Clathrate hydrate

Clathrate hydrates, or gas hydrates, clathrates, hydrates, etc., are crystalline water-based solids physically resembling ice, in which small non-polar molecules (typically gases) or polar molecules with large hydrophobic moieties are trapped inside "cages" of hydrogen bonded, frozen water molecules.[1] In other words, clathrate hydrates are clathrate compounds in which the host molecule is water and the guest molecule is typically a gas or liquid. Without the support of the trapped molecules, the lattice structure of hydrate clathrates would collapse into conventional ice crystal structure or liquid water. Most low molecular weight gases, including O2, H2, N2, CO2, CH4, H2S, Ar, Kr, and Xe, as well as some higher hydrocarbons and freons, will form hydrates at suitable temperatures and pressures. Clathrate hydrates are not officially chemical compounds, as the enclathrated guest molecules are never bonded to the lattice. The formation and decomposition of clathrate hydrates are first order phase transitions, not chemical reactions. Their detailed formation and decomposition mechanisms on a molecular level are still not well understood.[2][3][4] Clathrate hydrates were first documented in 1810 by Sir Humphry Davy who found that water was a primary component of what was earlier thought to be solidified chlorine.[5][6]

Methane clathrate block embedded in the sediment of hydrate ridge, off Oregon, USA

Clathrates have been found to occur naturally in large quantities. Around 6.4 trillion (6.4×1012) tonnes of methane is trapped in deposits of methane clathrate on the deep ocean floor.[7] Such deposits can be found on the Norwegian continental shelf in the northern headwall flank of the Storegga Slide. Clathrates can also exist as permafrost, as at the Mallik gas hydrate site in the Mackenzie Delta of northwestern Canadian Arctic. These natural gas hydrates are seen as a potentially vast energy resource and several countries have dedicated national programs to develop this energy resource.[8] Clathrate hydrate has also been of great interest as technology enabler for many applications like seawater desalination,[9] gas storage,[10] carbon dioxide capture & storage,[11] cooling medium for data centre[12] and district cooling etc. Hydrocarbon clathrates cause problems for the petroleum industry, because they can form inside gas pipelines, often resulting in obstructions. Deep sea deposition of carbon dioxide clathrate has been proposed as a method to remove this greenhouse gas from the atmosphere and control climate change. Clathrates are suspected to occur in large quantities on some outer planets, moons and trans-Neptunian objects, binding gas at fairly high temperatures.[13]

The three major areas that drive scientific and industrial interest on clathrate hydrates are flow assurance, energy resource and technological applications. The technological applications include seawater desalination; natural gas storage and transport; gas separations including CO2 capture; cooling applications for district cooling and data centre cooling.

Structure
Cages building the different gas hydrate structures.

Gas hydrates usually form two crystallographic cubic structures: structure (Type) I (named sI) and structure (Type) II (named sII)[14] of space groups and respectively. Seldom, a third hexagonal structure of space group may be observed (Type H).[15]

The unit cell of Type I consists of 46 water molecules, forming two types of cages – small and large. The unit cell contains two small cages and six large ones. The small cage has the shape of a pentagonal dodecahedron (512) (which is not a regular dodecahedron) and the large one that of a tetradecahedron, specifically a hexagonal truncated trapezohedron (51262). Together, they form a version of the Weaire–Phelan structure. Typical guests forming Type I hydrates are CO2 in carbon dioxide clathrate and CH4 in methane clathrate.

The unit cell of Type II consists of 136 water molecules, again forming two types of cages – small and large. In this case there are sixteen small cages and eight large ones in the unit cell. The small cage again has the shape of a pentagonal dodecahedron (512), but the large one is a hexadecahedron (51264). Type II hydrates are formed by gases like O2 and N2.

The unit cell of Type H consists of 34 water molecules, forming three types of cages – two small ones of different types, and one "huge". In this case, the unit cell consists of three small cages of type 512, two small ones of type 435663 and one huge of type 51268. The formation of Type H requires the cooperation of two guest gases (large and small) to be stable. It is the large cavity that allows structure H hydrates to fit in large molecules (e.g. butane, hydrocarbons), given the presence of other smaller help gases to fill and support the remaining cavities. Structure H hydrates were suggested to exist in the Gulf of Mexico. Thermogenically-produced supplies of heavy hydrocarbons are common there.

