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Molecular Mechanisms of Gas Diffusion in CO Hydrates Shuai Liang, De-Qing Liang, Nengyou Wu, Li-Zhi Yi, and Gaowei Hu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03111 • Publication Date (Web): 05 Jul 2016 Downloaded from http://pubs.acs.org on July 6, 2016

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The Journal of Physical Chemistry

Molecular Mechanisms of Gas Diffusion in CO2 Hydrates Shuai Liang,1* Deqing Liang,1 Nengyou Wu,2,3 Lizhi Yi,1 and Gaowei Hu2,3 1

Key Laboratory of Gas Hydrate, Guangzhou Institute of Energy Conversion, Chinese Academy of

Sciences, Guangdong Key Laboratory of New and Renewable Energy Research and Development, Guangzhou, China 2

Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and

Technology, Qingdao, China 3

The Key Laboratory of Gas Hydrate, Ministry of Land and Resources, Qingdao Institute of Marine

Geology, Qingdao, China

*Corresponding Author E-mail: [email protected]

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Abstract: The gas diffusion is considered a rate-limiting step in the formation of gas hydrates, yet its molecular mechanisms remain unclear. In this work, we present the molecular mechanisms of the CO2 cage-to-cage transport in gas hydrates, as directly observed from molecular dynamics simulations performed at elevated temperatures. We found that at least one water vacancy is required for the CO2 molecules to pass through 5-membered water rings, while only the distortion of the local ring structure is required for the CO2 molecules to pass through the 6-membered water rings. We used the transition state theory to estimate the relevant kinetic parameters associated with the CO2 diffusion in gas hydrates. The calculated free energy of activation is about 44 ± 6 kJ/mol, and the diffusion coefficient is in the range of 1.0 × 10-16 ∼ 2.0 × 10-14 m2/s, for the CO2 diffusion at 270 K, in close agreement with previous experiments. This work suggests that the presence of empty cages is crucial for the CO2 cage-to-cage transport in gas hydrates.


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1. Introduction Gas clathrate hydrates are crystalline compounds within which water molecules form hydrogen-bonded cage structures that can be stabilized by small guest molecules such as CH4, H2S, CO2, etc.1 Gas hydrates have gained wide attention as a potential major energy source, with the amount of energy deposited in natural gas hydrates has been estimated to be equivalent to more than twice that in all other fossil fuels.1 Gas hydrates can form under relatively moderate temperature and pressure conditions, and may form in oil and gas pipelines, causing flow blockage and flow assurance failure, which is a current major concern in oil and gas industry.2 Gas hydrates have also gained wide interests due to their possible critical roles in climate change,3 CO2 capture,4-6 energy storage,7 etc. When a gas phase is exposed to a water/ice phase, a thin film of gas hydrates can form rapidly along the water/gas interface where the concentration of both water and gas species are relatively high. Once formed, the hydrate film provides an effective mass transfer barrier between the water and gas phases, which significantly slows down further gas hydrate growth. However, rapid and continuous gas hydrate formation techniques are required for a number of practical applications of gas hydrates including CO2 sequestration, gas separation, energy storage and transportations.8-11 A better understanding of the mass transfer mechanisms within gas hydrate phases is clearly in need to improve the hydrate formation techniques. In addition, in recent years there are growing interests in replacing CH4 in natural gas hydrate deposits with CO2 molecules.12-16 Such replacement processes are typically rapid at the early stage and subsequently becomes slow,17 which cannot satisfy the current economic requirements of commercial production of gas hydrates. Improving the replacing kinetics and methane replacement efficiency also requires a deep understanding of the mass transfer mechanisms in gas hydrates. Water molecules have been demonstrated to be relatively more mobile in gas hydrate phases.18,19 Several possible mechanisms for water transport within gas hydrate phases have been proposed, 3 ACS Paragon Plus Environment


