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J. Phys. Chem. B 2001, 105, 4200-4204
Structure, Composition, and Thermal Expansion of CO2 Hydrate from Single Crystal X-ray Diffraction Measurements† Konstantin A. Udachin, Christopher I. Ratcliffe, and John A. Ripmeester* Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6 ReceiVed: December 6, 2000; In Final Form: March 7, 2001
The structure and composition of CO2 hydrate were determined from single-crystal X-ray diffraction data at 173 K for a crystal grown over heavy water and liquid CO2. Superior diffraction data allowed the derivation of a structural model of unprecedented quality for the hydrate, giving the location of the disordered CO2 molecules in the two cages. In the large cage, the guests are shown to be off-center, with a bimodal distribution of out-of-plane orientations for the long axis of the molecule (173 K). Also, the absolute cage occupancies were determined from the structural model, thus allowing a reliable and direct evaluation of the hydrate composition for this crystal, CO2‚6.20(15) D2O. The temperature dependence of the lattice parameters for the single crystal was measured between 123 and 223 K and found to be in good agreement with recent neutron powder diffraction results, and data from all sources were fit to a single polynomial function. The hydrate composition and density are discussed in terms of the information needed for the deep-sea sequestration of CO2. The guest disorder and dynamics are discussed in terms of the model derived from earlier NMR data.
Introduction As clathrate hydrates have considerable potential for affecting human welfare,1 their study continues to be a very active topic of research. Natural gas hydrates are seen as potential sources of energy as well as possible agents of global climate change.2 On the other hand, deep-sea disposal of CO2, as a greenhouse gas byproduct of energy production,3 is certain to lead to CO2 hydrate formation.4 The fact that the CO2 molecule forms a hydrate has been known for many years.5 It is a structure I hydrate with a unit cell formula of 2MS‚6ML‚46H2O, where MS and ML are the small 512 and large 51262 cages, respectively.6 A number of spectroscopic and diffraction studies 7-13 have addressed various aspects of its structure and composition. Generally, it is agreed that CO2 molecules occupy most of the large cages in structure I as well as a fraction of the small cages, thus giving a composition between 5 3/4 and 7 2/3 waters/guest, and experimentally determined values indeed tend to lie within this range. Some key information about CO2 hydrate that is required for the modeling of CO2 dispersal is the density of the hydrate, as there are questions about the depth at which CO2 hydrate will sink or float. Clearly, this information is needed if accurate models are to be formulated for the eventual dispersion of CO2 in the world’s oceans after initial injection, and this can be calculated knowing both the lattice parameters and composition for samples produced under the conditions appropriate to the depth of CO2 injection. As a first step in obtaining such information, we have determined the structure and composition of CO2 hydrate using X-ray diffraction of a single crystal. The information obtained can serve as a starting point for estimating the density of CO2 hydrate. Also, the location of the disordered CO2 molecule in the hydrate cages can serve as input for the †
NRCC no: 43884. * Corresponding author. E-mail:
[email protected]. Fax: 613 9987833.
