Reversible thermodynamic pathways in shock-compressed liquid nitrogen: Unveiling the role of molecular dissociation in shock cooling and phase transition

Akram Muhammad Sabeeh; Sattar Shumail; Wei Yi-Wen; Yang Lei; Yuan Wen-Shuo; Fan Zhuo-Ning; Liu Qi-Jun; Liu Fu-Sheng

doi:10.1063/5.0311261

Volume 11 Issue 3

May 2026

Turn off MathJax

Article Contents

Article Navigation > Matter and Radiation at Extremes > 2026 > 11(3): 037602

Akram Muhammad Sabeeh, Sattar Shumail, Wei Yi-Wen, Yang Lei, Yuan Wen-Shuo, Fan Zhuo-Ning, Liu Qi-Jun, Liu Fu-Sheng. Reversible thermodynamic pathways in shock-compressed liquid nitrogen: Unveiling the role of molecular dissociation in shock cooling and phase transition[J]. Matter and Radiation at Extremes, 2026, 11(3): 037602. doi: 10.1063/5.0311261

Citation:

Akram Muhammad Sabeeh, Sattar Shumail, Wei Yi-Wen, Yang Lei, Yuan Wen-Shuo, Fan Zhuo-Ning, Liu Qi-Jun, Liu Fu-Sheng. Reversible thermodynamic pathways in shock-compressed liquid nitrogen: Unveiling the role of molecular dissociation in shock cooling and phase transition[J]. Matter and Radiation at Extremes, 2026, 11(3): 037602. doi: 10.1063/5.0311261

Citation:

Akram Muhammad Sabeeh, Sattar Shumail, Wei Yi-Wen, Yang Lei, Yuan Wen-Shuo, Fan Zhuo-Ning, Liu Qi-Jun, Liu Fu-Sheng. Reversible thermodynamic pathways in shock-compressed liquid nitrogen: Unveiling the role of molecular dissociation in shock cooling and phase transition[J]. Matter and Radiation at Extremes, 2026, 11(3): 037602. doi: 10.1063/5.0311261

PDF( 7843 KB)

Reversible thermodynamic pathways in shock-compressed liquid nitrogen: Unveiling the role of molecular dissociation in shock cooling and phase transition

doi: 10.1063/5.0311261

Akram Muhammad Sabeeh^{1, 2, 3
,
,
,},
Sattar Shumail⁴,
Wei Yi-Wen^{2, 3},
Yang Lei^{2, 3},
Yuan Wen-Shuo^{2, 3
,},
Fan Zhuo-Ning^{2, 3},
Liu Qi-Jun^{2, 3
,},
Liu Fu-Sheng^{2, 3
,
,}

1.
School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
2.
School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
3.
Sichuan Provincial Key Laboratory (for Universities) of High-Pressure Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
4.
Department of Physics, University of Agriculture, Faisalabad 38040, Pakistan

More Information

Corresponding author: a)Authors to whom correspondence should be addressed: Sabeeh@my.swjtu.edu.cn and Fusheng_l@163.com
Received Date: 2025-11-08
Accepted Date: 2026-02-08

Available Online: 2026-05-01

Publish Date: 2026-05-28

Abstract

Abstract

This study investigates the high-pressure behavior of liquid nitrogen (LN₂), under dynamic compression from 19 to 89 GPa and corresponding temperatures from 4000 to 8200 K. Using Doppler velocimetry and multichannel pyrometry, we determine the Hugoniot states, shock temperatures, and emissivity. The application of sequential shocks and subsequent pressure release process lead to significant variations in radiance and radiative temperature, which help to predict the optical transparency at the LN₂/LiF interface. Our results indicate the existence of two distinct thermodynamic pathways. In experiments with an initial shock >30 GPa, at the second shock (re-shock), the fluid undergoes shock cooling, which we attribute to the formation of a transient complex molecular state. Further, during pressure release, we observe thermal energy emission, which indicates that decompression primarily governs the phase transitions as well as the reversible thermodynamic pathways. By contrast, LN₂ initially shocked to 19 GPa undergoes dissociation upon re-shock, followed by recombination during pressure release, with no evidence of cooling being observed. A comparison of these results suggests that shock cooling consistently appears above 30 GPa and 6500 K. Furthermore, these two regimes are differentiated by their response to pressure release: while both show a decrease in emissivity that reflects restoration of the fluid’s transparency, the magnitudes are dramatically different. A 21% decrease occurs in the shock-cooling regime, compared with a 39% reduction in the dissociation-dominated regime.

Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Muhammad Sabeeh Akram: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Methodology (lead); Validation (lead); Writing – original draft (lead); Writing – review & editing (lead). Shumail Sattar: Formal analysis (supporting); Visualization (supporting); Writing – original draft (supporting); Writing – review & editing (equal). Yi-Wen Wei: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (supporting); Software (lead). Lei Yang: Data curation (supporting); Investigation (supporting); Methodology (supporting); Resources (equal). Wen-Shuo Yuan: Data curation (equal); Investigation (supporting); Methodology (supporting); Resources (supporting); Software (lead); Validation (equal); Visualization (equal). Zhuo-Ning Fan: Data curation (supporting); Formal analysis (supporting); Methodology (lead); Resources (supporting). Qi-Jun Liu: Investigation (equal); Project administration (supporting); Resources (supporting). Fu-Sheng Liu: Conceptualization (lead); Data curation (equal); Formal analysis (equal); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Resources (supporting); Supervision (lead); Validation (equal).
The data that support the findings of this study are available from the corresponding authors upon reasonable request.

FullText(HTML)

References(67)

References

[1]	K. Takemura, S. Minomura, O. Shimomura, and Y. Fujii, “Observation of molecular dissociation of iodine at high pressure by x-ray diffraction,” Phys. Rev. Lett. 45, 1881–1884 (1980).10.1103/physrevlett.45.1881
[2]	E. Katoh, H. Yamawaki, H. Fujihisa, M. Sakashita, and K. Aoki, “Raman study of phase transition and hydrogen bond symmetrization in solid DCl at high pressure,” Phys. Rev. B 61, 119–124 (2000).10.1103/physrevb.61.119
[3]	A. F. Goncharov, V. V. Struzhkin, H.-k. Mao, and R. J. Hemley, “Raman spectroscopy of dense H2O and the transition to symmetric hydrogen bonds,” Phys. Rev. Lett. 83, 1998–2001 (1999).10.1103/physrevlett.83.1998
[4]	W. B. Hubbard, “Interiors of the giant planets,” Science 214, 145–149 (1981).10.1126/science.214.4517.145
[5]	L. N. Fletcher, I. de Pater, G. S. Orton, M. D. Hofstadter, P. G. J. Irwin et al., “Ice giant circulation patterns: implications for atmospheric probes,” Space Sci. Rev. 216(2), 21 (2020).10.1007/s11214-020-00646-1
[6]	S. Jiang, N. Holtgrewe, S. S. Lobanov, F. Su, M. F. Mahmood et al., “Metallization and molecular dissociation of dense fluid nitrogen,” Nat. Commun. 9, 2624 (2018).10.1038/s41467-018-05011-z
[7]	R. L. Hudson and M. H. Moore, “The N3 radical as a discriminator between ion-irradiated and UV-photolyzed astronomical ices,” Astrophys. J. 568, 1095–1099 (2002).10.1086/339039
[8]	D. M. Badgujar, M. B. Talawar, S. N. Asthana, and P. P. Mahulikar, “Advances in science and technology of modern energetic materials: An overview,” J. Hazard. Mater. 151, 289–305 (2008).10.1016/j.jhazmat.2007.10.039
