Studying viscoelastic response

The ramp of pressure to about 3 GPa observed in shock-loaded fused quartz has been used very effectively in acceleration-pulse loading studies of viscoelastic responses of polymers by Schuler and co-workers. The loading rates obtained at various thicknesses of fused quartz have been accurately characterized and data are summarized in Fig. 3.6. At higher peak pressures there are no precise standard materials to produce ramp loadings, but materials such as the ceramic pyroceram have been effectively employed. (See the description of the piezoelectric polymer in Chap. 5.)... 

The time and temperature dependent properties of crosslinked polymers including epoxy resins (1-3) and rubber networks (4-7) have been studied in the past. Crosslinking has a strong effect on the glass transition temperature (Tg), on viscoelastic response, and on plastic deformation. Although experimental observations and empirical expressions have been made and proposed, respectively, progress has been slow in understanding the nonequilibrium mechanisms responsible for the time dependent behavior. 

Experimentally a variety of quantities are used to characterise linear viscoelasticity (Ferry 1980). There is no need to consider all the characteristics of linear viscoelastic response of polymers which are measured under different regimes of deformation in linear region, they are connected with each other. The study of the reaction of the system in the simple case, when the velocity gradients are independent of the co-ordinates and vary in accordance with the law... 

For a sinusoidal steady excitation and small deflections, the elastic and viscoelastic solutions are formally similar, as the separation of variables methodology outlined above suggests. Thus, in this case, the viscoelastic response is dependent on only the specific material properties of the sample under study. Moreover, on the basis of one of the hypotheses mentioned above, the thermoviscoelastic problem can be reduced to a thermoelastic one. Therefore, in the present context only the elastic solution of the problem will be discussed. 

This book is concerned mainly with the study of the viscoelastic response of isotropic macromolecular systems to mechanical force fields. Owing to diverse influences on the viscoelastic behavior in multiphase systems (e.g., changes in morphology and interfaces by action of the force fields, interactions between phases, etc.), it is difficult to relate the measured rheological functions to the intrinsic physical properties of the systems and, as a result, the viscoelastic behavior of polymer blends and liquid crystals is not addressed in this book. 

The principal advantage of this technique is that the viscoelastic response of any material can be probed directly on different time scales (l/cu) of interest by simply varying the angular frequency u. If the material studied Ts a perfectly elastic solid, then the stress in the sample will be related to the strain through Hooke s law [Eq. (7.98)] ... 

Dynamics in polymer networks and also in polymer liquids can be studied by a variety of viscoelasticity experiments. For networks and gels, these methods determine the modulus from the long time (or low frequency) viscoelastic response and directly measure the relaxation of dangling structures and sol fraction at higher frequencies. For polymer... 

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. 

In contrast to other Tg methods, dynamic measurements easily detect glassy state relaxations and have been extensively applied to their study. These include dynamic mechanical methods, dielectric relaxation, and nuclear magnetic resonance (NMR). Since we are primarily concerned with viscoelastic response at this point, we shall confine the discussion to the dynamic mechanical technique and delay our consideration of dielectric and NMR methods until Chapter 7. 

In the present work the effect of temperature on the rheological behaviour of wheat gluten in D20 is compared to that in water. The viscoelastic response was studied in shear by combining dynamical measurements and creep and recovery tests, in order to encompass a large timescale. 

TMA and DMA are widely used to study the properties of polymers and other materials under various experimental conditions in the temperature range from —200 to approximately 850CC. The former usually gives limited information on viscoelastic responses as well as dimensional changes, whereas the latter is concerned with viscous responses. 

DMA instruments use different principles to study the viscoelastic response of a sample under oscillatory load ). They are (1) The sample may be driven in forced oscillation or allowed to resume its natural frequency ... 

Stable Systems. The viscoelastic response of a concentrated noncoagulating suspension is strong when the average distance between the suspended particles is of the same order as the distance at which the interparticle repulsive forces become important. Hence, the viscoelastic behavior originates from the interparticle repulsive potential. Several studies have been carried out on hard sphere systems (72, 204, 205), steric systems (88, 94, 203, 206), and electrostatic systems (163,... 

Prestidge and Tadros (96), Liang et al. (95), and Tadros et al. (209) studied the viscoelastic responses of both electrostatically and sterically stabilized systems. 

We have used the generalized phenomenological Maxwell model or Boltzmann s superposition principle to obtain the basic equation (Eq. (4.22) or (4.23)) for describing linear viscoelastic behavior. For the kind of polymeric liquid studied in this book, this basic equation has been well tested by experimental measurements of viscoelastic responses to different rate-of-strain histories in the linear region. There are several types of rate-of-strain functions A(t) which have often been used to evaluate the viscoelastic properties of the polymer. These different viscoelastic quantities, obtained from different kinds of measurements, are related through the relaxation modulus G t). In the following sections, we shall show how these different viscoelastic quantities are expressed in terms of G(t) by using Eq. (4.22). 

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