A stochastic slip-link model with discrete numbers of Kuhn steps.

Prof. Jay D. Schieber and Renat Khaliullin

Department of Chemical Engineering, and Director, Center of Excellence in Polymer Science and Engineering

Illinois Institute of Technology, 10 W. 33rd Street, Chicago, Illinois 60616

Doi and Edwards originally used a slip-link picture to justify a certain stress tensor expression in their tube model. We have instead been using the slip-link picture to derive all dynamics and stresses in a thermodynamically consistent way. Key to this novel development is the use of monomer density between entanglements as a stochastic variable. The resulting model contains only a single phenomenological parameter (a time constant), which is determined by linear viscoelastic experiments (or possibly by molecular dynamics). All nonlinear flow dynamics are then explained without adjusting parameters. This approach offers a way to model systems that have been modeled by separate equations, to date. So far, theoretical predictions for linear chains in a melt have shown an ability to make accurate, quantitative predictions of transient and steady shear flows, and of steady elongational flows. However, a description of transient elongational melt, and steady elongational solution predictions are off. Here we examine assumptions in our stochastic model by considering a more fundamental description of dynamics, which avoids arbitrary assumptions about the dynamics at the ends of the chains. We can then use this more-fundamental model to re-examine elongational flows, and to study star-branched relaxation dynamics. We argue that slip-links offer a way to unify the description of linear and branched liquids, and lightly cross-linked elastomers.