Stress Relaxation of Comb Polymers Keith M. Kirkwood a, Dimitris Vlassopoulos b,c, and L. Gary Leal a a Department of Chemical Engineering, University of California at Santa Barbara Santa Barbara, California b Institute of Electronic Structure & Laser, FORTH, Heraklion 71110, Crete, Greece c Department of Materials Science & Technology, University of Crete Heraklion 71003, Crete, Greece Linear Current understanding of comb relaxation (hierarchy of processes, plus dynamic dilution) was found to even apply to combs with unentangled or weakly entangled branches Existing linear theory captures behavior of short arm combs by increasing effective branch entanglement Nonlinear Understanding of relaxation mechanisms extended into nonlinear deformations Derived architecture dependent damping function for comb backbone Model captures the experimentally observed behavior Architecture dependence of backbone response to strong flows Model incorporating CCR captures nonlinear shear behavior of comb backbone using linear chain results CCR insensitive to architecture Interest is focused on understanding the relationship between polymer chain architecture and rheological properties Linear Viscoelastic Behavior Identify relevant relaxation mechanisms Test limits of current theory Nonlinear Regime Does understanding of relaxation processes extend to nonlinear flow situations Architecture dependence of stress relaxation Linear Viscoelastic Behavior of Short Arm Combs Nonlinear Rheology: Stress Relaxation after Step Strain Introduction Conclusions Materials polyisoprene short arm combs polybutadiene exact comb Synthesized by P. Driva and N. Hadjichristidis (Univ. of Athens) via the macromonomer strategy with high-vacuum anionic techniques Synthesized by A. Nikopoulou and N. Hadjichristidis (Univ. of Athens) Nikopoulou et al. J. Polym. Sci., Part A: Polym. Chem. 2009, 47, Anionic synthesis with exact placement of branch points along backbone Molecular Weight q (# branches) Z (# entanglements) Diluted Z CodeCombBackboneBranchbranchbackbone PI132k PI159k PI211k PI472k Molecular Weight q (# branches) Z (# entanglements) Diluted Z CodeCombBackboneBranchbranchbackbone ac-3# Tube based theoretical model for comb architecture by Kapnistos et al. (Macromolecules 2005, 38, ) Hierarchical relaxation (HR): backbone immobile until branches relax Dynamic dilution (DTD): relaxation of branches releases entanglements on backbone Branches and backbone ends relax with mechanisms equivalent to star arm Backbone relaxes as linear chain with less entanglements and enhanced friction at the branch points Unentangled branches still exhibit DTD and HR Model underpredicts friction of branch point for Increase branch entanglement to capture both branch and backbone relaxation Methods such as modifying only change backbone relaxation entanglement Create stress relaxation mastercurves Shift at long times to analyze damping function for comb backbone No dependence on concentration for Recent work* suggests no architecture dependence of damping function Suggest well-entangled comb backbone will follow Doi-Edwards (DE) prediction Deviations from DE due to backbone entanglement Damping behavior of well-entangled backbones of polyisoprene combs has weaker dependence on strain relative to Doi-Edwards * Vega, D.A.; Milner, S.T. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, Kapnistos et al. J. Rheol Unique damping functions for each comb Suggests architecture dependent response Damping Function for Comb Architecture Need to account for release of constraints due to branch relaxation After branches relax, backbone resembles “linear” chain deformed at lower strain due to dynamic dilution Tube length changes due to constraint release, scales as with and Uncertainty bars indicate change in dilution parameter from to Comb backbone is actually retracting as a linear chain Recover the DE theory for all of the combs considered in this study with the scaling Nonlinear Steady Shear Linear and Star architectures require new relaxation mechanism Convective Constraint Release (CCR) in non-stretching flows Need to account for release of constraints due to flow Use Phase Modulated Flow Birefringence technique to measure birefringence and orientation angle Study polybutadiene exact comb in squalene at 20% Model Asymptotic approach to including CCR (Tezel et al. Macromolecules 2005, 38, ) Use prefactors for linear chain Relate optical measurements to mechanical stresses via stress –optical rule Capture the qualitative behavior of the comb polymer with model incorporating CCR Suggests that the CCR mechanism is active for the comb architecture