Group contribution models linear

The simple Flory-Huggins %-function, combined with the solubility parameter approach may be used for a first rough guess about solvent activities of polymer solutions, if no experimental data are available. Nothing more should be expected. This also holds true for any calculations with the UNIFAC-fv or other group-contribution models. For a quantitative representation of solvent activities of polymer solutions, more sophisticated models have to be applied. The choice of a dedicated model, however, may depend, even today, on the nature of the polymer-solvent system and its physical properties (polar or non-polar, association or donor-acceptor interactions, subcritical or supercritical solvents, etc.), on the ranges of temperature, pressure and concentration one is interested in, on the question whether a special solution, special mixture, special application is to be handled or a more universal application is to be foxmd or a software tool is to be developed, on munerical simplicity or, on the other hand, on numerical stability and physically meaningftd roots of the non-linear equation systems to be solved. Finally, it may depend on the experience of the user (and sometimes it still seems to be a matter of taste). 

The subunits defined in the model are listed in Table I. Also shown are the group molar volume and the group contribution to the COj permeability and the CO2/CH4 permselectivity the best fit solution to the matrix of linear equations. The gas permeability of each polymer in the dataset was calculated firom the resultant subunit permeability indicated in Table I and the normalized structural equation for each polymer. The CO2 and CH4 permeability (in Barrers) predicted by the group contribution model is compared to experimental values in Figure 1. An excellent correlation is evident for both gases. The correlation between model predicted and experimental CO2/CH4 selectivity is shown in Figure 2. 

In the remainder of this chapter, newly developed methods such as a molecular modeling approach (Bodor and Huang, 1992 Zhou et al., 1993), a group contribution approach (V Mita et al., 1986 Klopman et al., 1992 Kthne et al., 1995 Myrdal et al., 1995), and a frequently used linear free-energy relationship method (Taft et al., 1985 Lee, 1996) will be discussed. 

The Fujita-Ban model is a linear transformation of the classical Free-Wilson model indeed, group contributions of the Free-Wilson model can be transformed to Fujita-Ban group contributions by subtracting the group contributions of the corresponding substituents of the reference compound. 

In particular, the Fujita-Ban group contributions implicitly contain all the possible physico-chemical contributions of a substituent as a consequence, the Fujita-Ban models always give an upper limit of correlation which can be achieved by Hansch linear models. 

The subscripts eg and cs refer to end-group contribution and to elementary contribution of constitutive segments, respectively, and n is the number of segments per molecular chain. This model was applied satisfactorily to n-paraffins, but also to n-esters and n-ether. A linear variation of both the activation enthalpy and entropy as a function of n has been observed experimentally (22). One may designate as 7 the parameter that joins the intrinsic components describing the elementary contributions of the crystalline relaxation, i.e.,... 

Free Wilson analyses may include far fewer variables than substituents, if group contributions being not significant are eliminated. Indicator variables for 28 different structural features and different test models and 15 interaction terms were investigated to describe the inhibition of dihydrofolate reductase by 2,4-diaminopyri-midines (52) 9 indicator variables and 2 interaction terms were selected and eq. 197 was derived out of the 2047 theoretically possible linear combinations of any numbers of these variables [412]. 

Binary variables are used to represent the occurrence of molecular structural groups (e.g. -CH3, -CHO, -OH. ..) found in the group contribution correlations. This allows molecules to be generated according to a set of structural and chemical feasibility constraints. In addition, a variety of pure component physical and environmental property prediction equations, non-ideal multi-component vapour-liquid equilibrium equations (UNIFAC), process operational constraints and an aggregated process model form part of the overall procedure. Finally, the solvent identification task is solved as a mixed integer non-linear programming (MINLP) problem (Buxton et ai, 1999). 

The underlying concept of all QSAR analyses is the additivity of substituent group contributions to biological activity values in the logarithmic scale. This additivity comes from the fact that QSAR models are linear free-energy related. All... 

Density is another important physico-chemical property based essentially in the mass of the elements of the compoxmd and their inter-molecular forces. The complexity of this property is lower than the melting point, but in order to have quantitative values, several models were constructed using empirical, group contribution, linear and quantum mechanic methods. The obtained predictions are generally accurate. 

---