Skip to main content
SpringerLink
Log in

Nonlinear Oscillatory Shear Mechanical Responses

  • Chapter
  • First Online:
Nonlinear Dielectric Spectroscopy

Part of the book series: Advances in Dielectrics ((ADVDIELECT))

Abstract

Mechanical dynamic oscillatory shear test is generally used to characterize and investigate mechanical properties of complex fluids or soft matters. Especially, small amplitude oscillatory shear (SAOS) tests are the canonical method for probing the linear viscoelastic properties of complex fluids because of the firm theoretical background and the ease of implementing suitable test protocols. Material functions of SAOS tests are analogous with dielectric functions from dielectric spectroscopy. However, recently nonlinear responses under large amplitude oscillatory shear (LAOS) flows are also under the spotlight due to usefulness to characterize complex fluids. In this chapter, LAOS tests are reviewed. The key to successful LAOS test is the analysis and fundamental understanding of the nonlinear mechanical responses. To analyze nonlinear responses, there are several analyzing methods and various nonlinear material functions suggested by several researchers. Among the several methods available, FT (Fourier transform)-rheology is intensively reviewed. Finally, several applications to investigate complex fluids (polymer melt and solution, polymer composite and blend, emulsion and block copolymer, and so on) are introduced.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R.G. Larson, The structure and rheology of complex fluids (Oxford University Press, New York, 1999)

    Google Scholar 

  2. F.A. Morrison, Understanding Rheology (Oxford University Press, New York, 2001)

    Google Scholar 

  3. K. Hyun, M. Wilhelm, C.O. Klein, K.S. Cho, J.G. Nam, K.H. Ahn, S.J. Lee, R.H. Ewoldt, G.H. McKinley, A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS). Prog. Polym. Sci. 36, 1697–1753 (2011)

    Article  CAS  Google Scholar 

  4. J.D. Ferry, Viscoelastic Properties of Polymers (Wiley, NY, 1980)

    Google Scholar 

  5. R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of polymeric Liquids, vol. 1 (Wiley, NY, 1987)

    Google Scholar 

  6. N.W. Tschoegl, The phenomenological theory of linear viscoelastic behavior: an introduction (Springer-Verlag, NY, 1989)

    Book  Google Scholar 

  7. J.M. Dealy, K.F. Wissbrun, Melt rheology and its role in plastics processing: theory and applications (VNR, NY, 1990)

    Google Scholar 

  8. F. Kremer, A. Schönhals, Broadband Dielectric Spectroscopy (Springer, Berlin, 2003)

    Book  Google Scholar 

  9. Dealy J.M., Larson R.G. Structure and rheology of molten polymers (2006)

    Google Scholar 

  10. M. Wilhelm, Fourier-transform rheology. Macromol. Mater. Eng. 287, 83–105 (2002)

    Article  CAS  Google Scholar 

  11. A.J. Giacomin, J.M. Dealy, Large-amplitude oscillatory shear, in Techniques in Rheological Measurements, Chapter 4, ed. by A.A. Collyer (Chapman and Hall, London, 1993)

    Google Scholar 

  12. H.M. Wyss, K. Miyazaki, J. Mattsson, Z. Hu, D.R. Reichmann, D.A. Weitz, Strain-Rate Frequency Superposition: A Rheological Probe of Structural Relaxation in Soft Materials. Phys. Rev. Lett. 98, 238303 (2007)

    Article  CAS  PubMed  Google Scholar 

  13. Y.H. Wen, J.L. Schaefer, L.A. Archer, Dynamics and Rheology of Soft Colloidal Glasses. ACS Macro Lett. 4(1), 119–123 (2015)

    Article  CAS  Google Scholar 

  14. K. Hyun, S.H. Kim, K.H. Ahn, S.J. Lee, Large amplitude oscillatory shear as a way to classify the complex. J. Non-newtonian Fluid Mech. 107, 51–65 (2002)

