Abstract
A slight rearrangement of the classical Cox and Merz rule suggests that the shear stress value of steady shear flow, \(\tau (\mathop \gamma \limits^. )\), and complex modulus value of small amplitude oscillatory shear, G ∗ (ω) = (G′2 + G″2)1/2, are equivalent in many respects. Small changes of material structure, which express themselves most sensitively in the steady shear stress, τ, show equally pronounced in linear viscoelastic data when plotting these with G ∗ as one of the variables. An example is given to demonstrate this phenomenon: viscosity data that cover about three decades in frequency get stretched out over about nine decades in G ∗ while maintaining steep gradients in a transition region. This suggests a more effective way of exploiting the Cox–Merz rule when it is valid and exploring reasons for lack of validity when it is not. The τ −G ∗ equivalence could also further the understanding of the steady shear normal stress function as proposed by Laun.
References
Booij HC, Palmen JHM (1992) Linear viscoelastic properties of melts of miscible blends of poly (methylmethacrylate) with poly (ethylene oxide). In: Moldenaers P, Keunings R (Eds) Theoretical and applied rheology. Elsevier, Brussels, p 321
Cox WP, Merz EH (1958) Correlation of dynamic and steady-flow viscosities. J Polym Sci 28:619–622
Doraiswamy D, Mujumdar AN, Tsao I, Beris AN, Danforth SC, Metzner AB (1991) The Cox-Merz rule extended: a rheological model for concentrated suspensions and other materials with a yield stress. J Rheol 35:647–685
Ferry JD (1980) Viscoelastic properties of polymer. J. Wiley and Sons, New York
Laun HM (1986) Prediction of elastic strains of polymer melts in shear and elongation. J Rheol 30:459–501
Lin YG, Zhou R, Chien JCW, Winter HH (1988) Rheology of a twin liquid crystalline polymer. Macromolecules 21:2014–2018
Winter HH, Mours M (2006) The cyber infrastructure initiative for rheology. Rheol Acta 45:331–338
Winter HH (2007) Rheology cyberinfrastructure for integrated research and learning at ARC 07. Applied Rheol 17:302–304
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Winter, H.H. Three views of viscoelasticity for Cox–Merz materials. Rheol Acta 48, 241–243 (2009). https://doi.org/10.1007/s00397-008-0329-5
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DOI: https://doi.org/10.1007/s00397-008-0329-5