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including interstitial water,20 lattice vacancy,21 and Bjerrum defect19 assisted diffusion mechanisms. Our molecular dynamics (MD) simulation study has suggested that interstitial diffusion could be a dominate mechanism for water diffusion in gas hydrates.22 The observed transport pathways can allow interstitial water molecules diffusing rather easily through hydrate crystals. Gas hopping through hydrate cages would involve substantially larger free energy barriers, perhaps with the exception of small molecules like H2,23,24 and the gas diffusion is considered to be a rate-limiting process for gas hydrate formation under most experimental conditions.11,15,23-27 Previous molecular simulation studies have suggested that gas hopping between hydrate cages are assisted by the presence of water vacancies in cage walls (“hole-in-the-cage” mechanism).20,21,28 The free energy barrier for gas hopping from a full cage to an empty cage was shown to be reduced substantially by introducing a water vacancy in the cage wall.20,21 The concentration of water vacancy in CO2 hydrates has been estimated to be about 1.0×10-4 at 273 K using Monte Carlo simulations with a thermodynamic integration method.21 The work by Buch et al.20 suggested that the gas diffusion can be assisted by thermally activated water interstitial-vacancy pair defects. However, neither permanent water vacancies nor the thermally activated water interstitial-vacancy pair defects at the host lattice of gas hydrate crystals have been observed directly in previous MD simulation studies of the nucleation and crystal growth of gas hydrates (to the best of our knowledge),29-36 perhaps due to their rare event nature. In a combined NMR and MD simulation study of binary hydrates with THF + CO2 and isobutane + CO2, Moudrakovski et al.41 have observed the formation of Bjerrum defects in the water lattices of sII hydrates and the presence of these defects in water lattices can help CO2 guests to rotate more freely inside 512 cages. They have proposed that the presence of hydrogen bonding guests may enhance the migration of gas molecules through hydrate phases. Recently a direct hopping mechanism for gas diffusion in gas hydrates was proposed based on DFT calculations,37 where the cage-to-cage hopping of CO2 and CH4 molecules through the 5- and 6-membered water rings involves only distortion of the local water rings and requires no other 4 ACS Paragon Plus Environment

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structural defects within the hydrate cage frameworks. An earlier calculation using a van der Waals

density functional formalism reported essentially the same behavior for CO2 and CH4 molecules to pass 6-membered rings, but found that forcing the gas molecules to pass the 5-membered water rings destroys the hydrate cage structure.38 In both calculations37,38 the cage structures are partially constrained, therefore these calculations may not be able to fully reveal the important factors related to the gas cage-to-cage hopping in gas hydrates. In a recent MD simulation study of the homogeneous melting processes of gas hydrates,39 we were able to directly observe gas cage-to-cage hopping at an elevated temperature, where the formation of water interstitial-vacancy pair defects apparently plays a key role. We observed that the gas cage-to-cage hopping is coupled with gas aggregation and homogeneous melting of the system since the simulations were performed on a fully occupied model hydrates. In this work, we report the molecular mechanisms of gas transport within CO2 hydrates, as directly observed in MD simulations that were performed on a CO2 hydrate system with gas occupancies of 50% for small (512) cages and about 96% for large (51262) cages. The data were collected from the trajectories at elevated temperatures of 310, 315, and 320 K. We found that at least one water vacancy need to be formed for the gas molecules to pass through the 5-membered water rings, consistent with previously proposed “hole-in-the-cage” mechanism.20,21,28 For the gas molecules to pass through the 6-member rings, we found that the local ring structures were significantly distorted but no evident water vacancies can be observed. The molecular O–C–O axis of CO2 molecules are always perpendicular to the ring plane when passing through the rings. The free energy of activation and the diffusion coefficient for the gas hopping processes are estimated to be about 44 ± 6 kJ/mol and in the range of 1.0 × 10-16 ∼ 2.0 × 10-14 m2/s, in close agreement with previous experiments.11,40,41



