Network chain — continued elastically active

The number of elastically active chains, N, determining the equilibrium rubber elasticity, is derived from the following consideration. A chain in the gel is elastically active, if the branch points at each of its ends issue at least three paths to infinity. Such elastically active network chain (EANC) can have many long side branches but none of them may have an infinite continuation. The number of EANC s, N, is thus calculated from the number of EANC ends, i.e., branch points issuing three or more bonds with infinite continuation. The distribution of units according to the number of bonds with infinite continuation is described by a pgf T(z)... 

An elastically active network chain is active in the equilibrium elastic response of the network to deformation. From the topological point of view, an EANC is a chain between two active branch points. An active branch point is a imit from which at least three paths issue to infinity. In the case under consideration, only some of the chemically tetrafunctional diamine units can become active branch points. If the polyepoxide were more than bifunctional, it would also contribute to the number of EANC s. In analogy with Eq. (14), the pgf for the numbo- of bonds with infinite continuation issuing from a diamine unit T,(z) is given by... 

The number of elastically active network chains EANC, N, is contributed only by diepoxide units. According to the reasoning given in Section 4.2.3, the distribution of diepoxide units with respect to the number of bonds with infinite continuation is given by the pgf... 

Figure 2.32 (a) Effect of ends of molecules on network structure, (b) Network structure and defects cross-links ° terminus of a molecule (1) elastically active chain (2) inactive loop (3) inactive loose end. An arrow (—>) signifies continuation of the network strucmre. (After Flory, 1944.)... 

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