Entanglement onset molecular weight

The direct observation of the onset molecular weight of entanglement at Me (M ) breaks the traditional belief that chain entanglements start to occur at The traditional idea was based on the observation... 

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... 

Each of the viscoelastic parameters G°, rj0, and Je° has associated with it a characteristic molecular weight which either measures an equivalent spacing of entanglement couples along the chain (Me, deduced from G with the kinetic theory of rubber elasticity), or marks the onset of behavior attributed to the presence of entanglements (Mc and AT, deduced from r/0 and Je° as functions of molecular weight). Table 5.2 lists Me, Mc, and M c for several polymers. Aside from certain difficulties in their evaluation, each is a rather direct and independent reflection of experimental fact. 

Bates et al. 1990 Rosedale and Bates 1990). It was pointed out that the onset of measurable fluctuation effects depends on molecular weight in a manner that suggests that entanglements play an important role in coupling fluctuations... 

Then, they defined Mg (which they also linked with the plateau modulus Gjv according to Eq. (13.2) as described below) as the molecular weight of a chain at which Ngp = 2, that is, when there is just one other chain in the sparmed volume. Since Vsp is proportional to a at M = Mg, the argument naturally leads to an equation equivalent to Elq. (13.4), disregarding the difference in the proportional constant. The arbitrariness of setting Ngp = 2 at M = Mg is absorbed in the proportional constant as well. Fetters et al. started by setting Ngp equal to 2 at the onset of entanglement, which they assumed to be Mg, and then they moved on to link this Mg with the plateau... 

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