Clathrate Hydrate Formation - American Chemical Society

Jun 15, 2009 - Steven F. Dec*. Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, Colorado 80401. ReceiVed: February 3, 2009;...
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J. Phys. Chem. C 2009, 113, 12355–12361

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Clathrate Hydrate Formation: Dependence on Aqueous Hydration Number Steven F. Dec* Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, Colorado 80401 ReceiVed: February 3, 2009; ReVised Manuscript ReceiVed: May 13, 2009

The formation of methane-ethane (C1-C2) clathrate hydrate was studied with high-resolution, solid-state 13 C NMR and density functional theory techniques. The 13C NMR experiments yield a number of significant findings: (1) the hydration number of C2(aq) is 26, (2) the initial quantity of C2-51262 sI hydrate cages outnumber C1-512 cages at 274 K, (3) C1-C2 sII hydrate forms at a C1-C2 gas phase composition where only sI hydrate is thermodynamically stable, (4) the initial composition of C1-C2 sII hydrate at 268 K contains less than the original amount of C1, (5) a quasi-liquid water layer solvating both C1 and C2 exists at 268 K, (6) any C1(qll) and C2(qll) present at 253 K is too small to be detected, (7) the initial amounts of C1-C2 sI and sII hydrates formed at 253 K are much smaller than those formed at 268 and 274 K, and (8) C1(aq), C2(aq) and C1(qll), C2(qll) facilitate the formation of C1-C2 sI and sII clathrate hydrate at 268 and 274 K, respectively. On the basis of these experimental observations, a model is developed that states that the aqueous hydration number of the most water-soluble clathrate hydrate former controls the structure of the clathrate hydrate that forms during the initial stages of the clathrate hydrate formation reaction. For methane-ethane clathrate hydrate, this means that ethane in a water liquid phase or quasi-liquid layer eliminates or adds two water molecules to its hydration shell to form the ethane-filled 51262 or 51264 cage building blocks of structure I or structure II clathrate hydrate, respectively. Density functional theory computations on methane-filled 512, 51262, and 51264 and ethane-filled 51262, 51263, and 51264 clathrate hydrate cages yield the stabilization energy of the gas-filled cages and provide theoretical evidence consistent with the experimentally based clathrate hydrate formation model. The proposed model is found to explain the results of other clathrate hydrate formation reactions. Introduction Many organic and inorganic molecules can react with water in its various phases to form a variety of clathrate hydrates.1 Clathrate hydrates are nonstoichiometric crystalline compounds that occur when water molecules hydrogen bond to each other to form a lattice that contains a set of cages that encapsulate small molecules, such as dihydrogen, methane, ethane, and carbon dioxide, to form structure I clathrate hydrate (sI hydrate)2 and structure II clathrate hydrate (sII),2 whereas larger molecules, such as adamantane, can form structure H clathrate hydrate (sH hydrate).3 Many clathrate hydrates form only at low temperatures and high pressures.2 The low-temperature condition potentially promotes the formation of metastable states presumably because of the energy cost required to rearrange hydrogen bonds in the relatively rigid water lattice and the slow rate of diffusion of the small guest molecules through the lattice. Clathrate hydrates formed from methane-ethane gas mixtures are particularly interesting. Pure methane and pure ethane each form sI hydrate.1 Certain mixtures of the two gases form sII hydrate4,5 over a substantial region of the pressure-composition phase diagram, Figures 1 and S1 (Supporting Information).6 For the compositions of this study, the most interesting region of the phase diagram is that near the lower sI-to-sII hydrate transition point, which occurs at about 72 mol % gas phase methane for temperatures near 274 K.4 Figures 1 and S1 (Supporting Information) show that the lower transition point occurs at a higher gas phase methane mole fraction as the temperature decreases. The water-lattice building blocks or * Corresponding author. E-mail: [email protected]. Phone: 303-384-2109. Fax: 303-273-3629.

