Thermodynamics of cavity formation

Postma J P M, H J C Berendsen and J R Haak 1982. Thermodynamics of Cavity Formation ui Wat - Faraday Symposium of the Chemical Society 1755-67. 

Postma, J. Berendsen, H. Haak, J., Thermodynamics of cavity formation in water. A molecular dynamics study, Far. Symp. Chem. Soc. 1982,17, 55-67... 

It should be noted that the expression of the cavity term in Eq. (22) differs fiom that given by Halicio o and Sinano u (79/, 792) who presented a more exacting treatment of the thermodynamics of cavity formation. However, the difference between the energy calculated by the rigorous formulation and by the iq>proximation in Eq. (22) is only a few percent and seldom exceeds 0.4 kcal/mel. 

Thermodynamics of Cavity Formation in Water, a Molecular Dynamics Study. 

SPT = scaled particle theory TCF = thermodynamics of cavity formation. 

There is naturally a wealth of publications on aspects of solvation and a comprehensive review would need a whole book. Hence, it is not practical to wade through all the developments in solvent effect theory, especially as other articles in this encyclopedia also deal with some aspects of solvation (see Related Articles at the end of this article). Instead, the focus will be on the methods used for the evaluation of the thermodynamics of cavity formation (TCF), which is a large part of solvation thermodynamics, and in particular on the application of the most successful statistical mechanical theory for this purpose, namely, the scaled particle theory (SPT) for hard sphere fluids (see Scaled Particle Theory). This article gives a brief introduction to the thermodynamic aspects of the solvation process, defines energy terms associated with solvation steps and presents a short review of statistical mechanical and empirical... 

Figure 9 Thermodynamics of cavity formation as a function of solvent mole fraction (water, Xw, and benzene, xb .) - (a) free energy Cc, (b) enthalpy H, and (c) entropy...

Dissociation rates were obtained at high acidity where kn is fast and were corrected for ionic strength using a Debye-Huckel equation. The results show that the cryptate selectivity results mainly from kh and that the transition state for the reaction has little interaction between the metal and the cryptand to differentiate between metals. Rates kt increase with increasing cavity size. The thermodynamics of cryptand formation in water and methanol have also been used to calculate the free energy and enthalpy of transfer of the free ions between the two media. 

Table 7.4 hows some values for the free energy enthalpy 5, and entropy Ss of cavity formation, computed by Pierotti (1963, 1965) for water and benzene at 25°C and at 1 atm. The effective diameters of argon and water for these calculations are Og = 3.4 A and Ow = 2.75 A, respectively. (The subscript S stands for solute. Here, for argon, the superscript H stands for the hard part of the corresponding thermodynamic quantity, and the bar is added to remind us that these quantities are computed from the pseudo-chemical potential, i.e., they all refer to a fixed position in the solvent.)... 

In this section two prediction techniques are discussed, namely, the gas gravity method and the Kvsi method. While both techniques enable the user to determine the pressure and temperature of hydrate formation from a gas, only the KVSI method allows the hydrate composition calculation. Calculations via the statistical thermodynamics method combined with Gibbs energy minimization (Chapter 5) provide access to the hydrate composition and other hydrate properties, such as the fraction of each cavity filled by various molecule types and the phase amounts. 

A general picture of the specific interactions of aromatics on a-, (3- and Y-CD can be obtained by comparing the results of the chromatographic study with previously published data. The thermodynamic quantities indicate that only part of the benzene molecule is included in the a-CD cavity, whereas the contact with the 3-CD cavity is very intimate. The published values of the formation equilibrium constants of the complexes formed also follows the order (3- )>> a- > Y-CD for the compounds studied. 

An illustration is given in fig. 3.16 for a spherical cavity. As with convex double layers, the potential drops more rapidly (inweird from the surface) with distance in 10 M than in 10" M solution in the latter case the decrease is so weak that in the centre a substantial overlap potential remains. Similar results have been obtained by others 2-3 emphasizing other aspects, such as the ton uptake (or exclusion), the Gibbs energy and the disjoining pressure. This information underlies the thermodynamics of vesicle and micro-emulsion formation. 

Figure 4,14. Diagram of the thermodynamic cycle used to explain retention in reversed-phase chromatography by solvophobic theory. Na = Avogadro number, AA = reduction of hydrophobic surface area due to the adsorption of the analyte onto the bonded ligand, y = surface tension, = energy correction parameter for the curvature of the cavity, V = molar volume, R = gas constant, T = temperature (K), Pq = atmospheric pressure, AGydw.s.i a complex function of the ionization potential and the Clausius-Moscotti functions of the solute and mobile phase. Subscripts i = ith component (solute or solvent), S = solute, L = bonded phase ligand, SL = solute-ligand complex, R = transfer of analyte from the mobile to the stationary phase (retention), CAV = cavity formation, VDW = van der Waals interactions, ES = electrostatic interactions.

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