Rouse segment modulus

No shift along the modulus axis is involved in obtaining the very close superposition of the measured and calculated spectra as shown in Fig. 11.9. This indicates that the force constant on the Rouse segment, which gives... 

If the molecular weight of a Rouse segment, m, is known, the upper modulus bound G (w —> oo) = pRT/m (or in terms of Young s modulus. 

The shear relaxation modulus Gs t) and the first normal-stress difference function G i(t), both normalized on a per-segment basis and with kT set to 1, are obtained from the constitutive equation of the Rouse model (Eq. (7.55) with Sp replaced by Tp) as... 

The number of segments between entanglements, was identified above as the boundary between the wavelength of Rouse modes which could and could not rapidly relax orientation in the presence of entanglements. In real space the associated distance between entanglements is = a The Rouse theory, shown above to be consistent with rubber elasticity ideas, relates to the plateau modulus by Gjv c kT/N. ... 

Figure 5.2 Relaxation moduli of three samples of a linear polymer A) an unentangled molten sample, B) an entangled,monodisperse molten sample,C) an entangled, polydisperse molten sample, and D) acrosslinked sample. At short times,all the samples relax first by a glassy mechanism and then by Rouse relaxation involving only very short segments of the chain (log scales). The unentangled melt then flows in the terminal zone.The entangled, monodisperse melt has a plateau modulus followed by terminal relaxation, while in the polydisperse melt the plateau zone of the longest molecules overlaps with the terminal zones of the shorter molecules.

---