Relations among melt viscosity, solution viscosity, molecular weight, and long‐chain branching in polyethylene

According to the segmental theory of flow, the viscosity ηm of a polymer melt should be given by where the jump frequency J is a function of temperature and free volume, and a statistical factor F, depending on chain length, expresses the requirement that the motions of the segments be coordinated. Peticolas and Watkins found that, at the same weight‐average molecular weight, branched polyethylenes have considerably lower viscosities than linear polyethylenes. They attributed this reduction in viscosity to an increased free volume (which would increase the jump frequency) brought about by short‐chain branches. Marshall, however, pointed out that the required increase in free volume is not found by experiment. This paper presents an alternative theory whereby the reduction in viscosity is attributed to the presence of long‐chain branches which help coordinate the movement of the various segments and thereby reduce the coordination factor F. As a result of certain theoretical considerations, a linear relation is predicted between the log of the melt index and the intrinsic viscosity in an ideal or Θ‐solvent. This relation is confirmed by a plot of data from 27 samples of polyethylene obtained from four commercial sources and having melt indices ranging from 0.12 to 26.6. Bis(2‐ethvlhexyl) adipate at 145°C. was used as the ideal solvent. Further insight into the viscous and viscoelastic behavior of polyethylene samples was obtained when it was observed that detailed interpretation of light‐scattering data explained the fact that samples with practically the same melt indices had different solution viscosities in a good solvent such as Tetralin at 100°C. These variations were attributed to differences in the expansion factor α. This factor depends on molecular weight, long‐chain branching, and solvent power and probably reflects the ease with which a molecule may be deformed. This α‐factor then should probably be related to the spectrum of relaxation times which would influence such important processing variables as melt elasticity and non‐Newtonian flow.