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Molecular size-dependent subcontinuum solvent permeation and ultrafast nanofiltration across nanoporous graphene membranes


Selective solvent and solute transport across nanopores is fundamental to membrane separations, yet it remains poorly understood, especially for non-aqueous systems. Here, we design a chemically robust nanoporous graphene membrane and study molecular transport in various organic liquids under subnanometre confinement. We show that the nature of the solvent can modulate solute diffusion across graphene nanopores, and that breakdown of continuum flow occurs when pore size approaches the solvent’s smallest molecular cross-section. By holistically engineering membrane support, modelling pore creation and defect management, high rejection and ultrafast organic solvent nanofiltration of dye molecules and separation of hexane isomers are achieved. The membranes exhibit stable fluxes across a range of solvents, consistent with flow across rigid pores whose size is independent of the solvent. These results demonstrate that nanoporous graphene is a rich materials system for controlling subcontinuum flow that could enable new membranes for a range of challenging separation needs.

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Fig. 1: Design and architecture of solvent-compatible atomically thin nanoporous graphene membranes.
Fig. 2: Solute diffusion across nanoporous atomically thin graphene membranes.
Fig. 3: Subcontinuum pressure-driven liquid flow through atomically thin nanoporous graphene membranes.
Fig. 4: Stability of atomically thin nanoporous graphene membranes demonstrated in diffusion and pressure-driven experiments.
Fig. 5: Organic solvent nanofiltration with atomically thin nanoporous graphene membranes.

Data availability

All data that support the findings of this study are available in the main text, figures and Supplementary Information. Source data for the main figures are provided with this paper. Source data for Supplementary Figs. 1–19 are available upon reasonable request from the corresponding author.

Code availability

Code for Supplementary Figs. 1215 is available upon reasonable request from the corresponding author.


  1. 1.

    Bocquet, L. & Charlaix, E. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39, 1073–1095 (2010).

    CAS  Article  Google Scholar 

  2. 2.

    Bocquet, L. & Tabeling, P. Physics and technological aspects of nanofluidics. Lab. Chip 14, 3143–3158 (2014).

    CAS  Article  Google Scholar 

  3. 3.

    Bocquet, L. Nanofluidics coming of age. Nat. Mater. 19, 254–256 (2020).

    CAS  Article  Google Scholar 

  4. 4.

    Holt, J. K. et al. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312, 1034–1037 (2006).

    CAS  Article  Google Scholar 

  5. 5.

    Marchetti, P., Jimenez Solomon, M. F., Szekely, G. & Livingston, A. G. Molecular separation with organic solvent nanofiltration: a critical review. Chem. Rev. 114, 10735–10806 (2014).

    CAS  Article  Google Scholar 

  6. 6.

    Chmiola, J. et al. Anomalous increase in carbon capacitance at pore sizes less than 1 nanometer. Science 313, 1760–1763 (2006).

    CAS  Article  Google Scholar 

  7. 7.

    Siria, A. et al. Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 494, 455–458 (2013).

    CAS  Article  Google Scholar 

  8. 8.

    Xie, J., Liang, Z. & Lu, Y.-C. Molecular crowding electrolytes for high-voltage aqueous batteries. Nat. Mater. 19, 1006–1011 (2020).

    CAS  Article  Google Scholar 

  9. 9.

    Grommet, A. B., Feller, M. & Klajn, R. Chemical reactivity under nanoconfinement. Nat. Nanotechnol. 15, 256–271 (2020).

    CAS  Article  Google Scholar 

  10. 10.

    Branton, D. et al. The potential and challenges of nanopore sequencing. Nat. Biotechnol. 26, 1146–1153 (2008).

    CAS  Article  Google Scholar 

  11. 11.

    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 

  12. 12.

    Majumder, M., Chopra, N., Andrews, R. & Hinds, B. J. Enhanced flow in carbon nanotubes. Nature 438, 44 (2005).

