Separating the effects of sparse long-chain branching on rheology from those due to molecular weight in polyethylenes

Abstract

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.

Using viscoelastic properties to quantitatively estimate the amount of modified poly(lactic acid) chains through reactive extrusion

“…Obtaining molecular information about LCB using only rheology-based methods is not trivial. Numerous studies reported that increasing the MW, broadening the MW distribution (MWD), or increasing the content of LCB have similar effects on the shear viscosity function [Shroff and Mavridis (1999); Vega et al (2002); Doerpinghaus and Baird (2003); Shroff and Mavridis (1999); van Ruymbeke et al (2005); Stadler and Munstedt (2008b)]. That is, the distribution of relaxation times is not a unique function of chain architecture.…”

“…A couple of noteworthy features specific to the viscosity function in LCB polymers are the g 0 increase and the enhanced shear-thinning regime while its onset is shifted to lower frequencies [Vega et al (1998);Dorgan et al (1999); ; Lohse et al (2002); Doerpinghaus and Baird (2003); Auhl et al (2004); ]. Stadler and Munstedt (2008a) also observed several distinct curvatures in the high frequency region.…”

“…One of the most useful methods is the time-MW (TMW) superposition principle, which is fulfilled for polymer exhibiting similar and narrow MWD (e.g., PLA and PLA-REX samples, cf. Table IV) [Doerpinghaus and Baird (2003)]. Initially, this concept assumes that the dependence of g 0 on M w follows Eq.…”

“…In principle, the application of the shift factor, a M , should reveal the individual contribution of the topological modifications on the jg*(x)j function [Doerpinghaus and Baird (2003)]. For the purpose to remove the MW effects of the viscosity functions of PLA-REX samples, the established dependence of g 0 on M w for linear polydisperse PLA at 180 C [i.e., g 0 ¼ 5.5 Â 10 À15 M w 3.4 , Dorgan et al (2005)] is used to estimate g 0 of their corresponding linear sample of equivalent MW.…”

“…Consequently, when these concepts are combined, an equivalent shifting along the time, or rate, axis and the viscosity axis is achieved. On this basis, the TMW superposition is applied using the shift factor, a M , as follows [Doerpinghaus and Baird (2003)]:…”