SynopsisThe effects of sparse ͑ Ͻ 1 branch per chain͒ long-chain branching ͑LCB͒, molecular weight ͑MW͒, and molecular weight distribution on the shear rheological properties of commercial polyethylenes are often convoluted. In this paper a method for separating the effects of sparse LCB in metallocene-catalyzed polyethylenes ͑mPE͒ from those of molecular weight and its distribution based on time-molecular weight superposition is proposed. Four metallocene polyethylenes with degrees of long-chain branching ͓i.e., M of the arm (M a ) is greater than that for the onset of entanglements, M c ] as determined from dilute solution measurements ranging from zero ͑linear͒ to 0.79 LCB/10 4 CH 2 , along with a conventional Ziegler-Natta polymerized linear low-density polyethylene ͑LDPE͒, and a tubular free-radical polymerized LDPE are investigated. In general, it is observed that sparse LCB ͑for levels Ͻ 1.0 LCB/10 4 CH 2 ) increases the zero shear viscosity, 0 ͑e.g., by a factor of 7͒ and decreases, but even to a greater degree, the critical shear rate (␥ c ) for the onset of shear thinning ͑e.g., by a factor of 100͒. The breadth of the molecular weight distribution just affects ␥ c but not 0 for the range of data used in this study. Furthermore, the dynamic storage modulus G Ј shows similar enhancement at low frequencies as viscosity does, while the primary normal stress difference coefficient, ⌿ 1,0 , exhibits a greater dependence on long-chain branching than that predicted from the zero-shear viscosity enhancement. The results for the mPEs are consistent with recent molecular theories for randomly branched molecules in that it is the spacing between branch points and not the number of branches at a point that is important. Furthermore, the results are consistent with the idea that the branches are located on the longest chains, and hence, have the greatest effects on the longest relaxation modes.

The model parameters for the multimode differential pompom constitutive equation were determined for densely branched, sparsely branched, and linear polyethylene resins. The versatility and robustness of the pompom model is demonstrated through good rheological predictions in both shear and extensional deformations. The model parameters obtained for the sparsely branched materials indicate that the frequency of long-chain branching dominates the degree of strain hardening observed in uniaxial extension. This finding agrees well with the proposed mechanism of long-chain branching using constrained-geometry metallocene catalysts. The model parameters agree qualitatively with the longchain branch content determined from dilute solution measurements. Furthermore, the values of the number of pompom arms (i.e., the priority) were found to be quite high even for the sparsely branched materials but were only associated with the longest relaxation times. This suggests that branching for the metallocene systems may be highly concentrated on the longest chains rather than randomly distributed on all of the chains.

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The influence of sparse long chain branching on the onset and propagation of isothermal draw resonance in fiber spinning of polyethylene melts was investigated. Six polyethylene melts were used in this study: three sparsely branched metallocene polyethylenes, a linear low-density metallocene polyethylene, a conventional linear low-density polyethylene, and a conventional low-density polyethylene (LDPE). The sparsely branched metallocene polyethylenes have almost identical shear rheology and molecular weight distributions, but strain harden to different extents under extensional deformation because of slight differences in the amount of sparse long chain branching. Critical draw ratios and the ratios of minimum to maximum diameter were found to be different for each of these polyethylenes. The two linear low-density polyethylenes, which have no long chain branching, had critical draw ratios similar to those of the sparsely branched polyethylenes, but failed (necked to the point of filament breakage) during monofilament extrusion at draw ratios significantly lower than those measured for the sparsely branched polyethylenes. In contrast, the LDPE, which has the highest degree of branching and largest molecular weight distribution, had a much higher critical draw ratio than that obtained for the other five polyethylenes. These results suggest that the degree of extensional strain hardening, arising from differences in long chain branching, has a significant effect on the onset and propagation of draw resonance in isothermal fiber spinning. In the case of LLDPE, broadening the MWD seemed to affect the drawability of LLDPE, but had no effect on the critical draw ratio.

The ability to accurately predict the pressure profile along an abrupt 4:1 planar contraction is in®estigated. Predicted