Editing Clathrate hydrate (section)

== Empty clathrate hydrates ==
Empty clathrate hydrates<ref>{{cite journal|doi=10.1021/acsearthspacechem.9b00009 |bibcode=2019ESC.....3..789C |volume=3 |title=Low-Temperature Thermodynamic Study of the Metastable Empty Clathrate Hydrates Using Molecular Simulations |year=2019 |journal=ACS Earth and Space Chemistry |pages=789–799 |last1=Cruz |first1=Fernando J. A. L. |last2=Alavi |first2=Saman |last3=Mota |first3=José P. B.| issue=5 |s2cid=140362440 }}</ref> 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&nbsp;K), Falenty et al.<ref>{{cite journal |author=Falenty A. |author2=Hansen T.C.|author3=Kuhs F. |year=2014 |title=Formation and Properties of Ice XVI Obtained by Emptying a Type sII Clathrate Hydrate |volume=516 |issue=7530| pages=231–234 |doi=10.1038/nature14014 |pmid=25503235| journal=Nature| bibcode=2014Natur.516..231F |s2cid=4464711}}</ref> 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 {{nowrap|''T'' ≥ 145&nbsp;K}} and, furthermore, (ii) the empty hydrate shows a negative thermal expansion at {{nowrap|''T'' < 55&nbsp;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.<ref>{{cite journal |author=Kosyakov V.I. |year=2009 |title=Structure Formation Under Negative Pressures |volume=50 |pages=60–65 |doi=10.1007/s10947-009-0190-0 |journal=J. Struct. Chem|bibcode=2009JStCh..50S..60K | s2cid=97767359 }}</ref> 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 H<sub>2</sub>O at negative pressures and {{nowrap|''T'' ≤ 300&nbsp;K}},<ref>{{cite journal |author=Conde M.M. |author2=Vega C.|author3=Tribello G.A. |author4=Slater B.| year=2009 |title=The Phase Diagram of Water at Negative Pressures: Virtual Ices |volume=131 |issue=3| pages=034510 |doi=10.1063/1.3182727 |pmid=19624212| journal=J. Chem. Phys.|bibcode=2009JChPh.131c4510C}}</ref> 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<ref>{{cite journal |author=Jacobson L.C. |author2=Hujo W.|author3=Molinero V. |year=2009 |title=Thermodynamic Stability and Growth of Guest-Free Clathrate Hydrates: A Low-Density Crystal Phase of Water |volume=113 |issue=30| pages=10298–10307 |doi=10.1021/jp903439a |pmid=19585976| journal=J. Phys. Chem. B| doi-access=free }}</ref> simulations using a monoatomic (coarse-grained) model developed for H<sub>2</sub>O 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, {{nowrap|1=''T'' = 245 ± 2&nbsp;K}} and {{nowrap|1=''T'' = 252 ± 2&nbsp;K}}, respectively. Matsui et al. employed<ref>{{cite journal |author=Matsui T.|author2=Hirata M.|author3=Yagasaki T. |author4=Matsumoto M. |author5=Tanaka H.| year=2017 |title=Hypothetical Ultralow-density Ice Polymorphs |volume=147 |issue=9| pages=091101 |doi=10.1063/1.4994757 |pmid=28886658| journal=J. Chem. Phys.| doi-access=free }}</ref> 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, {{nowrap|100&nbsp;K ≤ ''T'' ≤ 220&nbsp;K}} and {{nowrap|100&nbsp;kPa ≤ ''p'' ≤ 500&nbsp;MPa}}, by Cruz et al.<ref>{{cite journal |author=Cruz F.J.A.L. |author2=Alavi S.|author3=Mota J.P.B. |year=2019 |title=Low-Temperature Thermodynamic Study of the Metastable Empty Clathrate Hydrates Using Molecular Simulations |doi=10.1021/acsearthspacechem.9b00009 |journal=ACS Earth and Space Chemistry|volume=3|issue=5|pages=789–799|bibcode=2019ESC.....3..789C|s2cid=140362440}}</ref> using large-scale simulations and compared with experimental data at 100&nbsp;kPa. 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&nbsp;K at 100&nbsp;kPa to 166.2&nbsp;K at 500&nbsp;MPa. Response to the applied (''p'',&nbsp;''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'',&nbsp;''T'') > (200&nbsp;MPa,&nbsp;200&nbsp;K). The length of the hydrogen bonds responsible for framework integrity was insensitive to the thermodynamic conditions and its average value is {{nowrap|1=r(̅O H) = 0.25&nbsp;nm}}.