Packing length influence in linear polymer melts on the entanglement, critical, and reptation molecular weights

We have shown in previous studies that the entanglement molecular weight fo r a polymer melt, M-e, is related by a power law to p, the packing length o f the polymer species. We now find that power laws also describe the molecu lar weights characterizing the melt viscosity, M-c marking the onset of ent anglement 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 l ong-held notion that the ratio M-c/M-e has the same value for all species i s therefore incorrect. Further, the observed and predicted values of M-r fo r two species, 1,4-polybutadiene and polyisobutylene, have been found to ag ree, within the uncertainties, with the projected values. Finally, the vari ations with packing length are such that all three characteristic molecular weights would appear to converge on the same value near p = 9 Angstrom. As yet, no species with such a large packing length has been completely studi ed theologically. But the range is not outlandish and is clearly reachable by appropriate synthetic methods.