Tube disengagement

We can characterise the relaxation of the chain by two dominant relaxation processes a short time process due to the fluctuations of the polymer within the tube, characterised by time tr and a longer time process for the polymer to start to disengage itself from the tube xe. This process of tube disengagement is discussed further in Section 6.4.3. The characteristic time for the polymer to begin the process of escaping the constraints of a tube is given by... 

The plateau modulus is determined by the region in which these two relaxation modes cross. The plateau modulus, the low shear viscosity and the tube disengagement time are given in Section 6.4.3 as... 

Figure 6.23 Prediction of stress overshoot for different tube disengagement times. The shear rate used for the calculation was 5 s l...

These results indicate that some fast intra-tube modes tend to disorient the molecular conformation on a very short time scale, but that only complete tube disengagement, due to the slow unbiased reptation process, can restore the true molecular randomness. 

It is clear from Eq. (7.43) that the tube disengagement time depends on the number of segments Z. when constrain release is included in the tube model. By substituting Eq. (7.43) into (7.38), with the aid of Eq. (7.42), we obtain... 

An alternative approach to obtaining information on polymer dynamics and network structure was developed by Ball, Callaghan, and Samulski and called the j3 function. This experiment amounts to a clever combination of various echoes (both Hahn and solid) Hke the type used to obtain Tj decay curves, and has been employed to probe interproton dipolar interactions. To explain the resultant data, a simple dynamical correlation function was introduced that depended only on the strength of the RDC and a measure of the tube disengagement time. Values extracted from data on PDMS melts were shown to be consistent with those derived via other methods [59]. These treatments were then extended... 

Fig. 42. Time-dependent diffusion coefficient measured in a polyethyleneoxide melt (M =5,000,000) at 353 K as a function of the diffusion time [12]. The data were evaluated according to Eq. 27. The Rouse relaxation time Tr and the tube disengagement time predicted by the tube/reptation model based on the neutron scattering value of the ratio (R ee)/M = 1.01x10 ° m mol/g [179, 180] are indicated. The broken line represents the power law D(t)(xr which, according to the tube/reptation model, should appear in the time interval above Tr as limit (III)de and not below (see Table 1). The time range where this power law appears and the value for Zr estimated on the basis of the tube/reptation model are not consistent with each other. The plateau of the experimental data for f 0.1 s is due to flip-flop spin diffusion which physically limits the detection of molecular displacements by NMR diffusometry...

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