analysis of powder diffraction data for hydrate samples prepared under conditions of high pressure. Experimental Section A single crystal of CO2 hydrate was grown in a sealed tube above a D2O-liquid CO2 interface at ∼3 °C over a period of several months. Crystals suitable for diffraction were selected using a microscope mounted on a cold box. Subsequent handling and transfer of the crystals were always done under cold conditions where the crystals were stable. The crystal was mounted on a Bruker Smart CCD Diffractometer, and diffraction data were collected at -100 °C. In addition, unit cell parameters were determined at a number of temperatures in order to determine the temperature coefficient of the lattice parameter. The structural model was refined with the SHELXTL software package.14 Crystal data and structural refinement information are given in Table 1. Table 2 gives the atomic coordinates and isotropic displacement parameters. Both site occupancy factors were used as free parameters in the refinement; however, the fraction for the large cage always tended toward a value of unity. For the small cage, the error in the cage occupancy fraction was estimated by varying the thermal parameters between reasonable limits as these and the occupancy factor were coupled. Results and Discussion Structure and Guest Disorder at 173 K. As expected, the structure was found to be a regular cubic structure I hydrate, space group Pm3n, with a unit cell edge of 11.893(2) Å. The water oxygens define the vertexes of the cages with their usual geometries. Guest atoms were located from the difference electron map. In the large cage, the guests lie near to the equatorial plane of the cage, and in fact, the refinement forces the long axis of the guest to lie in the plane. However, the C-O bond lengths are foreshortened considerably by being forced
10.1021/jp004389o CCC: $20.00 Published 2001 by the American Chemical Society Published on Web 04/12/2001
CO2 Hydrate
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TABLE 1: Crystal Data and Structure Refinement CO2 Hydrate empirical formula formula weight temperature wavelength crystal system, space group unit cell dimensions volume Z, calculated density absorption coefficient F(000) crystal size θ range for data collection index ranges reflections collected/unique completeness to 2θ ) 28.68 refinement method data/restraints/parameters goodness-of-fit on F2 final R indices [I > 2 Σ(I)] R indices (all data) largest diff. peak and hole
C7.34D92O60.86 1247.20 (1154.65 for C7.34H92O60.86) 173(2) K 0.71073 Å cubic, Pm3n a ) 11.893(2) Å 1682.4(5) Å3 1, 1.140 Mg/m3 0.126 mm-1 623 0.3 × 0.3 × 0.3 mm3 2.42-28.68° -16 r h r 16, -15 r k r 16, -16 r l r 16 17380/478 [R(int) ) 0.0309] 95.7% full-matrix least-squares on F2 478/0/108 1.031 R1 ) 0.0266, wR2 ) 0.0720 R1 ) 0.0314, wR2 ) 0.0765 0.132 and -0.127 e Å-3
TABLE 2: Atomic Coordinates (×104) and Isotropic Displacement Parameters O1 O2 O3 C1A O1A O2A C1B O1B O2B C1D O1D O2D O1E O2E O1F O2F
x
y
z
U(eq)
0 1835(1) 0 5029 5243(1) 4829(1) 4935 4090(1) 5779(1) 0 0 0 165(2) 165(2) 0 0
3092(1) 1835(1) 5000 16 -882(1) 919(1) 99 -365(1) 567(1) 0 683(1) 683(1) 358(1) 358(1) 288(1) 288(1)
1166(1) 1835(1) 2500 2378 2059(1) 2696(1) 2458 2613(1) 2305(1) 0 696(1) 696(1) 892(1) 892(1) 931(1) 931(1)
43(1) 46(1) 42(1) 155(1) 170(1) 144(1) 127(1) 111(1) 158(1) 42(1) 111(1) 107(1) 111(1) 107(1) 111(1) 107(1)
to the equatorial plane. The extent to which the OCO axes are tilted out of the plane can be found by fixing the C-O distances to their usual value of 1.16 Å and tilting the OCO axes out of the plane. At the initial stages of refinement, the guest molecules were fixed to be linear, and the molecule was centered in the cage. Further improvement resulted when the carbon atom was allowed to move away from the center of the cage, and during the last stages of refinement, all restraints were canceled. The best model derived using this procedure shows that there are 16 positions for a CO2 guest in each large cage, 8 of which have their long axis at an angle of 14.4° and the 8 others at an angle of 6.5° (Figure 1). The relative occupancies are 41% and 59%, respectively, and within experimental error, the large cages are fully occupied (occupancy ) 1.00(2)). The disordered guest in the small pentagonal dodecahedral cage is best modeled by allowing the CO2 molecule to be disordered over four positions (two are symmetry-related) around the line that connects the centers of opposite pentagonal faces (Figure 2). The angle between this line and the linear guest molecule is 10-15°. Multiplied by 6, the number of pairs of opposite faces, this gives 24 positions for a CO2 molecule in the cage. Site occupancies for these positions are 0.38, 0.19 (the two symmetry-related positions), and 0.14, giving an overall occupancy of the cage of 0.71(3). The final R1 value for this arrangement of the guest molecules is 0.0266. Such a small
Figure 1. Structure I large (51262) cage: (top) view along the symmetry axis of the cage; (bottom) view along the equatorial plane of the cage. The CO2 molecule is shown distributed over the 16 sites (8 symmetryrelated sites, 2 sets of tilt angles) determined for the model from the refinement of the diffraction data
Figure 2. Structure I small (512) cage, showing the 24 symmetryrelated sites for the CO2 molecule.
