J. Phys. Chem. C 2007, 111, 2341-2346
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NMR Investigation of Methane Hydrate Dissociation Arvind Gupta, Steven F. Dec,* Carolyn A. Koh, and E. D. Sloan, Jr. Center for Hydrate Research, Colorado School of Mines, Golden, Colorado 80401 ReceiVed: October 4, 2006; In Final Form: NoVember 15, 2006
The methane hydrate dissociation mechanism was studied on the molecular scale using 13C magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy. Analysis of time-resolved 13C MAS NMR spectra for methane Structure I (sI) hydrate dissociation obtained by raising the temperature above the hydrate equilibrium conditions permitted the cage occupancy and pressure to be determined during this process. The relationship between NMR methane gas chemical shift, pressure, and temperature was developed, which allows estimating the system pressure in the sealed glass tube sample at any temperature. The large to small cage occupancy ratio remained constant during hydrate dissociation suggesting that there is no preferential dissociation of hydrate cavities and the whole unit cell decomposes during dissociation. This decomposition rate is virtually the same for both the large and the small cages in methane hydrate on a per cage basis. The similar decomposition rate of both cage types shows that the sI methane hydrate dissociation mechanism differs from the formation process where preferential formation of specific hydrate cages has been observed.
Introduction Gas clathrate hydrates are naturally occurring icelike crystalline solids in which gas molecules are trapped in a network of hydrogen-bonded water cavities. There are three common types of gas hydrate structures: cubic structure I (sI), cubic structure II (sII), and hexagonal structure H (sH).1 The type of hydrate structure depends on the guest molecule(s), pressure, and temperature. Each crystal unit cell consists of two or more types of hydrogen-bonded water cavities and the distribution of guest molecules in the cages is a strong function of the system pressure and temperature. For this study, methane hydrate was used, where sI is the stable structure. The cubic unit cell of sI methane hydrate consists of two pentagonal dodecahedral cavities (512) and six tetrakaidecahedral cavities (51262). Naturally occurring methane hydrates present a potential future energy resource due to their significant abundance in oceanic and permafrost geological settings. Natural deposits of gas hydrates are estimated to contain significant amounts of hydrocarbons (mainly methane), on the order of 1-5 × 1015 m3 at standard temperature and pressure (STP).2 Recovery of even a small fraction of methane contained within these natural hydrate deposits would provide an alternative energy resource. In order to produce natural gas from these hydrate deposits or prevent hydrate plugs from forming in gas/oil flow lines, an understanding of the hydrate formation and dissociation on both the microscopic and macroscopic scales is important. Various researchers have studied hydrate formation kinetics using gas consumption measurements as a function of time in liquid water and gas systems.3,4 The time-dependent hydrate formation process was characterized by nucleation (induction time) and growth periods. However, no molecular-scale information could be obtained from these macroscopic experiments, such as the rate of formation of the hydrate cavity type (512, 51262, and 51264), or the presence of any precursors before hydrate nucleation. Raman and NMR spectroscopy have been * To whom correspondence should be addressed. E-mail: sdec@ mines.edu, Phone: (303)-384-2109, Fax: (303)-273-3629.
used to study the molecular-scale hydrate formation processes. Time-resolved hydrate formation experiments have been performed to detect any changes in the hydrate structure and the distribution of methane in the hydrate cages during formation. Applying Raman spectroscopy, Subramanian et al.5 found that the formation of the large 51262 cages from liquid water may be rate limiting during sI methane hydrate formation. Hyperpolarized 129Xe NMR spectroscopy studies have also shown that more 512 cages (so-called precursors) are present in the early stage of hydrate formation formed from ice.6 These results suggest that hydrate cavities have different formation rates and that hydrate formation mechanism and kinetics can be determined on the microscopic scale. In contrast, there have been limited reports explaining the hydrate dissociation mechanism on the microscopic scale, that is, what is the dissociation rate of different hydrate cavities. Commonly, the hydrate dissociation is modeled as a heat-transfer process (analogous to ice melting), in which heat is supplied to dissociate the hydrogen bonds between water molecules associated with hydrate cavities.7-9 In a heat-transfer limited process, there is no measurable intermediate or activated state between the reactant (hydrate) and product (ice/water and gas), and the process is controlled by the rate of heat supplied to the system. Bishnoi and co-workers developed an intrinsic Arrheniustype kinetic rate equation for hydrate dissociation.10,11 From macroscopic hydrate dissociation data at different temperatures, they determined the values of the pre-exponential frequency factor (Ko) and activation energy (Ea) for pure and binary hydrate systems.11,12 For methane hydrate decomposition, the reported Ea and Ko values are equal to 81 kJ/gas mol and 3.6 × 104 mol/m2-Pa-s, respectively.13 Moudrakovski and co-workers estimated the activation energy to be equal to 37 ( 7 kJ/mol gas for dissociation of 129Xe hydrate using NMR.6 The hydrate decomposition rate was measured from the decay of the 129Xe NMR peak intensities in the hydrate phase at different temperatures, but no information was provided for the relative dissociation rate of the large and the small cages. The reason behind the difference in the reported activation values of CH4
10.1021/jp066536+ CCC: $37.00 © 2007 American Chemical Society Published on Web 01/18/2007
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Figure 1. (a) The pyrex glass tube with a brass fitting used to prepare the NMR sample. (b) Zirconium rotor and sealed glass sample cell assembly. (c) Nonspinning sample cell connected to pressure gauge.