Hydrates in the universe

Iro et al.,[16] trying to interpret the nitrogen deficiency in comets, stated most of the conditions for hydrate formation in the protoplanetary nebulae, surrounding the pre-main and main sequence stars were fulfilled, despite the rapid grain growth to meter scale. The key was to provide enough microscopic ice particles exposed to a gaseous environment. Observations of the radiometric continuum of circumstellar discs around -Tauri and Herbig Ae/Be stars suggest massive dust disks consisting of millimeter-sized grains, which disappear after several million years (e.g.,[17][18]). A lot of work on detecting water ices in the Universe was done on the Infrared Space Observatory (ISO). For instance, broad emission bands of water ice at 43 and 60 μm were found in the disk of the isolated Herbig Ae/Be star HD 100546 in Musca. The one at 43 μm is much weaker than the one at 60 μm, which means the water ice, is located in the outer parts of the disk at temperatures below 50 K.[19] There is also another broad ice feature between 87 and 90 μm, which is very similar to the one in NGC 6302[20] (the Bug or Butterfly nebula in Scorpius). Crystalline ices were also detected in the proto-planetary disks of ε-Eridani and the isolated Fe star HD 142527[21][22] in Lupus. 90% of the ice in the latter was found crystalline at temperature around 50 K. HST demonstrated that relatively old circumstellar disks, as the one around the 5-million-year-old B9.5Ve[23] Herbig Ae/Be star HD 141569A, are dusty.[24] Li & Lunine[25] found water ice there. Knowing the ices usually exist at the outer parts of the proto-planetary nebulae, Hersant et al.[26] proposed an interpretation of the volatile enrichment, observed in the four giant planets of the Solar System, with respect to the Solar abundances. They assumed the volatiles had been trapped in the form of hydrates and incorporated in the planetesimals flying in the protoplanets’ feeding zones.

Kieffer et al. (2006) hypothesized that the geyser activity in the south polar region of Saturn's moon Enceladus originates from clathrate hydrates, where carbon dioxide, methane, and nitrogen are released when exposed to the vacuum of space through the "Tiger Stripe" fractures found in that area.[27] However, subsequent analysis of plume material makes it more likely that the geysers on Enceladus derive from a salty subsurface ocean.[28]

Carbon dioxide clathrate is believed to play a major role in different processes on Mars. Hydrogen clathrate is likely to form in condensation nebulae for gas giants.

Hydrates on Earth

Natural gas hydrates
Main article: Methane clathrate

Naturally on Earth gas hydrates can be found on the seabed, in ocean sediments,[29] in deep lake sediments (e.g. Lake Baikal), as well as in the permafrost regions. The amount of methane potentially trapped in natural methane hydrate deposits may be significant (1015 to 1017 cubic metres),[30] which makes them of major interest as a potential energy resource. Catastrophic release of methane from the decomposition of such deposits may lead to a global climate change, referred to as the "clathrate gun hypothesis", because CH4 is a more potent greenhouse gas than CO2 (see Atmospheric methane). The fast decomposition of such deposits is considered a geohazard, due to its potential to trigger landslides, earthquakes and tsunamis. However, natural gas hydrates do not contain only methane but also other hydrocarbon gases, as well as H2S and CO2. Air hydrates are frequently observed in polar ice samples.

Pingos are common structures in permafrost regions.[31] Similar structures are found in deep water related to methane leakages. Significantly, gas hydrates can even be formed in the absence of a liquid phase. Under that situation, water is dissolved in gas or in liquid hydrocarbon phase.[32]

In 2017, both Japan and China announced that attempts at large-scale resource extraction of methane hydrates from under the seafloor were successful. However, commercial-scale production remains years away.[33][34]

Gas hydrates in pipelines

Thermodynamic conditions favouring hydrate formation are often found in pipelines. This is highly undesirable, because the clathrate crystals might agglomerate and plug the line[35] and cause flow assurance failure and damage valves and instrumentation. The results can range from flow reduction to equipment damage.

Hydrate formation, prevention and mitigation philosophy

Hydrates have a strong tendency to agglomerate and to adhere to the pipe wall and thereby plug the pipeline. Once formed, they can be decomposed by increasing the temperature and/or decreasing the pressure. Even under these conditions, the clathrate dissociation is a slow process.

