko, N. & Roderick, M. Structural basis of inward rectification: cytoplasmic pore of the G protein-gated inward rectifier GIRK1 at 1.8 Å resolution. Cell 111, 957–965 (2002).Article Google Scholar Hibino, H. et al. Inwardly rectifying potassium channels: their structure, function, and physiological roles. Physiol. Rev. 90, 291–366 (2010).Article CAS PubMed Google Scholar Mandala, V. S., Liao, S.-Y., Kwon, B. & Hong, M. Structural basis for asymmetric conductance of the influenza M2 proton channel investigated by solid-state NMR spectroscopy. J. Mol. Biol. 429, 2192–2210 (2017).Article CAS PubMed PubMed Central Google Scholar Huang, X., Kong, X. Y., Wen, L. & Jiang, L. Bioinspired ionic diodes: from unipolar to bipolar. Adv. Funct. Mater. 28, 1801079 (2018).Article Google Scholar Kavokine, N., Netz, R. R. & Bocquet, L. Fluids at the nanoscale: from continuum to subcontinuum transport. Annu. Rev. Fluid Mech. 53, 377–410 (2021).Article Google Scholar Karnik, R., Duan, C., Castelino, K., Daiguji, H. & Majumdar, A. Rectification of ionic current in a nanofluidic diode. Nano Lett. 7, 547–551 (2007).Article CAS PubMed Google Scholar Vlassiouk, I. & Siwy, Z. S. Nanofluidic diode. Nano Lett. 7, 552–556 (2007).Article CAS PubMed Google Scholar Tunuguntla, R. H. et al. Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins. Science 357, 792–796 (2017).Article CAS PubMed Google Scholar Chen, L. et al. Unidirectional ion transport in nanoporous carbon membranes with a hierarchical pore architecture. Nat. Commun. 12, 4650 (2021).Article CAS PubMed PubMed Central Google Scholar Zhang, X. P. et al. Asymmetric electrokinetic proton transport through 2D nanofluidic heterojunctions. ACS Nano 13, 4238–4245 (2019).Article CAS PubMed Google Scholar Lu, J. et al. Ultrafast rectifying counter-directional transport of proton and metal ions in metal-organic framework-based nanochannels. Sci. Adv. 8, eabl5070 (2022).Article CAS PubMed PubMed Central Google Scholar Siwy, Z. S. Ion-current rectification in nanopores and nanotubes with broken symmetry. Adv. Funct. Mater. 16, 735–746 (2006).Article CAS Google Scholar Gin, D. L. & Noble, R. D. Designing the next generation of chemical separation membranes. Science 332, 674–676 (2011).Article CAS PubMed Google Scholar Su, Y. et al. Separating water isotopologues using diffusion-regulatory porous materials. Nature 611, 289–294 (2022).Article CAS PubMed Google Scholar Woods, L. M. et al. Materials perspective on Casimir and van der Waals interactions. Rev. Mod. Phys. 88, 045003 (2016).Article Google Scholar Hermann, J., DiStasio, R. A. Jr & Tkatchenko, A. First-principles models for van der Waals interactions in molecules and materials: concepts, theory, and applications. Chem. Rev. 117, 4714–4758 (2017).Article CAS PubMed Google Scholar Shen, B. Y. et al. A single-molecule van der Waals compass. Nature 592, 541–544 (2021).Article CAS PubMed Google Scholar Yuan, Z. et al. Mechanism and prediction of gas permeation through sub-nanometer graphene pores: comparison of theory and simulation. ACS Nano 11, 7974–7987 (2017).Article CAS PubMed Google Scholar Yuan, Z., Misra, R. P., Rajan, A. G., Strano, M. S. & Blankschtein, D. Analytical prediction of gas permeation through graphene nanopores of varying sizes: understanding transitions across multiple transport regimes. ACS Nano 13, 11809–11824 (2019).Article CAS PubMed Google Scholar Liu, M. C., Song, D. X., Wang, X., Sun, C. Z. & Jing, D. W. Asymmetric two-layer porous membrane for gas separation. J. Phys. Chem. Lett. 11, 6359–6363 (2020).Article CAS PubMed Google Scholar Jiang, H. F. et al. Confined facilitated transport within covalent organic frameworks for propylene/propane membrane separation. Chem. Eng. J. 439, 135657 (2022).Article CAS Google Scholar Koenig, S. P., Wang, L. D., Pellegrino, J. & Bunch, J. S. Selective molecular sieving through porous graphene. Nat. Nanotechnol. 