Molecular Insights into the Homogeneous Melting of Methane

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Molecular Insights into the Homogeneous Melting of Methane Hydrates Shuai Liang, Li-Zhi Yi, and De-Qing Liang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511362s • Publication Date (Web): 19 Nov 2014 Downloaded from http://pubs.acs.org on November 25, 2014

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The Journal of Physical Chemistry

Molecular Insights into the Homogeneous Melting of Methane Hydrates Shuai Liang*, Lizhi Yi and Deqing Liang Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou, China 510640

*Corresponding author. Email: [email protected]

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Abstract: While the melting of gas hydrates tends to be heterogeneous in most cases, in principle this process can also be homogenous when surface melting is properly inhibited. Here we investigate the molecular mechanisms of the homogeneous melting of superheated methane hydrates by means of molecular dynamics simulations. The homogeneous melting processes are found to be stochastic with varied induction times. We observe the formation of structural defects within the hydrogen-bonded water lattices of hydrate crystals during the induction times. The methane molecules are relatively more stable within the gas hydrate phases, which might be responsible for the high stability of the superheated metastable methane hydrates. Although the melting processes involve the collective motion of water and methane molecules, the current work suggests that the migration and aggregation of methane molecules are critical in initiating the homogeneous melting of gas hydrate crystals.


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1. INTRODUCTION Gas hydrates are crystalline compounds in which water molecules form hydrogen-bonded cage structures that are typically stabilized by gas molecules such as methane, ethane, propane, hydrogen sulfide and carbon dioxide.1 Gas hydrates occur abundantly in deepwater ocean sediments near the continents, where methane hydrates are the most common gas hydrates in the world. The amount of energy deposited in gas hydrates has been estimated to be more than twice of that in all other fossil fuels.1 Gas hydrates have gained wide attention as a major energy source for the future. Gas hydrates are also of great interests because of their potential roles in carbon dioxide capture,2 hydrogen storage,3,4 water desalination,5 and the prevention of gas hydrate blockage in oil/gas pipelines.6 The nucleation of supercooled liquids and melting of superheated solids are well-known phenomenon for many materials.7-10 As to gas hydrate systems, the homogenous nucleation processes of supercooled gas solutions have been extensively studied in recent years.11-19 These studies have revealed many interesting thermodynamic and kinetic behaviors, including a two-step nucleation mechanism that intermediates an amorphous solid phase,17,18 of the homogenous formation of gas hydrates. To date, most reported studies of gas hydrate melting have focused on the heterogeneous processes.20-31 When surface melting is properly inhibited, solid melting can occur homogenously through ultrafast heating.32 This process is generally expected to involve the formation and growth of melting nuclei inside the superheated solids, analogous to the homogenous nucleation inside the supercooled liquids.8,33-36 The homogenous melting of superheated ice, on the other hand, have been demonstrated to be a more complicated processes in experimental32 and molecular dynamics (MD) simulation37-39 studies, mainly related to the resilient hydrogen bonds formed between neighboring water molecules. In the case of gas hydrates, the interaction between polar water molecules and relatively non-polar gas molecules may introduce additional complexity. MD simulation studies have shown that gas hydrate


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crystals can endure large superheatings of over 100 K,40,41 in comparison with a superheating limit of about 40 K for an ice system.37 Experimentally the anomalous preservation of metastable methane hydrate at atmospheric pressure and temperatures below the ice melting point has been discovered42-44 and proposed in the storage and transportation of natural gas.45 A superheated hydrate method has also been considered towards the improvement of kinetic hydrate inhibitors.46 The underlying molecular mechanisms of the superheating and homogenous melting of gas hydrates, however, have remained unclear, which are crucial for a fundamental understanding of the unusual behavior of gas hydrate systems and are potentially helpful for the practical applications mentioned above. In this work, we report MD simulations of homogeneous melting of superheated methane hydrates. We present, for the first time, the molecular mechanisms of the homogeneous melting processes. We observe a variety of structural defects within the hydrogen-bonded water lattices of gas hydrate crystals. A number of unusual ring and cage structures have been identified, similar to that observed within the homogenous nucleation simulations of gas hydrates from supercooled gas solutions.16,17,47 Methane molecules appear to be relatively stable during the initial induction period of the homogeneous melting. The current work suggests that the migration and aggregation of methane molecules are critical in initiating the homogeneous melting of gas hydrate crystals.

