Filling Ices with Helium and the Formation of Helium Clathrate Hydrate

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Filling Ices With Helium and the Formation of Helium Clathrate Hydrate Werner F. Kuhs, Thomas Christian Hansen, and Andrzej Falenty J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 29, 2018

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The Journal of Physical Chemistry Letters

Filling Ices with Helium and the Formation of Helium Clathrate Hydrate Werner F. Kuhs*1, Thomas C. Hansen2, and Andrzej Falenty1 1

GZG Abt. Kristallographie, Universität Göttingen, Goldschmidtstr. 1, 37077 Göttingen, Germany

2

Institut Laue-Langevin (ILL), 6 rue Jules Horowitz, BP 156, 38042 Grenoble Cedex, France

*To whom correspondence should be addressed. E-mail: [email protected]

ABSTRACT. We have formed the long-searched He-clathrate. This was achieved by refilling helium into ice XVI, opening a new synthesis route for exotic forms of clathrate hydrates. The process was followed by neutron diffraction; structures and cage fillings were established. The stabilizing attractive van der Waals interactions are enhanced by multiple cage fillings with theoretically up to four helium atoms per large cage and up to one per small one; He clathrate hydrates can be considered as a solid-state equivalent of the clustering of small apolar entities dissolved in the liquid state of water. Unlike most other guests, helium easily enters and leaves the water cages at temperatures well below 100 K, hampering applications as a gas storage material. Despite the weak dispersive interactions, the inclusion of helium has a very significant effect on lattice constants; this is also established for helium inclusion in ice Ih and suggests that lattice parameters are arguably the most sensitive measure to gauge dispersive water-gas interactions.

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Crystalline molecular compounds of water and gases give access to dispersive interactions as they affect in a very sensitive way the interatomic distances as well their stoichiometry. Due to their simple electronic structure and spherical atomic shape systems with noble gases are an promising choice to study quantitatively dispersive gas-water interactions on a molecular level1 and make related experimental studies a worthwhile undertaken for testing theoretical predictions. A prominent group of gas-water compounds are clathrate hydrates with their large structural variability and water cages at various proportions to match gas molecules or atoms with different shapes and sizes2. Pure helium clathrate hydrate is in fact the only compound of water and atmospheric gases not yet formed and characterized experimentally, while clathrates of all other gaseous constituents of air are known to exist naturally or have been formed in the laboratory3, 4. In fact, the helium-water interactions are the weakest known of all gases and consequently, the stabilizing energy of helium inclusion is expected to be quite low. Only at higher pressures these interactions become stronger5 and may eventually lead to stable heliumwater compounds. Helium clathrate hydrate has been suspected to exist at pressures of 100 to 500 MPa by Dyadin et al. 6, yet all attempts to form this compound remained inconclusive and any structural characterization is still missing. Only some double hydrates in which helium enters alongside with other molecules in a clathrate hydrate are known7, 8 but the effect of helium in


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stabilizing these compounds was found to be very small9. This illustrates the general reluctance of helium to enter into clathrate water cages; they are simply too large to produce substantial dispersive interactions with small guest atoms. Nevertheless, we now have succeeded to form pure helium clathrate by filling the empty deuterated sII clathrate structure, i.e. ice XVI4, with helium gas and have studied its stability, cage filling and structure using in situ neutron diffraction. We also report on very substantial structural effects of helium inclusion into ordinary ice Ih; upon helium inclusion at increasing gas pressure the crystal lattice is heavily distorted and quantified here for the first time. All our attempts to form sII He helium clathrate hydrate directly via a high pressure transformation near 300 MPa and 245 K starting from He-filled ice Ih, as demonstrated for Neclathrate4 or D2-clathrate10, were unsuccessful and produced only He-filled ice II (i.e. the socalled structure C1); this preference for C1 agrees with an earlier observation11. To circumvent the formation of C1 we therefore chose to proceed with a low temperature process by first emptying Ne-clathrate by pumping out the neon atoms near 141 K and subsequently re-filling the empty clathrate with helium at pressures up to 150 MPa. Details of the experimental procedure to obtain ice XVI are described in Supporting Information. The obtained empty hydrate was subjected to increasing helium pressure while the structure and cage filling was studied by in situ neutron diffraction; lattice constants and cage fillings were deduced from the diffraction data. Helium in the large cages of the sII clathrate structure are located on tetrahedrally degenerate positions around the cage center close to the 6-membered water rings of the cage; this allows in principle for a simultaneous occupation of up to 4 helium atoms in one large cage12, shown in Figure 1. In the small cages the helium atoms are located in the cage center.


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Figure 1: Adopted model of a multiple cage filling (up to four molecules) of helium in the large cages of a sII clathrate hydrate structure. Small cages accept up to one guest.

