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:

Rich proton dynamics and phase behaviours of nanoconfined ices

Nature Physics volume 20, pages 456–464 (2024)Cite this article

Subjects

Abstract

Water confined in nanopores is ubiquitous in geological, planetary and biological environments and in nanofluidic settings. Understanding the phase behaviour and proton dynamics of nanoconfined water under high-pressure conditions is therefore important from both fundamental and applied points of view. Here we report a machine learning potential and present evidence from large-scale path-integral molecular dynamics simulations of the proton dynamics and phase behaviours of monolayer and bilayer ice under nanoconfinement and high pressures. We find that the symmetry breaking of the underlying hydrogen-bonding network of the two-dimensional (2D) ices together with strong nuclear quantum effects are responsible for the rich proton dynamics, such as the ultrafast one-dimensional proton-hopping within 2D ices. We also predict ten 2D ice phases. Notably, a 2D dynamic partially ionic phase and a superionic phase can be produced in the laboratory at pressures one order of magnitude lower than those measured for the bulk superionic phase or predicted for the partially ionic phase. We also identify a 2D solid-melting behaviour, namely consecutive double or triple continuous phase transitions from bilayer molecular ice to plastic ice and then to hexatic ice and the superionic fluid.

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: Phase diagrams and snapshots of 2D water ice confined in nanopores.
Fig. 2: Dynamic behaviour of local H and O in various 2D ice phases.
Fig. 3: PIMD simulations showing NQE-promoted proton-hopping.
Fig. 4: Melting of 2D ice into a superionic fluid.

Similar content being viewed by others

Data availability

The data, such as atomic structures and the machine learning force field, required to reproduce the key findings of this work, are available from the GitHub repository (https://github.com/jianjiang12/MLP-for-2D-ices). More detailed data are available from the corresponding authors upon request.

References

  1. Loerting, T., Fuentes-Landete, V., Tonauer, C. M. & Gasser, T. M. Open questions on the structures of crystalline water ices. Commun. Chem. 3, 109 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  2. Stanley, S. & Bloxham, J. Convective-region geometry as the cause of Uranus’ and Neptune’s unusual magnetic fields. Nature 428, 151–153 (2004).

    ADS  CAS  PubMed  Google Scholar 

  3. Soderlund, K. & Stanley, S. The underexplored frontier of ice giant dynamos. Philos. Trans. R. Soc. A 378, 20190479 (2020).

    ADS  CAS  Google Scholar 

  4. Millot, M. et al. Experimental evidence for superionic water ice using shock compression. Nat. Phys. 14, 297–302 (2018).

    CAS  Google Scholar 

  5. Millot, M. et al. Nanosecond X-ray diffraction of shock-compressed superionic water ice. Nature 569, 251–255 (2019).

    ADS  CAS  PubMed  Google Scholar 

  6. Prakapenka, V. B., Holtgrewe, N., Lobanov, S. S. & Goncharov, A. F. Structure and properties of two superionic ice phases. Nat. Phys. 17, 1233–1238 (2021).

    CAS  Google Scholar 

  7. Pickard, C. J., Martinez-Canales, M. & Needs, R. J. Decomposition and terapascal phases of water ice. Phys. Rev. Lett. 110, 245701 (2013).

    ADS  PubMed  Google Scholar 

  8. Cavazzoni, C. et al. Superionic and metallic states of water and ammonia at giant planet conditions. Science 283, 44–46 (1999).

    ADS  CAS  PubMed  Google Scholar 

  9. Liu, C. et al. Multiple superionic states in helium–water compounds. Nat. Phys. 15, 1065–1070 (2019).

    CAS  Google Scholar 

  10. Liu, C. et al. Plastic and superionic helium ammonia compounds under high pressure and high temperature. Phys. Rev. X 10, 021007 (2020).

    ADS  CAS  Google Scholar 

  11. Cheng, B., Bethkenhagen, M., Pickard, C. J. & Hamel, S. Phase behaviours of superionic water at planetary conditions. Nat. Phys. 17, 1228–1232 (2021).