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2. Methods MD simulations are performed on a system of 4×4×4 unit cells of a structure I CO2 hydrate. The starting coordinates of the oxygen atoms of water molecules in the initial crystal structure were taken from experimental data.42 The hydrogen-bond networks were generated according to Bernal-Fowler ice rules43 and subjected to a minimum-dipole-moment constraint.44 The CO2 molecules were randomly removed from a fully occupied hydrate, leaving a gas occupancy of 50% for small cages and about 96% for large cages. Such cage occupancies are typical in the processes of hydrate formation from ice particles.25 The final system is consisted of 2944 water and 432 CO2 molecules (with 64 CO2 molecules in small cages, and 368 CO2 molecules in large cages). An equilibrium simulation of 10 ns at 250 K was performed, following by production runs at temperatures of 300, 310, 320 K and 330K. Ten independent simulations are performed at each temperature, with different initial molecular velocities. We observed gas hoppings at 310 and 320 K, but not at 300 K in the ten independent trajectories performed. The system melted rather quickly at 330 K, thus the results generated at this temperature were not considered in this report. Ten additional simulations are performed at 315K to help estimate the relevant kinetic parameters of the gas diffusion processes. The observed gas transport pathways are consistent across the three temperatures (310, 315, and 320 K) studied, although the crystal structure of the gas hydrates are clearly more distorted at the high temperatures. All the simulations in this work were performed at a pressure of 100 MPa. In this work, water molecules are modeled by TIP4P/200545 and CO2 molecules are modeled by EPM246 potential. The velocity Verlet algorithm was used for integrating the equations of motion with a timestep of 2 fs. The simulations were performed under a constant temperature and pressure ensemble, where a Nosé-Hoover thermostat and barostat were applied to maintain the desired temperature and pressure conditions.47 The relaxation times for the thermostat and the barostat were 1.0 ps and 5.0 ps, respectively. A real space cutoff of 9 Å was utilized and the electrostatic interactions were evaluated 6 ACS Paragon Plus Environment

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with the smooth particle mesh Ewald method.48 All the MD simulations were performed using DL_POLY 4.07 software. We used transition state theory (TST)49, which assumes that the activated transition state complexes are in quasi-equilibrium with the reactants, to estimate the hopping rates of the CO2 molecules at lower temperatures. In TST, the gas hopping rates can be calculated using the equation,

k=

 ∆G ≠  k BT exp  −  h  k BT 

Field

(1)

where k is the gas hopping rate, T is the temperature, kB is Boltzmann’s constant, h is Planck’s constant, and ∆G≠ is the Gibbs free energy of activation. It can be rewritten as,

k=

 ∆H ≠ − T ∆S ≠  k BT exp  −  h k BT  

Field

(2)

where ∆H≠ is the enthalpy of activation, and ∆S≠ is the entropy of activation. The TST has been successfully applied to calculate kinetic parameters of molecular diffusion in solids.50 As we will show below, the TST can give rather accurate estimation of the relevant kinetic parameters of gas diffusion processes in CO2 hydrates.

3. Results and discussion Figure 1 shows an example of CO2 transport through a 5-membered water ring on the hydrate host lattice. The CO2 molecule originally resides within a 51262 cage, which has an empty 512 neighboring cage (Figure 1a). The two cages share a 5-member ring, which would yield a very high free energy barrier for the gas molecules to pass through if the ring structure contains no defects.20,21 In this trajectory, we observe a water molecule from the shared 5-member ring moves off from its original host 7 ACS Paragon Plus Environment