These configurations are quite similar to the case of sII Ne-clathrate4 established by diffraction and to sII hydrogen clathrate (center of mass of D2 or H2) established by path-integral molecular dynamics simulations13. For full occupancy of all cages a water-to-gas ratio (called hydration number in the clathrate community) of 2.833 results. Figure 2 shows the cage filling for small and large cages as a function of pressure, temperature as well as time. The imposed gas pressure increase is rapidly (on a minute time scale) followed by an increase of cage filling for the large cages, and about one order of magnitude slower for the small cage filling. Apparently, there is some slow readjustment of the small cage filling with time by inter-cage hopping of helium atoms from large into small cages as the highest small cage filling of 0.71(4) is obtained after going back to ambient pressure. The predicted (equilibrated) cage fillings of small and large cages12 are distinctly higher than our observations, which is likely to be a consequence of the unattainable equilibration on our experimental time-scales, in particular for the small cages. It is interesting to note that the lattice constants at 100 MPa is shrinking from an initial value of 17.0832(6) Å to a very significantly different value of 17.0763(6) Å when the filling increases


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from a hydration number of 5.92 to 4.56. This confirms that filling clathrate cages lead to increased attractive van der Waals interactions and consequently reduced lattice constants as observed also for other clathrates4, 14. More specifically, the value 17.1163(6) Å obtained at 80 K at ambient pressure for partly filled He-clathrate is located between the corresponding 80 K values of the empty clathrate (17.1260 Å) and of N2-clathrate (17.0995 Å) as expected for a guest with considerably weaker attractive interactions than N2-molecules; all quoted values refer to the deuterated form of the water frame. Further details of the data analysis as well as the crystallographic description of the obtained He-clathrate are given as Supplementary Information.

Figure 2: Small and large cage filling of sII He-clathrate as a function of pressure and temperature Reducing the helium pressure applied to He-clathrate leads to reduced cage fillings for large cages at comparable rates as was found upon pressure increase. The occupancy of small cages


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seems to be far less affected by the depressurization as long as temperature is held below ~70 K (Fig.2 and 3). To study this leakage further a sample was recovered, cooled to a temperature of 5 K and then slowly heated up under diffraction control to 130 K. The small cage filling as a function of temperature is shown in Figure 3; the helium filling at low temperatures is 0.81(6), i.e. higher than after initial filling, which supports the view that some of the helium atoms initially located in the large cages have been migrating into the small cages during sample recovery and cooling. This reshuffling of helium seems to take place also during heating up to ~ 70 K before a steady reduction of cage filling is observed, accelerating at 110 K and rapidly leading to (almost) completely empty small cages at 130 K. This means that helium is not imprisoned in the water cages of the sII structure, at least for laboratory time scales, and the label “clathrate” is in fact a misnomer for this material.

Figure 3: Small cage filling of sII He-clathrate as a function of temperature at low helium pressure. Red line is a guide to the eye.

During attempts to form sII He-clathrate directly by compression of fine-grained ice Ih powder at He-pressures exceeding 300 MPa and temperatures in the range of 240 to 250 K some


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striking changes on the ice Ih powder patterns were observed. In particular, the c/a ratio of the lattice constants exhibit highly significant changes as a function of helium pressure as shown in Figure 4; this is due to the c-axis is shrinking in an over-proportional manner with increasing pressure and is also manifest in the shift of oxygen position Oz. It means that helium must enter into the ice Ih structure in significant amounts to provoke such drastic changes of the lattice constants. Indeed, considerable gas uptake has been suggested by thermodynamic work9 and found support by lattice dynamical studies15; our observation is, however, the first direct structural evidence for a helium inclusion in ice Ih. The c/a changes are dramatic as ice Ih is known to exhibit only two orders of magnitude smaller c/a changes as a function of either pressure16 or temperature17. Unfortunately, the exact location of the helium atoms inside the channels of the ice Ih structure remains elusive as they are smeared out very considerably along the channel axis. In any case, the very significant change of lattice constants must be ascribed to dispersive interactions between helium und the surrounding water molecules, similar to the Heclathrate case discussed above. We conclude that lattice constants (which can be easily measured to a precision of 10-5 to 10-6) are arguably the most sensitive, experimentally accessible measures to gauge dispersive gas-water interactions. Taking the changing c/a ratio as an indicator for cage filling, it appears that the equilibration process upon changing pressure is relatively fast on a time-scale of less than 30 minutes, yet still distinctly slower than what we have observed and discussed above for helium atoms in a sII clathrate hydrate. This can be rationalized by the 1-dimensional nature of the migration paths in ice Ih as compared to the 3-dimensional migration network of connected cages in a sII clathrate structure. Helium diffusion inside ice Ih has been studied in the past18,19; the latter have deduced an activation energy of ~ 11 kJ/mole at temperatures between 173 and 253 K, more than an order


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of magnitude higher than the 0.75 kJ/mole established20 for H2 in D2O ice Ih. As a consequence of the high gas mobility, the promotion of ice Ih as a means of efficient gas storage21 appears premature as the bleeding by out-diffusion starts immediately after external pressure release. Clearly, more experimental work is needed to elucidate the diffusion and bleeding behavior of small gases in ice Ih.

