In this paper, we examine the melt rheology of well-defined, model polymers where the long chain branching (LCB) is precisely known from the synthesis. All of these are made by the hydrogenation of polybutadiene, but they vary greatly in the level and type of LCB present. We find that all polymers that have LCB show a greater degree of shear thinning than linear chains. This applies both to those with a single branch (stars) and also to those with multiple branches per chain (such as combs). However, only molecules with multiple branches induce extensional thickening in a sample. Only a small amount of these comblike molecules, on the order of 5%, are needed to show this effect. We also show here how a new method of treating the shear data, the so-called Van Gurp−Palmen analysis, can give a more easily interpreted form of the results that can reveal the length and amount of branches in a sample. The insights generated from this work show the importance of access to well-defined polymers with several kinds of branching architecture for the development of a deeper understanding of polymer rheology.

It has previously been shown that the entanglement molecular weight (Me) and the plateau modulus (G N 0 ) of flexible polymers can be correlated to the unperturbed chain dimension, 〈R 2 〉0/M, chain density (F) via the use of the packing length (p), which is defined as the volume of a chain divided by its mean square end to end distance. For polyolefins and co-polyolefins where 〈R 2 〉0/M remains unmeasured a method is presented herein where knowledge of the average molecular weight per backbone bond (mb) allows G N 0 and thus Me to be estimated. This is particularly valuable for the case of polyolefin copolymers where the melt chain dimensions (and thus the packing length) are unknown.

We describe the synthesis and characterization of a number of polymers with well-defined structures that serve as models for polyethylene with long chain branching. All of them have been made by using anionic polymerization techniques and controlled chlorosilane chemistry to give nearly monodisperse polybutadienes with precise control of the number, length, and placement of long (M h w > 1500 g/mol) branches on each chain. This was followed by hydrogenation to give saturated polymers with the same well-defined long chain branching and the local structure of a typical linear low-density polyethylene. That is, both the backbones and the long branches had 17-25 ethyl branches per 1000 total carbons. Among the structures made were some with no long branches ("linears"), some with a single long branch ("stars"), others with exactly two branch points (the R-ω type, "H's", "super-H's", and "pom-poms"), and some with several long branches randomly distributed along the backbone ("combs"). Essentially all types of branching from a linear backbone can be made by the techniques described herein. While linear and symmetrical star models of polyethylene have been made previously, the other structures are the first examples of polyethylene models with multiple branches and precise control of the molecular architecture. We use the results given here to discuss how long chain branching can be detected in polyethylene. We also show how the branching structure controls chain dimensions. The Zimm-Stockmayer model works well to describe the sizes of the lightly branched molecules, but its predictions are too small for those with many long branches. This is presumably due to crowding of the branches. The rheological properties of these polymers will be described in subsequent publications.

Introduction.Very low levels of long chain branching (LCB) are known to have large effects on the rheological behavior of polymers. These effects are essential to the utility of polymers that have LCB, such as low-density polyethylene. However, the fact that only a few long branches are required means that they are difficult to detect by most means. Here we show how the level of LCB can be correlated with a rheological measure of the gel-like behavior of a polymer, which may prove useful as a characterization technique.Rheology of Polymers at the Gel Point. Longrange connectivity in a polymeric material can be achieved by either chemical or physical gelation. Chemical gelation occurs when permanent covalent bonds connect polymer chains into a three-dimensional network. In contrast, physical gelation occurs when temporary or reversible bonds, such as crystallites, hydrogen bonds, phase-separated domains, etc., connect the chains. A key difference between the two forms of gelation is that the molecular weight is finite for physical gels but diverges at the gel point for chemical gels. 1 Critical gels exhibit simple relaxation behavior following a self-similar relaxation modulus, first described

A series of carefully synthesized ethylene/butene copolymers (0.2-0.85 mole fraction butene) were synthesized using metallocene catalysts to probe the relationship between the chemical architecture of polyolefins and their rheology. The dependence of G N 0 , the plateau modulus, on m b , the molecular weight per backbone bond, which we have seen previously for polyolefins is obeyed by these copolymers. Moreover, the modulus at the frequency at which G′ ) G′′ also scales with copolymer composition. We also show that the van Gurp-Palmen plots (|G*| vs δ) for these copolymers show a universal behavior, which could allow for the characterization of copolymer composition by rheology. We demonstrate that combining small-amplitude oscillatory shear data with stress relaxation experiments the theory of linear viscoelasticity allows us to determine lowfrequency behavior much more rapidly. The zero shear viscosity of these ethylene copolymers also shows a regular dependence on the copolymer composition, and we propose a new scaling relationship for zero shear viscosity in terms of m b . We show that this applies to a wide range of polyolefins and show similar relations for the equilibration time, τ e , and monomeric friction factor, ζ.