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lattice, forming a pair of water vacancy-interstitial defects (Figure 1b and d). Two hydrogen bonds from the shared 5-member ring were clearly broken with the formation of the interstitial-vacancy defects. Note the water molecule shown on the right of Figure 1(d) is also about 2 Å off the ring plane. Therefore it should be considered an interstitial water here. We can see that with the broken of the ring structure, the CO2 molecule can now transport from its host 51262 cage to the neighboring 512 cage through the relatively open ring structure. To minimize the hindrance from the surround water molecules, the CO2 molecule transport with the molecular O–C–O axis perpendicular to the ring plane, as can be seen clearly in Figure 1(b) and (d). After the CO2 molecule hopped to the neighboring 512 cage, the interstitial-vacancy defect was able to anneal and both cages quickly reformed their original crystalline structure (Figure 1c). The transport process shown in Figure 1 can be envisaged as the CO2 molecule hopped through the center of the shared 5-member ring, Figure 2 presents an example of CO2 passed roughly through an edge of the shared 5-member ring. The CO2 molecule was originally resides in a 51262 cage, which is connected to an empty 51262 cage by a 5-member ring (Figure 2a). At some point within this trajectory, two water molecules from one edge of the original shared 5-member ring left their host lattices (Figure 2d and e). We can see that one water molecule was completely off its original lattice position and the other water molecule was also significantly deviated from its original lattice position. The combination of these defects generated a very large “hole” (a 9-member ring) in the host lattice, which effectively provided a pathway for the CO2 molecule to hop between the two cages. We see the CO2 molecule passed roughly through the edge of the original shared 5-member ring (Figure 2e) and transported from its host cage to the neighboring cage (Figure 2b and c). The edge which the CO2 molecule passed through was originally shared by the 5-member ring that connected the two 51262 cages and one of its neighboring 5-member rings, in another trajectory we also observed that the CO2 molecules passed through an edge that was shared by a 5-member ring and its neighboring 6-member ring (see SI). In both cases, the CO2 molecules passed with their molecular O–C–O axis perpendicular to the ring 8 ACS Paragon Plus Environment

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planes to minimize the possible hindrance from the surround water molecules, even though the rings seem sufficiently large in comparison with the size of the CO2 molecules. We note a mechanism that a double vacancy may be required for CO2 molecules to hop through a 5-member ring has been recently proposed by Ripmeester and coworkers,41 based on their observations from NMR experiments. The hopping pathway shown in Figure 2, although captured at elevated temperatures, are consistent with the experimental observation. The two possible pathways for gas hoppings through 5-member rings observed here are consistent with previously proposed “hole-in-the-cage” mechanism.20,21,28 Here we observe that at least one water vacancy should form in order to allow the gas molecule to pass through the 5-membered water rings. In a previous Monte Carlo simulation study, the formation of a water vacancy has also been observed when using a umbrella sampling technique to enforce gas passing through intact hydrate cages.21 These observations suggest that it is critical to form water vacancies in order to allow gas molecules to pass through a 5-membered water ring in gas hydrates. For gas molecules to pass 6-membered water rings, we observe a somewhat different mechanism. Figure 3 shows an example that a CO2 molecule transported from one 51262 cage to a neighboring 51262 cage through the shared 6-member ring. At the point of the CO2 passing through the 6-member ring, we observed three hydrogen bonds of the ring broke and two water molecules were significantly deviated from their original lattice positions (Figure 3, b and d). We did not observe clear evidence of the formation of water vacancies here. Similar gas transport processes involving the breaking of hydrogen bonds in 6-member rings and water molecules deviate from their crystalline lattices were also observed in previous DFT calculations when local flexibility were introduced for water molecules near the central shared rings.37,38 Here the CO2 molecule passed through the 6-member ring also with the molecular O-C-O axis perpendicular to the ring plane (Figure 2, b and d). Hence the linear shape of CO2 molecule helped to reduce the possible energy barrier for passing through the water rings. In future studies, it would be interesting to see if a methane molecule can hop through a 6-member ring without the 9 ACS Paragon Plus Environment


