As was mentioned in chapter 10, end-linking reactions can be used to make networks of known structures, including those having unusual chain-length distributions. One of the uses of networks having a bimodal distribution is to clarify the dependence of ultimate properties on non-Gaussian effects arising from limited-chain extensibility, as was already pointed out. The following chapter provides more detail on this application, and others. In fact, the effect of network chain-length distribution, is one aspect of rubberlike elasticity that has not been studied very much until recently, because of two primary reasons. On the experimental side, the cross-linking techniques traditionally used to prepare the network structures required for rubberlike elasticity have been random, uncontrolled processes, as was mentioned in chapter 10. Examples are vulcanization (addition of sulfur), peroxide thermolysis (free-radical couplings), and high-energy radiation (free-radical and ionic reactions). All of these techniques are random in the sense that the number of cross-links thus introduced is not known directly, and two units close together in space are joined irrespective of their locations along the chain trajectories. The resulting network chain-length distribution is unimodal and probably very broad. On the theoretical side, it has turned out to be convenient, and even necessary, to assume a distribution of chain lengths that is not only unimodal, but monodisperse! There are a number of reasons for developing techniques to determine or, even better, control network chain-length distributions. One is to check the “weakest link” theory for elastomer rupture, which states that a typical elastomeric network consists of chains with a broad distribution of lengths, and that the shortest of these chains are the “culprits” in causing rupture. This is attributed to the very limited extensibility associated with their shortness that is thought to cause them to break at relatively small deformations and then act as rupture nuclei. Another reason is to determine whether control of chain-length distribution can be used to maximize the ultimate properties of an elastomer. As was described in chapter 10, a variety of model networks can be prepared using the new synthetic techniques that closely control the placements of crosslinks in a network structure.
Method of Moments Applied to Most-Likely High-Temperature Free-Radical Polymerization Reactions
