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Two-component dynamics in supercritical \(\text {CO}_2\) from inelastic X-ray scattering
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  • Published: 11 February 2026

Two-component dynamics in supercritical \(\text {CO}_2\) from inelastic X-ray scattering

  • Arijit Majumdar1,
  • Peihao Sun2,
  • Madison Singleton3,
  • Luigi Paolasini4,
  • Alexey Bosak4,
  • Alfred Q. R. Baron5,
  • Jerome Hastings6 &
  • …
  • Matthias Ihme1,6,7 

Scientific Reports , Article number:  (2026) Cite this article

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We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Biophysics
  • Chemistry
  • Materials science
  • Physics

Abstract

Supercritical fluids are characterized by unique thermodynamic properties. One of these properties is the existence of two-component dynamics that is associated with distinct low-frequency and high-frequency vibrational responses of the fluid. However, the origin of this behavior remains unknown. By combining inelastic X-ray scattering and molecular dynamics simulations, we show that this behavior can be connected to density heterogeneities arising from molecular clusters. Analyses of measurements and molecular trajectories suggest that the two-component dynamics emerges due to distinct momentum fluctuations of clustered and unbound molecules. This connection between clusters and two-component dynamics highlights the importance of molecular-structural heterogeneities in supercritical fluids, colloids, and condensed-matter systems.

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Data availability

The data supporting the findings of the study are included in the main text and supplementary information files. Source data have been deposited in the Supplementary Material and Stanford Digital Repository52: https://doi.org/10.25740/sj299gg3375. Additional data are available from the corresponding authors upon request.

Code availability

The MD simulations were performed with the open-source software LAMMPS (release date 8 April, 2021). Code for the analysis of the experimental data is available from the corresponding author upon request.

References

  1. Correa, C. R. & Kruse, A. Supercritical water gasification of biomass for hydrogen production-review. J. Supercrit. Fluids 133, 573–590 (2018).

    Google Scholar 

  2. Kendall, J. L., Canelas, D. A., Young, J. L. & DeSimone, J. M. Polymerizations in supercritical carbon dioxide. Chem. Rev. 99, 543–564 (1999).

    Google Scholar 

  3. Brunner, G. Applications of supercritical fluids. Annu. Rev. Chem. Biomol. Eng. 1, 321–342 (2010).

    Google Scholar 

  4. Benson, S. M. & Cole, D. R. CO\(_2\) sequestration in deep sedimentary formations. Elements 4, 325–331 (2008).

    Google Scholar 

  5. Gallo, P., Corradini, D. & Rovere, M. Widom line and dynamical crossovers as routes to understand supercritical water. Nat. Commun. 5, 5806 (2014).

    Google Scholar 

  6. Simeski, F. & Ihme, M. Supercritical fluids behave as complex networks. Nat. Commun. 14, 1996 (2023).

    Google Scholar 

  7. Simeoni, G. G. et al. The Widom line as the crossover between liquid-like and gas-like behaviour in supercritical fluids. Nat. Phys. 6, 503–507 (2010).

    Google Scholar 

  8. Gorelli, F., Santoro, M., Scopigno, T., Krisch, M. & Ruocco, G. Liquidlike behavior of supercritical fluids. Phys. Rev. Lett. 97, 245702 (2006).

    Google Scholar 

  9. Xu, L. et al. Relation between the Widom line and the dynamic crossover in systems with a liquid-liquid phase transition. Proc. Natl. Acad. Sci. 102, 16558–16562 (2005).

    Google Scholar 

  10. Brazhkin, V. V., Fomin, Y. D., Lyapin, A. G., Ryzhov, V. N. & Tsiok, E. N. Widom line for the liquid-gas transition in Lennard-Jones system. J. Phys. Chem. B 115, 14112–14115 (2011).

    Google Scholar 

  11. Brazhkin, V. V. et al. “Liquid-gas’’ transition in the supercritical region: Fundamental changes in the particle dynamics. Phys. Rev. Lett. 111, 145901 (2013).

    Google Scholar 

  12. Yang, C., Brazhkin, V. V., Dove, M. T. & Trachenko, K. Frenkel line and solubility maximum in supercritical fluids. Phys. Rev. E 91, 012112 (2015).

    Google Scholar 

  13. Fomin, Y. D., Ryzhov, V. N., Tsiok, E. N., Brazhkin, V. V. & Trachenko, K. Crossover of collective modes and positive sound dispersion in supercritical state. J. Phys. Condens. Matter 28, 43LT01 (2016).

    Google Scholar 

  14. Prescher, C. et al. Experimental evidence of the Frenkel line in supercritical neon. Phys. Rev. B 95, 134114 (2017).

    Google Scholar 

  15. Proctor, J., Pruteanu, C., Morrison, I., Crowe, I. & Loveday, J. Transition from gas-like to liquid-like behavior in supercritical \(\rm N_2\). J. Phys. Chem. Lett. 10, 6584–6589 (2019).

