Cavity term

Tlic cavity and van der Waals contributions may also be modelled as separate terms. In som implementations an estimate of the cavity term may be obtained using scaled particle theor [Eierotti 1965 Claverie et al. 1978], which uses an equation of the form ... 

Prop = cavity term + dipolar term + hydrogen-bonding terms... 

Attempts have been made to distinguish between these theories on the basis of the AH° and values anticipated for the two theories, but it may be illusory to think of them as independent alternatives. The eavity model has been criticized on the basis that it eannot account for certain observations such as the denaturing effect of urea, but it must be noted that the cavity theory includes not only the cavity term AAy, but also a term (or terms) for the interaction of the solutes and the solvent. A more eogent objeetion might be to the extension of the macroseopic concepts of surface area and tension to the molecular scale. A demonstration of the validity of the cavity concept has been made with silanized glass beads, which aggregate in polar solvents and disperse in nonpolar solvents. 

AGg (X) can be removed by assuming that it is equivalent to the polar contribution to the free energy of solution of solute X in a nonpolar hydrocarbon solvent, such as squalane. A second reason for using a reference hydrocarbon solvent is to correct, at least partially, for the fact that the hardcore van der Haals volume is a poor estimate of the size of the cavity and its accessible surface for solvent interactions for aromatic and cyclic solutes. The solvent accessible surface area would logically be the preferred parameter for the cavity term but is very difficult to calculate while the van der Haals volume is readily accessible. With the above approximations the solvent interaction term for... 

Leahy, D. E. (1986) Intrinsic molecular volume as a measure of the cavity term in linear solvation energy relationships octanol-water partition coefficients and aqueous solubilities. J. Pharm. Sci. 75, 629-636. 

Non-electrostatic terms, comprising the solvent-solvent cavity term and solute-solvent van der Waals term, may be linearly related to solvent-accessible surface area (SA)... 

Abraham MH, McGowan JC (1987) The use of characteristic volumes to measure cavity terms in reversed phase liquid chromatography. Chromatographia 23 243-246. 

The approach to calculate the van der Waals and cavity terms from the molecular surface areas can be used for the calculation of partition coefficients. The results show that for the distribution of hydrocarbons between water and n-octanol the calculated partition coefficient is linear in carbon number. Qualitatively similar data are obtained for the distribution between other solvents and water and the results can be used to predict the retention in liquid>liquid chromatography. On the other hand, if retention in RPC occurs due to reversible binding at the surface of the stationary phase, the significant parameter is not the total surface area of the eiuite but rather the net decrease in the molecular surface area of the stationary phase ligates and that of the eiuite upon binding, i.e., the contact area in the complex. 

Equation (22) has been found to be somewhat more useful than Eq. (20) for evaluation of the free energy change related to caSdty formation when more than one solute species is present. In the form given by Eq. (22) the cavity term can be c culated if macroscopic sur K e tension, y, K, and molecular surface area of both the solute and solvent are known. The latter values may be calculated for spherical or quasi-spherical mole- cules as... 

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. 

As already mentioned, the cavity term corresponds to the endoeigic process of separating the solvent molecules to provide a suitably sized and shaped enclosure for the solute, and measures the work required for such a purpose. This term is related to the tightness or structuredness of solvents as caused by intermolecular solvent/solvent interactions. The association of solvent molecules in the liquid state in order to accommodate the solute molecules can be quantified by means of the surface area and texture of the solute that are related with the m coefficient and by the cohesive pressure of the solvent given by fl. 

The topological structure of X- and Y-type zeolites (also known as faujasites) consists of an interconnected three-dimensional network of relatively large spherical cavities termed supercages (diameter of about 13 A Figure 12). Each supercage is connected tetrahedrally to four other super-... 

Solvatochromic Approach The solvatochromic approach describes a solvent-dependent property, XYZ, as a function of a cavity term, a dipolar term, and terms that account for hydrogen bonding [21] ... 

LSER Model of Leahy In the LSER model of Leahy [22], the cavity term is substituted by the molar volume, Vm, at 25°C in g cm-3 or by the intrinsic molecular volume, V), in mLmoL1. The dipolar term and the hydrogen-bonding terms are represented by the dipole moment, n, and the HBA basicity, (3, respectively. Group contribution schemes have been developed to calculate the solvatochromic parameters from molecular structure input [23]. Leahy [22] gives the following equation derived with a diverse set of monofunctional liquids ... 

The correlation between aqueous solubility and molar volume discussed by McAuliffe [5] for hydrocarbons, and the importance of the cavity term in the solvatochromic approach, indicates a significant solubility dependence on the molecular size and shape of solutes. Molecular size and shape parameters frequently used in quantitative structure-water solubility relationships (QSWSRs) are molecular volume and molecular connectivity indices. Moriguchi et al. [33] evaluated the following relationship to estimate Cw of apolar compounds and a variety of derivatives with hydrophilic groups ... 

Leahy, D. E., Intrinsic Molecular Volume as a Measure of the Cavity Term in linear Solvation Energy Relationships Octanol-Water Partition Coefficients and Aqueous Solubilities. J. Pharrn. Sci., 1986 75, 629-636. 

For molten salts one sets so = 1. For electrolyte solutions solvent-averaged potential [37]. Then, in real fluids, eo in Eq. (11) depends on the ion density [167]. Usually, one sets so = s, where e is the dielectric constant of the solvent. A further assumption inherent in all primitive models is in = , where is the dielectric constant inside the ionic spheres. This deficit can be compensated by a cavity term that, for electrolyte solutions with e > in, is repulsive. At zero ion density this cavity term decays as r-4 [17, 168]. At... 

Another option evolves from the cavity terms already mentioned in Section TVA. We recall that these cavity interactions arise from the assumption that in the RPM the dielectric continuum penetrates the ions, so that the dielectric constant , inside the ions is equal to 5. To counterbalance this effect, a cavity term is introduced. The standard situation in electrolyte solutions is certainly that 5 > , which implies that the cavity interaction is repulsive. jn > 5 would imply an attractive interaction. 

If the r 4-dependent attractive interactions were unscreened, they would indeed give rise to mean-field criticality. On the other hand, an unscreened repulsive interaction would suppress the development of a critical point, giving rise instead to a charge-density wave instability in the neighborhood of where criticality would take place in the absence of the r-4 cavity term. The latter scenario was developed some time ago by Nabutovskii et al. [305] using a Ginzburg-type analysis. 

The solvation free energy is usually considered to consist of a solvent-solvent cavity term (Gcav), a solute-solvent van der Waals term (Gvsolute-solvent electrostatic polarization term (Ges) (Eq. 2.37). 

A fuller discussion of the quantities %, a, and P is given in Chapter 4. The cavity term itself can be expressed either in terms of the Hildebrand solubility parameter, i.e., where A, is a solute- and... 

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