Figure 1. Pressure versus methane gas phase mole fraction for methane-ethane clathrate hydrates at (a) 274, (b) 268, and (c) 263 K. Only the lower sI-to-sII transition is clearly shown on this scale. Figure S1 (Supporting Information) shows a similar plot expanded about 72 mol % CH4(g).

cages that form the cubic unit cells of sI and sII hydrates are depicted in Figure 2. The sI hydrate unit cell consists of two dodecahedra (512 cages) containing 20 water molecules and six tetrakaidecahedra (51262 cages) containing 24 water molecules.7 The sII hydrate unit cell consists of sixteen 512 cages and eight hexakaidecahedra (51264 cages) containing 28 water molecules.8 The first NMR study of methane-ethane sI and sII hydrates used hydrates synthesized from H2O(s).5 For methane-ethane compositions near the lower sI-to-sII transition point (Figures 1 and S1 (Supporting Information)), 13C NMR resonance lines from methane (C1) and ethane (C2) in both sI and sII hydrate phases were observed. Because the C1-C2 hydrates were synthesized from C1-C2 gas mixtures and H2O(s) in a closed

10.1021/jp9009977 CCC: $40.75  2009 American Chemical Society Published on Web 06/15/2009

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Figure 2. Number and structure of cages of sI and sII clathrate hydrate unit cells.

system in this case, one possible mechanism to explain the observations is that sI hydrate forms first, while denuding the gas phase of C2; sII hydrate forms when the C1 gas phase composition crosses the transition point where sII is the thermodynamically stable hydrate phase. Such a two-step process has been observed in the methane-propane system where sII hydrate forms until only methane remains in the gas phase to subsequently form methane sI hydrate.9 A two-step process cannot, however, provide a satisfactory explanation for the transient coexistence of sI and sII hydrates for single-component gas systems as observed in a Raman study of methane clathrate hydrate formation10 and a neutron diffraction study of the formation of carbon dioxide clathrate hydrate.11,12 In addition, nonequilibrium sI hydrate phases have been observed in the early stages of xenon13,14 and methane15 sI hydrate formation; that is, the ratios of 51262 to 512 cages occupied by the guests were smaller than equilibrium values. Similarly, nonequilibrium sII hydrate phases were observed at early reaction times in methane-propane sII hydrate.16 In all of these studies, the mechanisms responsible for the observations are not completely understood. In this work, experimental and computational studies are described that provide a basis for a plausible model for the simultaneous formation of methane-ethane sI and sII hydrates, one of which may be a metastable state. The proposed model is also consistent with the observations that methane preferentially occupies 512 cages in the early stages of methane sI hydrate formation15 and that propane occupies the 51264 cages more rapidly than C1 occupies the 512 cages in methane-propane sII hydrate.16 Elements of this model should be applicable to other reactions that occur at liquid-solid interfaces, studies of hydrophobic association of apolar molecules,17 and studies of incorporation of cations into interstitial sites in ice.18 Experimental Section Sample Preparation. The equipment and procedures used to synthesize the methane-ethane clathrate hydrate in a sealed glass ampule have been described.19,20 Briefly, powdered H2O(s) was initially reacted with a gas mixture consisting of 60% 13CH4 (99% 13C, Cambridge Isotope Laboratory) and 40% 13CH3CH3 (99% 13C at one carbon, Isotec). After initial hydrate formation and sealing of the ampule, the hydrate was melted and allowed to re-form while stored in a freezer at 253 K for 1 year. Complete details of the sample synthesis are provided in the Supporting Information. NMR Spectroscopy. All 13C magic-angle spinning (MAS) NMR spectra were recorded on a Chemagnetics Infinity 400 NMR spectrometer operating at 100.5 MHz for 13C. Unless otherwise stated, 1H decoupling fields of 50 kHz and MAS speeds of about 2 kHz were used. Unless stated otherwise, single-pulse excitation (90° pulse was 5 µs) and pulse delays

Figure 3. 13C MAS NMR spectra: (a) initial C1-C2 sI and sII hydrate at 253 K and (b) melted C1-C2 sI and sII hydrate at 291 K.

