On the Polymer Entropic Force Singularity and Its
Relation to Extensional Stress Relaxation and Filament
Eric S. G. Shaqfeh (1), Gareth H. McKinley (2), Nathanael Woo (3), D. A. Nguyen (4), Tam Sridhar (4)
(1) Departments of Chemical and Mechanical Engineering, Stanford University, Stanford, CA
(2) Department of Mechanical Engineering, M.I.T., Cambridge, MA
(3) Scientific Computing and Computational Math. Program, Stanford University, Stanford, CA
(4) Department of Chemical Engineering, Monash University, Melbourne, Victoria, Australia
We examine the use of transient extensional rheology as a means of examining worm-like and freely-jointed chain behavior of polymers in dilute solution at high extension. We demonstrate theoretically that both chain types follow different power-law stress decay functions for short times after cessation of strong extensional flow. The different power laws are universal for different strain and strain-rate histories and, moreover, are signatures of the singularities in the entropic-spring force laws that develop close to full extension. We also demonstrate that these power law exponents are directly related to the inertialess elastic recoil of an extensionally stretched filament of polymer solution. Finally, these theoretical predictions are compared to experimental results for the relaxation of stress following extension for monodisperse polystyrene solutions. When modeled as freely-jointed chains, we find excellent agreement with the theoretical predictions.