    CAS  Article  Google Scholar 

  13. 13.

    Esfandiar, A. et al. Size effect in ion transport through Angstrom-scale slits. Science 358, 511–513 (2017).

    CAS  Article  Google Scholar 

  14. 14.

    Feng, J. et al. Observation of ionic Coulomb blockade in nanopores. Nat. Mater. 15, 850–855 (2016).

    CAS  Article  Google Scholar 

  15. 15.

    Cheng, C., Jiang, G., Simon, G. P., Liu, J. Z. & Li, D. Low-voltage electrostatic modulation of ion diffusion through layered graphene-based nanoporous membranes. Nat. Nanotechnol. 13, 685–690 (2018).

    CAS  Article  Google Scholar 

  16. 16.

    Fumagalli, L. et al. Anomalously low dielectric constant of confined water. Science 360, 1339–1342 (2018).

    CAS  Article  Google Scholar 

  17. 17.

    Mouterde, T. et al. Molecular streaming and its voltage control in Angström-scale channels. Nature 567, 87–90 (2019).

    CAS  Article  Google Scholar 

  18. 18.

    Siria, A., Bocquet, M. L. & Bocquet, L. New avenues for the large-scale harvesting of blue energy. Nat. Rev. Chem. 1, 0091 (2017).

    CAS  Article  Google Scholar 

  19. 19.

    Tang, C. Y., Zhao, Y., Wang, R., Hélix-Nielsen, C. & Fane, A. G. Desalination by biomimetic aquaporin membranes: review of status and prospects. Desalination 308, 34–40 (2013).

    CAS  Article  Google Scholar 

  20. 20.

    Jain, T. et al. Heterogeneous sub-continuum ionic transport in statistically isolated graphene nanopores. Nat. Nanotechnol. 10, 1053–1057 (2015).

    CAS  Article  Google Scholar 

  21. 21.

    Wang, L. et al. Fundamental transport mechanisms, fabrication and potential applications of nanoporous atomically thin membranes. Nat. Nanotechnol. 12, 509–522 (2017).

    CAS  Article  Google Scholar 

  22. 22.

    Faucher, S. et al. Critical knowledge gaps in mass transport through single-digit nanopores: a review and perspective. J. Phys. Chem. C 123, 21309–21326 (2019).

    CAS  Article  Google Scholar 

  23. 23.

    Falk, K., Coasne, B., Pellenq, R., Ulm, F. J. & Bocquet, L. Subcontinuum mass transport of condensed hydrocarbons in nanoporous media. Nat. Commun. 6, 6949 (2015).

    CAS  Article  Google Scholar 

  24. 24.

    King, H. E. et al. Pore architecture and connectivity in gas shale. Energy Fuels 29, 1375–1390 (2015).

    CAS  Article  Google Scholar 

  25. 25.

    Vincent, O., Szenicer, A. & Stroock, A. D. Capillarity-driven flows at the continuum limit. Soft Matter 12, 6656–6661 (2016).

    CAS  Article  Google Scholar 

  26. 26.

    Zhong, J. et al. Exploring anomalous fluid behavior at the nanoscale: direct visualization and quantification via nanofluidic devices. Acc. Chem. Res. 53, 347–357 (2020).

    CAS  Article  Google Scholar 

  27. 27.

    Epsztein, R., DuChanois, R. M., Ritt, C. L., Noy, A. & Elimelech, M. Towards single-species selectivity of membranes with subnanometre pores. Nat. Nanotechnol. 15, 426–436 (2020).

    CAS  Article  Google Scholar 

  28. 28.

    Thompson, K. A. et al. N-Aryl-linked spirocyclic polymers for membrane separations of complex hydrocarbon mixtures. Science 369, 310–315 (2020).

    CAS  Article  Google Scholar 

  29. 29.

    Celebi, K. et al. Ultimate permeation across atomically thin porous graphene. Science 344, 289–292 (2014).

    CAS  Article  Google Scholar 

  30. 30.