of 66 s were used to record fully relaxed spectra. As previously described,19,20 the methylene carbon resonance line of adamantane was used as an external chemical shift standard and was assigned a value of 38.83 ppm. The spectrometer was equipped with Chemagnetics solid-state MAS speed and temperature controllers. Temperature calibration at the position of the sample using methanol has been described.19 Computational Methods. The energy of various clathrate hydrate cage structures was calculated using the Amsterdam Density Functional theory software package ADF2007.01.21-23 All computations were performed using a tz2p basis set, the LDA energy functional, a large frozen core, and an integration accuracy of 4.0. All water oxygen atoms of the hydrate cages were fixed at their lattice positions as determined from X-ray analysis.7,8,24 Two hydrogen atoms were added to each oxygen atom with an O-H bond length of 97 pm and an initial H-O-H bond angle of 105°. The hydrogen atoms were rotated to maximize the number hydrogen bonds between neighboring oxygen atoms. The carbon atom of methane was initially placed at the center of each cage for which a calculation was performed. The center of the carbon-carbon bond of ethane was initially placed at the center of each cage, and the carbon-carbon bond was initially collinear with the longest cage axis for each calculation. The geometry of each gas-filled cage was optimized with the water oxygen atoms and water hydrogen atoms at their fixed positions. When the optimized geometry was used, a fragment analysis was performed for each gas-filled cage with C1 or C2 as one fragment; a second fragment consisted of all water molecules of the cage. The fragment analysis total bonding energy is the stabilization energy obtained by filling the cage with either C1 or C2 relative to the empty cage and gas at infinity. The final coordinates are provided for each C1-filled and C2-filled cage in the Supporting Information. The stabilization energy of H2O(aq) was computed using the Solvent Model provided with ADF2007.01.21-23 Results and Discussion Methane-Ethane Clathrate Hydrate NMR Spectroscopy. Figures 3, spectrum a, and S2 (Supporting Information) show the initial 253 K 13C MAS NMR spectrum of the C1-C2 hydrate to be discussed in this work. Seven 13C NMR resonance lines are observed and are assigned as follows: C2-51262 sI cage peak at 7.8 ppm,5,20 C2-51264 sII cage peak at 6.5 ppm,5,20,25 C2 gas phase peak (C2(g)) at 3.7 ppm,20 C1-512 sI and sII cage peak at -3.8 ppm,5,20,26 C1-51262 sI cage peak at -6.0 ppm,5,20,26 C1-51264 sII cage peak at -7.5 ppm,5,20,26 and C1 gas phase peak (C1(g)) at -10.6 ppm.19,20 Figures 3, spectrum b, and S3 (Supporting Information) show the 13C MAS

Clathrate Hydrate Formation

Figure 4. 13C MAS NMR spectra: (a) re-formation at 274 K of C1-C2 hydrate after 12 h, (b) re-formation at 268 K of C1-C2 hydrate, and (c) re-formation at 268 K of C1-C2 hydrate with only 11 kHz 1H decoupling during signal acquisition.

NMR spectrum of the C1-C2 hydrate after melting at 291 K. In addition to the dominant C2(g) and C1(g) peaks at about 3.7 and -10.6 ppm, respectively, low intensity peaks at 7.15 and -3.7 ppm are observed. The 13C resonance line at -3.7 ppm has previously been assigned to aqueous C1 (C1(aq)) with a hydration number of 20.27 The 13C resonance line at 7.15 ppm must be due to C2 in the aqueous phase (C2(aq)) and has a peak position about equidistant between the C2-51262 sI cage (24 water molecules) and the C2-51264 sII cage (28 water molecules). On the basis of the correlation between the 13C chemical shift of a hydrocarbon molecule in a hydrate cage and the number of water molecules forming the cage,28,29 the hydration number of C2(aq) is ∼26 (interpolation of the aqueous C2 13C peak position between the peak position of the C2-51262 and C2-51264 cages yields 25.7). This is the first experimental determination of this important parameter. Literature values for the hydration number of C2(aq) from a surface area calculation and Monte Carlo simulation are 2130 and 23,31 respectively, both lower than the new experimental result. Immediately after melting the sample, the C1(g) composition was 49.8% (Figure S3, Supporting Information), which corresponds to the region of the phase diagram where the thermodynamically stable C1-C2 hydrate phase is sI, Figures 1 and S1 (Supporting Information). Figures 4, spectrum a; S4 (Supporting Information); and S5 (Supporting Information) show 13 C MAS NMR spectra for two independent C1-C2 hydrate re-formation experiments obtained after the melted C1-C2 hydrate sample was cooled to 274 K in the MAS NMR probe. The appearance of peaks due to the C2-51262 sI cage at 7.8 ppm, the C1-512 sI cage at -3.7 ppm, and the C1-51262 sI cage at -6.0 ppm indicates C1-C2 sI hydrate re-formation; there is also intensity evident at the position of the C2(aq) resonance line at 7.15 ppm in Figure 4, spectrum a. The formation of C1-C2 sI hydrate is expected because, as shown in Figure S4 (Supporting Information), the C1(g) composition was 53.9 mol %, in the range where C1-C2 sI hydrate is thermodynamically stable, Figures 1, line a, and S1, line a (Supporting Information). The results of the more extensive set of 13C MAS NMR experiments on the re-formation from the melted state, Figures 3, spectrum b, and S3 (Supporting Information), of C1-C2 sI hydrate at 274 K, Figure S5 (Supporting Information), are shown in Figure 5 where the intensity of the C2-51262 resonance line, I(C2-51262), is plotted versus time. The C2-51262 intensity increases over the time scale of the experiment. Of more interest is the plot of the ratio of the C2-51262 intensity to the C1-512 intensity, I(C2-51262)/I(C1-512), versus time shown in Figure 6. A small, but significant, decrease of I(C2-51262)/I(C1-512)

