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Hydrogen Storage in sH Hydrates: A Monte Carlo Study N. I. Papadimitriou,*,†,‡ I. N. Tsimpanogiannis,†,§ C. J. Peters,| A. Th. Papaioannou,‡ and A. K. Stubos† EnVironmental Research Laboratory, National Center for Scientific Research “Demokritos”, 15310 Agia ParaskeVi, Greece, School of Chemical Engineering, National Technical UniVersity of Athens, Heroon Polytechniou 9, 15780 Zografou, Greece, and Laboratory of Process Equipment, Department of Process and Energy, Faculty of Mechanical, Maritime and Materials Engineering, Delft UniVersity of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands ReceiVed: July 4, 2008; ReVised Manuscript ReceiVed: September 1, 2008
Grand canonical Monte Carlo simulations are performed to evaluate the hydrogen-storage capacity of the recently discovered hydrogen hydrates of the sH type, at 274 K and up to 500 MPa. First, the pure H2 hydrate is investigated in order to determine the upper limit of H2 content in sH hydrates. It is found that the storage capacity of the hypothetical pure H2 hydrate could reach 3.6 wt % at 500 MPa. Depending on pressure, the large cavity of this hydrate can accommodate up to eight H2 molecules, while the small and medium ones are singly occupied even at pressures as high as 500 MPa. Next, the binary H2-methylcyclohexane sH hydrate is examined. In this case, the small and medium cavities are again singly occupied, resulting in a maximum H2 uptake of 1.4 wt %. Finally, the results from simulations on pure H2 and binary hydrates are utilized to investigate the potential of H2 storage in sH hydrates where the promoter molecules occupy the medium instead of the large cavities. 1. Introduction Clathrate hydrates are nonstoichiometric inclusion compounds consisting of a hydrogen-bonded network of water molecules that form cavities (cages) inside which small guest molecules can be encaged.1,2 Hydrates have been under investigation for many years due to their wide variety of applications in engineering and scientific problems. In particular, they are related to flow assurance of natural-gas pipelines3 and have been examined as a possible means of transportation of stranded gas,4 for water desalination,5 for gas separation,6 for future energy production from on-shore/off-shore methane hydrate deposits,7 and for sequestration of CO2 via oceanic disposal8 or injection in oceanic sediments.9 In addition, they are considered as a possible cause of global warming due to sudden release of methane from oceanic/permafrost deposits10,11 and as indicators for paleoclimates due to their presence in ice cores.12 As a result of their capacity to store large volumes of gas, hydrates have been considered as an alternative material for storing and transporting hydrogen.13 The major advantages of hydrates as hydrogen-storage materials, comparatively to other materials investigated for the same purpose, include reversibility, low cost, almost not any environmental hazards, and safety (in terms of toxicity and flammability). However, further research and development is required in order for these materials to achieve such a volumetric and gravimetric storage capacity that would render them suitable for practical applications. Until recently, it was believed that H2 was too small to stabilize the hydrate cages and, therefore, could not form hydrates by itself.1,2 This perception changed when, initially, * Corresponding author. E-mail:
[email protected]. Fax: +302106525004. † National Center for Scientific Research “Demokritos”. ‡ National Technical University of Athens. § Visiting scientist. E-mail:
[email protected]. | Delft University of Technology.
