Group-contribution methods

Group contribution methods do not show these weaknesses discussed for the regular solution theory. 

The required equation of the solution of groups concept can be derived from the excess Gibbs energy of the groups in the mixture and the excess Gibbs energy in the pure compound. 

For the pure compound i built up by functional groups one can derive the following expression for the molar (g ) and total Gibbs energy (g )  

From the difference of the excess Gibbs energies for the groups in the mbcture and in the pure compound (standard state) one can derive an expression for the required activity coefficient y,  

This method is certainly valid when the property in question is the molecular weight, which is precisely the sum of the contributions from each atom according to the atomic weights and number of occurrences. For some properties, this method can be reasonably effective. But this method does not work very well if the property is not additive, or if the groups have strong interactions in a way that is either synergistic or antagonistic. 

Joback s method is an improved version of earlier methods, and attempts to estimate many properties of all the organic compounds. Table 5.13 shows the recommended Joback coefficients to build up the boiling and melting points of a compound, according to the formula 

An examination of table 5.13 shows that the effects of substituting the —H group with any group will increase the boiling point, except for —F. The hydrocarbon groups add electrons, and thus increase the dispersion forces. Since the group contributions A Tb are ranked in the order 

The melting points do not behave in parallel with the boiling points, and the group contributions ATf are ranked in the reverse order  

So this method predicts that the more highly branched isomers will have higher melting points, despite their having lower boiling points. This can be interpreted as a manifestation of the generally higher symmetry of the C molecules. 

As we discussed in Section 1.3, on inorganic materials, industrial crystallization rarely takes place in systems that contain only the solute and solvent. In many situations, additional components are present in the solution that affect the solubility of the species of interest. With an organic solute, data for solubility in a particular solvent is often not available, while data for the effect of other species on the solubility is virtually nonexistent. This means that the only option available for determining solubility in a complex mixture of solute, solvent, and other components (impurities or by-products) is through calculation or experimental measurement. While experimental measurement is often necessary, estimation through calculation can be worthwhile. 

Both of these methods rely on the use of experimental activity coefficient data to obtain parameters that represent interaction between pairs of structural groups. These parameters are then combined to predict activity coefficients for complex species and mixtures of species made up from a number of these functional groups. An example of this would be the calculation of the behavior of a ternary system by employing data on the three possible binary pairs. Lists of parameters and detailed explanations of these calculations can be found in the references previously mentioned. 

The groups contribution methods can also be used to calculate solubility in binary (solute-solvent) systems. A comparison of solubilities calculated employing the UNIFAC method with experimental values and values obtained from the Scatchard-Hildebrand theory is given in Table 1.9. 

We have shown how the concept of bond energy could facilitate an estimation of the standard enthalpies of formation on the basis of the 

Different evaluation methods exist, and are generally applied to a family of products. Two important categories are fiequently used that applied to metals and liquid metal alloys and that used for organic products. 

For this latter family, most methods for evaluating the thermodynamic data are inspired by what we have seen for bond energies, based on the structure of the molecule. The most significant methods ate based on what we call the functional-group substitution method. They are founded on a certain number of observations. For example  

when we know that the standard Gibbs energy of formation of ethane at 298 K is -32,604J/mol. For propane, which results from the substitution of a hydrogen atom by a methyl group on a carbon atom from ethane, we then calculate a standard Gibbs energy of formation at 298 K of  

Similarly, for ethyl alcohol, we can easily calculate a standard Gibbs energy of formation at 298 K  

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The third edition of "Properties of Gases and Liquids" by Reid et al. (1977) lists useful group contribution methods for predicting critical properties. Contributions to the second... 

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... 

Fredenslund, Aa., Gmehling, J., Rasmussen, P., "Vapor-Liquid Equilibria Using ONIFAC, a Group-Contribution Method,"... 

The use of group contribution methods for the estimation of properties of pure gases and Uquids [20, 21] and of phase equilibria [22] also has a long history in chemical engineering. 

An extensive series of studies for the prediction of aqueous solubility has been reported in the literature, as summarized by Lipinski et al. [15] and jorgensen and Duffy [16]. These methods can be categorized into three types 1 correlation of solubility with experimentally determined physicochemical properties such as melting point and molecular volume 2) estimation of solubility by group contribution methods and 3) correlation of solubility with descriptors derived from the molecular structure by computational methods. The third approach has been proven to be particularly successful for the prediction of solubility because it does not need experimental descriptors and can therefore be applied to collections of virtual compounds also. 

The group contribution method allows the approximate calculation of solubility by summing up fragmental values associated with substmctural units of the compounds (see Section 7.1). In a group contribution model, the aqueous solubility values are computed by Eq. (12), where log S is the logarithm of solubility, C is the number of occurrences of a substmctural group, i, in a molecule, and is the relative contribution of the fragment i. 

The disadvantages of the group contribution method are that 1) the groups included must be defined in advance and therefore the solubility of a new compound... 

The magnitude of the induced dipole moment depends on the electric field strength in accord with the relationship = nT, where ]1 is the induced dipole moment, F is the electric field strength, and the constant a is caHed the polarizabHity of the molecule. The polarizabHity is related to the dielectric constant of the substance. Group-contribution methods (2) can be used to estimate the polarizabHity from knowledge of the number of each type of bond within the molecule, eg, the polarizabHity of an unsaturated bond is greater than that of a saturated bond. 

