Entanglement critical chain length

Critical Entanglement Chain Length Viscoelasticity in polymers ultimately relates back to a few basic molecular characteristics involving the rates of chain molecular motion and chain entanglement. The increasing ability of chains to slip past one another as the temperature is increased governs the temperature dependence of the melt viscosity. One embodiment... 

We saw in Sec. 2.9 that the viscosity of a bulk polymer is proportional to M, where a is either 1.0 or 3.4, depending on whether the polymer is below or above, respectively, the critical chain length for entanglement. For solutions, a similar result is obtained, only it is [r ] rather than r itself which is proportional to M ... 

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... 

In applying equation (l) Cardenas and 0 Driscoll use Xq as the critical chain length for chain entanglement and permit Xq to decrease as ( )p increases during the polymerization according to equation (l). Therefore, during the course of polymerization they note three kinds of termination reactions ... 

Above the critical chain length, where both the friction and entanglement are important, the relationship is ... 

The value of / is 1 when the fibers are aligned and /j when the fibers are randomly oriented, i.e., isotropic composites. The value of /is decreased when the length of the fiber is less than the critical length (minimum chain length required for entanglement of the polymer chains). 

For polymers, the chains must reach a critical length before effective entanglement can occur. This number varies from one type of polymer to another. For poly(methyl methacrylate), for example, the critical entanglement degree of polymerization is approximately 300 (M approximately 30,000). 

The minimum polymer chain length or critical molecular weight, M for the formation of stable entanglements depends upon the flexibility of a polymer chain which is affected by the polarity and shape of the polymer. Relatively flexible polymer chains, such as polystyrene, have a... 

Bueche suggests that this factor be applied to modify the structural factor to correct for entanglement effects. Thus, only the asymptotic form of Eq. (3.5) is utilized, the predictions at intermediate molecular weight being scarded. Equating the two asymptotic forms at the critical chain length Z (not to be confused with Z ) results in expressions for F that can be written in a form identical to Eq. (2.6) in terms of the parameter X = s )p/M) Z/v as ... 

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