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 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 angstroms. 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.