and Xe hydrate decomposition is not understood; both molecules have comparable molecular diameters and form structure I hydrate.1 In essence, the following questions arise, such as “If kinetics is the dominant mechanism, what is the activated state during hydrate dissociation and what is the physical interpretation of kinetic parameters, Ko and Ea?” or “What is the role of the guest molecule during hydrate dissociation?” Molecular dynamics simulations have been applied to study methane sI hydrate dissociation at the hydrate/gas interface. The molecular simulations have shown that for methane sI hydrate dissociation there is neither evidence of clathrate-like clusters nor clusters of structured water molecules.14 In a separate molecular dynamics simulation, the partial cavities were found to exist during methane sI hydrate dissociation with a pentagonal dodecahedral cavity being the last structure left before melting was completed.15 Moridis and co-workers9 suggested that the knowledge of the dissociation reaction kinetics and importance of heat transfer is of critical importance to reliably predicting the gas production potential of natural gas hydrate deposits. The objective of the present study is to investigate the microscopic hydrate dissociation mechanism and relate this to the macroscopic dissociation data. Raman and NMR spectroscopy are two of the principal experimental techniques used to obtain in situ molecular-scale hydrate properties such as structure type and cage occupancy (hydration number).5,6,16-18 Because of its inherent quantitative nature, NMR is the preferred method. Temperature control of the NMR samples is readily regulated in these systems, but pressure measurements have been limited to low-resolution, nonspinning NMR experiments where a pressure gauge can be
connected to the sample container via some type of tubing. To date, MAS NMR of gas hydrate systems has been performed only with open systems, usually at very low temperature,16,17 or on closed systems where the pressure is not very well known.18 The inability to determine the pressure of gas hydrate samples in sealed samples has greatly limited the knowledge of where on the phase diagram the MAS NMR experiments of methane sI hydrates are performed. As a result, the distribution of methane in the sI hydrate cages in the methane-water phase diagram is often not well known because the severe overlap of the methane resonance lines without MAS limits the accuracy of cage occupancy measurements.19 In this work, 13C MAS NMR spectroscopy was used to provide molecular-scale experimental evidence during hydrate dissociation in order to increase our understanding of the hydrate dissociation mechanism. Specifically, 13C MAS NMR spectra obtained as a function of time permitted the assignment of the hydrate structure and the quantitative measurement of the distribution of methane in the 512 and 51262 cavities during dissociation. Development of a simple chemical shift-referencing scheme provided accurate measurements of the high pressures in this system. Experimental Section Hydrate Sample Preparation. The sample was prepared in a pyrex glass tube with a constriction at one end that defines the sample bulb, as shown in Figure 1a. A brass 0.125-cm Swagelok fitting was glued to the glass tube using epoxy. The volumes of the bulb and tube were approximately 0.2 and 1.0
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cm3, respectively. About three-quarters of the bulb was filled with sieved granular ice (250-500 µm), and the tube was pressurized to about 5.0 MPa with enriched 13CH4 gas (99%, Cambridge Isotopic Laboratory). During hydrate formation the pressure drop was measured within (0.007 MPa using a Sensotec pressure transducer. After pressurizing, the tube was placed in temperature bath, set at 271 K, for 1 day. The bath temperature was then increased to 273 K and the temperature was maintained within (0.1 K of the ice point until all the ice converted into hydrate as evidenced by a final stable pressure reading of the pressure transducer (typically over 5-7 days). After methane hydrate formation reached completion, the free gas was removed from the glass tube using a vacuum pump, keeping the hydrate portion submersed in liquid nitrogen. The glass bulb, with the hydrate portion submerged in liquid nitrogen, was sealed using a flame torch and transferred to a freezer at a constant temperature of 253 K. Some hydrate invariably melts during the sealing procedure yielding an unknown amount of methane in the gas phase of the sealed sample. NMR Spectroscopy. All 13C MAS NMR spectra were recorded on a Chemagnetics Infinity 400 NMR spectrometer operating at 100.5 MHz for 13C. Proton-decoupling fields of 50 kHz and MAS speeds of about 2 kHz were used. Two different types of 13C MAS NMR spectra were