Reptation in polymer melts

He carefully reserves the possibility for reptation in polymer melts. 

J. des Cloiseaux, Double Reptation vs. Simple Reptation in Polymer Melts Europhys. Lett. 5, 437-442 (1988). 

R. Granek. Stress relaxation in polymer melts and solutions Bridging between the breathing and reptation regimes. Macromolecules 2<5 5370-5371, 1995. 

Diffusion of flexible macromolecules in solutions and gel media has also been studied extensively [35,97]. The Zimm model for diffusion of flexible chains in polymer melts predicts that the diffusion coefficient of a flexible polymer in solution depends on polymer length to the 1/2 power, D N. This theoretical result has also been confirmed by experimental data [97,122]. The reptation theory for diffusion of flexible polymers in highly restricted environments predicts a dependence D [97,122,127]. Results of various... 

Figure 4.53 Schematic illustration of the reptation process in polymer melts, showing chain entanglements (light arrows), the wriggling motion of the polymer chain (darker arrows), and the primitive path of the polymer chain (dark Une). Reprinted, by permission, from G. Strobl, The Physics of Polymers, 2nd ed., p. 283. Copyright 1997 by Springer-Verlag.

H.M. Lauti Orientation of macromolecules and elastic deformations in polymer melts. Influence of molecular structure on the reptation of molecules. Progr. Colloid Polymer Sci. 75 (1987) 111-139... 

For both linear and star polymers, the above-described theories assume the motion of a single molecule in a frozen system. In polymers melts, it has been shown, essentially from the study of binary blends, that a self-consistent treatment of the relaxation is required. This leads to the concepts of "constraint release" whereby a loss of segmental orientation is permitted by the motion of surrounding species. Retraction (for linear and star polymers) as well as reptation may induce constraint release [16,17,18]. In the homopol5mier case, the main effect is to decrease the relaxation times by roughly a factor of 1.5 (xb) or 2 (xq). In the case of star polymers, the factor v is also decreased [15]. These effects are extensively discussed in other chapters of this book especially for binary mixtures. In our work, we have assumed that their influence would be of second order compared to the relaxation processes themselves. However, they may contribute to an unexpected relaxation of parts of macromolecules which are assumed not to be reached by relaxation motions (central parts of linear chains or branch point in star polymers). 

G"(ffl) CO. In rheology, it is well known that often G"(more information about the relaxation processes in polymer melts than G (co) does. Our analysis shows that this is also tme for -t(dG/dt) as compared to G(t). The physical reason for this observation is clear according to the reptation theory, the stress relaxation function at times tfunctional form G(t) Gi - G2t, where Cj and G2 are constants. This function will not look like a straight line on the log-log plot, whereas its derivative -t(dG/dt) = will do so. Similar arguments... 

The minor chain (MC) model of reptating chains as shown in Figure 1 was proposed by Kim and Wool to analyze interdiffusion in polymer melts. Only those parts of the chains which have escaped by reptation from their initial tubes (the minor chains) at the time of contact can contribute to interdiffusion. Using this model, the average molecular properties of the interface were derived and are summarized in Table 1. The molecular properties have a common scaling law which relates the dynamic properties, H t)y to the static equilibrium properties, //, via the reduced time, t/T, by t ... 

The subject of this paper is limited to the dynamics of a single entangled polymer chain, just as in the original de Gennes paper on reptation. In a melt or concentrated solution, the dynamics of any chain would be affected by the motion of surrounding polymers (by constraint release), and this effect has to be self-consistently taken into account. In order to do that, one has to start from a reliable model of the single-chain dynamics, such the reptation model, Doi s fluctuation theory,or the repton modeldescribed in the present paper. 

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]. 

A similar anomalous behavior has been detected also in 3d polymer melts but only for rather short chains [41] for longer chains, several regimes occur because of the onset of entanglement (reptation ) effects. In two dimensions, of course, the topological constraints experienced by a chain from... 

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