Chemistry Reference
In-Depth Information
of loss modulus analysed in dynamic oscillatory shear. Viscoelastic
solutions also show extensional viscosity,
η
e
, behaviour deviating from
Trouton's law:
η
e
=
3
η
(4.9)
where
is the shear viscosity.
In a dynamic oscillatory shear test, a sample is subjected to periodic
sinusoidal shear in the form of a shear stress or a shear strain. In a
shear stress controlled experiment, the shear strain is measured, and
vice versa. The frequency of oscillation is either kept constant or varied.
If the material response is in-phase with the deformation, the material
behaviour is fully elastic:
η
τ
=
G
γ
(4.10)
where
is the
shear strain. Purely viscous material behaviour manifests itself in a
material response out-of-phase with the deformation (corresponding to
a phase shift of π
τ
is the shear stress,
G
is the elastic modulus and
γ
2or90
◦
), and shear stress is proportional to the
time derivative of the shear strain. Viscoelastic solutions show a phase
shift,
/
2or90
◦
, and the elastic modulus will show
an in-phase component and an out-of-phase component corresponding
to the elastic and viscous contributions to the material behaviour. The
values of these two components are denoted as the storage modulus,
G
, and the loss modulus,
G
, respectively. It is customary to report
the tangent of the phase, tan
δ
, between 0 and π
/
, which is equal to the ratio
G
/
G
.In
order to assess
G
and
G
at a range of frequencies, it is important
to ensure that the material response is not additionally affected by the
deformation amplitude imposed. Therefore, so-called frequency tests
are carried out by applying a stress or strain amplitude chosen from the
linear viscoelastic domain which is evaluated in an 'amplitude sweep'
conducted at a constant frequency. The linear viscoelastic domain is
recognised as the region where
G
is independent of the deformation
amplitude. Hydrocolloid solutions may show a highly extended linear
viscoelastic domain such as up to 100% strain, whereas simple emulsion
formulations tend to show much smaller critical strains in the order
of 1%.
δ
4.3
HYDROCOLLOID GELATION AND GEL RHEOLOGY
Many random coil hydrocolloids possess the ability to form a physi-
cally cross-linked gel network, given appropriate solvent conditions or
