Permittivity glass

C = Q/V. In a vacuum, the charge density on the surfaces of the conductors is affected by the permittivity of free space, q. When a dielectric material is placed between the conductors, the capacitance increases because of the higher permittivity, e, of the material. The ratio of e and q gives the dielectric constant, K, of the material, k = e/eg The dielectric constant of siHca glass is 3.8. 

An alternative electrical method that has been used in the study of glass-ionomer cements has been the measurement of dielectric properties. Tay Braden (1981, 1984) measured the resistance and capacitance of setting cements at various times from mixing. From the results obtained, relative permittivity and resistivity were calculated. In general, as these cements set, their resistivity was found to fall rapidly, then to rise again. Both these results and the results of relative permittivity measurements were consistent with the cements comprising highly ionic and polar structures. 

The ratio of permittivity with the dielectric to the permittivity in vacuum, e/eo, is called the relative permittivity, s, or dielectric constant. The dielectric constant is a material property. Some values of dielectric constants for common ceramic and glass insulators are given in Table 6.3. Since a polarizable material causes an increase in charge per unit area on the plates of a capacitor, the capacitance also increases, and it can be shown that the dielectric constant is related to the capacitance and displacement in vacuum and with the dielectric material as follows ... 

Most of the physical properties of the polymer (heat capacity, expansion coefficient, storage modulus, gas permeability, refractive index, etc.) undergo a discontinuous variation at the glass transition. The most frequently used methods to determine Tg are differential scanning calorimetry (DSC), thermomechanical analysis (TMA), and dynamic mechanical thermal analysis (DMTA). But several other techniques may be also employed, such as the measurement of the complex dielectric permittivity as a function of temperature. The shape of variation of corresponding properties is shown in Fig. 4.1. 

Figure 4.1 Variation of physical properties vs temperature, used to determine the glass transition (a) volume (V) or enthalpy (H) (b) expansion coefficient (a) or heat capacity (cp) (c) storage modulus (E ) (d) dissipation modulus (E") and dumping factor (tan 8) (e) real part of the complex dielectric permittivity (s ) (f) imaginary part of the complex dielectric permittivity (e").

Dielectric permittivity and loss for both polymers under study can be observed on Figs. 2.17 and 2.18. In both figures a prominent peak corresponding to the dynamic glass transition temperature can be observed, which at low frequencies is overlapped by conductivity effects. Moreover, in both polymers a broad secondary peak is observed at about -50°C. This peak is more prominent in P2tBCHM which is in good... 

Figures 2.31 and 2.32 show the dielectric permittivity and loss for poly(cyclobutyl methacrylate) (PCBuM) and poly(cyclobutylmethyl methacrylate) (see Scheme 2.5). In these figures the a relaxation is associated to the glass transition temperature and the p relaxation appear as a shoulder of the a relaxation.

Figures 2.37 and 2.38, show the isochronal curves of the permittivity and loss factor for P2NBM and P3M2NBM as a function of temperature at fixed frequencies. A prominent relaxation associated with the dynamic glass transition is observed in both polymers. Clearly the effect of the methyl substitution in position 3 of the norbornyl group is to decrease the temperature of this relaxational process.

Figure 2.40 show the loss permittivity of P4THPMA where three subglass absorptions, labeled as 5, y and j3 relaxations, centered at 140, 190, and 260 K at 1 Hz respectively, followed in the increasing order of temperatures by glass-rubber process or a relaxation located at 420 K at the same frequency. 

Figures 2.82, 2.83, and 2.84 illustrate the dielectric permittivity and loss for PD-CBI, PDCHpI and PDCOI at different frequencies. The a relaxation associated to the glass transition is clearly observed in these Figures. The P relaxation is also observed as a shoulder in the low temperature side of the a relaxation. Moreover, Y and 5 relaxations are also present depending on the structure of the polymer. Particularly, for PDCHpI only a weak subglass activity is observed in the low range of temperatures.

