Loss tangent illustrations

Figure 1.3 Dielectric spectra for range of alcohols in the frequency range of 107-10n Hz. The absolute permittivities at low frequencies fall as the size of the alcohol increases and they began to respond to the microwave fields at lower frequencies because their relaxation times become longer. The loss factors that control the efficiency of conversion of microwave into thermal energies also reach their maxima at lower frequencies. The loss tangent is the ratio of the loss factor and permittivity at that frequency. (Idealised from the raw data illustrated in Ref. 10.)...

To illustrate the transitions occurring in the glassy state, the temperature dependencies of the dynamic mechanical loss tangent at 1 Hz of the DGEBA/HMDA, DGEBA/tetramethylene diamine and DEBA/dodecamethyl-ene diamine systems [65] are shown in Fig. 93. They clearly exhibit two transitions ... 

Fig. 18. Schematic illustration of loss tangent behavior during a hypothetical cure for indicated values of the ratio L/2tb. (Reprinted from Ref. 381 with permission of Gordon and Breach Science Publishers)...

The dielectric constant and loss tangent are the substrate variables. The loss tangent is apparently related to variables such as the molecular weight, viscosity, and conductivity of the material to be dried. Some examples will serve to illustrate the difficulty in predicting the rate at which a material will be heated. 

Basic aspects of the resonance technique may be illustrated by considering a linear visco-elastic medium between two parallel plates, one undergoing forced harmonic displacement, amplitude a (= cos cat), the other being fixed. As 0) is varied, resonances occur and a resonance bandwidth analysis yields the loss tangent, tan 5 [Whorlow, 1992 Ingard 1988]. 

The sequence of events as the system passes through film resonance is illustrated schematically in Fig. 4 [25], in which the total (observed) impedance (full line) is the combination of the crystal (dotted hne), and film (dashed hne) components. As film thickness increases (moving from frame 1 to frame 5), the film component moves rapidly downwards in frequency. As it passes through the crystal component, the prediction is that the total resonance will - transiently - split into two peaks (frame 3). As the resonance condition is passed (frame 5), the response returns to a more normal appearance. More detailed theoretical exploration of this phenomenon [25] shows that both the absolute and relative values of the shear modulus components have significant influence over the resonator response. In particular, the double-peak nature of the response shown in Fig. 4 is only predicted for low loss films (i.e. films for which the loss tangent, G"jG < 1). 

Figure 5.2. Illustration of loss tangent (damping) and storage modulus characteristics for a linear amorphous polymer illustrating various distinct physical states that the polymer assumes with varying temperature or frequency (Collins et al. 1973). Reprinted with permission of John Wiley and Sons, Inc.

In many studies, isochronal measurements have been made at two or more different frequencies and the loci of maxima in the loss tangent mapped against temperature and frequency, often supplemented by dielectric and nuclear magnetic resonance data, as illustrated for polystyrene in Fig. 15-11. Here, five mechanisms... 

Pyrolytic BN in the form of a pure, dense, anistropic film can be deposited at high temperatures from a mixture of ammonia and boron halide. It has a higher electrical resistivity than hot-pressed BN (see Fig. 2.24), but its dielectric constant and loss tangent are about the same. The dielectric strength of BN is rated at 4,000 volts/mil at room temperature, which makes it an excellent insulator. As is illustrated in Fig. 2.25, the oxidation rate of pyrolytic BN is significantly less that that of pyrolytic graphite below 2000°C. 

In endeavoring to reduce the rate of oxidation many approaches have been studied in considerable detail, but none more than that of alloy selection. The corrosion rates for a typical series of commercial aluminum alloys are illustrated in Fig. 5, which demonstrates the correlation between the defect constitution of the oxide film as reflected in the dielectric loss tangent and the weight loss under standard conditions in a fixed period of time ( ). These... 

As illustrated in Appendix 1 it can be proved that the relaxation time T2 corresponds to the frequency of the maximum in dielectric loss tangent (tan ). In this method the characteristic time constant T2 was chosen from the frequency at the maximum in tan( ). Hence, by using the relation T2 = T -JS equation (20) can be modified to... 

The mechanical spectra of fully cured adhesive measured by shear rheometry, are shown In Figures 5 and 6. These figures Illustrate how modulus (loss and storage) and tangent delta vary with temperature and frequency. To evaluate the variation of mechanical properties with respect to percent conversion of an adhesive containing low boiling monomers, as In the case with the adhesive of this study. It was decided to assess only property/frequency response. 

Behavior of the d5mamie module (E ) and tangent of angle of mechani-eal loss (tg5) for eopol mier nanocomposites which content different amount of SWCNT is illustrated in Figures 7.5a and 7.5b. 

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