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Numerical simulation results of the nonlinear coefficient *Q* from FT-Rheology using a single mode pom-pom model

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10.1122/1.4754444

### Abstract

In previous experimental observations, Hyun and Wilhelm [Macromolecules **42**, 411–422 (2009)] proposed a nonlinear coefficient *Q* (*≡ I* _{3/1}/*γ* _{0} ^{2}) that was determined from Fourier transform rheology experiments under dynamic oscillatory shear flow. Additionally an intrinsic *zero-strain nonlinearity*, *Q* _{0} ( ), was defined. It was found that this nonlinear coefficient *Q*(*ω,γ* _{0}), also given as *Q* _{0}(*ω*), is a very promising parameter to quantify nonlinear mechanical properties that are highly affected by polymer topology, e.g., branched structures. In this study, we systematically investigated the effect of polymer topology on the nonlinear parameters *Q*(*ω,γ* _{0}) and *Q* _{0}(*ω*) with a single mode differential pom-pom model. A number of parameters are affecting the topology of a pom-pom polymer, such as the number of dangling arms (*q*) and the dimensionless molecular weight of both the backbone (*s* _{b}) and the arms (*s* _{a}). In the here presented work, the linear viscoelastic properties *G*′(*ω*) and *G*″(*ω*) were compared with the nonlinear viscoelastic property *Q* _{0}(*ω*) for variety of molecular parameters. The intrinsic nonlinearity *Q* _{0}(*ω*) displayed two distinct relaxation processes for pom-pom architectures even though *G*′(*ω*) and *G*″(*ω*) could not distinguish two relaxation processes. Furthermore, the behavior of *Q*(*γ* _{0}) as a function of strain amplitude was also investigated in detail. From the results of these numerical simulations, it was concluded that polymer topology had a stronger influence on the nonlinear viscoelastic properties *Q* and *Q* _{0} than on the linear viscoelastic properties.

© 2013 The Society of Rheology

Received 11 February 2011
Revised 05 September 2012
Published online 03 October 2012

Acknowledgments: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No. 2010-0024466). The authors also appreciate Dr. Jennifer Kübel for providing suggestions on improving the English in this publication. The authors thank Dr. David M. Hoyle at University of Durham for helpful discussion about LAOS behavior of pom-pom constitutive equation.

Article outline:

I. INTRODUCTION

II. THEORY

A. Definition of the nonlinear coefficient *Q* and *Q* _{0}

B. Single mode pom-pom model

C. Simulation details

D. Strain sweep test

III. RESULTS AND DISCUSSION

A. Zero-strain nonlinearity *Q* _{0}(ω)

B. *Q* _{0,max} as a function of branching parameters

C. *Q*(γ_{0}) under LAOS

D. Lissajous curve under LAOS

IV. CONCLUSIONS

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2012-10-03

2014-04-23

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