    Article  CAS  Google Scholar 

  15. M. Sugimoto, Y. Suzuki, K. Hyun, K.H. Ahn, T. Ushioda, A. Nishioka, T. Taniguchi, K. Koyama, Melt rheology of long-chain-branched polypropylenes. Rheol. Acta 46, 33–44 (2006)

    Article  Google Scholar 

  16. K. Hyun, J.G. Nam, M. Wilhelm, K.H. Ahn, S.J. Lee, Nonlinear response of complex fluids under LAOS (large amplitude oscillatory shear) flow. Korea-Australia Rheology J 15, 97–105 (2003)

    Google Scholar 

  17. O.C. Klein, H.W. Spiess, A. Calin, C. Balan, M. Wilhelm, Separation of the nonlinear oscillatory response into a superposition of linear, strain hardening, strain softening, and wall slip response. Macromolecules 40, 4250–4259 (2007)

    Article  CAS  Google Scholar 

  18. K.S. Cho, K. Hyun, K.H. Ahn, S.J. Lee, A geometrical interpretation of large amplitude oscillatory shear response. J. Rheol. 49, 747–758 (2005)

    Article  CAS  Google Scholar 

  19. R.H. Ewoldt, A.E. Hosoi, G.H. McKinley, New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J. Rheol. 52, 1427–1458 (2008)

    Article  CAS  Google Scholar 

  20. W. Yu, P. Wang, C. Zhou, General stress decomposition in nonlinear oscillatory shear flow. J. Rheol. 53, 215–238 (2009)

    Article  CAS  Google Scholar 

  21. K. Reinheimer, J. Kübel, M. Wilhelm, Optimizing the sensitivity of FT-Rheology to quantify and differentiate for the first time the nonlinear mechanical response of dispersed beer foams of light and dark beer. Z. Phys. Chem. 226, 547–567 (2012)

    Article  CAS  Google Scholar 

  22. S. Onogi, T. Masuda, T. Matsumoto, Nonlinear behavior of viscoelastic materials. I. Disperse systems of polystyrene solution and carbon black. Trans. Soc. Rheol. 14, 275–294 (1970)

    Article  CAS  Google Scholar 

  23. S.G. Hatzikiriakos, J.M. Dealy, Wall slip of molten high density polyethylene. I. Sliding plate rheometer studies. J. Rheol. 35, 497–523 (1991)

    Article  CAS  Google Scholar 

  24. S.G. Hatzikiriakos, J.M. Dealy, Role of slip and fracture in the oscillating flow of HDPE in a capillary. J. Rheol. 36, 845–884 (1992)

    Article  CAS  Google Scholar 

  25. M.D. Graham, Wall slip and the nonlinear dynamics of large amplitude oscillatory shear flows. J. Rheol. 39, 697–712 (1995)

    Article  CAS  Google Scholar 

  26. D.W. Adrian, A.J. Giacomin, The quasi-periodic nature of a polyurethane melt in oscillatory shear. J. Rheol. 36, 1227–1243 (1992)

    Article  CAS  Google Scholar 

  27. A.S. Yoshimura, R.K. Prud’homme, Wall slip effects on dynamic oscillatory measurements. J. Rheol. 32, 575–584 (1988)

    Article  CAS  Google Scholar 

  28. K. Atalık, R. Keunings, On the occurrence of even harmonics in the shear stress response of viscoelastic fluids in large amplitude oscillatory shear. J. Non-newtonian Fluid. Mech. 122, 107–116 (2004)

    Article  CAS  Google Scholar 

  29. M. Wilhelm, D. Maring, H.W. Spiess, Fourier-transform rheology. Rheol. Acta. 37, 399–405 (1998)

    Article  CAS  Google Scholar 

  30. J.A. Yosick, A.J. Giacomin, W.E. Stewart, F. Ding, Fluid inertia in large amplitude oscillatory shear. Rheol. Acta 37, 365–373 (1998)