number indicates a high-quality structural solution, unprecedented in hydrate work. Alternatively, this structure could be refined with just six positions of the guest molecule in the dodecahedral cage, each with an oxygen atom pointed at the center of a pentagonal face. In this case, however, the oxygen atoms have large anisotropic thermal parameters, and the R1 value increases to 0.05. Hydration Number. A variety of approaches has been used to measure the hydration number of CO2 hydrate. Classical approaches include the application of the Clausius-Clapeyron equation to the water-hydrate-gas equilibrium data, as illustrated in the work by Bozzo et al.,15 giving a value of 7.3. Spectroscopic measurements are based on the ability to distinguish large and small cage populations, which, together with the application of the solid-solution theory, can be used to give hydration numbers.16,8 This requires knowledge of the relative cage occupancies and the free energy difference between ice and the hypothetical empty hydrate lattice, ∆µ. Unfortunately, Raman spectroscopic measurements are not able to distinguish the large and small cage populations in CO2 hydrate,8 although recent single-crystal measurements with polarized radiation have shown some promise.9 For a sample prepared under equilibrium conditions, solid-state NMR has been used to give a lower limit to the hydration number of 7.0, assuming a ∆µ value of 1297 J m-1, and a measurement of the relative cage occupancies.10 In principle, diffraction data can be used to give structural models that include absolute cage occupancies, and hence, the hydration numbers can be obtained directly. Recently, two
4202 J. Phys. Chem. B, Vol. 105, No. 19, 2001
Figure 3. Lattice parameter for CO2 hydrate as a function of temperature: filled circles, single-crystal data (this work); open circles, neutron powder data (refs 11 and 12). The solid line is the polynomial fit described in the text.
neutron diffraction studies on powder samples of perdeuterated CO2 hydrate were reported.11,12 The quality of the structural models developed depends a great deal on the ability to model the disordered CO2 molecules in the two cages. In one study, difficulties were encountered in determining the cage occupancies, as the thermal parameters were observed to be strongly coupled to the cage occupancies.12 The structural model developed showed that the large cage was more than 95% filled, with the small cage occupancy between 60% and 80%. This gives hydration numbers between 6.05 and 6.67, assuming limits of 95-100% filling of the large cage. Recourse was taken to a calculation using a hydrate prediction program that gave values of 73% and 98% for the small and large cage occupancies, respectively, giving a hydration number of 6.27. This sample was prepared at temperatures between 263 and 278 K with pressures as high as 60 atm, thus at pressures well above the equilibrium pressure for hydrate formation. Since the composition of the hydrate should reflect the gas pressure P above the hydrate equilibrium pressure Po, the ratio P/Po should be a good relative indicator of sample composition for purposes of comparing samples prepared under different conditions. For the sample used in the neutron study, P/Po varied between ∼3 and 8 during sample preparation. Cage occupancies were not determined in the second diffraction study,11 although an estimate made from a solid solution model calculation gave values of 99% and 90% filling of the large and small cages, respectively. Especially for the small cage, this estimate is almost certainly too high, considering the synthetic conditions (253 K, 13 atm, P/Po ≈ 2) and the other results on hydrate composition summarized here. The cage occupancies determined from the current singlecrystal X-ray diffraction study were 100(2)% and 71(3)%, yielding a hydration number of 6.20(15). The crystal was prepared at 276 K in the presence of excess liquid CO2 (∼38 atm, P/Po ≈ 2), so again cage occupancies can be expected to be rather greater than those for a sample prepared under fourphase equilibrium conditions (273 K, 12.4 atm). Unit Cell Parameters, Thermal Expansion, and Density. The unit cell parameter for polycrystalline samples of CO2 deuteriohydrate has been measured by neutron diffraction at 14 K12 and also at five temperatures between 7 and 213 K.11 These values, as well as those obtained from our single crystal data, are shown in Figure 3. Considering the diversity of samples and experimental approaches, the measurements can be considered to be in good agreement, although our data contribute
Udachin et al.
