Rheologica Acta

, Volume 52, Issue 3, pp 201–219 | Cite as

Low-dimensional intrinsic material functions for nonlinear viscoelasticity

Original Contribution

Abstract

Rheological material functions are used to form our conceptual understanding of a material response. For a nonlinear rheological response, the possible deformation protocols and material measures span a high-dimensional space. Here, we use asymptotic expansions to outline low-dimensional measures for describing leading-order nonlinear responses in large amplitude oscillatory shear (LAOS). This amplitude-intrinsic regime is sometimes called medium amplitude oscillatory shear (MAOS). These intrinsic nonlinear material functions are only a function of oscillatory frequency, and not amplitude. Such measures have been suggested in the past, but here, we clarify what measures exist and give physically meaningful interpretations. Both shear strain control (LAOStrain) and shear stress control (LAOStress) protocols are considered, and nomenclature is introduced to encode the physical interpretations. We report the first experimental measurement of all four intrinsic shear nonlinearities of LAOStrain. For the polymeric hydrogel (polyvinyl alcohol - Borax) we observe typical integer power function asymptotics. The magnitudes and signs of the intrinsic nonlinear fingerprints are used to conceptually model the mechanical response and to infer molecular and microscale features of the material.

Keywords

Large amplitude oscillatory shear Nonlinear viscoelasticity Material functions Rheometer Transient polymer network Polyvinyl alcohol 

Notes

Acknowledgements

The authors are grateful to Prof. Jozef Kokini and Dr. Francesca Devito of the University of Illinois at Urbana-Champaign for use of the ARES-G2 rheometer.