7, 728–732 (2012).Article CAS PubMed Google Scholar Sun, P. Z. et al. Exponentially selective molecular sieving through angstrom pores. Nat. Commun. 12, 7170 (2021).Article CAS PubMed PubMed Central Google Scholar Wang, L. D. et al. Molecular valves for controlling gas phase transport made from discrete ångström-sized pores in graphene. Nat. Nanotechnol. 10, 785–790 (2015).Article CAS PubMed Google Scholar Keerthi, A. et al. Ballistic molecular transport through two-dimensional channels. Nature 558, 420–424 (2018).Article CAS PubMed Google Scholar Wang, L. D. et al. Fundamental transport mechanisms, fabrication and potential applications of nanoporous atomically thin membranes. Nat. Nanotechnol. 12, 509–522 (2017).Article PubMed Google Scholar Radha, B. et al. Molecular transport through capillaries made with atomic-scale precision. Nature 538, 222–225 (2016).Article CAS PubMed Google Scholar Li, Z. W. et al. Breakdown of the Nernst–Einstein relation in carbon nanotube porins. Nat. Nanotechnol. 18, 177–183 (2023).Article CAS PubMed Google Scholar Boutilier, M. S. et al. Molecular sieving across centimeter-scale single-layer nanoporous graphene membranes. ACS Nano 11, 5726–5736 (2017).Article CAS PubMed Google Scholar Zhao, J. et al. Etching gas-sieving nanopores in single-layer graphene with an angstrom precision for high-performance gas mixture separation. Sci. Adv. 5, eaav1851 (2019).Article CAS PubMed PubMed Central Google Scholar Thiruraman, J. P. et al. Gas flow through atomic-scale apertures. Sci. Adv. 6, eabc7927 (2020).Article CAS PubMed PubMed Central Google Scholar Yuan, Z. et al. Predicting gas separation through graphene nanopore ensembles with realistic pore size distributions. ACS Nano 15, 1727–1740 (2021).Article CAS PubMed Google Scholar Chang, H. P. & Bard, A. J. Scanning tunneling microscopy studies of carbon oxygen reactions on highly oriented pyrolytic-graphite. J. Am. Chem. Soc. 113, 5588–5596 (1991).Article CAS Google Scholar Ozeki, S., Ito, T., Uozumi, K. & Nishio, I. Scanning tunneling microscopy of UV-induced gasification reaction on highly oriented pyrolytic graphite. Jpn. J. Appl. Phys. 35, 3772–3774 (1996).Article CAS Google Scholar Huang, S. Q. et al. Millisecond lattice gasification for high-density CO2- and O2-sieving nanopores in single-layer graphene. Sci. Adv. 7, eabf0116 (2021).Article CAS PubMed PubMed Central Google Scholar Huang, S. Q. et al. Single-layer graphene membranes by crack-free transfer for gas mixture separation. Nat. Commun. 9, 2632 (2018).Article PubMed PubMed Central Google Scholar Li, S. X. et al. Structure evolution of graphitic surface upon oxidation: insights by scanning tunneling microscopy. JACS Au 2, 723–730 (2022).Article CAS PubMed PubMed Central Google Scholar Mehio, N., Dai, S. & Jiang, D. E. Quantum mechanical basis for kinetic diameters of small gaseous molecules. J. Phys. Chem. A 118, 1150–1154 (2014).Article CAS PubMed Google Scholar Lee, W. C. et al. Enhanced water evaporation from Å-scale graphene nanopores. ACS Nano 16, 15382–15396 (2022).Article CAS PubMed PubMed Central Google Scholar Vallejos-Burgos, F., Coudert, F. X. & Kaneko, K. Air separation with graphene mediated by nanowindow-rim concerted motion. Nat. Commun. 9, 1812 (2018).Article PubMed PubMed Central Google Scholar Brenner, D. W. et al. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter 14, 783–802 (2002).Article CAS Google Scholar Chen, X. B. et al. Tunable pore size from sub-nanometer to a few nanometers in large-area graphene nanoporous atomically thin membranes. ACS Appl. Mater. Interfaces 13, 29926–29935 (2021).Article CAS PubMed Google Scholar Krivanek, O. L. et al. Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464, 571–574 (2010).Article CAS PubMed Google Scholar Zheng, L. M. et al. Robust ultraclean atomically thin membranes for atomic-resolution electron microscopy. Nat. Commun. 