Chain average tensile stress

The average tensile stress for a completely bonded chain follows from... 

Here A and t are the extension ratio and tensile stress respectively, V is the volume of the strained specimen and a reference volume which may usually be taken as the unstrained volume. p,R,T, and A/<, are, respectively, density, gas constant, absolute temperature and repeat unit molecular weight. The parameter G, defined by Flory and Abe, provides a measure of the average correlation of local transition moment directions with respect to the chain end-to-end vector. Positive values of denote a tendency for the transition moments to orient in line with the end-to-end vector and negative G values are characteristic of... 

Zhurkov et al. [42] derived the degree of chain orientation from the dichroism of deformed-IR bands of PETP (cf. Chapter SIB and Fig. 8.5) they observed that for highly stressed segments an initial orientation with cos d = 0.75 had turned into practically complete orientation (cos — 1.0). The problems posed by an application of this method are discussed in detail by Read et al. [43]. Bouriot [44] deduced from IR measurements a reversible cis-trans transformation of the ethylene glycol segment in PETP fibers under the effect of tensile stresses. In polyamide 66 he observed a reversible increase of free (non-assodated) NH groups and an increase in the average chain orientation with chain tension. 

The essential requirement for a substance to be rubbery is that it consist of long flexible chainlike molecules. The molecules themselves must therefore have a backbone of many noncolinear single valence bonds, about which rapid rotation is possible as a result of thermal agitation. Some representative molecular subunits of rubbery polymers are shown in Fig. 1 thousands of these units linked together into a chain constitute a typical molecule of the elastomers listed in Fig. 1. Such molecules change their shape readily and continuously at normal temperatures by Brownian motion. They take up random conformations in a stress-free state but assume somewhat oriented conformations if tensile forces are applied at their ends (Fig. 2). One of the first questions to consider, then, is the relationship between the applied tension / and the mean chain end separation r, averaged over time or over a large number of chains at one instant in time. 

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