(306a) Linear and Nonlinear Rheology Predictions of Entangled Polymers in Complex Flows from First Principles

We present a novel approach to modeling entangled polymer dynamics, which makes quantitative predictions without parameter adjustment. Nearly since its introduction by Doi and Edwards in 1978, the "tube model" has been the dominant approach to understanding relaxation and rheology in polymer melts. However, despite great efforts and countless additions, consistent quantitative description of data has remained elusive. Moreover, the model still lacks a microscopic basis. Instead, we adopt an alternative approach, mentioned by Doi, Edwards and de Gennes, but never before pursued quantitatively, called "slip-links".

We use a series of hypothesis-driven coarse-graining steps to create a hierarchy of integrated slip-link models. This procedure produces a mathematical model whose calculations are 3 million times faster than the most-detailed level of description, and 20 billion times faster than atomistic-level calculations. Predictions of experiment are quantitative.

As an example, we show that the theory predicts the formation of an unusually shaped vortex in a journal bearing flow, which might be examined experimentally. More important than computational speed up is the dramatic reduction in the number of dynamic variables necessary to describe the system, which suggests a deep understanding of the physics of entangled polymers, justifying the postulates made by Sam Edwards and Pierre-Gilles de Gennes more than 40 years ago.