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Hydrogen bonding in water under extreme confinement

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Data availability

The raw data examined in the figures in the main text have been made available at the following Zenodo repository: https://zenodo.org/records/20534179 (ref. 66). The Jupyter Notebooks used to process and visualize the figures in the main text have been made available at the following GitHub repository: https://github.com/hachteja/HydrogenBonding_MainTextFigures. All other codes and data are available on request from the corresponding authors.

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Acknowledgements

We would like to thank N. Aluru of the University of Texas at Austin for discussions on modelling and simulations. We would also like to thank D. Kozawa from the National Institute for Materials Science in Japan for helpful discussions about excitonic transitions in the CNTs.

Funding

This research was primarily supported as part of the Center for Enhanced Nanofluidic Transport (CENT), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019112. vEELS research was supported by the Center for Nanophase Materials Sciences (CNMS), which is a DOE Office of Science User Facility using instrumentation within Oak Ridge National Laboratory’s Materials Characterization Core provided by UT-Battelle, LLC, under contract no. DE-AC05- 00OR22725 with the DOE and sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy. The MD simulations were supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences (BES), Materials Science and Engineering Division grant no. DE-FG02-09ER46554 and by the McMinn Endowment at Vanderbilt University. Computations were performed at the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy, Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under contract no. DE-AC02-05CH11231.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

    Xintong Xu, Joel Martis & Arun Majumdar

  2. Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Matthias Kuehne, Yu-Ming Tu, Cody L. Ritt & Michael S. Strano

  3. Department of Physics, Brown University, Providence, RI, USA

    Matthias Kuehne

  4. Interdisciplinary Materials Science Program, Vanderbilt University, Nashville, TN, USA

    Harrison A. Walker & Sokrates T. Pantelides

  5. Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, USA

    Harrison A. Walker, De-Liang Bao, Xin Jin & Sokrates T. Pantelides

  6. Department of Physics, Hampton University, Hampton, VA, USA

    De-Liang Bao

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

    Xin Jin

  8. Department of Chemical Engineering, National Taiwan University, Taipei City, Taiwan

    Yu-Ming Tu

  9. Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO, USA

    Cody L. Ritt

  10. Bruker AXS LLC, Kirkland, WA, USA

    Joel Martis

  11. Materials Science and Engineering, University of Washington, Seattle, WA, USA

    Juan Carlos Idrobo

  12. Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA, USA

    Juan Carlos Idrobo

  13. Department of Electrical and Computer Engineering, Vanderbilt University, Nashville, TN, USA

    Sokrates T. Pantelides

  14. Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Jordan A. Hachtel

  15. Department of Photon Science, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    Arun Majumdar

Authors

  1. Xintong Xu
  2. Matthias Kuehne
  3. Harrison A. Walker
  4. De-Liang Bao
  5. Xin Jin
  6. Yu-Ming Tu
  7. Cody L. Ritt
  8. Joel Martis
  9. Juan Carlos Idrobo
  10. Sokrates T. Pantelides
  11. Michael S. Strano
  12. Jordan A. Hachtel
  13. Arun Majumdar

Contributions

Experiments were conceived and designed by X.X., J.C.I., A.M. and J.A.H. vEELS data were acquired and analysed by X.X., H.A.W. and J.A.H., with guidance from J.M. and A.M. Samples were synthesized and prepared by X.X., M.K., Y.-M.T., C.L.R. and M.S.S. Morse oscillator modelling was conducted by X.X., with the guidance from A.M. MD simulations were conducted by H.A.W. and X.J., with guidance from D.-L.B. and S.T.P. The manuscript was written by X.X., A.M. and J.A.H. The section on MD simulations was written by H.A.W., X.J. and D.-L.B., with guidance from S.T.P.

Corresponding authors

Correspondence to Jordan A. Hachtel or Arun Majumdar.

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Competing interests

The authors declare no competing interests.

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Peer review information

Nature 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.

Extended data figures and tables

Extended Data Fig. 1 Procedure for CNT water filling.

a, A custom-built humidity chamber with a microscope. b, Optical micrograph of a holey SiNx TEM chip after CVD growth and FIB cutting (along the dashed green lines) of CNTs (schematically illustrated as continuous white lines), as well as their exposure to above 99% relative humidity conditions and Torr Seal application. Note that Torr Seal covers the FIB cut regions but not the holey SiNx membrane.

