Cage occupancies

Consequently the methane content in hydrates can be calculated based on the hydration number and density, which is approximately -160-180 v/v depending on the cage occupancy and temperature. 

Inerbaev, T.M. Belosludov, V.R. Belosludov, R.V. Sluiter, M. Kawazoe, Y. (2006). Dynamics and equation of state of hydrogen clathrate hydrate as a function of cage occupation. Computational Materials Science, 36 (1-2), 229-233. 

Kuhs, W.F. Chazallon, B. Radaelli, P.G. Pauer, F. (1997). Cage Occupancy and Compressibility of Deuterated N2-Clathrate Hydrate by Neutron Diffraction. J. lncl. Phen. Microcyclic Chem., 29, 65-77. 

Ripmeester, J.A. Ratcliffe, C.I. (1988). Low-temperature cross-polarization/magic angle spinning carbon-13 NMR of number solid methane hydrates structure, cage occupancy, and hydration. J. Phys. Chem., 92, 337-339. 

Udachin, K.A. Ratcliffe, C.I. Ripmeester, J.A. (2002). Single Crystal Diffraction Studies of Structure I, II and H Hydrates Structure, Cage Occupancy and Composition. J. Supra. Chem. 2, 405-408. 

Table 2.4 indicates the structures that have been confirmed by single crystal x-ray analysis by Udachin et al. (2002). In this work, Udachin et al. were able to obtain high-quality single crystals on these compounds and therefore obtained the absolute cage occupancies. For ethane si hydrate, the large cages are filled with a very low fraction (0.058) of the small cages occupied. 

A systematic determination of both hydration number (Cady, 1983) and relative cage occupancies (Davidson and Ripmeester, 1984) shows that molecules such as CH3CI and SO2 are the most nonstoichiometric. Although theoretical calculations using the van der Waals and Platteeuw model provides some rationale for the nonstoichiometry, experimental quantification of nonstoichiometry as a function of guest/cavity size ratio has yet to be determined. 

The above findings are analogous to those reported by the same research group for ethane (Morita et al., 2000) and ethylene (Sugahara et al 2000) hydrates. Based on Raman spectroscopy, ethane or ethylene occupancy of the small cavities of structure I increases with increasing pressure. The low small cage occupancy of ethane in structure I hydrate was also detected from single crystal x-ray diffraction measurements (Udachin et ah, 2002). 

The size ratio of the guest to cavity, is a general guide to determining crystal structures and cage occupancy. In turn, crystal structure determines equilibrium pressures and temperatures for the hydrate phase, as shown in Example 2.1. 

Critical hydrate parameters, such as cage occupancies and structural transitions can be predicted a priori, without fitting the model to spectroscopic measurements. 

Structure identification, quantifying relative cage occupancies. 1II NMR has been used for ethane, propane, and isobutane hydrates (Davidson et al., 1977 Garg et al., 1977), while 2H, 19F, 31P, and 77 Se NMR have been used for several si guests (Collins et al., 1990). 13C cross-polarization and magic angle spinning (MAS) NMR techniques have been applied to study hydrates of carbon dioxide, methane, and propane (Ripmeester and Ratcliffe, 1988, 1999 Wilson et al., 2002 Kini et al., 2004). 

Structure identification and relative cage occupancies. The hydration number and relative cage occupation for pure components and guests were measured by Sum et al. (1997), Uchida et al. (1999), and Wilson et al. (2002). Raman guest spectra of clathrate hydrates have been measured for the three known hydrate crystal structures si, sll, and sH. Long (1994) previously measured the kinetic phenomena for THF hydrate. Thermodynamic sl/sll structural transitions have been studied for binary hydrate systems (Subramanian et al., 2000 Schicks et al., 2006). 

Offretite, E and omega syntheses are strongly aided by the presence of TMA. Gmellnite cage occupancy by TMA in offretite and omega is near unity(6). 

Sodalite Cage Occupancy in Y. The sodalite cage occupancy by A of three Y zeolites synthesized in Series 1 was determined by C... 

The results suggest that the sodalite cages of Y synthesized in the presence of TMA are filled by a random process the fit for two sodium ions/cage is slightly better than for three sodium ions/cage. Sodalite cage occupancy by approximately two sodium ions is consistent with many XRD studies(13). 

If the free energy of the host water does not change upon encaging, the free energy of cage occupancy by nonlinear (/ = 3) or by linear (Z = 2) molecule is given by... 

Here, we show how the free energy of cage occupancy is calculated for clathrate hydrates encaging such as propane and argon. As shown above,... 

Table 7. Free energy of cage occupation by nonspherical propane and ethane evaluated by the direct calculation of anharmonic contributions and by the mean occupation according to equation (26). The free energy of the corresponding free rotor is omitted. Free energy is in kJ mol and pressure is in 0.1 MPa.

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