SIMPLE PRESENTATION OF NETWORK THEORY OF RUBBER, WITH A DISCUSSION OFOTHER THEORIES

It seems now to be generally agreed that soft rubberlike materials con sist of long flexible molecules more or less completely linked into a coherent network by chemical bonds formed during cure. These bonds sup press, for the most I!art, the plasticity that the liquid-like mass of molecules would otherwise have, but leave the molecules free to take on a great many configurations of essentially the same energy under th e influence of thermal agitation. The tendency of stretched rubber to retract is then understood as a kinetic phenomenon, like the tendency of a gas to expand; it is the tendency of a system to assume the form of maximum entropy when the internal energy is essentially independent to form. There is no similar agreement as to what constitutes an adeq uate theoretical treatment of such:materials. In particular, there exi sts a wide variety of formalisms for the derivation of the stress-stra in relation of an ideal soft rubber. These are usually referred to as network theories, though the only treatment that actually deals with a general network of flexible molecular chains is that of the authors ( 1). Other treatments have been based on the consideration Of individua l elements or small groups of elements from networks,concerning the be havior of which special assumptions were made, or they have proceeded on the basis of general ideas that involve no reference whatever to th e network structure of the material. The relation of these theories to the general network theory of rubber is the subject of the present pa per. As background for the discussion of other theories we shall first develop the theory of rubber, considered as a random network of long flexible molecules, in a particularly simple way. The ease with which a network of general form can be treated will make it evident that the re is little need to base network theories of rubber on the use of mor e special models. Next, we shall examine an idea that appears in many discussions of rubber which employ simplified models the idea that the junctions of the rubber network can be treated as if they were fixed in space. We shall show that this picture of the situation is quite un realistic: the junctions have a Brownian motion comparable to that of any portion of the intervening molecular segments. The common assumpti on to the contrary does not affect the results of some types of calcul ations, but it is inadmissible in the treatment of other problems. Fin ally, we shall show that the theory of Wall (2), which employs no spec ial model, is based on postulates that are inconsistent with the netwo rk structure of rubber.