Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Beyond steric selectivity of ions using ångström-scale capillaries

Nature Nanotechnology volume 18, pages 596–601 (2023)Cite this article

Subjects

Abstract

Ion-selective channels play a key role in physiological processes and are used in many technologies. Although biological channels can efficiently separate same-charge ions with similar hydration shells, it remains a challenge to mimic such exquisite selectivity using artificial solid-state channels. Although there are several nanoporous membranes that show high selectivity with respect to certain ions, the underlying mechanisms are based on the hydrated ion size and/or charge. There is a need to rationalize the design of artificial channels to make them capable of selecting between similar-sized same-charge ions, which, in turn, requires an understanding of why and how such selectivity can occur. Here we study ångström-scale artificial channels made by van der Waals assembly, which are comparable in size with typical ions and carry little residual charge on the channel walls. This allows us to exclude the first-order effects of steric- and Coulomb-based exclusion. We show that the studied two-dimensional ångström-scale capillaries can distinguish between same-charge ions with similar hydrated diameters. The selectivity is attributed to different positions occupied by ions within the layered structure of nanoconfined water, which depend on the ion-core size and differ for anions and cations. The revealed mechanism points at the possibilities of ion separation beyond simple steric sieving.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Conductivity of salt solutions under Å-scale confinement.
Fig. 2: Effect of ion-core size on their mobility under Å-scale confinement.
Fig. 3: Ion positioning in 2D water and mobility reduction.

Similar content being viewed by others

Data availability

The data supporting the findings of this study are available within the article, extended data and its Supplementary Information. Source data are provided with this paper.

References

  1. Nightingale, E. R. Phenomenological theory of ion solvation. Effective radii of hydrated ions. J. Phys. Chem. 63, 1381–1387 (1959).

    Article  CAS  Google Scholar 

  2. Tansel, B. Significance of thermodynamic and physical characteristics on permeation of ions during membrane separation: hydrated radius, hydration free energy and viscous effects. Sep. Purif. Technol. 86, 119–126 (2012).

    Article  CAS  Google Scholar 

  3. Speight, J. Lange’s Handbook of Chemistry 16th edn (McGraw Hill Education, 2005).

  4. Jentsch, T. J. & Günther, W. Chloride channels: an emerging molecular picture. BioEssays 19, 117–126 (1997).

    Article  CAS  Google Scholar 

  5. Hille, B. Ion Channels of Excitable Membranes (Sinauer, 2001).

  6. Dudev, T. & Lim, C. Factors governing the Na+ vs K+ selectivity in sodium ion channels. J. Am. Chem. Soc. 132, 2321–2332 (2010).

    Article  CAS  Google Scholar 

  7. Lj, M. The penetration of some cations into muscle. J. Gen. Physiol. 42, 817–829 (1959).

    Article  Google Scholar 

  8. Doyle, D. A. et al. The structure of the potassium channel: molecular basis of K+ conduction and selectivity. Science 280, 69–77 (1998).

    Article  CAS  Google Scholar 

  9. Sahu, S. & Zwolak, M. Colloquium: ionic phenomena in nanoscale pores through 2D materials. Rev. Mod. Phys. 91, 021004 (2019).

    Article  CAS  Google Scholar 

  10. 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).

    Article  CAS  Google Scholar 

  11. Gao, J., Feng, Y., Guo, W. & Jiang, L. Nanofluidics in two-dimensional layered materials: inspirations from nature. Chem. Soc. Rev. 46, 5400–5424 (2017).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  13. Epsztein, R., Shaulsky, E., Dizge, N., Warsinger, D. M. & Elimelech, M. Role of ionic charge density in Donnan exclusion of monovalent anions by nanofiltration. Environ. Sci. Technol. 52, 4108–4116 (2018).

    Article  CAS  Google Scholar 

  14. 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).

    Article  CAS  Google Scholar 

  15. Thiruraman, J. P., Masih Das, P. & Drndić, M. Ions and water dancing through atom-scale holes: a perspective toward ‘size zero’. ACS Nano 14, 3736–3746 (2020).