Dyadin et al.14 and, later, Mao et al.15 synthesized pure H2 hydrate that was found to be of the sII type. This hydrate structure contains 136 water molecules per unit cell that form two types of cavities: the small, consisting of 12 pentagonal faces (512), and the large, consisting of 12 pentagonal and 4 hexagonal faces (51264).1-3 Each unit cell contains 8 large and 16 small cavities. Pure H2 hydrate is stable only at very high pressures or low temperatures (e.g., at 220 MPa and 280 K or at ambient pressure and 145 K15). Stabilization of pure H2 hydrate was considered a significant advancement (despite the fact that the required temperature and pressure conditions were not very satisfactory for every-day applications) in the field of H2 storage materials, as it was initially estimated to be able to store up to 5.0 wt % H2 (a value that is close to the U.S. DOE target of 6.0 wt % by 2010). Later, Florusse et al.16 succeeded to stabilize binary H2 hydrate (sII) at close-to-ambient conditions (274 K, 5 MPa) by using tetrahydrofuran (THF) as a promoter. The role of the promoter is to stabilize the hydrate at moderate pressure and temperature conditions, albeit at the cost of reducing the H2 storage capacity, since the promoter molecules occupy the large cavities, leaving only the small ones available for hydrogen enclathration. Lee et al.17 suggested that the H2 content of the binary H2-THF hydrate can be “tuned” by suitably adjusting the THF concentration in the equilibrium solution. In this case, H2 content could reach up to 4.1 wt % when an optimal THF concentration of approximately 0.15 mol % was used.17 However, recent experimental18-21 and computational22,23 studies do not support the concept of “tuning” hydrates. These works reported various values of H2 content ranging from 0.3 up to 1.1 wt %, but in all cases, it was found to be constant regardless of the THF concentration in the solution. The most recent advancement in H2 hydrates was the synthesis of sH binary H2 hydrates in early 2008, by Strobel et al.24 and Duarte et al.25 using several organic promoters
10.1021/jp805906c CCC: $40.75 2008 American Chemical Society Published on Web 10/18/2008
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TABLE 1: Radii of the Various Cavities That Appear in sI, sII, and sH Hydrate Structures1 cavity radius (Å) hydrate structure
small
sI sII sH
3.95 3.91 3.91
medium
large
4.06
4.33 4.73 5.71
including methylcyclohexane (MCH), 1,1-dimethylcyclohexane (DMCH), and methyl tert-butyl ether (MTBE). The new binary hydrates were found to be stable in the pressure range 60-100 MPa at close-to-ambient temperatures (269-280 K).25 The sH hydrate crystal contains three small (512), two medium (435663), and one large (51268) cavity per unit cell that consists of 34 water molecules.1-3 The promoter molecules occupy the large cavities and H2 molecules can enter both the small and the medium ones. The size of the small and medium cavities of the sH hydrate is approximately the same as the size of the small cavity of the sII hydrate,1 as shown in Table 1. The small cavity of the sII hydrate has been found to accommodate one H2 molecule at most,18,19,22 although there is some evidence that double occupancy can also occur.16,17 If one assumes that the small and medium cavities of the sH hydrate can also be occupied by a single H2 molecule at most, sH hydrates can reach a H2 uptake of 1.42 wt % (when MTBE is used as the promoter). This value is by 35% higher than the corresponding value of binary sII hydrates (1.05 wt %, with THF as the promoter); however, it remains relatively low if hydrates are to be considered as hydrogen-storage materials for practical applications. The volumetric H2 content is also increased (13.1 kg/m3 for sH hydrate compared to 10.5 kg/m3 for sII hydrate, i.e., an increase of 25%). Although it has been found that pure H2 forms sII hydrates,15 there is not yet experimental evidence that it can form sH hydrates by itself (without promoter). Note, however, that other small molecules (known as sII hydrate formers), such as nitrogen26 and argon,27,28 can form sH hydrates without the assistance of promoters, within a specific pressure range, exhibiting an “sII-to-sH” structural transformation. In the case of a possible sH hydrate of pure H2, Strobel et al.24 estimated that the H2 content could reach up to 5.6 wt %. This high value of H2 uptake is attributed mainly to the size of the large cavity of the sH hydrate. This cavity is the largest among all the cavities that appear in the three common hydrate structures (Table 1), and its volume is almost twice the volume of the large cavity of the sII hydrate. The aforementioned value of H2 uptake is derived from the size of the H2 molecule relatively to the size of each type of cavity. It can be expected that up to eight H2 molecules could