    Cohen-Tanugi, D. & Grossman, J. C. Water desalination across nanoporous graphene. Nano Lett. 12, 3602–3608 (2012).

    CAS  Article  Google Scholar 

  31. 31.

    Wyss, R. M., Tian, T., Yazda, K., Park, H. G. & Shih, C. J. Macroscopic salt rejection through electrostatically gated nanoporous graphene. Nano Lett. 19, 6400–6409 (2019).

    CAS  Article  Google Scholar 

  32. 32.

    Yang, Y. et al. Large-area graphene-nanomesh/carbon-nanotube hybrid membranes for ionic and molecular nanofiltration. Science 364, 1057–1062 (2019).

    CAS  Article  Google Scholar 

  33. 33.

    Prozorovska, L. & Kidambi, P. R. State-of-the-art and future prospects for atomically thin membranes from 2D materials. Adv. Mater. 30, 1801179 (2018).

    Article  CAS  Google Scholar 

  34. 34.

    Heiranian, M., Farimani, A. B. & Aluru, N. R. Water desalination with a single-layer MoS2 nanopore. Nat. Commun. 6, 8616 (2015).

    CAS  Article  Google Scholar 

  35. 35.

    Thiruraman, J. P., Masih Das, P. & Drndić, M. Stochastic ionic transport in single atomic zero-dimensional pores. ACS Nano 14, 11831–11845 (2020).

    CAS  Article  Google Scholar 

  36. 36.

    Culp, T. E. et al. Nanoscale control of internal inhomogeneity enhances water transport in desalination membranes. Science 371, 72–75 (2021).

    CAS  Article  Google Scholar 

  37. 37.

    Marchena, M. et al. Dry transfer of graphene to dielectrics and flexible substrates using polyimide as a transparent and stable intermediate layer. 2D Mater. 5, 035022 (2018).

    Article  CAS  Google Scholar 

  38. 38.

    Kim, S. et al. Robust graphene wet transfer process through low molecular weight polymethylmethacrylate. Carbon 98, 352–357 (2016).

    CAS  Article  Google Scholar 

  39. 39.

    Boutilier, M. S. et al. Implications of permeation through intrinsic defects in graphene on the design of defect-tolerant membranes for gas separation. ACS Nano 8, 841–849 (2014).

    CAS  Article  Google Scholar 

  40. 40.

    Boutilier, M. S. H. et al. Molecular sieving across centimeter-scale single-layer nanoporous graphene membranes. ACS Nano 11, 5726–5736 (2017).

    CAS  Article  Google Scholar 

  41. 41.

    O’Hern, S. C. et al. Selective molecular transport through intrinsic defects in a single layer of CVD graphene. ACS Nano 6, 10130–10138 (2012).

    Article  CAS  Google Scholar 

  42. 42.

    O’Hern, S. C. et al. Selective ionic transport through tunable subnanometer pores in single-layer graphene membranes. Nano Lett. 14, 1234–1241 (2014).

    Article  CAS  Google Scholar 

  43. 43.

    Karan, S., Jiang, Z. & Livingston, A. G. Sub-10 nm polyamide nanofilms with ultrafast solvent transport for molecular separation. Science 348, 1347–1351 (2015).

    CAS  Article  Google Scholar 

  44. 44.

    Yang, Q. et al. Ultrathin graphene-based membrane with precise molecular sieving and ultrafast solvent permeation. Nat. Mater. 16, 1198–1202 (2017).

    CAS  Article  Google Scholar 

  45. 45.

    Gobin, O. C., Reitmeier, S. J., Jentys, A. & Lercher, J. A. Role of the surface modification on the transport of hexane isomers in ZSM-5. J. Phys. Chem. C 115, 1171–1179 (2011).

    CAS  Article  Google Scholar 

  46. 46.