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Figure 5. Plot of C2-51262 resonance line intensity versus time for re-formation of C1-C2 clathrate hydrate at 274 K (Figure S5, Supporting Information) and 253 K (Figure S8, Supporting Information) after melting at 291 K. Each spectrum required 32 min to record. Time values are assigned as the midpoint of the time required to record each spectrum; for example, spectrum 1 is 16 min, spectrum 2 is 16 + 32 min, and so on. Symbols: ([) 274 K and (9) 253 K.

Figure 6. Plot of I(C2-51262)/I(C1-512) ratio versus time for re-formation of C1-C2 clathrate hydrate at 274 K (Figure S5, Supporting Information) after melting at 291 K. Each spectrum required 32 min to record. Time values are assigned as the midpoint of the time required to record each spectrum; for example, spectrum 1 is 16 min, spectrum 2 is 16 + 32 min, and so on.

is observed, suggesting that C2-51262 cages outnumber C1-512 cages at early stages of the clathration reaction. Figures 4, spectrum b, and S6 (Supporting Information) show the 13C MAS NMR spectrum recorded of the sample shown in Figure 4, spectrum a, about 6 h after the temperature of the probe was decreased from 274 to 268 K. The appearance of the peak at 6.5 ppm (Figures 4, spectrum b, and S6 (Supporting Information)) due to the C2-51264 sII cage shows that C1-C2 sII hydrate formed at 268 K even though, as indicated in Figure S6 (Supporting Information), the C1(g) composition of 59.3 mol % is well within the range where only sI hydrate is thermodynamically stable, Figures 1, line b, and S1, line b (Supporting Information). Comparison of Figures 3, spectrum a (or S2, Supporting Information), and S6 (Supporting Information) clearly shows that the system has not returned to its initial state, and therefore, excess H2O(s) must be present. Intensity is also evident in Figure 4, spectrum b, at the position assigned to C2(aq), indicating that a premelting or quasi-liquid water layer (H2O(qll))32 exists at 268 K. The peaks due to C1 and C2 in the quasi-liquid water layer, C1(qll) and C2(qll), respectively, are clearly seen in Figure 4, spectrum c, where the result expected when the 1H decoupling field is decreased to 11 kHz is observed; that is, the C1 and C2 sI and sII hydrate peaks are

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Figure 8. 13C MAS NMR spectrum after re-formation for 7.5 h at 253 K of C1-C2 hydrate with only 11 kHz 1H decoupling during signal acquisition. Figure 7. Plot of C2-51262 and C2-51264 resonance line intensity versus time for re-formation of C1-C2 clathrate hydrate at 268 K (Figure S7, Supporting Information) after re-formation at 274 K (Figure S5, Supporting Information). Each spectrum required 32 min to record. Time values are assigned as the midpoint of the time required to record each spectrum; for example, spectrum 1 is 16 min, spectrum 2 is 16 + 32 min, and so on. Symbols: ([) C2-51262 and (9) C2-51264.

