Group contribution models

Computable molecular descriptors differ from experimentally derived properties in two important ways  

They can be derived from the compound structure alone, (i.e., can be determined 

These characteristics distinguish QPPRs from QSPRs in terms of their statistical evaluation and in terms of their applicability. Note that to estimate the property of interest with a QPPR model, certain other properties of a query compound must be available. 

Computable molecular descriptors that occur most frequently in QSPRs in this book are explained in Chapter 2. QSPRs and their statistical parameters are presented in the same way as shown for QPPRs in Section 1.4. Often, QSPR studies apply a set of molecular descriptors to compare their significance for the particular correlation. In this book we present only the most significant QSPRs as judged in the source or by the authors. 

Oishi and Prausnitz [47] proposed writing the solvent activity coefficient for polymer-solvent systems as the sum of three terms [Eq. (53)]. 

In the entropic-free volume model, the activity coefficient of the solvent is given by Eqs. (44)-(48) with p = 1 [52]. The residual contribution is represented by the residual contribution of the UNIFAC model with temperature-dependent interaction parameters [53]. The liquid molar volumes needed for the calculation of the free volume of a component can be taken from experiment or calculated from the Tait equation [4] or by the group contribution method of Elbro et al. [56]. This model is relatively easy to use. 

The combinatorial term is calculated by means of the original Flory-Huggins expression, Eq. (54). 

The free-volume and residual terms are calculated from a modification of the original Flory equation of state, Eq. (55), where v is the reduced volume, defined by Eq. (56). 

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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. 

First a database of solute-solvent properties are created in SoluCalc. The database needs the melting point, the enthalpy of fusion and the Hildebrand solubility parameter of the solute (Cimetidine) and the solvents for which solubility data is available. Using the available data, SoluCalc first prepares a list of the most sensitive group interactions and fits sequentially, the solubility data for the minimum set of group interaction parameters that best represent the total data set. For a small set of solvents, the fitted values from SoluCalc are shown in Table 9. It can be noted that while the correlation is very good, the local model is more like a UNIQUAC model than a group contribution model... 

The performance of many process equipment encountered in crystallization practice is often profoundly affected by the flow properties of the liquid media. Heat transfer, for example, may be severely impeded in thick sluggish liquors or magmas crystallization may occur only with difficulty, and filtration and washing of crystalline product may be impaired (Mullin, 1961). Since viscosity is a function of temperature the viscosity at the average temperature of crystallization is considered. The viscosity of the solvent can be estimated using the following group contribution model (ICAS, 2003)... 

Pure component property group contribution model parameters ... 

Campbell, J.R. and Luthy, R.G. Prediction of aromatic solute partition coefficients using the UNIFAC group contribution model. Environ. Sci. Technol, 19(10) 980-985, 1985. 

Group contribution models (GCMs) Fragment constants... 

Another frequently used method to derive empirical relationships between structure and property is to divide the structure into chemically logic parts such as groups of atoms (functional groups) and to assign each group a contribution to the property of the whole molecule. This approach is termed the group contribution model (GCM). Since groups cannot be measured individually, it is necessary to derive... 

Lai, W. Y., D. H. Chen, and R. N. Maddox, Application of a Nonlinear Group-Contribution Model to the Prediction of Physical Constants 1. Predicting Normal Boiling Points with Molecular Structure. Ind. Eng. Chem. Res., 1987 26, 1072-1079. 

It is very satisfying and useful that the COSMO-RS model—in contrast to empirical group contribution models—is able to access the gas phase in addition to the liquid state. This allows for the prediction of vapor pressures and solvation free energies. Also, the large amount of accurate, temperature-dependent vapor pressure data can be used for the parameterization of COSMO-RS. On the other hand, the fundamental difference between the liquid state and gas phase limits the accuracy of vapor pressure prediction, while accurate, pure compound vapor pressure data are available for most chemical compounds. Therefore, it is preferable to use experimental vapor pressures in combination with calculated activity coefficients for vapor-liquid equilibria predictions in most practical applications. 

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