Advances in modeling of polymer melt rheology

T he development of theories to predict the rheological (i.e., flow) properties of densely packed polymers in the melt or solution state is important because such theories might enable rational design of polymer processing methods for shaping polymers into products, and because they can be used in rheological characterization of polymer molecular weight and long-chain branching. These are important topics, given the enormous volume of polymers produced each year (100’s of billions of pounds).The seminal work of de Gennes and Doi and Edwards in the late 1970s established their ‘‘tube model’’ as the standard theory for predicting polymer rheological properties. The ‘‘tube’’ idea arises from the notion that entanglements of a long polymer with its neighbors in a dense melt restrict motion of the polymer to a ‘‘tubelike’’ region — see Figure 1a. Until very recently, the ‘‘entanglements’’ between densely packed long chains that produce a phenomenological ‘‘tube’’ constraining the motion of each chain could not be experimentally imaged or simulated, nor could their existence be rigorously derived from microscopic physics, and so acceptance of the tube model has not come without controversy. In addition, most predictions of the tube model in the early years were hardly better than qualitative. Still, it was generally recognized early on that, despite its limitations, the Doi-Edwards ‘‘tube’’ provides a plausible ansatz for understanding qualitatively how linear polymers in the entangled state relax, namely, they relax by ‘‘reptation’’ or sliding of the chain along its tube axis, and by retraction within the tube. Moreover, the tube model offered the greatest hope for eventually attaining a quantitative understanding of polymer melt rheology. In the years since 1978, many efforts have been made to improve upon the Doi-Edwards model. Broadly speaking, the 1980s witnessed a sustained attack on the problems of ‘‘primitive-path fluctuations’’ — that is, changes in the length of the tube due to accordion-like motions of the chain in the tube, and of ‘‘constraint release’’ — that is, loss of entanglements due to motions of the surrounding chains that define the tube. It was found that as long as the chain ‘‘feels’’ the existence of the tube before the entanglements are lost, one can describe the chain’s relaxation as reptation in a tube, where the tube itself is moving through space due to loss, and recreation of entanglements with surrounding mobile chains. This tube movement (now called ‘‘constraint release Rouse motion’’) is especially significant for polydisperse polymers, where the entanglements imposed on long chains by surrounding short chains can relax quite rapidly, and, hence, enhance the mobility of the tube containing the long chain. Finally, in some cases, one can regard the tube diameter to be continuously expanding or ‘‘dilating,’’ if the surrounding chains are so much more mobile than the chain in the tube that they act as ‘‘solvent’’ that ‘‘dynamically dilutes’’ the entanglement density. These ways of incorporating constraint release into tube models have Perspective