ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 15, 2007
Fast Sampling in Oscillation Mode
Peter Hodder and Dr Bernard Costello
TA Instruments Ltd, Fleming Centre, Fleming Way, Crawley, West Sussex, RH10 9NB.
Fast Sampling
Using standard fast oscillation, one of
the two new methods of increased data
acquisition, introduced in the latest version
of TA Instruments Rheology Advantage
software, the analysis is conducted at twice
the experimental frequency by running two
correlators in parallel, offset by 180 degrees.
This gives a maximum rate of two sample
points per cycle. Figure 1 shows an example
of data points acquired using this technique
where direct strain control oscillation was
used at a frequency of 50 Hz resulting in a
1.000E6
1.000E6
1.000E5
1.000E5
10000
30.00
30.20
30.40
30.60
time (s)
30.80
10000
31.00
Figure 1: Standard fast oscillation mode,
showing data points collected at twice the oscillatory
frequency of 50Hz.
As mentioned previously, one area
where this new fast sampling mode would
be of benefit is in rapidly curing systems
such as uv. Figure 2 shows a comparison
between a cure made with and without fast
sampling and clearly demonstrates the
improved definition of the cross over point
often used as a unique characteristic value.
The test was run at a frequency of 25Hz,
providing 50 points per second in fast
sampling mode.
G'' (Pa)
INTRODUCTION
The limitations in data acquisition in
conventional oscillatory rheology is linked
to the actual frequency of oscillation. For
example, a frequency of 5 Hz can only
provide 5 points per second. Such sampling
rates are not always adequate; processes
such as the UV curing of coatings occur too
rapidly to be captured at this sampling at
reasonable frequencies, and so in the past
certain practical limitations have existed.
data point every 0.02 seconds. The test
sample used for this demonstration was
polydimethylsiloxane (PDMS) at 20°C.
G' (Pa)
ABSTRACT
Conventional
oscillatory
rheology
requires at least one cycle of data to be
analysed. This limits the rate at which
sample points can be acquired to the
frequency of oscillation. TA Instruments
have therefore developed two methods of
increasing the rate of acquisition of sample
points.
1.000E5
1.000E5
G cross-over point
time: 31.61 s
G': 10160 Pa
10000
10000
G' (Pa)
G'' (Pa)
G cross-over point
time: 32.45 s
G': 9596 Pa
1000
100.0
5.000
20.00
time (s)
1000
100.0
50.00
35.00
Data Storage
A further refinement is for the software
to allow the storage of up to 1024 data
points per cycle for later analysis. This
technique can be used to obtain the higher
harmonics of the output signal for a high
amplitude sinusoidal input signal, or to plot
data as Lissajous figures, for example.
Figure 4 shows data plotted in this way for a
commercial hair gel at a stress of 10Pa and
angular frequency of 6.28 rad s-1.
New LED RFSC 50mW-0004o, Time sweep step
New LED 50mW FS RFSC 200m sync nfw NF-0005o, Time sweep step
15
Figure 2: Comparison between standard and fast
sampling oscillation mode for UV curing system.
NF
5.0E-04
-3
-4
-5.0E-04
-5
-6
D
7
-0.02
0
0.02
Harmonic Analysis
As an alternative to a Fourier transform1
it is possible to perform the harmonic
analysis with the correlator used by the
rheometer firmware. Figure 5 shows the odd
harmonics for a commercial hair gel at 6.28
rad/s
-1
100.00
10.000
-1.5E-03
6
-0.04
Figure 4: Lissajous figure for a commercial hair
gel at an angular frequency of 6.28 rad/s and a stress
of 10 Pa.
8
-2.5E-03
9
10
time / seconds
1.0000
0.010000
1.0000E-3
1.0000E-4
1.0000E-5
1.0000E-6
1.0000E-7
0.01000
Figure 3: Results obtained using the raw signal data
logger. Shown fluctuating at twice the frequency of
oscillation, as expected, are the displacement (D),
torque (T) and normal force (NF).
Stress sweep step - Fundamental
Stress sweep step - Harmonic 3
Stress sweep step - Harmonic 5
Stress sweep step - Harmonic 7
Stress sweep step - Harmonic 9
0.10000
strain
-2
5
-0.06
Strain
1.5E-03
T
-10
1000.0
-1
-8
0
-5
-0.08
0
-7
5
-15
2.5E-03
torque / Nm
nforce / N, displacement / rad
1
Stress / Pa
Raw Signal Data Logger
Using a raw signal data logger, which
operates in real time, fundamental
instrument information such as the torque,
displacement, normal force and geometry
gap can be logged at just under a kilohertz.
The user can access this data and analyse it
as required. The raw signal data logger
shows rapid transitions occurring during an
oscillation cycle that could not be captured
using conventional rheology. Figure 3 shows
data for PDMS at a frequency of 0.5 Hz and
strain of 10000. The asinusoidal form of the
torque signal is due to the sample nonlinearity at that strain. Note the normal force
is seen to fluctuate at twice the frequency of
the oscillation, as expected.
10
0.1000
1.000
10.00
osc. stress (Pa)
100.0
1000
Figure 5: Fundamental and odd harmonics
obtained using the AR-G2 correlator for a
commercial hair gel at 6.28 rad/s.
Figure 5 clearly indicates that a
contribution is being made from the third
harmonic prior to the perceived critical
stress that may have been suggested from
just the fundamental frequency data.
ACKNOWLEDGEMENTS
The authors would like to thank the
management of TA Instruments Ltd., New
Castle, Delaware U.S.A., for permission to
present this work.
REFERENCES
1. M.Wilhelm, D.Maring and H.W.Speiss
(1998) “Fourier Transform Rheology”
Rheol. Acta. 37, 399.