Critical entangled length

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 ... 

Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

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

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). 

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 ... 

O Driscoll has proposed that the auto-acceleration can be modeled by recognizing that the termination reaction is diffusion controlled but will also depend on the size of the chain involved. The critical chain length for entanglement then becomes an important parameter, and two termination rate constants can also be defined, one for chains smaller than and one for large entangled chains. These are, respectively, and k. If v is the kinetic chain length and Vp is the conventional steady-state polymerization, then the observed rate v is given by... 

Here do is the critical interface width corresponding to Pc, which will be of order the radius of gyration of the entanglement length, and below which no strength exists, other than that of simple pullout and surface energy terms, as described by the nail solution. Letting the normalized width w = d/dc, this equation becomes... 

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