Dynamical strain sweep

In many studies it is presumed that linear viscoelastic behaviour always occurs, but this is not the case for many reactive systems. Conventional experimental rheology utilizes a dynamic strain sweep, which examines the dynamic rheological response to varied strain amplitudes, at a fixed frequency. If the system shows an effect of strain amplimde on dynamic properties (such as G or G") the system is said to be exhibiting a non-linear (viscoelastic) response. If the properties are independent of strain amplitude, then the system is said to be exhibiting linear viscoelastic behaviour. Figure 4.2 shows the response of an industrial epoxy-resin moulding compound (approximately 70 wt.% silica) at 90 °C at strain amplitudes of 0.1% to 10% for frequencies of 1, 10 and lOOrad/s. 

Fig. 11 The storage modulus (O ) for the neat PBT and PCTs samples obtained in dynamic strain sweep (reproduced with permission of John Wiley Sons, Inc., D. Wu et al., Journal of Polymer Science Part B Polymer Physics [29])...

A Simple Discussion on the Possible Networks Deformation in the Dynamical Strain Sweep... 

Dynamic rheological properties of the melt are very sensitive to the molecular structure of a polymer. It is essential to perform dynamic strain sweep test before... 

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... 

Experiments on recovery of dynamic functions after the application of large strain amplitude perturbation were performed to understand the modulus recovery kinetics. To determine the recovery kinetics, samples underwent the following test sequences (a) frequency sweep, (b) strain sweep, (c) relaxation time of 2 min, (d) frequency sweep, (e) strain sweep, (f) relaxation time of 2 min, (g) frequency sweep, and (h) strain sweep [50]. Figure 7 shows the comparative subsequent strain sweep results performed immediately after a relaxation time of... 

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. 

A schematic of the system is illustrated in Figure 1. For dynamic frequency sweeps (refer to Figure 2), the polymer is strained sinusoidally and the stress is measured as a function of the frequency. The strain amplitude is kept small enough to evoke only a linear response. The advantage of this test is that it separates the moduli into an elastic one, the dynamic storage modulus (G ) and into a viscous one, the dynamic loss modulus (G"). From these measurements one can determine fundamental properties such as ... 

Dynamic-mechanical testing of cross-linked samples are often carried out with high precision on specimen strips in torsion mode, e.g., with a Rheo-metrics Dynamic Analyzer II (RDA) with a sample size of 28x10x2 mm. Here, temperature-and strain sweeps are performed in a displacement range from 0.01% to about 5% strain and a frequency range between 0.1 and 100 Hz. Dynamic mechanical testing of uncross-linked samples can be made, e.g., with a Rubber Process Analyzer RPA 2000 (Alpha Technologies) from 0.28% to 350% strain at various frequencies and elevated temperatures. 

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... 

Fig. 1 a,b. Strain amplitude dependence of the complex dynamic modulus E E l i E" in the uniaxial compression mode for natural rubber samples filled with 50 phr carbon black of different grades a storage modulus E b loss modulus E". The N numbers denote various commercial blacks, EB denotes non-commercial experimental blacks. The different blacks vary in specific surface and structure. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 1 Hz, and static pre-deformation of -10 %. The x-axis is the double strain amplitude 2eo... 

Another important point is the question whether static offsets have an influence on strain amplitude sweeps. Shearing data show that this seems not to be the case as detailed studied in [26] where shear rates do not exceed 100 %.However, different tests with low dynamic amplitudes and for different carbon black filled rubbers show pronounced effects of tensile or compressive pre-strain [ 14,28,29]. Unfortunately, no analysis of the presence of harmonics has been performed. The tests indicate that the storage (low dynamic amplitude) modulus E of all filled vulcanizates decreases with increasing static deformation up to a certain value of stretch ratio A, say A, above which E increases rapidly with further increase of A. The amount of filler in the sample has a marked effect on the rate of initial decrease and on the steady increase in E at higher strain. The initial decrease in E with progressive increase in static strain can be attributed to the disruption of the filler network, whereas the steady increase in E at higher extensions (A 1.2. .. 2.0 depending on temperature, frequency, dynamic strain amplitude) has been explained from the limited extensibility of the elastomer chain [30]. 

Fig. 2. Comparison of strain sweeps in shearing mode and uniaxial compression mode for different static offsets. Obviously, the influence of offsets is weaker in shearing. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 10 Hz...

Fig. 6. Strain sweeps for the dynamic loss (shear) modulus G" of styrene-butadiene rubber samples filled with various carbon blacks (from [81])...

Figure 3-40 Illustration of Estimation of Critical Stress from a Stress Sweep at a Fixed Frequency Dynamic Rheological Experiment. Alternatively, as described in the text, one may conduct a strain sweep experiment.

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.)...

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. 

The complex viscosity as a function of frequency, maximum strain and temperature is generally determined with one rheometer. Standard ASTM 4440-84/90 defines the measurement of rheological parameters of polymer samples using dynamic oscillation. This standard reiterates the importance of determining the linear viscoelastic region prior to performing dynamic frequency sweeps. 

Rheological measurements were performed in shear using a stress controlled rheometer (Carri-Med CSL 100) operating in cone-plate geometry. Each sample is submitted successively to a first frequency sweep in range 10 3-40 Hz under 3% strain, to a creep and recovery test, and finally to a second frequency sweep identical to the first one. The dynamical strain amplitude (3%) and the value of the creep stress (chosen so as to keep the maximum strain below 10%) were set in order to remain within the linear viscoelasticity domain. Creep and creep recovery were recorded during 20 h and 80 h, respectively, times which allowed the steady state to be reached in all cases. A fresh sample was used for each solvent/temperature combination. 

Fig. 4 Structure and properties of nanocellulose, (a) Hierarchical assembly of cellulose molecules into cellulosic fibers. Adapted, with permission, from [131]. Copyright 2012 Elsevier, (b) Proposed mechanism of formation of CNF cross-linked with metal cations. Reproduced, with permission, from [132]. Copyright 2013 American Chtanical Society, (c) Effect of the type of metal cation on the frequency-dependent storage modulus of CNF hydrogels, probed by dynamic frequency sweeps (25 °C) at a strain rate of 0.5 %. Adapted, with permission, from [132]. Copyright 2013 American Chemical Society, (d) Polarization optical microscopy photograph of a biphasic 8.78 % (w/w) CNC suspension. Adapted, with permission, from [133]. Copyright 1996 American Chemical Society, (e) Polarization optical microscopy photograph of a CNC suspension. Scale bar. 200 pm. Reproduced, with permission, from [134]. Copyright 2000 Amaiean Chemical Society...

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