Sol fractions

The pre-gel model calculates the weight average molecular weight of the reaction mixture, while the post-gel model calculates the weight of the sol fraction and the effective crosslink density. A simple computer program using the derived expressions has been written in BASIC and runs on IBM-PC compatible computers. The importance of secondary reactions on cure in typical coatings is discussed. 

If the mixture has gelled, the program proceeds to calculate P(Fa° ) and P(Fg° ) using a binary search method (lines 2510-2770). This method is more convenient that the earlier approach of Bauer and Budde (10) who used Newton s method, since derivatives of the functions are not required. The program also calculates the probability generating functions used to calculate sol fractions and the two crosslink densities (lines 2800-3150). Finally, the sol fraction and crosslink densities are calculated and printed out (lines 3160-3340). The program then asks for a new percents of reaction for the A and B groups. To quit enter a percent reaction for A of >100. 

In the stochastic theory of branching processes the reactivity of the functional groups is assumed to be independent of the size of the copolymer. In addition, cyclization is postulated not to occur in the sol fraction, so that all reactions in the sol fraction are intermolecular. Bonds once formed are assumed to remain stable, so that no randomization reactions such as trans-esterification are incorporated. In our opinion this model is only approximate because of the necessary simplifying assumptions. The numbers obtained will be of limited value in an absolute sense, but very useful to show patterns, sensitivities and trends. 

In POLYM the output data of KINREL are used with compositional information to calculate the number and mass average molecular masses (Rn and Rm, respectively) and number and end-group average functionalities (fp and fg> respectively) in the pre-gel region in all stages. In addition, the network characteristics such as sol fraction, mj, and the number of elastically active network chains per monomer (5), Ng, are calculated in the post-gel regime of stage 3. 

As might be expected, these differences in the pre-gel properties are also reflected in the post-gel regime. The sol fraction varies more smoothly with conversion for the branched prepolymer compositions, cf. Figures 3 and 6. But because the gel point is at (so... 

Rn, and the gel point, Figure 16 concerns the sol fraction and Figure 17 the number of EANC s per monomer. The differences are most pronounced near the gel points and they vanish with completion of the reaction. 

The parenthesis in Equation 19 is the probability that a randomly selected monomer unit bound in the polymer chain belongs to the sol fraction, and therefore, the meaning of the above equation is obvious. At conversion 4 the weight fraction of the primary molecules which were formed at x=0 is given by ... 

The accumulated sol fraction which is measured in experiments is given by the integration over all birth conversion. 

Number- and Weight-Average Chain Length of the Primary Molecules which Belong to the Sol Fraction. 

The sol fractions occurring in a series of cross-linked Tutyl rubber copolymers consisting of a small proportion of isoprene with isobutylene units have been found to vary with y in accordance with Eq. (50). The unfortunately large experimental inaccuracy precluded a precise test, however. 

The relative abundances of cross-linkages and of various primary species in the sol and in the gel fractions may be obtained by extension of this procedure. Since 4>l equals the fraction of the cross-linkages (or of the cross-linked units) occurring in the sol fraction, we can write... 

The number and weight average values of y in the sol fraction are, respectively, ... 

The total number of molecules in the sol fraction, neglecting intramolecular cross-linking, will equal the number of primary molecules minus the number of cross-linkages in the sol. Expressing these as numbers of moles per equivalent of structural units, we have N = 1/% primary molecules and p /2 cross-linkages in the sol. The number average degree of polymerization in the sol is then... 

The molecular distributions for polymers formed by condensations involving polyfunctional units of the type R—A/ resemble those for the branched polymers mentioned above, except for the important modification introduced by the incidence of gelation. The generation of an infinite network commences abruptly at the gel point, and the a-mount of this gel component increases progressively with further condensation. Meanwhile, the larger, more complex, species of the sol are selectively combined with the gel fraction, with the result that the sol fraction decreases in average molecular complexity as well as in amount. It is important to observe that the distinction between soluble finite species on the one hand and infinite network on the other invariably is sharp and by no means arbitrary. 

It is worth emphasizing that formulas (39) and (40) may be invoked to determine the statistical characteristics of the sol-fraction provided the probability parameters are replaced in these equations by their modified values... 

If the content of the test tube was solid at ambient temperature, an electric drill equipped with a carbide bit produced, upon drilling, a thin ribbon that had a high surface area to volume ratio. This was leached with tetrahydrofuran at ambient conditions until chromatography analysis of the sol fraction indicated that equilibrium had been established. A gram of resin was leached with 25 ml of solvent. 

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