Onset of entanglement

A similar anomalous behavior has been detected also in 3d polymer melts but only for rather short chains [41] for longer chains, several regimes occur because of the onset of entanglement (reptation ) effects. In two dimensions, of course, the topological constraints experienced by a chain from... 

We can use Equation (5.73) to define the dilute to semi-dilute transition, Equation (5.80) to define the concentrated region and Equation (5.83) to define the onset of entanglements. An example of this is shown in Figure 5.23 for poly butadiene. 

The second critical shear rate is much higher (i.e., 100 times Chauveteau, 1981) than the first one. The first critical shear rate is equal to the inverse of the longest rotational relaxation time k in the solution. Dilatancy starts as soon as the product of Rouse relaxation time and the maximum stretch rate, e, is greater than 4 (Chauveteau, 1981). The Rouse relaxation time demarcates the onset of entanglement effects (Roland et al., 2004). Chauveteau reported that the ratio of shear rate y to the maximum stretch rate e at the contraction was about 2.5 by laser anemometry for similar polymer solutions and flow geometries. Therefore, the second stretch rate (elongation rate) corresponds to the product of shear rate and Rouse relaxation time equal to 10. 

The curve In Figure 6 shows the expected break point In slope believed to be due to the onset of entanglement. For undiluted... 

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-... 

The existence of entanglement in between Mg and Mg will be further supported by the study in Chapter 11 — the direct observation of the onset of entanglement at Mg by monitoring the initial deviation of the viscoelastic... 

Concentration Dependence and Onset of Entanglement, and Tube Dilation... 

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