DHR/AR Rheometer: Setting Up an Oscillation Frequency Sweep Test

In this topic
Overview
Suggested Use
Test Setup

Overview

The frequency sweep is the most significant test for polymer melt characterization. In a frequency sweep, the frequency is varied linearly or logarithmically. Strain, stress, and phase are recorded. Typically, the strain or stress amplitude of the sinusoidal deformation remains constant. The dynamic moduli G’ (storage) and G” (loss) are calculated from the sinusoidal stress response. The complex viscosity, often used instead of the complex modulus, is the complex modulus divided by the applied frequency. Frequency tests are usually performed in the linear region (small strain)—in this case the results obtained are independent of the applied strain.

For viscoelastic fluids, including polymer melts, the dynamic moduli are dependent on the frequency. With decreasing frequency, the material behaves more and more viscous. The storage modulus decreases from the frequency-independent rubbery plateau to the terminal region with the frequency squared. The loss modulus, dominated by G’ in the rubbery region, decreases much slower, crosses G‘ at tan d=1, and determines the material flow behavior in the terminal region. Since G“ decreases linear with the angular frequency in the terminal region, the complex viscosity, the ratio of modulus and frequency, becomes independent of frequency and reaches a plateau value: the zero shear viscosity.

Materials with a yield stress, gels, or cross-linked rubbers do not exhibit a terminal region. The modulus remains mostly independent of frequency. The storage modulus is larger than the loss modulus; the material behaves elastic. Only if the strain amplitude is too high does the material structure (responsible for the energy storage mechanisms) disappear; the viscous deformation prevails and the materials now exhibit a pronounced terminal region. For non-linear testing at high strain amplitude, the magnitude and the phase up to the 9th harmonic can be evaluated.

The Oscillation Frequency Sweep test makes a series of dynamic mechanical measurements over a range of frequencies, or at a set of selected frequencies, while holding a constant oscillation amplitude and a constant temperature command. The amplitude can be chosen by a specified strain, strain rate, or stress value.

Suggested Use

Frequency sweeps are typically used to measure the frequency dependence (and equivalently, time dependence) of the viscoelastic properties of a material. In general, high frequencies correspond to short time scales, and low frequencies correspond to long time scales.

Test Setup

To select an Oscillation Frequency test, see Using Experimental Procedures for detailed instructions.

When you perform an Oscillation Frequency Sweep test, the following parameters need to be chosen.

Environmental Control

Select the following environmental control parameters:

Temperature: The temperature selection to maintain throughout the test. Enter the desired test temperature, or select Inherit set point to maintain the previously-specified temperature at the start of this step. The temperature range is dependent on the configuration of your instrument and the installed environment control system.
Soak time: The amount of time to delay data acquisition at the start of the step, typically to allow for temperature equilibration. This time is measured from the start of the step if Wait for temperature is not selected, or from the point at which the measured temperature becomes stabilized at the specified Temperature if Wait for temperature is selected. Because of the mass of the sample, test fixtures, and environmental control systems, a "soak time" (i.e., time to equilibrate at temperature) is recommended, particularly when starting steps at different temperatures. A five-minute soak time is sufficient for most samples in cases where the change in temperature is not too large. This time is also used at each increment temperature.
Wait for Temperature: Select this option to wait until the measured sample temperature reaches the specified temperature before beginning data acquisition. If you wish to begin data collection without waiting for the sample temperature to reach the specified value, disable this option.

Test Parameters

Set up the following test parameters:

Select between Torque, Stress, Displacement, Strain, Strain%, or Strain Rate. This test can be run using either torque/stress or displacement/strain as the controlling variable.
Torque: The torque is defined as the specified amplitude of the torque to be applied by the motor at each measurement. This value is used to extract the torque M_s applied to the sample during the measurement. The torque should be selected to be within the linear viscoelastic range of the sample, yet still provide a large enough signal to ensure good data.
Stress: The stress is defined as the specified amplitude of the stress to be applied to the sample at each measurement. This value is determined from the sample torque M_s applied to the sample during the measurement and the sample geometry and dimensions. The stress can be selected to simulate real-life end-use conditions, or it can be a value selected to be within the linear viscoelastic range of the sample, and still provide a large enough signal to ensure good data.
Displacement: The displacement is defined as the specified amplitude of the displacement to be applied to the sample by the motor at each measurement. The angular displacement should be selected to be within the linear viscoelastic range of the sample, yet still provide a large enough signal to ensure good data.
Strain: The strain is defined as the specified amplitude of the strain applied to the sample at each measurement. This value is used, along with the sample geometry and dimensions, to calculate the peak angular deflection to be applied to the sample during the measurement. The strain can be selected to simulate real-life end-use conditions, or it can be a value selected to be within the linear viscoelastic range of the sample, and still provide a large enough signal to ensure good data. Strain may be entered also as a percentage.
Strain Rate: This parameter is defined as the specified amplitude of the of the shear rate to be applied to the sample at each measurement. This value is used, along with the test frequency, sample geometry and dimensions, to calculate the peak angular deflection or linear displacement to apply to the sample during measurement. Running the test with a fixed strain rate has the advantage of maintaining a more uniform torque or force across the range of frequencies used for fluids that are close to Newtonian in behavior. However, as a result, the strain increases with decreasing frequency, driving the sample into non-linear response.

Frequency Sweep Parameters

Three types of frequency sweeps can be run. Choose the desired method from the list below. The available frequency range is dependent on your instrument type and configuration.