    Article  CAS  Google Scholar 

  31. R. Mas, A. Magnin, Experimental validation of steady shear and dynamic viscosity relation for yield stress fluids. Rheol. Acta 36, 49–55 (1997)

    Article  CAS  Google Scholar 

  32. J.L. Leblanc, Investigating the nonlinear viscoelastic behavior of rubber materials through Fourier transform rheometry. J. Appl. Polym. Sci. 95, 90–106 (2005)

    Article  CAS  Google Scholar 

  33. V. Hirschberg, M. Wilhelm, D. Rodrigue, Fatigue Behavior of Polystyrene (PS) analyzed from the Fourier Transform (FT) of its Stress Response: First evidence of I2/1(N) and I3/1(N) as new fingerprints. Polym. Test. 60, 343–350 (2017)

    Article  CAS  Google Scholar 

  34. K. Hyun, E.S. Baik, K.H. Ahn, S.J. Lee, M. Sugimoto, K. Koyama, Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts. J. Rheol. 51, 1319–1342 (2007)

    Article  CAS  Google Scholar 

  35. K. Hyun, M. Wilhelm, Establishing a New Mechanical Nonlinear coefficient Q from FT-Rheology: first investigation on entangled linear and comb polymer model systems. Macromolecules 42, 411–422 (2009)

    Article  CAS  Google Scholar 

  36. D.M. Holye, D. Auhl, O.G. Harlen, V.C. Barroso, M. Wilhelm, T.C.B. McLeish, Large amplitude oscillatory shear and Fourier transform rheology analysis of branched polymer melts. J. Rheol. 58, 969–997 (2014)

    Article  CAS  Google Scholar 

  37. A.K. Gurnon, N.J. Wagner, Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameter: giesekus model of banding and nonbanding wormlike micelles. J. Rheol. 56, 333–351 (2012)

    Article  CAS  Google Scholar 

  38. R.B. Bird, A.J. Giacomin, A.M. Schmalzer, C. Aumnate, Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: shear stress response. J. Chem. Phys. 140, 074904 (2014)

    Article  CAS  PubMed  Google Scholar 

  39. D.S. Pearson, W.E. Rochefort, Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields. J. Polym. Sci. Polym. Phys. Ed. 20, 83–98 (1982)

    Article  CAS  Google Scholar 

  40. M.H. Wagner, V.H. Rolón-Garrido, K. Hyun, M. Wilhelm, Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers. J. Rheol. 55, 495–516 (2011)

    Article  CAS  Google Scholar 

  41. M. Abbasi, N.G. Ebrahimi, M. Wilhelm, Investigation of the rheological behavior of industrial tubular and autoclave LDPEs under SAOS, LAOS, and transient shear, and elongational flows compared with predictions from the MSF theory. J. Rheol. 57, 1693–1714 (2013)

    Article  CAS  Google Scholar 

  42. A.J. Giacomin, R.B. Bird, L.M. Johnson, A.W. Mix, Large-amplitude oscillatory shear flow from the corotational Maxwell model. J. Non-Newt. Fluid Mech. 166, 1081–1099 (2011)

    Article  CAS  Google Scholar 

  43. D. Merger, M. Abbasi, J. Merger, A.J. Giacomin, Ch. Saengow, M. Wilhelm, Simple scalar model for large amplitude oscillatory shear. Appl. Rheol. 26, 53809 (2016)

    Google Scholar 

  44. M.A. Cziep, M. Abbasi, M. Heck, L. Arens, M. Wilhelm, Effect of molecular weight, polydispersity and monomer of linear homopolymer melts on the intrinsic mechanical nonlinearity 3Q0(w) in MAOS. Macromolecules 49, 3566–3579 (2016)

    Article  CAS  Google Scholar 

  45. H.Y. Song, S.J. Park, K. Hyun, Characterization of Dilution Effect of Semi-dilute Polymer Solution on Intrinsic Nonlinearity Q0 via FT-rheology. Macromolecules 50, 6238–6254 (2017)