    CAS  Google Scholar 

  12. French, M., Desjarlais, M. P. & Redmer, R. Ab initio calculation of thermodynamic potentials and entropies for superionic water. Phys. Rev. E 93, 022140 (2016).

    ADS  PubMed  Google Scholar 

  13. Hernandez, J.-A. & Caracas, R. Superionic-superionic phase transitions in body-centered cubic H2O ice. Phys. Rev. Lett. 117, 135503 (2016).

    ADS  PubMed  Google Scholar 

  14. Sun, J., Clark, B. K., Torquato, S. & Car, R. The phase diagram of high-pressure superionic ice. Nat. Commun. 6, 8156 (2015).

    ADS  CAS  PubMed  Google Scholar 

  15. Wilson, H. F., Wong, M. L. & Militzer, B. Superionic to superionic phase change in water: consequences for the interiors of Uranus and Neptune. Phys. Rev. Lett. 110, 151102 (2013).

    ADS  PubMed  Google Scholar 

  16. Hernandez, J.-A. & Caracas, R. Proton dynamics and the phase diagram of dense water ice. J. Chem. Phys. 148, 214501 (2018).

    ADS  PubMed  Google Scholar 

  17. Benoit, M., Bernasconi, M., Focher, P. & Parrinello, M. New high-pressure phase of ice. Phys. Rev. Lett. 76, 2934 (1996).

    ADS  CAS  PubMed  Google Scholar 

  18. Demontis, P., LeSar, R. & Klein, M. L. New high-pressure phases of ice. Phys. Rev. Lett. 60, 2284 (1988).

    ADS  CAS  PubMed  Google Scholar 

  19. Wang, Y. et al. High pressure partially ionic phase of water ice. Nat. Commun. 2, 563 (2011).

    ADS  PubMed  Google Scholar 

  20. Takii, Y., Koga, K. & Tanaka, H. A plastic phase of water from computer simulation. J. Chem. Phys. 128, 204501 (2008).

    ADS  PubMed  Google Scholar 

  21. Zhao, W.-H. et al. Highly confined water: two-dimensional ice, amorphous ice, and clathrate hydrates. Acc. Chem. Res. 47, 2505–2513 (2014).

    CAS  PubMed  Google Scholar 

  22. Zhu, C. et al. Computational prediction of novel ice phases: a perspective. J. Phys. Chem. Lett. 11, 7449–7461 (2020).

    CAS  PubMed  Google Scholar 

  23. Algara-Siller, G. et al. Square ice in graphene nanocapillaries. Nature 519, 443 (2015).

    ADS  CAS  PubMed  Google Scholar 

  24. Chen, J., Schusteritsch, G., Pickard, C. J., Salzmann, C. G. & Michaelides, A. Two dimensional ice from first principles: structures and phase transitions. Phys. Rev. Lett. 116, 025501 (2016).

    ADS  PubMed  Google Scholar 

  25. Chen, J., Schusteritsch, G., Pickard, C. J., Salzmann, C. G. & Michaelides, A. Double-layer ice from first principles. Phys. Rev. B 95, 094121 (2017).

    ADS  Google Scholar 

  26. Jiang, J. et al. First-principles molecular dynamics simulations of the spontaneous freezing transition of 2D water in a nanoslit. J. Am. Chem. Soc. 143, 8177–8183 (2021).

    CAS  PubMed  Google Scholar 

  27. Koga, K., Tanaka, H. & Zeng, X. C. First-order transition in confined water between high-density liquid and low-density amorphous phases. Nature 408, 564 (2000).

    ADS  CAS  PubMed  Google Scholar 

  28. Ma, R. et al. Atomic imaging of the edge structure and growth of a two-dimensional hexagonal ice. Nature 577, 60–63 (2020).

