Essentials of Viscoelasticity

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.

Glossary

Variable

Definition (Comments)

A

Area

a _T

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

J̃

Shear compliance (J̃ = 1/G̃)

J′

Elastic compliance

J′′

Viscous compliance

G̃

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

δ _L

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

{Δf̃ _n }

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

$\widetilde{\upeta}$

Viscosity ($\widetilde{\upeta}$ = G̃/(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