    Google Scholar 

  16. Bryk, T. et al. Behavior of Supercritical Fluids across the “Frenkel Line’’. J. Phys. Chem. Lett. 8, 4995–5001 (2017).

    Google Scholar 

  17. Proctor, J. E., Bailey, M., Morrison, I., Hakeem, M. A. & Crowe, I. F. Observation of liquid-liquid phase transitions in ethane at 300 K. J. Phys. Chem. B 122, 10172–10178 (2018).

    Google Scholar 

  18. Ishii, R. et al. A neutron scattering study of the structure of supercritical carbon dioxide. Chem. Phys. Lett. 240, 84–88 (1995).

    Google Scholar 

  19. Nishikawa, K., Tanaka, I. & Amemiya, Y. Small-angle X-ray scattering study of supercritical carbon dioxide. J. Phys. Chem. 100, 418–421 (1996).

    Google Scholar 

  20. Morita, T., Nishikawa, K., Takematsu, M., Iida, H. & Furutaka, S. Structure study of supercritical CO\(_2\) near higher-order phase transition line by X-ray diffraction. J. Phys. Chem. B 101, 7158–7162 (1997).

    Google Scholar 

  21. Botti, A., Bruni, F., Ricci, M. A. & Soper, A. Neutron diffraction study of high density supercritical water. J. Chem. Phys. 109, 3180–3184 (1998).

    Google Scholar 

  22. Pipich, V. & Schwahn, D. Densification of supercritical carbon dioxide accompanied by droplet formation when passing the Widom line. Phys. Rev. Lett. 120, 145701 (2018).

    Google Scholar 

  23. Sator, N. Clusters in simple fluids. Phys. Rep. 376, 1–39 (2003).

    Google Scholar 

  24. Fan, J., Ly, N. & Ihme, M. Heterogeneous cluster energetics and nonlinear thermodynamic response in supercritical fluids. Phys. Rev. Lett. 133, 248001 (2024).

    Google Scholar 

  25. Maddox, M. W., Goodyear, G. & Tucker, S. C. Origins of atom-centered local density enhancements in compressible supercritical fluids. J. Phys. Chem. B 104, 6248–6257 (2000).

    Google Scholar 

  26. Majumdar, A. et al. Direct observation of ultrafast cluster dynamics in supercritical carbon dioxide using X-ray photon correlation spectroscopy. Nat. Commun. 15, 10540 (2024).

    Google Scholar 

  27. Sun, P., Hastings, J. B., Ishikawa, D., Baron, A. Q. R. & Monaco, G. Two-component dynamics and the liquidlike to gaslike crossover in supercritical water. Phys. Rev. Lett. 125, 256001 (2020).

    Google Scholar 

  28. Boon, J. P. & Yip, S. Molecular Hydrodynamics (Courier Corporation, 1991).

  29. Sun, P., Hastings, J., Ishikawa, D., Baron, A. Q. R. & Monaco, G. Universal two-component dynamics in supercritical fluids. J. Phys. Chem. B 125, 13494–13501 (2021).

    Google Scholar 

  30. Baron, A. Q. R. High-resolution inelastic x-ray scattering I: Context, spectrometers, samples, and superconductors. In Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications (eds Jaeschke, E. et al.) 2131–2212 (Springer, 2020).

  31. Lemmon, E. W., Bell, I. H., Huber, M. L. & McLinden, M. O. Thermophysical properties of fluid systems. In NIST Chemistry WebBook, NIST Standard Reference Database Number 69 (eds Linstrom, P. J. & Mallard, W. G.) (National Institute of Standards and Technology, 2025).

  32. 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).

    Google Scholar 

  33. Potoff, J. J. & Siepmann, J. I. Vapor-liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen. AIChE J. 47, 1676–1682 (2001).

    Google Scholar 

  34. Aimoli, C. G., Maginn, E. J. & Abreu, C. R. A. Force field comparison and thermodynamic property calculation of supercritical CO\(_2\) and CH\(_4\) using molecular dynamics simulations. Fluid Ph. Equilib. 368, 80–90 (2014).

    Google Scholar 

  35. Bencivenga, F. et al. High-frequency dynamics of liquid and supercritical water. Phys. Rev. E 75, 051202 (2007).

    Google Scholar 

  36. Monaco, G., Cunsolo, A., Ruocco, G. & Sette, F. Viscoelastic behavior of water in the terahertz-frequency range: An inelastic x-ray scattering study. Phys. Rev. E 60, 5505 (1999).

    Google Scholar 

  37. Ishikawa, D. & Baron, A. Q. R. Interaction of acoustic and quasi-elastic modes in liquid water on nanometer length scales. J. Phys. Soc. Jpn. 90, 083602 (2021).

    Google Scholar 

  38. Sun, P. Molecular Dynamics of Supercritical Fluids. Ph.D. thesis, Stanford University (2021).

  39. Sampoli, M., Ruocco, G. & Sette, F. Mixing of longitudinal and transverse dynamics in liquid water. Phys. Rev. Lett. 79, 1678 (1997).

    Google Scholar 

  40. Bolmatov, D., Zav’Yalov, D., Gao, M. & Zhernenkov, M. Structural evolution of supercritical CO\(_2\) across the Frenkel line. J. Phys. Chem. Lett. 5, 2785–2790 (2014).

    Google Scholar 

  41. Giordano, V. M. & Monaco, G. Fingerprints of order and disorder on the high-frequency dynamics of liquids. Proc. Natl. Acad. Sci. 107, 21985–21989 (2010).

    Google Scholar 

  42. Scopigno, T., D’astuto, M., Krisch, M., Ruocco, G. & Sette, F. Observation of Umklapp processes in noncrystalline materials. Phys. Rev. B 64, 012301 (2001).

    Google Scholar 

  43. Muhunthan, P. et al. A self-consistent analysis of cluster morphology in supercritical carbon dioxide from small angle x-ray scattering. Chem. Phys. Lett. 142190 (2025).

  44. Hill, T. L. Molecular clusters in imperfect gases. J. Chem. Phys. 23, 617–622 (1955).

    Google Scholar 

  45. Simdyankin, S. I., Taraskin, S. N., Dzugutov, M. & Elliott, S. R. Vibrational properties of the one-component \(\sigma\) phase. Phys. Rev. B 62, 3223 (2000).

    Google Scholar 

  46. Kittel, C. & McEuen, P. Introduction to Solid State Physics (Wiley, 2018).

  47. Kalinichev, A. G. Molecular simulations of liquid and supercritical water: Thermodynamics, structure, and hydrogen bonding. Rev. Mineral. Geochem. 42, 83–129 (2001).

    Google Scholar 

  48. Boero, M., Terakura, K., Ikeshoji, T., Liew, C. C. & Parrinello, M. Hydrogen bonding and dipole moment of water at supercritical conditions: A first-principles molecular dynamics study. Phys. Rev. Lett. 85, 3245 (2000).

    Google Scholar 

  49. Rowlinson, J. S. & Swinton, F. L. Liquids and Liquid Mixtures (Butterworth-Heinemann, 2013).

  50. Mattenet, M. et al. An X-Ray Thermo-Pressure Cell For Carbon Dioxide. In AIP Conference Proceedings, Vol. 1234, 111–114 (American Institute of Physics, 2010).

  51. Walters, A. C. Using X-ray and neutron scattering to study the dynamics of low-dimensional systems. Ph.D. thesis, University College London (2009).

  52. Majumdar, A. et al. Database for heterogeneity induced universal two-component dynamics in supercritical fluids, https://doi.org/10.25740/sj299gg3375 (2025).

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Funding

Financial support from the U.S. Department of Energy, Office of Science under DOE (BES) Awards DE-SC0022222 and DE-SC0026165 (A.M. and M.I.) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Stanford University, Stanford, 94305, USA

    Arijit Majumdar & Matthias Ihme

  2. Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova, 35131, Padua, Italy

    Peihao Sun

  3. Applied Physics Department, Stanford University, Stanford, 94305, USA

    Madison Singleton

  4. European Synchrotron Radiation Facility, 38000, Grenoble, France

    Luigi Paolasini & Alexey Bosak

  5. Materials Dynamics Laboratory, RIKEN SPring-8 Center, Sayo, 679-5148, Japan

    Alfred Q. R. Baron

  6. SLAC National Accelerator Laboratory, Menlo Park, 94025, USA

    Jerome Hastings & Matthias Ihme

  7. Energy Science and Engineering Department, Stanford University, Stanford, 94305, USA

    Matthias Ihme

Authors
  1. Arijit Majumdar
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  2. Peihao Sun
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  4. Luigi Paolasini
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Contributions

A.M.: Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing original draft, Writing - review & editing; P.S.: Data curation, Formal analysis, Investigation, Methodology, Writing - review & editing; M.S.: Data curation, Formal analysis, Investigation, Methodology, Software, Writing - review & editing; L.P.: Investigation, Methodology, Resources, Writing - review & editing; A.B.: Investigation, Methodology, Resources, Writing - review & editing; A.Q.R.B.: Formal analysis, Investigation, Methodology, Software, Writing - review & editing; J.H.: Investigation, Methodology, Resources, Project administration, Supervision, Writing - review & editing; M.I.: Conceptualization, Investigation, Methodology, Resources, Funding acquisition, Project administration, Supervision, Writing - review & editing

Corresponding authors

Correspondence to Peihao Sun or Matthias Ihme.

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Majumdar, A., Sun, P., Singleton, M. et al. Two-component dynamics in supercritical \(\text {CO}_2\) from inelastic X-ray scattering. Sci Rep (2026). https://doi.org/10.1038/s41598-026-38697-z

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  • Received: 22 December 2025

  • Accepted: 30 January 2026

  • Published: 11 February 2026

  • DOI: https://doi.org/10.1038/s41598-026-38697-z

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Keywords

  • Inelastic X-ray scattering
  • Supercritical fluids
  • Two-component dynamics
  • Cluster dynamics
  • Carbon dioxide
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