    ADS  CAS  PubMed  Google Scholar 

  29. Bai, J. & Zeng, X. C. Polymorphism and polyamorphism in bilayer water confined to slit nanopore under high pressure. Proc. Natl Acad. Sci. USA 109, 21240–21245 (2012).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  30. Koga, K., Zeng, X. C. & Tanaka, H. Freezing of confined water: a bilayer ice phase in hydrophobic nanopores. Phys. Rev. Lett. 79, 5262 (1997).

    ADS  CAS  Google Scholar 

  31. Kapil, V. et al. The first-principles phase diagram of monolayer nanoconfined water. Nature 609, 512–516 (2022).

    ADS  CAS  PubMed  Google Scholar 

  32. Lin, B., Jiang, J., Zeng, X. C. & Li, L. Temperature–pressure phase diagram of confined monolayer water/ice at first-principles accuracy with a machine-learning force field. Nat. Commun. 14, 4110 (2023).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  33. Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).

    ADS  PubMed  Google Scholar 

  34. Meier, T., Petitgirard, S., Khandarkhaeva, S. & Dubrovinsky, L. Observation of nuclear quantum effects and hydrogen bond symmetrisation in high pressure ice. Nat. Commun. 9, 2766 (2018).

    ADS  PubMed  PubMed Central  Google Scholar 

  35. Benoit, M., Marx, D. & Parrinello, M. Tunnelling and zero-point motion in high-pressure ice. Nature 392, 258–261 (1998).

    ADS  CAS  Google Scholar 

  36. Tian, Y. et al. Visualizing Eigen/Zundel cations and their interconversion in monolayer water on metal surfaces. Science 377, 315–319 (2022).

    ADS  CAS  PubMed  Google Scholar 

  37. Ye, Q.-J., Zhuang, L. & Li, X.-Z. Dynamic nature of high-pressure ice VII. Phys. Rev. Lett. 126, 185501 (2021).

    ADS  CAS  PubMed  Google Scholar 

  38. Kapil, V., Wilkins, D. M., Lan, J. & Ceriotti, M. Inexpensive modeling of quantum dynamics using path integral generalized Langevin equation thermostats. J. Chem. Phys. 152, 124104 (2020).

    ADS  CAS  PubMed  Google Scholar 

  39. Rossi, M., Kapil, V. & Ceriotti, M. Fine tuning classical and quantum molecular dynamics using a generalized Langevin equation. J. Chem. Phys. 148, 102301 (2018).

    ADS  PubMed  Google Scholar 

  40. Rossi, M., Liu, H., Paesani, F., Bowman, J. & Ceriotti, M. Communication: on the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase. J. Chem. Phys. 141, 181101 (2014).

    ADS  PubMed  Google Scholar 

  41. Bronstein, Y., Depondt, P., Finocchi, F. & Saitta, A. M. Quantum-driven phase transition in ice described via an efficient Langevin approach. Phys. Rev. B 89, 214101 (2014).

    ADS  Google Scholar 

  42. Young, A. Melting and the vector Coulomb gas in two dimensions. Phys. Rev. B 19, 1855 (1979).

    ADS  CAS  Google Scholar 

  43. Kosterlitz, J. M. & Thouless, D. Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory). J. Phys. C: Solid State Phys. 5, L124 (1972).

    ADS  CAS  Google Scholar 

  44. Singraber, A., Morawietz, T., Behler, J. R. & Dellago, C. Parallel multistream training of high-dimensional neural network potentials. J. Chem. Theory Comput. 15, 3075–3092 (2019).

    CAS  PubMed  Google Scholar 

  45. Singraber, A. et al. CompPhysVienna/n2p2: Version 2.1.4. Zenodo. https://doi.org/10.5281/zenodo.4750573 (2021).

  46. Hutter, J., Iannuzzi, M., Schiffmann, F. & VandeVondele, J. CP2K: atomistic simulations of condensed matter systems. Wiley Interdiscip. Rev. Comput. Mol. Sci. 4, 15–25 (2014).

