- Physical Review Journals
All JournalsPhysics Magazine

PRX Energy

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Measuring hydrogen ortho-para composition with a microwave cavity resonator

Guinevere M. Sellner1,2, Matthew G. Hopkins1, Maxim Goryachev3, Liam D. Tenardi1,2, Eric F. May1,2, and Paul L. Stanwix1,*

  • 1Fluid Science and Resources Research Group, School of Engineering, The University of Western Australia, Crawley, Western Australia 6009, Australia
  • 2Future Energy Exports Cooperative Research Centre (FEnEx CRC), Crawley, Western Australia 6009, Australia
  • 3Quantum Technologies and Dark Matter Research Lab, Department of Physics, The University of Western Australia, Crawley, Western Australia 6009, Australia

  • *Contact author: paul.stanwix@uwa.edu.au
PDF

PRX Energy 5, 013010 – Published 9 March, 2026

DOI: https://doi.org/10.1103/lf6d-nnr8

Abstract

The nuclear spin-isomer (ortho-para) composition of molecular hydrogen strongly influences the safety and efficiency of cryogenic hydrogen handling, as the energy of ortho-para conversion exceeds the enthalpy of vaporization of liquid hydrogen, generating boil-off losses. Accurate in situ measurement of spin-isomer composition at cryogenic conditions is therefore essential for liquefaction process design, spin-isomer catalyst characterization, and custody transfer. Here we demonstrate a microwave cavity resonator as a novel sensor for real-time quantification of hydrogen ortho-para composition. The method exploits contrast in the dielectric permittivity of the nuclear-spin isomers, enabling precise tracking of natural ortho-para conversion dynamics in solid (10.0 K), liquid (16.6–19.9 K), and supercritical (40.4 K) hydrogen. Measurement uncertainties averaged 0.007 mol/mol across all phases. During conversion, the resonant frequencies followed a second-order kinetic model consistent with theoretical predictions and prior studies, with final equilibrium compositions independently validated by Raman spectroscopy. The determined conversion rate constants agree with the empirical correlation of a previous study, while also revealing the potential errors introduced from measuring natural conversion kinetics over a limited concentration range. Furthermore, our results identify significant discrepancies between experimental dielectric data and current predictive models, underscoring the need to refine hydrogen property models at cryogenic conditions. This work establishes microwave cavity resonators as a powerful tool for ortho-para hydrogen sensing at cryogenic conditions, with applications spanning industrial liquid hydrogen process monitoring, hydrogen isomer conversion catalyst development, and high-energy physics.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Hydrogen is a promising clean fuel, but storing it as a liquid at very low temperature (~20 K) brings unique challenges. A latent quantum effect can occur at low temperature - the conversion between molecular hydrogen's two nuclear-spin-isomer states, called ortho and para, releasing more heat than it takes to boil the liquid. If uncontrolled, this can lead to inefficient and unsafe production and handling of liquid hydrogen. Measuring the ratio of these isomers is therefore crucial, yet existing methods struggle under cryogenic conditions. In this work, the authors introduce microwave cavity resonators as a new modality for sensing the isomer state of cryogenic hydrogen. By detecting subtle changes in hydrogen's dielectric properties, this device was able to monitor the slow natural conversion between ortho and para-hydrogen in solid, liquid, and supercritical phases between 10 and 40 K. The sensor achieved high accuracy and revealed conversion behavior consistent with quantum theory. This work also exposed shortcomings in current hydrogen property models, pointing the way toward more reliable predictions. This sensor enables improved monitoring of industrial hydrogen liquefaction, enhancing efficiency and safety. It also has potential as a valuable tool for aiding in developing spin-conversion catalysts and in fundamental physics applications where cryogenic hydrogen plays a key role.

