Dielectric-loss index

Rolla et ah, used microwave dielectric measurements to monitor the polymerization process of mono functional n-butyl acrylate as well as 50/50 w/w blends with a difunctional hexane-diol diacrylate that gave highly cross-linked networks. In these real time cure experiments the decreasing acrylate monomer concentration was studied via a linear correlation with the dielectric loss index at microwave frequencies. This correlation is a result of the largely different time scales for dipolar polarization in the monomer on one hand and in the polymerized reaction product on the other hand. 

Dielectric Loss Index. A measure of a dielectric loss defined by the product of the power factor and the permittivity (dielectric constant). 

Fig. 28. Schematic representation of the dielectric constant and dielectric loss index as a function of frequency.

By monitoring the insulation condition of the windings during maintenance, at least once a year, which can be carried out by measuring (a) the polarization index (Section 9.5.3) and (b) the dielectric loss factor, tan S (Section 9.6) and making up the insulation as in Section 9.5.2, when the condition of the insulation is acceptable and only its level is less than permissible. 

The dielectric constant (permittivity) and loss index are determined by ASTM-D150. Permittivity is the ratio of the capacitance of the polymer to that of air. 

The loss index of silicone elastomers made from polydimethyl siloxane, generally speaking, is low due to their low values of dielectric constant and loss tangent. The dielectric constant of polydimethylsiloxane is almost independent of the frequency, where as the tan 6 is highly dependent on the frequency in the micro-wave region (3, 4 ) At 3 x 109 Hz, a 1000 cs polydimethylsiloxane fluid has a tan 6 of about 0.0096 and a dielectric constant of 2.76. This gives a loss index of 0.0264, which puts polydimethyl siloxane in the poor heatability category. 

In the former approach, the loss index can be increased by changing the substituents on silicone. Vincent et al (5 ) reported that as the R group in Me3SiO(MeRSiO)xSiMe3 was changed from methyl to a bulky polar group, the dielectric constant and loss factor increased drastically. This is shown in Table I. 

Solution In the case of harmonic motion, for which Sj= joiSj, Equation 2.17 implies that attenuation may be accounted for by representing the elastic constants cjj by complex elastic constants cu + jmr u. (This is analogous to accounting for dielectric loss in electromagnetic and optical waveguides by the well-known method of postulating a complex dielectric constant or a complex index of refraction.) Equation 2.13, the lossless wave equation for this shear wave, becomes... 

ASTM D150 Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation includes the determination of relative permittivity, dissipation factor, loss index, power factor, phase angle, and loss angle through specimens of solid electrical insulating materials when the standards used are lumped impedances. The frequency range that can be covered extends from less than 1 Hz to several hundred megahertz. 

The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. 

At microwave frequencies in the range 72-145 GHz, the critical parameters for high-power transmission are the dielectric characteristics of the window material the dielectric loss factor tan 5 and the permittivity e[. (or the refractive index n = because they affect power absorption and reflection [42]. The dielectric loss factor tan 8 in low loss samples is usually measured as the decrease in the Q factor of a resonant cavity [43]. Low dielectric loss materials find application as the output windows of high-power microwave tubes. A specific case is that of windows for Gyrotron tubes operating in the 70-170 GHz frequency region with output powers in excess of 1 MW, as will be discussed later. 

The critical parameters for high-power windows are the dielectric characteristics of the window material the dielectric loss-factor tan 6 and the permittivity 8r (or the refractive index n = r,r -) because they affect power absorption and reflection. The power absorption coefficient a is related to tan 6 by [43]... 

Now, we turn our attention to the dielectric relaxation. The decrease of dynamic dielectric constant Ae and the dielectric loss e" have the mode distribution (cf. Equation 3.18) formally identical to the viscoelastic mode distribution, and the above explanation for the viscoelastic relaxation applies also to the dielectric relaxation For the simplest case, the relaxation times and nonnormalized intensities of fhe dielectric modes exhibit the same change with T irrespective of the mode index q as... 

There are various methods of the glass transition temperature evaluation based on temperature dependence of polymer physical properties in the interval of glass transition 1) specific volume of polymer at slow cooling (dilatometric method) 2) heat capacity (calorimetric method),3) refraction index (refractometric method) 4) mechanical properties 5) electrical properties (temperature dependence of electric conductivity) or maximum of dielectric loss 6) NMR ° 7) electronic paramagnetic resonance, etc. 

The numerical value of the glass-transition temperature depends on the rate of measurement (see Section 10.1.2). The techniques are therefore subdivided into static and dynamic measurements. The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. Static and dynamic glass transition temperatures can be interconverted. The probability p of segmental mobility increases as the free volume fraction / Lp increases (see also Section 5.5.1). For /wlf = of necessity, p = 0. For / Lp oo, it follows that p = 1. The functionality is consequently... 

Fig. 16-15. Frequency-temperature contours of dielectric constants, e, and loss index, e", for nylon.

Fig. 1 Schematic frequency dependence of (a) the relative permittivity, s (v), and (b) the total loss, T "(v) dashed line), and the dielectric loss, s"(v) solid line), of a sample with dc conductivity, static relative permittivity, 8, infinite-frequency permittivity, and optical refractive index,...

The chemical and therefore structural nature of the polymer determines Tg. For most commercial polymers, values lie in the range — 100 °C to 250 °C as illustrated in Table 1.1. The value can be >250°C (e.g. in thermosets) but decomposition often occurs before it is reached. Tg can be determined by any technique which shows a change in a particular property of the polymer with temperature, e.g. density, modulus, heat capacity, refractive index, dielectric loss, X- and j8-ray adsorption, gas permeability, proton and NMR. The value of Tg can be obtained from plots of the magnitude of this property against temperature and is indicated by a break in linearity. Figure 1.4 shows modulus (i.e. strength) v. temperature and Figure 1.5 specific volume v. temperature for a typical polymer. 

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