Relative quantification of long chain branching in essentially linear polyethylenes

The aim of this work is to describe a method whereby low levels of long chain branching, LCB, can be quantified on a relative basis for whole, unfractionated, and essentially linear ethylene/α-olefin copolymers. The method is based on a well established, relatively fast and robust experiment, namely the measurement of the linear viscoelastic properties by a single, isothermal, small amplitude oscillatory shear experiment. The analysis of the data is predicated on the use of the so-called van Gurp–Palmen plots (the phase angle, δ (=tan−1(G″/G′)), plotted against the absolute value of the dynamic complex modulus, |G∗| = (G′2+G″2)1/2). From this plot, the value of δ at |G∗| = 10 kPa is recorded, and it is demonstrated that the amount of LCB inversely correlates with such value of the phase angle, δ. Depending on the desired frequency range, the experiment duration varies between 15 and 60 min rendering this technique well suited for high throughput parallel testing. Its applicability is critically examined with a wide variety of commercial ethylene/α-olefin copolymers. Moreover, we have improved on the long chain branching index (LCBI) proposed by Shroff and Mavridis [Shroff RN, Mavridis H. Long-chain-branching index for essentially linear polyethylenes. Macromolecules 1999;32:8454–64] by basing it on data of truly linear polyethylenes (hydrogenated anionically synthesized polybutadienes) instead of apparently linear commercial polyethylenes.