Other Methods for Estimating Me

Instead of integrating over the entire maximum of J or G , one can obtain the value of J% or simply from the peak value of the respective loss component if the shape of the maximum is specified. For example, a phenomenological theory of Marvin and Oser predicts the relations 

The Critical Molecular Weight Me from Viscosity or Viscoelastic Time Scale 

The minimum in tan 5 as portrayed in Fig. 13-4 is closely related to Me- According to the Marvin-Oser theory, the depth of this minimum for a polymer with sharp molecular weight distribution is given by  

Critical Molecular Weight Me for Entanglement Coupling from Dependence of Viscosity on Molecular Weight32.34 

From the Marvin-Oser theory, the location of the maximum in J on the frequency scale can also be related to entanglement parameters. However, both Me and Me are involved the frequency at the maximum is independent of M (if sufficiently high) but is inversely proportional to MeMc- The maximum in G occurs at a frequency which is proportional to Mc/Me and hence is essentially independent of the entanglement spacing, though it is inversely proportional to A/.  

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