severely broadened, whereas the quasi-liquid layer and gas phase C1 and C2 peaks remain sharp. Figure S7 (Supporting Information) shows a more extensive set of time-dependent 13C MAS NMR spectra obtained when the temperature of the sample used to obtain the final spectrum of Figure S5 (Supporting Information) was decreased from 274 to 268K. The C2-51262 and C2-51264 resonance line intensities plotted versus time in Figure 7 clearly show that both C1-C2 sI and sII clathrate hydrates continuously form over the course of the experiment even though the C1(g) mol % was 58.2 and 59.8% at 0.5 and 5.6 h, respectively, where Figures 1, line b, and S1, line b (Supporting Information), indicate that C1-C2 sI clathrate hydrate is the only thermodynamically stable phase. Because of the finite solubility of C1(g) and C2(g) in water, the observation of C1(aq) and C2(aq) during the re-formation of C1-C2 clathrate hydrate at 274 K, as shown in Figure 4, spectrum a, is expected. The persistence of C1(qll) and C2(qll) in a quasi-liquid layer during the re-formation of C1-C2 clathrate hydrate, Figure 4, spectra b and c, suggests that C1(aq), C2(aq) and C1(qll), C2(qll) may play a central role in the formation of C1-C2 sI and sII clathrate hydrates. To investigate this hypothesis further, the C1-C2 clathrate hydrate sample was, again, completely melted at 291 K, Figures 3, spectrum b, and S3 (Supporting Information), and then 13C MAS NMR spectra were recorded as a function of time after the probe was cooled to 253K, Figure S8 (Supporting Information). Only C1-C2 sI hydrate was observed to form (Figure S8, Supporting Information), and on the basis of a comparison of the C2-51262 resonance line intensities obtained at 253 and 274 K, Figure 5, the amount of C1-C2 sI hydrate formed at 253 K is significantly smaller than that observed to form at 274 K. Figure 8 shows the 13C MAS NMR spectrum recorded at 253 K with 11 kHz 1 H decoupling that shows only C1(g), C2(g), and C2 liquid phase (C2(l))33 peaks, indicating that the intensity of any C1(qll) and C2(qll) resonance line at 253 K is much smaller than that observed at 268 K. Comparison of the C1-C2 clathrate hydrate re-formation experiments performed at 253, 268, and 274 K suggests that higher concentrations of C1(qll), C2(qll) or C1(aq), C2(aq) species at 268 and 274 K, respectively, facilitate the more extensive formation of C1-C2 sI and sII clathrate hydrates at these higher temperatures. The 13C MAS NMR spectra of Figures 3 and 4 and the Supporting Information yield eight significant results: (1) the

hydration number of C2(aq) is 26, (2) the initial quantity of C2-51262 sI hydrate cages outnumber C1-512 cages at 274 K, (3) C1-C2 sII hydrate forms at a C1-C2 gas phase composition where only sI hydrate is thermodynamically stable, (4) the initial composition of C1-C2 sII hydrate at 268 K contains less than the original amount of C1, (5) a quasi-liquid water layer solvating both C1 and C2 exists at 268 K, (6) any C1(qll) and C2(qll) present at 253 K is too small to be detected, (7) the initial amounts of C1-C2 sI and sII hydrates formed at 253 K are much smaller than those formed at 268 and 274 K, and (8) C1(aq), C2(aq) and C1(qll), C2(qll) facilitate the formation of C1-C2 sI and sII clathrate hydrate at 268 and 274 K, respectively. Methane-Ethane Clathrate Hydrate Formation Model. Any model used to interpret the experimental results presented in this work must take into consideration the characteristic time span of experiments. Two models, the labile cluster model34-38 and the local structure model,39-41 have been developed to describe clathrate hydrate nucleation from water and the clathrate hydrate guest molecule, whereas only a conceptual model of clathrate hydrate growth on an existing clathrate hydrate crystal has been proposed.42,43 The time scale of the NMR experiments presented here is too long to observe clathrate hydrate nucleation other than to provide an approximate time of its occurrence as manifested in the appearance of a 13C resonance line at a clathrate hydrate peak position. Nucleation of C1-C2 sI and sII hydrate crystals must occur, but only C1-C2 sI and sII hydrate growth is measured in the NMR experiments described in this work. The observation that significant amounts of C1-C2 sI and sII hydrates form at 268 and 274 K where either C1(qll), C2(qll) or C1(aq), C2(aq), respectively, are simultaneously observed compared to the much smaller amount of C1-C2 sI and sII hydrate formed at 253 K, where no C1(qll) or C2(qll) is observed, suggests that an aqueous phase or quasi-liquid layer phase solvating C1(g) and C2(g) plays a significant role in the early stages of C1-C2 sI and sII hydrate formation. The observation that C2-51262 and C2-51264 cages initially outnumber C1-filled cages suggests that the formation of C1-C2 sI and sII hydrates is primarily controlled by the formation of C2-51262 and C2-51264 cages, respectively. Inspection of any of the 13C MAS NMR spectra reported in this work shows no evidence of any mobile C1 and C2 species other than those assigned to C1(g), C2(g), C1(aq), C2(aq), C1(qll), and C2(qll); that is, for example, no mobile species, such as a C2(qll) species with a hydration number of 24, is observed. This means that such species do not exist or have too low a concentration to be detected with 13C MAS NMR. Finally, note that C2 is about 1.7 times more soluble in water than C1 at 275 K.44 A model to describe the early stages of C1-C2 sI and sII hydrate formation consistent with experimental results reported

