Chemistry Reference
In-Depth Information
approach to establishing a yield value is to apply an ever-increasing stress to a
sample with time. The strain is monitored and once the strain increases
appreciably the yield stress has been found. The major problem with relying
on this technique lies in the speed at which the stress is increased. In the
previous section we have seen how ramping the strain gives a multitude of
different material behaviour. The same applies to linearly ramping the stress. If
this experiment is performed quickly a small strain displacement will go
undetected by the instrument and the instrument will increment on to the next
stress. The yield stress will be overestimated. This is an important failing in
sedimentation control since an overestimated yield could lead to a system that
on paper seems stable but in reality separates. A gradual application of
the stress is to be preferred over a more rapid sequence. Perhaps the best tests
are those often employed in linear viscoelastic measurements. A sinusoidal
oscillating stress or strain can be applied to the sample and storage and loss
moduli can be measured. At low stresses or strains a frequency sweep will
illustrate the presence of static modulus G(0). This is indicative of the presence
of a yield. This will be observed by the storage modulus failing to reach the
baseline at low frequencies, the value of the modulus being displaced from
the base line by G(0). However, a broad relaxation spectra or a Maxwell model
with a long-time relaxation process can also give rise to this observation, so it is
not unambiguous. Complementary to this test is the strain and stress sweep.
This is a very good method of establishing linearity and its breakdown. In
this test an oscillating strain (or stress) is applied to the sample. For a system
where the storage modulus is greater than the loss, normally the case in
materials with a yield, as the strain is increased past the linear limit the storage
modulus reduces. Ideally, this test is best performed in the lower-frequency
limit to avoid to greater contribution from the high-frequency elastic compo-
nents. If a stress is applied the critical stress can be established directly from the
curve. If a strain sweep is applied the apparent yield in the sample can be
established by multiplying the critical strain by the value of G*(o) at that
strain. A typical strain sweep for a charged colloidal dispersion is shown in
Figure 6.5.
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A note of caution should be sounded here. Whilst the curves shown are
characteristic of many charged dispersions it should be recalled that once we
apply a sinusoid to a nonlinear system the response need not be a sinusoid. As
the strain is increased into the nonlinear region the waveform passing through
the sample becomes progressively distorted. The instrumental analysis in this
case involves applying a numerical Fourier transform to the signal and filtering
to allow only components of the wave at the applied frequency to be analysed.
Various harmonics can develop and this can provide further information
on linearity. Inclusion of different terms and methods of analysis can change
the form in the nonlinear region. Without doubt the application and analysis of
oscillating waves in the nonlinear regime is the most dicult to model with
rigorous viscoelastic equations. We have said that stress- or strain-controlled
instrumentation can be used to obtain a test of linearity. Stress instrumentation
can be designed to mimic strain-rate responses. In order to achieve this, a