possibly be accommodated in this cavity, while double occupancy is assumed for the small and medium cavities. For single occupancy of the small and medium cavities, the corresponding value is 4.1 wt %.29 Consequently, the determination of the occupancy of each type of cavity is an issue of crucial importance for the evaluation of the hydrogen-storage capacity of hydrates. An accurate calculation of the H2 content of hydrates from experimental measurements is a demanding and difficult task. For this reason, molecular simulations such as molecular dynamics (MD)23,30-32 and Monte Carlo33-37 could have an important contribution toward obtaining some gas-content estimates, as well as elucidating the hydrate behavior. For example, the MD simulations of Alavi et al.30 have shown that energy minimization is achieved when the small and medium cavities of the binary sH hydrate are singly occupied by H2 molecules and all the large
cavities occupied by the promoter (MTBE) molecules. Another MD study on sH hydrates32 has led to the determination of the cavity occupancies by molecules of the noble gases (Ne, Ar, Kr, and Xe). Recently, Katsumasa et al.36 used grand canonical Monte Carlo (GCMC) simulations to study pure H2 sII hydrates. Papadimitriou et al.22 have employed GCMC simulations to calculate the cavity occupancies for pure H2 and binary H2-THF sII hydrates. The main objective of this work is to apply the GCMC methodology in order to estimate the hydrogen content of sH hydrates. In our approach, the formation of hydrates is treated as a process of gas adsorption in a solid material. GCMC simulation is a very efficient computational tool for such kind of studies. The following cases are considered: (a) the hypothetical sH hydrate where H2 is the single guest component (without promoter), (b) the experimentally demonstrated binary sH hydrate with promoter (MCH) in the large cavities, and (c) the hypothetical promoter-stabilized sH hydrate where the promoter occupies the medium instead of the large cavities. 2. Simulation Details In this work, the GCMC approach developed by Metropolis et al.38 has been used to study the hydrogen-storage capacity of sH hydrates. A detailed presentation of the method can be found in the book of Allen and Tildesley.39 Our simulations are carried out on a simulation box of 27 (3 × 3 × 3) unit cells containing 918 water molecules in total that are placed on a rigid lattice. The use of a flexible lattice of water molecules could be an alterative approach. In this approach, the water molecules have translational and rotational degrees of freedom. However, Sizov and Piotrovskaya,34 who applied this approach to study methane hydrates, concluded that the results from the rigid lattice are in better agreement with the experimental data and the results from other theoretical calculations. As long as there is no obvious improvement in the results when a flexible lattice is used and considering that it is much more computationally expensive, we have opted for the approach of a rigid lattice. The lattice constants used are a ) 12.203 Å and c ) 9.894 Å.24 3D periodic boundary conditions are applied. Fractional coordinates of oxygen and hydrogen atoms of the water molecules are taken from the work of Okano and Yasuoka.40 The proton configuration they suggested presents the minimum dipole moment and potential energy among more than 1.2 × 106 configurations examined, all of them being consistent with the Bernal-Fowler “ice rules”.41 In the present study, water molecules are described with the extended simple point charge (SPC/E) model.42 This model accurately correlates several properties of water and has been widely used in various types of simulations on hydrates30-32,34,35,37 with significant success. Alternatively, the TIP4P model43 could be used to describe the water molecules. This model has also been used for hydrate simulations.33,36,44-47 Our simulations have shown that both models yield cavity occupancy results that are very similar, and therefore, we present the results from the SPC/E model only. Frankcombe and Kroes48 presented an extended discussion about the efficiency of several water models in predicting hydrate stability. Interaction parameters and partial charges of the SPC/E model are shown in Table 2. Regarding the H2 molecule, it has been represented by a Lennard-Jones interaction site placed in the middle of the H-H bond with the bond length taken as 0.7414 Å.49 Electrostatic interactions are taken into account by assigning partial charges to each H atom and to the middle of the H-H bond. Parameters for the H2 molecules are also shown in Table 2. This set of
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Figure 1. Partial charges in the MCH molecule after the geometry optimization using the Universal force field and the QEq charge equilibration approach.
