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Phase Diagram of Methane Hydrates and Discovery of MH-VI Hydrate Yingying Huang, Keyao Li, Xue Jiang, Yan Su, Xiaoxiao Cao, and Jijun Zhao J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02590 • Publication Date (Web): 02 Jul 2018 Downloaded from http://pubs.acs.org on July 5, 2018

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The Journal of Physical Chemistry

Phase Diagram of Methane Hydrates and Discovery of MH-VI Hydrate Yingying Huang1, 2, Keyao Li1, Xue Jiang1, Yan Su1, Xiaoxiao Cao3*, and Jijun Zhao1* 1

Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University

of Technology), Ministry of Education, Dalian 116024, China 2

Department of Chemistry, University of Nebraska, Lincoln, NE 68588, USA

3

College of Physics and Electronic Engineering, Jiangsu Second Normal University, Nanjing

210013, China

ACS Paragon Plus Environment

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ABSTRACT

Methane hydrate is not only the predominantly natural deposits of permafrost and continental margins of Earth but also the dominant methane-containing phase in the nebula and major moons of gas giants. Depending on the surrounding environment (mainly pressure), seven methane hydrate phases have been discovered by experiment or predicted by computer simulation, such as clathrate methane hydrates I, II, H, and K, and filled-ice methane hydrates III, IV, and V. Using extensive Monte Carlo packing algorithm and density functional theory optimization, here we predict a partial clathrate methane hydrate VI built by basic units of 4262 water bowl encapsulating a methane molecule, which is dynamically stable from the computed phonon dispersion. Its density and structural characteristics are comparable to that of filled-ice methane hydrate III. By calculating the formation enthalpies of a variety of candidate phases at different pressures, a phase diagram of methane hydrates is constructed. As pressure rises, phase transitions occur in the methane hydrates along with the decreasing water/methane molecular ratios. The newly predicted methane hydrate VI emerges as the most stable phase in the region between clathrate phase II and filled-ice phase III, suggesting that methane hydrate VI might be synthesized in laboratory under accessible conditions.


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INTRODUCTION Gas hydrates are crystalline inclusion compounds consisting of a hydrogen-bonded network of polyhedral water cavities, which encage small gas molecules (such as Ne, Ar, H2, H2S, CO2, CH4, C2H6, and C3H8)1-3. Particularly, when the methane molecules contact water at low temperature (close to 0 ℃) and under moderate pressure (a few MPa and up), methane hydrates (MHs) would form. On the earth, methane hydrate (as the major component of natural gas hydrates) is the predominantly natural deposit of permafrost and continental margins. By estimation, the amount of energy stored in the form of MHs is twice of all conventional fossil deposits together4, 5. On the other hand, methane hydrate is thought to be the dominant methanecontaining phase in the nebula of Saturn, Uranus, Neptune, Titan, and their major moons6, 7. Therefore, researches on the formation and phase transformation behavior of methane hydrates under high pressures are of importance to solve the urgent problems of future energy resource, gas storage and transportation, and to understand the formation process of outer solar system. MH, also known as flammable ice, is a special class of ice that contains methane molecules in water cages or networks of hydrogen-bonded water molecules. To date, at least four clathrate methane hydrates and three filled-ice methane hydrates have been experimentally identified7-13 or theoretically proposed14, 15. The four clathrate hydrates are cubic structure I methane hydrate (MH-I) with two 512 (i.e., twelve pentagons) cages and six 51262 cages per unit cell, cubic structure II methane hydrate (MH-II) with sixteen 512 cages and eight 51264 cages per unit cell, hexagonal structure H methane hydrate (MH-H) with three 512 cages, two 435663 cages, and one 51268 cage per unit cell, and tetragonal structure K methane hydrate (MH-K) with six 512 cages, four 51263 cages, and four 51262 cages per unit cell, respectively. The three filled-ice phases of


