Elastically Active Chain Sections

The statistical theory of crosslinking used in the last section also gives the theoretical concentration of elastically-active chains, N, which in turn determines the rubbery modulus E = 3NRT (R is the gas constant and T is the absolute temperature). At 70% reaction one calculates E - 2 x 10 dyn/cm1 2 3 4 5 6 7 8 9 10, in agreement with the apparent level in Figure 1. 

In the following, we will briefly outline the use of the link p.g.f. (l.p.g.f.) for the calculation of the gel point in /-functional polycondensation without and with cyclization including the f.s.s.e. In Chapter II, section 2.2 we will consider an application in connection with the number of elastically active network chains in random polycondensates or in a collection of randomly crosslinked chains. 

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... 

As explained above, a number of chain sections, such as loops and chain ends, do not contribute to the elasticity of the network. It is therefore necessary to develop an expression for the number ng of active chain sections in a real structure containing a total number n of both active and inactive chain sections. 

The number of junctions with specified type can be found as a function of the degree of reaction for polycondensation systems and the random cross-linking of prepolymers. Also, there has been much research into the nature of the active chains and elastic moduli near the gelation point. Some results will be presented in Section 8.2. 

A typical example of the master curve [2] is shown in Figure 9.3 for HEUR (polyethylene oxide) end-capped with -C16H33. The reference temperature is chosen at 5 C. From the horizontal shift factor, the activation energy is found to be 67kJmol . From the high-frequency plateau of the storage modulus, the number of elastically effective chains is found as a function of the polymer concentration, which was already studied in Section 8.2 (Figure 8.10). 

Let us consider a polymeric network that contains solvent, usually called a polymeric gel. There are several types of gels. A previously cross-linked polymer subsequently swollen in a solvent follows the Flory-Rehner equation (Section 9.12). If the network was formed in the solvent so that the chains are relaxed, the Flory-Rehner equation will not be followed, but rubber elasticity theory can still be used to count the active network segments. 

The bonds between the chains are weaker than covalent or metallic bonds and may be overcome by thermal activation even at room temperature. Thus, as we will see in detail in section 8.1, polymers are in their high-temperature regime even at room temperature. Their deformation is therefore time-dependent, and it is not always easy to distinguish elastic and plastic deformations. The mechanical properties of polymers are the subject of sections 8.2 to 8.4. Methods to improve the mechanical properties of polymers are discussed subsequently. The chapter closes with a brief discussion of the sensibility of polymers against environmental influences. 

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