Bondi method

Table 2.2 Calculated fractional free volume for representative membrane materials at ambient temperatures (Bondi method)...

Figure 2.24 Correlation of the oxygen permeability coefficient for a family of related polysulfones with inverse fractional free volume (calculated using the Bondi method) [33]. Reprinted with permission from C.L. Aitken, W.J. Koros and D.R. Paul, Effect of Structural Symmetry on Gas Transport Properties of Polysulfones, Macromolecules 25, 3424. Copyright 1992, American Chemical Society...

Another group contribution method that has been applied to the prediction of soil sorption is the UNIquac Functional-group Activity Coefficient (UNIFAC, where UNIQUAC = Universal Quasichemical) approach (Fredenslund et al., 1977). Ames and Grulke (1995) applied the method to a small diverse set of chemicals, with rather poor results. They did not report any correlations, but from their results it can be shown that the correlation of observed and predicted log values using the Bondi method was n = 17, R2 = 0.571, 5 = 0.524, and F = 20.0 eight chemicals were predicted with an error of < 0.5 log units, 7 chemicals were predicted with an error between 0.5 and 1.0 log units, and 2 chemicals were predicted with an error of > 1.0 log units. 

The van der Waals volume and area are characterizing parameters relating molecular configurations. Bondi describes group contribution methods for their calculatiou. 

Bondy, S.C. (1979). Rapid screening of neurotoxic agents by in vivo means. In Effects of Food and Drugs on the Development and Function of the Nervous System Methods for Predicting Toxicity. Gryder, R.M. and Frankos, VFL, (Eds.) Office of Health Affairs, FDA, Washington, D.C., pp. 133-143. 

In a reversed-phase liquid chromatography system, if the hydrogen-bonding and Coulombic forces are negligible, the retention of molecules depends upon their size, and the presence of n electrons enhances the selectivity. The molecular size, i.e. the van der Waals volume, can be calculated by hand, by Bondi s method,29 or by certain computer programs. 

Bondi s calculation method is simple. The van der Waals volumes are the sum of the van der Waals volumes of fragments, as given in Table 6.3. The calculated van der Waals volumes are summarized in Table 6.4. However, these volumes are different from those calculated using the MOPAC-BlogP program, even though the correlation is excellent. 

Figure 42. Molecular volumes of 2-nonanone and its initial Norrish II photoproducts from MNDO-optimized geometries [265a] using the method of Bondi [265b].

Because of the lipophilic nature of the biological membrane and the importance of size and charge distribution, the formal charge at position 7 of the 1,2,4-benzothiadiazine 1,1-dioxide systems and two other parameters, Hansch s hydrophobic 1r parameter and the van der Waals volume (as calculated by Bondi s method), are included in a structure-activity rela-... 

There is very little problem in calculating an acceptable measure of solute size. Simple calculations of either molecular volume or area based on either Bondi s (Bondi, 1964) or McGowan s (Abraham, 1987) methods work almost as well as those derived from molecular mechanics and quantum chemistry (Leo, 1993). When volume in cubic Angstroms is used, V is normally scaled by 0.01 to produce a coefficient comparable to the others in the equation polarity/polarizability. 

The bottleneck of GB calculations is the determination of the effective Born radii (a), since their magnitude depends not only on the intrinsic atomic (Bondi, or atomic) radii of the atom (p), but also on the geometry of the rest of the molecule, which modulates the average distance of the atom to the solvent. Original formulations of the method used Equation (4.19) for the computation of Born s radii, but all current version rely on an approximate formalism, such as that developed by Hawkins et al. [34], where a pairwise approximation to atomic overlap is used to simplify Equation (4.19) see Equations (4.20)-(4.22). Using this approach Born s radii can be computed very fast, which makes the method suitable for MD calculations ... 

This equation provides a way to estimate the molecular cavity volume for any system but the shape of the cavity has also to be defined. Constant coordinate cavities such as the sphere or the ellipsoid are obviously not appropriate for most systems and they have been almost definitively abandoned in favor of molecular-shaped cavities. The majority of current continuum methods, and MPE as well, use van der Waals-type molecular surfaces. Atomic radii are in general larger than standard Bondi radii so that the obtained surface is close to the so-called solvent-excluding surface [64,65], Consistent with the expression for the volume given above, the order of magnitude of atomic radii should be... 

On the other hand, the volume contribution of structural groups already contains inbuilt information on the influence of the atomic surroundings. As a consequence the Van der Waals volume of the structural units can approximately be calculated as the sum of the Van der Waals volumes of the composing structural groups. Bondi (1964,1968) was the first to calculate the contributions of about 60 structural groups to Vw. Later Slonimskii et al. (1970) and Askadskii (1987) calculated about 100 values of atomic increments in different surroundings. Since the two approaches used the same method of calculation, and nearly equal basic data on the atomic radii, the calculated values for the structural units are approximately equal. In Table 4.2 also the group increments of Vw are shown, next to those of M. By means of these data the Van der Waals volumes of the Structural Units are easily calculated. 