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assistance of the vacancy defects. As discussed in a previous paper,41 the rotational defects in water lattices can help CO2 molecules rotate more freely inside hydrate cages. Therefore the rotational defects of water molecules may be able to help the CO2 molecules rotate to their favorite orientations to transport through the water rings and hence enhance the migration of gas molecules through hydrate phases. After the CO2 molecule transported to the neighboring cage, we can see that the two 51262 cages involved were able to anneal back to their original crystalline structures (Figure 3c). While various pathways have been observed, an empty neighboring cage appears to be crucial for the gas molecule to hop between hydrate cages. From all the MD trajectories performed here, we found no gas hopping from its host cage to an occupied cage, although the vacancy defects were also observed to form in rings that are shared by occupied cages. Figure 4 shows an example of the formation of a vacancy defect that is surrounded by a 512 cage and two other 51262 cages. Each of the three cages contained a CO2 molecule as their guest. At around 7404 ps of this trajectory, a water vacancy formed in the host lattice of the 512 cage (Figure 4b). Together with the severe distortions of surrounding ring structures, the vacancy defect opened two possible paths for the CO2 molecule in the 512 cage to hop to other cages, as evident in Figure 4(b) and (d). We see the CO2 molecule moved to the boundary of the 512 cage a few times but was unable to hop into other occupied cages. About 100 ps later, the local structures annealed back to regular hydrate cage structures (Figure 4c). These observations suggest that the neighboring empty cages are crucial for the gas transport processes, consistent with our previous observation that gas hopping from an occupied cage to another occupied cage can initiate the catastrophic homogenous melting of gas hydrates at proper temperature and pressure conditions.39 We next estimate the enthalpy of activation (∆H≠), the entropy of activation (∆S≠), the free energy of activation (∆G≠) associated with the cage-to-cage hopping of the CO2 molecules using the transition state theory.49 Eq. (2) can be rewritten in a linear form, k ∆H ≠ 1 k B ∆S ≠ ln = − + ln + T kB T h kB

Field

(3) 10

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where ln is the natural logarithm. The kinetic parameters ∆H≠ and ∆S≠ can now be estimated using Eq. (3) once the hopping rates (k) at different temperatures are determined. Here we determine the hopping rates by counting the gas molecules that moved more than 5 Å in the 10 ns simulations. Within the 10 trajectories performed at each temperature, we detected 5, 16, and 32 hopping events at 310, 315, and 320 K, respectively, which corresponds to a hopping rate of 5 × 107, 1.6 × 108 and 3.2 × 108 hops/s at 310, 315 and 320 K. We then use a weighted linear regression method to solve Eq.(3) to find these kinetic parameters (see SI for details). Figure 5 presented the fitted results. The enthalpy of activation (∆H≠) and the entropy of activation (∆S≠) were estimated to be about 138 ± 3 kJ/mol and 348 ± 10 J/(K⋅mol), respectively, where the uncertainties represent the standard deviation of the fitted values. The free energy of activation (∆G≠) for the cage-to-cage hopping of CO2 molecules can then be calculated with ∆G ≠ = ∆H ≠ − T ∆S ≠ , which gives about 44 ± 6 kJ/mol at 270K, where the uncertain is from the combination of the standard deviations of the ∆H≠ and ∆S≠. The calculated ∆G≠ agrees very well with previous estimations from experimental observations. For example, Takeya et al.40 have reported a value of 39 kJ/mol based on their observations of CO2 hydrate growth by using high-energy X-rays; Falenty et al.11 have deduced a value of 46 kJ/mol from their neutron diffraction and gas consumption experiments for the temperature range of 225 ~ 272 K. Henning et al.51 have reported a value of 27 kJ/mol, but from a less comprehensive experimental data in comparison with the data from the works by Takeya et al.40 and Falenty et al.11 These calculated kinetic parameters and relevant experimental results are summarized in Table 1. Note that these calculations assume that the enthalpy of activation and the entropy of activation of the gas hopping are temperature-independent. This assumption should be reasonable considering that these quantities are mainly determined by the hydrate structures at the ground- and excited- states of the gas hopping process, which are not expected to be sensitive to the temperatures within the temperature range studied here. In addition, the values reported here are only very rough estimates of these kinetic parameters, as our calculations are from the results of a limited number and length of trajectories from force-field based MD simulations. More extensive 11 ACS Paragon Plus Environment


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simulations, perhaps with enhanced sampling methods and more accurate simulation methods, are clearly needed to accurately estimate these kinetic parameters associated with the gas hopping processes. With the free energy of activation determined, we can calculate the CO2 hopping rate using Eq. (1), which gives a range of 1.2 × 103 ∼ 2.5 × 105 hops/s at 270 K. The CO2 diffusion coefficient can then be estimated by a random walk model, D = τ 2 / 6t , where τ and t is the averaged distance (7 Å, see SI for the radial distribution function of CO2 molecules in sI hydrates) and time interval for each hop. This gives a diffusion coefficient in the range of 1.0 × 10-16 ∼ 2.0 × 10-14 m2/s at 270 K, which agrees well with previous experimental values, 7.4 × 10-16 m2/s at 263 K,40 and 5.1 × 10-15 m2/s (1.83 × 10-11 m2/h) at 272 K.11 A recent work by Moudrakovski et al.41 suggested a diffusion coefficient less than 1.1 × 10-15 m2/s at 273 K, which was estimated by extrapolating the gas hopping rate measured in low temperature NMR experiments to 273 K. These values are also presented in Table 1. The good agreement between the calculated values in the current work and the previous experimental values also indicates that the gas diffusion processes in the gas hydrate solids can be well described by the TST over a proper range of temperatures.

