Calculation from structural group contributions

Values of the activity coefficients are deduced from experimental data of vapor-liquid equilibria and correlated or extended by any one of several available equations. Values also may be calculated approximately from structural group contributions by methods called UNIFAC and ASOG. For more than two components, the correlating equations favored nowadays are the Wilson, the NRTL, and UNIQUAC, and for some applications a solubility parameter method. The fust and last of these are given in Table 13.2. Calculations from measured equilibrium compositions are made with the rearranged equation... 

There have been several efforts to provide means for computation of the interfacial tension coefficient from characteristic parameters of the two fluids [Luciani et al., 1996a]. The most interesting relation was that found between the interfacial tension coefficient and the solubility parameter contributions, that are calculable from the group contributions. The relation makes it possible to estimate the interfacial tension coefficient from the unit structure of macromolecules at any temperature. The correlation between the experimental and calculated data for 46 polymer blends was found to be good — the correlation coefficient R = 0.815 — especially when the computational and experimental errors are taken into account. 

Figure 11.15b shows a comparison of various fractional free volumes in ER6. The total free volume is defined as the difference between the total, V, and the van der Waals specific volume, Vvdw, which was calculated from the group contributions given by van Krevelen [1993]. In the temperature range from Tg (PVT) = 325 to 470 K,/f varies between 0.316 and 0.373. Its value for a hexagonal close-packed (hep) structure is 0.26. The Bondi free volume [Bondi, 1968] assumes a occupied volume of 1.3Vvdw-/Bondi varies between 0.111 and 0.185. It is distinctly larger than the hole free volume determined from the S-S equation of state of PVT (and from PALS) experiments, h = Vf IV, which increases from 0.0576 to 0.134. 

Experimental data on Op and On for different polymer materials exhibit unique correlations with (hydrogen bonding) and 6(j (dispersion) components respectively of solubility parameter 6gp of polymer (53,60) which can be calculated from data on structural group contributions to and available in the literature (61). The existence of such correlations (Figures 9(a) and 9(b)) indicate that LSC data can be used to characterize the chemical nature of polymeric membrane materials. 

Here k f k2f and kare microscopic ionization constants defined in section 4.6. From this it was possible to calculate and plot variation in Dnoh with pH for pentazocine as shown in Figure 2. The fourth partition coefficient was obtained by structural group contribution to the measured partition coefficient of a reference compound (morphine). This was done following the Hansch approach. 

The second column of Table 6.7 gives the y values estimated from Ps. There is a rather large discrepancy from those obtained by contact angle experiments (which is in the last column). Clearly, the parachor approach is not suitable for the surface tension estimation of TLCPs. The third column summarizes the ys estimated from Ecoh- In order to calculate Ecoh values, three structural group contribution tables have been chosen and evaluated. They are Hoftyzer and Van Krevelen, Hayes, and Fedors tables [60]. The Ecoh value used for the p-naphthalene group is estimated from a combination of Ecoh values of p-phenylene, ethylene, and other groups. For readers information, Hoftyzer and Van Krevelen and Hayes do not provide Ecoh value for the p-naphthalene group. 

The ability to reproduce thermodynamic quantities by means of the structural parameters is usually better than 5% for substances belonging, or similar, to those taken into consideration in the fitting of the data. It is however very difficult to make prediction about the ability of the structural parameters to reproduce satisfactory values for compounds which are not similar to those considered in the calculation of the group contributions. As an example the experimental value of the AG of acetamide (= -40.6 K J mol )(21) resulted very different with respect to that expectable from Hine s bond contributions (= -31.4 K J mol )(3). That is not surprising in view of the characteristics the water has to discriminate the various type of solutes better than others solvents do, see f.i. the peculiarity that the Barclay-Butler s plot presents in water with respect to non-aqueous solvents. 

Moreover, the objective function obtained by minimizing the square of the difference between the mole fractions calculated by UNIQUAC model and the experimental data. Furthermore, he UNIQUAC structural parameters r and q were carried out from group contribution data that has been previously reported [14-15], The values of r and q used in the UNIQUAC equation are presented in table 4. The goodness of fit, between the observed and calculated mole fractions, was calculated in terms RMSD [1], The RMSD values were calculated according to the equation of percentage root mean square deviations (RMSD%) ... 

Van Krevelen s group contributions are widely used for the prediction of Tg and perform reasonably well. When experimentally determined Tg values for 600 polymers are compared to predictions from group contributions, it could be shown that approximately 80% of the calculated Tg values were within 20 K of the experimental result [122]. A serious limitation of any group contribution method, however, is that only polymers with structural groups for which contributions have been developed can be predicted. 

C—OH = 1.36 0.01 A, and these values have been supported by several infrared and microwave spectroscopic investigations. Nearly the same values have been reported also for many other carboxylic acids. The bond numbers calculated from these bond lengths are about 1.85 and 1.15, respectively that is, the presence of the hydrogen atom causes structure A to make an 85 percent and structure B only a 15 percent contribution. Essentially the same resonance is found in esters for methyl formate, for example, the bond lengths in the carboxylate group are88 C=0 = 1.22 0.03 A and C—OCH3 = 1.37 0.04 A. 

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 ... 

Within this group of structures, none of the different combinations of factors gave an R-value significantly worse - at the 5% level of probability - than the best. Thus there is no justification for choosing any one in preference to any other, and so the mean was taken as the best structure. The standard deviations of the parameters of this model were calculated from the overall variance within a structure factor set. That is, the contribution to uncertainty due to errors in the structure factor set have been omitted. Thus these standard deviations are almost certainly underestimates, for whilst the structure factors of Yokouchi et al might be significantly better than those of the other authors, they are certain to contain some error. 

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