Waals Volume

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. 

Prediction of Retention Times Based on van der Waals Volumes 

Influence of Physical Chemistry on Separations in Liquid Chromatography 

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Solvent-excluded surfaces correlate with the molecular or Connolly surfaces (there is some confusion in the literature). The definition simply proceeds from another point of view. In this c ase, one assumes to be inside a molecaile and examines how the molecule secs the surrounding solvent molecules. The surface where the probe sphere does not intersect the molecular volume is determined. Thus, the SES embodies the solvent-excluded volume, which is the sum of the van der Waals volume and the interstitial (re-entrant) volume (Figures 2-119. 2-120). 

Material properties can be further classified into fundamental properties and derived properties. Fundamental properties are a direct consequence of the molecular structure, such as van der Waals volume, cohesive energy, and heat capacity. Derived properties are not readily identified with a certain aspect of molecular structure. Glass transition temperature, density, solubility, and bulk modulus would be considered derived properties. The way in which fundamental properties are obtained from a simulation is often readily apparent. The way in which derived properties are computed is often an empirically determined combination of fundamental properties. Such empirical methods can give more erratic results, reliable for one class of compounds but not for another. 

The van der Waals volume of a molecule is the volume actually occupied by the atoms. It is reliably computed with a group additivity technique. Connectivity indices can also be used. 

The molar volume is usually larger than the van der Waals volume because two additional influences must be added. The first is the amount of empty space in the bulk material due to constraints on how tightly together the chains can pack. The second is the additional space needed to accommodate the vibrational motion of the atoms at a given temperature. 

Many polymers expand with increasing temperature. This can be predicted with simple analytic equations relating the volume at a given temperature V T) to the van der Waals volume F and the glass transition temperature, such as... 

More economically competitive if ideal permselectivity is >15 (highly dependent on membrane selection) indication of feasibiUty obtained with information on critical temperature and van der Waals volume. 

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

The secondary and tertiary structures of myoglobin and ribonuclease A illustrate the importance of packing in tertiary structures. Secondary structures pack closely to one another and also intercalate with (insert between) extended polypeptide chains. If the sum of the van der Waals volumes of a protein s constituent amino acids is divided by the volume occupied by the protein, packing densities of 0.72 to 0.77 are typically obtained. This means that, even with close packing, approximately 25% of the total volume of a protein is not occupied by protein atoms. Nearly all of this space is in the form of very small cavities. Cavities the size of water molecules or larger do occasionally occur, but they make up only a small fraction of the total protein volume. It is likely that such cavities provide flexibility for proteins and facilitate conformation changes and a wide range of protein dynamics (discussed later). 

In this approach, connectivity indices were used as the principle descriptor of the topology of the repeat unit of a polymer. The connectivity indices of various polymers were first correlated directly with the experimental data for six different physical properties. The six properties were Van der Waals volume (Vw), molar volume (V), heat capacity (Cp), solubility parameter (5), glass transition temperature Tfj, and cohesive energies ( coh) for the 45 different polymers. Available data were used to establish the dependence of these properties on the topological indices. All the experimental data for these properties were trained simultaneously in the proposed neural network model in order to develop an overall cause-effect relationship for all six properties. 

Experimental data for Van der Waals volumes Molar volumes Heat capacities Solubility parameter and glass transition temperature... 

Figure 25 ANN model (5-8-6) training and testing results for van der Waals volume, molar volume, heat capacity, solubility parameter, and glass transition temperature of 45 different polymers.

From van der Waals volumes calculated from atomic increments [57],... 

For each binary pair, there are two adjustable parameters that must be determined from experimental data, that is, (uy - ujj), which are temperature dependent. Pure component properties rl and ql measure molecular van der Waals volumes and surface areas and have been tabulated6. 

Fig. 4. A schematic two-dimensional illustration of the idea for an information theory model of hydrophobic hydration. Direct insertion of a solute of substantial size (the larger circle) will be impractical. For smaller solutes (the smaller circles) the situation is tractable a successful insertion is found, for example, in the upper panel on the right. For either the small or the large solute, statistical information can be collected that leads to reasonable but approximate models of the hydration free energy, Eq. (7). An important issue is that the solvent configurations (here, the point sets) are supplied by simulation or X-ray or neutron scattering experiments. Therefore, solvent structural assumptions can be avoided to some degree. The point set for the upper panel is obtained by pseudo-random-number generation so the correct inference would be of a Poisson distribution of points and = kTpv where v is the van der Waals volume of the solute. Quasi-random series were used for the bottom panel so those inferences should be different. See Pratt et al. (1999).

Hanai, T., Hubert, J. (1984) Retention versus van der Waals volume and 3 energy in liquid chromatography. J. Chromatogr. 290, 197-206. 

SCHEME 2. Van der Waals volumes, partial molar volumes and packing coefficients... 

From the data listed in Table 6 the van der Waals volume of the Diels-Alder reac-tion13,25,52,65 can be calculated to be with AVw = — 11.2 cm3 mol 1 only roughly one-quarter of the experimentally accessible volume of reaction (AV = —41.7 cm3 mol-1) (Scheme 3). Consequently, a significant part of the observed A V results from the higher packing of the cyclic product (compared to the acyclic reactants) rather than from the changes in bonding. The difference between the van der Waals volume of activation calculated for the pericyclic and stepwise reaction is small (5AV y = —1.7 cm3 mol-1) and is inconsistent with the experimental data listed in Tables 4 and 5. In order to explain... 

TABLE 6. Comparison between molar volumes V, van der Waals volumes Vw (cm3 mol 1) and packing coefficients t) for selected examples of acyclic and cyclic ground and transition states... 

SCHEME 3. Comparison of van der Waals volumes of reaction and activation with the volumes of reaction and activation calculated for a pericyclic and stepwise Diels-Alder reaction of 1,3-butadiene with ethene... 

All volumes are given in cm3 mol-1. The structural parameters necessary for the calculation of the van der Waals volume for the transition state (TS) were taken from ab initio calculations159,160. The partial molar volume for the TS was calculated from the equation ... 

SCHEME 18. van der Waals volume of activation AV and volume of activation calculated for degenerate Cope rearrangement of 1,5-hexadiene... 

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