The Loss Tangent

Loss tangent plotted logarithmically for the eight systems identified as in Fig. 2-1. 

For the very lightly cross-linked polymer (curve VII), there is a subsidiary maximum at lower frequencies associated with the losses involved in entanglement slippage as discussed in connection with J(t) and J . In this case, also, the maximum in J lies to the left of that in tan d. Smaller maxima occur in the curves for the glassy and highly crystalline polymers, reflecting other dissipative mechanisms. 

The loss tangent determines such macroscopic physical properties as the damping of free vibrations, the attenuation of propagated waves, and the frequency width of a resonance response. It can often be more conveniently measured than any other viscoelastic function, by observations of these phenomena, and is of considerable practical interest. It is less susceptible of direct theoretical interpretation than the other functions, however. 

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The loss tangent rather than the loss modulus is plotted, also at 1 Hz. 

A diblock copolymer, 71% polyisoprene (1) by weight and 29% polybutadiene (B), was blended in different proportions into a 71%-29% mixture of the individual homopolymers. The loss tangent was measured as a function of temperature for various proportions of copolymer. Two peaks are observed ... 

The position of the loss tangent maximum is quite different for pure B and pure I, indicating distinctly different Tg values for the two. 

Briefly explain each of the following points Does it make sense that the loss tangent is larger when a condition of poor adhesion exists between the cord and the rubber Is the adhesive effective Is it equally effective for both of the cord materials ... 

Dynamic techniques are used to determine storage and loss moduli, G and G respectively, and the loss tangent, tan 5. Some instmments are sensitive enough for the study of Hquids and can be used to measure the dynamic viscosity T 7 Measurements are made as a function of temperature, time, or frequency, and results can be used to determine transitions and chemical reactions as well as the properties noted above. Dynamic mechanical techniques for sohds can be grouped into three main areas free vibration, resonance-forced vibrations, and nonresonance-forced vibrations. Dynamic techniques have been described in detail (242,251,255,266,269—279). A number of instmments are Hsted in Table 8. Related ASTM standards are Hsted in Table 9. 

The loss tangent should be measured on the samples at room temperature at voltages varying from 20% to... 

However, use of the loss tangent in Eq. (13) is an oversimplification. Instead, we shall make use of an empirical dissipation law obtained in the study of rate-dependent adhesion of elastomers (19). Maugis and Barquins [19], in order to explain the dynamic adhesion of elastomers in a variety of test configurations (peel, flat punch, etc), proposed the following relation ... 

Fig. 21. Loss tangent, tan 3, for five partially crosslinked PDMS samples at different extents of reactions. For the liquid, a negative slope is observed. At the LST, tan 3 is independent of frequency. The loss tangent of the solid material exhibits a positive slope...

There are also some far-fetched proposals for the LST a maximum in tan S [151] or a maximum in G" [152] at LST. However, these expectations are not consistent with the observed behavior. The G" maximum seems to occur much beyond the gel point. It also has been proposed that the gel point may be reached when the storage modulus equals the loss modulus, G = G" [153,154], but this is contradicted by the observation that the G — G" crossover depends on the specific choice of frequency [154], Obviously, the gel point cannot depend on the probing frequency. Chambon and Winter [5, 6], however, showed that there is one exception for the special group of materials with a relaxation exponent value n = 0.5, the loss tangent becomes unity, tan Sc = 1, and the G — G" crossover coincides with the gel point. This shows that the crossover G = G" does not in general coincide with the LST. 

TANDEL is the loss tangent, GSP and GDP is the loss modulus. is the storage modulus... 

Figure 3. Plot of the loss tangent with temperature for Hytrel in the temperature range of 0 to 140 Deg. The x s represent the experimental values, while the solid line represents the results of smoothing using the Savitzky-Golay technique.

Figure 5. The loss tangent (tan 8) plotted as a function time during a UV cross-linking reaction. All the values of tan 8 for the different frequencies intersect at the gel time of 1660 s, indicating that the sample has reached its gd point. Here, the incident UV light intensity is 0.02 mW cm . ...

Nakao, T., Okano, T. and Asano, I. (1983). Effects of heat treatment on the loss tangent of wood. Mokuzai Gakkaishi, 29(10), 657-662. 

When the relaxation time lo = tpa is long, mo is a slow varying function of time and may be approximated by a constant. In addition, the relaxation rate is known to be quite small and, therefore, can be related to the loss tangent by the equation (19)... 

Note 2 The ratio of the loss to the storage flexural modulus (E7E ) is derived from the loss tangent (tan 5) of the forcedflexural oscillation with... 

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