Stockmayer’s treatment

Fig. 3.9 Weight fraction of the gel part plotted against the reactivity. (Stockmayer s treatment (S), Flory s treatment (F), and Ziff-Stell s treatment (ZS).)...

Stockmayer, and is called Stockmayer s treatment of the postgel regime (the solid line... 

The difference in the two approaches was later clarifled from a kinetic point of view by Ziff and Stell [13]. It was shown that Stockmayer s treatment allows reaction neither between sol and gel, nor between gel and gel. The increase of the gel fraction is only by the cascade growth of the sol clusters to infinity, while in Flory s treatment sol and gel interact, and reaction within the gel is also allowed. Ziff and Stell proposed a new treatment in which intramolecular reaction of the gel is not allowed but reaction between sol and gel is allowed. Their result on the gel fraction is shown in Figure 3.9 by the broken line (ZS). 

Within Stockmayer s treatment of the postgel regime, after a complex calculation, it turns out that there is no singularity up to the second derivatives, but the third derivative contains a discontinuity... 

In the postgel regime we foUow Stockmayer s treatment, and assume that the degree of reaction a in the sol part remains at constant a. The corresponding value of z is given by z = f- 2y /(f — The polymer volume fraction of the sol part... 

Buckingham and Pople gave a more complete treatment than Stockmayer s of the interaction between two molecules having non-central force fields. Their treatment allows not only for dipole-dipole interaction but also for dipole-quadrupole, quadrupole-quadrupole, dipole-induced dipole, steric, anisotropic, and other effects. An important feature of the Buckingham-Pople procedure is that the various integrals needed can be calculated from a master table that they give. Buckingham and Pople applied their method to four polar compounds for which values of the dipole moment and the polarizability were known, and used B(T) to... 

Although the major interest in experimental and theoretical studies of network formation has been devoted to elastomer networks, the epoxy resins keep apparently first place among typical thermosets. Almost exclusively, the statistical theory based on the tree-like model has been used. The problem of curing was first attacked by Japanese authors (Yamabe and Fukui, Kakurai and Noguchi, Tanaka and Kakiuchi) who used the combinatorial approach of Flory and Stockmayer. Their work has been reviewed in Chapter IV of May s and Tanaka s monograph Their experimental studies included molecular weights and gel points. However, their conclusions were somewhat invalidated by the fact that the assumed reaction schemes were too simplified or even incorrect. It is to be stressed, however, that Yamabe and Fukui were the first who took into account the initiated mechanism of polymerization of epoxy groups (polyetherification). They used, however, the statistical treatment which is incorrect as was shown in Section 3.3. 

The numerical coefficient 7.16 is much larger than Flory s value of 2.60 from his slightly more complicated treatment, as it depends on different assumptions made in the derivations. Other variations on the method le.g. use of a more accurate sum of n Gaussian functions for p(s)] lead to still other values for the coefficient. Given the arbitrariness of the assumptions, no great significance can be attached to the numerical value, and it seems reasonable to follow a recommendation of Stockmayer and let... 

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