obtained. Standard single-pulse excitation (90° pulses of 5 µs) and pulse delays of 20 s were used to record high signal-to-noise ratio spectra at various temperatures. Time-resolved 13C MAS NMR spectra were recorded with single-pulse excitation (45° pulses of 2.5 µs) and pulse delays of 5 s in the hydrate dissociation experiment. Taking into account the acquisition time of 0.2048 s, the time resolution in the time-resolved 13C MAS NMR experiment was TR ) 5.2048 s. In an independent experiment, spin-lattice relaxation times (T1) were measured at 270 K using an inversion-recovery pulse sequence. The T1 values are 2.51 ( 0.12, 2.29 ( 0.08, and 0.43 ( 0.08 s for the small cage, large cage, and gas phase, respectively. Under the conditions of the time-resolved 13C MAS NMR experiment the magnetization M(TR) is given by20
1 - e-TR/T1
M(TR) ) Meq 1 - cos(45°)e-TR/T1
(1)
Meq is the equilibrium magnetization. M(TR) reached its steady state value after about five pulse repetitions. The external chemical shift reference was adamantane, and its 13C MAS NMR spectrum was measured simultaneously with the methane hydrate sample. The methylene carbon resonance line of adamantane was assigned a value of 38.834 ppm (see below). Temperature Calibration. The spectrometer is equipped with a Chemagnetics solid-state temperature controller. Cold air was supplied to the heater circuit using a FTS Systems XR 401 Air Jet Crystal Cooler equipped with TC84 temperature controller, AF6 flow regulator, and AD80 dryer. Methanol was used to calibrate the sample temperature.21 Because of the small sample size (∼50 mg), the temperature gradients across the sample are negligibly small. Independent temperature ramps using the temperature standard methanol showed that the sample reached thermal equilibrium in about 80 s. Gas-Phase Pressure Measurements. The 13C chemical shift of 13C-enriched methane was measured as a function of pressure and temperature in the gas phase using a modified version of an NMR probe described elsewhere.19,22 The main modifications
Figure 2. The slope of the 13CH4 gas pressure-chemical shift relation as a function of temperature.
are the replacement of the metal Swagelok connectors and stainless steel tubing with 0.0625 cm ChromTech fittings and Tefzel tubing. Figure 2 compares the results of the literature22,23 with those obtained in this work. The results from this work are summarized in the following expression
P ) (δ - δo) (0.0593T - 7.05)
(2)
P (MPa) is the pressure, T (K) is the temperature, δ (ppm) is the observed 13C chemical shift, and δo ) -10.84 ppm is the temperature-independent 13C chemical shift of methane gas at P ) 0 MPa.23 Equation 2 can be used to calculate the pressure from the 13C δ value of methane in the gas phase of sealed methane sI hydrate samples if this δ value can be determined. Because there is no reliable 13C internal chemical shift reference present in the sealed methane hydrate samples, an external chemical shift reference must be used. The choice of an external chemical shift reference generally requires that the observed chemical shifts of the sample and reference material be corrected for bulk diamagnetic susceptibility effects, which are sample composition and container shape dependent.24 To circumvent the need for this correction, we measured the 13C chemical shift of the methylene carbons of external adamantane relative to a methane gas sample at the magic angle, with a pressure of 0.165 MPa at 298 K with the nonspinning system shown in Figure 1c. The sample containers of parts b and c of Figure 1 are both cylinders, and because the bulk diamagnetic susceptibility correction of a cylindrical sample at the magic angle is zero,24 the bulk diamagnetic susceptibility correction does not need to be known. The observed 13C chemical shift of the methylene carbons of adamantane measured with this system is 38.834 ppm relative to the gas-phase 13C methane resonance line includes the bulk diamagnetic susceptibility correction for adamantane, which is a constant for all experiments described in this work. To employ the pressure dependence of the 13C chemical shift of methane in the gas phase the following expression was used to correct the observed slopes of the pressure versus chemical shift lines24
( ) ( ) ∂δMA ∂P
)
T
∂δper ∂P
T
+
χM 6RT
(3)
In eq 3 δMA is the observed chemical shift measured with a cylindrical sample at the magic angle, δper is the observed chemical shift measured with a cylindrical sample perpendicular to the applied field, and χM is the molar diamagnetic susceptibil-
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Figure 3. 100.5-MHz time-resolved 13C MAS NMR of sI methane hydrate dissociation during the temperature ramp from 269 to 271 K. Timeresolution was 5.2048 s, but only every fifth spectrum is plotted here.
