Packing Length Influence in Linear Polymer Melts on the Entanglement, Critical, and Reptation Molecular Weights

Abstract

We have shown in previous studies that the entanglement molecular weight for a polymer melt, M e, is related by a power law to p, the packing length of the polymer species. We now find that power laws also describe the molecular weights characterizing the melt viscosity, M c marking the onset of entanglement effects and M r the crossover to the reptation form. The packing length exponents for M e, M c, and M r differ significantly, however. The long-held notion that the ratio M c/M e has the same value for all species is therefore incorrect. Further, the observed and predicted values of M r for two species, 1,4-polybutadiene and polyisobutylene, have been found to agree, within the uncertainties, with the projected values. Finally, the variations with packing length are such that all three characteristic molecular weights would appear to converge on the same value near p = 9 Å. As yet, no species with such a large packing length has been completely studied rheologically. But the range is not outlandish and is clearly reachable by appropriate synthetic methods.

Rheological Properties of 1,4-Polyisoprene over a Large Molecular Weight Range

“…Constraint-release processes additionally reduce the viscosity sensitively and only the prefactor Q should then be rescaled appropiately to a smaller value than 15/4 ) 3.75. The reduction to 30% of its value as was suggested earlier by Fetters et al 7 to give ∼1.13 was physically wrong due to a confusing error in the used ref 4. Only the use of this particular wrong "Q" prefactor together with the fixed exponent 3.4 and fixed M c /M e leads to the erroneous prediction for M r .…”

“…where p* ) 9.2Å and T in absolute K. 7 Equation 11c is based on some assumptions which will be reevaluated here (strictly speaking, the packing length has been linked in a rigorous fashion only to M e ). At p* the entanglement and critical molecular weights become equal.…”

Model for the fracture energy of glassy polymer–polymer interfaces

“…According to Fetters and coworkers 13,22,23 The significance of this relationship is to imply that the topological constraint associated with chain entanglement is universal. Lin proposed that a certain one-to-one correspondence must exist between the size of a reptation tube, d t , and the number of entangled strands per unit volume, n v .…”

“…ϫ dy͓1 ϩ tanh͑2y/w͔͓͒1 ϩ tanh͑Ϫ2y/w͔͒ (23) which is equal to 0.5. The effect of is to decrease the entanglement density within the interface by that factor.…”

A stick-slip/Rouse hybrid model for viscoelasticity in polymers

“…The value of M 0 was given above as M 0 = 68.114. For the polymer density we use the value given by Abdel-Goad, et al, [1], as ρ = 0.90 × 10 −24 g/Å 3 at T = 298 K (values range from 0.9 × 10 −24 to 1 × 10 −24 g/Å 3 , [14], [16], [17], [18], but most commonly 0.9 × 10 −24 g/Å 3 ). The segment density is then…”