Electrical loss modulus

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. 

Figure 14.14 The stress dependence of the storage modulus and loss modulus of suspensions containing nanocables with a conducting PANI core (a) and with a nonconducting PANI core (b) at a frequency of 1.0 Hz under various DC electric fields.

Dissipation di-s9- pa-shon n. The loss modulus in a plastic part when imparted with rapid, cyclic changes (or even reversals) of stress. The product of mechanical dissipation is heat, which can raise the temperature of the part and cause it to weaken, creep rapidly, or even fail prematurely. Dissipation can also apply to electrical systems, whereby a material with small dissipation will tend to better insulate heat. This is a desirable property in electrical insulations for high-frequency applications because it minimizes the waste of electrical energy as heat. 

Yingwei et al. [151] have investigated the rheological electrical and thermal properties of polylactic acid-organoclay nanocomposites. Both storage and loss modulus increased with clay loading at all frequencies. 

In addition to the shear stress, the storage modulus (G ) and loss modulus (G") are two important parameters for characterizing ER suspensions. Linear viscoelastic behavior of ER suspensions is always addressed before the frequency sweep experiment. Typically at small strain amplitude both G and G" show an independence of strain amplitude, and then decrease with the increase of strain amplitude. Figure 30 shows strain dependence of both the storage modulus (O ) and loss modulus (G") for 1 pm in diameter silica/PDMS suspension with the particle volume fraction 17.1 vol% at various electric fields. Without an electric field, the loss... 

The loss modulus G" may have a different strain dependence than the storage modulus G. Figure 33 shows strain dependence of the storage and loss moduli scaled by the squared electric field strength for 20 wt% acidic alumina/PDMS suspension. At different combination of the electric field strength and oscillation frequency, shows a plateau value at small... 

Figure 33. Strain sweep results for different combinations of electric field strength and oscillation frequency for a 20 wt.% acidic alumina/PDMS suspension (a) storage modulus scaled by electric field strength squared, as a function of strain amplitude, yo, and (b) loss modulus scaled by electric field strength squared, G" Ias a function of strain amplitude,...

Figure 35 Frequency dependence of loss modulus G" (a) and storage modulus G (b) for oxidi/ed polyacrylonilrile/silicone oil suspension of particle volume fraction 14.4 wt% at various electric field strengths. The...

The frequency dependence of storage modulus G and loss modulus G" for 1 pm silica/PDMS suspension with the particle volume fraction 10.7 vol% is shown in Figure 38. Without an electric field the loss modulus shows the typical power law behavior with G"ac at, and the storage modulus... 

However, in contrast to the cases of complex elastic modulus G and dielectric constant e, the imaginary part of the piezoelectric constant, e", does not necessarily imply an energy loss (Holland, 1967). In the former two, G"/G and e"/e express the ratio of energy dissipation per cycle to the total stored energy, but e"/e does not have such a meaning because the piezoelectric effect is a cross-coupling effect between elastic and electric freedoms. As a consequence, e" is not a positive definite quantity in contrast to G" and e". In a similar way to e, however, the Kramers-Kronig relations (Landau and Lifshitz, 1958) hold for e ... 

The mechanical properties (tensile strength, modulus) and electrical properties (resistivity, power factor) of EPDM blends with polypropylene, PP, have been shown to deteriorate during thermal aging [Roy et al., 1990]. Interestingly, cross-linked samples were more susceptible to property loss. 

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