ity. Equation 3 assumes that methane gas has ideal gas behavior at the pressures of interest in this work. For methane gas χM ) -33.8 ppm cm3 mol-1.25 Results and Discussion The 13C MAS NMR spectrum of methane sI hydrate with the adamantane external reference recorded at 253 K showed five different 13C resonance lines. The two different 13C resonance lines from adamantane are observed at about 38.8 and 29.9 ppm, while the resonance lines at -3.80, -6.13, and -10.57 ppm are due to methane in the small (512) and large (51262) hydrate cages and the gas phase, respectively.26 The large cage peak is more intense than the small cage peak, indicating that more CH4 occupies large cages than the small cages. The methane gas peak has a line width, about 3 Hz, that is limited by the acquisition time of the experiment. The pressure inside the sealed tube was calculated from the methane gas-phase chemical shift at 253 K and eq 2 and found to be 2.10 ( 0.20 MPa indicating the hydrate should be stable up to 267 ( 3.0 K; the methane hydrate equilibrium pressure is 2.09 MPa at 267 K.27 Similarly, 13C MAS NMR spectra collected at 258, 263, 267, and 269 K indicated that no hydrate dissociated at these higher temperatures because the intensities of methane in the hydrate cages and gas-phase remained constant. The methane sI hydrate dissociation was thermally activated by increasing the temperature from 269 to 271 K. A set of timeresolved 13C MAS NMR spectra were recorded with a time resolution of 5.2048 s for a total time of about 500 s. This process permitted the methane sI hydrate and gas-phase 13C peak positions and intensities to be monitored with time. Figure 3 shows the time-resolved 13C MAS NMR spectra for sI methane hydrate dissociation during the temperature ramp from 269 to 271 K. The intensities of the three peaks at -3.80, -6.13, and -10.57 ppm (initially) are observed to change as the time increases. The area of each peak in Figure 3 was determined by deconvolution of each individual spectrum using Spinsight software. The hydrate cage occupancy ratio is defined as the ratio of the large peak area divided by the small peak area and divided by a factor of 3 to account for the large to small cage ratio in the structure I unit cell.1 At t ) 0 s, the resulting large
to small cage occupancy ratio is 1.16 ( 0.10 for methane hydrate at 269 K. The experimentally derived cage occupancy is in close agreement with the predicted value of 1.14 for methane hydrate at 269 K, predicted using a statistical thermodynamics program, CSMGem.27 The changes in normalized peak area of methane in the small and large cages, and the gas phase, corrected to their equilibrium values using eq 1, are shown in Figure 4a. Each peak area was normalized by the sum of small cages, large cages, and gasphase peak area. During the hydrate dissociation, the relative peak area of methane in the large cages and small cages decreased and the relative gas peak area increased by a factor of about two during the total time of the experiment. During the initial time of the decomposition process, only small changes are observed in the relative peak area because a finite amount of time (∼80 s) is required for the sample to reach 271 K. Figure 4b shows the same small and large cage data plotted on an expanded scale between 100 and 200 s. By use of linear regression, we determined that the large and small cages were dissociated approximately in the ratio of three (large/small cages) between 100 and 200 s. After accounting for the sI hydrate unit cell consisting of three large cages to one small cage (that is, dividing by a factor of 3), the modified ratio became equal to 1.0. The time-resolved 13C MAS NMR spectra also show that the methane gas chemical shift (δ) changed during the course of the dissociation process, from an initial value of -10.56 ppm to a final one of -10.41 ppm. By use of eq 2, the pressure of the system during the thermally activated decomposition of methane sI hydrate was calculated. Plots of the sealed glass methane hydrate sample pressure as a function of time and the methane gas-phase relative peak area versus time are shown in Figure 5. During the initial time (∼80 s) of the decomposition process, the pressure of the system is observed to increase more rapidly than the relative intensity of the methane gas-phase peak; this is probably due to the temperature of the gas phase increasing more rapidly than the hydrate phase during the initial time interval. At times between 100 and 200 s, both the system pressure and gas-phase peak area rapidly increase. At even longer times, both the system pressure and methane gas-phase
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Figure 6. Change in occupancy ratio with time from NMR data during dissociation. The triangles represent the experimental data, and the dashed line shows the calculated incipient equilibrium occupancy ratio at 271 K using CSMGem.
