Evidence for Reptation

Despite these complications, there are now numerous evidences that the tube model is basically con-ect. The signatory mark that the chain is trapped in a tube is that the chain ends relax first, and the center of the chain remains unrelaxed until relaxation is almost over. Evidence that this occurs has been obtained in experiments with chains whose ends are labeled, either chemically or isotopically (Ylitalo et al. 1990 Russell et al. 1993). These studies show that the rate of relaxation of the chain ends is distinctively faster than the middle of the chain, in quantitative agreement with reptation theory. The special role of chain ends is also shown indirectly in studies of the relaxation of star polymers. Stars are polymers in which several branches radiate from a single branch point. The arms of the star cannot reptate because they are anchored at the branch point (de Gennes 1975). Relaxation must thus occur by the slower process of primitive-path fluctuations, which is found to slow down exponentially with increasing arm molecular weight, in agreement with predictions (Pearson and Helfand 1984). 

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Callaghan, P. T., and Coy, A. (1992). Evidence for reptational motion and the entanglement tube in semi-dilute polymer solutions. Phys. Rev. Lett. 68, 3176-3179. 

J. Klein, "Evidence for Reptation in an Entangled Polymer Melt,"... 

Klein J. Evidence for reptation in an entangled polymer melt Nature 1978 271 143-145. 

Figure 4 Plot of the normalized intermediate scattering function [S(Q,f)/S(Q.O)] versus time for hydrogenous polyethylene (12% w/w) in deuterated polyethylene at 509 K for Q = 0.050 and 0.077 A . Also shown are the predictions from the reptation model (solid line) and competing (dashed and dot-dashed lines). (Data recorded with IN15 at the ILL). Reproduced with permission from Schleger P, Farago B, Lartigue C, Kollmar Aand Richter D (1998) Clear evidence for reptation in polyethylene from neutron spin echo spectroscopy. Physical Review Letters 81 124-127.

Klein, J., Evidence for Reptation in an Entangled Pol3mier Melt, Nature, 271, 143-145, 1978. 

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. 

Spin-echo neutron scattering measurements on molten poly (tetrahydrofuran) led Higgins et al. [53] to report that they found evidence for Rouse-like chain motion. The experiment was concerned with A > 0.3 nm". However, such k does not satisfy the condition l/dt > k, since dt for molten poly (tetrahydrofuran) is estimated to be 3 nm [53]. Hence, it is doubtful if the finding of Higgins et al. can rule out the possibility of reptation. 

By now, sufficient information on the dynamics of macroinolecules in solution has bci ii accumulated by means of dynamic light scattering, this method being sensitive to the internal modes of a macromolecule s motion and to the process of its reptation among similar molcondensed state. At the same time, there is a lack of unambiguous evidence for association mode s" or the lifetime of as.sociates in the voluminous literature on dynamic light scattering from polymer solutions. 

For 100 < P < 1000, the measured diffusion coefficients for N = P no longer follow the N 2 reptation prediction. In the same range of N values, D remains proportional to N 2 if P N, i.e. if the motion of the chains surrounding the test chain are frozen down during the diffusion time of the test chain. The comparison of the data obtained with N = P and with N P clearly puts into evidence the acceleration of the dynamics associated with the matrix chains, similarly to what has yet been observed with other polymers [11, 12, 42 to 44] or in solutions [10]. This acceleration, by a factor close to three, can be attributed to the constraint release mechanism [7, 8, 13], the effects of fluctuations of the test chain inside its tube [9] being a priori the same in the two situations P = N and P N. 

There is growing evidence that t-T superposition is not valid even in miscible blends well above the glass transition temperature. For example, Cavaille et al. [1987] reported lack of superposition for the classical miscible blends — PS/PVME. The deviation was particularly evident in the loss tangent vs. frequency plot. Lack of t-T superposition was also observed in PI/PB systems [Roovers and Toporowski, 1992]. By contrast, mixtures of entangled, nearly mono-dispersed blends of poly(ethylene-a/f-propylene) with head-to-head PP were evaluated at constant distance from the glass transition temperature of each system, homopolymer or blend [Gell et al, 1997]. The viscoelastic properties were best described by the double reptation model , viz. Eq 7.82. The data were found to obey the time-temperature superposition principle. 

A dozen measurements of Dg on concentrated polymer solutions have been carried out with well-characterized polymers in solvents of different quality, with the aim of checking the concentration dependence predicted by scaling arguments (eq 2.35 for 0 solvents and eq 2.37 for good solvents) as well as the molecular weight dependence. As can be seen from Tirrell s review [2], it was evident already in 1984 that the topological factor Fg as a function of c does not follow a simple power law, while its M dependence appears to be consistent with the reptation theory over a wide range of c. However, it was... 

At present, there appears no definitive evidence against the general validity of the empirical 3.4 power law for rn,. To reconcile this fact with the reptation... 

Because diffusion thickness) is proportional to ujpech (in the interface) and because I>pech (or Df) is proportional to rfpEcn (diffusion thickness) and, in addition, because 6 pvac (diffusion thickness) is proportional to ct>pvAC (in interface) and because A>vac (or i>e) is proportional to (ipvAC (diffusion thickness) the reptation behaviour for Z>a and I>q is confirmed experimentally. This is evidence in support of Eq. (15). 

More evidence comes from the study of viscoelasticity, which has been done extensively in the past and established the characteristic aspects common to all flexible polymers. The reptation model has succeeded in explaining many of these features and also predicting some of the behaviour in nonlinear viscoelasticity. In this chapter we shall describe the reptation theory for viscoelasticity in detail, and discuss the validity of the reptation model in solutions and melts. 

Prom this contour diffusion constant, we may deduce the time for a chain to diffuse its own contour length K. This time is called the reptation time We may express it as Trep ( A ) iP/Cbiob- This r ep is evidently proper-... 

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