Logarithmic sweep: The logarithmic sweep uses the entered values as the starting and ending range of the test, with intermediate points spaced logarithmically. Logarithmic sweeps can be run in ascending or descending order.
Choose between Frequency (Hz) or Angular frequency (rad/s), then enter the desired range.
Enter the desired Points per decade. This sets the number of points collected in each decade, based on the initial value. The final value is always collected, regardless of whether it is part of the normal pattern. Click here for an example.
Linear sweep: The linear sweep uses the entered values as the starting and ending range of the test, with intermediate points calculated by adding or subtracting the increment until the final value is reached.
Choose between Frequency (Hz) or Angular frequency (rad/s), then enter the desired frequency values.
Choose between Increment or Number of points and enter the desired increment method:

Increment: The frequency increment specifies the change in frequency between subsequent measurements. If the final frequency is greater than the initial frequency, then this value is added at each measurement. If the final frequency is less then the initial value, then this value is subtracted. The final frequency is always measured, regardless of whether it is generated by the frequency increment or not. Click here for an example.
Number of points: The number of points determines the total number of frequencies collected between the specified frequency range. This includes both the initial and final frequency. Click here for an example.

Discrete frequency sweep: The discrete frequency sweep takes a measurement at each frequency in a list of frequency values, with up to 10 discrete frequencies being specified. The test frequencies in the list can be run in any order (i.e., do not have to be monotonic).

If you want to edit the values already displayed in the table, place the cursor in the table at the desired point and make your editing changes. The entries will be used in order until the first 0.00 entry is encountered, which is recognized as the end of the table.

Select Add to add a new value at the selected location, shifting all of the other table entries down one position.
Select Delete to remove the selected value, shifting all of the table values below the deleted entry up one position.
Select Reset to clear all of the table values, leaving only one entry.

Controlled Stress/Strain Advanced

Select from the parameters listed below:

Select the Controlled stress type (Torque and Stress only):
Standard: Oscillation stress/torque is applied to the sample during data acquisition only.
Continuous oscillation: Oscillation torque/stress is applied continuously during the test. Selecting Continuous oscillation will ensure that there is no break in the oscillation during the Fourier transform (data analysis) and data transmission to the computer. Parallel superposition and harmonic analysis are not available in this mode.
Select the Controlled strain type (Displacement, Strain, Strain% only):
Non-iterative sampling: Determines the torque command for the motor. The software uses the last stress value and predicts the new value required to obtain the target strain based on the previous test results. Use this option when it is more important to make rapid measurements (such as monitoring a cure process) rather than accurately control the strain.
Precision sampling: This mode controls the strain by adjusting the motor torque at the end of an oscillation cycle by an iterative approach. Several test cycles are necessary to reach the target strain. If it is more important to make rapid measurements (such as a monitoring cure process), use the Non-iterative option.
Continuous oscillation (direct strain): In this mode, the motor torque is adjusted during the oscillation cycle to apply the strain. Selecting this option will ensure that there is no break in the oscillation during the Fourier transform (data analysis) and data transmission to the computer. Parallel superposition and harmonic analysis are not available in this mode.
Motor mode (Displacement, Strain, Strain% only): Choose between Auto, Soft, Medium, and Stiff, depending on the sample stiffness. As a rule of thumb, leave this option set to Auto. Matching the mode to the stiffness of your sample may increase the quality of your data.

Data Acquisition

There are additional data collection options that can be adjusted to control how data is obtained and what additional information is collected during the measurement. To access these options, click on the “arrow” to display these test fields.

Select the desired Conditioning time:
Time: This is the time, in seconds, during which an oscillation torque is applied before enabling the data acquisition.
Number of cycles: This is the period, in number of oscillation cycles, during which an oscillation torque is applied before enabling the data acquisition.

Select the desired Sampling time:

Time: This is the time, in seconds, during which an oscillation torque is applied before enabling the data acquisition.
Number of cycles: This is the period, in number of oscillation cycles, during which an oscillation torque is applied before enabling the data acquisition.
Save waveform (point display): Select this option to store a snapshot of the data correlation buffer used for the calculation of the oscillatory data along within the data file for future recall. Note that this waveform snapshot is a small subset of the actual data used in the calculation, and can be used to provide insight into the quality of the stress and strain signals used based on the shape of the waveforms and noise levels present.
Numbers of points in waveform: Select the size of the data subset. The default is 64 points. The maximum is 1024 (full data set).

See Also
Viewing the Point Graph

Save image: Select to store images of the test within the data file for future recall when using the camera accessory.
Use additional harmonics: Select this option to specify that additional correlations be made at the specified harmonics. These calculations result in additional variables to be added to the test. Two modes are possible:
Multiwave: In this mode, up to the first 100 harmonics of the fundamental excitation signal (torque or displacement) can be added. The amplitude for each harmonic, in terms of a multiplier of the amplitude of the fundamental excitation signal, can be specified. Use this mode to determine the sample response for the selected frequencies simultaneously.
Harmonic analysis only: In this mode, the excitation frequency is not modified and remains sinusoidal. Select up to the first 100 harmonics of the excitation frequency to analyze the response signal (torque or displacement). Use this mode to quantify non-linearities in the sample response.

Controlled Flow

This is used to superpose a continuous flow onto the oscillation signal (parallel superposition). This option is not available for continuous oscillation in controlled stress and strain mode. Select the flow control below:

Torque: Enter the desired torque in N.m to control the flow.
Stress: Enter the desired stress in Pa to control the flow.
Velocity: Enter the desired velocity in rad/s to control the superposed flow.
Shear rate: Enter the desired shear rate in 1/s to control the flow.

Step Termination

TRIOS Software allows you to define conditions in which a step is halted ahead of its normal termination conditions (Limit checking). You can use this to ensure that, for instance, the instrument does not over speed or apply excessive strains.

Rather than running a step for a certain amount of time, you may wish to run it until stable data is obtained. You can set an Equilibrium limit (such as the viscosity value becoming constant when running a single shear with time) that will stop the currently active test.