Tube renewal time

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 NN[Pg.121]

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],...

VII.2 The Critical Time To obtain the critical time x (A ) and the tube-renewal time i Back calculate the velocity ViN tJ of a... 

The end-to-end distance thus decreases exponentially with time during a reverse pulse to eventually take the minimum value given by (75b) for XBaek> fi om (77), the tube renewal time Xsaek is given by ... 

This result indicates that the net electrophoretic velocity is, in fact, V o P lse durations t smaller than the tube-renewal time... 

Although intra-tube effects may be expected to play a larger role in pulsed field techniques and transient effects, the form of the model which averages over these effects offers a good framework to discuss the experimental results even in these cases. The orientation overshoot observed with linear dichroism is a transient effect that occurs at a time which is smaller than the tube-renewal time we thus conclude... 

The upper limit on the summation is r, the degree of polymerization, which is M/Mq. In a polydisperse system, this approach must be modified. Montfort etal. [48] account for the effects of polydispersity in two ways. First, they use the double reptation concept with the Doi-Edwards kernel function to account for constraint release, but they also let the relaxation times depend on the molecular weight distribution, a concept originally proposed by Graessley [49]. Specifically, they represent the terminal relaxation time in a polydisperse system as the harmonic average of the reptation time and a tube renewal time, Tp which depends on the molecular weight distribution. 

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