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methane hydrate are orthorhombic structure III (MH-III), orthorhombic structure IV methane hydrate (MH-IV), and monoclinic structure V methane hydrate (MH-V). For all the clathrate hydrates, methane molecules are encapsulated in the water cages to stabilize the hydrogenbonded framework via van der Waals interaction. Small cages such as 512 and 435663 can only accommodate one methane molecule; medium cages such as 51262, 51263, and 51264 are able to encapsulate two or three methane molecules; large cages such as 51268 can be filled with up to seven methane molecules16. For the filled-ice phases, methane molecules are filled in the channels of water hydrogen-bonded networks. The topological water networks of MH-III, MHIV, and MH-V are closely related to that of hexagonal ice (Ih)17, ice i18, and ice XI19, respectively. Besides these seven types of methane hydrates, there are some other types of gas clathrate hydrates, including two tetragonal hydrates20, 21 with two 425864 cages per unit cell and with ten 512 cages and twenty 51262 cages per unit cell, respectively, and two hexagonal hydrates21 with eight 512 cages and four 51264 cages per unit cell and with six 512 cages and eight 51263 cages per unit cell, respectively. Though the methane hydrates have been discovered for over a century, there were only few experiments on the phase transformation of methane hydrates under high pressure7-10. Using Xray diffraction and Raman spectroscopy in a diamond anvil cell, Chou et al.8 observed that MH-I transforms to MH-II at 1 kbar and room temperature, then to the MH-H phase at 6 kbar. Along with the occurrence of phase transition, the water/methane molecular ratio (R) varies from 5.75 (one CH4 in each cage for MH-I) to 5.67 (one CH4 in each cage for MH-II), then to 4.86 or lower (one CH4 in each smaller cage and two or more CH4 in large cage for MH-H). Later, neutron and synchrotron X-ray diffraction studies by Loveday et al.7 revealed structural transitions from MHI to MH-II at about 10 kbar, further to MH-III at about 20 kbar, and MH-III phase can remain


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stable up to at least 100 kbar. During such phase transformation, water/methane molecular ratios for MH-I and MH-III are 5.75 and 2, respectively. However, R of MH-II phase varies between 4 and 3 with increasing pressure, suggesting that each large cavity of MH-II may contain 2 or 3 CH4 molecules while each small cage is occupied by one CH4. Similarly, in situ Raman measurement by Shimizu et al.10 at room temperature also found that the MH-I phase changes to MH-II phase at 9 kbar, and MH-II transforms to MH-III at 19 kbar, respectively. Using in situ Xray diffractometry and Raman spectroscopy, Hirai et al.9 found that MH-I decomposes into MHH at 8 kbar; then MH-H transforms into an unknown structure B phase at 16 kbar and further transforms to MH-III at 21 kbar, which survives above 78 kbar. Generally speaking, as pressure increases, phase transition firstly occurs between clathrate methane hydrates at low pressures, then from clathrate hydrate to filled-ice hydrate at high pressures. No doubt, under very low pressure MH-I can crystalline firstly with one methane molecule in each cage, while MH-III will be the most stable phase under very high pressure. In the medium pressure region, however, there are still several unclear issues that need theoretical verification. For example, it is controversial that MH-I phase can transform to MH-II or MH-H, because these two methane hydrates have very similar structures7. Besides, the occupancy numbers of methane molecules in the large cages of MH-II and MH-H are also unknown. Further, there might even exist some undiscovered phases of methane hydrates. Given the unsolved questions mentioned above, using comprehensive Monte Carlo packing algorithm and density functional theory (DFT) calculations, here we predict a monoclinic phase of methane hydrate with (H2O)3(CH4) stoichiometry, namely methane hydrate VI (MH-VI), which is dynamically stable and a partial clathrate structure intermediate between clathrate phase and filled-ice phase. A formation enthalpy-pressure (H-P) phase diagram of all the candidate


