Skip to main content

Thank you for visiting 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.

Ionic Coulomb blockade as a fractional Wien effect


Recent advances in nanofluidics have allowed the exploration of ion transport down to molecular-scale confinement, yet artificial porins are still far from reaching the advanced functionalities of biological ion machinery. Achieving single ion transport that is tunable by an external gate—the ionic analogue of electronic Coulomb blockade—would open new avenues in this quest. However, an understanding of ionic Coulomb blockade beyond the electronic analogy is still lacking. Here, we show that the many-body dynamics of ions in a charged nanochannel result in quantized and strongly nonlinear ionic transport, in full agreement with molecular simulations. We find that ionic Coulomb blockade occurs when, upon sufficient confinement, oppositely charged ions form ‘Bjerrum pairs’, and the conduction proceeds through a mechanism reminiscent of Onsager’s Wien effect. Our findings open the way to novel nanofluidic functionalities, such as an ion pump based on ionic Coulomb blockade, inspired by its electronic counterpart.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



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

Fig. 1: Brownian dynamics simulations of ionic CB in a nanochannel.
Fig. 2: Analytical theory for the fractional Wien effect mechanism of ionic CB.
Fig. 3: Conditions for observation of ionic CB.
Fig. 4: Ionic-CB-based ion pump.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The Brownian dynamics code used within this study is available from the corresponding authors upon reasonable request.


  1. Schoch, R. B., Han, J. & Renaud, P. Transport phenomena in nanofluidics. Rev. Mod. Phys. 80, 839 (2008).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  3. Elimelech, M. & Phillip, W. A. The future of seawater desalination: energy, technology and the environment. Science 333, 712–717 (2011).

    Article  CAS  Google Scholar 

  4. Lauger, P. Mechanisms of biological ion transport—carriers, channels and pumps in artificial lipid membranes. Angew. Chem. Int. Ed. 24, 905–923 (1985).

    Article  Google Scholar 

  5. Apell, H. J. & Karlish, S. J. Functional properties of Na,K-ATPase, and their structural implications, as detected with biophysical techniques. J. Membr. Biol. 180, 1–9 (2001).

    Article  CAS  Google Scholar 

  6. Heginbotham, L., Kolmakova-Partensky, L. & Miller, C. Functional reconstitution of a prokaryotic K+ channel. J. Gen. Physiol. 111, 741–749 (1998).

    Article  CAS  Google Scholar 

  7. Dayan, P. Theoretical Neuroscience (MIT Press, 2000).

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  10. Feng, J. et al. Single-layer MoS2 nanopores as nanopower generators. Nature 536, 197–200 (2016).

    Article  CAS  Google Scholar 

  11. Tunuguntla, R. H. et al. Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins. Science 357, 792–796 (2017).

    Article  CAS  Google Scholar 

  12. Nazarov, Y. V. & Blanter, Y. M. Quantum Transport: Introduction to Nanoscience (Cambridge Univ. Press, 2009).

  13. Beenakker, C. W. J. Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Phys. Rev. B 44, 1646–1656 (1991).

    Article  CAS  Google Scholar 

  14. Stopa, M. Rectifying behavior in Coulomb blockades: charging rectifiers. Phys. Rev. Lett. 88, 146802 (2002).

    Article  CAS  Google Scholar 

  15. Krems, M. & Di Ventra, M. Ionic Coulomb blockade in nanopores. J. Phys. Condens. Matter 25, 065101 (2013).

    Article  Google Scholar 

  16. Tanaka, H., Iizuka, H., Pershin, Y. V. & Di Ventra, M. Surface effects on ionic Coulomb blockade in nanometer-size pores. Nanotechnology 29, 025703 (2017).

    Article  Google Scholar 

  17. Li, W. et al. Gated water transport through graphene nanochannels: from ionic Coulomb blockade to electroosmotic pump. J. Phys. Chem. C 121, 17523–17529 (2017).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  19. Kaufman, I. K. et al. Ionic Coulomb blockade and anomalous mole fraction effect in the NaChBac bacterial ion channel and its charge-varied mutants. EPJ Nonlinear Biomed. Phys. 5, 4 (2017).

    Article  Google Scholar 

  20. Fedorenko, O. A. et al. Quantized dehydration and the determinants of selectivity in the NaChBac bacterial sodium channel. Preprint at (2018).

