Viscoelastic material storage modulus

Fig. 13.32. Frequency response of a viscoelastic material. Storage modulus (C, solid line) and loss modulus (C", broken line) are shown.

The majority of foods show viscoelastic properties. This means that these foods react, when exposed to apphed force, by both the elastic component (which behave as in sohds) and the viscous component (which behaves as in hquids). The rheological characterisation of these materials, in addition to flow curves, requires knowledge of other parameters, complex (dynamic) modulus G, which is related to the elastic component of the material (storage modulus G ) and the viscous component of the material (loss modulus G") by the fohowing equation = (G + G" ). With the so-called... 

For a viscoelastic solid, the loss modulus which reflects the viscous processes in the material is unaffected by the presence of a spring without a dashpot. The storage modulus includes the elastic component G(0) ... 

The dynamic mechanical thermal analyzer (DMTA) is an important tool for studying the structure-property relationships in polymer nanocomposites. DMTA essentially probes the relaxations in polymers, thereby providing a method to understand the mechanical behavior and the molecular structure of these materials under various conditions of stress and temperature. The dynamics of polymer chain relaxation or molecular mobility of polymer main chains and side chains is one of the factors that determine the viscoelastic properties of polymeric macromolecules. The temperature dependence of molecular mobility is characterized by different transitions in which a certain mode of chain motion occurs. A reduction of the tan 8 peak height, a shift of the peak position to higher temperatures, an extra hump or peak in the tan 8 curve above the glass transition temperature (Tg), and a relatively high value of the storage modulus often are reported in support of the dispersion process of the layered silicate. 

In a rheomety experiment the two plates or cylinders are moved back and forth relative to one another in an oscillating fashion. The elastic storage modulus (G - The contribution of elastic, i.e. solid-like behaviour to the complex dynamic modulus) and elastic loss modulus (G" - The contribution of viscous, i.e. liquid-like behaviour to the complex modulus) which have units of Pascals are measured as a function of applied stress or oscillation frequency. For purely elastic materials the stress and strain are in phase and hence there is an immediate stress response to the applied strain. In contrast, for purely viscous materials, the strain follows stress by a 90 degree phase lag. For viscoelastic materials the behaviour is somewhere in between and the strain lag is not zero but less than 90 degrees. The complex dynamic modulus ( ) is used to describe the stress-strain relationship (equation 14.1 i is the imaginary number square root of-1). 

This section examines the dynamic behavior and the electrical response of a TSM resonator coated with a viscoelastic film. The elastic properties of viscoelastic materials must be described by a complex modulus. For example, the shear modulus is represented by G = G + yG", where G is the storage modulus and G" the loss modulus. Polymers are viscoelastic materials that are important for sensor applications. As described in Chapter S, polymer films are commmily aj lied as sorbent layers in gas- and liquid-sensing applications. Thus, it is important to understand how polymer-coated TSM resonators respond. 

The damping performance of a free layer treatment for plate bending waves is shown in Figure 4 (lH,UL) This chart, which is Oberst s result, gives the system loss factor T relative to T 2/ the loss factor of the viscoelastic material, as a function of the thickness ratio H2/H1 (viscoelastic layer to plate). Each of the several curves corresponds to a particular value of the relative Young s storage modulus E2/E1 (viscoelastic layer to plate). 

To find convenient expressions for the storage modulus and the loss tangent for a viscoelastic material under free oscillation in torsion, it is necessary to return to the equation of motion given by... 

Double logarithmic plots of the storage relaxation modulus versus frequency for a viscoelastic material are shown in Figure 8.12 (9). By taking into account Eq. (6.3), the correspondence between the results at tempera-... 

Remember that a viscoelastic flnid has two components related to y by Eq. 6.1 and y by Eq. 6.2. Erom Eq. 6.5, it is clear that for such dynamic oscillatory displacement, the measnred stress response has two components an in-phase component (sincot) and an ont-of-phase component (coscot). Viscoelastic materials prodnce this two-component stress response when they undergo mechanical deformation becanse some of the energy is stored elastically and some is dissipated or lost. The stress response, which is in-phase with the mechanical displacement, defines a storage or elastic modulus, G, and the out-of-phase stress response defines a loss or viscous modulus, G"". The storage modulus (G ) provides information about the fluid s elasticity and network structure. 

FIGURE 10.9 Vector diagram of the relationships between the elastic (storage) modulus (G ), viscous (loss) modulus (G") and the phase angle, depicting the complex modulus (G ) for viscoelastic materials. 

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