Figure 4: The c/a ratio and oxygen Oz position in ice Ih as a function of time and helium pressure. The oxygen Oz position clearly changes with the increasing He content at constant T. Later on its increase is correlated with the increase of temperature at constant pressure, probably related to a loss of helium.

The clustering of up to four helium atoms in the large cages of sII clathrate is interesting also in another aspect. The very low solubility of helium in water22, the lowest of all gases, is a consequence of the entropically driven excluded volume effect23. Moreover, as helium is a very


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small atom, the persisting H-bonded network around this small solute necessitates a water cage too large to permit substantial attractive dispersive interactions between water and solute, which eventually lead to a clustering of several helium atoms in this cage; this is manifest in the negative osmotic second virial coefficient of helium in liquid water24, the most negative of all gases. Clustering permits a reduction of the entropic free energy costs by an enhanced enthalpic dispersion interaction of the hydrophobic water frame with small clusters of hydrophobic gases. Such a clustering has indeed been observed in recent molecular dynamics simulations of helium in water25. While the multiple cage occupancies observed in clathrate hydrates can be considered as the solid-state equivalent of this well-established clustering phenomena of small hydrophobic gases in the liquid26 the reason is somewhat different as there is no entropic cost for filling a preexisting cage, only some stabilizing enthalpic gain. Indeed, the 3-dimensional inner surfaces of the water framework in clathrate hydrates must be considered as hydrophobic, similar to 1dimensional water sheets27, as they do not provide any H-bond donor or acceptor sites28, at least for cases of purely hydrophobic guests. Helium atoms and water molecules are the most frequent mono- respectively triatomic entities in the universe, yet the interactions are weak and compounds are difficult to form. The Heclathrate described here as well as previously known forms of He-filled ices are characterized by the ease with which helium can enter and leave the water frameworks even at temperatures well below 100 K. As shown above, the van der Waals interactions are far from being negligible and stabilize these gas-filled structures at higher gas pressures. Such helium pressures exist in the atmospheres of gaseous planets where also water molecules are generally present. However, it is sometimes forgotten that the formation of crystalline water structures of complex topologies needs a sufficient mobility of orientational defects in the water frame29, unlikely to be available


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below 100 to 120 K. Thus, clathrate structures are not expected to form at lower temperatures even on geological timescales. The search for clathrate hydrates in the celestial bodies and their atmospheres thus can only be expected at higher temperatures and sufficient gas pressures of the constituting gases30. Ices consisting predominantly of H2O, CH4 and NH3 are the dominant material in Uranus and Neptune31, planets which also contain substantial amounts of helium and hydrogen from their gaseous envelope down deep towards the core. Thus, one can expect that He- (and H2-) filled ice Ih exists in the troposphere of Uranus (and Neptune) within suspected water ice clouds of the troposphere32, 33. Whether also mixed He-H2-clathrates exist in these clouds is uncertain as the high-temperature phase stability limit of the clathrate form is not yet established; from preliminary work it can, however, be expected that only at pressures of a few hundred MPa the clathrate compound has a higher melting point than gas-filled ice Ih or ice II6. Somewhat more likely is the inclusion of small amounts of helium into clathrates of CH4 and H2S in higher parts of the troposphere at temperatures exceeding 100 K. It is hardly conceivable that these He-filled ices or clathrates modify substantially the surrounding gaseous composition as the uptake and release is very rapidly following environmental changes. However, heavier noble gases as well as CH4, CO2 and CO may well be removed permanently from gaseous atmospheres by clathration with water (and subsequent segregation), provided that the temperatures are high enough to allow a crystallization of the clathrate frame. In summary, we have shown that He-clathrate can be formed by refilling an empty clathrate structure. We also have found clear evidence for helium entering into ice Ih. The attractive van der Waals interactions lead to very distinct changes in the lattice constants of these compounds. The uptake and release kinetics are fast and do not permit to store these gases efficiently at low