    CAS  Google Scholar 

  47. Tribello, G. A., Bonomi, M., Branduardi, D., Camilloni, C. & Bussi, G. PLUMED 2: new feathers for an old bird. Comput. Phys. Commun. 185, 604–613 (2014).

    ADS  CAS  Google Scholar 

  48. Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).

    CAS  PubMed  Google Scholar 

  49. 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).

    ADS  PubMed  Google Scholar 

  50. Lee, C., Yang, W. & Parr, R. G. Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785 (1988).

    ADS  CAS  Google Scholar 

  51. Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38, 3098 (1988).

    ADS  CAS  Google Scholar 

  52. Lee, K., Murray, É. D., Kong, L., Lundqvist, B. I. & Langreth, D. C. Higher-accuracy van der Waals density functional. Phys. Rev. B 82, 081101 (2010).

    ADS  Google Scholar 

  53. Zhang, Y. & Yang, W. Comment on ‘Generalized gradient approximation made simple’. Phys. Rev. Lett. 80, 890 (1998).

    ADS  CAS  Google Scholar 

  54. Adamo, C. & Barone, V. Toward reliable density functional methods without adjustable parameters: the PBE0 model. J. Chem. Phys. 110, 6158–6170 (1999).

    ADS  CAS  Google Scholar 

  55. Brandenburg, J. G., Zen, A., Alfè, D. & Michaelides, A. Interaction between water and carbon nanostructures: how good are current density functional approximations? J. Chem. Phys. 151, 164702 (2019).

    ADS  PubMed  Google Scholar 

  56. Pickard, C. J. & Needs, R. Ab initio random structure searching. J. Phys. Condens. Matter 23, 053201 (2011).

    ADS  PubMed  Google Scholar 

  57. Ceriotti, M. & Manolopoulos, D. E. Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei. Phys. Rev. Lett. 109, 100604 (2012).

    ADS  PubMed  Google Scholar 

  58. Ceriotti, M., Bussi, G. & Parrinello, M. Nuclear quantum effects in solids using a colored-noise thermostat. Phys. Rev. Lett. 103, 030603 (2009).

    ADS  PubMed  Google Scholar 

  59. Cheng, B. & Ceriotti, M. Computing the absolute Gibbs free energy in atomistic simulations: applications to defects in solids. Phys. Rev. B 97, 054102 (2018).

    ADS  CAS  Google Scholar 

  60. Ceriotti, M., More, J. & Manolopoulos, D. E. i-PI: A Python interface for ab initio path integral molecular dynamics simulations. Comput. Phys. Commun. 185, 1019–1026 (2014).

    ADS  CAS  Google Scholar 

  61. Thompson, A. P. et al. LAMMPS–a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).

    CAS  Google Scholar 

  62. Singraber, A., Behler, J. R. & Dellago, C. Library-based LAMMPS implementation of high-dimensional neural network potentials. J. Chem. Theory Comput. 15, 1827–1840 (2019).

    CAS  PubMed  Google Scholar 

  63. Humphrey, W., Dalke, A. & Schulten, K. VMD: visual molecular dynamics. J. Mol. Graph. 14, 33–38 (1996).

    CAS  PubMed  Google Scholar 

  64. Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys. Condens. Matter 29, 273002 (2017).

    Google Scholar 

  65. Hunter, J. D. Matplotlib: A 2D graphics environment. Comput. Sci. Eng. 9, 90–95 (2007).

    Google Scholar 

Download references

Acknowledgements

C.Z. would like to acknowledge the National Key Research and Development Program of China (2021YFA 1500700) and the National Natural Science Foundation of China (Grant No. 22173011). X.C.Z. acknowledges computational support from the University of Nebraska Holland Computing Center and support from the Hong Kong Global STEM Professorship Scheme and the Research Grants Council of Hong Kong (GRF Grant No. 11204123).

