Essentials of Viscoelasticity

  • Diethelm Johannsmann
Part of the Soft and Biological Matter book series (SOBIMA)


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.


Shear Rate Shear Modulus Bulk Modulus Storage Modulus Loss Modulus 
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Definition (Comments)




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


Young’s modulus (E = G(1 + 2ν))


Tangential force

Shear compliance ( = 1/)


Elastic compliance


Viscous compliance

Shear modulus


Storage modulus


Loss modulus


Bulk modulus (an inverse compressibility)


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


As an index: reference frequency or reference temperature



β′, β′′

Power law exponents (see Eq. 10.4.1)


Shear angle


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


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

\( \widetilde{\upeta} \)

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


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


Poisson ratio


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


Angular frequency


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

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

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