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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.


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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. 16, 989–995 (2021).

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