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, City University of Hong Kong, Kowloon, Hong Kong

    Jian Jiang & Xiao Cheng Zeng

  2. Department of Chemistry, University of Nebraska-Lincoln, Lincoln, NE, USA

    Jian Jiang & Xiao Cheng Zeng

  3. Laboratory of Theoretical and Computational Nanoscience, National Center for Nanoscience and Technology, Chinese Academy of Sciences, Beijing, China

    Yurui Gao

  4. Department of Materials Science and Engineering, Southern University of Science and Technology, Shenzhen, China

    Lei Li

  5. School of Chemical Engineering and Technology, Sun Yat-Sen University, Zhuhai, China

    Yuan Liu

  6. School of Physics, Hefei University of Technology, Hefei, China

    Weiduo Zhu

  7. College of Chemistry, Key Laboratory of Theoretical & Computational Photochemistry of Ministry of Education, Beijing Normal University, Beijing, China

    Chongqin Zhu

  8. Department of Earth & Environmental Science, University of Pennsylvania, Philadelphia, PA, USA

    Joseph S. Francisco

Authors
  1. Jian Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yurui Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Weiduo Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Chongqin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Joseph S. Francisco
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xiao Cheng Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X.C.Z. and C.Z. conceived the project. J.J. performed the simulations. J.J., C.Z. and X.C.Z. analysed the data. J.J., C.Z., J.S.F. and X.C.Z. wrote the manuscript. All authors discussed the results and computational methods and commented on the manuscript.

Corresponding authors

Correspondence to Chongqin Zhu, Joseph S. Francisco or Xiao Cheng Zeng.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers 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.

Supplementary information

Supplementary Information

Supplementary Figs. 1–28.

Reporting Summary

Supplementary Video 1

Top and side views of ML-PL-Hexc in a 6-Å-wide nanopore at 440 K and 15.0 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 2

Top and side views of ML-Hexc-SI in a 6-Å-wide nanopore at 1,000 K and 15.0 GPa through PIMD. The white and green balls represent the hydrogen atoms. The red balls represent the oxygen atoms.

Supplementary Video 3

Top and side views of BL-Sq-SI in a 6-Å-wide nanopore at 1,000 K and 45.0 GPa through PIMD. The white and green balls represent the hydrogen atoms. The red balls represent the oxygen atoms.

Supplementary Video 4

Top and side views of BL-iVII-SI in a 7-Å-wide nanopore at 80 K and 21.4 GPa through PIMD. The white and green balls represent the hydrogen atoms. The red balls represent the oxygen atoms.

Supplementary Video 5

Top and side views of BL-iVII-PL in a 8-Å-wide nanopore at 600 K and 11.2 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 6

Top and side views of ZZMI in a 6-Å-wide nanopore at 80;K and 5.0 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 7

Top and side views of bZZ-qBI in a 6-Å-wide nanopore at 80 K and 30.0 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 8

Top and side views of ZZ-pMI in a 6-Å-wide nanopore at 80 K and 35.0 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 9

Top and side views of ZZBI in a 6-Å-wide nanopore at 80 K and 45.0 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 10

Top and side views of BL-iVII-FE in a 7-Å-wide nanopore at 80 K and 21.4 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 11

Top and side view of BL-iVII-Zundel in a 7-Å-wide nanopore at 80 K and 64.3 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 12

Top and side views of BL-iVII-FE' in an 8-Å-wide nanopore at 80 K and 18.8 GPa through PIMD. The white and red balls represent the hydrogen and oxygen atoms, respectively.

Supplementary Video 13

Top view of BL-Hexc-sSI in an 8-Å-wide nanopore at 1,000 K and 11.2 GPa through metadynamics simulations. The white (left panel) and green (left panel) balls represent the hydrogen atoms. The red balls (left panel) represent the oxygen atoms. The red (right panel) and blue (right panel) represent the oxygen atoms on the upper layer and lower layer, respectively.

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

Jiang, J., Gao, Y., Li, L. et al. Rich proton dynamics and phase behaviours of nanoconfined ices. Nat. Phys. 20, 456–464 (2024). https://doi.org/10.1038/s41567-023-02341-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-023-02341-8

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