2. METHODS The homogeneous melting simulations were performed on two systems, one with 3×3×3 unit cells and the other with 4×4×4 unit cells, of fully occupied sI methane hydrates. The former system contains 1242 water and 216 methane molecules, while the latter system contains 2944 water and 512 methane molecules. Water molecules are represented by the TIP4P/2005 potential model48 and methane


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molecules are modeled as a single Lennard-Jones interaction site.49 An equilibrium simulation of 10 ns at 250 K was performed following by a temperature jump to 300 K. Then a temperature jump of 10 K were applied after every 10 ns simulations, until the homogeneous melting were observed. The starting coordinates of the oxygen atoms in the initial crystal structure of sI hydrate was taken from experimental data.50 The hydrogen-bond networks were generated according to BF rules51 and subject to a minimum dipole moment constraint.52 Four independent starting configurations were generated for the 3×3×3 system, and three independent starting configurations were generated for the 4×4×4 system, each with different initial orientations of hydrogen atoms of water molecules. All the seven MD trajectories are performed under NPT ensembles with a pressure of 10 MPa. The interactions between water and methane molecules were calculated as the sums of Coulomb and Lennard-Jones potentials. The cross terms for the Lennard-Jones parameters were determined using Lorentz-Berthelot mixing rules.53 The equations of motion were integrated by velocity Verlet algorithms for translational and rotational motions.54 A timestep of 2 fs was employed in the current study. A spherical cutoff of 11 Å was utilized for the short-ranged interactions, and the electrostatic interactions were evaluated with the smooth particle mesh Ewald method.55 Periodic boundary conditions are applied in all three directions. The molecular configurations presented in this work are averaged over a sampling time of 1 ps.52 In the current work, the F4 structural order parameter for each water molecule was averaged over all neighboring water molecules within 3.5 Å of the central water molecule.56

3. RESULTS AND DISCUSSION We observe the homogenous melting at 380 K within three of the four trajectories for the 3×3×3 system. The hydrate structures in the fourth trajectory were not melted in the 10 ns simulation at 380 K


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but collapsed immediately if heating up to 390 K. For the 4×4×4 system, we observe the homogeneous melting for all three trajectories within 10 ns simulations at 380 K. Figure 1 shows the potential energy changes along the trajectories where homogenous melting were observed. We can see the induction periods for the melting of the 3×3×3 system are about 800, 2200, and 3800 ps, respectively (see Figure 1a), and that for the melting of the 4×4×4 system are about 1200, 1600, and 2000 ps, respectively (see Figure 1b), indicating the stochastic nature of the homogenous melting processes. While the systems show induction times from several hundred picoseconds to several nanoseconds (and over 10 ns for the fourth trajectory of the 3×3×3 system) at this temperature, we find that all the seven configurations collapse immediately if heating up to 390 K. Note the melting temperature of the model hydrate system is about 265±3 K under the present simulation conditions, as estimated previously.40 Therefore the superheating limit for the model sI methane hydrates is around 115 K. This value is consistent with a previous estimation of 115±5 K using a TIP4P/Ice water model by Conde and Vega,40 but about 30 K lower than that estimated using much higher heating rates by Smirnov and Stegailov41 where as demonstrated in the same work, a larger heating rate can increase the observed superheating limit. Since the trajectories shown in Figure 1 show consistent melting behaviors, we will focus our discussion on trajectory III in the following, and present other relevant results in Supporting Information (SI). We observe a variety of structural defects during the initial induction periods. The formation and migration of oriental defects of water molecules have been observed, similar to that identified in ice systems.38,57 The formation of vacancy and interstitial water defects, as discussed previously,58-60 has also been observed in the present study (see SI). The formation of these defects, together with the structural reorganization of neighboring water molecules, can result various defect ring and cage structures. Figure 2 presents some observed defect ring and cage structures. We can see the appearance of 4-, 7-, and 8-member rings that are not native to the sI hydrate structures (a sI crystal is composed of