Figure 4. (a) Changes in the normalized peak area of the large and small cage, and the gas phase with time during hydrate dissociation. (The slope change for the large cage plot appears more pronounced than that for the small cage plot due to a scaling factor, i.e., there are three times more large cages than small cages in sI. Therefore, although both large and small cage plots have in fact similar slope changes (as shown in Figure 4b), the slope change is more clearly seen for the large cage than the small cage in this plot). (b) Expanded view of Figure 4a showing the large and small cage data between 100 and 200 s.
Figure 5. Plot of the system pressure and normalized methane gas peak area vs time.
peak intensity increase more slowly. At long times (∼350 s or more) the decomposition rate becomes slower because the system P and T are such that the methane sI hydrate is approaching a new stable thermodynamic condition. The occupancy ratio profile is plotted as a function of time in Figure 6. The occupancy ratio fluctuated between 0.98 and 1.37 with an averaged occupancy ratio of 1.17 over 500 s during
hydrate dissociation. The experimental occupancy ratio data are compared with the predicted equilibrium methane hydrate cage occupancy at 271 K using CSMGem.27 The measured occupancy agrees within (0.13 of the equilibrium ratio over the time interval shown in Figure 6. At a time on the order of 100 s, the fluctuation in the occupancy ratio becomes larger and is attributed to the decreased signal-to-noise ratio, which is due to the reduction (due to dissociation) in the hydrate phase amount in the sealed glass tube. The error in the measured occupancy ratios is larger than that of the observed peak areas used to derive the ratios and can be understood based on a simple propagation of errors treatment.28 The peak areas obtained from the 13C MAS NMR spectra are directly proportional to the number of methane molecules in each cage. The fact that the occupancy ratio is constant and virtually equal to its equilibrium value near 271 K during the decomposition experiment suggests that both the small and large cages decompose at the same rate on a per cage basis, that is, whole unit cells decompose under the conditions used here. The simultaneous decomposition of small and large cages in methane sI hydrate is in contrast to results observed during hydrate formation. Various studies have shown that the hydrate cavities form at different rates in hydrate formation of sI and sII hydrates. For example, the rate of formation of the 51262 cage was limiting in sI hydrate formation as confirmed by both Raman and NMR spectroscopy.5,6 The difference in rate of formation of hydrate cages (512 and 51262) is attributed to the relatively large stability of the small cage (512) compared to the large cavity (51262) in structure I hydrate.22 In addition, the absence of any preferential dissociation rate of hydrate cavities suggests that there is no activated state on the time scale of these measurements during methane hydrate dissociation. This result implies that the rate of hydrate dissociation depends on the rate of heat transfer to the system instead of intrinsic dissociation kinetics. Our interpretation of the results is in agreement with the macroscopic and numerical simulations results, which have shown that hydrate dissociation is a heat-transfer limited process.7-9 During hydrate dissociation, the hydrogen bonds between the water molecules associated with the hydrate crystal (ordered) dissociate and the gas molecules diffuse out from the partially dissociated hydrate cavities. This study suggests that there was no presence of any large and small cages occupied with methane gas during dissociation, which were not part of the hydrate unit cell. However, no information was obtained about the presence