11, 541 (2020).Article CAS PubMed PubMed Central Google Scholar Sun, P. Z. et al. Limits on gas impermeability of graphene. Nature 579, 229–232 (2020).Article CAS PubMed Google Scholar Kresse, G. & Hafner, J. Ab initio molecular dynamics for open-shell transition metals. Phys. Rev. B 48, 13115–13118 (1993).Article CAS Google Scholar Kresse, G. & Furthmuller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 6, 15–50 (1996).Article CAS Google Scholar Kresse, G. & Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).Article CAS Google Scholar Blochl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).Article CAS Google Scholar Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).Article CAS Google Scholar Becke, A. D. On the large-gradient behavior of the density functional exchange energy. J. Chem. Phys. 85, 7184–7187 (1986).Article CAS Google Scholar Klimes, J., Bowler, D. R. & Michaelides, A. Chemical accuracy for the van der Waals density functional. J. Phys. Condens. Mat. 22, 022201 (2010).Article Google Scholar Klimes, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).Article Google Scholar Takeuchi, K. et al. Adsorption of CO2 on graphene: a combined TPD, XPS, and vdW-DF Study. J. Phys. Chem. C 121, 2807–2814 (2017).Article CAS Google Scholar Rodriguez, A., Schlichting, K. P., Poulikakos, D. & Hu, M. Ab initio energetic barriers of gas permeation across nanoporous graphene. ACS Appl. Mater. Interfaces 13, 39701–39710 (2021).Article CAS PubMed Google Scholar Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).Article CAS PubMed Google Scholar Langreth, D. C. et al. A density functional for sparse matter. J. Phys. Condens. Matter 21, 084203 (2009).Article CAS PubMed Google Scholar Berland, K. et al. Van der Waals forces in density functional theory: a review of the vdW-DF method. Rep. Prog. Phys. 78, 066501 (2015).Article PubMed Google Scholar Neugebauer, J. & Scheffler, M. Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111). Phys. Rev. B 46, 16067–16080 (1992).Article CAS Google Scholar Jiang, D. E., Cooper, V. R. & Dai, S. Porous graphene as the ultimate membrane for gas separation. Nano Lett. 9, 4019–4024 (2009).Article CAS PubMed Google Scholar Vahdat, M. T., Campi, D., Colonna, N., Marzari, N. & Agrawal, K. V. Gas transport across carbon nitride nanopores: a comparison of van der Waals functionals against the random-phase approximation. J. Phys. Chem. C 125, 18896–18904 (2021).Article CAS Google Scholar Hassani, N. et al. Gas permeability and selectivity of a porous WS2 monolayer. J. Phys. Chem. C 125, 25055–25066 (2021).Article CAS Google Scholar Wang, Y., Yang, Q. Y., Zhong, C. L. & Li, J. P. Theoretical investigation of gas separation in functionalized nanoporous graphene membranes. Appl. Surf. Sci. 407, 532–539 (2017).Article CAS Google Scholar Humphrey, W., Dalke, A. & Schulten, K. VMD: visual molecular dynamics. J. Mol. Graph. Model. 14, 33–38 (1996).Article CAS Google Scholar Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).Article CAS Google Scholar Wang, V., Xu, N., Liu, J. C., Tang, G. & Geng, W. T. VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using VASP code. Comput. Phys. Commun. 267, 108033 (2021).Article CAS Google Scholar Kühne, T. D. et al. CP2K: an electronic structure and molecular dynamics software package - Quickstep: efficient and accurate electronic structure calculations. J. Chem. Phys. 152, 194103 (2020).Article PubMed Google Scholar VandeVondele, J. & Hutter, J. Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. J. Chem. Phys. 127, 114105 (2007).Article PubMed Google Scholar Goedecker, S., Teter, M. & Hutter, J. Separable dual-space Gaussian pseudopotentials. Phys. Rev. B 54, 1703–1710 (1996).Article CAS Google Scholar Download referencesWe thank H. Zeng, Y. Liu and B. Feng for help in preparing the mechanically exfoliated graphene samples; Z. Jiang for help with the temperature-controlled stage; X. Han for help with Raman spectroscopy; X. Li for help in processing the DFT data; J. Du for discussions on the EELS measurements and data; the Electron Microscopy Laboratory at Peking University for the use of Cs-corrected Nion U-HERMES200 scanning transmission electron microscope; Peking Nanofab for fabrication of the microcavities; the High-performance Computing Platform of Peking University for supporting the DFT calculations; and the Texas Advanced Computing Center (TACC) at the University of Texas at Austin for the use of the parallel computing resource Lonestar6. This work was funded by the National Natural Science Foundation of China (NSFC), including grant number 62274004 (L.W.), grant number 52521007 (B.S.), grant number T2188101 (L.W.), grant number 52076002 (B.S.) and grant number 62004004 (L.W.) and the Scientific Research Innovation Capability Support Project for Young Faculty (ZYGXQNJSKYCXNLZCXM-E1) (B.S.) from the Ministry of Education of China. B.S. acknowledges support by the New Cornerstone Science Foundation through the XPLORER PRIZE. The work was also facilitated by the Instrumental Analysis Fund from Peking University.These authors contributed equally: Hongwei Duan, Jing Yang, Nianjie Liang, Xiaobo Chen.National Key Laboratory of Advanced Micro and Nano Manufacture Technology, School of Integrated Circuits, Peking University, Beijing, ChinaHongwei Duan, Jing Yang, Xiaobo Chen, Shengping Zhang, Zeyu Zhuang, Ruiyang Song, Junhe Tong, Bai Song & Luda WangAcademy for Advanced Interdisciplinary Studies, Peking University, Beijing, ChinaHongwei Duan, Shengping Zhang & Luda WangSchool of Mechanics and Engineering Science, Peking University, Beijing, ChinaNianjie Liang & Bai SongBeijing Innovation Center for Engineering Science and Advanced Technology, Peking University, Beijing, ChinaNianjie Liang & Bai SongOden Institute for Computational Engineering and Sciences, Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX, USAAnshul Saxena & Narayana R. AluruState Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, ChinaKaihui LiuBeijing Advanced Innovation Center for Integrated Circuits, Beijing, ChinaLuda WangTechnology Innovation Center of Graphene Metrology and Standardization for State Market Regulation, Beijing Graphene Institute, Beijing, ChinaLuda WangSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarL.W. and B.S. conceived the idea and supervised the project, focusing on the experiments and simulations, respectively. X.C., H.D. and J.Y. built the ozone etching system. H.D., J.Y. and Z.Z. fabricated and characterized the resonator devices. H.D. and J.Y. conducted the transport measurements. N.L. established the framework for the DFT simulations in this work. N.L. and J.Y. performed the DFT calculations. A.S. and N.R.A. performed the AIMD simulations. H.D., J.Y. and Z.Z. processed the experimental data. S.Z. and J.T. performed STEM and EELS characterizations. L.W., B.S., H.D., N.L., J.Y., S.Z., N.R.A., A.S., K.L. and R.S. analysed and discussed all the results. B.S., L.W., S.Z., H.D., N.L., J.Y., N.R.A. and A.S. wrote the paper. H.D., J.Y., N.L. and X.C. contributed equally. All authors contributed to reviewing and editing of the paper.Correspondence to Bai Song or Luda Wang.The authors declare no competing interests.Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.The apertures are indexed in the order of increasing size as measured by the vdW diameter (DvdW), and are also named based on the number of carbon atoms removed and oxygen atoms added. The blue circles visualize the effective sizes of the apertures. Most of these relatively small apertures have Janus structures, except for two of them which are labeled with blue text.The apertures are indexed in the order of increasing size as measured by the vdW diameter (DvdW), and are also named based on the number of carbon atoms removed and oxygen atoms added. The blue circles visualize the effective sizes of the apertures. Many of these relatively large apertures do not have Janus structures, and are labeled with blue text.The snapshots a-c are taken at 0 fs, 500 fs and 1000 fs, respectively, for reverse transport, while the snapshots d-f are taken correspondingly for forward transport. The reverse energy barrier is higher than the forward barrier since the gas molecule is not able to transport from left-to-right even after 2 ps. These results qualitatively agree with the static DFT energy barrier calculations. Animation of the transport process is provided as Supplementary Video 1.The snapshots a-c are taken at 0 fs, 750 fs and 1500 fs, respectively, for reverse transport, while the snapshots d-f are taken correspondingly for forward transport. Notably, the O2 molecule cannot pass in either direction, which agrees with the static DFT calculations that show higher energy barriers without non-local vdW interactions (Supplementary Fig. 24). Animation of the transport process is provided as Supplementary Video 3.Supplementary Notes 1–10, Figs. 1–37, Tables 1 and 2 and references.Animation of O2 translocation through the C10-O6 aperture for an applied force of 0.8 eV Å−1 per atom with the aperture frozen. This video visualizes AIMD trajectories corresponding to Extended Data Fig. 3. The left panel depicts reverse transport, while the right panel shows forward transport.Animation of O2 translocation through the C10-O6 aperture for an applied force of 1.0 eV Å−1 per atom with the aperture frozen. This video visualizes AIMD trajectories corresponding to Supplementary Fig. 32. The left panel depicts reverse transport, while the right panel shows forward transport.Animation of O2 translocation through the C10-O6 aperture for an applied force of 0.8 eV Å−1 per atom with the aperture frozen but without non-local vdW interactions. This video visualizes AIMD trajectories corresponding to Extended Data Fig. 4. The left panel depicts reverse transport, while the right panel shows forward transport.Animation of the thermal fluctuations of the C10-O6 aperture. This video visualizes AIMD trajectories corresponding to Supplementary Fig. 33.Animation of O2 translocation through the C11-O8 aperture under an applied force of 0.1 eV Å−1 per atom without freezing the aperture. This video visualizes AIMD trajectories corresponding to Supplementary Fig. 35. The left panel depicts reverse transport, while the right panel shows forward transport.Animation of O2 translocation through the C11-O8 aperture under an applied force of 0.2 eV Å−1 per atom without freezing the aperture. This video visualizes AIMD trajectories corresponding to Supplementary Fig. 36. The left panel depicts reverse transport, while the right panel shows forward transport.Animation of O2 translocation through the C11-O8 aperture under an applied force of 0.15 eV Å−1 per atom without freezing the aperture. This video visualizes AIMD trajectories corresponding to Supplementary Fig. 37. The left panel depicts reverse transport, while the right panel shows forward transport.Raw data for Fig. 2b,c,e,g,i.Raw data for Fig. 3b–d.Raw data for Fig. 4a–f.Raw data for Fig. 5c–e.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsDuan, H., Yang, J., Liang, N. et al. An ångström-scale Janus aperture as a gas flow rectifier. Nat. Mater. (2026). https://doi.org/10.1038/s41563-026-02513-wDownload citationReceived: 17 September 2024Accepted: 22 January 2026Published: 25 February 2026Version of record: 25 February 2026DOI: https://doi.org/10.1038/s41563-026-02513-wAnyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative