Reports: AC7
46399-AC7 Nonlinear Rheology of Branched Polymers
Progress Report-PRF(2009) During the course of this project, we have made major progress in understanding the rheological behavior of branched and entangled polymeric liquids. Our focus has been on the behavior of polymers that have the so-called comb architecture, namely a linear chain with a number of equal length branches that are randomly (though relatively uniformly) placed along the backbone. The transition from simpler chain architectures, such as the linear chain or the star, that have been the focus of most academic research is extremely important since many of the most important polymers for industrial application are branched.
Previous experimental studies from our group have considered systems with long branches (i.e. highly entangled) in linear viscoelastic and step shear strain (nonlinear) flows1, and we have developed a fundamental model for the linear viscoelastic behavior of comb polymers2. This theory agreed quantitatively with linear viscoelastic data for these long branch combs, and suggests that comb polymers can be treated as linear chains for longer time scales and/or low frequency linear flows. Step strain experiments, on the other hand, showed a systematic departure from the expected (Doi-Edwards) predictions for a linear chain, which we speculated was due to the small degree of entanglement that is left after the branches relax and account is taken of dynamic dilution.
During the past couple of years, we have studied a new class of combs with short branches that remain highly entangled even after the short branches relax. The molecular weight of the branches ranges from approximately 0.6 of the entanglement molecular weight (Me) to approximately 2Me. These studies3 show (1) that these short nearly unentangled branches have an unexpectedly large effect on the dynamics of the comb; (2) that the deviation from theory in the step-strain experiment is not due to weak entanglement levels of the backbone, but is a systematic consequence of the multibranch chain architecture. In the linear viscoelastic regime, the theory for highly entangled branches is surprisingly found to give quantitative agreement with experiments for the case in which M/Me=2. On the other hand, the comb with branches below the entanglement molecular weight, M/Me≈0.6, still did not show agreement with the linear chain LV theory4, but rather still showed sign of hierarchical relaxation typical of entangled combs. Good agreement with the comb theory for this case as well as two intermediate cases where M/Me≈1 was achieved, but only by assuming that the short branches are more entangled than suggested by the ratio of M/Me. This is consistent with an idea originally due to Larson and coworkers5 based upon their study of asymmetric star polymers with on very short arm. As far as the nonlinear step-strain data is concerned, we have developed a theoretical explanation that explains why there is a systematic deviation between the damping function for the linear backbone of a comb polymer and the predicted (Doi-Edwards) result for a linear chain. This is not a result of dynamic dilution leading to a relatively un-entangled backbone as surmised in our earlier study, but rather has to do with the fact that the tube for the backbone dilates and the backbone retracts somewhat during branch relaxation. The resulting scaling theory now reduces all data, including that in our earlier study1, to a universal result that agrees with the Doi-Edward prediction. This provides a basis for predicting the response of even more complex chain architectures to a step-strain type of experiment.
Finally, in a third part to our study (3) we have used rheo-optical methods to study the behavior of the comb polymers in steady shearing flow. In this case, it is expected (and we corroborate) that convective constraint release (CCR) ideas play a dominant role in the rheology of comb polymers for steady shear flows. Further, we use a comparison between experimental data and a simple theoretical model for CCR for steady shear flow that the CCR mechanism is basically independent of the chain architecture, taking the same form for linear, star6 and comb polymers. Additional experiments were carried out for transient/startup flows. We are currently analyzing these experiments.
References:
1. Nonlinear rheology of model comb polymers, Kapnistos, M., Kirkwood, K.M., Ramirez, J., Vlassopoulos, D., and Leal, L.G. Journal of Rheology 53, 1133-1153 (2009).
2. Linear rheology of architecturally complex macromolecules: comb polymers with linear backbones, Kapnistos, M, Vlassopoulos, D, Roovers, J and Leal, L.G. Macromolecules, 38, 7852-7862 (2005)
3. Stress relaxation of comb polymers with short branches, Kirkwood, K.M., Leal, L.G., and Vlassopoulos, D., Macromolecules (accepted for publication) (2009)
4. Reptation and contour-length fluctuations in melts of linear polymers, Milner ST, McLeish TCB, Physical Review Letters, 81, 725-728 (1998)
5. Direct molecular dynamics simulation of branch point motion in asymmetric star polymer melt, Zhou, Q, and Larson, RG, Macromolecules, 40, 3443-3449 (2007)
6. Rheo-optical evidence of CCR in an entangled four-arm star, Tezel AK, Leal LG, and McLeish TCB, Macromolecules, 38, 1451-1455 (2005)
