High functionality networks

To compare the predictions of the various molecular theories of rubber elasticity, three sets of high functionality networks were prepared and tested In this Investigation. The first set of networks tested were formed In bulk and attained a high extent of the endllnklng reaction, i.e., eX).9 where e Is the extent of reaction of the terminal vinyl groups. The second set of networks studied were formed In the presence of diluent and also achieved a high extent of reaction (e>0.9). The final group of experiments were performed on networks formed In bulk at low extents of reaction (0.4 [Pg.333]

It is necessary to emphasize that the common use of v, instead of v in Equation (10) for end-linked model netwoiks is only an ai oximation when the networks are formed with nonstoichiometric ratio between the crosslinking molecules and end-reactive chains. Nevertheless this sq proximation seems not to be serious and we shall see that it is certainly valid for high functionality networks. 

It s obvious that in high functionality networks v is not very different from v. The number of difunctional junctions is expected to be small relative to the number of junctions of higher functionalities if the reaction is near completion. It follows from Eq. (2), (3) and (41) that... 

Although the reaction scheme shows a complete hydrolysis before condensation begins, this is likely not correct as stated earlier. The relative rates and extents of these two reactions will particularly depend on the amount of water added and the acidity of the system (10,11). The high functionality of the triethoxysilane endcapped PTMO oligomer should enhance the incorporation of PTMO molecules into the TEOS network. It was also assumed that the reactivities would be the same between silanol groups from silicic acid and endcapped PTMO. Therefore, no preferential condensation was expected and the deciding factors for which type of condensation (self- or co-) took place would be the diffusivities and local concentrations. 

If restricted junction fluctuations are taken into account, the chain deformation is increased, and is more anisotropic. The effect of increasing k is much more evident in networks of low functionality, since fluctuations of junction points are of minor importance in networks of high functionality. 

Attainment of a maximum double bond conversion is typical in multifunctional monomer polymerizations and results from the severe restriction on bulk mobility of reacting species in highly crosslinked networks [26]. In particular, radicals become trapped or shielded within densely crosslinked regions known as microgels, and the rate of polymerization becomes diffusion limited. Further double bond conversion is almost impossible at this point, and the polymerization stops prior to 100% functional group conversion. In polymeric dental composites, which use multifunctional methacrylate monomers, final double bond conversions have been reported ranging anywhere from 55-75% [22,27-29]. 

To form a polymer network, at least one of the starting components must have functionality,/, (equal to the number of functional groups per molecule) larger than two if > 2). This is a necessary but often not a sufficient condition. The precursors of networks differ in two ways (1) they are of low or of high functionality, (2) they bear functional groups that are engaged in bond formation either by stepwise or chain mechanisms. 

Differences in Network Structure. Network formation depends on the kinetics of the various crosslinking reactions and on the number of functional groups on the polymer and crosslinker (32). Polymers and crosslinkers with low functionality are less efficient at building network structure than those with high functionality. Miller and Macosko (32) have derived a network structure theory which has been adapted to calculate "elastically effective" crosslink densities (4-6.8.9). This parameter has been found to correlate well with physical measures of cure < 6.8). There is a range of crosslink densities for which acceptable physical properties are obtained. The range of bake conditions which yield crosslink densities within this range define a cure window (8. 9). 

Usually, the Tg vs x relationship shows an upward curvature related to the shape of the curves describing the increase in the concentration of branching points and high-functional crosslinks as a function of conversion (Chapter 3). Theoretical equations relating the Tg increase to structural parameters of the polymer network have been proposed. But, in every case, adjustable parameters are required to fit experimental results. 

Suckling)., Bullmore E. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. J Neurosci, 2006, 26(l) 63-72. 

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