Figure 4. 13C NMR static line shapes of 13C enriched CO2 hydrate at 238 K (with 1H decoupling) and 170 K (with1H cross-polarization and decoupling). The dashed line shows the static line shape of solid 13CO2 at 77 K (from ref 7). CO2 in the small cages contributes to the sharp line at the isotropic shift in the 238 K spectrum, together with any intensity from free CO2.
only to the high-temperature portion of the temperature range of study. Following earlier work on ethylene oxide hydrate,17 we have chosen to fit the data in terms of a polynomial function as follows:
a(T)/Å ) 11.81945-9.08711 × 10-5T + 4.59676 × 10-6T2 - 8.35548 × 10-9T3 (1) As noted before,17 thermal expansion of the clathrate hydrate crystal lattice is much greater than that measured for ice. For CO2 hydrate, the lattice parameter increases by ∼1% over a temperature range from 5 to 223 K, a value similar to that determined for structure I ethylene oxide hydrate.17 With the data now available, a realistic estimate can be made of the density of CO2 hydrate. For instance, the calculated lattice constant at 4 °C for the sample studied in this work is 11.970(5) Å. For a composition of CO2‚6.20(15) H2O, the calculated density is 1.12 (1) g/cm3, with the main estimated uncertainty arising from the cage occupancies. More complete knowledge of the buoyancy behavior of CO2 hydrate will require the measurement of density and, hence, the composition and lattice parameter as a function of synthetic conditions (T, P). Undoubtedly other factors such as hydrate morphology will play a role in determining the physical properties of hydrate under deep-sea conditions; however, that is beyond the scope of the current work. With increasing pressure (at depths considered for CO2 injection into the deep sea, 3200 m, the hydrostatic pressures will be as high as ∼325 bar), the composition will tend toward complete filling of the cages, hence a composition that approaches CO2‚5 3/4 H2O. The lattice parameter will respond in an as yet unknown way to increasing cage occupancy and compression of the lattice under hydrostatic pressure. However, the hydrate will certainly be denser than that of liquid CO2 at that depth (1.085). Structure, Dynamics, and Guest-Host Interactions. It is important to establish consistency between the structure determined by X-ray diffraction (XRD) and the dynamics determined by NMR. From the information about dynamics available from the previous 1H and 13C NMR studies as a function of temperature,7 it is known that the 13C NMR line shapes (Figure 4) are influenced by the reorientation not only of the CO2 itself but also of the host H2O molecules. At 238 K, the highest temperature for which a 13C NMR line shape was obtained, both motions are rapid. At the 173 K temperature of the single-crystal XRD study, however, the water dynamics are a factor of ∼400 times slower than those at 238 K and effectively static on the
CO2 Hydrate time scale corresponding to the reciprocal of the static 13C NMR line width of the CO2 molecule. Although the H2O molecules freeze into disordered positions, the XRD sees an apparently high-symmetry structure involving 1/2H atoms because of spatial averaging; i.e., all information from the lattice is projected back into the unit cell and therefore produces an average picture. However, at 173 K, each CO2 sees not this high symmetry, but the local structure of the cage in which it sits, and because of the static disorder in the H positions, there is a large distribution of slightly different cage configurations. Consequently, each CO2 sees a slightly different potential surface, which thus modifies its reorientation. In contrast, at 238 K, rapid dynamic averaging among the proton positions means that all the (large) cages are effectively identical with the high crystallographic symmetry, and every CO2 experiences the same potential surface. These two situations give profoundly different NMR line shapes for the CO2 in the large cages (Figure 4): at 238 K, all the CO2 molecules in the large cages behave in the same way and give rise to an averaged 13C NMR chemical shift anisotropy (csa) powder pattern (∆δ ) 101 ppm) with sharp features, corresponding to rapid axially symmetric reorientation. However, the 13C line shapes in the region of 173 K are no longer simple csa powder patterns and are significantly broader than at 238 K (halfwidth ) ∼134 ppm), since they arise from a sum over a distribution of csa line shapes. It is entirely possible that the CO2 in the small cages, which give an isotropic line shape at 238 K, also become anisotropic at 170 K for the same reasons, although this is quite a small contribution to the overall intensity of the line. It is very interesting that the spatially averaged XRD results can best be modeled with just two preferred CO2 orientations at 14.4° and 6.4° and their symmetry equivalents, quite close to the equatorial plane of the large cage, rather than a distribution of