Korea-Australia Rheology Journal

, Volume 30, Issue 1, pp 1–10 | Cite as

First-harmonic nonlinearities can predict unseen third-harmonics in medium-amplitude oscillatory shear (MAOS)

  • Olivia Carey-De La Torre
  • Randy H. EwoldtEmail author


We use first-harmonic MAOS nonlinearities from G1′ and G1″ to test a predictive structure-rheology model for a transient polymer network. Using experiments with PVA-Borax (polyvinyl alcohol cross-linked by sodium tetraborate (borax)) at 11 different compositions, the model is calibrated to first-harmonic MAOS data on a torque-controlled rheometer at a fixed frequency, and used to predict third-harmonic MAOS on a displacement controlled rheometer at a different frequency three times larger. The prediction matches experiments for decomposed MAOS measures [e3] and [v3] with median disagreement of 13% and 25%, respectively, across all 11 compositions tested. This supports the validity of this model, and demonstrates the value of using all four MAOS signatures to understand and test structure-rheology relations for complex fluids.


large-amplitude oscillatory shear LAOS MAOS supramolecular polymer network constitutive model testing prediction experimental methods parameter calibration 


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  1. Bharadwaj, N.A. and R.H. Ewoldt, 2015, Constitutive model fingerprints in medium-amplitude oscillatory shear, J. Rheol. 59, 557–592.CrossRefGoogle Scholar
  2. Bharadwaj, N.A., K.S. Schweizer, and R.H. Ewoldt, 2017, A strain stiffening theory for transient polymer networks under asymptotically nonlinear oscillatory shear, J. Rheol. 61, 643–665.CrossRefGoogle Scholar
  3. Chen, C.Y. and T.-L. Yu, 1997, Dynamic light scattering of poly (vinyl alcohol)-borax aqueous solution near overlap concentration, Polymer 38, 2019–2025.CrossRefGoogle Scholar
  4. Davis, W.M. and C.W. Macosko, 1978, Nonlinear dynamic mechanical moduli for polycarbonate and PMMA, J. Rheol. 22, 53–71.CrossRefGoogle Scholar
  5. Ewoldt, R.H., 2013, Defining nonlinear rheological material functions for oscillatory shear J. Rheol. 57, 177–195.CrossRefGoogle Scholar
  6. Ewoldt, R.H., A. Hosoi, and G.H. McKinley, 2008, New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear, J. Rheol. 52, 1427–1458.CrossRefGoogle Scholar
  7. Ewoldt, R.H. and N.A. Bharadwaj, 2013, Low-dimensional intrinsic material functions for nonlinear viscoelasticity, Rheol. Acta 52, 201–219.CrossRefGoogle Scholar
  8. Ewoldt, R.H., M.T. Johnston, and L.M. Caretta, 2015, Experimental challenges of shear rheology: How to avoid bad data, In: Spagnolie, S.E. eds., Complex Fluids in Biological Systems, Springer, New York, 207–241.Google Scholar
  9. Gurnon, A.K. and N.J. Wagner, 2012, Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles. J. Rheol. 56, 333–351.CrossRefGoogle Scholar
  10. Huang, G., H. Zhang, Y. Liu, H. Chang, H. Zhang, H. Song, D. Xu, and T. Shi, 2017, Strain hardening behavior of poly (vinyl alcohol)/borate hydrogels, Macromolecules 50, 2124–2135.CrossRefGoogle Scholar
  11. Hyun, K., E.S. Baik, K.H. Ahn, S.J. Lee, M. Sugimoto, and K. Koyama, 2007, Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts, J. Rheol. 51, 1319–1342.CrossRefGoogle Scholar
  12. Hyun, K. and M. Wilhelm, 2009, Establishing a new mechanical nonlinear coefficient Q from FT-rheology: First investigation of entangled linear and comb polymer model systems, Macromolecules 2, 411–422.CrossRefGoogle Scholar
  13. Hyun, K., M. Wilhelm, C.O. Klein, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, and G.H. McKinley, 2011, A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS), Prog. Polym. Sci. 36, 1697–1753.CrossRefGoogle Scholar