In the case where y is not available from the literature it can be calculated from solu-bihty parameters which themselves are related to the cohesive energy density (C.E.D.) and hence to the strength of the internal pressure of the structural molecules The binary parameter, Sj/Sj is obtainable from the method of group contribution given by Bondi It can alternatively be calculated by casting shadows of models of the molecules for various orientations, where the area for the monomer unit is estimated from the area of the projections. 

The compilations of CRC (2-3) Daubert and Danner (4) Domalski and Hearing (6) and Yaws (18-21) were used extensively. Estimates for enthalpy of fusion at the freezing point were primarily based on methods of Bondi (1, entropy), Joback (8, group contribution), and Chickos et al (11, group contribution). 

The compilations of Daubert and Danner (3) and Yaws (6-7) were used extensively. Van der Waals area and volume involve the surface area and volume of an atom and maybe ascertained from bond distances, contact distances and shapes of atoms. Methods of calculation are described by Bondi (1). 

Radebaugh GW, Murtha JL, Julian TN, Bondi JN. Methods for evaluating the puncture and shear properties of pharmaceutical polymeric films. Int ] Pharm 1988 45 39 6. 

Bondi developed a method based on covalent bond distances and van der Waals radii to calculate van der Waals volume [Bondi, 1964]. The volume calculated in this way is sometimes called the Bondi volume. It is obtained easily by summing appropriate volume contributions of atoms and functional groups, as proposed by Bondi note that the Bondi volume does not account for the overlaps which are possible whenever three or more atomic spheres intersect it is roughly 60 - 70 % of the -> molecular volume. 

Basabe-Desmonts, L. Zimmerman, R. S. Reinhoudt, D. N. Crego-Calama, M., Combinatorial method for surface-confined sensor design and fabrication, In Springer Series on Chemical Sensors and Biosensors Vol. 3 Frontiers in Chemical Sensors Orellana, G. Moreno-Bondi, M.C., (Eds.) Springer, Berlin 2005... 

The concept of free volume has been of more limited use in the prediction of solubility coefficients although, Peterlin (H) has suggested that the solubility coefficient is directly proportional to the free volume available in the polymer matrix. In many respects, the free volume expressions closely resemble the relationships developed in the activated state approach. In fact for the case of diffusivity, the two models can be shown to be mathematically equivalent by incorporating thermal expansion models such as the one proposed by Fox and Flory (12). The usefulness of the free volume model however, lies in the accessibility of the fractional free volume, through the use of group contribution methods developed by Bondi (12.) and Sugden (li), for correlation of barrier properties of polymers of different structure as demonstrated by Lee (15.). ... 

The free volume approach has been an increasingly popular method to relate polymer structure to gas transport properties. The basic premise of this technique is that a polymer with an open, poorly packed structure will have a large unoccupied free volume through which a gas can diffuse with ease. In a typical model, set forth by Lee (d2.) a specific free volume, SFV, is derived from the difference between the molar volume, Vm, (determined from the experimental density of a polymer) and the occupied volume, Vo, (calculated using a group additive method, in this case, that of Bondi) (4(1). ... 

When a molecule is represented as an object with well-defined boundaries, geometric methods of analysis may be applied. Several steric parameters have been derived from the model in w hich atoms, hence molecules, are represented as geometric objects with surfaces and volumes. The boundary of an atom is usually determined by its van der Waals radius. Surface area and volume of groups and molecules can be estimated. Bondi,Hermann, and Pearlman are among those who have studied surface area and volume. Molar refractivity (MR), calculated from density and refractive index, has frequently been used to estimate the bulk or global volume of a molecule or group. A more recent trend is to use MR as a model for dispersion interactions. 

The high concentration of OCT is in hepatic tissue relative to other tissues this leads to this enzyme being regarded as a liver-specific enzyme. OCT is localized in the periportal mitochondria and is the second of the five enzymes in the urea cycle. The enzyme measurement should not be confused with ornithine decarboxylase (ODC), which is of interest in studies of polyamine metabolism. The use of the method has been limited by some of technical requirements for the older assays, but newer enzymatic methods may increase its use (Peltenburg et al. 1991 Isobe, Matsuzawa, and Nagamura 1993 Ishikawa et al. 2002). In a number of rat studies, ALT was found to be more predictive of hepatotoxicity than OCT (Bondy et al. 2000). 

Detailed methods of computation of the van der Waals excluded volume (for any chemical structure) have been developed [Bondi, 1964 van Krevelen, 1976]. Thermodynamically, the free volume is expressed in terms of the entropy of vaporization ... 

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