Article Text

References (86)

  1. I. E. A. (IEA, “Global Hydrogen Review 2023,” License: CC BY 4.0, Paris (2023). Available: https://www.iea.org/reports/global-hydrogen-review-2023.
  2. S. Z. Al Ghafri, S. Munro, U. Cardella, T. Funke, W. Notardonato, J. M. Trusler, J. Leachman, R. Span, S. Kamiya, G. Pearce, et al., Hydrogen liquefaction: a review of the fundamental physics, engineering practice and future opportunities, Energy Environ. Sci. 15 (7), 2690 (2022).
  3. J. W. Leachman, R. T. Jacobsen, S. G. Penoncello, and E. W. Lemmon, fundamental equations of state for parahydrogen, normal hydrogen, and orthohydrogen, J. Phys. Chem. Ref. Data 38 (3), 721 (2009).
  4. P. Atkins and T. Overton, Shriver and Atkins’ Inorganic Chemistry (OUP, Oxford, 2010), pp. 274–292.
  5. L. Barrón-Palos, R. Alarcon, S. Balascuta, C. Blessinger, J. D. Bowman, T. E. Chupp, S. Covrig, C. B. Crawford, M. Dabaghyan, J. Dadras, et al., Determination of the parahydrogen fraction in a liquid hydrogen target using energy-dependent slow neutron transmission, Nucl. Instrum. Methods Phys. Res., Sect. A 659 (1), 579 (2011).
  6. A. Braeuer, In Situ Spectroscopic Techniques at High Pressure (Elsevier, Erlangen-Nürnberg, Germany, 2015).
  7. D. R. Farley, D. P. Stotler, D. P. Lundberg, and S. A. Cohen, Modeling of hydrogen ground state rotational and vibrational temperatures in kinetic plasmas, J. Quant. Spectrosc. Radiat. Transfer 112 (5), 800 (2011).
  8. P. E. Falloon, C. J. Baker, D. Rowland, V. Jusko, D. Zhu, X. Xiao, X. Yang, Z. Aman, O. Frotscher, and E. F. May, “ThermoFAST 2. Thermodynamic Calculator for Fluid Mixture Properties,” ed: Fluid Science and Resources Research Group, The University of Western Australia (2022).
  9. H. W. Woolley, R. B. Scott, and F. G. Brickwedde, Compilation of thermal properties of hydrogen in its various isotopic and ortho–para modifications, J. Res. Natl. Bur. Stand. 41 (5), 379 (1948).
  10. J. K. Peng and R. K. Ahluwalia, Enhanced dormancy due to para-to-ortho hydrogen conversion in insulated cryogenic pressure vessels for automotive applications, Int. J. Hydrogen Energy 38 (31), 13664 (2013).
  11. P. J. Donaubauer, U. Cardella, L. Decker, and H. Klein, Kinetics and heat exchanger design for catalytic ortho–para hydrogen conversion during liquefaction, Chem. Eng. Technol. 42 (3), 669 (2019).
  12. Y. Y. Milenko, R. M. Sibileva, and M. A. Strzhemechny, Natural ortho–para conversion rate in liquid and gaseous hydrogen, J. Low Temp. Phys. 107 (1), 77 (1997).
  13. S. Eisenhut and C. Haberstroh, Ortho-parahydrogen catalyst test facility, IOP Conf. Ser.: Mater. Sci. Eng. 1301 (1), 012058 (2024).
  14. G. Romanelli, S. Rudić, M. Zanetti, C. Andreani, F. Fernandez-Alonso, G. Gorini, M. Krzystyniak, and G. Škoro, Measurement of the para-hydrogen concentration in the ISIS moderators using neutron transmission and thermal conductivity, Nucl. Instrum. Methods Phys. Res., Sect. A 888, 88 (2018).
  15. R. C. Gillis, T. Bailey, F. X. Gallmeier, M. A. Hartl, and E. B. Iverson, Raman Spectroscopy as an ortho–para diagnostic of liquid hydrogen moderators, J. Phys.: Conf. Ser. 1021 (1), 012062 (2018).
  16. D. A. Skoog, F. J. Holler, and S. R. Crouch, in Principles of instrumental analysis, 7th ed. (Cengage learning, Boston, MA, 2017), pp. 453–500.