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methane hydrates with all the possible water/methane molecular ratios is then constructed, where MH-VI shows up as the most stable phase in the intermediate region between the clathrate phase MH-II and the filled-ice phase MH-III. Such a phase diagram of methane hydrates not only provides the relative stabilities of the competing phases, but also guides scientists to explore more possibly new phases in the future. COMPUTATIONAL METHODS MC search of candidate MH phases. Possible methane hydrates with (H2O)x(CH4) (x = 2, 3, 4, 5, 6, 7) stoichiometry were searched using the Monte Carlo packing algorithm and simulating annealing method22 with the consistent valence force field (CVFF)23, as implemented in the Polymorph module of the Materials Studio 7.0 package. All 230 space groups had been explored for each stoichiometry. All the possible clathrate hydrates and filled-ice phases after the Monte Carlo simulations were chosen as the candidate methane hydrates. In our recent studies, this Mote Carlo search method has been employed to discover two ice clathrates24,25, two filled-ice methane hydrates15 and an ionic phase of ammonia dihydrate26, confirming its feasibility and efficiency in prediction of molecular crystal. DFT calculation. To compare with the known methane hydrates, i.e., MH-I8, MH-II7,8, MH-H9, MH-K14, MH-III11, MH-IV15, and MH-V15, the total energies and enthalpies of different candidate methane hydrates with possible stoichiometric ratios at selected pressures were computed with DFT method, as implemented in the VASP27. For filled-ice phases MH-III11, MH-IV15 and MH-V15, the guest occupancies are fixed, and their water/methane molecular ratios are 2, 4, and 4, respectively. Based on previous molecular dynamics simulation14, when every cage of MH-K contains one methane molecule, i.e., the water/methane molecular ratio being


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5.71, the system is optimal. For clathrate MH-I, four situations are examined, namely, each small cage occupied by one methane molecule, every large cage filled with one methane molecule, every cage encapsulated with one methane molecule, and every large cage stuffed with two methane molecules while each small cage sealed with one methane molecule. The corresponding water/methane molecular ratios are 23, 7.7, 5.75, and 3.29, respectively. For clathrate MH-II, every large cage is encapsulated with three, two, and one methane molecules, respectively, while every small cage is stuffed with one methane molecule. The resulting water/methane molecular ratios are 3.4, 4.25, and 5.67, respectively. For clathrate MH-H, four situations are considered, i.e., while the large cavity is stuffed with one, two, three, four methane molecules, respectively, every smaller cage is inserted with one methane molecule. As a result, the water/methane molecular ratios of MH-H systems are 5.67, 4.86, 4.25, and 3.78, respectively. The electron-ion interactions were described by the projector augmented wave (PAW) potential28 and the exchange-correlation interaction was described by the vdW-DF2 functional29 with inclusion of a long-range term of the correlation energy to account for the intermolecular dispersion interactions. The electron wave function was expanded by the plane wave basis up to 700 eV, and the Brillouin zones were sampled by k point grids with a uniform spacing of 2π × 0.04 Å‒1. In addition, the Raman spectra of MH-VI and MH-III phases were computed using the CASTEP program30 based on DFT and plane-wave pseudopotential technique. The PBE functional and norm-conserving pseudopotential were adopted to account for non-covalent interaction and ion-electron interaction, respectively. The cutoff for plane-wave basis was chosen as 1000 eV. RESULTS AND DISCUSSION


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Phase diagram. We firstly investigated the phase stabilities of all the known methane hydrates MH-I, MH-II, MH-III, MH-IV, MH-V, MH-H, and MH-K and all the candidate phases from Mote Carlo simulations by calculating their formation enthalpies (H) in a pressure range from 0 to 30 kbar. The formation enthalpy of methane hydrate was calculated from the enthalpy difference between the methane hydrate and solid ice phase plus methane phase, both of which are the most stable structures at the given pressure. The formula is given as Hf (m H2O • n CH4) = [H (m H2O • n CH4) – m H (solid ice) – n H (solid methane)] / (m + n) (1) where H (m H2O • n CH4), H (solid ice), and H (solid methane) are the enthalpies of methane hydrate, solid ice crystal per water molecule and solid methane per methane molecule at the given pressure. The ice phases II, VI, VIII, IX, XI, XIII, XIV, and XV31, 32 existing in the low temperatures and methane phases I, II33 and III34 are considered to find out the most stable phase in the desired pressure range. As shown in Figure S1 and Figure S2, ices XI, IX, XIV, VIII are the most stable phase at pressure points of 0 kbar, 5 kbar, 10 and 15 kbar, and 20 – 30 kbar, respectively, while methane phase III is the most stable structure within the entire pressure range. For clathrate MH-I, the formation enthalpies of system with water/methane molecular ratio of 5.75 are negative when P ≤ 5 kbar, while those of the other three systems are positive at any pressure. Therefore, MH-I with full guest occupancy (corresponding to R = 5.75) is chosen (as measured in the experiment8) as the representative to compare with the other methane hydrates. Given the higher formation enthalpies of the clathrate phases MH-II with R = 5.67 and 3.4 and MH-H with R = 5.67, 4.86, and 3.78 (see Figure S3 and Figure S4), when P ≤ 10 kbar, the MH-II with R = 4.25, i.e., every large cage accommodating two methane molecules, and the MH-H with R = 4.25, i.e., the large


