Figure 2 . Energy versus volume curve for NH3,
N2O and NO hydrates using revPBE XC functional and
fitted using Murnaghan equation, respectively.
3.2. Elastic properties
The theoretical prediction of the elastic mechanical properties of
NH3, NO and N2O hydrates are carried out
in this work. To the authors’ knowledge, this is the first time that the
sI crystalline structures of NH3, N2O
and NO hydrates have been studied with DFT. The calculation results for
single-crystal SOEC are given in Table 1 and all energy-strain
curves are shown in Figure 3 for NH3,
N2O and NO hydrates with 100% cage occupancy. FromTable 1 , the N2O hydrate is found to have a
slightly lower bulk modulus than the methane hydrate. Unlike nitrous
oxide, hydrogen atoms in methane molecules are more likely to generate
hydrogen bonds with water molecules aligned in a tetrahedron pattern,
which may increase the rigidity of the skeleton between guest molecules
and water molecules. The NH3 and NO hydrates have a
slightly higher bulk modulus than the methane hydrate as Table
1 shows. On the one hand, higher B for NH3 can be
attributed to three hydrogen atoms per molecule that facilitate the
formation of multiple hydrogen bonds to the water molecules and NO is a
polar molecule that adds to the intermolecular interactions with the
water molecules; on the other hand, unlike methane, nitrogen atoms in
ammonia and nitric oxide are more electronegative compared with carbon
atoms in methane.
On the whole, the characteristics of the three hydrates are similar in
most respects with N2O showing a higher curvature. All
hydrates are almost isotropic as reflected by the Zener anisotropy
factor AZ. A similar observation of isotropy was
obtained in the experimental work of Shimizu et
al .48 using Brillouin spectroscopy on methane hydrate
single crystals. They attributed this isotropy to the void-rich network
and departure from the ideal tetrahedral arrangement of oxygen atoms in
methane hydrates. In addition to these reasons, we believe that the
randomness of the hydrogen positions in the cubic lattice may contribute
to this isotropy. The slightly lower isotropy of nitrous oxide hydrates
in this work may be due to the geometry or bond orientation in nitrous
oxide molecules.
The SOEC of N2O has large difference relative to those
of methane hydrate, especially c 12 andc 44. The polarity of this molecule may be a
reason since it induces stronger hydrogen bonding between host and guest
molecules than methane, which can be more susceptible to structural
deformation and results in a significant impact on the elastic
constants. As a result, the Bulk and shear modulus differ significantly
between methane and N2O hydrates. The shape of the
N2O molecule and its interaction with the host water
molecules might also explain this. From the geometric perspective, the
ratio of molecular diameter to cage diameter is larger for
N2O hydrate than methane hydrate, which enhances the
stiffness of the hydrate. Interestingly, the NH3 hydrate
is predicted to be closer to the methane hydrate in both elastic
constants as well as mechanical modulus than NO and N2O.
It is probably because NH3’s interaction with
H2O as both the hydrogen bond donor and acceptor allows
more flexibility to adapt to the shear distortion. These demonstrate
that the encaged species indeed have significant impact on the
mechanical behavior of the hydrates. When a shear strain takes place, it
induces stronger hydrogen bonding change between host and guest
molecules since NO and N2O are both highly polar
molecules, resulting in a relatively high shear modulus; When tensile
strain occurs, hydrogen atoms in CH4 and
NH3 molecules are more likely to generate hydrogen bonds
with hydrogen atoms in water molecules, increasing the intermolecular
interaction between guest molecules and water molecules, resulting in a
relatively high Poisson’s ratio.