Crosslink functionality

We have investigated the static and dynamic mechanical properties of networks of different chemical and topological structures ( 19,20). In a previous paper, we reported results obtained on networks with crosslink functionality four (21). In the present study, we investigated the effect of the structure of junctions on the mechanical behaviour of PDMS. Rather uncommon networks with comb-like crosslinks were employed, intending that these would be most challenging to theoretical predictions. 

Calculated network densities and corresponding crosslink functionalities... 

Figure 10. Ratio C2/Ct vs. crosslink functionality f = ft. The dash-dotted line represents the upper bound of theory.

As expected, addition of IV tended to increase the sol fraction in the cured specimens. The statistical theory of gelation (9) can be used to calculate the expected gel fraction as a function of crosslink functionality, extent of reaction, and proportion of difunctional units in the mixture. For these mixtures, an adequate fit to the extraction data was obtained by assuming that the primary reaction is isoindoline formation (Figure 5). Triazine or phthalocyanine formation alone cannot account for the data. 

Let us compare the behavior of networks exhibiting different crosslink functionalities. Qualitatively it is known that an increase of/results in a small decrease of the swelling ratio Q — at constant molecular weight of the elastic chains34 -, and in a rather sharp increase of the reduced modulus G 22 ... 

Comparison is thus rendered possible between networks with elastic chains of the same average length, but exhibiting different crosslink functionalities. From the ratio... 

For networks in which the average crosslink functionality exceeds the above-mentioned values, the ratios of the slopes lead to functionalities which are obviously too high. The assumption according to which the connectivity factor x2 is equal to unity cannot hold any more. This means that a fraction of the network chains connect nodules which are not first neighbors. The probability for permanent entanglements to occur is increased. No quantitative treatment of the experimental data is possible in that case, because of the number of parameters to consider, none of them being accessible by independent experiments. 

Homologous series of networks, prepared under the same experimental conditions, and differing only by the length of their elastic chains have been made available, and were used to investigate their structure, their swelling behavior, and their mechanical deformation properties. It was assumed that within a homologous series of networks the crosslink functionality remains constant, an assumption which is supported by results on star-polymers11. ... 

Figure 12.8 Variation in the compression yield stress with (fc — 2)/fc 2/Me for both aliphatic (open symbols) and aromatic (closed symbols) networks. Fc is the crosslink functionality. (Crawford and Lesser, 1998, Copyright 2001, with permission of John Wiley Sons, Inc.)...

In their work on a specific class of amine-crosslinked epoxy thermosets, Lesser and Crawford [140,141] found that Tg was affected strongly by Mc, by the average crosslink functionality fav (because of the effects of crosslink mobility, as will be discussed in Section 1 l.B.3.a for the equilibrium shear modulus Ge°), and by the chain stiffness. Their data were best represented by Equation 6.18, where Tg(° ) and C, were treated as fitting parameters. 

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