Stress Relaxation of Comb Polymers

1. Stress Relaxation of Comb Polymers Keith M. Kirkwooda , Dimitris Vlassopoulosb,c , and L. Gary Leala aDepartment of Chemical Engineering, University of California at Santa Barbara Santa Barbara, California 93106 bInstitute of Electronic Structure & Laser, FORTH, Heraklion 71110, Crete, Greece cDepartment of Materials Science & Technology, University of Crete Heraklion 71003, Crete, Greece Linear Viscoelastic Behavior of Short Arm Combs Introduction • 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 • Tube based theoretical model for comb architecture by Kapnistos et al. (Macromolecules 2005, 38, 7852-7862) • Hierarchical relaxation (HR): backboneimmobile 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 chainwith 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 bothbranch and backbone relaxation • Methods such as modifying only change backbone relaxation Materials polyisoprene short arm combs Synthesized by P. Driva and N. Hadjichristidis (Univ. of Athens) via the macromonomerstrategy with high-vacuum anionic techniques entanglement Nonlinear Rheology: Stress Relaxation after Step Strain • Create stress relaxation mastercurves • Shift at long times to analyze damping function for comb backbone • 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 polybutadiene exact comb • No dependence on concentration for Synthesized by A. Nikopoulou and N. Hadjichristidis (Univ. of Athens) Nikopoulou et al. J. Polym. Sci., Part A: Polym. Chem.2009, 47, 2597-2607. Anionic synthesis with exact placement of branch points along backbone Unique damping functions for each comb Suggests architecture dependent response * Vega, D.A.; Milner, S.T. J. Polym. Sci., Part B: Polym. Phys.2007, 45, 3117-3136. Kapnistos et al. J. Rheol.2009 Conclusions Damping Function for Comb Architecture Nonlinear Steady Shear • 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 • 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 aswith and • Linear and Star architectures require new relaxation mechanismConvective 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. Macromolecules2005, 38, 1451-1455.) • 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 • 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 Uncertainty bars indicate change in dilution parameter from to