Parachor method

Values of Rj, probably close to the required accuracy, can be estimated from the parachor, P the parachor can be calculated from a group-contribution method given by Reid et al. The... 

The Parachor is a parameter used to determine the interfacial tension. It can be estimated by a simple method proposed by Quayle in 1953 ... 

Group contributions for estimating the parachor by Quayle s method (1953). 

The surface tension is calculated starting from the parachor and the densities of the phases in equilibrium by the Sugden method (1924) J... 

Diffiusion Coefficient. The method of Reference 237 has been recommended for many low pressure binary gases (238). Other methods use solvent and solute parachors to calculate diffusion coefficients of dissolved organic gases in Hquid solvents (239,240). Molar volume and viscosity are also required and may be estimated by the methods previously discussed. Caution should be exercised because errors are multiphcative by these methods. 

The temperature-independent parachor [P] may be calculated by the additive scheme proposed by Quale.The atomic group contributions for this method, with contributions for silicon, boron, and aluminum from Myers,are shown in Table 2-402. At low pressures, where Pi. pc, the vapor density term may be neglected. Errors using Eq. (2-168) are normally less than 5 to 10 percent. 

Values for hydrocarbons other than alkynes and alkadienes can be predicted by the method of Suzuki et al. The best model includes the descriptors T, P, the parachor, the molecular surface area (which can be approximated by the van der Waals area), and the zero-order connectivity index. Excluding alkynes and alkadienes, a studv for 58 alkanes, aromatics, and cycloalkanes showed an average deviation from experimental values of about 30 K. 

Tyn-Calus This correlation requires data in the form of molar volumes and parachors = ViCp (a property which, over moderate temperature ranges, is nearly constant), measured at the same temperature (not necessarily the temperature of interest). The parachors for the components may also be evaluated at different temperatures from each other. Quale has compiled values of fj for many chemicals. Group contribution methods are available for estimation purposes (Reid et al.). The following suggestions were made by Reid et al. The correlation is constrained to cases in which fig < 30 cP. If the solute is water or if the solute is an organic acid and the solvent is not water or a short-chain alcohol, dimerization of the solute A should be assumed for purposes of estimating its volume and parachor. For example, the appropriate values for water as solute at 25°C are = 37.4 cmVmol and yn = 105.2 cm g Vs mol. Finally, if the solute is nonpolar, the solvent volume and parachor should be multiplied by 8 Ig. 

Liquid surface tension is calculated using the Sugden Parachor method [242]. Neglecting vapor density, surface tension for the liquid mixture is ... 

If reliable values of the liquid and vapour density are available, the surface tension can be estimated from the Sugden parachor which can be estimated by a group contribution method, Sugden (1924). 

The vapour density can be neglected when it is small compared with the liquid density. The parachor can be calculated using the group contributions given in Table 8.7. The method is illustrated in Example 8.13. 

Recently, Tichy investigated 41) the dependencies of the steric constants, Es, v, L, Bj, B4, MV (molar volume), [P] (parachor), MR (molar refraction), MW (molecular weight), and % (molecular connectivity index) on lipophilicity, as it is measured by n 42) and f43) constants. The data were treated by factor analysis methods. 

For pure liquids, an empirical estimation method for surface tension is that of McLeod and Sudgen, based on the parachor (P), which be calculated from the chemical groups of the molecule [13]. 

Estimation of a with 5.3.1 requires solely the input of pi and parachor. Parachor can be derived from molecular structure with schemes based on group additivity. Exner [4] gives an excellent review and discussion of various group contribution methods for parachor. A very simple method has been developed by McGowan [5] employing only atomic contribution and the number of bonds, A bonds ... 

Ixspcr has compiled the xurlave icnsiun ol ucetaldchsdc. propi waldehydc. and butyraldehyde at various tempera lure. I he surface tension ot formaldehyde wav estimated h the method described in Appendix A This method relate surface tension lo (he parachor. density, and molcculur weight I hr error is less than 50r. 

To present to the reader some "new" methods not previously highlighted in handbooks or textbooks. These methods may not be universally better than more well known methods, but we believe they are generally better in terms of range of applicability and accuracy. The "new" methods also avoid the need to calculate intermediate parameters such as molar refraction, parachor, or critical constants. (Such were required in the estimation methods of Meissner, Lydersen-Forman-Thodos, and Miller, recommended in the estimation methods handbook by Lyman et al. [1982].)... 

Table 8.2 compares the experimental values of the surface tension of polymers (obtained by different methods) and the calculated values, the latter being obtained by means of the parachor. The discrepancies between the different experimental values are reasonably small. The calculated values are, with a few exceptions, in reasonable agreement with the experimental values. 

If no experimental data are available, calculation by means of the group contributions to the parachor gives a reliable approximation. A still higher accuracy can be reached if the methods of "standard properties" or "standard substances", discussed in Chap. 3, are applied. 

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