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above is provided in the following chemical equations and discussion

C2(g) + 26H2O(qll) f C2 · (H2O)26(qll)

(1)

C2 · (H2O)26(qll) f C2 · (H2O)26(ice surface)

(2)

C2 · (H2O)26(ice surface) f C2 · (H2O)24(sI 51262) + 2H2O(qll) (3) C2 · (H2O)26(ice surface) + 2H2O(qll) f C2 · (H2O)28(sII 51264) C1(g) + 20H2O(qll) f C1 · (H2O)20(qll)

(4) (5)

20H2O(qll) + C2 · (H2O)24(sI 51262) f C1-C2(partial sI hydrate unit cell) (6) 20H2O(qll) + C2 · (H2O)28(sII 51264) f C1-C2(partial sII hydrate unit cell) (7) Cl · (H2O)20(qll) + C2 · (H2O)24(sI 51262) f C1-C2(partial sI hydrate unit cell) (8) Cl · (H2O)20(qll) + C2 · (H2O)28(sII 51264) f C1-C2(partial sII hydrate unit cell) (9) The number of water molecules contained in each structure is now explicitly shown, and the notation CJ · (H2O)n indicates that gas CJ has a hydration shell or cage of nH2O molecules. For simplicity, the model of eqs 1-9 is described for ice surfaces (temperatures less than or equal to 273 K), but clathrate hydrate surfaces are also applicable. A structure such as C2 · (H2O)26(ice surface) of eq 2 is not assigned to any resonance line in any 13 C NMR spectrum reported in this work. Any such resonance line would be difficult to detect with 13C MAS NMR because it would be low in concentration (a surface site) and its 13C MAS NMR resonance line would probably be broad due to the disordered nature of the “liquid-like” surface site hydration shell; hence, these types of structures shown in eqs 1-9 should be considered hypothetical structures. Because of its larger solubility, C2(g) more readily dissolves in the quasi-liquid layer, H2O(qll) of H2O(s), eq 1. The C2 · (H2O)26(qll) molecule diffuses to the ice surface while maintaining its average hydration number of 26. The C2 · (H2O)26(qll) molecule becomes immobilized for some period of time at the ice surface when some of the water molecules at the ice surface become part of the hydration shell of C2 · (H2O)26(qll), eq 2. The C2 · (H2O)26(ice surface) structure immobilized at the ice surface can lose or gain two H2O molecules to form C2 · (H2O)24(sI 51262) cages, eq 3, or C2 · (H2O)28(sII 51264) cages, eq 4, respectively. C1(g) can also dissolve in H2O(qll) to form C1 · (H2O)20(qll), eq 5. During the time that the C2 · (H2O)24(sI 51262) cages are immobilized at the ice surface, additional H2O(qll) molecules or C1 · (H2O)20(qll) may bind to the C2 · (H2O)24(sI 51262) cage to form a partial sI unit cell, eqs 6 and 8, which can continue to grow to form a C1-C2 sI clathrate hydrate phase. Alternatively, during the time

TABLE 1: Stabilization Energy of C1-Filled and C2-Filled Clathrate Hydrate Cages structure

Nw

Es (kJ mole-cage-1)

C1-512 C1-51262 C1-51264 C2-51262 C2-51263 C2-51264 H2O(aq)

20 24 28 24 26 28

-37.70 -23.83 -17.87 -48.02 -40.41 -34.43 -22.05a

a Es of H2O(aq) is relative to the isolated water molecule and the water molecules solvating that water molecule at infinity.

