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.
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The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.
The Brownian dynamics code used within this study is available from the corresponding authors upon reasonable request.
Schoch, R. B., Han, J. & Renaud, P. Transport phenomena in nanofluidics. Rev. Mod. Phys. 80, 839 (2008).
Bocquet, L. & Charlaix, E. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39, 1073–1095 (2010).
Elimelech, M. & Phillip, W. A. The future of seawater desalination: energy, technology and the environment. Science 333, 712–717 (2011).
Lauger, P. Mechanisms of biological ion transport—carriers, channels and pumps in artificial lipid membranes. Angew. Chem. Int. Ed. 24, 905–923 (1985).
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).
Heginbotham, L., Kolmakova-Partensky, L. & Miller, C. Functional reconstitution of a prokaryotic K+ channel. J. Gen. Physiol. 111, 741–749 (1998).
Dayan, P. Theoretical Neuroscience (MIT Press, 2000).
Siria, A. et al. Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 494, 455–458 (2013).
Radha, B. et al. Molecular transport through capillaries made with atomic-scale precision. Nature 538, 222–225 (2016).
Feng, J. et al. Single-layer MoS2 nanopores as nanopower generators. Nature 536, 197–200 (2016).
Tunuguntla, R. H. et al. Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins. Science 357, 792–796 (2017).
Nazarov, Y. V. & Blanter, Y. M. Quantum Transport: Introduction to Nanoscience (Cambridge Univ. Press, 2009).
Beenakker, C. W. J. Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Phys. Rev. B 44, 1646–1656 (1991).
Stopa, M. Rectifying behavior in Coulomb blockades: charging rectifiers. Phys. Rev. Lett. 88, 146802 (2002).
Krems, M. & Di Ventra, M. Ionic Coulomb blockade in nanopores. J. Phys. Condens. Matter 25, 065101 (2013).
Tanaka, H., Iizuka, H., Pershin, Y. V. & Di Ventra, M. Surface effects on ionic Coulomb blockade in nanometer-size pores. Nanotechnology 29, 025703 (2017).
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).
Feng, J. et al. Observation of ionic Coulomb blockade in nanopores. Nat. Mater. 15, 850–855 (2016).
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).
Fedorenko, O. A. et al. Quantized dehydration and the determinants of selectivity in the NaChBac bacterial sodium channel. Preprint at https://arxiv.org/abs/1803.07063 (2018).
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).
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).
von Kitzing, E. in Membrane Proteins: Structures, Interactions and Models (eds Pullman, A., Jortner, J. & Pullman, B.) 297–314 (Springer, 1992).
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 https://arxiv.org/abs/1604.05758 (2016).
Schlaich, A., Knapp, E. W. & Netz, R. R. Water dielectric effects in planar confinement. Phys. Rev. Lett. 117, 048001 (2016).
Fumagalli, L. et al. Anomalously low dielectric constant of confined water. Science 360, 1339–1342 (2018).
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).
Zhang, J., Kamenev, A. & Shklovskii, B. I. Ion exchange phase transitions in water-filled channels with charged walls. Phys. Rev. E 73, 051205 (2006).
Cooper, K., Jakobsson, E. & Wolynes, P. The theory of ion transport through membrane channels. Prog. Biophys. Mol. Biol. 46, 51–96 (1985).
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).
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).
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).
Onsager, L. Deviations from Ohm’s law in weak electrolytes. J. Chem. Phys. 2, 599–615 (1934).
Kaiser, V., Bramwell, S. T., Holdsworth, P. C. W. & Moessner, R. Onsager’s Wien effect on a lattice. Nat. Mater. 12, 1033–1037 (2013).
Redner, S. A Guide to First Passage Problems (Cambridge Univ. Press, 2001).
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).
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.
The authors declare no competing interests.
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.
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Kavokine, N., Marbach, S., Siria, A. et al. Ionic Coulomb blockade as a fractional Wien effect. Nat. Nanotechnol. 14, 573–578 (2019). https://doi.org/10.1038/s41565-019-0425-y