General remarks

The main goal of this chapter is to introduce a convenient view of the basic physics and elasticity of the rubber matrix. The easiest way to consider an elastic polymeric solid is as a crosslinked polymer melt. Polymer melts, however, already exhibit some properties of networks, at least on some time scales. This can be seen most beautifully by considering the storage modulus of a polymer melt.

The melt can be made a true solid by adding a reagent which joins each chain to a neighbor. For lightly crosslinked material there will be a few links per chain, but material can also be highly crosslinked [6]. Alternatively irradiation by gamma rays, X-rays, or by electrons will create crosslinks. There is ample evidence that polymers in melts are in random walk configurations, i. e. the molecule has a large choice of configurations and these differ by energies much less than the thermal energy kBT. The kind of picture one has then is as in a computer simulation. The real difficulty is that rubbers are fundamentally three-dimensional and, unlike for crystals, two-dimensional pictures are not comprehensive. However, the reader can imagine a very kinky spaghetti-like mixture with permanent crosslinking bonds along the length. There is ample experimental evidence that perhaps 90% of the free energy of the material is entropic; see [6] for a general discussion and references.

In a network, however, the problem is that all the structural elements that make precise theories for melts difficult become frozen in.