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Beyond steric selectivity of ions using ångström-scale capillaries


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.

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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.

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.


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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



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.

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The authors declare no competing interests.

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

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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) ClO4in 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.

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Goutham, S., Keerthi, A., Ismail, A. et al. Beyond steric selectivity of ions using ångström-scale capillaries. Nat. Nanotechnol. (2023).

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