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cage containing three methane molecules, are chosen as the representatives of MH-II and MH-H, respectively. Eventually, an H-P phase diagram for methane hydrates with all different stoichiometry was derived. As shown in Figure 1, the relative phase stabilities of methane hydrates with the known phases MH-I with R = 5.75, MH-K with R = 5.71, MH-II with R = 4.25, MH-H with R = 4.25, MH-IV with R = 4, and MH-III with R = 2 under different pressures are displayed in the H-P phase diagram. The filled-ice phase MH-V with R = 4 and clathrate phase MH-H with R = 5.67 do not appear because of their positive formation enthalpies. Moreover, among all the candidate methane hydrate phases from our MC calculations, only one new phase with (H2O)3(CH4) stoichiometry shows up, namely MH-VI. Below 5 kbar, the clathrate phase MH-K instead of MH-I emerges as the most stable phase with the lowest formation enthalpy. Then, clathrate phase MH-II will be the most favorable one until the pressure reaches 8.12 kbar. Thus, the phase stability of MH-K lies between MH-I and MH-II, probably because it is an intermediate phase connecting MH-I and MH-II14. Without MH-K, clathrate phase MH-I would transform to MH-II at pressure of 3.33 kbar, which corresponds to the critical pressure of 9 kbar10 or 10 kbar7 observed in experiments. Next, the newly predicted MH-VI phase occupies the most stable region between 8.12 kbar and 11.63 kbar. Further, filled-ice phase MH-III will take over as the most stable phase up to 60 kbar (from extrapolation), comparable to the experimental values of 80 kbar9 and 100 kbar7. If there is no MH-VI phase, MH-III would directly replace MH-II and become the most stable phase under pressure beyond 9.31 kbar, in contrast to the experimental value of about 20 kbar7,9. As for the filled-ice phase MH-IV and clathrate phase MH-H, they are always metastable because of their higher formation enthalpies.


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Based on the established H-P phase diagram, the sequence of most favorable phase is MH-K, MH-II, MH-VI and MH-III with increasing pressure. Meanwhile, as phase transition occurs, the corresponding water/methane molecular ratios decrease as 5.71, 4.25, 3, and 2, respectively. Overall, the formation enthalpy is reasonable to describe the relative phase stabilities of methane hydrates with different stoichiometry. In particular, our theoretical H-P phase diagram suggests that the newly predicted MH-VI phase can potentially be synthesized under accessible condition. Crystal structure. After DFT optimization with vdW-DF2 functional, MH-VI phase was identified as a monoclinic lattice crystal with P21/c space group. Its equilibrium lattice parameters are a = 6.434 Å, b = 11.299 Å, c = 6.691 Å, α = γ = 90˚, β = 69.987˚. The fractional coordinates of MH-VI are given in Table S1. Then the phonon dispersion (see Figure S5) was computed from the real-space force constants using the Phonopy package35. No imaginary frequency is found within the entire Brillouin zone, confirming its dynamic stability. As shown in Figure 2, its unit cell contains 12 water molecules and 4 methane molecules. The basic unit is a 4262 water bowl encapsulated with a methane molecule. The basic units are connected with each other either by two quadrangles or two hexagon faces of water bowl or by face to face of methane molecules next to each other. By removing the methane molecules, the water network is constituted by partial water cages, i.e., the water bowls in several stacking patterns. From this point of view, the MH-VI phase can be considered as a partial clathrate methane hydrate between the clathrate phase with clathrate water network and methane guest molecules such as MH-I, MH-II, MH-H8, and MH-K14, and the filled-ice phase with water network resembling the pure ice phase and methane molecules sitting inside channels like MHIII11 based on Ih, MH-IV based on ice i, and MH-V15 based on ice XI. In previous studies, it was found that the interconversion between MH-I and MH-II structures occurs through intermediate


