Tubes renewal

The primitive chain in panel a slides along its own contour. The advancing end emerges from the existing tube and finds a new path, just as a random walker moves another step forward, as shown in panel b. A new section is added 

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The two situations are displayed in Fig.3.13b and c. The first process, where the chain performs Rouse motion along the tube, is called local reptation the creeplike diffusion along the tube which eventually leads to a complete tube renewal is also termed pure reptation. 

Figure 17 The tube renewal concept an internal tube segment is lost when the attached entanglement disappears.

The so-called tube renewal time Xf can be compared to the reptation time x if the prefactor is known in the above relation. Xr, /xc = (N/N ) / IStc for Klein... 

For weakly entangled polymers or long N-chains surrounded by shorter P-chains, a tube renewal time x shorter than Xc can be expected. If the two mechanisms are assumed to be independent of each other [17], the overall relaxation time x can be put as the harmonic average of the two times ... 

In a polydisperse sample, each N-chain is surrounded by chains of different lengths. Therefore, the constraint release time x. varies according to the reptation time of the passing chain. Some entanglements can be considered as permanent (P N), while others will disappear quickly (Ptime distribution will affect the tube renewal time and consequently the overall relaxation time of each chain. 

The simplest case for testing the tube renewal models is to isolate a long N-chain in a matrix of shorter entangled P-chains. A chain can be viewed as isolated from similar N-chains when the volume fraction N in the blend is such as NNtube renewal time is expected to scale as ... 

As the data of cOn, are straightforward and experimentally connected to the longest time by co = 0.7x [21], they will be used along with the reptation time in order to calculate the tube renewal time Xren of the diluted chains ... 

Figure 20 Experimental relation between the tube renewal time Xrg and the reptation time Xg of the matrix for different molecular weights of various polymers [ data from ref 19].

For monodisperse polymers, the tube renewal time scales as ... 

Each molecule is surrounded by the above distribution of chain lengths and the tube renewal time has to take into account the distribution of the attached constraint release times. For a monodisperse sample, Graessley [17] defines the constraint release time x from the Doi-Edwards relaxation function F(t) such as ... 

The expression of < x > has been checked for binary blends of monodisperse polystyrenes (Fig. 21). The tube renewal time of the high N-component is measured at different volume fractions ( )n and the molecular weight distribution is defined by two step functions 1-( )) at Mp and ( )i4 at Mn. The experimental data fit well the model with z=3. 

Figure 21 Variations of the tube renewal time of N-chains (Mn = 2 700 000 g.mol l) in a matrix of shorter chains (Mp = 100 000 g.mol l) of polystyrene, as a function of concentration (t>N [21],...

Moreover, as far as relaxation times are concerned, the reptation mechanism in an enlarged tube should lead us to favour the tube renewal process. The expression of... 

The experimental evidence of the importance of the tube renewal mechanism when short molecules are added to a high polymer is provided by blends of narrow polystyrene (Mg = 8 500 and Ml = 900 OOO) [28]. 

Figure 29 Average relaxation time of a high molecular weight polystyrene (M = 900 000) in the presence of short chains (M = 8 500). The dotted line represents pure reptation and the full line stands for the contribution of tube renewal according to relation (6-8).[from ref. 28]...

Many interesting little tricks have been devised in order to overcome some of these difficulties. The external field is periodically switched off (or rotated through 90 ). The time taken for the field to go through one cycle should be roughly the same as the typical time of tube renewal, that is T (see (12.13)). In this case electrophoretic motion will only occur... 

NMR data on poly(dimethylsiloxane) are shown in Figure 8-5. Typical features are that, as P increases, Dtr for a fixed N decreases sharply and tends to be insensitive to P for P somewhat leuger than N, unless N is in the region of oligomers. Those who are in favor of the reptation theory would explain the observed N dependence of in terms of the concept of tube renewal, while Tanner gave it a different interpretation. Klein [28] confirmed the insensitivity of Ptr to P above N with blended polyethylene melts. 

The findings of Kim et al. and Nemoto et al. on the M dependence of Dg cannot be explained not only by de Gennes original reptation theory but also by its current modifications taking the tube renewal into account. Although it is still too early to conclude that they are definite evidence for the anti-reptation opinion, the following remark may be of some interest. 

Reptation assumes that the mobility of the matrix polymer plays no role in the relaxation of the tube constraint felt by a test molecule. However, if the matrix chains were very much more mobile than the test chain, additional lateral motion of the chain might be permitted by virtue of the constraining chains themselves moving away. This type of motion is called constraint release or tube renewal , and may be operative if some of the matrix chains are significantly shorter or intrinsically more mobile than the test chain (Green 1991, Composto etal. 1992). 

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