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.