Melt Viscosity-Molecular Weight Relationship for Linear Polymers

The relationship between melt viscosity ή₀ and molecular weight M for entangled linear polymers is accurately described by a power law,ή₀ α M^3.4, up to M/M_e~ 150, where M_eis the entanglement molecular weight. We have sought here to test the range of validity of that law by measurements on polymers with M/M_eas large as practically possible. Anionic polymerization was used to prepare a series of narrow distribution polybutadienes with low vinyl content and molecular weights ranging from 1 × 10³to 1.65 × 10⁷(0.5 < M/M_&< 8000). Several linear viscoelastic techniques were used to determine viscosities ranging from 1 × 10° P to 2 × 10¹²P. Significant departures from the 3.4 power law were found beyond M/M_e~ 200. The results are consistent with an approach to M³dependence as suggested by reptation theory, but the scatter is too large to allow a definite conclusion. The apparent ή₀/M³asymptote is within a factor of 2 of a prediction based on reptation theory, modified by the contributions of tube renewal. Additionally, a comparison was made of the monomeric friction coefficient obtained from viscosities at low molecular weight and from transition responses at high molecular weight. Values of the modulus shift factor b_Twere obtained for an unusually wide range of temperatures and are briefly discussed.