
7.8.2
Viscoelasticity
Viscoelasticity refers to rheological behavior that is a combination of viscous (liq-
uid-like) and elastic (solid-like) behavior. Ideal elastic behavior is called Hookean,
where the stress is directly proportional to the strain. A Hookean solid deforms as
long as stress is applied. Once stress is removed, it fully recovers its original shape.
This behavior can be modeled by a spring that stores energy under deformation
and then releases it. Ideal viscous behavior is called “Newtonian”, where the stress
is directly proportional to the rate of strain.
A Newtonian fluid flows as long as a stress is applied and retains its final shape
once the stress is removed. This behavior is modeled by a dashpot that consists of
a piston moving in a viscous liquid.
Paper coatings can be generally considered as viscoelastic fluids. The viscoelas-
ticity of a material is most often measured by applying oscillatory shear instead of
steady shear. There are two common types of oscillatory tests. A strain sweep test is
carried out at a fixed frequency while the amplitude of the oscillation is varied. As
the amplitude is increased, more energy (or shear) is applied to the sample. This
energy may begin to break down the internal structure of the material. This is
analogous to stretching a spring too far. The strain at which the coating structure
begins to break down is called the critical strain, which gives some information on
the nature of the internal structure of the material. For example, flocculated disper-
sions have critical strains of about 1%, polymer solutions have critical strains of
about 10%, and polymer melts have critical strains of about 100 %. Most paper
coatings have critical strains of about 0.5–5%, indicating that their elastic behavior
is a result of a weak network structure between pigment particles and/or thickener.
The second common type of oscillatory test is a frequency sweep where the ampli-
tude of oscillation is fixed while the frequency of oscillation is varied. The ampli-
tude for the frequency sweep is chosen to be within the linear viscoelastic region,
as determined by the amplitude sweep measurement.
An alternative way to measure the viscoelastic properties of a material is to apply
a step change in stress or strain and then measure the response of the material
over time. This is the basis for stress relaxation and creep testing of materials. In a
stress-relaxation test a constant strain (or shear) is applied for a period of time and
then removed. Upon removal of the strain, the stress begins to relax. Typically, one
measures the relaxation time needed for the stress to relax to half of its equilib-
rium value at long times. Closely related to stress relaxation is a stress-growth test.
Here a sudden increase in strain is applied to the sample, and the growth in stress
is monitored over time. Both stress-relaxation and stress-growth measurements
are used to characterize paper coatings. A correlation between the stress-relaxation
time and the healing of coating defects can be observed in practice: Coatings with
a shorter relaxation time (more fluid-like) show narrower residual widths of an
induced blade streak. Stress-relaxation properties of a coating also correlate with
improved leveling of orange peel patterns for high-speed metered film coatings.
7.8 Measurements of Coating Colors 367