Essentials of Viscoelasticity

Chapter
Part of the Soft and Biological Matter book series (SOBIMA)

Abstract

Viscoelastic dispersion is a rather essential element of the modeling process. The viscoelastic parameters of soft matter (such as shear modulus) depend on frequency because soft matter often relaxes on the time scale of the experiment. Mechanical relaxation can even be viewed as characteristic of soft condensed matter. The chapter discusses the basics of viscoelasticity and its relevance to QCM-based sensing.

Notes

Glossary

Variable

Definition (Comments)

A

Area

aT

Shift factor (to be used when producing a master curve, making use of time-temperature superposition)

E

Young’s modulus (E = G(1 + 2ν))

F

Tangential force

Shear compliance ( = 1/)

J

Elastic compliance

J′′

Viscous compliance

Shear modulus

G

Storage modulus

G′′

Loss modulus

K

Bulk modulus (an inverse compressibility)

M

Longitudinal modulus (M = K + 4G/3, governs the propagation of compressional waves, also called “plate modulus”)

ref

As an index: reference frequency or reference temperature

t

Time

β′, β′′

Power law exponents (see Eq. 10.4.1)

γ

Shear angle

δL

Loss angle (tan(δL) = G′′/G′ = J′′/J′, often called tan(δ) in rheology)

n}

As set of complex resonance frequencies acquired at the different overtone orders

\( \widetilde{\upeta} \)

Viscosity (\( \widetilde{\upeta} \) = /(iω))

η

“Viscosity” in “Voigt-based modeling” (equal to G′′/ω)

ν

Poisson ratio

μ

Shear modulus as used in “Voigt-based modeling” (equal to G′)

ω

Angular frequency

References

  1. 1.
    Shaw, M.T., MacKnight, W.J.: Introduction to Polymer Viscoelasticity. Wiley, New York (2005)Google Scholar
  2. 2.
    Larson, R.G.: The Structure and Rheology of Complex Fluids. Oxford University Press, Oxford (1998)Google Scholar
  3. 3.
    Persson, B.N.J.: Sliding Friction: Physical Principles and Applications. Springer, New York (2000)Google Scholar
  4. 4.
    Fang, N., Xi, D.J., Xu, J.Y., Ambati, M., Srituravanich, W., Sun, C., Zhang, X.: Ultrasonic metamaterials with negative modulus. Nat. Mater. 5(6), 452–456 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    Gradzielski, M., Bergmeier, M., Muller, M., Hoffmann, H.: Novel gel phase: a cubic phase of densely packed monodisperse, unilamellar vesicles. J. Phys. Chem. B 101(10), 1719–1722 (1997)CrossRefGoogle Scholar
  6. 6.
  7. 7.
    Kremer, F., Schönhals, A., Luck, W.: Broadband Dielectric Spectroscopy. Springer, New York (2002)Google Scholar
  8. 8.
    Kaatze, U., Hushcha, T.O., Eggers, F.: Ultrasonic broadband spectrometry of liquids: a research tool in pure and applied chemistry and chemical physics. J. Solution Chem. 29(4), 299–368 (2000)CrossRefGoogle Scholar
  9. 9.
    Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists: A Comprehensive Guide, 7th edn. Academic, Waltham (2012)Google Scholar
  10. 10.
    Mobley, J., Waters, K.R., Miller, J.G.: Causal determination of acoustic group velocity and frequency derivative of attenuation with finite-bandwidth Kramers-Kronig relations. Phys. Rev. E 72(1), 016604 (2005)Google Scholar
  11. 11.
    Marrucci, G.: Dynamics of entanglements: a nonlinear model consistent with the Cox-Merz rule. J. Nonnewton. Fluid Mech. 62(2–3), 279–289 (1996)CrossRefGoogle Scholar
  12. 12.
    Nandi, N., Bhattacharyya, K., Bagchi, B.: Dielectric relaxation and solvation dynamics of water in complex chemical and biological systems. Chem. Rev. 100(6), 2013–2045 (2000)CrossRefGoogle Scholar
  13. 13.
    Voinova, M.V., Rodahl, M., Jonson, M., Kasemo, B.: Viscoelastic acoustic response of layered polymer films at fluid-solid interfaces: continuum mechanics approach. Phys. Scr. 59(5), 391–396 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    Ferry, J.D.: Viscoelastic Properties of Polymers. Wiley, New York (1980)Google Scholar
  15. 15.
    Fritz, G., Pechhold, W., Willenbacher, N., Wagner, N.J.: Characterizing complex fluids with high frequency rheology using torsional resonators at multiple frequencies. J. Rheol. 47(2), 303–319 (2003)ADSCrossRefGoogle Scholar
  16. 16.
    Hillman, A.R., Efimov, I., Ryder, K.S.: Time-scale- and temperature-dependent mechanical properties of viscoelastic poly (3,4-ethylenedioxythlophene) films. J. Am. Chem. Soc. 127(47), 16611–16620 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Physical ChemistryClausthal University of TechnologyClausthal-ZellerfeldGermany

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