Dielectric loss factors

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

Electrical Properties. AH polyolefins have low dielectric constants and can be used as insulators in particular, PMP has the lowest dielectric constant among all synthetic resins. As a result, PMP has excellent dielectric properties and alow dielectric loss factor, surpassing those of other polyolefin resins and polytetrafluoroethylene (Teflon). These properties remain nearly constant over a wide temperature range. The dielectric characteristics of poly(vinylcyclohexane) are especially attractive its dielectric loss remains constant between —180 and 160°C, which makes it a prospective high frequency dielectric material of high thermal stabiUty. 

The observed dielectric constant M and the dielectric loss factor k = k tan S are defined by the charge displacement characteristics of the ceramic ie, the movement of charged species within the material in response to the appHed electric field. Discussion of polarization mechanisms is available (1). 

Theory of dielectric loss factor or dissipation factor (tan 5) 9/227... 

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 tests for insulation resistance and dielectric loss factor should, however, be carried out on a completed machine also with formed coils to establish reference data for field tests, as noted in Section 9.6. However, these tests on a completed machine with formed coils do not monitor the process quality of insulation. 

Table 11.5 Highest permissible values of loss tangent or dielectric loss factor at rated voltages not exceeding 11 kV...

For lower voltage systems, say. 2.5 to lU kV, measurement of dielectric loss factor tan 5. along similar lines, to those recommended... 

Dielectric loss The dielectric loss factor represents energy that is lost to the insulator as a result of its being subjected to alternating current (AC) fields. The effect is caused by the rotation of dipoles in the plastic structure and by the displacement effects in the plastic chain caused by the electrical fields. The frictional effects cause energy absorption and the effect is analogous to the mechanical hysteresis effects except that the motion of the material is field induced instead of mechanically induced. 

FIGURE 31.14 (a) Variation of the dielectric constant with temperature at different radiation doses, (b) Variation of the dielectric loss factor with temperature at different radiation doses. (From Banik, I., Chaki, T.K., Tikku, V.K., and Bhowmick, A.K., Angew. Makromol. Chem., 263, 5, 1998. With permission.)... 

Microwave energy is not transferred primarily by conduction or convection as with conventional heating, but by dielectric loss [28]. The dielectric loss factor (loss factor, e") and the dielectric constant (e ) of a material are two determinants of the efficiency of heat transfer to the sample. Their quotient is the dissipation factor (tan 8),... 

Fig. 1.55.5. The take-of frequency, at a given temperfature, occurs at the first minimunm in the dielectric loss factor (e ) versus frequency curve as frequency increases (Fig. 9 from [ 1.126]).

Morris et al. [1.126] proposed to use dielectric analysis (DEA) to predict the collapse temperature of two component systems. The background of DEA is explained and the take off frequency (TOF) is chosen as the best analytical method to identify the collapse temperature. Figure 1.55.5 shows the dielectric loss factor as a function of the frequency. 

The electric properties of polymers are also related to their mechanical behavior. The dielectric constant and dielectric loss factor are analogous to the elastic compliance and mechanical loss factor. Electric resistivity is analogous to viscosity. Polar polymers, such as ionomers, possess permanent dipole moments. These polar materials are capable of storing... 

The technique for monitoring the dielectric loss factor is relatively simple. Two metal electrodes are placed opposite each other at critical locations on opposite sides of the mold. When the sheet molding compound (SMC), is placed between the electrodes, a capacitor is formed. The dielectric power loss is monitored continually throughout the molding cycle, as outlined in Section 6.1.2.2. 

Figure 6.44 Dielectric loss factor as a function of cure time and frequency of the oscillating electric field in a fiber-reinforced polymer. Reprinted, by permission, from P. K. Mallick, Fiber-Reinforced Composites, p. 365. Copyright 1988 by Marcel Dekker, Inc.

In order to quantify diffiisional effects on curing reactions, kinetic models are proposed in the literature [7,54,88,95,99,127-133]. Special techniques, such as dielectric permittivity, dielectric loss factor, ionic conductivity, and dipole relaxation time, are employed because spectroscopic techniques (e.g., FT i.r. or n.m.r.) are ineffective because of the insolubility of the reaction mixture at high conversions. A simple model, Equation 2.23, is presented by Chem and Poehlein [3], where a diffiisional factor,//, is introduced in the phenomenological equation, Equation 2.1. 

Two other important electrical properties must be taken into consideration when polymers are used as insulation for a high-voltage power cable or electronic wires. ° These are the dielectric constant and the dielectric loss factor, which characterize the energy dissipation in the insulation, the capacitance, the impedance, and the attenuation. 

For many applications low-temperature flexibility of the plasticized composition is also important. Plasticizers of low viscosity and low viscosity-temperature gradient are usually effective at low temperature. There is also a close relationship betv/een rate of oil extraction and low-temperature flexibility plasticizers effective at low temperature are usually rather readily extracted from the resin. Plasticizers containing linear alkyl chains are generally more effective at low temperature than those containing rings. Low-temperature performance is evaluated by measuremen t of stiffness in flexure or torsion or by measurement of second-order transition point, brittle point or peak dielectric loss factor. 

Here e represents the relative values of permittivity with respect to that of free space. The term permittivity is not in common usage in the United States in the field of food science. Instead, the term dielectric constant is used. Thus, in Equation 1, e is called the complex dielectric constant, e, the dielectric constant and e", the dielectric loss factor. 

Where Pv is the power absorbed per unit volume (watt/cm ), f, the frequency (GHz), e" the dielectric loss factor and E the rms electric field (volt/cm). 

Ions in a food oscillate transversely under the influence of the microwave electric field, colliding with their neighboring atoms or molecules. These collisions impart molecular motion which is defined as heat. Materials with mobile ions are conductive. The more available ions in a food, the higher the electrical conductivity. Microwave absorption in a food thus increases with its ionic content. The portion of microwave absorption due to ionic conduction can be described as a portion of the dielectric loss factor, ec. Geyer (1990) recently discussed this concept in his publication. 

Figure 3. Dielectric Loss Factor vs. Frequency (Adapted from Roebuck et al. 1972)...

Distell Industries (1993) has developed hand-held instruments for the measurement of fat content in fish and meat. The technology evolved from the knowledge that the dielectric loss factor of fish has a reasonably linear dependence on water content (Ohlsson et al. 1974). In fish, fat accumulates at the expense of water and protein, making estimation of fat content based on water content practical (Kent 1990). In meat products, fat accumulation is independent of water and protein, i.e., it is additive, and thus makes the calculation of fat based on water amount more difficult. A hand-held meat instrument has been developed, but requires calibration depending on the type of meat measured. 

---