    Article  CAS  Google Scholar 

  46. J.L. Leblanc, Large amplitude oscillatory shear experiments to investigate the nonlinear viscoelastic properties of highly loaded carbon black rubber compounds without curatives. J. Appl. Poly. Sci. 109, 1271–1293 (2008)

    Article  CAS  Google Scholar 

  47. J.L. Leblanc, Non-linear viscoelastic characterization of natural rubber gum through large amplitude harmonic experiments. J. Rubber. Res. 10, 63–88 (2007)

    CAS  Google Scholar 

  48. G. Fleury, G. Schlatter, R. Muller, Nonlinear rheology for long chain branching characterization, comparison of two methodologies: fourier Transform rheology and relaxation. Rheol. Acta 44, 174–187 (2004)

    Article  CAS  Google Scholar 

  49. G. Schlatter, G. Fleury, R. Muller, Fourier transform rheology of branched polyethylene: experiments and models for assessing the macromolecular architecture. Macromolecules 38, 6492–6503 (2005)

    Article  CAS  Google Scholar 

  50. I. Vittorias, M. Parkinson, K. Klimke, B. Debbaut, M. Wilhelm, Detection and quantification of industrial polyethylene branching topologies via Fourier-transform rheology. NMR and simulation using the Pom-pom model Rheol. Acta 46, 321–340 (2007)

    CAS  Google Scholar 

  51. T. Neidhöfer, S. Sioula, N. Hadjichristidis, M. Wilhelm, Distinguishing linear from star-branched polystyrene solutions with Fourier-Transform rheology. Macromol. Rapid Commun. 25, 1921–1926 (2004)

    Article  CAS  Google Scholar 

  52. M. Kempf, D. Ahirwal, M. Cziep, M. Wilhelm, Synthesis and linear and nonlinear melt rheology of well-defined comb architectures of PS and PpMS with a low and controlled degree of long-chain branching. Macromolecules 46, 4978–4994 (2013)

    Article  CAS  Google Scholar 

  53. H.T. Lim, K.H. Ahn, J.S. Hong, K. Hyun, Nonlinear viscoelasticity of polymer nanocomposites under large amplitude oscillatory shear flow. J. Rheol. 57, 767–789 (2013)

    Article  CAS  Google Scholar 

  54. L. Schwab, N. Hojdis, J. Lacayo-Pineda, M. Wilhelm, Fourier-Transform rheology of unvulcanized, carbon black filled styrene butadiene rubber. Macromol. Mat. Eng. 301, 457–468 (2016)

    Article  CAS  Google Scholar 

  55. W. Yu, M. Bousmina, C. Zhou, Note on morphology determination in emulsions via rheology. J. Non-newtonian Fluid. Mech. 133, 57–62 (2006)

    Article  CAS  Google Scholar 

  56. C. Carotenuto, M. Gross, P.L. Maffetone, Fourier transform rheology of dilute immiscible polymer blends: a novel procedure to probe blend morphology. Macromolecules 41, 4492–4500 (2008)

    Article  CAS  Google Scholar 

  57. K. Reinheimer, M. Grosso, F. Hetzel, J. Kübel, M. Wilhelm, Fourier Transform Rheology as a universal non-linear mechanical characterization of droplet size and interfacial tension of dilute monodisperse emulsions. J. Colloid Interface Sci. 360, 818–825 (2011)

    Article  CAS  PubMed  Google Scholar 

  58. K. Reinheimer, M. Grosso, F. Hetzel, J. Kübel, M. Wilhelm, Fourier Transform Rheology as an innovative morphological characterization technique for the emulsion volume average radius and its distribution. J. Colloid Interface Sci. 380, 201–212 (2012)