  14. Inoue, T. and K. Osaki, 1993, Rheological properties of poly (vinyl alcohol)/sodium borate aqueous solutions, Rheol. Acta 32, 550–555.CrossRefGoogle Scholar
  15. Keita, G., A. Ricard, R. Audebert, E. Pezron, and L. Leibler, 1995, The poly (vinyl alcohol)-borate system: Inuence of polyelectrolyte effects on phase diagrams, Polymer 36, 49–54.CrossRefGoogle Scholar
  16. Kirkwood, J.G. and R.J. Plock, 1956, Non-Newtonian viscoelastic properties of rod-like macromolecules in solution, J. Chem. Phys. 24, 665–669.CrossRefGoogle Scholar
  17. Koike, A., N. Nemoto, T. Inoue, and K. Osaki, 1995, Dynamic light scattering and dynamic viscoelasticity of poly (vinyl alcohol) in aqueous borax solutions. 1. Concentration effect, Macromolecules 28, 2339–2344.CrossRefGoogle Scholar
  18. Kurokawa, H., M. Shibayama, T. Ishimaru, S. Nomura, and W.-L. Wu, 1992, Phase behaviour and sol-gel transition of poly (vinyl alcohol)-borate complex in aqueous solution, Polymer 33, 2182–2188.CrossRefGoogle Scholar
  19. Lin, H.-L., Y.-F. Liu, T.L. Yu, W.-H. Liu, and S.-P. Rwei, 2005, Light scattering and viscoelasticity study of poly (vinyl alcohol)-borax aqueous solutions and gels, Polymer 46, 5541–5549.CrossRefGoogle Scholar
  20. Macosko, C.W., 1994, Rheology: Principles, Measurements, and Applications, Wiley-VCH, New York.Google Scholar
  21. Merger, D. and M. Wilhelm, 2014, Intrinsic nonlinearity from LAOStrain-experiments on various strain-and stress-controlled rheometers: A quantitative comparison, Rheol. Acta 53, 621–634.CrossRefGoogle Scholar
  22. Nemoto, N., A. Koike, and K. Osaki, 1996, Dynamic light scattering and dynamic viscoelasticity of poly (vinyl alcohol) in aqueous borax solutions. 2. polymer concentration and molecular weight effects, Macromolecules 29, 1445–1451.CrossRefGoogle Scholar
  23. Onogi, S., T. Masuda, and T. Matsumoto, 1970, Non-linear behavior of viscoelastic materials. I. Disperse systems of polystyrene solution and carbon black, J. Rheol. 14, 275–294.Google Scholar
  24. Paul, E., 1969, Non-Newtonian viscoelastic properties of rodlike molecules in solution: Comment on a paper by Kirkwood and Plock, J. Chem. Phys. 51, 1271–1272.CrossRefGoogle Scholar
  25. Rogers, S.A., 2012, A sequence of physical processes determined and quantified in LAOS: An instantaneous local 2D/3D approach, J. Rheol. 56, 1129–1151.CrossRefGoogle Scholar
  26. Rogers, S.A., 2017, In search of physical meaning: Defining transient parameters for nonlinear viscoelasticity, Rheol. Acta 56, 501–525.CrossRefGoogle Scholar
  27. Saengow, C., A.J. Giacomin, and C. Kolitawong, 2017, Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress, Phys. Fluids 29, 043101.CrossRefGoogle Scholar
  28. Wagner, M.H., V.H. Rolón-Garrido, K. Hyun, and M. Wilhelm, 2011, Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers, J. Rheol. 55, 495–516.CrossRefGoogle Scholar
  29. Wang, S.-Q., S. Ravindranath, and P.E. Boukany, 2011, Homogeneous shear, wall slip, and shear banding of entangled polymeric liquids in simple-shear rheometry: A roadmap of nonlinear rheology, Macromolecules 44, 183–190.Google Scholar
  30. Wilhelm, M., 2002, Fourier-transform rheology, Macromol. Mater. Eng. 287, 83–105.CrossRefGoogle Scholar

Copyright information

© Korean Society of Rheology (KSR) and the Australian Society of Rheology (ASR) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of Mechanical Science and Engineering and Frederick Seitz Materials Research LaboratoryUniversity of Illinois at Urbana ChampaignUrbanaUSA

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