Viscoelastic behavior losses

Dynamic mechanical analysis (DMA) or dynamic mechanical thermal analysis (DMTA) provides a method for determining elastic and loss moduli of polymers as a function of temperature, frequency or time, or both [1-13]. Viscoelasticity describes the time-dependent mechanical properties of polymers, which in limiting cases can behave as either elastic solids or viscous liquids (Fig. 23.2). Knowledge of the viscoelastic behavior of polymers and its relation to molecular structure is essential in the understanding of both processing and end-use properties. 

Fig. 4. The five regions of viscoelastic behavior. All polymers exhibit these five regions, but crosslinking, crystallinity, and varying molecular weight alter the appearance of this generalized curve. The loss modulus Tg peak appears just after the storage modulus enters the glass transition region.

In this book, we review the most basic distinctions and similarities among the rheological (or flow) properties of various complex fluids. We focus especially on their linear viscoelastic behavior, as measured by the frequency-dependent storage and loss moduli G and G" (see Section 1.3.1.4), and on the flow curve— that is, the relationship between the "shear viscosity q and the shear rate y. The storage and loss moduli reveal the mechanical properties of the material at rest, while the flow curve shows how the material changes in response to continuous deformation. A measurement of G and G" is often the most useful way of mechanically characterizing a complex material, while the flow curve q(y ) shows how readily the material can be processed, or shaped into a useful product. The... 

David and Augsburger (63) studied the decay of compressional forces for a variety of excipients, compressed with flat-faced punches on a Stokes rotary press. They found that initial compressive force could be subject to a fairly rapid decay and that this rate was dependent on the deformation behavior of the excipient for the materials studied, they found that maximum loss in compression force was for compressible starch and MCC, which was followed by compressible sugar and DCP. This was attributed to differences in the extent of plastic flow. The decay curves were analyzed using the Maxwell model of viscoelastic behavior. Maxwell model implies first order decay of compression force. 

These equations are often used in terms of complex variables such as the complex dynamic modulus, E = E + E", where E is called the storage modulus and is related to the amount of energy stored by the viscoelastic sample. E" is termed the loss modulus, which is a measure of the energy dissipated because of the internal friction of the polymer chains, commonly as heat due to the sinusoidal stress or strain applied to the material. The ratio between E lE" is called tan 5 and is a measure of the damping of the material. The Maxwell mechanical model provides a useful representation of the expected behavior of a polymer however, because of the large distribution of molecular weights in the polymer chains, it is necessary to combine several Maxwell elements in parallel to obtain a representation that better approximates the true polymer viscoelastic behavior. Thus, the combination of Maxwell elements in parallel at a fixed strain will produce a time-dependent stress that is the sum of all the elements ... 

When the strain amplitude Is relatively large as In the case of tire cord In a running tire, the viscoelastic behavior Is no longer linear. The stress-strain loop Is not elliptic but distorted (Figure 1). The material properties In the nonlinear regime can not be represented with the real and Imaginary moduli. In the present study, we characterize the viscoelastic properties In nonlinear regime by the effective dynamic modulus and mechanical loss.(J )... 

Curemeters, oscillating disc, and reciprocating paddle types are forms of plastimeter that measure plasticity before the onset of cure, as well during the cure. The viscoelastic behavior of uncured rubber tested by dynamic measurement is characterized by in-phase and out-of-phase moduli and loss tangent. 

S.3.2 Dynamic Mechanical Analysis (DMA) Storage and Loss Modulus Dynamic mechanical analysis (DMA) is typically performed to measure the viscoelastic behavior of polymer networks. A sinusoidal force (stress) is applied to a material and the resulting displacement (strain) is measured, allowing one to determine the complex modulus. 

The effects of the interchange reactions on the viscoelastic behavior of binary blends based on PET, PEN, and their nanocomposites have been studied [80]. With an increase in the number of extrusion runs and mixing temperature, the extent of reaction and the degree of randomness both increased, whereas the average sequence block length values decrease. The addition of nanoclay inhibits the transreactions in the PET/PEN blends. The addition of PEN into the PEN/PET blends enhances the storage modulus, loss modulus, and complex viscosity. A significant increment in the viscoelastic properties was observed in the presence of nanoclay. 

However, one important energy loss which was explained was the effect of the viscoelastic behavior of the polymer. This was studied by varying the crosslink density of the rubber, to alter the loss of elastic energy as the material relaxed. As the viscoelastic loss increased, so did the adhesive hysteresis, as shown in Fig. 8.13. 

Reinforced vulcanized samples generally present a marked viscoelastic behavior that is usually studied by dynamic viscoelastic measurements. In this experiment, a sample is subjected to periodic sinusoidal shear strain y (at defined frequency (o and temperature T). Its dynamic shear modulus G is complex and can be written as the sum of the storage modulus G, and the loss modulus G". 

In accordance with the results of the adntittance measurements, the dependence of the change in the resonant frequency corresponding to the reduced state of the polymer on the charge injected during the electropolymerization is linear, except for very thick films (Fig. 3.15). Usually such a deviation indicates a transformation from elastic to viscoelastic behavior however, in this case it was assigned to the poor adherence of the deposited polymer, since the energy loss measured was small even for thick films [157]. 

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