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51263 cages14, and the interconversion between MH-I and MH-H hydrates is facilitated by intermediate 4151062 cages36. Considering that clathrate phase MH-II has 51264 cages and filledice phase MH-III has a series of hexagonal faces, we speculate that MH-II and MH-VI may interconvert through certain water cages with quadrangular faces, pentagonal faces and hexagonal faces, while MH-VI and MH-III may interconvert though certain water bowls with quadrangular faces and hexagonal faces. Thus, we further infer that MH-VI with 4262 partial cages may be intermediate between the common methane hydrates MH-II and MH-III. To compare the structural characteristics of MH-VI phase with the known methane hydrates MH-I, MH-II, MH-III, MH-IV, MH-H and MH-K, their equilibrium volume of unit cell, average distance between oxygen atoms in adjacent water molecules, shortest distance between oxygen atoms and carbon atoms, mass density, and bulk modulus are calculated using DFT with vdWDF2 functional and summarized in Table 1. As discussed above, MH-II with R = 4.25 and MH-H with R = 4.25 are regarded as the representatives because of their best stability. Our recent studies demonstrated that vdW-DF2 functional can reasonably describe the non-covalent intermolecular interactions and lattice structures of ices24, 25 and methane hydrate phases15. Upon relaxation, the mass density of MH-VI is 1.017 g/cm3, which is nearly equal to that of MH-III (1.016 g/cm3) and noticeably higher than that of MH-H (0.950 g/cm3), MH-IV (0.986 g/cm3), MH-II (0.966 g/cm3), MH-K (0.949 g/cm3), and MH-I (0.954 g/cm3). Its bulk modulus is 15.32 GPa, which is comparable to other calculated values of MH-III (17.29 GPa), MH-H (15.92 GPa), MH-IV (17.76 GPa), MH-II (12.59 GPa), and MH-K (15.33 GPa) and significantly higher than the value of MH-I (7.07 GPa). The average O-O distance between oxygen atoms in adjacent water molecules (dO-O) is 2.795 Å for MH-VI, comparable to the values of 2.765 Å for MH-H, 2.775 Å for MH-IV and MH-II, 2.755 Å for MH-K and MH-I, and 2.885 Å for MH-III. The


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shortest distances between oxygen atom and carbon atom (dC-O) and between carbon atoms in adjacent methane molecules (dC-C) are 3.495 Å and 4.065 Å, respectively. Though these two distances are lower or higher than the other methane hydrate phases, both of them are closest to those of MH-III (3.285 Å and 3.985 Å). Therefore, in terms of structural characteristics from DFT calculations at zero pressure, MH-VI is similar to MH-III phase. Using MH-III as a reference, we further examined the variation of structural properties of MHVI versus pressure. As shown in Figure 3, as pressure rises, the mass densities of them increase with nearly equal value at each pressure point while their average O-O distance (dO-O) and shortest C-O distance (dC-O) decrease by almost constant differences. Although the shortest C-C distances (dC-C) in adjacent methane molecules of MH-III and MH-VI keep going down with increasing pressure, their relative sequences vary with pressure, that is, dC-C of MH-III is shorter under pressure below 13.33 kbar, then that of MH-VI becomes shorter. In brief, the partial clathrate MH-VI phase possesses reasonable crystalline structure, whose structural properties are comparable to filled-ice phase MH-III. Raman spectra. To provide the fingerprint information of MH-VI for experimental identification, we computed the vibrational property of MH-VI crystal at pressure of 10 kbar (at this pressure MH-VI has the best stability, as shown in Figure 1). We also considered MH-III phase as a reference and simulated the Raman spectra of both MH phases. As described in our latest work15, the positions of simulated Raman peak are usually acceptable, considering the deficiency of the DFT/GGA methodology itself and the harmonic approximation on the frequency calculations. Figure 4 gives the characteristic Raman speaks of MH-III and MH-VI in the frequency range of 2900 ‒ 3450 cm‒1 at pressure of 10 kbar. For MH-III phase, C-H symmetric stretching peak, C-H antisymmetric stretching peak, and O-H symmetric stretching


