Hydrated cavity volume

In particular, the extension of the van der Waals and Platteeuw method addresses the first assumption listed at the beginning of Section 5.1.1—namely that encaged molecules do not distort the cavity. In the development of the statistical thermodynamic hydrate model (Equation 5.23), the free energy of water in the standard hydrate (empty hydrate lattice), gt, is assumed to be known at a given temperature (T) and volume (v). Since the model was developed at constant volume, the assumption requires that the volume of the empty hydrate lattice, 7, be equal to the volume of the equilibrium hydrate, v11, so that the only energy change is due to occupation of the hydrate cavities, as shown in Figure 5.3. 

Fig. 33. Schematic representation of the effects of pressure on oligomeric proteins a) native dimeric protein with cavities/voids b) dissociation of the oligomer, hydration with electrostriction of polar/ionic groups, hydrophobic hydration of unpolar groups (-CR), release of void volume c) weakening of hydrophobic interactions provides pathways for water to penetrate into the interior of the protein, swelling of the core - molten-globule like state d) unfolding of subunits, disruption of the secondary/tertiary structure (hydration of residues not plotted here), loss of cavity volume within protein (adopted from ref. 139).

Figure 5 shows pn distributions for spherical observation volumes calculated from computer simulations of SPC water. For the range of solute sizes studied, the In pn values are found to be closely parabolic in n. This result would be predicted from the flat default model, as shown in Figure 5 with the corresponding results. The corresponding excess chemical potentials of hydration of those solutes, calculated using Eq. (7), are shown in Figure 6. As expected, /x x increases with increasing cavity radius. The agreement between IT predictions and computer simulation results is excellent over the entire range d < 0.36 nm that is accessible to direct determinations of po from simulation.

Ideal hydrate numbers validate the notion that a substantial amount of hydrocarbon is present in the hydrate. For example, if all cavities of structure II are filled, each volume of hydrate may contain 182 volumes of gas at standard temperature and pressure. This ratio shows the hydrated gas density to be equivalent to a highly compressed gas, but somewhat less than the density of a liquid hydrocarbon. The similarity of hydrates to a highly compressed gas suggests their use for storage, or as an unconventional gas resource, where they occur in situ in the deep oceans or permafrost. 

Glew (1959) suggested that the most nonstoichiometric guest molecules are those for which the size of the guest approaches the upper limit of the free volume of a cavity. For two molecules that approach the size limit of cavities, Glew and Rath (1966) presented experimental evidence that hydrate nonstoichiometry for both chlorine and ethylene oxide was due to the composition of the phase in equilibrium with the hydrates. 

However, it should be remembered that the fractional filling is a function of the product Cjjfj, rather than either factor in the product. Finally, in the original van der Waals and Platteeuw approach the Langmuir constants for both adsorption and enclathration were only functions of temperature for each molecule type retained at the individual site or cavity. In the modified approach below, the Langmuir constants are also a function of cage size, or the unit cell volume, which is a function of the hydrate guests, temperature, and pressure. 

This procedure can be carried out for observation volumes of different sizes. Of particular interest to us are the sizes 3.0 to 3.4 A that bracket the minimum in goo( ) (Fi - 7-3)- Figure 7.6 shows the hydration free energy for cavity sizes in this regime. In Fig. 7.6 the minimum for is obtained for R = 33 A. This is consistent with the expectations from goo( ) (Fig- 7.3). 

Most zeolites have three-dimensional structures with cavities connected to charmels that exhibit ion sieve properties. If the pore volume of the cavity is large enough, the hydration stripped cations exchanged can be rehydrated in the cavity to simulate their hydration in the solution. The large cations (Rb, Cs, organic cations) cannot enter the channels or windows of the cavities of zeolites with small pores. Table 3 lists the pore openings of some hydrated zeolites [133]. 

Frank HS, Evans MW. Eree volume and entropy in condensed systems. 3. entropy in binary liquid mixtures - partial molar entropy in dilute solutions - structure and thermodynamics in aqueous electrolytes. J. Chem. Phys. 1945 13 507-532. Gallicchio E, Kubo MM, Levy RM. Enthalpy-entropy and cavity decomposition of alkane hydration free energies numerical results and implications for theories of hydrophobic solvation. J. Phys. Chem. B 2000 104 6271-6285. 

As the volumes of the atoms may be considered, as a first approximation, to be temperature and pressure independent, it follows that both the thermal expansion and the compression are composed of two main terms, the cavity and the hydration. For the thermal expansion this... 

On the basis of the low compressibilities and the average high packing densities, the protein interior is often considered as a solidlike material with little free volume. However when one considers the free volume distribution, proteins look more like liquids and glasses [30]. The free volume is often called cavities, voids or pockets. Their role in the volume changes of protein reactions or interactions was suggested by Silva and Weber [31]. A recent review paper emphasizes the similarities between the role of hydration and cavities in protein-protein interactions and protein unfolding [32]. 

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