orientations. If the CO2 were to undergo rapid reorientation between all these XRD-defined orientations weighted by their populations, the 13C NMR csa line shape (calculated using standard equations for the tensor averaging7 and based on the static anisotropy of ∆δ ) -334 ppm determined for solid CO2 at 77 K, Figure 4) would have an axial anisotropy of ∆δ ) 150.5 ppm. Therefore, the csa line shape would have a greater width and sharper features than that observed at 170 K. However, there is no reason to expect such symmetric reorientation since in any one cage the lowered symmetry means that some related positions are not necessarily present and thus the dynamics become more complicated. It is also clear that these restricted orientations do not survive at 238 K because of the increased dynamics of the water molecules (Figure 5). The dynamic models,7 which fit the observed axial anisotropy of 101 ppm, all suggest that the CO2 is at larger angles with respect to the plane of the cage (up to 31° for a model involving orientations over a solid angle and 21.3° for a single preferred orientation). The X-ray data are more consistent with a single, smaller angle than with the larger distributed value. Some words of caution need to be said about the use of dynamic information obtained from NMR for developing models for guest disorder in analyzing diffraction data, for instance by Rietveld analysis. Specific NMR models should be strictly confined to their appropriate temperature regions. For instance, above ∼220 K, the axial model for guest reorientation in the large cage and isotropic motion in the small cage are perfectly valid. However, as the 13C NMR line shape at 175 K shows, the guest dynamics are much more restricted once the water molecules freeze in to their disordered positions. Although the diffraction model for the guests at low temperature still
J. Phys. Chem. B, Vol. 105, No. 19, 2001 4203
Figure 5. Models for the dynamic state of the CO2 molecule encaged in the large cage of CO2 hydrate. On the right is the high-temperature picture (T > ∼220 K). The heavy line represents the long axis of the molecule that is inclined to the equatorial plane of the cage by an angle θ. Both θ and φ can be time-dependent, as described in the detailed model published previously (ref 7). Below ∼200 K (on the left), the motion of the CO2 axis can be best described as varying over an elliptical cone, with the size of the ellipse a function of temperature and varying from cage to cage because of the frozen-in proton disorder associated with the orientation of the water molecules. The heavy line in this case represents the symmetry axis of the cone and is more or less fixed in each cage. However, φ varies from cage to cage to give the space averaging evident from the crystallography and θ has a value of 6.6° or 14.4° at 173 K.
superficially resembles the high-temperature NMR model, the high apparent symmetry arises strictly from space averaging of highly restricted guest positions. In fact, only a single set of the many disordered positions is likely to be occupied in any particular cage, with a motion where the CO2 long axis varies over a roughly conical volume, much as described in our earlier study7 (Figure 5). Our diffraction study found that there were no structural features that could be attributed to specific guest-host interactions, something alluded to in earlier diffraction work. We do note that evidence for guest-host interactions comes from earlier dielectric and NMR work, where it was noted that the activation energy for reorientation of water molecules in a hydrate is significantly lower if the guest contains an oxygen atom. The mechanism for this is thought to be the injection of Bjerrum defects into the lattice by the formation of a transient guest-host hydrogen bond.18 CO2 hydrate is no exception, as the activation energy for water reorientation in CO2 hydrate was measured7 to be ∼35 kJ m-1, as compared to the value of ∼50 kJ m-1 in ice Ih and hydrates of nonpolar guests with no oxygen atom in the molecule.19 Conclusions A high-quality structural model was developed from singlecrystal X-ray diffraction data, giving guest locations and cage occupancies, and this has allowed the calculation of the composition and density of the hydrate crystal. A polynomial function was fit to data from a number of studies to obtain the thermal expansion of the CO2 hydrate lattice, and this property was found to be similar to that determined earlier for ethylene oxide hydrate. It is emphasized again that the structure of CO2 hydrate is both dynamic and disordered and that both aspects must be taken into account in order to arrive at structural models that are meaningful. Supporting Information Available: Tables of crystal data and structure refinement, bond lengths, isotropic displacement parameters, and structure factors (5 pages). This information is available free of charge via the Internet at http://pubs.acs.org.