TABLE 2: Interaction Parameters and Partial Charges for Each Molecule molecule
atom
H2 O
O H H middle of H-H bond C H
H2 MCH
σ (Å) ε (kJ/mol) 3.166 0.000 0.000 3.038 3.431 2.571
0.6502 0.0000 0.0000 0.2852 0.4393 0.1841
charge (e) -0.8476 +0.4238 +0.4932 -0.9864 see Figure 1 see Figure 1
parameters has been derived from experimental data of the solid and gas phase of H2 and has been used in MD and GCMC simulations of hydrogen hydrates.22,23,31 Finally, the geometry of MCH has been optimized (Figure 1) prior to the simulation using the Universal force field (UFF)50 where the partial charges of the atoms have been calculated with the QEq charge equilibration approach.51 Interaction parameters between different types of atoms are calculated using the Lorentz-Berthelot combining rules.39 All molecules were considered to be rigid during the simulations. For the simulations on the binary H2-MCH hydrates, the following approach was adopted: a preliminary GCMC simulation where MCH was the only “adsorbed” component determined the position and orientation of the MCH molecules within the large cavities. The main simulation of H2 “adsorption” was carried out on the lowest energy configuration that had resulted from this preliminary simulation, but the positions and orientations of the MCH molecules were kept fixed. This approach significantly reduces the computational effort because a large number of steps are required for the number of “adsorbed” promoter molecules to equilibrate (i.e., to occupy all the large cavities). Each GCMC run includes 107 steps where creation, destruction, and displacement are chosen with equal probabilities. The maximum displacement distance is set to 1.0 Å. The total energy of the system configuration after each trial “move” is calculated by atom-atom summations within a cutoff distance of 20 Å (applied to both van der Waals and electrostatic interactions). This relatively long cutoff distance allows the calculation of the interactions between one H2 molecule and multiple shells of water molecules52 as well as between H2 molecules that reside in different cavities. The Ewald summation technique39 is also used for the long-range electrostatic interactions. For the calculation of the occupancy of each type of cavity, a sample configuration every 25 steps is taken and all of the H2 molecules are assigned to the closest center of cavity. At the end of the
Figure 2. Hydrogen content from GCMC simulations for two hydrogen hydrates (at 274 K), where H2 is the single guest component: hypothetical sH hydrate (solid line); sII hydrate22 (dashed line).
simulation, the average occupancy of every cavity is calculated, and finally, occupancies are averaged separately for the small, medium, and large cavities, as it was observed that no cavity presented a different occupancy trend relative to the other cavities of the same type. 3. Results and Discussion 3.1. Pure H2 sH Hydrate. Initially, we begin with the examination of the pure H2 sH hydrate. Although the stability of the pure H2 sH hydrate has not been experimentally confirmed yet, these molecular simulations can give important information on the possible hydrogen-storage efficiency of this hydrate, independently of the selected promoter. In particular, the case of pure H2 sH hydrate represents an upper limit for the storage capacity of binary H2-promoter sH hydrate systems. Essentially, in binary H2-promoter hydrates, we replace hydrogen molecules with a component that has significantly higher molecular weight, therefore reducing the overall hydrogen content, since the promoter makes up a relatively large weight percentage of the hydrate system. Consequently, the determination of the H2 uptake of the pure H2 hydrate could lead to the overall evaluation of the efficiency of sH hydrates in H2 storage. The H2 content of the hypothetical pure H2 sH hydrate is presented in Figure 2. Within the pressure range examined (1-500 MPa), this material can store up to 3.6 wt % H2. This hydrogen content value, along with the other advantages of hydrates, highlights the potential of this material for application in hydrogen storage and emphasizes the need for further research and development in the specific material. On the other hand, these values of H2 uptake still do not meet the requirements for use in practical applications, especially in transportation. This deficiency becomes more pronounced if one considers the high pressures required in order for those storage values to be achieved. For comparison purposes, Figure 2 also shows the hydrogen content of the pure H2 sII hydrate that was reported earlier22 based on similar GCMC simulations. When comparing the hydrogen-storage capacity of the sH and sII hydrates, it is obvious that the sH hydrate presents an increased storage capacity relative to the sII hydrate. In particular, the sH hydrate can store approximately 5-20% larger amounts of H2 gravimetrically and up to 30% volumetrically, than the sII hydrate. Our GCMC simulations can give more detailed results concerning the number of H2 molecules enclosed in each type of cavity. Both small and medium cavities are found to be occupied by a single H2 molecule (Figure 3). This finding should
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Figure 3. Average occupancies for each type of cavity obtained from GCMC simulations on the hypothetical pure H2 sH hydrate as a function of pressure at 274 K: small (dashed line), medium (circles), and large (solid line) cavity.