  17. C. D. Bunge, A high-fidelity, continuous ortho-parahydrogen measurement and conversion system, Ph.D. thesis, School of Mechanical and Materials Engineering, Washington State University, Washington, United States, 2021.
  18. B. Krasch, S. Mirz, A. Smolinski, O. Süß, and R. Größle, Raman spectroscopy for ortho–para hydrogen catalyst studies, Int. J. Hydrogen Energy 48 (77), 29952 (2023).
  19. B. da Silva Falcão, K. Jeong, S. Al Ghafri, N. Robinson, L. Tang, K. Kozielski, and M. L. Johns, Ortho- to para-hydrogen catalytic conversion kinetics, Int. J. Hydrogen Energy 62, 345 (2024).
  20. F. Luther, G. M. Sellner, M. Richter, and P. L. Stanwix, Inherent single-point calibration for quantitative Raman analysis of ortho–para hydrogen composition, Int. J. Hydrogen Energy 102, 778 (2025).
  21. A. J. Parrott, P. Dallin, J. Andrews, P. M. Richardson, O. Semenova, M. E. Halse, S. B. Duckett, and A. Nordon, Quantitative in situ monitoring of parahydrogen fraction using raman spectroscopy, Appl. Spectrosc. 73 (1), 88 (2018).
  22. E. Karlsson, Catalytic ortho- to parahydrogen conversion in liquid hydrogen, Master’s thesis, Materials Engineering, Lund University, Lund, Sweden, 2017. Available: http://lup.lub.lu.se/student-papers/record/8929488.
  23. D. N. Mitchell and D. J. Le Roy, Theoretical and experimental behaviour of a thermal conductivity detecter for the determination of the ortho/para hydrogen composition of gas mixtures in the temperature-jump region, Can. J. Chem. 56 (13), 1817 (1978).
  24. E. W. Lemmon, I. H. Bell, M. L. Huber, and M. O. McLinden, “NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties—REFPROP 10.0,” ed: National Institute of Standards and Technology (NIST), (2018).
  25. S. R. Lydzinski, D. Celik, A. Hemmati, and S. W. Van Sciver, Ortho and para hydrogen concentration determination based on vapor pressure, AIP Conf. Proc. 823 (1), 475 (2006).
  26. H. L. Hutchinson, Analysis of catalytic ortho-parahydrogen reaction mechanisms, Master’s thesis, Chemical and Biological Engineering, University of Colorado Boulder, Boulder, CO, 1966.
  27. D. H. Weitzel, W. V. Loebenstein, J. W. Draper, and O. E. Park, Ortho–para catalysis in liquid-hydrogen production, J. Res. Natl. Bur. Stand. 60 (3), 221 (1958).
  28. E. R. Grilly, A simple thermal conductivity analyzer for ortho–para hydrogen, Rev. Sci. Instrum. 24 (1), 72 (1953).
  29. M. J. Assael, J.-A. M. Assael, M. L. Huber, R. A. Perkins, and Y. Takata, Correlation of the thermal conductivity of normal and parahydrogen from the triple point to 1000 K and up to 100 MPa, J. Phys. Chem. Ref. Data 40 (3), 033101 (2011).
  30. T. W. Bradshaw and J. O. W. Norris, Observations on the use of a thermal conductivity cell to measure the para hydrogen concentration in a mixture of para and ortho hydrogen gas, Rev. Sci. Instrum. 58 (1), 83 (1987).
  31. G. Tsankova, M. Richter, A. Madigan, P. L. Stanwix, E. F. May, and R. Span, Characterisation of a microwave re-entrant cavity resonator for phase-equilibrium measurements and new dew-point data for a (0.25 argon + 0.75 carbon dioxide) mixture, J. Chem. Thermodyn. 101, 395 (2016).