  21. Kaufman, I., Luchinsky, D. G., Tindjong, R., McClintock, P. V. E. & Eisenberg, R. S. Multi-ion conduction bands in a simple model of calcium ion channels. Phys. Biol. 10, 026007 (2012).

    Article  Google Scholar 

  22. Kaufman, I. K., McClintock, P. V. E. & Eisenberg, R. S. Coulomb blockade model of permeation and selectivity in biological ion channels. New J. Phys. 17, 083021 (2015).

    Article  Google Scholar 

  23. von Kitzing, E. in Membrane Proteins: Structures, Interactions and Models (eds Pullman, A., Jortner, J. & Pullman, B.) 297–314 (Springer, 1992).

  24. Luchinsky, D. G., Gibby, W. A. T., Kaufman, I., Timucin, D. A. & McClintock, P. V. E. Statistical theory of selectivity and conductivity in biological channels. Preprint at (2016).

  25. Schlaich, A., Knapp, E. W. & Netz, R. R. Water dielectric effects in planar confinement. Phys. Rev. Lett. 117, 048001 (2016).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  27. Zhang, J., Kamenev, A. & Shklovskii, B. I. Conductance of ion channels and nanopores with charged walls: a toy model. Phys. Rev. Lett. 95, 148101 (2005).

    Article  CAS  Google Scholar 

  28. Zhang, J., Kamenev, A. & Shklovskii, B. I. Ion exchange phase transitions in water-filled channels with charged walls. Phys. Rev. E 73, 051205 (2006).

    Article  CAS  Google Scholar 

  29. Cooper, K., Jakobsson, E. & Wolynes, P. The theory of ion transport through membrane channels. Prog. Biophys. Mol. Biol. 46, 51–96 (1985).

    Article  CAS  Google Scholar 

  30. Edwards, S. F. & Lenard, A. Exact statistical mechanics of a one-dimensional system with Coulomb forces. II. The method of functional integration. J. Math. Phys. 3, 778–792 (1962).

    Article  Google Scholar 

  31. Démery, V., Dean, D. S., Hammant, T. C., Horgan, R. R. & Podgornik, R. The one-dimensional Coulomb lattice fluid capacitor. J. Chem. Phys. 137, 064901 (2012).

    Article  Google Scholar 

  32. Kamenev, A., Zhang, J., Larkin, A. I. & Shklovskii, B. I. Transport in one-dimensional Coulomb gases: from ion channels to nanopores. Physica A 359, 129–161 (2006).

    Article  CAS  Google Scholar 

  33. Onsager, L. Deviations from Ohm’s law in weak electrolytes. J. Chem. Phys. 2, 599–615 (1934).

    Article  CAS  Google Scholar 

  34. Kaiser, V., Bramwell, S. T., Holdsworth, P. C. W. & Moessner, R. Onsager’s Wien effect on a lattice. Nat. Mater. 12, 1033–1037 (2013).

    Article  CAS  Google Scholar 

  35. Redner, S. A Guide to First Passage Problems (Cambridge Univ. Press, 2001).

  36. Pothier, H., Lafarge, P., Urbina, C., Esteve, D. & Devoret, M. H. Single-electron pump based on charging effects. Eur. Phys. Lett. 17, 249–254 (1992).

    Article  Google Scholar 

Download references


The authors thank V. Démery, R. Vuilleumier, B. Rotenberg, D. Dean, R. Netz, A. Poggioli, T. Mouterde, L. Jubin and H. Yoshida for useful discussions. S.M. and L.B. acknowledge support from ANR Neptune. L.B. acknowledges support from ERC, project Shadoks, and European Union’s H2020 Framework Programme/FET NanoPhlow. This work was granted access to the HPC resources of MesoPSL financed by the Region Ile de France and the project Equip@Meso (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche, as well as to the HPC resources of CINES under allocation 2018-A0040710395 made by GENCI.

Author information

Authors and Affiliations



L.B. and A.S. conceived the project. N.K. carried out the theoretical analysis and Brownian dynamics simulations. N.K. and L.B. co-wrote the paper. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Lydéric Bocquet.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Journal peer review information: Nature Nanotechnology thanks Peter (V. E.) McClintock, Aleksandra Radenovic 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

Supplementary Methods, Results and Figs. 1–5.

Supplementary Video

Fractional Wien effect as observed in simulations.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kavokine, N., Marbach, S., Siria, A. et al. Ionic Coulomb blockade as a fractional Wien effect. Nat. Nanotechnol. 14, 573–578 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research