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peak are at 2975 cm‒1, 3099 cm‒1, and 3170 cm‒1, respectively. Comparable to MH-III phase, the C-H symmetric stretching frequency (2968 cm‒1), C-H antisymmetric stretching frequency (3093 cm‒1), and O-H symmetric stretching frequency (3158 cm‒1) of MH-VI show red shift by 7 cm‒1, 6 cm‒1, and 12 cm‒1, respectively. In general, we expect that our theoretical results can provide useful spectroscopy information for identifying MH-VI phase and distinguishing it from MH-III in experiment. CONCLUSION To summarize, using extensive MC simulations combined with DFT calculations, we predict a new MH-VI phase of methane hydrate with (H2O)3(CH4) stoichiometry, which is dynamically stable from phonon computation. MH-VI is packed by a basic unit of 4262 water bowl containing a methane molecule in different patterns. Although it is a partial clathrate structure between the clathrate phase and filled-ice phase, its density and structural characteristics are close to the filled-ice phase MH-III. We constructed a H-P phase diagram describing the relative phase stabilities of all the methane hydrate phases and identified the water/methane molecular ratios of experimental phases MH-II with R = 4.25 (corresponding to two methane molecules inside each large cage) and MH-H with R = 4.25 (corresponding to three methane molecules in large cage). Moreover, the newly predicted MH-VI emerges as the most stable phase in the region between MH-II and MH-III, suggesting that MH-VI is likely to be synthesized in laboratory under accessible conditions. Besides, as pressure rises, the phase transitions occur in the sequence of MH-K, MH-II, MH-IV, and MH-III along with water/methane molecular ratios decreasing. The discovery of MH-VI phase not only enriches the high-pressure region of phase diagram of methane hydrates but also stimulates scientists to explore more possibly new phases in the future.


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In previous studies by Firoozabadi et al.37, 38, it has been pointed that hydrate nucleation by molecular dynamics simulation is a more straightforward approach to obtain the new gas hydrates or new cages and nucleation time can be significantly reduced with the initial simulation system of gas-water mixture. In the future, we will perform molecular dynamics simulation with methane-water mixed system at different pressures and temperatures to explore the new methane hydrates including our newly predicted MH-VI. ASSOCIATED CONTENT Supporting Information. The fractional coordinates of the methane hydrate phase VI, average distance between oxygen atoms in adjacent water molecules and shortest distance between oxygen atom and carbon atom of clathrate phases MH-II and MH-H with different water/methane molecular ratios, the relative enthalpy of ices II, VI, IX, XI, XIII, XIV, and XIV referencing to ice VIII as a function of pressure, the relative enthalpy of solid methane phases II and III with respect to methane phase I as a function of pressure, the relative enthalpies of formation per molecule with respect to ice and methane phase for MH-II phases in different water/methane molecular ratios, the relative enthalpies of formation per molecule with respect to ice and methane phase for MH-H phases in different water/methane molecular ratios, the phonon dispersion for MH-VI phase from vdWDF2 DFT computation, the crystal structures of clathrate methane phases MH-I, MH-K, MH-II, and MH-H, and filled-ice phases MH-III, MH-IV, MH-VI, and MH-V are given in the Supporting Information. AUTHOR INFORMATION Corresponding Author


