Stress and Segmental Orientation

4 Similarities in Nonlinear Relaxation Modulus between Entangled Polymer and Entanglement-Pree R-aenkel-Chain Systems 

As shown in Fig. 18.10, the Fraenkel-chain Gs(t,X) curves at different A values can be superposed on one another over the entropic region closely by allowing a vertical shift. Thus from these simulation results, one can 

17) is simply the definition of the Doi-Edwards damping function with the independent-alignment approximation (Chapters 8 and 12). The damping functions of Doi and Edwards with and without the independent-alignment approximation both explain well the experimental results of a well-entangled nearly monodisperse polymer system (Fig. 9.2). Note that here the unit vector u° represents the orientation of a Fraenkel segment as opposed to the orientation associated with an entanglement strand or primitive step in the Doi-Edwards theory. 

In Fig. 18.11, ho X) is also compared with the damping factor associated directly with the unit vector u over the entropic region, hu X), defined by 

More directly representing the segmental orientation, the /i (A) values appear to have a closer agreement with ho X) than h ). The small differences between /i (A) and h X) — less than 10% — merely reflect the 

---