  32. F. Fogh and P. Rasmussen, Detection of high-pressure dew and bubble points using a microwave technique, Ind. Eng. Chem. Res. 28 (3), 371 (1989).
  33. E. F. May, T. J. Edwards, A. G. Mann, and C. Edwards, Dew point, liquid volume, and dielectric constant measurements in a vapor mixture of methane + propane using a microwave apparatus, Int. J. Thermophys. 24 (6), 1509 (2003).
  34. C. C. Sampson, M. Kamson, M. G. Hopkins, P. L. Stanwix, and E. F. May, Dielectric permittivity, polarizability and dipole moment of refrigerants R1234ze(E) and R1234yf determined using a microwave re-entrant cavity resonator, J. Chem. Thermodyn. 128, 148 (2019).
  35. W. J. Rogers, J. C. Holste, P. T. Eubank, and K. R. Hall, Microwave apparatus for phase transition studies of corrosive fluids to 1.7 kbar and 588 K, Rev. Sci. Instrum. 56 (10), 1907 (1985).
  36. M. E. Kandil, K. N. Marsh, and A. R. H. Goodwin, Determination of the relative permittivity and density within the gas phase and liquid volume fraction formed within the two-phase region for (0.4026 CH4 + 0.5974 C3H8) with a radio frequency re-entrant cavity, J. Chem. Eng. Data 52 (5), 1660 (2007).
  37. A. R. H. Goodwin and M. R. Moldover, Phase border and density determinations in the critical region of (carbon dioxide + ethane) determined from dielectric permittivity measurements, J. Chem. Thermodyn. 29 (12), 1481 (1997).
  38. M. G. Hopkins, A. Siahvashi, X. Yang, M. Richter, P. L. Stanwix, and E. F. May, A microwave sensor for detecting impurity freeze out in liquefied natural gas production, Fuel Process. Technol. 219, 106878 (2021).
  39. L. D. Tenardi, M. G. Hopkins, M. Richter, E. F. May, and P. L. Stanwix, A composite microwave cavity for liquid volume fraction and simultaneous phase permittivity measurements, Int. J. Thermophys. 45 (12), 168 (2024).
  40. E. F. May, An advanced microwave apparatus for the measurement of phase behaviour in gas condensate fluids, Ph.D. thesis, School of Mechanical Engineering, The University of Western Australia, Perth, Australia, 2003.
  41. R. Clausius, Die mechanische behandlung der electricität, 2nd ed. (Vieweg + Teubner Verlag, Wiesbaden, 1879).
  42. A. H. Harvey and E. W. Lemmon, Method for estimating the dielectric constant of natural gas mixtures, Int. J. Thermophys. 26 (1), 31 (2005).
  43. G. Garberoglio and A. H. Harvey, Path-integral calculation of the second dielectric and refractivity virial coefficients of helium, neon, and argon, j. Res. Natl. Inst. Stand. Technol. 125, 125022 (2020).
  44. A. H. Harvey and J. M. Prausnitz, Dielectric constants of fluid mixtures over a wide range of temperature and density, J. Solution Chem. 16 (10), 857 (1987).
  45. V. V. Pashkov and V. S. Marinin, Dielectric-constant anomalies of liquid ortho/para hydrogen mixtures, Sov. J. Low Temp. Phys. 13 (12), 706 (1987).
  46. Y. Y. Milenko and R. M. Sibileva, Dependence of dielectric constant of liquid hydrogen on ortho–para composition, Ukrains'kii Fizichnii Zhurnal 20 (11), 1806 (1975).
  47. E. F. May, M. R. Moldover, and J. W. Schmidt, Reference measurements of hydrogen’s dielectric permittivity, Mol. Phys. 107 (15), 1577 (2009).
  48. L. J. F. Hermans, J. J. De Groot, H. F. P. Knaap, and J. J. M. Beenakker, The polarizability of the hydrogen-isotopes and of ortho and para hydrogen, Physica 31 (10), 1567 (1965).