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*Jijun Zhao, Email: [email protected]; *Xiaoxiao Cao, Email: [email protected] ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (11674046), the Science Challenge Project (TZ2016001), and the Fundamental Research Funds for the Central Universities of China (DUT17GF203). REFERENCES 1. Sloan, E. D. Fundamental principles and applications of natural gas hydrates. Nature 2003, 426, 353-363. 2. Koh, C. A. Towards a fundamental understanding of natural gas hydrates. Chem. Soc. Rev. 2002, 31, 157-167. 3. Sloan Jr, E. D.; Koh, C.: Clathrate hydrates of natural gases; CRC press: Boca Raton, FL, 2008. 4. Holkrook, W.; Hoskins, H.; Wood, W. T.; Stephen, R. A.; Lizarralde, D. Methane hydrate and free gas on the Blake Ridge from vertical seismic profiling. Science 1996, 273, 1840-1842. 5. Boswell, R. Is gas hydrate energy within reach? Science 2009, 325, 957-958. 6. Lunine, J. I.; Stevenson, D. J. Clathrate and ammonia hydrates at high pressure: Application to the origin of methane on Titan. Icarus 1987, 70, 61-77. 7. Loveday, J.; Nelmes, R.; Guthrie, M.; Belmonte, S.; Allan, D.; Klug, D.; Tse, J.; Handa, Y. Stable methane hydrate above 2 GPa and the source of Titan's atmospheric methane. Nature 2001, 410, 661-663.


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8. Chou, I.-M.; Sharma, A.; Burruss, R. C.; Shu, J.; Mao, H.-k.; Hemley, R. J.; Goncharov, A. F.; Stern, L. A.; Kirby, S. H. Transformations in methane hydrates. Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 13484-13487. 9. Hirai, H.; Uchihara, Y.; Fujihisa, H.; Sakashita, M.; Katoh, E.; Aoki, K.; Nagashima, K.; Yamamoto, Y.; Yagi, T. High-pressure structures of methane hydrate observed up to 8 GPa at room temperature. J. Chem. Phys. 2001, 115, 7066-7070. 10. Shimizu, H.; Kumazaki, T.; Kume, T.; Sasaki, S. In situ observations of high-pressure phase transformations in a synthetic methane hydrate. J. Phys. Chem. B 2002, 106, 30-33. 11. Loveday, J.; Nelmes, R.; Guthrie, M.; Klug, D.; Tse, J. Transition from cage clathrate to filled ice: the structure of methane hydrate III. Phys. Rev. Lett. 2001, 87, 215501. 12. Ikeda, T.; Terakura, K. Structural transformation of methane hydrate from cage clathrate to filled ice. J. Chem. Phys. 2003, 119, 6784-6788. 13. Iitaka, T.; Ebisuzaki, T. Methane hydrate under high pressure. Phys. Rev. B 2003, 68, 172105. 14. Vatamanu, J.; Kusalik, P. G. Unusual crystalline and polycrystalline structures in methane hydrates. J. Am. Chem. Soc. 2006, 128, 15588-15589. 15. Cao, X.; Huang, Y.; Jiang, X.; Su, Y.; Zhao, J. Phase diagram of water–methane by firstprinciples thermodynamics: discovery of MH-IV and MH-V hydrates. Phys. Chem. Chem. Phys. 2017, 19, 15996. 16. Cao, X.; Su, Y.; Liu, Y.; Zhao, J.; Liu, C. Storage Capacity and Vibration Frequencies of Guest Molecules in CH4 and CO2 Hydrates by First-Principles Calculations. J. Phys. Chem. A 2014, 118, 215-222.


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26. Jiang, X.; Wu, X.; Zheng, Z.; Huang, Y.; Zhao, J. Ionic and superionic phases in ammonia dihydrate NH3·2H2O under high pressure. Phys. Rev. B 2017, 95, 144104. 27. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. 28. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758. 29. Lee, K.; Murray, É. D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Higher-accuracy van der Waals density functional. Phys. Rev. B 2010, 82, 081101. 30. Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert, M. I.; Refson, K.; Payne, M. C. First principles methods using CASTEP. Z. Krist.-Cryst. Mater. 2005, 220, 567-570. 31. Salzmann, C. G.; Radaelli, P. G.; Mayer, E.; Finney, J. L. Ice XV: A New Thermodynamically Stable Phase of Ice. Phys. Rev. Lett. 2009, 103, 105701. 32. Sanz, E.; Vega, C.; Abascal, J. L. F.; MacDowell, L. G. Phase Diagram of Water from Computer Simulation. Phys. Rev. Lett. 2004, 92, 255701. 33. Press, W. Structure and Phase Transitions of Solid Heavy Methane (CD4). J. Chem. Phys.1972, 56, 2597-2609. 34. Neumann, M. A.; Press, W.; Nöldeke, C.; Asmussen, B.; Prager, M.; Ibberson, R. M. The crystal structure of methane phase III. J. Chem. Phys. 2003, 119, 1586-1589. 35. Togo, A.; Oba, F.; Tanaka, I. First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures. Phys. Rev. B 2008, 78, 134106. 36. Liang, S; Kusalik, P. G. Communication: Structural interconversions between principal clathrate hydrate structures. J. Chem. Phys. 2015, 143, 011102.