[9]	M. Bagge-Hansen, S. Bastea, J. A. Hammons, M. H. Nielsen, L. M. Lauderbach et al., “Detonation synthesis of carbon nano-onions via liquid carbon condensation,” Nat. Commun. 10(1), 3819 (2019).10.1038/s41467-019-11666-z
[10]	M. C. Marshall, A. Fernandez-Pañella, T. W. Myers, J. H. Eggert, D. J. Erskine et al., “Shock Hugoniot measurements of single-crystal 1, 3, 5-triamino-2, 4, 6-trinitrobenzene (TATB) compressed to 83 GPa,” J. Appl. Phys. 127(18) 185901 (2020).10.1063/5.0005818
[11]	C. Mailhiot, L. H. Yang, and A. K. McMahan, “Polymeric nitrogen,” Phys. Rev. B 46, 14419–14435 (1992).10.1103/physrevb.46.14419
[12]	M. Bykov, E. Bykova, G. Aprilis, K. Glazyrin, E. Koemets et al., “Fe-N system at high pressure reveals a compound featuring polymeric nitrogen chains,” Nat. Commun. 9, 2756 (2018).10.1038/s41467-018-05143-2
[13]	H. Katzke and P. Tolédano, “Theoretical description of pressure-and temperature-induced structural phase transition mechanisms of nitrogen,” Phys. Rev. B 78(6), 064103 (2008).10.1103/PhysRevB.78.064103
[14]	A. Erba, L. Maschio, C. Pisani, and S. Casassa, “Pressure-induced transitions in solid nitrogen: Role of dispersive interactions,” Phys. Rev. B 84(1), 012101 (2011).10.1103/PhysRevB.84.012101
[15]	R. Turnbull, M. Hanfland, J. Binns, M. Martinez-Canales, M. Frost et al., “Unusually complex phase of dense nitrogen at extreme conditions,” Nat. Commun. 9, 4717 (2018).10.1038/s41467-018-07074-4
[16]	M. I. Eremets, A. G. Gavriliuk, I. A. Trojan, D. A. Dzivenko, and R. Boehler, “Single-bonded cubic form of nitrogen,” Nat. Mater. 3, 558–563 (2004).10.1038/nmat1146
[17]	C. Ji, A. A. Adeleke, L. Yang, B. Wan, H. Gou et al., “Nitrogen in black phosphorus structure,” Sci. Adv. 6(23), eaba9206 (2020).10.1126/sciadv.aba9206
[18]	M. Ross and F. Rogers, “Polymerization, shock cooling, and the high-pressure phase diagram of nitrogen,” Phys. Rev. B 74, 024103 (2006).10.1103/physrevb.74.024103
[19]	D. Donadio, L. Spanu, I. Duchemin, F. Gygi, and G. Galli, “Ab initio investigation of the melting line of nitrogen at high pressure,” Phys. Rev. B 82, 020102 (2010).10.1103/physrevb.82.020102
[20]	B. Boates and S. A. Bonev, “First-order liquid-liquid phase transition in compressed nitrogen,” Phys. Rev. Lett. 102, 015701 (2009).10.1103/physrevlett.102.015701
[21]	B. Boates and S. A. Bonev, “Electronic and structural properties of dense liquid and amorphous nitrogen,” Phys. Rev. B 83, 174114 (2011).10.1103/physrevb.83.174114
[22]	E. S. Yakub and L. N. Yakub, “Equation of state and second critical point of highly compressed nitrogen,” Fluid Phase Equilib. 351, 43–47 (2013).10.1016/j.fluid.2012.09.011
[23]	J. M. Winey and Y. M. Gupta, “Complete equation of state for shocked liquid nitrogen: Analytical developments,” J. Chem. Phys. 145, 054504 (2016).10.1063/1.4959770
[24]	D. Laniel, G. Geneste, G. Weck, M. Mezouar, and P. Loubeyre, “Hexagonal layered polymeric nitrogen phase synthesized near 250 GPa,” Phys. Rev. Lett. 122, 066001 (2019).10.1103/physrevlett.122.066001