4. Conclusion In this work, we present the molecular mechanisms of the gas cage-to-cage hopping in CO2 hydrates, as observed from MD simulations performed at elevated temperatures. We found that at least one water vacancy is required for the CO2 molecules to pass through 5-member rings, while only the distortion of the local ring structure but no water vacancies or other structural defects are required for the CO2 molecules to pass through the 6-member rings. The molecular O–C–O axis of CO2 molecules


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are always perpendicular to the ring plane when passing through the rings, to minimize the possible hindrance from the surrounding water molecules. We used the transition state theory to estimate the relevant kinetic parameters associated with the CO2 hopping processes within the gas hydrate phases. The calculated the free energy of activation is about 44 ± 6 kJ/mol, and the diffusion coefficient is in the range of 1.0 × 10-16 ∼ 2.0 × 10-14 m2/s at 270 K, in close agreement with previous experiments. This work suggests that the presence of the neighboring empty cages is crucial for the gas cage-to-cage hopping in gas hydrates. This work investigated the gas diffusion behavior within gas hydrate phases at elevated temperatures, and found transition state theory can be used to rather accurately predict the diffusion kinetics at around 270 K. The current observation of the diffusion mechanisms apparently did not cover the low temperature behaviors, as demonstrated by Falenty et al.11 that below about 225 K, the CO2 molecules are likely to transport through a mechanism different from that at high temperatures. Future work aiming at investigating the gas hopping mechanisms at low temperatures is clearly warranted, with possible acceleration using the hyperdynamics methods such as the nudged elastic band method52 and the temperature accelerated method53. This work suggests that the linear molecular shape of CO2 molecules helps reducing the barrier to pass through 5- and 6-membered water rings. A comparison with the diffusion behavior of methane molecules within gas hydrate phases is needed for a fully understanding of the molecular mechanism of the CO2-CH4 replacement in gas hydrates.



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Supporting information available: Another example of a CO2 molecule transport from a 51262 cage to a neighboring 51262 cage, and the details of the calculation of relevant kinetic parameters of the CO2 diffusion at lower temperatures. This material is available free of charge via the Internet at http://pubs.acs.org.

Notes The authors declare no competing financial interests.

Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant no. 41473063), CAS Program (KGZD-EW-301), and the National Natural Science Foundation of China (Grant no. 41474119).