Fig. 2.37 Permittivity dispersion and dielectric loss for a glass 18 Na2O-10CaO-72SiO2 (after Taylor, H.E., J. Soc. Glass Tech., 43, 124T, 1959. Also see Rawson, H. Properties and Applications of Glass. Elsevier, Amsterdam, p. 266, 1980).

Fig. 20. Plot of permittivity and loss factor versus temperature for EPON 828 resin in the vicinity of the glass transition. (Reprinted from Ref.461 with permission oftheauthors)...

Discussion of the dipolar relaxation involves two issues first, the average dipolar mobility at a given temperature and degree of conversion, as measured by the frequency of the maximum in the loss factor fmax (or by its reciprocal, the typical dipolar relaxation time xd), and, second, the detailed distribution of relaxation times as measured by the frequency dependence of the permittivity and loss factor. In spite of the clear evidence that the dipolar relaxation is associated with the glass transition... 

In Section 4, we have examined, from a fundamental point of view, how temperature and cure affect the dielectric properties of thermosetting resins. The principal conclusions of that study were (1) that conductivity (or its reciprocal, resistivity) is perhaps the most useful overall probe of cure state, (2) that dipolar relaxations are associated with the glass transition (i.e., with vitrification), (3) that correlations between viscosity and both resistivity and dipole relaxation time are expected early in cure, but will disappear as gelation is approached, and (4) that the relaxed permittivity follows chemical changes during cure but is cumbersome to use quantitatively. 

The third relaxation process is located in the low-frequency region and the temperature interval 50°C to 100°C. The amplitude of this process essentially decreases when the frequency increases, and the maximum of the dielectric permittivity versus temperature has almost no temperature dependence (Fig 15). Finally, the low-frequency ac-conductivity ct demonstrates an S-shape dependency with increasing temperature (Fig. 16), which is typical of percolation [2,143,154]. Note in this regard that at the lowest-frequency limit of the covered frequency band the ac-conductivity can be associated with dc-conductivity cio usually measured at a fixed frequency by traditional conductometry. The dielectric relaxation process here is due to percolation of the apparent dipole moment excitation within the developed fractal structure of the connected pores [153,154,156]. This excitation is associated with the selfdiffusion of the charge carriers in the porous net. Note that as distinct from dynamic percolation in ionic microemulsions, the percolation in porous glasses appears via the transport of the excitation through the geometrical static fractal structure of the porous medium. 

The dielectric relaxation at percolation was analyzed in the time domain since the theoretical relaxation model described above is formulated for the dipole correlation function T(f). For this purpose the complex dielectric permittivity data were expressed in terms of the DCF using (14) and (25). Figure 28 shows typical examples of the DCF, obtained from the frequency dependence of the complex permittivity at the percolation temperature, corresponding to several porous glasses studied recently [153-156]. 

Figure 14. Imaginary part of the dielectric permittivity e,(co) of (a) fluoroaniline (7 — 173 K) and (b) toluene (Tg = 117 K), both type B glass formers showing in addition to the main relaxation (a-process) a secondary relaxation peak (p-process) numbers indicate temperature in K. Unfilled symbols represent data obtained from a broad-band spectrometer [6,153]. Filled symbols represent data from a high-precision bridge [137] interpolations for fluoroaniline (solid lines) were done by applying the GGE distribution (a-process) and a Gaussian distribution (p-process) of relaxation times [142], and these for toluene (dashed lines) were done by the gamma distribution (a-process) and a Gaussian distribution (p-process) [6] (cf. Section IV.C.2).

Fig. 1. Normalized imaginary part of the dielectric permittivity of (a) GL (Tg = 189 K, compiled from Refs. 19, 22, 27) and (b) dielectric permittivity of TOL (Tg = 117 K, compiled from Refs. 19, 28). The latter glass former shows a second relaxation peak persisting below Tg. For GL, a lit (solid line) covering all the relaxation contributions above Tg is shown.38,39 In the case of TOL, the lit based on Eqs. (2) and (3) describes both a- and p-process.

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