De Gennes reptation theory

The Rouse-Bueche theory is useful especially below 1% concentration. However, only poor agreement is obtained on studies of the bulk melt. The theory describes the relaxation of deformed polymer chains, leading to advances in creep and stress relaxation. While it does not speak about the center-of-mass diffusional motions of the polymer chains, the theory is important because it serves as a precursor to the de Gennes reptation theory, described next. 

Kraus has studied the steady flow and dynamic viscosity of the following branched butadiene t) ene block copolymers (88)3, (88)3, (88)4 in comparison with 888 and 888 copolymers. He has found higher viscosities (at constant molecular weight and total styrene content for polymers terminated by styrene blocks) for the former inespective of branchii, but for copolymers of equal molecular weight the viscosity is smaller for branched than for linear copolymer. Kraus has also studied the effect of free polybutadiene molecules on the viscoelastic behaviour of branched (88)4 block copolymers which consist of styrene domains in a butadiene matrix and verified De Gennes s theory of reptation ... 

It should be noted that P L. However, as pointed out earlier, in the later versions of the LH theory the transport factor is derived from de Gennes s theory (the reptation model, see Chapter 6) and P is given by ... 

The five time regions are based on the reptation theory proposed by De Gennes [46,47] and Doi and Edwards [48,49] for bulk dynamics of polymer melts and concentrated polymer solutions, and are discussed in detail in Chapter 3 of Ref. [1]. 

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). 

In the subsequent 20 years (1960-80), the main principles of modern polymer physics were developed. These include the Edwards model of the polymer chain and its confining tube (Chapters 7 and 9), the modern view of semidilute solutions established by des Cloizeaux and de Gennes (Chapter 5), and the reptation theory of chain diffusion developed by de Gennes (Chapter 9) that led to the Doi-Edwards theory for the flow properties of polymer melts. 

Theories of gel electrophoretic mobility are usually based on the reptation theory introduced for polymer melts by de Gennes, as well as Doi and Edwards [32,33,7]. Their approach succeeded in explaining the inverse relationship between mobility and chain length for short fragments of DNA [7d], By replacing the tube in the reptation model by open spaces and lakes connected by straights, Zimm explained the antiresonance phenomena observed in the field inversion experiments that occur when the time scale for the formation of the conformational change of the DNA coincides with the time scale for the field cycle [7c]. 

The word reptation was created by De Gennes in 1971 (see De Gennes23). The term tube model is used to describe complete theories that incorporate Rouse and reptation motions within a tube-like constraint of the surrounding polymer chains. 

De Gennes (1971) postulated that polymer molecules were constrained to move along a tube formed by neighbouring molecules. In a deformed melt, the ends of the molecules could escape from the tube by a reciprocating motion (reptation), whereas the centre of the molecule was trapped in the tube. When the chain end advanced, it chose from a number of different paths in the melt. This theory predicts that the zero-shear rate viscosity depends on the cube of the molecular weight. However, in the absence of techniques to image the motion of single polymer molecules in a melt, it is hard to confirm the theory. 

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. 

Theoretical treatment of the statistical properties of linear polymers (LPs), shown schematically in Figure 7.1a, have been in existence since the 1950s (Rouse, 1953), and have undergone continuous refinement. In particular, tube theories (viz. reptation) (de Gennes, 1971 Doi and Edwards, 1986), and subsequent refinements, like constraint release (Viovy et al., 1991) and contour length fluctuation (Frischknecht and Milner, 2000) are some of the greatest... 

As indicated above, the term P allows for the diffusion of the stem to the site and is usually described by the WLF equation, h is Planck s constant, J is a dimensionless scaling constant, is a constant (dimensions J mol ) and is the temperature at which diffusion is stopped. If the polymer is of sufficiently high molar mass for entanglement to take place, then instead of the WLF theory the reptation theory of de Gennes should be used ... 

Figure 10.10 (15) also applies the molecular diffusion theories of de Gennes (17), Doi and Edwards (18), and Daoudi (19), which assume that the major mode of molecular relaxation is by reptation. In this way, the chains move back and forth within a hypothetical tube. Relaxation occurs by the chain disengaging itself from the tube, only at the ends, in a backward-and-forward reptation. 

When two otherwise identical polymer surfaces are brought into juxtaposition at r > Tg and annealed, a healing process may take place. As a result the interface gradually disappears. Basic additional requirements are that the polymer be linear (or branched) and amorphous. The major mechanism involves the interdiffusion of polymer chain segments across the interface. For polymer chain interdiffusion, the reptation theory of de Gennes (54) and Edwards (55)... 

Polymer melts and semidilute and concentrated solutions of polymer are highly viscous. Even at a concentration of 1 wt %, solutions of polymer with a molecular weight greater than several million g/mol can flow only slowly. Their behaviors are even elastic like rubber at accessible time and frequency ranges. These exquisite properties had eluded researchers for decades until the tube model and the reptation theory elegantly solved the mystery. The tube model and the reptation theory were introduced by de Gennes." They were refined and applied to the viscoelasticity of semidilute solutions of polymers and polymer melts in the late 1970s by Doi and Edwards." Until then, there had been no molecular theory to explain these phenomena. We will leam the tube model and the reptation theory here. 

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