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References (1) Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008. (2) Gao, S. Q. Investigation of Interactions between Gas Hydrates and Several Other Flow Assurance Elements. Energy Fuels 2008, 22, 3150-3153. (3) Bohannon, J. Energy - Weighing the Climate Risks of an Untapped Fossil Fuel. Science 2008, 319, 17531753. (4) Lee, H.; Seo, Y.; Seo, Y. T.; Moudrakovski, I. L.; Ripmeester, J. A. Recovering Methane from Solid Methane Hydrate with Carbon Dioxide. Angew. Chem.-Int. Edit. 2003, 42, 5048-5051. (5) Park, Y.; Kim, D. Y.; Lee, J. W.; Huh, D. G.; Park, K. P.; Lee, J.; Lee, H. Sequestering Carbon Dioxide into Complex Structures of Naturally Occurring Gas Hydrates. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 1269012694. (6) Ota, M.; Morohashi, K.; Abe, Y.; Watanabe, M.; Smith, R. L.; Inomata, H. Replacement of CH4 in the Hydrate by Use of Liquid CO2. Energy Conv. Manag. 2005, 46, 1680-1691. (7) Lee, H.; Lee, J. W.; Kim, D. Y.; Park, J.; Seo, Y. T.; Zeng, H.; Moudrakovski, I. L.; Ratcliffe, C. I.; Ripmeester, J. A. Tuning Clathrate Hydrates for Hydrogen Storage. Nature 2005, 434, 743-746. (8) Brown, T. D.; Taylor, C. E.; Bernardo, M. P. Rapid Gas Hydrate Formation Processes: Will They Work? Energies 2010, 3, 1154-1175. (9) Uras-Aytemiz, N.; Devlin, J. P. Communication: Fourier-Transform Infrared Probing of Remarkable Quantities of Gas Trapped in Cold Homogeneously Nucleated Nanodroplets. J. Chem. Phys. 2013, 139, 021107. (10) Devlin, J. P.; Monreal, I. A. Instant Conversion of Air to a Clathrate Hydrate: CO2 Hydrates Directly from Moist Air and Moist CO2(G). J. Phys. Chem. A 2010, 114, 13129-13133. (11) Falenty, A.; Genov, G.; Hansen, T. C.; Kuhs, W. F.; Salamatin, A. N. Kinetics of CO2 Hydrate Formation from Water Frost at Low Temperatures: Experimental Results and Theoretical Model. J. Phys. Chem. C 2011, 115, 4022-4032. (12) Goel, N. In Situ Methane Hydrate Dissociation with Carbon Dioxide Sequestration: Current Knowledge and Issues. J. Pet. Sci. Eng. 2006, 51, 169-184.



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(25) Salamatin, A. N.; Falenty, A.; Hansen, T. C.; Kuhs, W. F. Guest Migration Revealed in CO2 Clathrate Hydrates. Energy & Fuels 2015, 29, 5681-5691. (26) Moudrakovski, I. L.; McLaurin, G. E.; Ratcliffe, C. I.; Ripmeester, J. A. Methane and Carbon Dioxide Hydrate Formation in Water Droplets: Spatially Resolved Measurements from Magnetic Resonance Microimaging. J. Phys. Chem. B 2004, 108, 17591-17595. (27) Narayanan, T. M.; Imasato, K.; Takeya, S.; Alavi, S.; Ohmura, R. Structure and Guest Dynamics in Binary Clathrate Hydrates of Tetrahydropyran with Carbon Dioxide/Methane. J. Phys. Chem. C 2015, 119, 2573825746. (28) Peters, B.; Zimmermann, N. E. R.; Beckham, G. T.; Tester, J. W.; Trout, B. L. Path Sampling Calculation of Methane Diffusivity in Natural Gas Hydrates from a Water-Vacancy Assisted Mechanism. J. Am. Chem. Soc. 2008, 130, 17342-17350. (29) English, N. J.; MacElroy, J. M. D. Perspectives on Molecular Simulation of Clathrate Hydrates: Progress, Prospects and Challenges. Chem. Eng. Sci. 2015, 121, 133-156. (30) Liang, S.; Kusalik, P. G. Exploring Nucleation of H2s Hydrates. Chem. Sci. 2011, 2, 1286-1292. (31) Liang, S.; Kusalik, P. G. Nucleation of Gas Hydrates within Constant Energy Systems. J. Phys. Chem. B 2013, 117, 1403-1410. (32) Liang, S.; Kusalik, P. G. Structural Interconversions between Common Gas Hydrate Structures. J. Chem. Phys. 2015. (33) Tung, Y. T.; Chen, L. J.; Chen, Y. P.; Lin, S. T. Growth of Structure I Carbon Dioxide Hydrate from Molecular Dynamics Simulations. J. Phys. Chem. C 2011, 115, 7504-7515. (34) Míguez, J. M.; Conde, M. M.; Torré, J. P.; Blas, F. J.; Piñeiro, M. M.; Vega, C. Molecular Dynamics Simulation of Co2 Hydrates: Prediction of Three Phase Coexistence Line. J. Chem. Phys. 2015, 142, 124505. (35) Bai, D.; Chen, G.; Zhang, X.; Wang, W. Nucleation of the Co2 Hydrate from Three-Phase Contact Lines. Langmuir 2012, 28, 7730-7736. (36) Yi, L.; Liang, D.; Zhou, X.; Li, D.; Wang, J. Molecular Dynamics Simulations of Carbon Dioxide Hydrate Growth in Electrolyte Solutions of Nacl and Mgcl2. Mol. Phys. 2014, 112, 3127-3137. (37) Vidal-Vidal, A.; Perez-Rodriguez, M.; Pineiro, M. M. Direct Transition Mechanism for Molecular Diffusion in Gas Hydrates. RSC Adv. 2016, 6, 1966-1972. ACS Paragon Plus Environment