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5- and 6-member rings only). The formation of cage structures that do not belong to the sI hydrates is also observed. The observed cage structures include some regular and symmetric cages like 4151062, 425862, 425864, as shown in Figure 2(b), and some non-regular cage-like structures as shown in Figure 2(c). Interestingly, these cage structures have also been observed in previous homogenous nucleation processes of gas hydrates from supercooled gas solutions,16,17,47 indicating the fundamental resemblance of these two processes. These defect ring and cage structures can survive several picoseconds to several hundred picoseconds before annealing to regular sI hydrate structures. It is reasonable to assume these structural defects encourage the migration of gas molecules through hydrate cages. In particular, Demurov et al.58 and Buch et al.59 have demonstrated that the vacancy defects in the host lattice can assist guest transport from full to empty cages. Nonetheless, even with the relatively abundant occurrence of the vacancy and interstitial defects at the high temperature of 380 K (see SI), we observe very high stability of methane molecules during the induction periods among all trajectories performed here for the fully occupied hydrate crystals. We employ three order parameters to track the solid-liquid transitions of the system, as presented in Figure 3. These parameters include the potential energy per molecule (Figure 3a), the number of liquid-like water molecules (Figure 3b), and the number of pairs of methane molecules with distances less than 4.5 Å (Figure 3c). Here a water molecule is defined as liquid-like if the F4 value is less than 0.5. The F4 is a four-body order parameter defined as F4 = cos 3φ , where φ is the H-O⋅⋅⋅O-H torsion angle of adjacent water molecules.56 For ideal lattice of gas hydrates with nearly planer rings, F4 should have a value close to 1. Therefore water molecules with F4 < 0.5 should have one or more of their hydrogen bonds broken or severely distorted. We can see the existences of liquid-like water molecules through the entire induction periods (from 0 to about 3800 ps), as shown in Figure 3(b). The number of these liquid-like water molecules ranges from 16 to 92 within the first 3800 ps simulations, with an averaged value of 44 (corresponds to about 3.5%


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of the total water molecules). In other words, we observe considerable amount of defects in water lattices during the induction periods of the melting processes. The methane molecules, on the other hand, show relatively high stability (Figure 3c). The number of methane molecules with distances less than 4.5 Å is zero until very close to the bulk melting of the system. The low mobility of methane molecules is expected to be responsible for the high stability of the superheated metastable methane hydrates. Note the first peak in a radial distribution function of methane molecules within hydrate phases and separated gas phases correspond to distances of about 6.1 and 4.0 Å, respectively, under the present simulation conditions (see SI). Therefore 4.5 Å is a reasonable threshold distance to track the diffusion and migration of methane molecules (which is also confirmed by visual inspections). The first pair of methane molecules within this threshold distance appear at around 3870 ps, following with the sustained rapid melting of the system. The three order parameters shown in Figure 3 consistently show a transition of the system from solid-like to liquid-like. Once started, the entire system rapidly melted in about 200 ps. Figure 4 shows several cropped molecular configurations from stages close to the rapid melting of the system. We can see that at about 3865 ps essentially all methane molecules resides in their original cage structures while some defects in the host water lattice are evident (Figure 4a). At around 3869 ps, these defects effectively opened a 51262 cage and the guest molecule moved to the edge of this cage (Figure 4b-c). The opening structures (both are irregular 10-member rings here) can be envisaged as a combination of several neighboring vacancy defects in the hydrate host lattice, as shown in Figure 4(c), where the two openings of this cage and thereby two possible paths for the methane molecule to migrate to other cages are evident. Further collective motions of the surrounding molecules resulted in migration of this methane molecule to a distorted 512 cage and forming a small cluster with three other methane molecules at about 3901 ps (Figure 4d). With the migration of the methane molecule, it is very difficult


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for the defect cage structures to anneal back to the sI hydrate crystals. In a few tens of picoseconds the system started rapid melting together with the phase separation of gas and water molecules, and the system melted completely in about 200 ps (Figure 4 e-f). We observe consistent melting behavior among all the six trajectories shown in Figure 1 (see SI). Through these trajectories, we found the gas molecules moved to the edge of their original cages a couple times during the induction periods. In both cases, the gas molecules were not able to migrate to other cages and did not initiate the homogeneous melting of the system (see SI). Therefore, these observations suggest that the migration and aggregation of gas molecules are a key step to the homogeneous melting of the superheated metastable gas hydrate crystals. As mentioned above, previous MD studies have shown that the vacancy defects in the host lattice can assist guest transport from full to empty cages,58,59 where the calculated gas migration rate by MD simulation methods agrees well with a recent experimental estimation.61 NMR study has also shown that the transport of gas molecules appears to be an intrinsic process for hydrates containing some polar guest molecules.62 Here with the fully occupied hydrate crystals, we can only observe gas transport in the presence of several neighboring vacancy defects (i.e., a very large “hole” in the host lattice), indicating a higher free energy barrier for gas transport from full to full cages.