Therefore, preventing hydrate formation appears to be the key to the problem. A hydrate prevention philosophy could typically be based on three levels of security, listed in order of priority:

  1. Avoid operational conditions that might cause formation of hydrates by depressing the hydrate formation temperature using glycol dehydration;
  2. Temporarily change operating conditions in order to avoid hydrate formation;
  3. Prevent formation of hydrates by addition of chemicals that (a) shift the hydrate equilibrium conditions towards lower temperatures and higher pressures or (b) increase hydrate formation time (inhibitors)

The actual philosophy would depend on operational circumstances such as pressure, temperature, type of flow (gas, liquid, presences of water etc.)

Hydrate inhibitors

When operating within a set of parameters where hydrates could be formed, there are still ways to avoid their formation. Altering the gas composition by adding chemicals can lower the hydrate formation temperature and/or delay their formation. Two options generally exist:

The most common thermodynamic inhibitors are methanol, monoethylene glycol (MEG), and diethylene glycol (DEG), commonly referred to as glycol. All may be recovered and recirculated, but the economics of methanol recovery is not favourable in most cases. MEG is preferred over DEG for applications where the temperature is expected to be −10 °C or lower due to high viscosity at low temperatures. Triethylene glycol (TEG) has too low vapour pressure to be suited as an inhibitor injected into a gas stream. More methanol is lost in the gas phase when compared to MEG or DEG.

The use of kinetic inhibitors and anti-agglomerants in actual field operations is a new and evolving technology. It requires extensive tests and optimisation to the actual system. While kinetic inhibitors work by slowing down the kinetics of the nucleation, anti-agglomerants do not stop the nucleation, but stop the agglomeration (sticking together) of gas hydrate crystals. These two kinds of inhibitors are also known as low dosage hydrate inhibitors, because they require much smaller concentrations than the conventional thermodynamic inhibitors. Kinetic inhibitors, which do not require water and hydrocarbon mixture to be effective, are usually polymers or copolymers and anti-agglomerants (requires water and hydrocarbon mixture) are polymers or zwitterionic — usually ammonium and COOH — surfactants being both attracted to hydrates and hydrocarbons.

Empty clathrate hydrates

Empty clathrate hydrates[38] are thermodynamically unstable (guest molecules are of paramount importance to stabilize these structures) with respect to ice, and as such their study using experimental techniques is greatly limited to very specific formation conditions; however, their mechanical stability renders theoretical and computer simulation methods the ideal choice to address their thermodynamic properties. Starting from very cold samples (110–145 K), Falenty et al.[39] degassed Ne-sII clathrates for several hours using vacuum pumping to obtain a so-called ice XVI, while employing neutron diffraction to observe that (i) the empty sII hydrate structure decomposes at T ≥ 145 K and, furthermore, (ii) the empty hydrate shows a negative thermal expansion at T < 55 K, and it is mechanically more stable and has a larger lattice constant at low temperatures than the Ne-filled analogue. The existence of such a porous ice had been theoretically predicted before.[40] From a theoretical perspective, empty hydrates can be probed using Molecular Dynamics or Monte Carlo techniques. Conde et al. used empty hydrates and a fully atomic description of the solid lattice to estimate the phase diagram of H2O at negative pressures and T ≤ 300 K,[41] and obtain the differences in chemical potentials between ice Ih and the empty hydrates, central to the van der Waals−Platteeuw theory. Jacobson et al. performed[42] simulations using a monoatomic (coarse-grained) model developed for H2O that is capable of capturing the tetrahedral symmetry of hydrates. Their calculations revealed that, under 1 atm pressure, sI and sII empty hydrates are metastable regarding the ice phases up to their melting temperatures, T = 245 ± 2 K and T = 252 ± 2 K, respectively. Matsui et al. employed[43] molecular dynamics to perform a thorough and systematic study of several ice polymorphs, namely space fullerene ices, zeolitic ices, and aeroices, and interpreted their relative stability in terms of geometrical considerations.

The thermodynamics of metastable empty sI clathrate hydrates have been probed over broad temperature and pressure ranges, 100 ≤ T (K) ≤ 220 and 1 ≤ p (bar) ≤ 5000, by Cruz et al.[44] using large-scale simulations and compared with experimental data at 1 bar. The whole p−V−T surface obtained was fitted by the universal form of the Parsafar and Mason equation of state with an accuracy of 99.7–99.9%. Framework deformation caused by applied temperature followed a parabolic law, and there is a critical temperature above which the isobaric thermal expansion becomes negative, ranging from 194.7 K at 1 bar to 166.2 K at 5000 bar. Response to the applied (p, T) field was analyzed in terms of angle and distance descriptors of a classical tetrahedral structure and observed to occur essentially by means of angular alteration for (p, T) > (2000 bar, 200 K). The length of the hydrogen bonds responsible for framework integrity was insensitive to the thermodynamic conditions and its average value is r(̅O H) = 0.25 nm.

gollark: Also, it tends to result in stupidity like `getX()` instead of `thing.x` and most OOPy stuff is ridiculously verbose for no reason.
gollark: *does not like OOP*
gollark: I'm pretty sure it just has none.
gollark: In Java.
gollark: Also, there's no operator overloading.

