Frequency-sweep test

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

In the frequency sweep test, the idea is to obtain LVE data from the test material over the widest possible (or realistic) range of frequencies. The lower limit of testing is never difficult for a rheometer to achieve physically, but it may be impractical to explore. Typically, the time required to obtain data at frequencies of <0.01 rad/sec or 0.006 Hz is impractical for a laboratory schedule. (At 0.006 Hz, each data point would take 167 sec for a single iteration most rheometers perform at least two or three iterations.) Furthermore, samples may change or degrade in nonsterile conditions over extremely long tests (i.e., hours). If it is desirable to obtain... 

Fora farther discussion of a frequency sweep test, see UNITH3.1. The range of frequencies used here and in step 5 will depend on both the sample and the rheometer type. 

Figure H3.2.6 Three types of materials that are Theologically distinguishable based on a frequency sweep test. O, storage modulus G, loss modulus.

FIGURE 2.12 Rheometric frequency sweep test of slurries conducted at 5-30 °C. G, G", and complex = rj + if]" reduce as temperature increases. 

Frequency sweep studies in which G and G" are determined as a function of frequency (o)) at a fixed temperature. When properly conducted, frequency sweep tests provide data over a wide range of frequencies. However, if fundamental parameters are required, each test must be restricted to linear viscoelastic behavior. Figure 3-31... 

Rheology Rheological measurements were performed at 25°C with an ARES 2 KFRT controlled strain rheometer (Rheometric Scientific). For the measurements parallel plates of 50 mm diameter were used. The gels were loaded between the plates (2-mm gap) and allowed to rest for 3 min. A strain sweep (0.1 to 100%) was performed at 1 Hz frequency to determine the range of viscoelasticity for each sample and a 2% strain was selected for all samples. A frequency sweep test (0.1 to 16 Hz) was then performed. Samples of 30 and 50% s/w concentration could not be analyzed because of the difficulty in obtaining samples of proper and constant geometry. 

Figure 12.5 Frequency-sweep tests of ChEOis = 0.06 M and C12EO2, for several mole fractions, X. (a) Viscoelastic functions C and C"vs. frequency to. (b) Cole-Cole plot. Lines fitting to Maxwell model.

Figure 12.7 Frequency sweep tests and fitting of some CisSE-amphiphile-water systems (90% water) to Maxwell + Rouse models (reprinted from ref [9] with permission from ACS Publications).

Figure 12.7 shows, as ejamples, oscillatory functions obtained through frequency-sweep tests at several weight ratios (R) of amphiphile/CigSE, where, in all cases, a 90 wt% water and a 10 wt% total surfactant -F cosurfactant was maintained for allR. 

The test includes two procedures procedure A is called frequency sweep test and procedure B is called repeated shear test at constant height (of specimen). 

In the frequency sweep test, a repeated sinusoidal shear loading is applied at 10 frequencies and at a given temperature while a varying axial load is applied to prevent dilation of the specimen. The loads and deformations are used to calculate the complex shear modulus, G, and phase angle, 5, of the specimen at each frequency. 

To increase the viscosity of polymer blends, additives [such as traditional fire retardants (mainly oxides) and, more recently, nanoclays] are added to polymer blend systems. The present authors recently conducted dynamic rheological measurements for the EVA/LDPE nanocomposite, as reported in [27]. Figure 8.3 (a) and (b) compare the complex viscosity of the EVA/LDPE blend with and without nanoclay as a function of frequency and temperature, respectively. Measurements were carried out on 1 mm-thick samples using a Rheometrics RDA n Dynamic Analyzer rheometer. The frequency-sweep tests were conducted from 0.1 to 100 rad/s with constant temperature (140 °C) and strain amplitude (1%). Eor the temperature-sweep measurements, samples were heated from 300 to 530 °C (15 °C/min) under nitrogen with constant frequency (10 rad/s) and strain amplitude (10%). In both experiments, there is a significant increase of viscosity above that for the neat... 

RPA Frequency sweep tests at 1 deg. strain amplitude EPDM 2504... 

Oscillatory shear frequency sweep tests, in the linear viscoelastic range, were performed in a frequency window between 0.1 and 100 rad/s. 

Apart from relaxation and creep experiments, two major types of test mode can be used to monitor the viscoelastic properties of polymers, namely temperature sweep and frequency sweep tests. These experiments are usually performed at short strains (<0.5% of active length) so as to be within the linear region when a sinusoidal stress a (Eq. (12.3)) (i.e., force per area unit) is applied to a viscoelastic material the resultant strain (i.e., unitary relative geometric displacement) appears out-of-phase (Eq. (12.4)), with the angle d being a> the angular frequency... 

Figure 15. Storage and loss ( and (/ ") moduluses of a gluten - water mixture from frequency sweep tests at 28 and 43 °C (open and frill symbols) and 10% strain (modified from [101]).

State diagrams can be therefore drawn from / j, -v.v-moisture data and f/" and (/ trends in temperature and frequency sweep tests. Figure 43 shows the state diagram for gliadin. 

Fig. 8 Frequency sweep test in the sol (10 °C) and gel (37 °C) phases of the CS-g-(PAF-PEG) polymer aqueous solution (6.0 wt%). Reproduced with permission from [91]...

Figure 8.11. Comparison of the dynamic response of the baseline beam and nanotube reinforced sandwich beam for a frequency-sweep test at 50 Vrms. (cantilevered length of 22.86 mm) [60],...

The rheological properties of the nanocomposites were studied using an ARES, TA Instruments. A 25 mm parallel plate geometry in oscillatory shear mode with dynamic frequency sweep test was used at 340 C for a fixed strain amplitude of 2%. 

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