TABLE 3: Occupancy Ratios (%) of the Large Cavity of the Hypothetical Pure H2 sH Hydrate at Several Pressures number of H2 molecules per cavity pressure(MPa) 0 50 100 200 300 400 500
1
2
3
4
5
6
7
2.9 22.0 44.7 25.8 4.4 0.2 0.0 0.0 0.2 4.7 26.2 44.3 21.9 2.7 0.1 0.0 0.0 0.1 2.8 21.6 46.2 26.3 2.9 0.0 0.0 0.0 0.1 3.8 27.3 50.2 17.5 1.1 0.0 0.0 0.0 0.4 8.1 41.0 42.2 8.1 0.0 0.0 0.0 0.0 0.9 17.4 53.1 26.5
8 0.0 0.0 0.0 0.0 0.2 2.1
be expected because these cavities are of about the same size as the small cavity of the sII hydrate, which has been experimentally18,19,53 and computationally22,23,36 proven to accommodate one H2 molecule at most. However, it must be noted that, at very high pressures (above 350 MPa), a small fraction (up to 5%) of the medium cavities seem to be doubly occupied while the respective fraction of small cavities remains negligible (less than 0.1%) over the entire pressure range considered (up to 500 MPa). Next, we examine the hydrogen occupancy of the large cavity of the sH hydrate. As the results of our simulations show in Figure 3, the average occupancy is highly dependent on pressure and reaches a value of 6.0 at about 470 MPa. Even higher
occupancy values should be expected at higher pressures. Some previous estimates on the occupancy of the specific cavity based mainly on the size of the cavity compared to the size of the H2 molecule reported a maximum occupancy of 8.0.29 However, a more accurate investigation of the possible H2 occupancy had not been carried out. Previously, Alavi et al.32 had used molecular dynamics simulations to examine the stability of sH hydrates of noble gases with several numbers of guest molecules per cavity. The results of our work comprise the first accurate investigation of the possible H2 occupancy based on molecular simulations. Table 3 offers a more detailed description of the number of H2 molecules encaged in this type of cavity at various pressures. In the pressure range under examination, the large cavity of sH hydrate has been observed to accommodate even up to eight H2 molecules. The probability density of finding a H2 molecule within the large cavity is visually shown in Figure 4. The maximum hydrogen content calculated in this work (3.6 wt % at 500 MPa) is lower than the H2 content value (5.6 wt %) estimated by Strobel et al.24 The value of 3.6 wt % is the average result of storage of 11.3 hydrogen molecules per unit cell of hydrate, distributed in the cavities as follows: 1.0 in the small, 1.0 in the medium, and 6.2 in the large. For the hydrogen content to reach 5.6 wt %, 18 hydrogen molecules are required per unit cell, with a possible distribution as follows: 2 in the small, 2 in the medium, and 8 in the large. Recall that there are 3 small, 2 medium, and 1 large cavities per unit cell of the sH hydrate. Our results partially confirm this value of occupancy for the large cavity depending on pressure, but they do not give evidence in favor of the double occupancy of the small and medium cavities. Note, however, the limited double occupancy of the medium cavities at pressures above 350 MPa. 3.2. Binary H2-MCH sH Hydrates (MCH in the Large Cavities). GCMC simulations are performed for the binary H2-MCH hydrate in order to determine its H2 uptake at 274 K in the pressure range 1-500 MPa. The results are shown in Figure 5. Duarte et al.25 reported that, at a temperature of 274 K, the hydrate equilibrium pressure is 83.1 MPa. The H2 content as a function of pressure below 350 MPa presents a Langmuirtype trend with a plateau at 1.4 wt %. This value corresponds to the situation where all the small and medium cavities are occupied by one H2 molecule. It must be reminded that the large cavities are explicitly set to contain one MCH molecule each. The reason for this behavior is the single occupancy of the small
Figure 4. Probability density of finding a H2 molecule on a cross section of the large cavity: (a) parallel to the long axis; (b) vertical to the long axis. Red areas represent high probability and blue areas low probability.
14210 J. Phys. Chem. B, Vol. 112, No. 45, 2008
Figure 5. Hydrogen content obtained from GCMC simulations as a function of pressure for the binary H2-MCH sH hydrate (denoted with the solid line). The dashed line shows the GCMC simulations for the binary H2-THF sII hydrate.22 Dotted horizontal lines correspond to complete single occupancy of the small/medium cavities.
Figure 6. Comparison of the cavity occupancies between the pure H2 (solid lines) and the binary H2-MCH (dashed lines) sH hydrates: (a) small cavity; (b) medium cavity.
and medium cavities (Figure 6), which was also observed in the case of pure H2 hydrates. This finding is in agreement with the molecular dynamics simulations of Alavi et al.30 who reported that the system energy is minimized when the small and large cavities are singly occupied by H2 molecules while all the large ones are occupied by MTBE molecules. There is a large increase in the unit cell volume and inclusion energy when the small cages accept a second hydrogen guest molecule.30 The limiting value of 1.4 wt % is exceeded at pressures
Papadimitriou et al.
Figure 7. Hydrogen content as a function of pressure (at 274 K) for a hypothetical binary H2-promoter sH hydrate with the promoter (MW: 20, 50, 80) encaged in the medium cavities. The upper bound corresponding to the pure H2 hydrate is shown with a solid line.
above 350 MPa due to a small fraction of doubly occupied medium cavities. From the GCMC simulations of this work, we find that the binary H2-MCH sH hydrate presents an increased H2 content by up to 35%, when compared with the binary H2-THF sII hydrate (see Figure 5). This finding is in agreement with the estimates by Strobel et al.24 who stated that the binary sH hydrate could be up to 40% more efficient than the binary sII hydrate in storing hydrogen. In general, the hydrogen-storage capacity of both materials is considered relatively low. Furthermore, the inability of the small and medium cavities to accommodate more than one H2 molecule even at very high pressures results in limited prospects of application of these materials in hydrogenstorage applications. 3.3. Binary H2-Promoter sH Hydrates (Promoter in Medium Cavities). Figure 6a shows the comparison of the small-cage occupancies (from our GCMC simulations) for the pure H2 and the binary H2-MCH sH hydrates as a function of pressure at 274 K. The same comparison for the medium cages is shown in Figure 6b. From the good agreement observed, we can conclude that the presence of the promoter in the large cavities hardly affects the occupancy of the remaining cavities, although it has a crucial effect on the stability of the hydrate. Probably, the interactions between H2 and promoter molecules are insignificant compared to the interactions between H2 molecules and the solid lattice of water molecules. This fact can lead to the assumption that the gravimetric H2 content of the hydrate depends mostly on the molecular weight of the promoter and not on its chemical structure. On the basis of the aforementioned assumption, we have attempted a parametric analysis of a hypothetical binary sH hydrate where the promoter occupies the medium instead of the large cavities (Figure 7). A promoter of suitable size to fit the medium cavity is expected to have a molecular weight of approximately 20-100. As expected, this hydrate obviously presents a higher H2 content than the binary H2-MCH hydrate (where the promoter is in the large cavities) but lower than that of the pure H2 sH hydrate. Assuming a promoter with a molecular weight of 50, one should expect a H2 content of 2.0 wt % at 220 MPa. Figure 7 illustrates the comparison between the GCMC calculated H2 uptake of sH hydrate in the following cases: (a) sH hydrate of pure H2, (b) binary H2-MCH hydrate with the promoter in the large cavities, and (c) binary hydrate with a promoter of varying molecular weight in the medium