  49. V. S. Kogan, Y. Y. Milenko, and T. K. Grigorova, Dielectric constant measurement of hydrogen isotopes in the liquid phase, Physica 53 (1), 125 (1971).
  50. E. P. Wigner, in Part I: Physical Chemistry. Part II: Solid State Physics, edited by Arthur S. Wightman (Springer, Berlin, Heidelberg, 1933), pp. 126–130.
  51. K. Motizuki and T. Nagamiya, Theory of the ortho–para conversion in solid hydrogen, J. Phys. Soc. Jpn. 11 (2), 93 (1956).
  52. A. J. Berlinsky, Theory of ortho–para conversion in solid hydrogen at high densities, Phys. Rev. B 12 (4), 1482 (1975).
  53. A. Driessen, E. van der Poll, and I. F. Silvera, Ortho–para conversion of solid hydrogen as a function of density, Phys. Rev. B 30 (5), 2517 (1984).
  54. A. H. Larsen, F. E. Simon, and C. A. Swenson, The rate of evaporation of liquid hydrogen due to the ortho–para hydrogen conversion, Rev. Sci. Instrum. 19, 266 (1948).
  55. P. Pedroni, H. Meyer, F. Weinhaus, and D. Haase, Ortho–para conversion rate in solid hydrogen under pressure, Solid State Commun. 14 (3), 279 (1974).
  56. T. Bodziony, S. M. Kaczmarek, V. H. Tran, P. Figiel, A. Biedunkiewicz, and G. Leniec, Magnetic properties of AISI 316L stainless steel doped with nanocrystalline Ti–B–C powders, Mater. Res. Express 5 (12), 126105 (2018).
  57. Z. Xia, J. Bray-Ali, J. Zhang, B. R. Fink, K. S. White, C. M. Gould, and H. M. Bozler, Magnetization of materials used in cryostats, J. Low Temp. Phys. 126 (1), 655 (2002).
  58. S. Andersson and J. Harris, Observation of rotational transitions for H2, D2, and HD adsorbed on Cu(100), Phys. Rev. Lett. 48 (8), 545 (1982).
  59. P. Avouris, D. Schmeisser, and J. E. Demuth, Observation of rotational excitations of H2 adsorbed on Ag surfaces, Phys. Rev. Lett. 48 (3), 199 (1982).
  60. P. J. Petersan and S. M. Anlage, Measurement of resonant frequency and quality factor of microwave resonators: Comparison of methods, J. Appl. Phys. 84 (6), 3392 (1998).
  61. J. F. Rouleau, J. Goyette, T. K. Bose, and M. F. Fréchette, Investigation of a microwave differential cavity resonator device for the measurement of humidity in gases, Rev. Sci. Instrum. 70 (9), 3590 (1999).
  62. D. Kashchiev, Nucleation: Basic Theory with Applications (Butterworth-Heinemann (Elsevier), Oxford; Boston, 2000).
  63. R. E. Bedford, G. Bonnier, H. Maas, and F. Pavese, Recommended values of temperature on the International Temperature Scale of 1990 for a selected set of secondary reference points, Metrologia 33 (2), 133 (1996).
  64. H. Preston-Thomas, The International Temperature Scale of 1990 (ITS-90), Metrologia 27 (1), 3 (1990).
  65. B. A. Younglove, Polarizability, dielectric constant, pressure, and density of solid parahydrogen on the melting line, J. Chem. Phys. 48 (9), 4181 (1968).
  66. G. Ahlers, Lattice heat capacity of solid hydrogen, J. Chem. Phys. 41 (1), 86 (1964).
  67. V. V. Pashkov and M. P. Lobko, in Advances in Cryogenic Engineering, edited by K. D. Timmerhaus and H. A. Snyder (Springer US, Boston, MA, 1980), pp. 709–714.
  68. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, et al., SciPy 1.0: fundamental algorithms for scientific computing in Python, Nat. Methods 17 (3), 261 (2020).