A newer approach uses group-contribution methods to predict solubihty. It has been remarkably successful when apphed to nonpolymer solutions and there are indications that it will be equally successful for treating polymer solutions (17). 

Group Contribution Methods. It has been shown that many macroscopic physical properties, ie, those derived from experimental measurements of bulk solutions or substances, can be related to specific constituents of individual molecules. These constituents, or functional groups, are usually composed of commonly found combinations of atoms. One procedure for correlating functional groups to a property is as foUows. (/) A set of... 

Recognizing that there is presentiy a need for property values for tens of thousands of substances, but experimental data for only a small percentage of these substances, group contribution methods are viewed as the only choices for many problems such as newly or yet-to-be-synthesized compounds, situations where available data are well outside the conditions of interest, and reaction kinetics studies involving unknown intermediates. 

QSAJi Methods for Fluid Solubility Prediction. Several group contribution methods for predicting Hquid solubiHties have been developed. These methods as weU as other similar methods are often called quantitative stmcture-activity relationships (QSARs). This field is experiencing rapid development. 

Critica.1 Properties. Several methods have been developed to estimate critical pressure, temperature, and volume, U). Many other properties can be estimated from these properties. Error propagation can be large for physical property estimations based on critical properties from group contribution methods. Thus sensitivity analyses are recommended. The Ambrose method (185) was found to be more accurate (186) than the Lyderson (187) method, although it is computationally more complex. The Joback and Reid method (188) is only slightly less accurate overall than the Ambrose method, and is more accurate for some specific substances. Other methods of lesser overall accuracy are also available (189,190) (T, (191,192) (T, P ),... 

Constant volume heat capacities for Hquid organic compounds were estimated with a four parameter fit (219). A 1.3% average absolute error for 31 selected species was reported. A group contribution method for heat capacities of pure soHds andHquids based on elemental composition has also been provided (159). 

Suface Tension. The relationship between surface tension and Hquid molar volume (220), and the group contribution methods for Hquid molar volume can be utilized to estimate surface tension. 

Viscosity. A corresponding states method that requires critical pressure, temperature, and dipole moment has been developed for low pressure gas viscosity (221). This method, which includes a group contribution parameter, is also appHcable to gas mixtures. Whereas a group contribution method is not available for dipole moment, the influence this parameter has can be neglected for many species. 

Pure, low temperature organic Hquid viscosities can be estimated by a group contribution method (7) and a method combining aspects of group contribution and coimectivity indexes theories (222). Caution is recommended in the use of these methods because the calculated absolute errors are as high as 100% for individual species in a 150-compound, 10-family test set (223). A new method based on a second-order fit of Benson-type groups with numerous steric correctors is suggested as an alternative. Lower errors are claimed for the same test set. 

Hctivity Coefficients. Most activity coefficient property estimation methods are generally appHcable only to pure substances. Methods for properties of multicomponent systems are more complex and parameter fits usually rely on less experimental data. The primary group contribution methods of activity coefficient estimation are ASOG and UNIEAC. Of the two, UNIEAC has been fit to more combinations of groups and therefore can be appHed to a wider variety of compounds. Both methods are restricted to organic compounds and water. 

Second Virial Coefficient. A group contribution method including polar and nonpolar contributions has been proposed for second virial coefficients (241). This method has been appHed to both pure components and mixtures, the latter through prediction of cross-second virial coefficients. 

Owing to the original determination from uv—vis spectral solvatochromic shifts, 7T, B, and are called solvatochromic parameters. General rules for estimation of these variables have been proposed (258). Examples of individual parameter investigations are available (260,261). As previously mentioned, individual LEER—LSER studies are performed on related materials. A common method to link these individual studies to group contribution methods, and thereby expand the appHcabiUty, is by expansion of solvatochromic parameters to log—linear relationships, such as... 

A. Fredenslund, J. Gmehting, and P. Rasmussen, Uapor—Eiquid Using UNIFAC, a Group Contribution Method, Elsevier Scientific Publishing,... 

Gani" derived a group contribution method that shows promise. Initial evaluations show average errors of 5 to 10 percent (10-30 K) on a wide variety of compounds, but larger errors can occur. It is recommended that severaf compounds of Known melting point in the same or a similar family be predic ted in order to estimate the probable error. 

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

Enthalpy of Fusion The enthalpy (heat) of fusion AiTfus is defined as the difference of the enthalpies of a unit mole or mass of a solid and hquid at its melting temperature and one atmosphere pressure of a pure component. There are no generally apphcable estimation techniques that are very accurate. However, if the melting temperature is known, the atomic group contribution method of Chickos et al. " yields approximate results ... 

Data Reduction Correlations for G and the activity coefficients are based on X T.E data taken at low to moderate pressures. The ASOG and UNIFAC group-contribution methods depend for validity on parameters evaluated from a large base of such data. The process... 

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. 

In many cases, it is possible to replace environmentally hazardous chemicals with more benign species without compromising the technical and economic performance of the process. Examples include alternative solvents, polymers, and refrigerants. Group contribution methods have been conunonly used in predicting physical and chemical properties of synthesized materials. Two main frameworks have... 

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