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.