Critical entanglement

Since pc 1/2, we observe that Me 2Mg, as commonly observed. Mg is determined from the onset of the rubbery plateau by dynamic mechanical spectroscopy and Me is determined at the onset of the highly entangled zero-shear viscosity law, T) M. This provides a new interpretation of the critical entanglement molecular weight Mg, as the molecular weight at which entanglement percolation occurs while the dynamics changes from Rouse to reptation. It also represents the... 

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... 

The dynamic mechanical properties of elastomers have been extensively studied since the mid-1940s by rubber physicists [1], Elastomers appear to exhibit extremely complex behavior, having time-temperature- and strain-history-dependent hyperelastic properties [1]. As in polymer cures, DMA can estimate the point of critical entanglement or the gel point. 

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). 

For Ni>Ns> Ng Ng is the critical entanglement molecular weight), r,- is the reptation time, while for N Ng it represents the Rouse time [60,69]. Because Xi has a strong molecular weight dependence, long chains keep then-orientation while short already relax to the isotropic state. For Nt 2> N one finds [70]... 

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... 

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