that the C2 · (H2O)28(sII 51264) cages are immobilized at the ice surface, additional H2O(qll) molecules or C1 · (H2O)20(qll) may bind to the C2 · (H2O)28(sII 51264) cage to form a partial sII unit cell, eqs 7 and 9, which can continue to grow to form a C1-C2 sII clathrate hydrate phase. The NMR results show that addition of empty 512 cages to the C2 · (H2O)24(sI 51262) and C2 · (H2O)24(sI 51262) cages dominates the early stages of the C1-C2 sI and sII hydrate formation. Methane-Ethane Clathrate Hydrate Computations. The results of density functional theory computations provide evidence consistent with the methane-ethane clathrate hydrate formation model described in eqs 1-9. Figures S9-S14 (Supporting Information) show models of C1-filled and C2filled cage structures generated with ADF2007.01.21-23 Table 1 summarizes the stabilization energy, Es, for each gas-filled cage calculated in this study. The number of water molecules contained in each cage is Nw. Table 1 and Figure S15 (Supporting Information) indicate that |Es| decreases as the size of the cage increases for both C1-filled and C2-filled cages, indicating that, for a given guest, a larger gas-filled cage is less stable. Also note that a C2-filled cage is more stable than a C1-filled cage for which direct comparison is possible. The Es values agree well with literature values for the C1-512 and C1-51262 cages.45,46All the Es values are small and on the order of 1-2 times the Es value for H2O(aq). A fundamental hypothesis of the clathrate hydrate formation model of eqs 1-9 is that the hydration number of the most soluble clathrate hydrate-forming species present is the controlling factor regarding the type of clathrate hydrate structure formed in the early stages of the reaction. If care is taken to understand that the rigid structure depicted in Figure S13 (Supporting Information) does not exist in a liquid phase or quasi-liquid layer, we can choose the Es value of C2-51263 to represent the Es value of C2 · (H2O)26 in any phase. Although this approximation is very crude, it does permit relatiVe energy changes to be calculated and compared for various clathrate hydrate reactions. Thus, the change in energy, ∆E, for the reactions of eqs 3 and 4 can be calculated as follows

∆Ε(eq 3) ) Es[C2 · (H2O)24(sI 51262)] + 2Εs[H2O(aq)] - Es[C2 · (H2O)26(ice surface)] ) -52 kJ mol-cage-1

(10)

∆Ε(eq 4) ) Es[C2 · (H2O)28(sII 51264)] Εs[C2 · (H2O)26(ice surface)] - 2Es[(H2O)(aq)] ) + 50 kJ mol-cage-1

(11)

Equations 10 and 11 show that the energy change to subtract or add two H2O molecules, respectively, to the hydration shell

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of C2 · (H2O)26 is approximately the energy required to hydrate or dehydrate two H2O molecules, respectively. The absolute values of these two energy changes are also about equal to the stabilization energy per H2O molecule computed for the empty 512 cage.45 Even with the approximate nature of the calculations, eqs 10 and 11 provide insight regarding the clathrate hydrate formation process. Formation of the sI hydrate building block, the C2-51262 cage, is energetically more favorable than the corresponding sII hydrate building block, the C2-51264 cage, consistent with NMR results shown in Figure 4. The energetics for eq 11 suggest that fusion of additional cages, such as empty 512 or C1-512 cages to the C2-51264 cage, is needed to stabilize the C2-51264 cage; Khan45 has shown that fusion of two dodecahedra yields a stabilization energy of 80-100 kJ mol-1. The NMR results indicate that the stabilization energy due to fusion of empty 512 cages45 is sufficient to stabilize the C2-51264 cage at early stages of the reaction and permit subsequent growth of the sII unit cell. Other Clathrate Hydrates. The model presented above to describe the formation of both C1-C2 sI and C1-C2 sII clathrate hydrates is also consistent with the observation that C1-512 cages outnumber the C1-51262 cages during the early stages of C1 sI clathrate hydrate formation.15 On the basis of the model proposed in this work, the larger number of the C1-512 cages is due to two reasons. First, the hydration number of C1 is 20,27 and therefore, C1 · (H2O)20(qll) only needs to diffuse to the ice surface and become immobilized to form a C1-512 cage. Second, to form a C1-51262 cage, four water molecules must be added to C1 · (H2O)20(ice surface) as follows

C1 · (H2O)20(ice surface) + 4H2O(aq) f C1 · (H2O)24(sI 51262)

(12)

If we are, again, careful to understand that Es calculated for C1-512 (Figure S9, Supporting Information) corresponds to a rigid structure that does not exist in a liquid phase or quasiliquid layer, then we can choose Es of C1-512 to represent the stabilization energy of C1 · (H2O)20 in any phase, and using the other Es values of Table 1, the energy change for eq 12 is ∆E(eq 12) ) +102 kJ mole-cage-1. This ∆E value is relatively large and unfavorable and is approximately equal to the energy needed to dehydrate the four water molecules that are added to form the C1-51262 sI cage. On the basis of these results and considering that it must also take a finite amount of time to add four water molecules to C1 · (H2O)20(ice surface), it is not surprising that C1-512 cages predominate at the early stages of C1 sI clathrate hydrate formation. Similar arguments explain the rare occurrence of C1 sII hydrate.10 In this case, eight water molecules must add to C1 · (H2O)20(ice surface) to form C1 · (H2O)28(sII 51264) as follows

