Entanglement molecular length

Coran and Patel [33] selected a series of TPEs based on different rubbers and thermoplastics. Three types of rubbers EPDM, ethylene vinyl acetate (EVA), and nitrile (NBR) were selected and the plastics include PP, PS, styrene acrylonitrile (SAN), and PA. It was shown that the ultimate mechanical properties such as stress at break, elongation, and the elastic recovery of these dynamically cured blends increased with the similarity of the rubber and plastic in respect to the critical surface tension for wetting and with the crystallinity of the plastic phase. Critical chain length of the rubber molecule, crystallinity of the hard phase (plastic), and the surface energy are a few of the parameters used in the analysis. Better results are obtained with a crystalline plastic material when the entanglement molecular length of the... 

Low entanglement molecular length (high entanglement density) of the rubber. 

The best compositions are prepared when the surface energies of the rubber and plastic material are matched, when the entanglement molecular length of the rubber molecule is small, and when the plastic material is crystalline. It is also necessary that neither the plastic nor the rubber decompose in the presence of the other at temperatures required for melt-mixing. Also, in each case, a curing system appropriate for the rubber under the conditions of melt-mixing is required. 

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. 

The mathematical treatment that arises from the dynamic dilution hypothesis is remarkably simple - and very effective in the cases of star polymers and of path length fluctuation contributions to constraint release in Hnear polymers. The physics is equally appealing all relaxed segments on a timescale rare treated in just the same way they do not contribute to the entanglement network as far as the unrelaxed material is concerned. If the volume fraction of unrelaxed chain material is 0, then on this timescale the entanglement molecular weight is renormalised to Mg/0 or, equivalently, the tube diameter to However, such a... 

The critical molecular weight, Mc is related to the entanglement molecular weight, Me, as Me = Mc/2. The entanglement molecular weight specifies the length of a polymer that is required to cause interpenetration of the chains. If solvent is added to the melt, the... 

The molecular meaning of b is best seen from the second or third equality of Eq. (3). In other words, b is explicitly related to the steady shear melt viscosity q and depends on the chain-chain interactions near the melt/wall interface as quantified by the friction coefficient p. In the limit of no polymer adsorption or in absence of interfacial chain entanglements due to the coil-stretch transition, P involves an interfacial viscosity q , which is as small as the viscosity of a monomeric liquid and independent of the molecular weight Mw p=qj/a, where a is a molecular length. Thus at the stick-slip transition, the molecular weight dependence of b arises entirely from q in Eq. (3). 

Complex Architectures. Perhaps the most significant recent advances in molecular understanding of polymer melts have emerged from the study of branched polymer architectures. We have noted above how a tube theory for star-polymers provided the means to treat fluctuations in entangled path length in linear polymers (see Figure lb). This is simply due to the complete suppression of reptation in star polymers without fluctuation there is no stress-relaxation at all ... 

The Doi-Edwards theory treats monodisperse linear chain liquids by a model which suppresses fluctuations and assumes a topologically invariant medium. Two parameters are required, the monomeric friction coefficient which characterizes the local dynamics and the primitive path step length a which characterizes the topology of the medium. The step length is related to the entanglement molecular weight of earlier theories, = cRqT/Gn, by Eqs. 1 and 37 ... 

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