    Funke, H. H., Argo, A. M., Falconer, J. L. & Noble, R. D. Separations of cyclic, branched, and linear hydrocarbon mixtures through silicalite membranes. Ind. Eng. Chem. Res. 36, 137–143 (1997).

    CAS  Article  Google Scholar 

  47. 47.

    Bárcia, P. S., Zapata, F., Silva, J. A. C., Rodrigues, A. E. & Chen, B. Kinetic separation of hexane isomers by fixed-bed adsorption with a microporous metal—organic framework. J. Phys. Chem. B 111, 6101–6103 (2007).

    Article  CAS  Google Scholar 

  48. 48.

    Koh, D. Y., McCool, B. A., Deckman, H. W. & Lively, R. P. Reverse osmosis molecular differentiation of organic liquids using carbon molecular sieve membranes. Science 353, 804–807 (2016).

    CAS  Article  Google Scholar 

  49. 49.

    Heiranian, M., Taqieddin, A. & Aluru, N. R. Revisiting Sampson’s theory for hydrodynamic transport in ultrathin nanopores. Phys. Rev. Res. 2, 043153 (2020).

    CAS  Article  Google Scholar 

  50. 50.

    O’Hern, S. C. et al. Nanofiltration across defect-sealed nanoporous monolayer graphene. Nano Lett. 15, 3254–3260 (2015).

    Article  CAS  Google Scholar 

  51. 51.

    Dong, G. et al. Energy-efficient separation of organic liquids using organosilica membranes via a reverse osmosis route. J. Memb. Sci. 597, 117758 (2020).

    CAS  Article  Google Scholar 

  52. 52.

    Liu, Q. et al. Molecular dynamics simulation of water-ethanol separation through monolayer graphene oxide membranes: significant role of O/C ratio and pore size. Sep. Purif. Technol. 224, 219–226 (2019).

    CAS  Article  Google Scholar 

  53. 53.

    Jang, D., Idrobo, J. C., Laoui, T. & Karnik, R. Water and solute transport governed by tunable pore size distributions in nanoporous graphene membranes. ACS Nano 11, 10042–10052 (2017).

    CAS  Article  Google Scholar 

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This work was funded by Eni S.p.A. through the MIT Energy Initiative. Ion irradiation and SEM imaging were performed at the MRSEC Shared Experimental Facilities supported by the National Science Foundation under award number DMR-0819762 at MIT. We thank S. Carminati, L. Bonoldi, L. Wang, S. Zhang, A. Persad, C. M. Chow and R. Field for valuable discussions.

Author information




R.K. and C.C. conceived the project and designed the research. C.C. fabricated the membranes, performed the imaging characterization, carried out transport measurements and analysed the results. S.A.I. performed the Monte Carlo simulations. All authors were involved in the analysis and discussion of the results. C.C. and R.K. wrote the paper.

Corresponding author

Correspondence to Rohit Karnik.

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Competing interests

C.C. and S.A.I. declare no competing interests. R.K. is coinventor on patents and patent applications on nanoporous graphene membranes.

Additional information

Peer review information Nature Nanotechnology thanks Aleksandra Radenovic, Meni Wanunu and the other, anonymous, reviewer(s) 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.

Supplementary information

Supplementary Information

Detailed Materials and Methods, Figs. 1–19 and Tables 1–4.

Source data

Source Data Fig. 2

Statistical source data for solute diffusion across nanoporous atomically thin graphene membranes.

Source Data Fig. 3

Statistical source data for subcontinuum pressure-driven liquid flow through nanoporous atomically thin graphene membranes.

Source Data Fig. 4

Statistical source data for stability of nanoporous atomically thin graphene membranes.

Source Data Fig. 5

Statistical source data for organic solvent nanofiltration with nanoporous atomically thin graphene membranes.

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Cheng, C., Iyengar, S.A. & Karnik, R. Molecular size-dependent subcontinuum solvent permeation and ultrafast nanofiltration across nanoporous graphene membranes. Nat. Nanotechnol. (2021).

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