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FIGURES

Figure 1. (a-c) Molecular configurations showing the mechanism of a CO2 molecule transport from a 51262 cage to a neighboring 512 cage by passing through the shared 5-membered water ring, as observed from a MD trajectory at 310 K. (d) The rotated ring structure at the point of the CO2 passing through, showing the formation of a water vacancy-interstitial pair. The time indexes for each configuration are given in the legends. The hydrogen bonded network is represented by green sticks connecting water molecules that are within 3.5 Å of each other. The water molecules in (d) are represented by a red sphere (oxygen) connected to two white spheres (hydrogen). The CO2 molecules are represented by a light-blue sphere (carbon) connected to two blue spheres (oxygen). The water molecules are omitted in (a-c) for clarity.


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Figure 2. (a-c) Molecular configurations showing the mechanism of a CO2 molecule transport from a 51262 cage to a neighboring 51262 cage by passing through the shared 5-membered water ring, as observed from a MD trajectory at 315 K. (d-e) The rotated local structure at the point of the CO2 passing through, showing that one water molecule was completely off its original lattice position and the other water molecule (circled) significantly deviated from its original lattice position. The green dash lines in (e) represent the original cage structure, where one water molecule was circled to help compare its original lattice position (dashed circle) and the current position (solid circle). The time indexes for each configuration are given in the legends. The molecular configurations are represented and colored as in Figure 1.



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Figure 3. (a-c) Molecular configurations showing the mechanism of CO2 molecule transport from a 51262 cage to a neighboring 51262 cage by passing through the shared 6-membered water ring, as observed from a MD trajectory at 310 K. (d) The rotated ring structure at the point of the CO2 passing through, showing significant distortion of the ring structure. The time indexes for each configuration are given in the legends. The molecular configurations are represented and colored as in Figure 1.


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Figure 4. (a-c) Molecular configurations showing that with formation of a water vacancy defect, the CO2 molecule inside the 512 cage (bottom right) attempted but failed to migrate to other neighboring cages that are occupied by other gas molecules, as observed from a MD trajectory at 310 K. (d) The enlarged local structure shown in (b), showing that the CO2 molecule moved to the boundary of the 512 and 51262 cages on the left. The time indexes for each configuration are given in the legends. The molecular configurations are represented and colored as in Figure 1.



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Figure 5. The weighted linear regression analysis results using transition state theory Eq. (3). The solid square in black are the observed gas cage-to-cage hopping rates in CO2 hydrates at 310, 315, and 320 K, respectively. The solid line in black is from the weighted linear regression analysis. With the determined slope and intercept for the linear equation Eq. (3), we can extrapolate the observed gas hopping rate to low temperatures (dashed line and the open square in red), see main text.


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Table 1. The calculated diffusion coefficient (D) and free energy barrier (∆G≠) of the gas cage-to-cage hopping in CO2 hydrates, along with relevant experimental values. Experiments This work (270 K) D (m2/s)

∆G ≠ (kJ/mol)

ref.11 (272 K)

ref.40 (263 K)

ref.41 (273K)

1.0 × 10-16 ∼ 2.0 × 10-14

5.1 × 10-15

7.4 × 10-16

< 1.1 × 10-15

44 ± 6

46

39

-



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Table of Contents

Molecular trajectory of a CO2 cage-to-cage hopping in gas hydrates.


Molecular Mechanisms of Gas Diffusion in CO2 Hydrates - The

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