[25]	A. K. McMahan and R. LeSar, “Pressure dissociation of solid nitrogen under 1 Mbar,” Phys. Rev. Lett. 54, 1929–1932 (1985).10.1103/physrevlett.54.1929
[26]	M. M. G. Alemany and J. L. Martins, “Density-functional study of nonmolecular phases of nitrogen: Metastable phase at low pressure,” Phys. Rev. B 68, 024110 (2003).10.1103/physrevb.68.024110
[27]	D. C. Hamilton and F. H. Ree, “Chemical equilibrium calculations on the molecular‐to‐nonmolecular transition of shock compressed liquid nitrogen,” J. Chem. Phys. 90, 4972–4981 (1989).10.1063/1.456566
[28]	M. I. Eremets, A. G. Gavriliuk, N. R. Serebryanaya, I. A. Trojan, D. A. Dzivenko et al., “Structural transformation of molecular nitrogen to a single-bonded atomic state at high pressures,” J. Chem. Phys. 121, 11296–11300 (2004).10.1063/1.1814074
[29]	A. F. Goncharov, E. Gregoryanz, H.-k. Mao, Z. Liu, and R. J. Hemley, “Optical evidence for a nonmolecular phase of nitrogen above 150 GPa,” Phys. Rev. Lett. 85, 1262–1265 (2000).10.1103/physrevlett.85.1262
[30]	M. I. Eremets, R. J. Hemley, H.-k. Mao, and E. Gregoryanz, “Semiconducting non-molecular nitrogen up to 240 GPa and its low-pressure stability,” Nature 411, 170–174 (2001).10.1038/35075531
[31]	W. J. Nellis and A. C. Mitchell, “Shock compression of liquid argon, nitrogen, and oxygen to 90 GPa (900 kbar),” J. Chem. Phys. 73, 6137–6145 (1980).10.1063/1.440105
[32]	W. J. Nellis, H. B. Radousky, D. C. Hamilton, A. C. Mitchell, N. C. Holmes et al., “Equation-of-state, shock-temperature, and electrical-conductivity data of dense fluid nitrogen in the region of the dissociative phase transition,” J. Chem. Phys. 94, 2244–2257 (1991).10.1063/1.459895
[33]	R. F. Trunin, G. V. Boriskov, A. I. Bykov, A. B. Medvedev, G. V. Simakov et al., “Shock compression of liquid nitrogen at a pressure of 320 GPa,” JETP Lett. 88, 189–191 (2008).10.1134/s0021364008150095
[34]	M. A. Mochalov, M. V. Zhernokletov, R. I. Il’kaev, A. L. Mikhailov, V. E. Fortov et al., “Measurement of density, temperature, and electrical conductivity of a shock-compressed nonideal nitrogen plasma in the megabar pressure range,” J. Exp. Theor. Phys. 110, 67–79 (2010).10.1134/S1063776110010097
[35]	M. S. Akram, Z. Fan, M. Zhang, C. Zhang, Q. Liu et al., “Measuring the shock Hugoniot data of liquid nitrogen using a cryogenic system for shock compression,” J. Appl. Phys. 128, 225901 (2020).10.1063/5.0029911
[36]	M. S. Akram, S. Sattar, Z.-N. Fan, Q.-J. Liu, and F.-S. Liu, “Measurement of shock and re-shock Hugoniot data of liquid nitrogen,” High Pressure Res. 42, 57–68 (2022).10.1080/08957959.2022.2030325
[37]	Y.-J. Kim, B. Militzer, B. Boates, S. Bonev, P. M. Celliers et al., “Evidence for dissociation and ionization in shock compressed nitrogen to 800 GPa,” Phys. Rev. Lett. 129, 015701 (2022).10.1103/physrevlett.129.015701
