Long-Chain-Branching Index for Essentially Linear Polyethylenes

Abstract

Low levels of long-chain branching (LCB) in an otherwise linear polyethylene, such as HDPE or LLDPE, are known to affect dramatically the polymer melt rheological properties. However, reliable techniques to detect and quantify LCB at these levels (i.e., ≪1 LCB/1000 C) have not been available. In this work, the long-chain-branching index (LCBI) is developed for essentially linear, polydisperse polyethylenes, which are those containing a small level of LCB, such that the measured intrinsic viscosity is the same, within experimental error, to that calculated from MWD data, assuming the resins are linear. The long-chain-branching index (LCBI) is fundamentally related to the viscosity enhancement due to long-chain branching, and it is independent of molecular weight (MW) and molecular weight distribution (MWD). It is given by the relation: LCBI = ηo 0.179/4.8[η] − 1, where ηo (P) is the zero shear viscosity at 190 °C, and [η] (dL/g) is the intrinsic viscosity in trichlorobenzene at 135 °C. A suitable average molecular weight could substitute the intrinsic viscosity in this relation, if so desired. The numerical factors in the defining relation are derived on fundamental grounds such that the lowest value of 0.0 represents perfectly linear polyethylene. Various measures of LCB that have appeared in the literature, including the Dow rheology index (DRI) and those based on the activation energy of viscous flow, are critically examined and their limitations identified. The new index proposed here overcomes these limitations, as illustrated with a vast number of examples with commercial polyethylenes. The applicability of the LCBI for distinguishing LCB levels within conventional, free-radical polymerized LDPEs is also investigated.

Effect of long chain branching on linear-viscoelastic melt properties of polyolefins

“…This may be due to the inapplicability of the LCB index to highly branched polymers as indicated above [142]. Correlations between E a and the absolute number of LCB were recently made by Yan et al [143] and Hatzikiriakos [29].…”

“…In strictly linear polymers of moderate polydispersity index, i.e., mPEs, η o is directly proportional to τ o , which is an average relaxation time [125,135,142,144,146]. This conclusion is easily attainable from the linear viscoelastic model assuming a single exponential relaxation modulus G(t) in the terminal zone, and is considered to be consistent with the behaviour predicted by reptation theory for linear, long chain, branchless, monodisperse polymers [92,93].…”

“…Shroff and Mavridis [142] stated that DRI is a measure of rheological polydispersity and as such depends on both MWD and LCB. DRI could be used as a measure of LCB for polymers of known similar MWD, as could any other measure of rheological polydispersity [54].…”

“…Correlations between E a and the absolute number of LCB were recently made by Yan et al [143] and Hatzikiriakos [29]. However, these approaches have not been widely accepted since the range of temperature and frequency data employed in the calculation is likely to affect E a values [142]. Moreover, some published results suggest that the absence of an enhanced E a value in PEs does not necessary preclude the absence of low levels of LCB.…”

“…Published results indicate that these correlations are strongly dependent on the nature, i.e., the length and distribution of branches [71]. In other cases in which the TTSP is not fulfilled [142], which suggests a different mechanism of flow depending on the molecular structure, it is not possible to give a reliable value of E a . For example, values of E a,h ranging from 37.7 to 100.5 kJ·mol -1 and E a,v from 1.67 to 35.6 kJ·mol -1 were obtained for LLDPE modified with peroxide depending on the frequency range used in the calculation.…”