    Article  CAS  Google Scholar 

  16. Karahan, H. E. et al. MXene materials for designing advanced separation membranes. Adv. Mater. 32, 1906697 (2020).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  18. Ma, J. et al. Drastically reduced ion mobility in a nanopore due to enhanced pairing and collisions between dehydrated ions. J. Am. Chem. Soc. 141, 4264–4272 (2019).

    Article  CAS  Google Scholar 

  19. Fu, Y. et al. Dehydration-determined ion selectivity of graphene subnanopores. ACS Appl. Mater. Interfaces 12, 24281–24288 (2020).

    Article  CAS  Google Scholar 

  20. Li, X. et al. Fast and selective fluoride ion conduction in sub-1-nanometer metal–organic framework channels. Nat. Commun. 10, 2490 (2019).

    Article  Google Scholar 

  21. Xin, W. et al. Biomimetic KcsA channels with ultra-selective K+ transport for monovalent ion sieving. Nat. Commun. 13, 1701 (2022).

    Article  CAS  Google Scholar 

  22. You, Y. et al. Angstrofluidics: walking to the limit. Annu. Rev. Mater. Res. 52, 189–218 (2022).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  24. Gopinadhan, K. et al. Complete steric exclusion of ions and proton transport through confined monolayer water. Science 363, 145–148 (2019).

    Article  CAS  Google Scholar 

  25. Radha, B. et al. Molecular transport through capillaries made with atomic-scale precision. Nature 538, 222–225 (2016).

    Article  CAS  Google Scholar 

  26. Haynes, W. M. CRC Handbook of Chemistry and Physics 96th edn (CRC Press, 2003).

  27. Rollings, R. C., Kuan, A. T. & Golovchenko, J. A. Ion selectivity of graphene nanopores. Nat. Commun. 7, 11408 (2016).

    Article  CAS  Google Scholar 

  28. Hong, S. et al. Scalable graphene-based membranes for ionic sieving with ultrahigh charge selectivity. Nano Lett. 17, 728–732 (2017).

    Article  CAS  Google Scholar 

  29. Perram, J. W. & Stiles, P. J. On the nature of liquid junction and membrane potentials. Phys. Chem. Chem. Phys. 8, 4200–4213 (2006).

    Article  CAS  Google Scholar 

  30. Yu, Y. et al. Charge asymmetry effect in ion transport through angstrom-scale channels. J. Phys. Chem. C 123, 1462–1469 (2019).

    Article  CAS  Google Scholar 

  31. Razmjou, A. et al. Lithium ion-selective membrane with 2D subnanometer channels. Water Res. 159, 313–323 (2019).

    Article  CAS  Google Scholar 

  32. Bajaj, P., Richardson, J. O. & Paesani, F. Ion-mediated hydrogen-bond rearrangement through tunnelling in the iodide–dihydrate complex. Nat. Chem. 11, 367–374 (2019).

    Article  CAS  Google Scholar 

  33. Tocci, G., Joly, L. & Michaelides, A. Friction of water on graphene and hexagonal boron nitride from ab initio methods: very different slippage despite very similar interface structures. Nano Lett. 14, 6872–6877 (2014).

    Article  CAS  Google Scholar 

  34. Grosjean, B. et al. Chemisorption of hydroxide on 2D materials from DFT calculations: graphene versus hexagonal boron nitride. J. Phys. Chem. Lett. 7, 4695–4700 (2016).

    Article  CAS  Google Scholar 

  35. Robin, P., Kavokine, N. & Bocquet, L. Modeling of emergent memory and voltage spiking in ionic transport through angstrom-scale slits. Science 373, 687–691 (2021).