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environmental pressures, in contrast to previous claims. Moreover, our data provide very good testing grounds for computational chemistry to quantify the role of van der Waals forces in pure water and water-gas systems34, 35. Teeratchanan and Hermann1 have shown the path forward by screening suitable exchange-correlation functionals in order to describe properly the long-range dispersion interactions. Comparing our precise structural data with results from such DFT calculations should be the next step. Admittedly, the large unit cell of the He-clathrate structure could still pose a computational problem but should become tractable in the near future. On the experimental side, the proposed refilling strategy could also be applied to the C0-structure of the hydrogen form as it had been shown that the gas can be removed by pumping36. Certainly, helium as well as neon and argon is expected to enter into this chiral structure, which seems to be quite unspecific concerning its hosting properties as also a CO2-filled C0-structure is known to exist. Moreover, the C0 structure has wider channels than both ice Ih and ice II37 and, indeed, the thermodynamic stability of Ne-and Ar-filled C0-hydrate has been predicted1. Detailed experimental studies of these systems will add valuable quantitative insights to our still rudimentary knowledge of van der Waals interactions between gas and water molecules.

ASSOCIATED CONTENT Supporting Information. Experimental details, details of the data analysis and structural results (pdf-file) Crystallographic information (CIF-file) on He-clathrate at 120 K and 100 MPa


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Crystallographic information (CIF-file) on He-clathrate at 80 K and 100 MPa

ACKNOWLEDGMENT We thank the Bundesministerium für Bildung und Forschung (BMBF) for financial support in the framework of the SUGAR III (SUbmarine Gashydrat-Lagerstätten: Erkundung, Abbau und TRansport) project. Furthermore, we thank Dr. Kirsten Techmer (Göttingen) for her help in the SEM sessions, the Institut Laue-Langevin (ILL) at Grenoble for beam time and support, and Dr. Patrick Lafond (Göttingen) for assistance with the experiments. Neutron diffraction data for all runs can be access though the ILL data portal under: http://doi.ill.fr/10.5291/ILL-DATA.5-25226 REFERENCES (1) (2) (3) (4) (5) (6)

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Falenty, A.; Genov, G.; Hansen, T. C.; Kuhs, W. F.; Salamatin, A. N., Kinetics of CO2 hydrate formation from water frost at low temperatures: Experimental results and theoretical model. J. Phys. Chem. C 2011, 115, 4022-4032. Podolak, M.; Hubbard, W. B., Ices in the giant planets. In Solar system ices, Schmitt, B., Ed. Kluwer Academic Publishers: Netherlands, 1998. Lunine, J. I., The Atmospheres of Uranus and Neptune. Annu. Rev. Astron. Astrophys. 1993, 31, 217-263. Lindal, G. F.; Lyons, J. R.; Sweetnam, D. N.; Eshleman, V. R.; Hinson, D. P.; Tyler, G. L., The atmosphere of Uranus: Results of radio occultation measurements with Voyager 2. J. Geophys. Res.: Space Phys. 1987, 92, 14987-15001. Santra, B.; Klimeš, J.; Alfè, D.; Tkatchenko, A.; Slater, B.; Michaelides, A.; Car, R.; Scheffler, M., Hydrogen bonds and van der waals forces in ice at ambient and high pressures. Phys. Rev. Lett. 2011, 107, 185701. Santra, B.; Klimeš, J.; Tkatchenko, A.; Alfè, D.; Slater, B.; Michaelides, A.; Car, R.; Scheffler, M., On the accuracy of van der Waals inclusive density-functional theory exchange-correlation functionals for ice at ambient and high pressures. J. Chem. Phys. 2013, 139, 154702. del Rosso, L.; Grazzi, F.; Celli, M.; Colognesi, D.; Garcia-Sakai, V.; Ulivi, L., Refined structure of metastable ice XVII from neutron diffraction measurements. J. Phys. Chem. C 2016, 120, 26955-26959. Amos, D. M.; Donnelly, M.-E.; Teeratchanan, P.; Bull, C. L.; Falenty, A.; Kuhs, W. F.; Hermann, A.; Loveday, J. S., A chiral gas–hydrate structure common to the carbon dioxide–water and hydrogen–water systems. J. Phys. Chem. Lett. 2017, 8, 4295-4299.


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Figure 1: Adopted model of a multiple cage filling (up to four molecules) of helium in the large cages of a sII clathrate hydrate structure. Small cages accept up to one guest. 1323x991mm (96 x 96 DPI)



Figure 2: Small and large cage filling of sII He-clathrate as a function of pressure and temperature. 288x304mm (300 x 300 DPI)


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Figure 3: Small cage filling of sII He-clathrate as a function of temperature at low helium pressure. Red line is a guide to the eye. 288x201mm (300 x 300 DPI)



Figure 4: The c/a ratio and oxygen Oz position in ice Ih as a function of time and helium pressure. The oxygen Oz position clearly changes with the increasing He content at constant T. Later on its increase is correlated with the increase of temperature at constant pressure, probably related to a loss of helium. 288x304mm (300 x 300 DPI)


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Filling Ices with Helium and the Formation of Helium Clathrate Hydrate

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