Reptation mechanism

Tinland et al. [127] interpreted the Ds behavior of xanthan in the high concentration range by the reptation mechanism. As mentioned in Sect. 6.3.3,... 

A comparison of Eqs. 10.55 and 10.59 shows that the diffusivity of an isolated chain due to Brownian motion falls off more slowly with increasing chain size than the diffusivity of an entangled chain diffusing by the reptation mechanism. 

This is the point, above which the reptation mechanism of diffusion predominates. 

Note that the first and the second terms in (6.49) at w —> oo have the orders of magnitudes nTib 2 and nTy-1, respectively. The ratio of the quantities is very small for systems of long macromolecules, so that the contribution of the first, conformation branch to the linear viscoelasticity is negligibly small at X x. Note also that, for strongly entangled systems, at x X or Af M, as it was shown in Section 4.2.3, conformational relaxation cannot be occurred via the diffusive mechanism (considered here), but via the reptation mechanism, so that the first term in equation (6.49) ought to be replaced by other term, for example, in the form... 

Now, one has to rely on the reptation mechanism of changing conformation and use equations (7.32) to find the expansion of the quantity ufk. In the first-order approximation, one can obtain... 

One can see that introduction of the reptation mechanism of conformational relaxation, instead of diffusive mechanism, does not affect the values of the terminal quantities, but, one can expect, improves the situation in the region of the minima of the loss modulus G" reptation branch fill the gap between the orientational and the second conformational branches of relaxation times. Thus, the description with help of two relaxation branches is valid in the terminal zone and for higher frequencies close to it. 

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... 

When component-one s molecular weight is below Me, the viscoelastic response of component one is described by the Rouse theory, and tj (proportional to tci if the component-one chain reptates) can be equated to zero as the component-one chains lose the reptational mechanism. Then Eq. (ll.A.l) is transformed to... 

According to reptation mechanism, d equals to -1 for molecules without entanglements and to 2 for entangled molecules [70]. AEj, is the activation energy of molecular diffusion for the adsorbed molecule on the crystal surface. Taking these factors into account, the crystal growth rate is expressed as follows ... 

Jetmes [13] based on the conception of the reptational mechanism of the polymeric chain movement gives the following dependence ij t N. So, the index p = 3, 4 in the ratio (1) from the point of view of Ferry [1] remains by one among the main unsolved tasks of the Polymers Physics. 

The shear strain of the conformational volume of wi-ball and its rotation is realized in accordance with the reptational mechanism presented by De Jennes [13], that is via... 

For the time after the tube has regained its original contour length, the chain begins to disengage from the tube via the reptation mechanism. The relaxation response during this time is... 

The dynamics of linear or branched polymers is known to follow the reptation mechanism, in which the chain ends of polymer molecules play a critically important role. On the contrary, ring polymers are unique in the absence of the chain ends and therefore their non-reptation dynamics has been a fundamental issue in both theory and practice in polymer materials science. 

Ito, " Tulig and Tirrell, and de Geimes have proposed expressions for fe, based on a reptation mechanism. More recently, the manner in which the termination rate coefficient scales with chain length for entangled systems has been considered in some detail in studies by O Shaughnessy and... 

Like Leonardi et al [52] Van Ruymbeke et al [53] accounted for non-reptational mechanisms in their method, but they used different models for the relaxation processes. They inverted a model that they had previously proposed [54] for the calculation of rheological behavior from the molecular weight distribution. For the Rouse modes they used a modified version of an expression proposed by Pattamaprom et al [55]. Their modified equation is shown below. 

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