See also

References
  1. https://pubs.acs.org/doi/pdf/10.1021/ie00019a001
  2. Gao S; House W; Chapman WG (2005). "NMR MRI Study of Gas Hydrate Mechanisms". The Journal of Physical Chemistry B. 109 (41): 19090–19093. CiteSeerX 10.1.1.175.9193. doi:10.1021/jp052071w. PMID 16853461. Retrieved August 3, 2009.
  3. Gao S; Chapman WG; House W (2005). "NMR and Viscosity Investigation of Clathrate Formation and Dissociation". Ind. Eng. Chem. Res. 44 (19): 7373–7379. doi:10.1021/ie050464b. Retrieved August 3, 2009.
  4. Choudhary, Nilesh; Chakrabarty, Suman; Roy, Sudip; Kumar, Rajnish (January 2019). "A comparison of different water models for melting point calculation of methane hydrate using molecular dynamics simulations". Chemical Physics. 516: 6–14. Bibcode:2019CP....516....6C. doi:10.1016/j.chemphys.2018.08.036.
  5. Michael Faraday (1859). On Hydrate of Chlorine. Quarterly Journal of Science. Retrieved 20 March 2014.
  6. Ellen Thomas (November 2004). "Clathrates: little known components of the global carbon cycle". Wesleyan University. Retrieved 13 December 2007.
  7. Buffett, B.; Archer, D. (2004). "Global inventory of methane clathrate: sensitivity to changes in the deep ocean". Earth Planet. Sci. Lett. 227 (3–4): 185–199. Bibcode:2004E&PSL.227..185B. doi:10.1016/j.epsl.2004.09.005.
  8. Chong, Zheng Rong; Yang, She Hern Bryan; Babu, Ponnivalavan; Linga, Praveen; Li, Xiao-Sen (2016). "Review of natural gas hydrates as an energy resource: Prospects and challenges". Applied Energy. 162: 1633–1652. doi:10.1016/j.apenergy.2014.12.061.
  9. "Drinkable water from cold energy | Engineers Australia".
  10. "Eco-friendly ways to harness natural gas efficiently". 30 June 2017.
  11. Babu, Ponnivalavan; Linga, Praveen; Kumar, Rajnish; Englezos, Peter (1 June 2015). "A review of the hydrate based gas separation (HBGS) process for carbon dioxide pre-combustion capture". Energy. 85: 261–279. doi:10.1016/j.energy.2015.03.103.
  12. "NUS, Keppel, SLNG in tie-up to develop better cooling technology for data centres". 22 October 2019.
  13. Ghosh, Jyotirmoy; Methikkalam, Rabin Rajan J.; Bhuin, Radha Gobinda; Ragupathy, Gopi; Choudhary, Nilesh; Kumar, Rajnish; Pradeep, Thalappil (29 January 2019). "Clathrate hydrates in interstellar environment". Proceedings of the National Academy of Sciences. 116 (5): 1526–1531. doi:10.1073/pnas.1814293116. PMC 6358667. PMID 30630945.
  14. Stackelberg, M. v; Müller, H. R. (1954). "Feste Gashydrate II. Struktur und Raumchemie" [Solid gas hydrates II. Structure and space chemistry]. Zeitschrift für Elektrochemie, Berichte der Bunsengesellschaft für physikalische Chemie (in German). 58 (1): 25–39. doi:10.1002/bbpc.19540580105 (inactive 2020-06-05).
  15. Sloan E. D., Jr. (1998) Clathrate hydrates of natural gases. Second edition, Marcel Dekker Inc.:New York.
  16. Iro, Nicolas; Gautier, Daniel; Hersant, Franck; Bockelée-Morvan, Dominique; Lunine, Jonathan I. (February 2003). "An interpretation of the nitrogen deficiency in comets". Icarus. 161 (2): 511–532. Bibcode:2003Icar..161..511I. CiteSeerX 10.1.1.487.722. doi:10.1016/S0019-1035(02)00038-6.
  17. Beckwith, S. V. W.; Henning, T.; Nakagawa, Y. (2000). "Dust properties and assembly of large particles in protoplanetary disks". Protostars and Planets. IV: 533. arXiv:astro-ph/9902241. Bibcode:2000prpl.conf..533B.