Extended Data Fig. 2 TEM images of main-text CNTs.

TEM images of the most examined CNTs in the main text with large and medium diameters. a, The filled large-diameter tube from Figs. 1d–h, 2a and 3a is measured to have an inner diameter of about 2.3 nm. b, The filled medium-diameter tube from Figs. 2a and 3a is measured to have an inner diameter of about 1.4 nm.

Extended Data Fig. 3 Instrumental broadening versus spectral linewidth.

In this figure, we show that our instrumental resolution is far below the measured linewidth of the vibrational spectra for the vibrational spectra shown in the large (2.3 nm) diameter tube and the smaller (1.4 nm) diameter tube from the main-text figures. For the 2.3-nm tube, the full width at half maximum (FWHM) of the O–H stretch is 50.1 meV, whereas the FWHM of the 1.4-nm tube is 34.0 meV. For all vEELS spectra, the energy resolution can be quantified by measuring the FWHM of the ZLP, which corresponds to all electrons in the EELS that have either elastically scattered off the sample or not interacted with the sample at all. As a result, this peak represents the spread of electron energies in the beam with which all peaks are convolved and represents the instrumental broadening. For both spectra, the FWHM of the ZLP is 8.5 meV, indicating that the vibrational peak width is dominated by the native linewidth of the peak, not instrumental broadening.

Extended Data Fig. 4 vDOS trends of water in CNTs (MD + Gaussian fits).

a–c, Filled curves from MD simulations are overlaid with dashed black curves representing Gaussian fits. Each fit is decomposed into free O–H (dotted purple line) and bonded O–H (dotted green line) and an extra bonded O–H mode arising from a low-temperature phase transition (dotted blue line), possibly to a form of ice. Panel a varies nanotube diameter (0.8–2.3 nm), panel b varies water density (0.10–1.25 g cm−3 at 1.4 nm) and panel c varies temperature (100–500 K at 1.4 nm). In each case, the other two parameters are as indicated in the labels at the top. d,e, Quantification of fit results: the peak-area ratio of bonded to free O–H grows nearly linearly with increasing diameter and density, respectively. f, The separation between free and bonded O–H peaks decreases monotonically as temperature rises, reflecting thermal broadening and increased anharmonicity as temperature increases. Together, these panels show how geometric confinement, molecular packing and thermal effects influence H-bond networks and why real single-CNT vEELS spectra, subject to sample heterogeneity, can be so diverse.

Extended Data Fig. 5 Full vibrational spectrum of filled CNT, empty CNT and bulk water.

Here we show the full vibrational response of all three spectra in Fig. 1. In each, we show the spectrum in log scale and in the inset we show the SiN/G-band vibrations of the substrate/CNT. Top, filled CNT; middle, empty CNT; bottom, bulk liquid cell.

Extended Data Fig. 6 Valence EELS of filled and unfilled CNTs.

a, Vibrational/valence regime EELS for filled CNTs from the confined-water sample compared with valence EELS for unfilled commercial CNTs. b,c, Statistics of the peak distributions for the filled CNTs (b) and the commercial DWCNTs, with estimated inner diameters between 1.3 and 2.0 nm (c), showing a substantial difference between excitons and vibrations. d, Empirical formula for the relationship between CNT diameter and excitonic energies derived in Methods (ref. 15). e–g, Vibrational spectra from filled CNTs showing inconsistency with the empirical formula. h–j, Valence spectra from unfilled CNTs showing strong consistency with the empirical formula.

Extended Data Fig. 7 Background subtraction in vEELS.

a, A vEELS spectrum with the fit regions for a two-region, third-order exponential fit and the resulting background. b, Comparison of the background subtracted data and the actual peak.

Extended Data Fig. 8 Example of partial filling in CNTs.

Here we highlight a measurement of a water-filled CNT in which partial filling was observed. a, Defocused STEM image of the CNT on the SiN holey grid, with three locations highlighted showing a gradual decrease in the observed intensity of the O–H signal (b–d), in which further spectra were measured. The initial measurement and identification of the bulk-like water response is shown in c and is consistent with a strong observation of the O–H stretch. Moving further away from the CNT wall, the bonded O–H stretch was not observed (d), whereas closer to the edge, it was observed with an even higher intensity than in the initial observation (b). Whereas in most CNTs the O–H stretch measurements were consistent across the entire CNT, in this example, it was not. This same CNT is shown in other figures as well, namely, it is ‘bulk-water-like-2’ in Extended Data Fig. 10a and ‘CNT B’ in Extended Data Fig. 11.

