Cavity size ratio

A principal theme of this text is the direct relation of macroscopic properties to molecular structure. In concluding the discussion on the si and sll cavity size ratios, two examples are given of how macroscopic engineering properties (equilibrium pressure and temperature, and heat of dissociation) are determined by the size ratios in Table 2.4. 

We can interpret the 42% decrease in equilibrium pressure, caused by a 1% change in composition, in terms of cavity size ratios shown in Table 2.4. Propane only fits into the 51264 cavity of structure II, C3H8 is too large to occupy any other cavity. For CH4, diameter ratios in the 512 cavities of si (0.86) and sll (0.87) differ by 1.5%. 

In summary, the concept of guest to cavity size ratios (and hydrate structure change) can provide molecular comprehension of a substantial decrease in equilibriumpressure required for a small composition change. The sll stability by small amounts of propane results in the fact that most natural gases form sll, because most reservoirs contain small amounts of propane. 

Example 2.2 Cavity Size Ratios Determine Heat of Dissociation... 

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. 

Gas molecules in sufficient amount are a prereqnisite to stabilize the hydrate structures. In principle, the occupied hydrate cage is a function of the size ratio of the guest molecule to the host cavity. Figure 14.1 illustrates the guest/cavity size ratio for hydrates formed of a single guest component in either structure 1 or structure 11 (Sloan 1998). Molecules smallerthan... 

For many years, small animal models have been utihzed for modeling CPR in humans. Small animals, such as cats, pigs, and dogs, weighing from 5 to 20 kg have been used. Regrettably, smaU-animal experiments are dissimilar to the (elderly) human, but may be carefully appHed for neonatal or small pediatric models. More recently, swine, weighing at least 20 kg have become the standard for experiments. This is not only due to improved similarity between the position of the heart and availabihty of the model, but is mostly due to improved estimation of the cardiac to thoracic cavity size ratio, and the similar ventrodorsal and lateral ratios to humans. 

Fio. 1 Relation between log K and the ratio of cation diameter to cavity size for (cfa-syn-c r)-dicyclohexyl-18-crown-6 [20] in water at 2S°C. Ionic diameters taken from Pedersen (1967a), and log K values from Izatt et al. (1976a) and Frensforf (197 la)... 

Cavity size is certainly an important factor in determining the striking preference of ligands 28,29,30 respectively for cations Li+, Na+ and K+, whose size most closely fits the intramolecular spherical cavity (Table 6). The cavities of these ligands are larger than the minimum cavity determined by the minimum radius ratio (Table 4). In the systems 31—33... 

Figure 10 (a) Relation between log Ks and the ratio of cation diameter to cavity size for dicyclohexyl[18]crown-6 in water at 25 °C (b) log K, values of several crown ether-alkali cation complexes... 

As simple hydrates, methane, and hydrogen sulfide can stabilize the 512 cavities of structure I (size ratios of 0.86 and 0.90, respectively) and they can occupy all the large 51262 cavities of si (size ratios of 0.74 and 0.78, respectively). Ethane occupies the 51262 cavities of structure I with a ratio of 0.94. Propane and iso-butane each occupy the 51264 cavities of structure II with a size ratio of 0.94 and 0.98, respectively. 

Pure methane is stabilized in si only by the additional stability of the molecule in the 51262 cavity. With only a small amount of propane to encourage the stability of sll, the similar size ratios of methane in the 512 cavities and large degree of stability propane provides (0.94) to the sll large cage enable a structure transition. 

Structure H Size Ratios of Molecular Diameters1 to Cavity Diameterse for Alkanes, Cycloalkanes with Methane, and Other Small Molecules in Both the Small Cavities... 

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. 

Figure 1 shows - for Ne as an example - the cavity size dependence of the ratio (Vcoul,exact/ Vcoul,Poisson) between the classical electron-electron repulsion integrals calculated through Equation (15) (Vcoul,exact) and the... 

Table 14.2 shows the size ratio of several gas molecules within each of the four cavities of stractures 1 and 11. A ratio of molecule to cage size of approximately 0.9 is necessary for stability of a hydrate composed of a single gas. When the size ratio exceeds unity, the gas will not fit within the cage structure and hydrate... 

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