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37. Jiménez-Ángeles, F.; Firoozabadi, A. Nucleation of methane hydrates at moderate subcooling by molecular dynamics simulations. J. Phys. Chem. C 2014, 118, 11310-11318. 38. Jiménez-Ángeles, F.; Firoozabadi, A. Enhanced hydrate nucleation near the limit of stability. J. Phys. Chem. C 2015, 119, 8798-8804.


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Table 1. Water/methane molecular ratio (R), number of water (Zw) and methane molecules (Zm) per unit cell, equilibrium volume of unit cell Vcell, average distance between oxygen atoms in adjacent water molecules dO-O, shortest distance between oxygen atom and carbon atom dC-O, shortest distance between carbon atoms in adjacent methane molecules dC-C, mass density ρ, and bulk modulus B for various methane hydrate phases. The values in parentheses are experimental data.

Phase

R

Zw

Zm

Vcell (Å3)

dO-O (Å)

dC-O (Å)

dC-C (Å)

ρ (g/cm–3)

B (GPa)

MH-III

2

8

4

341

2.885

3.285

3.985

1.016

17.29

296

2.775

3.185

3.905

1.169

17.29

2

8

4 (300a)

(2.807a)

(3.297a)

(3.852a)

(1.152a)

(15.25a)

MH-III (30 kbar)

a

MH-VI

3

12

4

457

2.795

3.495

4.065

1.017

15.32

MH-IV

4

16

4

594

2.775

3.675

3.695

0.986

17.76

MH-II

4.25

136

32

5095 (5051d)

2.775

3.385

3.185

0.966

12.59

MH-H

4.25

34

8

1295 (1242c)

2.765

3.535

3.295

0.950

15.92 (9.8b)

MH-K

5.71

80

14

2914

2.755

3.565

5.885

0.949

15.33

MH-I

5.75

46

8

1666

2.755

3.715

5.895

0.954

7.07 (7.4b)

Experiment by Loveday et al. at room temperature1,2. bExperiment by Hirai et al. at room

temperature3.

c, d

X-ray diffraction experiment by Chou et al. at pressure of 6 kbar and 2.5 kbar,

respectively4.


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Figure 1. Relative enthalpy of formation per molecule with respect to solid ice and solid methane phases at selected pressures (0, 5, 10, 15, 20 kbar) for MH-I with R = 5.75, MH-K with R = 5.71, MH-II with R = 4.25, MH-H with R = 4.25, MH-IV with R = 4, MH-VI with R = 3, and MH-III with R = 2. R denotes the water/methane molecular ratio.


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Figure 2. Configurations of MH-VI phase. (a) 4262 water bowl encapsulated with a methane molecule. (b), (c) Views of 2 × 1 × 2 repeated unit cells in different directions. Red and green balls represent oxygen atom of water molecule and carbon atom of methane molecule, respectively. Specially, one water bowl is marked in blue color in Figure (c). Hydrogen atoms are not depicted for simplicity.


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Figure 3. Structural properties versus pressure for MH-VI phase with respect to MH-III. (a)-(d) are mass density, average distance of oxygen atoms in adjacent water molecules (dO-O), shortest distance between carbon atoms and oxygen atoms (dC-O), and shortest distance of carbon atoms in neighboring methane molecules (dC-C) as a function of pressure, respectively.


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Figure 4. (a) and (b) are Raman spectra of MH-VI and MH-III phases at 10 kbar from DFT calculation with vdW-DF2 functional.


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TOC Graphic


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Phase Diagram of Methane Hydrates and ... - ACS Publications

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