Loss tangent tan

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. 

Figure 15 Storage modulus, (E ), loss tangent (tanS), and loss modulus, (E ), as a function of temperature for P7MB and P8MB at 3 Hz.

For the microwave-assisted experiments, both solvents were replaced by 1,2-dichlorobenzene, as it couples very effectively with microwaves (loss-tangent (tan 5) at 20 °C 1,2-dichlorobenzene 0.280 as compared to 0.101 for chlorobenzene). Diels-Alder reactions of 3-methoxy or 3-phenyl pyrazinones with DMAD were performed at a pre-selected maximum temperature of 200 °C, whereas the intramolecular reaction of alkyne tethered pyrazinone required a higher temperature (220 °C). The yields obtained under microwave irradiation are comparable with those obtained under conventional conditions, while for the dihydrofuropyridinone the yield was improved from... 

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...

A constant loss tangent, tan <5 A /(co), requires dynamic moduli... 

The heating characteristics of a particular material (for example, a solvent) under microwave irradiation conditions are dependent on the dielectric properties of the material. The ability of a specific substance to convert electromagnetic energy into heat at a given frequency and temperature is determined by the so-called loss tangent, tan <5. The loss factor is expressed as the quotient tan (3 = "/ , where e" is the dielectric loss, indicative of the efficiency with which electromagnetic radiation is... 

Table 2.3 Loss tangents (tan 6) of various solvents (2.45 GHz, 20 °C) (data from [10]).

Table 7.1 Swelling behavior, loss tangents (tan <5), and boiling points for solvents used in microwave-assisted solid-phase synthesis.

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 . ...

Aside from this, the literature on the subject has largely been concerned with dynamic mechanical properties where experiments have been performed to gather data consisting of loss tangent (tan d) and storage tensile modulus (E). Rather than being... 

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... 

Note 3 For the Voigt-Kelvin behaviours specified in notes 1 and 2, the ratio of the width of the resonance curve ( Avr ) to the resonance frequency (vr) is equal to the loss tangent (tan S). 

Figure 9.9a Loss tangent (tan S) of raw tuber flesh temperature sweeps (heating). (Source Singh et al., 2008).

Microwaves. Among the lowest frequencies of interest in collisional absorption are radio- and microwaves. As will be seen below, the absorption coefficient a is extremely small at low frequencies because absorption falls off to zero frequency as of2 see Chapter 5 for details. As a consequence, it has generally been necessary to use sensitive resonator techniques for the measurement of the loss tangent, tan <5 = s"/s, where s and s" are the real and imaginary part of the dielectric constant. The loss tangent is obtained by determination of the quality factors Qa, Qo, of the cavity with and without the gas filling, as (Dagg 1985)... 

Solvent Solvent temperature (°C) Boiling point (°C) Loss tangent tan <5... 

Material Loss tangent tan 5 x 10-4 Material Loss tangent tan 6 x 10-4... 

Fig.6 Temperature dependence of the mechanical modulus, G and loss tangent, tan 5, at 1 Hz, for poly(cyclohexyl methacrylate) (from [5])...

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