Group contribution

The solubility parameter of a polymer can be calculated using something called group contributions. The essence of this approach 

A compilation taken from our own work is shown in Table 11-1. To calculate the solubility parameter of a polymer one uses the simple relationship (Equation 11-38)  

For example, say we wish to calculate the solnbility parameter of poly(methyl methacrylate) (PMMA)  

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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,"... 

Cj = group contributions see Table 4.2 dy = group contributions see Table 4.2... 

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

Lydersen, A.L. (1955), Estimation of critical properties of organic compounds by the method of group contributions . Uniu. Wisconsin Coll., Eng. Exp. Stn. report No. 4, Madison, Wl. 

Equations (2 -(4) clearly illustrate the increase in distance in the interactions between atoms X and Y in going from the additivity of atomic, to bond, and further to group contributions. 

Figure 7-1 shows the groups that are obtained for alkanes, and the corresponding notation of these groups as introduced by Benson [Ij. Table 7-2 contains the group contributions to important thermochemical properties of alkanes. Results obtained with these increments and more extensive tables can be obtained from Refs. [1] and [2]. 

Table 7.2. Group contributions to Cf, S°, and AHf for ideal gases at 25 °C, 1 atm, for alkanes.

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. 

The accuracy of an additivity scheme can be increased by going from atomic contributions through bond contributions to group contributions. 

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... 

Klopman G, S Wang and D M Balthasar 1992. Estimation of Aqueous Solubility of Organic Molecule by the Group Contribution Approach. Application to the Study of Biodegradation. Journal c Chemical Information and Computer Science 32 474-482. 

A 2-Alkyl group contributes to the basicity of the thiazole ring. The only significant fall in pK (for 2- -propyl and 2-r-butyl thiazole) is not... 

Groups Groups Contributing Groups Contributing Separation Remaining to Concentration to Concentration... 

In addition to thermodynamic appUcations, 62 values have also been related to the glass transition temperature of a polymer, and the difference 62-61 to the viscosity of polymer solutions. The best values of 6 have been analyzed into group contributions, the sum of which can be used to estimate 62 for polymers which have not been characterized experimentally. 

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). 

L/(mol-s) (39,40). QDI is also attacked by hydroxide ion (eq. 4) to produce a quinone monoimine (QMI), itself an oxidized developer derived from /)-aminopheno1. Such compounds can further react with coupler, albeit at a slower rate than QDI, to form a dye and were cited in the seminal patent as color developers (32). However, the dyes derived from this deaminated developer have different hues from the QDI dyes, and these hues are pH-dependent as a consequence of the phenoHc group contributed by the developer. Although the deamination reaction to produce QMI is fast, the rate constant is 10 to 10 L/(mol-s) (40—42), its effect is somewhat offset by the redox reaction of the QMI with the reduced developer, present in large excess, to regenerate the desired QDI. The primary net effect of the deamination reaction is to enlarge the resulting dye cloud (43). 

An area that has used chemical stmctures for predictive purposes quite successfully is the estimation of thermophysical properties of compounds. There has been an extensive compilation of estimation methods (81), and prediction of physical properties has been automated using these techniques (82). More recendy, the use of group contribution techniques to design new molecules that have specified properties has been described (83). This approach to compound design is being used to develop replacement materials for chloroduorocarbons. 

Crystallinity is low the pendent allyl group contributes to the amorphous state of these polymers. Propylene oxide homopolymer itself has not been developed commercially because it cannot be cross-baked by current methods (18). The copolymerization of PO with unsaturated epoxide monomers gives vulcanizable products (19,20). In ECH—PO—AGE, poly(ptopylene oxide- o-epichlorohydrin- o-abyl glycidyl ether) [25213-15-4] (5), and PO—AGE, poly(propylene oxide-i o-abyl glycidyl ether) [25104-27-2] (6), the molar composition of PO ranges from approximately 65 to 90%. 

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. 

Numerous other methods have been used to predict properties of gases and Hquids. These include group contribution, reference substance, approaches, and many others. However, corresponding states theory has been one of the most thoroughly investigated methods and has become an important basis for the development of correlation and property estimation techniques. The methods derived from the corresponding states theory for Hquid and gas property estimation have proved invaluable for work such as process and equipment design. 

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