    Article  CAS  Google Scholar 

  36. Sajja, R. et al. Hydrocarbon contamination in angström-scale channels. Nanoscale 13, 9553–9560 (2021).

    Article  CAS  Google Scholar 

  37. Berendsen, H. J. C., Grigera, J. R. & Straatsma, T. P. The missing term in effective pair potentials. J. Phys. Chem. 91, 6269–6271 (1987).

    Article  CAS  Google Scholar 

  38. Koneshan, S., Rasaiah, J. C., Lynden-Bell, R. M. & Lee, S. H. Solvent structure, dynamics, and ion mobility in aqueous solutions at 25 °C. J. Phys. Chem. B 102, 4193–4204 (1998).

    Article  CAS  Google Scholar 

  39. Agieienko, V. N., Kolesnik, Y. V. & Kalugin, O. N. Structure, solvation, and dynamics of Mg2+, Ca2+, Sr2+, and Ba2+ complexes with 3-hydroxyflavone and perchlorate anion in acetonitrile medium: a molecular dynamics simulation study. J. Chem. Phys. 140, 194501 (2014).

    Article  Google Scholar 

  40. Lorentz, H. A. Ueber die Anwendung des Satzes vom Virial in der kinetischen Theorie der Gase. Ann. Phys. 248, 127–136 (1881).

    Article  Google Scholar 

  41. Berthelot, D. Sur le mélange des gaz. Compt. Rendus 126, 1703–1706 (1898).

    Google Scholar 

  42. Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

    Article  CAS  Google Scholar 

  43. Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519 (1984).

    Article  Google Scholar 

  44. Hoover, W. G. Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31, 1695–1697 (1985).

    Article  CAS  Google Scholar 

  45. Delley, B. From molecules to solids with the DMol3 approach. J. Chem. Phys. 113, 7756–7764 (2000).

    Article  CAS  Google Scholar 

  46. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  CAS  Google Scholar 

  47. Delley, B. An all‐electron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 92, 508–517 (1990).

    Article  CAS  Google Scholar 

  48. Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H–Pu. J. Chem. Phys. 132, 154104 (2010).

    Article  Google Scholar 

Download references

Acknowledgements

B.R. acknowledges funding from the Royal Society University Research Fellowship URF\R1\180127 and Philip Leverhulme Prize PLP-2021-262. B.R., S.G., A.I. and Y.Y. acknowledge funding from the European Union’s H2020 Framework Programme/ERC Starting Grant 852674—AngstroCAP, RS enhancement award RF\ERE\210016 and EPSRC strategic equipment grant EP/W006502/1. A.K. acknowledges the Ramsay Memorial Fellowship, Royal Society International Exchanges grant IES\R1\201028 and EPSRC strategic equipment grant EP/W006502/1. F.W. acknowledges the Youth Innovation Promotion Association CAS (2020449) and Hefei Advanced Computing Center. H.J and M.N.-A. acknowledge the high-performance computing support from Shahid Rajaee Teacher Training University.

Author information

Authors and Affiliations

  1. Department of Physics and Astronomy, School of Natural Sciences, The University of Manchester, Manchester, UK

    Solleti Goutham, Abdulghani Ismail, Ankit Bhardwaj, Yi You, Marcos Vinicius Surmani Martins & Boya Radha

  2. National Graphene Institute, The University of Manchester, Manchester, UK

    Solleti Goutham, Ashok Keerthi, Abdulghani Ismail, Ankit Bhardwaj, Yi You, Marcos Vinicius Surmani Martins & Boya Radha

  3. Department of Chemistry, School of Natural Sciences, The University of Manchester, Manchester, UK

    Ashok Keerthi

  4. Department of Physics, Shahid Rajaee Teacher Training University, Tehran, Iran

    Hossein Jalali, Nasim Hassani & Mehdi Neek-Amal

  5. Chinese Academy of Sciences Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei, China

    Yiheng Li, Haoke Peng & Fengchao Wang

  6. Department of Physics, University of Antwerp, Antwerp, Belgium

    Mehdi Neek-Amal

Authors
  1. Solleti Goutham
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ashok Keerthi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdulghani Ismail
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ankit Bhardwaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hossein Jalali
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yi You
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Yiheng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Nasim Hassani
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Haoke Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Marcos Vinicius Surmani Martins
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Fengchao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Mehdi Neek-Amal
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Boya Radha
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