Hydrogen Storage in sH Hydrates cavities. This figure could give a general estimate of the hydrogen-storage capacity of sH hydrates either with or without promoter, and regardless if the promoter molecules occupy the medium or large cavities. 4. Conclusions We have utilized grand canonical Monte Carlo simulations to evaluate the hydrogen-storage capacity of pure and binary sH hydrates under a wide range of conditions. In this approach, hydrate formation is treated as a process of gas adsorption in a solid. According to our results, the hypothetical sH hydrate of pure H2 presents a significant H2 uptake (3.6 wt %) that justifies further research and development toward the use of the specific materials for hydrogen storage. Note, however, that pressures as high as 500 MPa are required in order for these materials to achieve such values of H2 content. The large cavity of the sH hydrate seems able to accommodate up to eight H2 molecules. On the other hand, the small and medium cavities tend to be singly occupied. Regarding the binary sH hydrates with the promoter in the large cavities, they seem to have very limited prospects of application in hydrogen storage in the future because the presence of the promoter sets an upper limit to their H2 uptake that is below the requirements for practical transportation applications. Specifically, this material cannot store more than 1.4 wt %, which is the result of single occupancy of both the small and medium cavities. However, a promising advance could be the synthesis of binary sH hydrates with the promoter occupying the medium instead of the large cavities. Such a material has not been experimentally stabilized yet, but it would present an increased H2 content of about 2 wt %. Acknowledgment. Partial funding by the European Commission DG Research (contract SES6-2006-518271/NESSHY) is gratefully acknowledged by the authors. The first of the authors wishes to acknowledge the Hellenic State Scholarships Foundation (I.K.Y.) for the financial support. References and Notes (1) Sloan, E. D. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker: New York, 1998. (2) Sloan, E. D. Nature 2003, 426, 353. (3) Koh, C. A. Chem. Soc. ReV. 2002, 31, 157. (4) Khokhar, A. A.; Gudmundsson, J. S.; Sloan, E. D. Fluid Phase Equilib. 1998, 150-151, 383. (5) Kubota, H.; Shimizu, K.; Tanaka, Y.; Makita, T. J. Chem. Eng. Jpn. 1984, 17, 423. (6) Kang, S. P.; Lee, H. EnViron. Sci. Technol. 2000, 34, 4397. (7) Collet, T. S. AAPG Bull. 2002, 86, 1971. (8) Brewer, P. G.; Friederich, C.; Peltzer, E. T.; Orr, F.M., Jr. Science 1999, 284, 943. (9) House, K. Z.; Schrag, D. P.; Harvey, C. F.; Lackner, K. S. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 12291. (10) Mac Donald, G. T. Clim. Change 1990, 16, 247. (11) Kvenvolden, K. A. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 3420. (12) Raynaud, D.; Jouzel, J.; Barnola, J. M.; Chappellaz, J.; Delmas, R. J.; Lorius, C. Science 1993, 259, 926. (13) Mao, W. L.; Mao, H. K. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 708. (14) Dyadin, Y. A.; Larionov, E. G.; Manakov, A. Y.; Zhurko, F. V.; Aladko, E. Y.; Mikina, T. V.; Komarov, V. Y. MendeleeV Commun. 1999, 9, 209.
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