2346 J. Phys. Chem. C, Vol. 111, No. 5, 2007 of partially dissociated hydrate cavities after hydrate dissociation, because we only measured the hydrate cages filled with methane gas and did not measure the number of unoccupied cages. Conclusions NMR spectroscopy was used to investigate methane hydrate dissociation on the microscopic scale. The time-resolved methane hydrate dissociation data showed that the hydrate occupancy ratio remained constant during dissociation. The constant occupancy ratio suggested that the unit cell of sI was dissociated as a whole and there is no preferential decomposition of sI methane hydrate cages. These dissociation results are different from methane hydrate formation, where the formation rate of large cages (51262) is slower than that of small cages (512). Acknowledgment. The authors wish to acknowledge the financial support received from the National Science Foundation through Research Grant CTS-0419204. We thank Kristin E. Bowler and Laura L. Stadterman for performing the T1 measurements. References and Notes (1) Sloan, E. D., Jr. Clathrate Hydrates of Natural Gases, 2nd ed.; Marcel Dekker: NY, 1998. (2) Milkov, A. V. Earth Sci. ReV. 2004, 66, 183. (3) Englezos, P.; Kalogerakis, N.; Dholabhai, P. D.; Bishnoi, P. R. Chem. Eng. Sci. 1987, 42 (11), 2659. (4) Lekvam, K.; Ruoff, P. J. Cryst. Growth 1997, 179, 618. (5) Subramanian, S.; Sloan, E. Fluid Phase Equilib. 1998, 813, 158160.
Gupta et al. (6) Moudrakovski, I. L.; Sanchez, A. A.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. B 2001, 105, 12338. (7) Kamath, V. A.; Holder, G. D. AIChE J. 1987, 33 (2), 347. (8) Ullerich, J. W.; Selim, M. S.; Sloan, E. D. AIChE J. 1987, 33 (5), 747. (9) Moridis, G. J.; Seol, Y.; Kneafsey, T. J. Fifth International Conference on Gas Hydrates 2005, 1004, 21. (10) Jamaluddin, A. K. M.; Kalogerakis, N.; Bishnoi, P. R. 3rd Chemistry Congress of North America, Toronto, June 5-10, 1988. (11) Kim, H. C.; Bishnoi, P. R.; Heidemann, R. A.; Rizvi, S. S. H. Chem. Eng. Sci. 1987, 42, No. 7, 1645. (12) Bishnoi, P. R.; Natarajan, V. Fluid Phase Equilib. 1996, 117, 168. (13) Clarke, M. A.; Bishnoi, P. R. Can. J. Chem. Eng. 2001, 79, 143. (14) Rodger, M. Methane hydrate/melting and memory. Gas hydrates, challenges for the future; New York, 2000. (15) Chen, T. S. A Molecular Dynamics Study of The Stability of Small Prenucleation Water Clusters; University Microfilms No. 8108116: University of MissourisRolla, 1980. (16) Clancy, P.; Baez, L. Ann. N. Y. Acad. Sci. 1994. (17) Ripmeester, J. A.; Ratcliffe, C. I. J. Phys. Chem. 1988, 92, 337. (18) Subramanian, S.; Kini, R.; Dec, S.; Sloan, E. D. Chem. Eng. Sci. 1999, 55, 1981. (19) Kini, R. A.; Dec, S. F.; Sloan, E. D. J. Phys. Chem. A 2004, 108, 9550. (20) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Claredon Press: Oxford, 1991. (21) van Geet, A. L. Anal. Chem. 1970, 42, 679. (22) Kini, R. A., Thesis, Colorado School of Mines, 2002. (23) Jameson, A. K.; Jameson, C. J. Chem. Phys. Lett. 1987, 134, 461. (24) Hoffman, R. E. J. Magn. Reson. 2006, 178, 237. (25) Weast, R. C.; Astle, M. J. Handbook of Chemistry and Physics, 62nd ed.; CRC Press: Boca Raton, FL, 1982. (26) Dec, S. F.; Bowler, K. E.; Stadterman, L. L.; Koh, C. A.; Sloan, E. D. J. Am. Chem. Soc. 2006, 128, 414. (27) Ballard, A. L.; Sloan, E. D., Jr. Fluid Phase Equilib. 2002, 371, 194-197. (28) Shoemaker, D. P.; Garland, C. W. Experiments in Physical Chemistry, 1962.
