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Fluctuation-induced quantum friction in nanoscale water flows

Nature volume 602, pages 84–90 (2022)Cite this article

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Abstract

The flow of water in carbon nanochannels has defied understanding thus far1, with accumulating experimental evidence for ultra-low friction, exceptionally high water flow rates and curvature-dependent hydrodynamic slippage2,3,4,5. In particular, the mechanism of water–carbon friction remains unknown6, with neither current theories7 nor classical8,9 or ab initio molecular dynamics simulations10 providing satisfactory rationalization for its singular behaviour. Here we develop a quantum theory of the solid–liquid interface, which reveals a new contribution to friction, due to the coupling of charge fluctuations in the liquid to electronic excitations in the solid. We expect that this quantum friction, which is absent in Born–Oppenheimer molecular dynamics, is the dominant friction mechanism for water on carbon-based materials. As a key result, we demonstrate a marked difference in quantum friction between the water–graphene and water–graphite interface, due to the coupling of water Debye collective modes with a thermally excited plasmon specific to graphite. This suggests an explanation for the radius-dependent slippage of water in carbon nanotubes4, in terms of the electronic excitations of the nanotubes. Our findings open the way for quantum engineering of hydrodynamic flows through the electronic properties of the confining wall.

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Fig. 1: Theory of solid–liquid quantum friction.
Fig. 2: Surface dielectric response of water.
Fig. 3: Quantum friction of water on a jellium surface.
Fig. 4: Quantum friction at the water–carbon interface.

Data availability

The MD simulation data (Fig. 2 and Supplementary Figs. 1 and 2) are available on Zenodo (https://doi.org/10.5281/zenodo.5242930). The rest of the data are included with the paper.

References

  1. Bocquet, L. Nanofluidics coming of age. Nat. Mater. 19, 254–256 (2020).

    Article  ADS  CAS  Google Scholar 

  2. Holt, J. K. et al. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312, 1034–1037 (2006).

    Article  ADS  CAS  Google Scholar 

  3. Whitby, M., Cagnon, L., Thanou, M. & Quirke, N. Enhanced fluid flow through nanoscale carbon pipes. Nano Lett. 8, 2632–2637 (2008).

    Article  ADS  CAS  Google Scholar 

  4. Secchi, E. et al. Massive radius-dependent flow slippage in carbon nanotubes. Nature 537, 210–213 (2016).

    Article  ADS  CAS  Google Scholar 

  5. Xie, Q. et al. Fast water transport in graphene nanofluidic channels. Nat. Nanotech. 13, 238–245 (2018).

    Article  ADS  CAS  Google Scholar 

  6. 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 

  7. Bocquet, L. & Barrat, J. L. Flow boundary conditions from nano- to micro-scales. Soft Matter 3, 685–693 (2007).

    Article  ADS  CAS  Google Scholar 

  8. Thomas, J. A. & McGaughey, A. J. Reassessing fast water transport through carbon nanotubes. Nano Lett. 8, 2788–2793 (2008).

    Article  ADS  CAS  Google Scholar 

  9. Falk, K., Sedlmeier, F., Joly, L., Netz, R. R. & Bocquet, L. Molecular origin of fast water transport in carbon nanotube membranes: superlubricity versus curvature dependent friction. Nano Lett. 10, 4067–4073 (2010).

    Article  ADS  CAS  Google Scholar 

  10. 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  ADS  CAS  Google Scholar 

  11. Kavokine, N., Netz, R. R. & Bocquet, L. Fluids at the nanoscale: from continuum to subcontinuum transport. Annu. Rev. Fluid Mech. 53, 377–410 (2021).

  12. Sam, A. et al. Fast transport of water in carbon nanotubes: a review of current accomplishments and challenges. Mol. Simul. 47, 905–924 (2021).

  13. Maali, A., Cohen-Bouhacina, T. & Kellay, H. Measurement of the slip length of water flow on graphite surface. Appl. Phys. Lett. 92, 2007–2009 (2008).

    Article  Google Scholar 

  14. Misra, R. P. & Blankschtein, D. Insights on the role of many-body polarization effects in the wetting of graphitic surfaces by water. J. Phys. Chem. C 121, 28166–28179 (2017).

    Article  CAS  Google Scholar 

  15. Wodtke, A. M., Tully, J. C. & Auerbach, D. J. Electronically non-adiabatic interactions of molecules at metal surfaces: can we trust the Born-Oppenheimer approximation for surface chemistry? Int. Rev. Phys. Chem. 23, 513–539 (2004).

    Article  CAS  Google Scholar 

  16. Dou, W. & Subotnik, J. E. Perspective: how to understand electronic friction. J. Chem. Phys. 148 (2018).

  17. Sokoloff, J. B. Enhancement of the water flow velocity through carbon nanotubes resulting from the radius dependence of the friction due to electron excitations. Phys. Rev. E 97, 33107 (2018).

    Article  ADS  CAS  Google Scholar 

  18. Volokitin, A. I. & Persson, B. N. Near-field radiative heat transfer and noncontact friction. Rev. Mod. Phys. 79, 1291–1329 (2007).

    Article  ADS  CAS  Google Scholar 

  19. Song, X., Chandler, D. & Marcus, R. A. Gaussian field model of dielectric solvation dynamics. J. Phys. Chem. 100, 11954–11959 (1996).

    Article  CAS  Google Scholar 

  20. Rammer, J. & Smith, H. Quantum field-theoretical methods in transport theory of metals. Rev. Mod. Phys. 58, 323–359 (1986).

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  22. Pendry, J. B. Shearing the vacuum – Quantum friction. J. Phys. Condens. Matter 9, 10301–10320 (1997).