C1 · (H2O)20(ice surface) + 8H2O(aq) f C1 · (H2O)28(sII 51264)

(13)

The energy change, ∆E(eq 13) ) +196 kJ mole-cage-1, approaches that for a weak covalent bond. In addition to the unfavorable energetics and as has been suggested by others,10 the large number of water molecules that must be added to the C1 · (H2O)20(ice surface) structure to form the C1-51264 cages is probably limited by the kinetics of the reaction. The observation that the ratio of the propane-filled 51264 cages to the methane-filled 512 cages in methane-propane sII hydrate

in the early stages of reaction16 is also explained by the clathrate hydrate formation model proposed in this work. The solubility of propane is about 1.6 times that of methane in water at 273 K,47 and a surface area calculation30 and a Monte Carlo simulation31 show that the aqueous hydration number of propane is near the 28 water molecules that form a 51264 cage. Thus, it is, again, not very surprising that propane-filled 51264 cages should preferentially form from a methane-propane gas mixture in contact with ice. Conclusions The formation of both structure I and structure II clathrate hydrates was observed using 13C MAS NMR for methane-ethane gas mixture where only structure I clathrate hydrate is thermodynamically stable. The hydration number of aqueous ethane was experimentally determined for the first time and found to be 26. On the basis of these experimental observations, a model was developed where the aqueous hydration number of the most water-soluble clathrate hydrate former controls the structure of the clathrate hydrate that forms during the initial stages of the clathrate hydrate formation reaction. Density functional theory computations provide theoretical evidence consistent with the proposed model. Acknowledgment. This work was partially fund by NSF Grant No. CTS-0419204. Kristen E. Bowler and Laura L. (Stadterman) Roberts synthesized the methane-ethane clathrate hydrate used in this study. I thank Travis Jones for advice regarding the density functional theory computations. Supporting Information Available: Methane-ethane clathrate hydrate synthesis details; full-scale 13C MAS NMR spectra of methane-ethane clathrate hydrate at various temperatures, including integrated intensities; gas-filled clathrate cage density functional theory stabilization energies versus average cage radius; and gas-filled clathrate cage density functional theory generated figures and final coordinates. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) von Stackelberg, M.; Muller, H. R. Z. Elektrochem. 1954, 58, 25– 39. (2) Davidson, D. W. Clathrate Hydrates. In Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, pp 115-234. (3) Ripmeester, J. A.; Tse, J. S.; Ratcliffe, C. I.; Powell, B. M. Nature 1987, 325, 135–136. (4) Hendriks, E. M.; Edmonds, B.; Moorwood, R. A. S.; Szczepanski, R. Fluid Phase Equilib. 1996, 117, 193–200. (5) Subramanian, S.; Kini, R. A.; Dec, S. F.; Sloan, E. D., Jr. Chem. Eng. Sci. 2000, 55, 1981–1999. (6) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: New York, 2008; pp 299-302 and included CSMGem software package. (7) McMullan, R. K.; Jeffrey, G. A. J. Chem. Phys. 1965, 42, 2725– 2732. (8) Mak, T. C. W.; McMullan, R. K. J. Chem. Phys. 1965, 42, 2732– 2737. (9) Uchida, T.; Moriwaki, M.; Takeya, S.; Ikeda, I. Y.; Ohmura, R.; Nagao, J.; Minagawa, H.; Ebinuma, T.; Narita, H.; Gohara, K.; Mae, S. AIChE J. 2004, 50, 518–523. (10) Schicks, J. M.; Ripmeester, J. A. Angew. Chem., Int. Ed. 2004, 43, 3310–3313. (11) Klapproth, A.; Goreshnik, E.; Staykova, D.; Klein, H.; Kuhs, W. F. Can. J. Phys 2003, 81, 503–518. (12) Staykova, D. K.; Kuhs, W. F.; Salamatin, A. N.; Hansen, T. J. Phys. Chem. B 2003, 107, 10299–10311. (13) Pietrass, T.; Gaede, H. C.; Bifone, A.; Pines, A.; Ripmeester, J. A. J. Am. Chem. Soc. 1995, 117, 7520–7525. (14) Moudrakovski, I. L.; Sanchez, A. A.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. B 2001, 105, 12338–12347.

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