Entanglement length

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

So far, the existence of a well-defined entanglement length in dense polymer systems has been inferred indirectly from macroscopic experiments like measurements of the plateau modulus. However, its direct microscopic observation remained impossible. The difficulty in directly evaluating the entanglement... 

First detailed studies of the dynamic structure factor of highly entangled polymer melts were reported at the beginning of the 90 s. At that time the attainable Fourier times were limited to about 40 ns. On this time scale, NSE has already played a crucial role in helping to understand the dynamics of polymeric systems [49, 50, 72, 73]. At that time the existence of an entanglement length scale in a linear polymer was been proven [72]. However, with the available time resolution, it was not possible to separate the predictions of the different confinement models addressed above. 

On the other hand, the group of Briels [54] recently proposed a coarse graining in terms of blobs with coarse grained properties determined beforehand by atomistic simulations. The mean-square displacement of these blobs displays only a very narrow Rouse regime and then is slowed down further, but never reaches the power law of reptation. The authors relate this observation to the shortness of the chains ( 8 entanglement lengths) and their averaging over all blobs (not only the innermost ). 

On the other hand, extensive viscosity measurements on PB by Colby et al. [88] show that above about 300 entanglement lengths AT-dependence (the slope of /] vs. N) turns from to AP, indicating that the deviations from reptation are due to finite size effects (see also very recent results by Pyckhout et al. [89]). 

If N is just larger than N, the entanglement length turns out to be larger than the asymptotic value for JV - co, and the dependence between and N may be expressed by N a where tr (> 0) decreases with N. This... 

FIG. 2.7 Relevant length scales for the colloidal structure of worm-like micelles contour length, Lc, entanglement length, /e, mesh size, m, persistence length, Zp and cross-sectional radius, rcs. Values shown are those measured for a solution with 1.5% total surfactant at a cetyltrimethylammonium tosylate (CTAT)/sodium dodecylbenzenesulfonate (SDBS) ratio of 97/3 with 0.10% added sodium tosylate. (Reproduced from Schubert, B.A., Kaler, E.W., and Wagner, N.J., Langmuir, 19, 4079 -089, 2003. With permission.)... 

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