Results and Discussion - New Synthetic Routes to Polyoxometalate Containing Ionic Liquids - page 48

For the representation of stress and strain in a viscoelastic material the following
sinusoidal expressions can be used:

strain:

ߝൌߝ ଴ ሺ߱ݐሻ

(I)

stress:

ߪൌߪ ଴ ሺ߱ݐ൅ߜሻ

(II)

where ɘൌʹɎ with f being the frequency of strain oscillation, t is the time and Ɂ is the
phase lag between stress and strain.

At hand of the so called modulus G* the stiffness of a material can be described. It can
be divided into two parts, the storage modulus G' which describes the elastic response
(stored energy), and G”, the loss modulus which describes the viscous properties
(energy dissipated as heat). The shear storage and loss moduli are defined as follows:

ܩƲൌ ఙ బ
ఌ బ

storage modulus

ܿ݋ݏߜ

(III)

ܩƲƲൌ ఙ బ
ఌ బ

loss modulus

ݏ݅݊ߜ

(I )

The sinusoidal stress V is dissipated in the sum of both moduli:

ߪൌߝ ଴ ሺܩƲ ሺ ఠ ሻ ݏ݅݊߱ݐ൅ܩƲƲ ሺ ఠ ሻ ܿ݋ݏ߱ݐሻ

( )

The moduli can be measured as shown in Figure 24 (see next page). A viscoelastic
material is poured into a cup and a concentrical cylinder (called "bob") is lowered into
the material. The cup is oscillating in a sinus like movement and the force which the
material is transferring is measured with the concentric cylinder. The force will also be
sinus like with the same frequency as the cup, but displaced in comparison to the
movement. The displacement is measured as a phase angel G . A totally elastic material,
such as steel, has no displacement at all, and the phase angel G = 0°, while a ideal liquid
has maximal displacement and G = 90°. The onset deformation, the measured force and
displacement are used to describe the storage modulus and the loss modulus.
Viscoelastic measurements at different frequencies can be used to describe the