Entanglement onset

Usually plots of In vs In c at constant molecular weight (Fig. 4a) or In vs In M at constant concentration (Fig. 4b) are used to measure entanglement onset. Measurements are made at constant shear rate, temperature, and solvent conditions. 

Figure 42 shows the concentration dependence of the terminal modulus. The terminal modulus is feeT per chain (G-UbTcIN) in the unentangled regime. The modulus at polymer concentrations above entanglement onset Cg increases rapidly with increasing concentration in the way expected by the scaling model... 

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... 

A similar anomalous behavior has been detected also in 3d polymer melts but only for rather short chains [41] for longer chains, several regimes occur because of the onset of entanglement (reptation ) effects. In two dimensions, of course, the topological constraints experienced by a chain from... 

We can use Equation (5.73) to define the dilute to semi-dilute transition, Equation (5.80) to define the concentrated region and Equation (5.83) to define the onset of entanglements. An example of this is shown in Figure 5.23 for poly butadiene. 

The percent conversion for the onset of the gel effect varies considerably depending on the monomer and the reaction conditions (which determine coil size, viscosity, entanglements). In some systems the gel effect has been reported as occurring at only a few percent... 

With increasing polymer concentration, we may expect that the polymer global motion changes from the fuzzy cylinder model mechanism to the repta-tion model mechanism. The onset of the crossover should depend on the degree in which the lateral motion of a polymer chain is suppressed by entanglement with its surrounding chains, but it is difficult to estimate this degree. There are some disputes over it in the case of flexible polymers [20]. 

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. 

The critical concentration c (Bouldin) denoting the onset of intermolecular entanglements and c (Graessley), which describes the transition from a semi-dilute to a concentrated solution, are of no interest in the field under consideration due to the fact that the applied concentrations are far smaller in every case. 

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... 

Such behavior has been interpreted in terms of a molecular model proposed by Brochard-Wyart and de Gennes [143] and further refined [145,146]. The first version of these models considers a solid surface bearing a few end grafted polymer chains, with a surface density, G, below the onset of the mushroom regime gAT<1, with N the polymerization index of the anchored chains). The melt chains have a polymerization index P. Both N and P are assumed to be much larger than Ne, the average number of monomers needed to form an entanglement. Thus the... 

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