Additive molar functions

Sometimes the discrepancies between numerical values calculated by means of the additivity principle and experimental values form an extremely important key to the disclosure of constitutional effects. 

Methods for expressing the additivity within structural units 

According to the nature of the structural elements used, three additive methods should be mentioned. 

Use of atomic contributions. If the additivity is perfect, the relevant property of a molecule may be calculated from the contributions of the atoms from which it is composed. 

The molar mass (molar weight) is an example (the oldest additive molar quantity). This most simple system of additivity however, has a restricted value. Accurate comparison of molar properties of related compounds reveals that contributions from the same atoms may have different values according to the nature of their neighbour atoms. The extent to which this effect is observed depends upon the importance of outer valence electrons upon the property concerned. 

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A survey of the Additive Molar Functions (AMFs), which will be discussed in this book, is given in Scheme 3.3. There the names, symbols and definitions are given of the 21 AMFs from which the majority of the physical and physicochemical properties of polymers can be calculated or at least estimated. Scheme 3.3 is at the same time a condensed list of the Nomenclature used. 

Seven Classes of Additive Molar Functions can be distinguished, each containing three AMFs ... 

SCHEME 3.3 Additive molar functions (per structural unit) ... 

We may conclude that Cp, and Cpare additive molar functions their group contributions, also valid for polymers, are given in Table 5.1. 

Table 7.11 gives a survey of the system of equations to be used. It contains four additive molar functions, a number of auxiliary equations and the final expressions for <5t(otai) and for the components of <5. 

The mechanical properties of polymers are controlled by the elastic parameters the three moduli and the Poisson ratio these four parameters are theoretically interrelated. If two of them are known, the other two can be calculated. The moduli are also related to the different sound velocities. Since the latter are again correlated with additive molar functions (the molar elastic wave velocity functions, to be treated in Chap. 14), the elastic part of the mechanical properties can be estimated or predicted by means of the additive group contribution technique. 

As will be demonstrated in Chap. 14, the different sound speeds are related with additive molar functions of the form ... 

Estimation and prediction of the bulk modulus from additive molar functions... 

We now summarise the relationships between K and some additive molar functions of a very different nature ... 

The speeds of longitudinal and transverse (shear) sonic waves can be estimated, c.q. predicted via two additive molar functions. From these sound velocities the four most important elastic parameters (the three elastic moduli and the Poisson ratio) can be estimated. 

In Chap. 13 we have already discussed the use of sound speed measurements for the derivation of elastic parameters. We shall come back on that, more elaborately, in this chapter. We have also seen that sound speeds can be expressed in terms of additive molar functions these are of course basic for estimations, as well for mechanical properties as for thermal conductivity (Chap. 17). 

This expression makes it possible to calculate the compression (bulk) modulus from the additive molar functions U and V. 

Table 14.5 shows the comparison of the values of the Ur and UH functions derived from experimental sound speed data with the values derived from the group contributions. It also shows a comparison between experimental sound speed values with those calculated purely from additive molar functions. The agreement is on the whole very satisfactory. 

SCHEME 14.1 Calculation of the elastic parameters EP and the additive molar functions U from the sound speed measurement u and vice versa. Valid only for elastic isotropic materials. 

Our conclusion is that by means of four additive molar functions (M, V, UR and Uh) all modes of dynamic sound velocities and the four dynamic elastic parameters (K, G, E and) can be estimated, c.q. predicted from the chemical structure of the polymer, including cross-linked polymers. 

The Permachor, an additive molar function for the estimation of the permeability... 

An additive molar function for the char-forming tendency Cft... 

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