The Group-Contribution Concept

Estimation techniques rely on the group-contribution approach that has found success with pure component properties (critical constants, heat capacities, etc.). The basic assumption behind this approach is that the property of a fluid can be approximated by the sum of the contributions of e functional groups of its molecules. 

Consider, for example, the system n-hexane - acetonitrile. The deviation from Raoult s law of this system - i.e. its activity coefficients - is described according to this concept, by  

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As an example of the group contribution concept, consider the Benson methylene groups shown below, where C represents a tetrahedral carbon, and Cb represents an aromatic carbon, Cd represents a doubly bonded carbon. Each of these values was determined from experimental thermodynamic data. Note that the contribution of the C-(H)2(X)(Y) group to the enthalpy of formation is different in each bonded environment. 

If experimental activity coefficients are unavailable, they can be estimated by, for example, the UNIFAC approach (Fredenslund, Gmehling and Rasmussen, 1977). The UNIFAC model is based on the group contribution concept, calculating the activity coefficients from two parts. The combinato-... 

Typical VLE results for different C02-alkane systems are shown in Figures 5.93 and 5.94. While in Figure 5.93 only VLE data for four different C02-alkane (propane, butane, hexane, decane) are shown, for the system ethane -CO2 additionally the experimental and predicted azeotropic and critical data are shown. As can be seen, excellent results are obtained for all systems considered. This means that the group contribution concept can also be applied for the gases included in the PSRK matrix. 

The development of new polymeric structures for different technological applications usually requires knowledge about properties of this material. The prediction of properties using additive group contribution method is a valuable procedure adopted during the developments presented here. The group contribution method concept was applied to obtain viscosity data versus temperature, an intermediate step of the free-volume parameters estimation procedure (equation (2) inputs). Detailed concepts about prediction of polymer properties were studied and applied as presented in specific literature (Van Krevelen, 1992 Bicerano, 2002). Equations (4) and (5) are the key equations of the procedure to obtain zero shear viscosity predicted data. The references adopted in this section also allows to predict many others polymer properties. 

The most accurate prediction methods ai e based on the mixture group contribution concept. The idea behind such models is that each molecule is considered to be a... 

Section 16.2 will discuss the concept and importance of the group-contribution (GC) approach in estimating two polymer properties, which are relevant for polymer solutions and blends the density and the solubility parameter. The GC technique is employed in several of the thermodynamic models discussed later in the chapter. 

Many chemical structure/physical property relations have been reported in literature but the most important contributions in this field have been made, we think, by Van Krevelen [1] and Bicerano [2]. Both authors present a total concept for polymer properties/molecular structure correlations based on the group contribution technique (Van Krevelen) and on connectivity indices calculations (Bicerano) covering all the properties mentioned in group A and B and some of the properties of group C. Seitz published a concept to estimate the mechanical properties (from group A and C) of polymers from their molecular structure [3]. 

Exponential temperature functions for the excluded volume parameter b and the attractive parameter a were introduced by Novenario et al. to apply this equation of state also to polar and associating fluids. Introducing a group-contribution concept leads to segment-molar values of aU parameters a, b, c which can easily be fitted to specific volumes of polymers. ... 

Allen and coworkers ° introduced a structural lumping approach based on group contribution concepts and pure-compound data. An oil fraction is assembled with a finite number of selected compound classes to capture key structural features of the oil. They calculated the number of CH, CH2, CH3 as well as terminal and nonterminal olefmic and aromatic carbons. They then followed the evolutions of carbon number distributions and carbon types in each compound class. 

The concept of hydrophile-lipophile balance (HLB) was first developed by Griffin [13] to correlate the structure of surfactant molecules with their surface activity. The HLB number (0-20) reflects the hydrophilicity of surfactant, and it increases with increasing hydrophilicity. A general trendi often observed in a family of surfactants is the increased CMC with HLB. Table 2.1 serves as a general guide for the formulator to choose surfactants that are most suited to meet the requirements of end-users. This semiempirical approach has been proved to be quite useful. Davies and Rideal [14] proposed that the HLB value of a particular surfactant could be calculated according to the group contribution approach. 

All models need some binary interaction parameters that have to be adjusted to some thermodynamic equihbriirm properties since these parameters are a priori not known (we will not discuss results from Monte Carlo simulations here). Binary parameters obtained from data of dilute polymer solutions as second virial coefficients are often different from those obtained from concentrated solutions. Distinguishing between intramolecular and intermolecular segment-segment interactions is not as important in concentrated solutions as it is in dilute solutions. Attempts to introduce local-composition and non-random-mix-ing approaches have been made for all the theories given above with more or less success. At least, they introduce additional parameters. More parameters may cause a higher flexibility of the model equations but leads often to physically senseless parameters that cause troubles when extrapolations may be necessary. Group-contribution concepts for binary interaction parameters in equation of state models can help to correlate parameter sets and also data of solutions within homologous series. 

Group contribution techniques are based on the concept that a particular physical property of a compound can be considered to be made up of contributions from the constituent atoms, groups, and bonds the contributions being determined from experimental data. They provide the designer with simple, convenient, methods for physical property estimation requiring only a knowledge of the structural formula of the compound. 

This book represents the effort of a group of scientists and clinicians to offer the reader an updated view of the main advances occurred in the field in the recent years. Every author has been selected because of his/her experience with modulators of estrogen receptors, either in basic or clinical grounds. This explains the structure of the book, which reviews the main basic concepts in the first part, to immediately concentrate in the recent news on the many uses of SERMs in clinical practice. We are very grateful with all of them for his excellent contribution. To conclude, we also would like to express our gratitude to Springer-Verlag for the excellent technical support as well as to those who, from different perspectives, are at the base of our work, our patients and our families. 

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