Extended Data Fig. 9 Example of CNT breaking during experiments.

Here we highlight an instance in which a CNT broke during the experiment. a, Reference image of the sample before measurement. b, Reference image after the measurement. Substantial build-up of contamination is present in a way that is not present in any of our other measurements. c, Defocused Ronchigram shows that the break occurs above the position of blowout (blue arrow). d, CNT spectra from before break. e, CNT spectra acquired immediately after the break. f, CNT spectra acquired from the area above the break (black circle). The CNT examined here is bulk-water-like-3 in Extended Data Fig. 10a.

Extended Data Fig. 10 Statistics of the water-filled CNT response.

a–c, Here we show a representative vibrational spectrum from each of eight filled CNTs that were observed across all experimental sessions (a), along with eight (out of 53 total) empty CNTs to illustrate the observed variance in the observed signal in this regime (b,c). Both the non-H-bonded and the bulk-water-like vibrational responses were observed on three separate samples on three separate sessions. Most of the empty CNTs show no peaks whatsoever in the 350–500-meV region (31 of 53) but some exhibit faint peaks across this range (or even sharp peaks at the C–H stretch from hydrocarbon contamination). All analysis was focused on samples exhibiting definitive signals. ‘Non-H-bonded 1’ and ‘bulk-water-like-1’ are the two spectra highlighted in Figs. 2 and 3 and were observed on the same sample during the same session in which cryogenic measurements were performed. The non-H-bonded 3–5 spectra were acquired during the very first session, all from the same sample; however, this sample was a mesoporous Si substrate. On this grid, the tubes were frequently bundled together and the random variations of the membrane made it impossible to track down the same CNTs later for TEM analysis. All other experiments were conducted on periodic SiNx hole grids, which enabled the CNTs to be found later for TEM.

Extended Data Fig. 11 Repeatability of phase-change signatures in large-diameter CNTs.

a, Comparison of the room-temperature (300 K) and cryogenic (100 K) spectra for the CNT shown in the main text (CNT A) and another one (CNT B). b, Difference spectra of the room-temperature and 100-K spectra for each CNT. c, Further measurements on the 2.3-nm CNT. The top (blue) spectra shows a cryo-measurement conducted many microns away from the original position of the spectra and the bottom (red) spectra shows a room-temperature measurement very close to the original position.

Extended Data Fig. 12 Machine learning potential performance.

a,b, Parity plots comparing DFT-calculated and machine-learning-predicted energies per atom (a) and atomic forces (b) for both DeePMD and MACE models. MACE achieves an RMSE of 0.48 meV per atom for energies and 0.005 eV Å−1 for forces, whereas DeePMD achieves 0.205 meV per atom for energies and 0.026 eV Å−1 for forces. MACE demonstrates far superior force accuracy, which is critical for reliable MD trajectories, and was therefore selected for all production simulations. c, vDOS is obtained from the Fourier transform of the velocity autocorrelation functions computed from DFT-based (blue) and MLIP-based (orange) MD simulations. Under the selected conditions, namely, 1.1-nm CNT diameter, water density of 1.0 g cm−3 and temperature of 300 K, the vDOS profiles from DFT and MLIP exhibit excellent agreement. The blue and red dashed lines denote two characteristic O–H stretching frequencies observed in different environments: about 420 meV for hydrogen-bonded O–H vibrational modes (as in bulk water) and about 455 meV for free O–H stretching modes.

Extended Data Fig. 13 Subsystem temperature equilibration in DFT-MD simulations.

Temperature profiles of the water subsystem (red), CNT subsystem (blue) and the entire system (black) during DFT-based MD at 300 K, for a 1.1-nm CNT containing water at 1.0 g cm−3. Although the overall system temperature (black) seems converged, the water and CNT subsystems can be at substantially different temperatures. This figure demonstrates that the average system temperature alone is insufficient as an equilibration criterion and motivated a stricter subsystem convergence check applied in subsequent MLIP-MD simulations before vDOS data collection.

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Xu, X., Kuehne, M., Walker, H.A. et al. Hydrogen bonding in water under extreme confinement. Nature (2026). https://doi.org/10.1038/s41586-026-10858-0

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