4204 J. Phys. Chem. B, Vol. 105, No. 19, 2001 References and Notes (1) Kvenvolden, K. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 3420. (2) Proc. N.Y. Acad. Sci. 2000, 912. (3) Herzog, H.; Golomb, D.; Zemba, S. EnViron. Prog. 1991, 10, 64. Saji, A.; Yoshida, H.; Sakai, M.; Tanii, T.; Kamata, T.; Kitamura, H. Energy ConVers. Manage. 1992, 33 643. Nishikawa, N.; Morishita, M.; Uchiyama, M.; Yamaguchi, F.; Ohtsubo, K.; Hiraoka, R. Energy ConVers. Manage. 1992, 33, 651. (4) Brewer, P. G.; Friederich, G.; Peltzer, E. T.; Orr, F. M., Jr. Science 1999, 284, 943. (5) von Wroblewski, S. Comptes. Rendu. Acad. Sci. 1882, XCIV, 212. Villard, P. Ann. Chim. Phys., Ser. 7 1897, 11, 289. (6) Jeffrey, G. A. In ComprehensiVe Supramolecular Chemistry; Atwood, L. L., Davies, J. E. D., MacNicol, D. D., Vogtle, F., Eds.; Pergamon-Elsevier: Oxford, 1996; Vol. 6, p 757. (7) Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. 1986, 90, 1259. (8) Sum, A. K.; Burruss, R. C.; Sloan, E. D., Jr. J. Phys. Chem. B 1997, 101, 7371. (9) Ikeda, T.; Mae, S.; Uchida, T. J. Chem. Phys. 1998, 108, 1352. (10) Ripmeester, J. A.; Ratcliffe, C. I. Energy Fuels 1998, 12, 197.
Udachin et al. (11) Ikeda, T.; Yamamuro, Matsuo, T.; Mori, K.; Torii, S.; Kamiyama, T.; Izumi, F.; Ikeda, S.; Mae, S. J. Phys. Chem. Solids 1999, 60, 1527. (12) Henning, R. W.; Schultz. A. J.; Thieu, V.; Halpern, Y. J. Phys. Chem. B 2000, 104, 5066. (13) Fleyfel, F.; Devlin, J. P. J. Phys. Chem. 1988, 92, 631. (14) Sheldrick, G. M. Acta Crystallogr. 1990, A46, 467. (15) Bozzo, A. T.; Chen, H.-S.; Kass, J. R.; Barduhn, A. J. Desalination 1975, 16, 303. (16) Davidson, D. W.; Handa, Y. P.; Ripmeester, J. A. J. Phys. Chem. 1986, 90, 6549. Ripmeester, J. A.; Ratcliffe. C. I. J. Phys. Chem. 1988, 97, 337. Collins, M. J.; Ratcliffe, C. I.; Ripmeester. J. A. J. Phys. Chem. 1990, 94, 157. Tulk, C. A.; Ratcliffe, C. I.; Ripmeester, J. A. Geol. SurVey Can. Bull. 1999, 544, 251. (17) Tse, J. S.; McKinnon, W. R.; Marchi, M. J. Phys. Chem. 1987, 91, 4188. (18) Davidson, D. W. In Water. A ComprehensiVe Treatise; Franks, F. Ed.; Plenum: New York, 1973; Vol. 2, 115. (19) Davidson, D. W.; Ripmeester, J. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.; Academic Press: London, 1984; Vol. 3, p 69.