  18. Natta, A.; Grinin, V.; Mannings, V. (2000). "Properties and Evolution of Disks around Pre-Main-Sequence Stars of Intermediate Mass". Protostars and Planets. IV: 559. Bibcode:2000prpl.conf..559N. hdl:2014/17884.
  19. Malfait, K., Waelkens, C., Waters, L. B. F. M., Vandenbussche, B., Huygen, E. & de Graauw, M. S.; Waelkens; Waters; Vandenbussche; Huygen; De Graauw (1998). "The spectrum of the young star HD 100546 observed with the Infrared Space Observatory". Astronomy and Astrophysics. 332: L25–L28. Bibcode:1998A&A...332L..25M.CS1 maint: multiple names: authors list (link)
  20. Barlow, M.J., In the proceedings of ‘ISO’s view on stellar evolution’, Noordwijkerhout, July 1–4, 1997
  21. Li, Aigen; Lunine, J. I.; Bendo, G. J. (2003). "Modeling the infrared emission from the ε-Eridani disk". The Astrophysical Journal. 598 (1): L51–L54. arXiv:astro-ph/0311069. Bibcode:2003ApJ...598L..51L. doi:10.1086/380495.
  22. Malfait, K.; Waelkens, C.; Bouwman, J.; De Koter, A.; Waters, L. B. F. M. (1999). "The ISO spectrum of the young star HD 142527". Astronomy and Astrophysics. 345: 181. Bibcode:1999A&A...345..181M.
  23. Jaschek, C.; Jaschek, M. (1992). "A southern be star survey : Spectra and envelope radii". Astronomy and Astrophysics Supplement Series. 95: 535. Bibcode:1992A&AS...95..535J.
  24. Clampin, M.; Krist, J. E.; Ardila, D. R.; Golimowski, D. A.; Hartig, G. F.; Ford, H. C.; Illingworth, G. D.; Bartko, F.; Bentez, N.; Blakeslee, J. P.; Bouwens, R. J.; Broadhurst, T. J.; Brown, R. A.; Burrows, C. J.; Cheng, E. S.; Cross, N. J. G.; Feldman, P. D.; Franx, M.; Gronwall, C.; Infante, L.; Kimble, R. A.; Lesser, M. P.; Martel, A. R.; Menanteau, F.; Meurer, G. R.; Miley, G. K.; Postman, M.; Rosati, P.; Sirianni, M.; et al. (2003). "Hubble Space TelescopeACS Coronagraphic Imaging of the Circumstellar Disk around HD 141569A". The Astronomical Journal. 126 (1): 385–392. arXiv:astro-ph/0303605. Bibcode:2003AJ....126..385C. doi:10.1086/375460.
  25. Li, A.; Lunine, J. I. (2003). "Modeling the infrared emission from the HD 141569A disk". Astrophysical Journal. 594 (2): 987–1010. arXiv:astro-ph/0311070. Bibcode:2003ApJ...594..987L. doi:10.1086/376939.
  26. Hersant, F (2004). "Enrichment in volatiles in the giant planets of the Solar System". Planetary and Space Science. 52 (7): 623–641. Bibcode:2004P&SS...52..623H. doi:10.1016/j.pss.2003.12.011.
  27. Kieffer, Susan W.; Xinli Lu; Craig M. Bethke; John R. Spencer; Stephen Marshak; Alexandra Navrotsky (2006). "A Clathrate Reservoir Hypothesis for Enceladus' South Polar Plume". Science. 314 (5806): 1764–1766. Bibcode:2006Sci...314.1764K. doi:10.1126/science.1133519. PMID 17170301. S2CID 41743663.
  28. Iess, L.; Stevenson, D.J.; Parisi, M.; Hemingway, D.; Jacobson, R.A.; Lunine, J.I.; Nimmo, F.; Armstrong, J.w.; Asmar, S.w.; Ducci, M.; Tortora, P. (April 4, 2014). "The Gravity Field and Interior Structure of Enceladus" (PDF). Science. 344 (6179): 78–80. Bibcode:2014Sci...344...78I. doi:10.1126/science.1250551. PMID 24700854.
  29. Kvenvolden, Keith A.; McMenamin, Mark A. (1980). Hydrates of natural gas; a review of their geologic occurrence (Report). doi:10.3133/cir825.
