Dynamical strain sweep amplitude

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. 

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... 

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 ... 

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]. 

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 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. 

Figure 12 (a) Time evolution of S and fi of a rejuvenated star glass (aging) at different frequencies and linear strain amplitude of 0.5%. With respect to S the frequencies are from bottom up 0.3,1,3, and 10 rad s The soft state (at intermediate times) and solid state (at long times) are indicated. (b) Respective dynamic frequency sweeps of soft and solid states. ... 

Using an Advanced Rheometric Expansion System (ARBS) with parallel plates of 2S mm diameter, we performed dynamic temperature sweep expo-iments under isochronal conditions with increasing temperature as well as decreasing temperature. The heating and cooling rate of these experiments was 0.5 °C/min. The strain amplitude (y,) and the angular frequency (ca) were low enough to satisfy a linear viscoelasticity. 

It is observed that the values do not reach its initial position within the relaxation time of the experiment, but a recovery of the E values have been attained (Fig. 18). This behaviour of a rubber can be explained by the stress softening effect during the dynamic strain. Nevertheless, a high extent of recovery in the reverse amplitude sweep indicates that a good filler-filler network has been re-established at a low loading of tubes in the S-SBR-BR matrix. So, at least it can be said that rather than damage or permanent break of the tubes, the amplitude sweep disrupted the filler-filler network in the rubber matrix. It is noted that the absolute values of E at small amplitudes are somewhat differed from each other as compared with the value obtained from the phr CNT-filled compound. The difference may be developed from ageing of the samples. 

Fig. 27 (a) Effect of dynamic strain amplitude on storage modulus, (b) stress-strain behaviour of CR/EPDM blend in absence and in presence of nanoclay. For strain sweep experiment, tension mode was selected for the variation of the dynamic strain from 0.01 % to 40 % at 10 Hz frequency [106]... 

Providing tests are performed at low strain amplitude, small enough for the complex modulus to exhibit no strain dependency, then dynamic testing yields in principle linear viscoelastic functions. This implies that, with an unknown material, a preliminary strain sweep test is performed in order to experimentally detect the maximum strain amplitude for a linear response to be observed [i.e. G lo, f(Y)]-As illustrated in Fig. 6 with data from Dick and Pawlowsky [20], such a requirement is practically never met within the available experimental window with filled rubber materials, whose linear region tends to move back to a lower and lower strain range as the filler content increases. 

An Advanced Rheometric Expansion System (ARES, TA Instruments) was used in oscillatory shear mode with parallel plate geometry. Strain amplitude was fixed at 2% and dynamic frequency sweep experiments with angular frequency ( ) from 0.1 to 100 s were performed at 280°C. PET and all blends were tested under nitrogen atmosphere, while pure LCP, which was found not to degrade, was tested under air. The complex viscosity ( 7 ), dynamic storage (GO and loss (G") moduli were obtained. All rheological measurements are an average of four runs. 

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%. 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

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... 

The linear viscoelastic response of LDPE/LDH nanocomposites has been studied using dynamic oscillatory measurements at constant strain amplitude of 2% and frequency sweep of 0.05-100 rad s . The response of aU nanocomposites is found to be quahtatively similar in the temperature range 160-240 °C. However, the time-temperature superposition principle is not... 

Dynamic viscoelastic parameters such as the storage modulus and the loss modulus offer another measure of the mechanical properties of hydrogels. The storage and loss moduli represent the stored energy (elastic portion) and the heat dissipated (viscous portion) respectively of a viscoelastic solid. These are determined using a rheometer. The most commonly used set up for these measurements is the rotational rheometer wherein the sample is placed between two discs, the top disc rotates in an oscillatory manner in order to introduce a small strain oscillatory shear, while the torque exerted by the sample on the lower disc is measured. This allows a shear stress-strain relationship to be determined and thus for the moduli in turn to be found. Usually an amplitude sweep will be done to ensure that the sample is in the linear viscoelastic range [73, 75, 79, 80]. 

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