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 93106bInstitute of Electronic Structure & Laser, FORTH, Heraklion 71110, Crete, Greece

cDepartment 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

NonlinearUnderstanding 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 Behaviorof Short Arm Combs

Nonlinear Rheology: Stress Relaxation after Step Strain

Introduction

Conclusions

Materialspolyisoprene short arm combs

polybutadiene exact comb

Synthesized by P. Driva and N. Hadjichristidis (Univ. of Athens) via the macromonomerstrategy 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, 2597-2607.Anionic synthesis with exact placement of branch points along backbone

  Molecular Weightq

(# branches) 

Z (# entanglements)

Diluted Z

Code Comb Backbone Branch branch backbone backbone

PI132k 132 85 10.2 4.6 2.2 18.0 12.0PI159k 159 137 2.7 8.2 0.6 29.0 25.0PI211k 211 157 6.3 8.6 1.3 33.2 25.0PI472k 472 370 5.8 17.6 1.2 78.2 61.0

310

4730eM

  Molecular Weightq

(# branches) 

Z (# entanglements)

Diluted Z

Code Comb Backbone Branch branch backbone backbone

ac-3#2 187 152.8 11.4 3 6.2 82.6 67.51850eM

310

• 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

entanglement

PI132k

2.2branchZ PI159k

0.6 0.9branchZ

PI211k

1.3 1.65branchZ PI472k

1.2 1.62branchZ

2

1

1 12p

2branchZ

2p

• Create stress relaxation mastercurves

• Shift at long times to analyze damping function for comb backbone

• No dependence on concentration for 3bbZ

• 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

h

* Vega, D.A.; Milner, S.T. J. Polym. Sci., Part B: Polym. Phys. 2007, 45, 3117-3136. Kapnistos et al. J. Rheol. 2009

Unique damping functions for each combSuggests 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 aswith and

1/ 2BB

,2bb c bb endBB

bb branch

M x M

M q M

0L

0L

1 20BB L

0L

1

Uncertainty bars indicate change in dilution parameter from to

1 4 3

• 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,

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

1 1d R

'n

12 sin 22

n

C

1 cos 2

nN

C