[38]	M. V. Zhernokletov, A. E. Kovalev, M. G. Novikov, V. K. Gryaznov, I. L. Iosilevskii et al., “Shock-wave compression of nitrogen fluid in the pressure range 140–250 GPa,” J. Exp. Theor. Phys. 136, 241–249 (2023).10.1134/s1063776123020140
[39]	H. B. Radousky, W. J. Nellis, M. Ross, D. C. Hamilton, and A. C. Mitchell, “Molecular dissociation and shock-induced cooling in fluid nitrogen at high density and temperatures,” Phys. Rev. Lett. 57, 2419–2422 (1986).10.1103/physrevlett.57.2419
[40]	H. B. Radousky and M. Ross, “Shock-induced cooling in high-density fluid nitrogen,” High Pressure Res. 1, 39–52 (1988).10.1080/08957958808202479
[41]	Q. F. Chen, J. Zheng, Y. J. Gu, Y. L. Chen, L. C. Cai et al., “Thermophysical properties of multi-shock compressed dense argon,” J. Chem. Phys. 140, 074202 (2014).10.1063/1.4865129
[42]	J. Zheng, Q. Chen, G. Yunjun, Z. Li, Z. Shen et al., “Multishock compression properties of warm dense argon,” Sci. Rep. 5, 16041 (2015).10.1038/srep16041
[43]	J. Li, X. Zhou, and J. Li, “A time-resolved single-pass technique for measuring optical absorption coefficients of window materials under 100 GPa shock pressures,” Rev. Sci. Instrum. 79, 126101 (2008).10.1063/1.3046279
[44]	X. Cao, Q. Wu, M. Sokol, J. Qi, Y. Yu et al., “Superior optical transparency of nano-grain magnesium aluminate spinel at high shock pressure,” Appl. Phys. Lett. 124, 054102 (2024).10.1063/5.0181667
[45]	S. Deemyad, A. N. Papathanassiou, and I. F. Silvera, “Strategy and enhanced temperature determination in a laser heated diamond anvil cell,” J. Appl. Phys. 105, 093502 (2009).10.1063/1.3117517
[46]	S. C. Gupta, S. G. Love, and T. J. Ahrens, “Shock temperature in calcite (CaCO3) at 95–160 GPa,” Earth Planet. Sci. Lett. 201, 1–12 (2002).10.1016/s0012-821x(02)00685-4
[47]	J. K. Wicks, S. Singh, M. Millot, D. E. Fratanduono, F. Coppari et al., “B1-B2 transition in shock-compressed MgO,” Sci. Adv. 10, eadk0306 (2024).10.1126/sciadv.adk0306
[48]	M. S. Akram, Z. Fan, C. Zhang, Q. Liu, and F. Liu, “Shock compression of liquefied gases: Molecular dissociation and radiance change at the sample/LiF interface,” J. Chem. Phys. 162, 054504 (2025).10.1063/5.0244257
[49]	M. S. Akram, Y. Wei, W. Yuan, L. Yang, Z. Fan et al., “Dynamic response of molecular liquids under multi-shock compression: Shock-induced cooling and thermodynamic pathways,” Phys. Fluids 37, 097125 (2025).10.1063/5.0288068
[50]	M. S. Akram, Z.-N. Fan, and F.-S. Liu, “Refractive index of shock-compressed liquid nitrogen up to 29 GPa,” High Pressure Res. 43, 81–95 (2023).10.1080/08957959.2023.2194022
[51]	J. D. Kress, S. Mazevet, L. A. Collins, and W. W. Wood, “Density-functional calculation of the Hugoniot of shocked liquid nitrogen,” Phys. Rev. B 63, 024203 (2000).10.1103/physrevb.63.024203
[52]	R. D. Dick, “Shock wave compression of benzene, carbon disulfide, carbon tetrachloride, and liquid nitrogen,” J. Chem. Phys. 52, 6021–6032 (1970).10.1063/1.1672902