4. COCLUSIONS In summary, we have performed MD simulations of the homogeneous melting of superheated methane hydrate crystals. The homogeneous melting processes are found to be stochastic with varied induction times. We observe a variety of lattice defects, including unusual water cages, within the gas hydrate phases during the induction periods. These defect structures have also been observed in previous MD simulation studies of the homogeneous nucleation of supercooled gas solutions, emphasizing the


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fundamental resemblance of these two processes. The migration of the gas molecules through hydrate cages, which is apparently assisted by vacancy defects in the host lattice, appears to be a key step in initiating the homogeneous melting of the fully occupied hydrate crystals. It is clear that further studies are required to elaborate the roles of the observed defect structures might play in the diffusion of gas molecules. The influences of empty cages and hydrogen-bonding guests that can stabilize the vacancy-interstitial pair defects59,63 on the homogeneous melting processes also warrant further investigations. Moreover, the mechanisms observed here are from two relatively small systems (with a total number of 216 and 512 cages, respectively), further studies with much bigger systems are needed to examine possible system-size effects and getting a more detailed understanding of the collective motion of gas and water molecules, and a more quantitative description of the initial melting nuclei. Finally, we remark that gas migration has been expected to play important roles in formation kinetics of gas hydrates,59,61 yet the molecular mechanisms have remained unclear. In this work we are able to directly observe the gas migration through hydrate cages at an elevated temperature, where the formation of vacancy and interstitial water defects apparently play a key role. Although here the migration of gas molecules is coupled with gas aggregation and homogeneous melting for the current fully occupied model hydrates, one may expect the gas migration without initiating the melting processes in real hydrates (by moving to a neighboring empty cage), as demonstrated in a recent study.62 Therefore the current study also provides a possible approach to investigate the molecular mechanisms of gas diffusion within gas hydrate phases.


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Acknowledgements We thank Prof. Peter Kusalik and Dr. Dmitri Rozmanov for sharing their MD code. This work was supported by the 100 talents program of the Chinese Academy of Sciences and the National Natural Science Foundation of China (award no. 41473063). We acknowledge the computational resources provided by National Supercomputing Center in Shenzhen.

Supporting information More extensive simulation results, and the RDF of methane molecules within gas hydrate and separated gas phases. This material is available free of charge via the Internet at http://pubs.acs.org.

Notes The authors declare no competing financial interests.


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FIGURES

Figure 1. The time evolution of the potential energy per molecule of the methane hydrate systems (a) with 3×3×3 unit cells, and (b) with 4×4×4 unit cells, during the homogeneous melting processes. At 0 ps, a temperature jump from 370 K to 380 K was applied (see text). The results of the independent trajectories are labeled as I to VII (see legend), where the fourth trajectory of the 3×3×3 unit cell system were not melted within the 10 ns simulation (see text).


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Figure 2. Typical defect structures observed within the induction times for the homogeneous crystal melting of methane hydrates. (a) shows several unusual ring structures (green lines). (b) shows some regular cages that are not native to sI methane hydrate crystals. (c) shows some non-regular cage-like structures. The neighboring water molecules with distances less than 3.5 Å are connected by solid lines, and the methane molecules are represented as cyan spheres.


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Figure 3. The time evolution of (a) the potential energy per molecule, (b) the number of liquid-like water molecules (see text), nLW, and (c) the number of pair of methane molecules, nC, with distances less than 4.5 Å, during the melting processes in trajectory III shown in Figure 1. The insets show enlarged plots close to the rapid melting.


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Figure 4. Molecular configurations showing the gas migration through hydrate cages that follows by rapid homogeneous melting of the system (the simulation time is indicated in the legend in af) in trajectory III shown in Figure 1. The migration of the methane molecule (circled blue sphere) was observed at around 3869 ps (a-b). An enlarged and rotated view of this molecule and surrounding ring structures are presented in (c). This methane molecule migrated to a 512 cage at about 3901 ps (d), and effectively making a methane cluster with three other surrounding methane molecules (blue spheres). This gas migration process is followed by the rapid melting of the entire system (e-f). Other methane molecules are represented as cyan spheres and water molecules with distances less than 3.5 Å are connected by red lines.


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Molecular Insights into the Homogeneous Melting of Methane

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