Progress in understanding entangled polymer dynamics

The surprising flow behavior of entangled polymer liquids has been of profound interest throughout the history of polymer science. In the last three decades, substantial progress has been made in mechanistic understanding of entangled polymer rheology, based on the tube ansatz. I will summarize the essential physics of the “success stories”: 1) linear dynamic rheology of entangled linear chains, stars, star-linear blends, H-polymers, polydisperse multiply branched chains, and polydisperse linear chains; and 2) nonlinear extensional flow of linear chains and branched polymers.

But how well do we understand where the tube comes from? Simulations are helpful: we can observe the “skeleton” of the tube with chain-shrinking methods, and “see” the tube using isoconfigurational averaging. And, we can relate the tube to how many knots the melt can tie, the “topological entropy”.

So can we predict the tube diameter from chain architecture? Here too there has been progress, with a coherent scaling theory that joins predictions for flexible chains and stiff chains. Entanglement is governed by the frequency of close encounters between chains, when they can “zig” one way or “zag” the other as they pass. These encounters are controlled by how close chains can get, which is governed by 1) the larger of the packing length p or chain diameter d, and 2) whether an entanglement strand is flexible.

Scaling based on packing length and flexible chains (Lin-Noolandi, LN) describes many real polymers; but simulated linear bead-spring chains behave as entangled “threads”, with no role for p. However, if we “bulk up” linear bead-spring chains with sidegroups, we can observe LN scaling in simulations. This raises the question of how to *measure* the packing length, which we do by asking how far from a given monomer most of the density comes from its own chain. Packing length measured this way is consistent with LN scaling, and differs from estimates based on the effective diameter of chains.