  30. Marshall, Michael (26 March 2009). "Ice that burns could be a green fossil fuel". New Scientist.
  31. Ussler, W.; Paull, C. K.; Lorenson, T.; Dallimore, S.; Medioli, B.; Blasco, S.; McLaughlin, F.; Nixon, F. M. (2005). "Methane Leakage from Pingo-like Features on the Arctic Shelf, Beaufort Sea, NWT, Canada". AGU Fall Meeting Abstracts. 2005: C11A–1069. Bibcode:2005AGUFM.C11A1069U.
  32. Youssef, Z.; Barreau, A.; Mougin, P.; Jose, J.; Mokbel, I. (15 April 2009). "Measurements of Hydrate Dissociation Temperature of Methane, Ethane, and CO2 in the Absence of Any Aqueous Phase and Prediction with the Cubic Plus Association Equation of State". Industrial & Engineering Chemistry Research. 48 (8): 4045–4050. doi:10.1021/ie801351e.
  33. "China claims breakthrough in 'flammable ice'". BBC News. 19 May 2017.
  34. "China and Japan find way to extract 'combustible ice' from seafloor, harnessing a legendary frozen fossil fuel". National Post. 19 May 2017.
  35. Gao, Shuqiang (2008). "Investigation of Interactions between Gas Hydrates and Several Other Flow Assurance Elements". Energy & Fuels. 22 (5): 3150–3153. doi:10.1021/ef800189k.
  36. Khodaverdiloo, Khadijeh Rostami; Erfani, Amir; Peyvandi, Kiana; Varaminian, Farshad (March 2016). "Synergetic effects of polyacrylamide and nonionic surfactants on preventing gas hydrate formation". Journal of Natural Gas Science and Engineering. 30: 343–349. doi:10.1016/j.jngse.2016.02.027.
  37. Erfani, Amir. "Gas hydrate formation inhibition using low dosage hydrate inhibitors" (PDF). 2nd National Iranian Conference on Gas Hydrat.
  38. Cruz, Fernando J. A. L.; Alavi, Saman; Mota, José P. B. (2019). "Low-Temperature Thermodynamic Study of the Metastable Empty Clathrate Hydrates Using Molecular Simulations". ACS Earth and Space Chemistry. 3 (5): 789–799. Bibcode:2019ECS.....3..789C. doi:10.1021/acsearthspacechem.9b00009.
  39. Falenty A.; Hansen T.C.; Kuhs .F. (2014). "Formation and Properties of Ice XVI Obtained by Emptying a Type sII Clathrate Hydrate". Nature. 516 (7530): 231–234. Bibcode:2014Natur.516..231F. doi:10.1038/nature14014. PMID 25503235.
  40. Kosyakov V.I. (2009). "Structure Formation Under Negative Pressures". J. Struct. Chem. 50: 60–65. doi:10.1007/s10947-009-0190-0.
  41. Conde M.M.; Vega C.; Tribello G.A.; Slater B. (2009). "The Phase Diagram of Water at Negative Pressures: Virtual Ices". J. Chem. Phys. 131 (3): 034510. Bibcode:2009JChPh.131c4510C. doi:10.1063/1.3182727. PMID 19624212.
  42. Jacobson L.C.; Hujo W.; Molinero V. (2009). "Thermodynamic Stability and Growth of Guest-Free Clathrate Hydrates: A Low-Density Crystal Phase of Water". J. Phys. Chem. B. 113 (30): 10298–10307. doi:10.1021/jp903439a. PMID 19585976.
  43. Matsui T.; Hirata M.; Yagasaki T.; Matsumoto M.; Tanaka H. (2017). "Hypothetical Ultralow-density Ice Polymorphs". J. Chem. Phys. 147 (9): 091101. doi:10.1063/1.4994757. PMID 28886658.
  44. Cruz F.J.A.L.; Alavi S.; Mota J.P.B. (2019). "Low-Temperature Thermodynamic Study of the Metastable Empty Clathrate Hydrates Using Molecular Simulations". ACS Earth Space Chem. 3 (5): 789–799. Bibcode:2019ECS.....3..789C. doi:10.1021/acsearthspacechem.9b00009.

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