Entanglement onset concentration

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... 

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. 

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]. 

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. 

Turner et al. [41-43] do not consider reduced coil mobility with increasing polymer concentration as decisive. Under these conditions, macromolecules behave as rigid balls, mutually hardly penetrable the probability of radical encounter decreases. The onset of autoacceleration is also ascribed to mutual coil entanglement which only occurs at and above the critical polymer concentration Cc and a certain minimum mean molecular mass A (0.5 < a < 1). The product of these critical quantities is constant... 

Concentration Dependence and Onset of Entanglement, and Tube Dilation... 

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