Waals Volume Vw

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. 

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... 

Thus another approach proved necessary. This new approach was found by plotting the values of Vr (298) versus the molar Van der Waals volume Vw. Fig. 4.1A shows the result the molar volumes Vr and Vw, show a simple linear relationship. The ratio Vr(298)/Vw has a value of 1.60 0.035 (see for the numerical values Table 4.6). 

Jinno and Kawasaki also obtained the best correlations between log k and topological index x. van der Waals volume (Vw)> and hydrophobic parameter (log P) for alkylbenzenes separated on reversed-phase C2, Cg, and Cl 8 columns by HPLC (r>0.94). In addition, Smith presented relationships between log k and connectivity index x for alkylbenzenes and n-alkylbenzenes separated by RP-HPLC on SAS-Hypersil and ODS-Hypersil columns (r>0.97). 

In the FH formula, the characteristic volume V can be the molar volume or a specific hard-core volume of the molecule such as the van der Waals volume Vw. The last of the above equations is the Entropic-FV formula, discussed earlier (Equation 16.51). As shown, in the Entropic-FV model the van der Waals volume is used, as a measure of the molecular volume with increments by Bondi. The Entropic-FV formula was shown to work satisfactorily for athermal polymer solutions and offers a substantial improvement over the FH term. The van der Waals repulsive term and the Entropic-FV form are functionally identical. 

Space truly occupied by atoms, often called the van der Waals volume Vw. More formally,... 

Table 3.2. Van der Waals volumes Vw calculated by group contributions, the "correction index" Nvd y used in the correlation for Vw, and the fitted values of Vw, for 110 polymers. Vw is in cc/mole. The list is in the order of increasing Vw(group). Polymers with equal values of Vw(group) are listed in the order of increasing Vw(fit). The values of the connectivity indices and 1xv, which are also used in the correlation, are listed in Table 2.2. 

Figure 7.3. The results of a fit using the van der Waals volume Vw and a correction index NPS, to the molar parachor P calculated by the group contributions of van Krevelen supplemented by the atomic and structural contributions of Sugden, for a set of 115 polymers.

The van der Waals volume Vw gave slightly improved results compared to molar volume V. 

Table 9.1. Experimental dielectric constants e(exp), the quantities (cohesive energy Ecohl in J/mole, correction index Ndc> and van der Waals volume Vw in cc/mole) used in the correlation for e, and fitted dielectric constants e(fit), for 61 polymers. Ecohl is calculated from equations 5.8-5.10, and Vw is calculated from equations 3.10 and 3.11, for use in this correlation. Calculations on random copolymers are discussed in Section 17.E. 

Table 17.7. Cohesive energy Ecohl (Equations 5.10-5.12), van der Waals volume Vw, the term N(jc used in predicting the dielectric constant e, and predicted e values at room temperature, for low-hydroxyl" grade of poly(vinyl butyral) containing roughly 12% by weight of poly(vinyl alcohol). The subscript 1 denotes poly(vinyl butyral), while the subscript 2 denotes poly(vinyl alcohol), for weight fractions and mole fractions which are denoted by w and m, respectively.

Step 6. Calculate the van der Waals volume Vw by using equations 3.10 and 3.11. These equations contain various types of structural parameters, atomic correction terms, and group correction terms, in addition to connectivity indices, as do many of the correlation equations to be used later. All such parameters are determined automatically by the software package from the connectivity table. The result is Vw=64.04 cc/mole for polystyrene. 

It, apparently, is connected by that organic phosphorus of compounds, borrowing free volumes in macro chain and getting in intermolecular "space", the polar groups strengthen intermolecular interaction a little. As confirmation of such assumption that circumstance, that at van-der-waals volume (Vw) polyethylene in 20,6 sm3/mol, found on can serve a known technique, the share of free volume (Ve) makes 7,6 sm3/mol, and volumes organic phosphorus of compounds - cyclohexyl phosphonic acids, potassium hydrocyclohexyl phosphonate, potassium cyclohexyl phosphonate - are accordingly equal 0,097 hm3, 0,144 hm3, 0,191 hm3. 

Scheme 2.2. Van der Waals volumes (Vw). partial molar volumes (V), and packing coefficients //).

Tab. 2.7. Molar volumes, VI van der Waals Volumes, Vw, and packing coefficients, calculated for acyclic and cyclic ground and transition structures needed for the explanation of the pressure effect on the Diels-Alder reaction of 1,3-butadiene with ethene.

Scheme 2.22. Partial molar volume [V], van der Waals volume (Vw) and the volumes of activation and reaction AV, AV) of the Cope rearrangement of 1,5-hexadiene.

Hydrophobic parameters are mostly experimentally obtained log P or calculated log P (C log P), where P is the octanol-water partition coefficient. n is the hydrophobic constant of the substituents. The electronic parameters (Hammett constants) a, a and appHes to substituent effects on aromatic systems and Taft s a appHes to ahphatic systems. Steric parameters are Tafts steric parameter Es, McGowan volume MgVol, van der Waals volume Vw, molecular weight MW. Verloop s sterimol parameters Bl, B5 and L... 

The cellulose affinity in dyeing process is another important property of dyestuff. The dyeing of textile fibers led to many theories, which tried to explain the mechanism of dye uptake. One of the most interesting topics is the relationships between the molecular structure and the cellulose affinity of dyestuffs [129]. Table 8.6 lists the data of cellulose affinity of 21 diazo dyes and the following kinds of molecular parameters of these dye molecules the length of the conjugated chain (n), the van der Waals volume (Vw), the dipole moment (p), the HOMO by PM3 method of quantum chemical calculation and six steric parameters ( i, A.2, A.3 and a,... 

---