    Article  ADS  CAS  Google Scholar 

  23. Carlson, S., Brünig, F. N., Loche, P., Bonthuis, D. J. & Netz, R. R. Exploring the absorption spectrum of simulated water from MHz to infrared. J. Phys. Chem. A 124, 5599–5605 (2020).

    Article  CAS  Google Scholar 

  24. Sato, T. & Buchner, R. Dielectric relaxation processes in ethanol/water mixtures. J. Phys. Chem. A 108, 5007–5015 (2004).

    Article  CAS  Google Scholar 

  25. Koeberg, M., Wu, C. C., Kim, D. & Bonn, M. THz dielectric relaxation of ionic liquid:water mixtures. Chem. Phys. Lett. 439, 60–64 (2007).

    Article  ADS  CAS  Google Scholar 

  26. Lang, N. D. & Kohn, W. Theory of metal surfaces: charge density and surface energy. Phys. Rev. B 1, 4555–4568 (1970).

    Article  ADS  Google Scholar 

  27. Paniagua-Guerra, L. E., Gonzalez-Valle, C. U. & Ramos-Alvarado, B. Effects of the interfacial modeling approach on equilibrium calculations of slip length for nanoconfined water in carbon slits. Langmuir 36, 14772–14781 (2020).

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  29. Portail, M., Carrere, M. & Layet, J. M. Dynamical properties of graphite and peculiar behaviour of the low-energy plasmon. Surf. Sci. 433, 863–867 (1999).

    Article  ADS  Google Scholar 

  30. Laitenberger, P. & Palmer, R. E. Plasmon dispersion and damping at the surface of a semimetal. Phys. Rev. Lett. 76, 1952–1955 (1996).

    Article  ADS  CAS  Google Scholar 

  31. Pitarke, J. M., Silkin, V. M., Chulkov, E. V. & Echenique, P. M. Theory of surface plasmons and surface-plasmon polaritons. Rep. Prog. Phys. 70, 1–87 (2007).

    Article  ADS  CAS  Google Scholar 

  32. Lavor, I. R., Cavalcante, L. S. R., Chaves, A., Peeters, F. M. & Van Duppen, B. Probing the structure and composition of van der Waals heterostructures using the nonlocality of Dirac plasmons in the terahertz regime. 2D Mater. 8, 015014 (2020).

    Article  Google Scholar 

  33. Tománek, D. et al. Theory and observation of highly asymmetric atomic structure in scanning-tunneling-microscopy images of graphite. Phys. Rev. B 35, 7790–7793 (1987).

    Article  ADS  Google Scholar 

  34. Endo, M. et al. Stacking nature of graphene layers in carbon nanotubes and nanofibres. J. Phys. Chem. Solids 58, 1707–1712 (1997).

    Article  ADS  CAS  Google Scholar 

  35. Franklin, R. E. The structure of graphitic carbons. Acta Crystallogr. 4, 253–261 (1951).

    Article  CAS  Google Scholar 

  36. Speck, J. S., Endo, M. & Dresselhaus, M. S. Structure and intercalation of thin benzene derived carbon fibers. J. Cryst. Growth 94, 834–848 (1989).

    Article  ADS  CAS  Google Scholar 

  37. Charlier, J. C., Blase, X. & Roche, S. Electronic and transport properties of nanotubes. Rev. Mod. Phys. 79, 677–732 (2007).

    Article  ADS  CAS  Google Scholar 

  38. Xie, Y., Fu, L., Niehaus, T. & Joly, L. Liquid-solid slip on charged walls: the dramatic impact of charge distribution. Phys. Rev. Lett. 125, 014501 (2020).

    Article  ADS  CAS  Google Scholar 

  39. Pham, T. A., Ping, Y. & Galli, G. Modelling heterogeneous interfaces for solar water splitting. Nat. Mater. 16, 401–408 (2017).

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

We thank A. Robert for help with MD simulations and acknowledge fruitful discussions with A. Robert, B. Douçot, R. Netz, B. Coasne, N. Lorente and B. Rotenberg. L.B. acknowledges funding from the EU H2020 Framework Programme/ERC Advanced Grant agreement number 785911-Shadoks and ANR project Neptune. This work has received the support of ‘Institut Pierre-Gilles de Gennes’, programmes ANR-10-IDEX-0001-02 PSL and ANR-10-LABX-31. We acknowledge the French HPC resources of GENCI for grant number A9-A0070807364. The Flatiron Institute is a division of the Simons Foundation. We acknowledge the inspiration and contributions to science of late Jorge Iribas Cerdá.

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Authors and Affiliations

  1. Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France

    Nikita Kavokine & Lydéric Bocquet

  2. Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA

    Nikita Kavokine

  3. PASTEUR, Département de Chimie, École Normale Supérieure, PSL University, Sorbonne Universités, CNRS, Paris, France

    Marie-Laure Bocquet

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  1. Nikita Kavokine
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Contributions

L.B., M.-L.B. and N.K. conceived the project. N.K. developed the theoretical framework. N.K. and L.B. co-wrote the paper, with input from M.-L.B. All authors discussed the results and commented on the manuscript.

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Correspondence to Nikita Kavokine or Lydéric Bocquet.

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Nature thanks Mischa Bonn and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary Information

Supplementary Sections 1–7 including Figs. 1–5. See contents page for details.

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Kavokine, N., Bocquet, ML. & Bocquet, L. Fluctuation-induced quantum friction in nanoscale water flows. Nature 602, 84–90 (2022). https://doi.org/10.1038/s41586-021-04284-7

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