B.R. designed and directed the project. A.K., Y.Y. and A.B. carried out the sample fabrication of several Å-channel devices. S.G. and A.I. performed the ion conductance measurements and their analysis. S.G. conducted the diffusion measurements and their analysis. A.K. and M.V.S.M. carried out the sample characterization. H.J., N.H., M.N.-A., Y.L., H.P. and F.W. provided the theoretical simulations. B.R., S.G., A.I. and A.K. wrote the manuscript with inputs from M.N.-A. and F.W. All the authors contributed to discussions.

Corresponding author

Correspondence to Boya Radha.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Nanotechnology thanks Nikita Kavokine and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Fabrication process flow.

The sequence of fabrication steps is indicated by the arrows. (a) Freestanding silicon nitride (SiNx) membrane (100 × 100 µm2) was prepared by wet etching. (b) Rectangular aperture (typically, 3 × 26 µm2) was made in the membrane using photolithography and dry etching. (c) Bottom 2D crystal was placed on top of the aperture. (d) Strips of bilayer graphene were transferred onto the bottom crystal. Then the two-layer assembly was dry etched from the back with the SiNx aperture serving as a protective mask. (e) Another 2D crystal (top layer) was placed on top to cover the entire etched microhole. (f) A gold stripe was deposited on top of the trilayer assembly. (g) This stripe was used as a mask for subsequent dry etching. The inset shows schematically a cross-section of the resulting Å-channels.

Extended Data Fig. 2 Optical micrographs of Å-channel devices.

(a) Top view of the trilayer assembly (hBN-graphene spacers-hBN) before depositing a gold mask. The graphene spacer is not clearly visible as it is very thin (height, ~0.7 nm). The rectangular microhole in the SiNx membrane is seen in dark blue. Top view of the same device (b) after the gold mask was deposited and (c) after etching away the exposed areas of the 2D crystals.

Extended Data Fig. 3 Equilibrium geometries and electrostatic potential (ESP) map of the hydrated anions.

The optimized structures and the natural bond orbitals (NBO) charges (black numbers) and ion distance to the water molecule (green numbers) of hydrated anions (a) F−, (b) Cl−, (c) I−, and (d) ClO4−in bulk with six water molecules (right hand side, RHS-bottom of each panel) and the hydrated anions between graphene layers (left hand side, LHS-bottom is zoomed in structure of each panel). In each panel, RHS-up is the electrostatic potential energy maps of the hydrated anions. Electrostatic potentials are mapped on the surface of the electron density of 0.002 units.

Extended Data Fig. 4 Equilibrium geometries and electrostatic potential (ESP) map of the hydrated cations.

The optimized structures and the NBO charges (black numbers) and ion distance to the water molecule (green numbers) of hydrated cations (a) Li+, (b) Na+, (c) K+, and (d) Cs+ in bulk with six water molecules (RHS-bottom of each panel) and the hydrated cations between graphene layers (LHS-bottom is zoomed in the structure of each panel). In each panel, RHS-up is the electrostatic potential energy maps of the hydrated cations. Electrostatic potentials are mapped on the surface of the electron density of 0.002 units.

Supplementary information

Supplementary Information

Supplementary Sections 1–9, Figs. 1–11, Tables 1–5 and Discussion.

Source data

Source Data Fig. 1

Statistical source data.

Source Data Fig. 2

Statistical source data.

Source Data Fig. 3

Statistical source data.

Rights and permissions

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 permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goutham, S., Keerthi, A., Ismail, A. et al. Beyond steric selectivity of ions using ångström-scale capillaries. Nat. Nanotechnol. 18, 596–601 (2023). https://doi.org/10.1038/s41565-023-01337-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-023-01337-y

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing