The rheology of polymer melts depends strongly on temperature. Quantifying this temperature dependence is very important for fundamental, as well as practical, reasons. The purpose of this paper is to present a unified framework for handling the temperature dependence of rheological data. We considered the case (by far the most common in polymer melts) where all relaxation times (in the context of linear viscoelasticity) have the same temperature dependence (characterized by a “horizontal shift activation energy”) and all relaxation moduli have the same temperature dependence (characterized by a “vertical shift activation energy”). The horizontal and vertical activation energies were extracted from loss tangent vs. frequency and loss tangent vs. complex modulus data, respectively. This is the recommended method of calculation, as it allows independent estimation of the two activation energies (statistically uncorrelated). It was shown theoretically, and demonstrated experimentally, that neglect of the vertical shift leads to a stress (or modulus) dependent activation energy and necessitates different activation energies for the superposition of loss and storage modulus data. The long standing problem of a stress‐dependent activation energy in long chain branched LDPE was identified as originating from the neglect of the vertical shift. The theory was applied successfully to many polyolefin melts, including HDPE, LLDPE, PP, EVOH, LDPE, and EVA. Linear polymers (HDPE, LLDPE, PP) and EVOH do not require a vertical shift, but long chain branched polymers do (LDPE, EVA). Steady‐shear viscosity data can be superimposed using activation energies extracted from dynamic data.

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.

The identification and characterization of low levels of long-chain-branching (LCB) in essentially linear polyethylenes has attracted significant interest in recent years. One experimental technique is nuclear magnetic resonance (NMR), which can detect LCB in essentially linear polyethylene homopolymers for LCB in the range 0.2-3 branches per 10 000 carbon atoms. Another approach has been the use of a rheological measurement in combination with a dilute-solution measurement (intrinsic viscosity or GPC). NMR is a direct method of LCB measurement, but it provides no information on branch length and has other limitations related to interference from short chain branches. Rheology provides a sensitive but indirect method of measurement, capitalizing on the strong effect of LCB (longer than M e, the entanglement molecular weight) on translational mobility of the polymer chains and thus viscosity. The purpose of the present work is to provide an assessment of the two approaches of LCB determination, using a series of well-characterized, essentially linear polyethylenes. NMR was shown to work satisfactorily in characterizing LCB for a series of metallocene-catalyzed polyethylenes, but it failed to detect LCB in other cases, including a series of linear polyethylenes where LCB was introduced deliberately via peroxide modification. A rheology-based index for LCB characterization was shown to be preferable, due to its robustness and general applicability in all cases examined.

SYNOPSISThe rheological properties of polymer melts depend strongly on the underlying molecular structure: molecular weight, molecular weight distribution, and long chain branching. It is of considerable importance, both fundamental and practical, to relate the molecular architecture to polymer melt rheology. The focus of the present work is in extracting a measure of polydispersity from rheological data. Various polydispersity measures that have been proposed in the literature are critically examined and their limitations are pointed out. New measures of polydispersity are proposed that overcome these limitations. The evaluation of the various polydispersity measures is performed by reference to rheology fundamentals, with model calculations and examples drawn from industrial practice. The issues of eliminating molecular weight and temperature effects in characterizing polydispersity are comprehensively addressed. The presence of small levels of long chain branching in an otherwise linear polymer alters most of these measures of polydispersity dramatically, while no detectable change appears in the molecular weight distribution obtained using a gel permeation chromatograph. It is demonstrated that the polydispersity measures proposed in the present work, and which are extracted from frequency response data in the linear viscoelastic region, can be used reliably to characterize polydispersity in polymer melts. 0 1995 John Wiley & Sons, Inc.