    Article  CAS  PubMed  Google Scholar 

  59. R. Salehiyan, Y. Yoo, W.J. Choi, K. Hyun, Characterization of morphologies of compatibilized polypropylene/polystyrene blends with nanoparticles via nonlinear rheological properties from FT-rheology. Macromolecules 47, 4066–4076 (2014)

    Article  CAS  Google Scholar 

  60. R. Salehiyan, H.Y. Song, W.J. Choi, K. Hyun, Characterization of effects of silica nanoparticles on (80/20) PP/PS blends via nonlinear rheological properties from fourier transform rheology. Macromolecules 48, 4669–4679 (2015)

    Article  CAS  Google Scholar 

  61. R. Salehiyan, H.Y. Song, M. Kim, W.J. Choi, K. Hyun, Morphological evaluation of pp/ps blends filled with different types of clays by nonlinear rheological analysis. Macromolecules 49, 3148–3160 (2016)

    Article  CAS  Google Scholar 

  62. H.G. Ock, K.H. Ahn, S.J. Lee, K. Hyun, Characterization of compatibilizing effect of organoclay in poly(lactic acid) and natural rubber blends by FT-rheology. Macromolecules 49, 2832–2842 (2016)

    Article  CAS  Google Scholar 

  63. T. Meins, N. Dingenouts, J. Kübel, M. Wilhelm, In-situ Rheo-Dielectric, ex-situ 2D-SAXS and FT-Rheology investigations of the shear induced alignment of Poly(styrene-b-1,4-isoprene) diblock copolymer melts. Macromolecules 45, 7206–7219 (2012)

    Article  CAS  Google Scholar 

  64. C. Oelschlaeger, J.S. Gutmann, M. Wolkenauer, H.W. Spiess, K. Knoll, M. Wilhelm, Kinetics of shear microphase orientation and reorientation in lamellar diblock and triblock copolymer melts as detected via FT-Rheology and 2D-SAXS. Macromol. Chem. Phys. 208, 1719–1729 (2007)

    Article  CAS  Google Scholar 

  65. S.H. Lee, H.Y. Song, K. Hyun, Lee JH. Nonlinearity from FT-rheology for liquid crystal 8CB under large amplitude oscillatory shear (LAOS) flow. J. Rheol. 59, 1–19 (2015)

    Article  CAS  Google Scholar 

  66. B. Struth, K. Hyun, E. Kats, T. Meins, M. Walther, M. Wilhelm, G. Grübel, Observation of New States of Liquid Crystal 8CB under Nonlinear Shear Conditions as Observed via a Novel and Unique Rheology/Small-Angle X-ray Scattering Combination. Langmuir 27, 2880–2887 (2011)

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

The KH acknowledge the financial support of the Alexander von Humboldt Foundation. The authors thank Valerian Hirschberg, Miriam Cziep, and Hyeong Yong Song for supplying figures and Carlo Botha for English proofreading.

Notes

Substantial parts (especially Sect. 3 and 4) of this chapter are taken from a rheological review [3] where rheological nonlinearities are explained in more detail but might not be read by scientists with a background in dielectric spectroscopy. Consequently, this chapter will be very helpful for the reader with a dielectric background to envision the similar concepts of both methodologies.

Author information

Authors and Affiliations

  1. School of Chemical and Biomolecular Engineering, Pusan National University, Busan, 46241, South Korea

    Kyu Hyun

  2. Institute for Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Manfred Wilhelm

Authors
  1. Kyu Hyun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manfred Wilhelm
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manfred Wilhelm .

Editor information

Editors and Affiliations

  1. School of Molecular Sciences, Arizona State University, Tempe, Arizona, USA

    Ranko Richert

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hyun, K., Wilhelm, M. (2018). Nonlinear Oscillatory Shear Mechanical Responses. In: Richert, R. (eds) Nonlinear Dielectric Spectroscopy. Advances in Dielectrics. Springer, Cham. https://doi.org/10.1007/978-3-319-77574-6_11

Download citation

Publish with us

Policies and ethics

Search

Navigation