Strain Sweep Measurements

In oscillatory measurements, two sets of experiments are carried out, namely strain sweep measurements and oscillatory sweep measurement. 

FIG. 4.26 Strain sweep measurements at 10 rad/sec (a) product A (concentrated fabric softener) (b) product B (concentrated fabric softener). 

Fig. 16 Strain sweep measurements of the 40 phr filled nanocomposites at 20 °C (Lefi), the lines are fits according the Kraus model Payne effect measure at different temperatures Right) for SBS filled with 40 phr Aerosil 200 (Reprinted from [54])...

In oscillatory measurements one carries out two sets of experiments (i) Strain sweep measurements. In this case, the oscillation is fixed (say at 1 Hz) and the viscoelastic parameters are measured as a function of strain amplitude. This allows one to obtain the linear viscoelastic region. In this region all moduli are independent of the appUed strain amplitude and become only a function of time or frequency. This is illustrated in Fig. 3.50, which shows a schematic representation of the variation of G, G and G" with strain amplitude (at a fixed frequency). It can be seen from Fig. 3.49 that G, G and G" remain virtually constant up to a critical strain value, y . This region is the linear viscoelastic region. Above y, G and G start to fall, whereas G" starts to increase. This is the nonlinear region. The value of y may be identified with the minimum strain above which the "structure of the suspension starts to break down (for example breakdown of floes into smaller units and/or breakdown of a structuring agent). 

It is clear that this data treatment is strictly valid providing the tested material exhibits linear viscoelastic behavior, i.e., that the measured torque remains always proportional to the applied strain. In other words, when the applied strain is sinusoidal, so must remain the measured torque. The RPA built-in data treatment does not check this y(o )/S (o)) proportionality but a strain sweep test is the usual manner to verify the strain amplitude range for constant complex torque reading at fixed frequency (and constant temperature). 

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. 

The dynamic Weissenberg number W can be calculated from data obtained by the strain frequency sweep measurement. It s the ratio of the elastic to the viscous shares in the measured gel and leads to an objective description of the sensoric properties, representing the basis for the standardization of pectins. 

The strain temperature sweep measurement is conducted with a preselected amplitude for the applied strain (y) and a constant frequency (f). The changing parameter is the temperature T, which is given in a temperature-time profile [T = T(t)]. This test method serves to illuminate the structural build-up, the softening, the melting and the gelation of pectins influenced when the temperature changes. 

The interaction between two fillers particles can be investigated by measuring the Payne effect of a filled rubber compounds. In this measurement, dynamic properties are measured with strain sweep from a very small deformation to a high deformation. With the increased strain, the filler-filler network breaks and results in a lower storage modulus. This behavior is commonly known as the Payne effect... 

Because the duration for one measurement is very short (e.g., with a 1-Hz input, a cycle is completed in 1 sec), a dynamic test is suitable for gaining information in a short time frame or for monitoring time-dependent changes in gel network properties. When monitoring the gelation process at a fixed frequency, it usually takes a few hours for G to become approximately constant. The constancy can be judged by a constant value of G at a fixed frequency during a subsequent frequency or strain sweep test, which usually takes several minutes. 

FIGURE 16. Strain amplitude sweep measurements on (a) CdS (low reactant concentrations), (b) CdS (high reactant concentrations), and (c) nanofilms formed at the toluene-water interface at 22 °C. Reproduced from ref 34. Copyright 2008 Elsevier. 

Wu et al. (73) studied the viscoelastic properties, viz. storage modulus (GO and complex viscosity (r 0 with respect to frequency (co) of PLA-carboxylic-acid-functionalized MWCNTs nanocomposites using a rheometer (HAAKE RS600, Thermo Electron Co., USA). The dynamic frequency sweep measurements were carried out at the pre-strain level of 1%. They observed that the addition of carboxylic-acid-functionalized MWCNTs weakened the dependence of G on go, especially at higher loading levels (Figure 9.12). This indicates... 

In addition, other measurement techniques in the linear viscoelastic range, such as stress relaxation, as well as static tests that determine the modulus are also useful to characterize gels. For food applications, tests that deal with failure, such as the dynamic stress/strain sweep to detect the critical properties at structure failure, the torsional gelometer, and the vane yield stress test that encompasses both small and large strains are very useful. 

Fig. 7 The Payne Effect measured on a rheometrics dynamic analyzer (RDA II), using a 10 Hz strain sweep from 0.05% to 10% strain, 65° C, on a typical tire tread containing 50phr HAF black. (View this art in color at www.dekker.com.)...

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. 

Strain sweep In which the frequency at is kept constant and G, G and G" are measured as a function of strain amplitude. 

An alternative rheological technique for assessing flocculation involves oscillatory measurements which, as noted above, can include two sets of experiments, namely strain and oscillatory sweep measurements. 

Dynamic-shear measurements are of the complex viscosity rj ) as a function of the dynamic oscillation rate (o), at constant temperature. These tests are defined as isothermal dynamic frequency sweeps. Since the dynamic frequency sweeps are conducted at a given amplitude of motion, or strain, it is necessary to ensure that the sweeps are conducted in the region where the response is strain-independent, which is defined as the linear viscoelastic region. This region of strain independence is determined by an isothermal strain sweep, which measures the complex viscosity as a function of applied strain at a given frequency. This ensures that a strain at which the dynamic frequency sweep may be conducted in the linear viscoelastic region is selected. 

Rheological measurements were made with rectangular gel samples in a torsion geometry. The gel samples had dimensions of approximately 12 x 4.5 x 28 mm. The measurements were made on a Rheometric Scientific ARES instrument at a frequency of 1 Hz and a scan rate of 2 °C/min. An environmentally controlled chamber permitted determination of the modulus over temperatures from -100 to 70 C. Strain sweeps were conducted at various temperatures to ensure that the modulus was independent of strain. 

Tan 5 of natural rubbers with different non-rubber content after 3- and 6-month storage measured at frequency- and strain-sweep modes. 

---