References

  1. Abramowitz M, Stegun IA (1964) Handbook of mathematical functions with formulas, graphs and mathematical tables. Dover, New YorkGoogle Scholar
  2. Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids. Volume 1: Fluid mechanics, 2nd edn. Wiley, New YorkGoogle Scholar
  3. Cho KS, Ahn KH, Lee SJ (2005) A geometrical interpretation of large amplitude oscillatory shear response. J Rheol 49(3):747–758CrossRefGoogle Scholar
  4. Davis WM, Macosko CW (1978) Nonlinear dynamic mechanical moduli for polycarbonate and PMMA. J Rheol 22(1):53–71CrossRefGoogle Scholar
  5. Davis VA, Ericson LM, Parra-Vasquez ANG, Fan H, Wang Y, Prieto V, Longoria JA, Ramesh S, Saini R, Kittrell C, Billups WE, Adams WW, Hauge RH, Smalley RE, Pasquali M (2004) Phase behavior and rheology of SWNTs in superacids. Macromolecules 37(1):154–160CrossRefGoogle Scholar
  6. Dealy JM (1995) Official nomenclature for material functions describing the response of a viscoelastic fluid to various shearing and extensional deformations. J Rheol 39(1):253–265CrossRefGoogle Scholar
  7. Dealy JM, Wissbrun KF (1990) Melt Rheology and its role in plastics processing: theory and applications. Van Nostrand Reinhold, New YorkCrossRefGoogle Scholar
  8. Dimitriou CJ, Ewoldt RH, McKinley GH (2013) Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory stress (LAOStress). J Rheol 57(1):27–70CrossRefGoogle Scholar
  9. Einstein A (1906) Eine neue Bestimmung der Moleküldimensionen. Ann Phys 19: 289CrossRefGoogle Scholar
  10. Einstein A (1911) Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen. Ann Phys 34: 591CrossRefGoogle Scholar
  11. Ewoldt RH (2013) Defining nonlinear rheological material functions for oscillatory shear. J Rheol 57(1):177–195CrossRefGoogle Scholar
  12. Ewoldt RH, Hosoi AE, McKinley GH (2008) New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J Rheol 52(6):1427–1458CrossRefGoogle Scholar
  13. Ewoldt RH, Gurnon AK, López-Barrón C, McKinley GH, Swan J, Wagner NJ (2012) LAOS rheology day, Friday the 13th, Colburn Laboratory, University of Delaware. Rheol Bull 81(2):12–18Google Scholar
  14. Fan X, Bird RB (1984) A kinetic theory for polymer melts. VI. Calculation of additional material functions. J Non Newtonian Fluid Mech 15(3):341–373CrossRefGoogle Scholar
  15. Ferry JD (1980) Viscoelastic properties of polymers, 3rd edn. Wiley, New YorkGoogle Scholar
  16. Giacomin AJ, Bird RB, Johnson LM, Mix AW (2011) Large-amplitude oscillatory shear flow from the corotational Maxwell model, vol 166, pp 1081–1099Google Scholar
  17. Gurnon AK, Wagner NJ (2012) Large amplitude oscillatory shear (LAOS) measurements to obtain constitutive equation model parameters: Giesekus model of banding and nonbanding wormlike micelles. J Rheol 56(2):333–351CrossRefGoogle Scholar
  18. Hair DW, Amis EJ (1989) Intrinsic dynamic viscoelasticity of polystyrene in \(\theta \) and good solvents. Macromolecules 22(12):4528–4536CrossRefGoogle Scholar
  19. Hyun K, Wilhelm M (2009) Establishing a new mechanical nonlinear coefficient Q from FT-rheology: first investigation of entangled linear and comb polymer model systems. Macromolecules 42(1):411–422CrossRefGoogle Scholar
  20. Hyun K, Kim SH, Ahn KH, Lee SJ (2002) Large amplitude oscillatory shear as a way to classify the complex fluids. J Non-Newton Fluid Mech 107(1–3):51–65CrossRefGoogle Scholar
  21. Hyun K, Ahn KH, Lee SJ, Sugimoto M, Koyama K (2006) Degree of branching of polypropylene measured from Fourier-transform rheology. Rheol Acta 46(1):123–129CrossRefGoogle Scholar
  22. Hyun K, Baik ES, Ahn KH, Lee SJ, Sugimoto M, Koyama K (2007) Fourier-transform rheology under medium amplitude oscillatory shear for linear and branched polymer melts. J Rheol 51(6):1319CrossRefGoogle Scholar
  23. Hyun K, Wilhelm M, Klein CO, Cho KS, Nam JG, Ahn KH, Lee SJ, Ewoldt RH, McKinley GH (2011) A review of nonlinear oscillatory shear tests: analysis and application of large amplitude oscillatory shear (LAOS). Prog Polym Sci 36(12):1697–1753CrossRefGoogle Scholar
  24. Johnson RM, Schrag JL, Ferry JD (1970) Infinite-dilution viscoelastic properties of polystyrene in \(\theta \)-solvents and good solvents. Polymer Japanese 1(6):742–749CrossRefGoogle Scholar
  25. Keita G, Ricard A, Audebert R, Pezron E, Leibler L (1995) The poly(vinyl alcohol) borate system—influence of polyelectrolyte effects on phase-diagrams. Polymer 36(1):49–54CrossRefGoogle Scholar
  26. Kirkwood JG, Plock RJ (1956) Non-Newtonian viscoelastic properties of rod-like macromolecules in solution. J Chem Phys 24(4):665–669CrossRefGoogle Scholar
  27. Koike A, Nemoto N, Inoue T, Osaki K (1995) Dynamic light-scattering and dynamic viscoelasticity of poly(vinyl alcohol) in aqueous borax solutions. 1. Concentration effect. Macromolecules 28(7):2339–2344CrossRefGoogle Scholar
  28. Kurokawa H, Shibayama M, Ishimaru T, Nomura S, Wu WI (1992) Phase-behavior and sol–gel transition of poly(vinyl alcohol) borate complex in aqueous-solution. Polymer 33(10):2182–2188CrossRefGoogle Scholar
  29. Lin HL, Liu YF, Yu TL, Liu WH, Rwei SP (2005) Light scattering and viscoelasticity study of poly(vinyl alcohol)-borax aqueous solutions and gels. Polymer 46(15):5541–5549CrossRefGoogle Scholar
  30. Macosko CW (1994) Rheology: principles, measurements and applications. Wiley, New YorkGoogle Scholar
  31. Onogi S, Masuda T, Matsumoto T (1970) Non-linear behavior of viscoelastic materials. I. Disperse systems of polystyrene solution and carbon black. J Rheol 14(2):275–294CrossRefGoogle Scholar
  32. Osaki K (1973) Viscoelastic properties of dilute polymer solutions. Advan Polym Sci 12: 1–64CrossRefGoogle Scholar
  33. Osaki K, Mitsuda Y, Johnson RM, Schrag JL, Ferry JD (1972) Infinite-dilution viscoelastic properties. Macromolecules 5(1):17–19CrossRefGoogle Scholar
  34. Paul E (1969) Non-Newtonian viscoelastic properties of rodlike molecules in solution: comment on a paper by Kirkwood and Plock. J Chem Phys 51(3):1271–1272CrossRefGoogle Scholar
  35. Pearson DS, Rochefort WE (1982) Behavior of concentrated polystyrene solutions in large-amplitude oscillating shear fields. J Poly Sci: Poly Phys Edit 20(1):83–98CrossRefGoogle Scholar
  36. Pipkin AC (1972) Lectures on viscoelasticity theory. Springer, New YorkCrossRefGoogle Scholar
  37. Ravindranath S, Wang S-Q, Olechnowicz M, Chavan VS, Quirk RP (2010) How polymeric solvents control shear inhomogeneity in large deformations of entangled polymer mixtures. Rheol Acta 50(2):97–105CrossRefGoogle Scholar
  38. Reinheimer K, Grosso M, Hetzel F, Kübel J, Wilhelm M (2012) Fourier transform rheology as an innovative morphological characterization technique for the emulsion volume average radius and its distribution. J Colloid Interface Sci 380(1):201–212CrossRefGoogle Scholar
  39. Rogers SA (2012) A sequence of physical processes determined and quantified in, LAOS: an instantaneous local 2D/3D approach. J Rheol 56(5):1129CrossRefGoogle Scholar
  40. Rogers SA, Lettinga MP (2012) A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS):application to theoretical nonlinear models. J Rheol 56(1):1–25CrossRefGoogle Scholar
  41. Tuteja A, Mackay ME, Hawker CJ, Van Horn B (2005) Effect of ideal, organic nanoparticles on the flow properties of linear polymers: Non-Einstein-like behavior. Macromolecules 38(19):8000–8011CrossRefGoogle Scholar
  42. Vrentas JS, Venerus DC, Vrentas CM (1991) Finite-amplitude oscillations of viscoelastic fluids. J Non-Newtonian Fluid Mech 40(1):1–24CrossRefGoogle Scholar
  43. Wagner MH, Rolon-Garrido VH, Hyun K, Wilhelm M (2011) Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers. J Rheol 55(3):495–516CrossRefGoogle Scholar
  44. Wang S, Ravindranath S, Boukany PE (2011) Homogeneous shear, wall slip, and shear banding of entangled polymeric liquids in simple shear rheometry: a roadmap of nonlinear rheology. Macromolecules 44(2):183–190CrossRefGoogle Scholar
  45. Wilhelm M (2002) Fourier-transform rheology. Macromol Mater Eng 287(2):83–105CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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