Extended reptation theory

Shown in Fig. 4.6 are the curves of relaxation modulus, G t), of a series of nearly monodisperse polystyrene samples of different molecular weights. The higher the molecular weight, the slower the relaxation rate. In these measurements, the step deformation rise time is 0.04 s, which is much shorter than the relaxation times of interest in these curves. The most noteworthy is the appearance of a modulus plateau when the molecular weight is sufficiently large. As will be discussed in the later chapters, the entanglement molecular weight Mg can be calculated from the plateau modulus Gn- The analyses of these relaxation modulus curves in terms of the extended reptation theory developed in Chapter 9 will be detailed... 

Since the viscosity is the integration of G t) (Eq. (4.30)), the relaxation modulus G t) should contain more detailed information than the single viscosity value r/o. A wrong conclusion can be made if the conclusion is simply based on the viscosity result. On the basis of the viscosity data (Fig. 4.7), the onset of entanglement was traditionally believed to occm at Me 2.4Me. Shown in Chapters 10 and 11, detailed studies of the viscoelastic spectra in terms of the extended reptation theory as well as the Rouse theory have indicated that the onset occurs at Me-... 

As the theory is based on the theoretical framework of the Doi-Edwards theory, it is referred to as the extended Doi-Edwards theory from the theoretical consideration at the same time, since the theory includes the intramolecular motions on top of the reptation process, physically it is referred to as the extended reptation theory. Considering that the Doi-Edwards theory covers the nonlinear region, while the extended reptation theory is limited to the linear region, the term extended reptation theory is used throughout this book instead of the extended Doi-Edwards theory. 

The r]o oc relation of Eq. (8.57) is still different from the experimental observation po oc (Fig. 4.7), while Eq. (8.58) agrees with the basic molecular-weight independence of J° in the high-molecular-weight region (Fig. 4.12). A detailed comparison of Eqs. (8.57) and (8.58) with the Rouse theory and the extended reptation theory as well as experimental results will be discussed in Chapter 10. 

Universality of the 0(t) Line Shape in Terms of the Extended Reptation Theory (ERT)... 

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