[53]	V. N. Zubarev and G. S. Telegin, “Impact compressibility of liquid nitrogen and solid carbon dioxide,” Sov. Phys. Dokl. 7, 34–36 (1962), available at https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=dan&paperid=26005&option_lang=eng.
[54]	G. L. Schott, M. S. Shaw, and J. D. Johnson, “Shocked states from initially liquid oxygen–nitrogen systems,” J. Chem. Phys. 82, 4264–4275 (1985).10.1063/1.448817
[55]	R. K. Lindsey, S. Bastea, Y. Lyu, S. Hamel, N. Goldman et al., “Chemical evolution in nitrogen shocked beyond the molecular stability limit,” J. Chem. Phys. 159, 084502 (2023).10.1063/5.0157238
[56]	P. A. Rigg, M. D. Knudson, R. J. Scharff, and R. S. Hixson, “Determining the refractive index of shocked [100] lithium fluoride to the limit of transmissibility,” J. Appl. Phys. 116, 033515 (2014).10.1063/1.4890714
[57]	Q. Liu, X. Zhou, X. Zeng, and S. N. Luo, “Sound velocity, equation of state, temperature and melting of LiF single crystals under shock compression,” J. Appl. Phys. 117, 045901 (2015).10.1063/1.4906558
[58]	G. Young, X. Liu, C. Leng, J. Yang, and H. Huang, “Refractive index of [100] lithium fluoride under shock pressures up to 151 GPa,” AIP Adv. 8, 125310 (2018).10.1063/1.5065543
[59]	M. Ross, “The dissociation of dense liquid nitrogen,” J. Chem. Phys. 86, 7110–7118 (1987).10.1063/1.452360
[60]	K. P. Driver and B. Militzer, “First-principles equation of state calculations of warm dense nitrogen,” Phys. Rev. B 93, 064101 (2016).10.1103/physrevb.93.064101
[61]	A. F. Goncharov, J. C. Crowhurst, V. V. Struzhkin, and R. J. Hemley, “Triple point on the melting curve and polymorphism of nitrogen at high pressure,” Phys. Rev. Lett. 101, 095502 (2008).10.1103/physrevlett.101.095502
[62]	M. Frost, R. T. Howie, P. Dalladay-Simpson, A. F. Goncharov, and E. Gregoryanz, “Novel high-pressure nitrogen phase formed by compression at low temperature,” Phys. Rev. B 93, 024113 (2016).10.1103/physrevb.93.024113
[63]	E. Gregoryanz, A. F. Goncharov, C. Sanloup, M. Somayazulu, H.-k. Mao et al., “High P-T transformations of nitrogen to 170 GPa,” J. Chem. Phys. 126, 184505 (2007).10.1063/1.2723069
[64]	D. Tomasino, M. Kim, J. Smith, and C.-S. Yoo, “Pressure-induced symmetry-lowering transition in dense nitrogen to layered polymeric nitrogen (LP-N) with colossal Raman intensity,” Phys. Rev. Lett. 113, 205502 (2014).10.1103/physrevlett.113.205502
[65]	S. Tateno, K. Hirose, Y. Ohishi, and Y. Tatsumi, “The structure of iron in Earth’s inner core,” Science 330, 359–361 (2010).10.1126/science.1194662
[66]	W. B. Hubbard, W. J. Nellis, A. C. Mitchell, N. C. Holmes, S. S. Limaye et al., “Interior structure of Neptune: Comparison with Uranus,” Science 253, 648–651 (1991).10.1126/science.253.5020.648
[67]	S. Mazevet, J. D. Johnson, J. D. Kress, L. A. Collins, and P. Blottiau, “Density-functional calculation of multiple-shock Hugoniots of liquid nitrogen,” Phys. Rev. B 65, 014204 (2001).10.1103/physrevb.65.014204