  69. A. D. May, V. Degen, J. C. Stryland, and H. L. Welsh, The Raman effect in gaseous hydrogen at high pressures, Can. J. Phys. 39 (12), 1769 (1961).
  70. Joint Committee for Guides in Metrology, “Guide to the Expression of Uncertainty in Measurement,” in “JCGM 100:2008,” BIPM, Sèvres, France (2008). Available: https://www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf.
  71. G. Tsankova, P. L. Stanwix, E. F. May, and M. Richter, Densities, dielectric permittivities, and dew points for (argon + carbon dioxide) mixtures determined with a microwave re-entrant cavity resonator, J. Chem. Eng. Data 62 (9), 2521 (2017).
  72. S. Andersson and B. N. J. Persson, Long-range scattering of electrons by electron-hole pair excitations at metal surfaces, Phys. Rev. Lett. 50 (25), 2028 (1983).
  73. J. T. Kummer, Ortho–para–hydrogen conversion by metal surfaces at 21°K, J. Phys. Chem. 66 (9), 1715 (1962).
  74. G. Breit and H. Kamerlingh Onnes, Preliminary measurements concerning the dielectric constants of liquid hydrogen and liquid oxygen and its dependence on temperature as regards the latter (Communication 171a), Proc. R. Acad. Amsterdam 27, 617 (1924).
  75. M. Wolfke and H. Kamerlingh Onnes, On the dielectric constants of liquid and solid hydrogen (Communication 171c), Proc. R. Acad. Amsterdam 27, 627 (1924).
  76. W. Werner and W. H. Keesom, The variation of the dielectric constant of liquid and solid hydrogen with temperature (Communication 178a), Proc. R. Acad. Amsterdam 28, 34 (1925).
  77. H. E. Johns and J. O. Wilhelm, The refractive indices of liquid oxygen, nitrogen, and hydrogen, Can. J. Res. 15a (7), 101 (1937).
  78. R. Guillien, La constante diélectrique au voisinage du point de fusion, J. Phys. Radium 1 (1), 29 (1940).
  79. A. Van Itterbeek and J. Spaepen, Détermination de la constante dielectricque du deuterium liquide, Physica 9 (3), 339 (1942).
  80. J. W. Stewart, Dielectric polarizability of fluid para-hydrogen, J. Chem. Phys. 40 (11), 3297 (1964).
  81. V. V. Pashkov and M. P. Lobko, The dielectric properties of liquid normal and parahydrogen, Sov. J. Low Temp. Phys. 5 (5), 203 (1979).
  82. T. Charignon, D. Celik, A. Hemmati, and S. W. Van Sciver, Dielectric coefficient and density of subcooled liquid hydrogen, Cryogenics 47 (4), 252 (2007).
  83. J. Rychlewski, An accurate calculation of the polarizability of the hydrogen molecule and its dependence on rotation, vibration and isotopic substitution, Mol. Phys. 41 (4), 833 (1980).
  84. A. N. Podgorny and V. V. Pashkov, Peculiarities of thermodynamic behaviour of liquid hydrogen, Int. J. Hydrogen Energy 13 (4), 231 (1988).
  85. C. Gaiser and B. Fellmuth, Highly-accurate density-virial-coefficient values for helium, neon, and argon at 0.01 °C determined by dielectric-constant gas thermometry, J. Chem. Phys. 150 (13), 134303 (2019).
  86. J. H. Constable, C. F. Clark, and J. R. Gaines, The dielectric constant of H2, D2, and HD in the condensed phases, J. Low Temp. Phys. 21 (5), 599 (1975).

Outline

Information

PRX Energy 5, 013010– Published 9 March, 2026
  • Received 12 September 2025
  • Revised 21 December 2025
  • Accepted 2 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation