Dielectric permittivity versus

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. 

Three-dimensional plots of both the measured real part s and the imaginary part s" of the complex dielectric permittivity versus frequency and temperature for 20-pm-thickness PS sample are shown in Fig. 17a,b. From the figure, one can identify three distinct processes, marked by I, II, and III, defined as follows ... 

FIGURE 53 Relative dielectric permittivity versus rare earth ionic radius. The dashed lines are linear fits CrtriO = IHIO Pr and r(rR) = —52 64 Tr. 

The dielectric spectra were obtained using the samples with thicknesses ranging between 80 and 150 pm, and in the temperature -130°C to 150°C range, except for the PVDF-h-PVCN block copolymer (-130°C to 100°C) [89]. The values of the dielectric permittivities versus temperature (Figure 20.19) show the existence of two relaxations. At room temperature (100 Hz), the values for PVDF homopolymer, PVDF-h-PAN, PVDF-h-MAN, and PVDF-h-PVCN block copolymers are 6.3, 3.9, 5.0, and 5.5 respectively. 

Paddison et al. performed high frequency (4 dielectric relaxation studies, in the Gig ertz range, of hydrated Nafion 117 for the purpose of understanding fundamental mechanisms, for example, water molecule rotation and other possible processes that are involved in charge transport. Pure, bulk, liquid water is known to exhibit a distinct dielectric relaxation in the range 10—100 GHz in the form of an e" versus /peak and a sharp drop in the real part of the dielectric permittivity at high / A network analyzer was used for data acquisition, and measurements were taken in reflection mode. 

Fig. 10.2. Dielectric permittivity of Ba Sr/TiOj films versus x and annealing temperature.

Fig. 11. Standard deviation of dielectric permittivity before and after the static mixer versus the number of revolutions in the Rotocube .

Much of the unnecessary failure to use the easier, modern theory of van der Waals forces comes from its language, the uncommon form in which the dielectric permittivity is employed. For many people "complex dielectric permittivity" and "imaginary frequency" are terms in a strange language. Dielectric permittivity describes what a material does when exposed to an electric field. An imaginary-frequency field is one that varies exponentially versus time rather than as oscillatory sinusoidal waves. 

Results of dielectric studies of a series of nanocomposites based on a semiaromatic PA-1 ITIO with HAp helped to explain the structure-property relationships [Sender, 2008], For dry, neat PA-llTlO, a symmetric depolarization peak, detected by TSC near Tg measured by DSC, was attributed to dielectric dynamic glass relaxation. By DDS, two distinct high-temperature processes were distinguished when plotting the experimental data points versus HT. The dependence is displayed in Figure 13.2, where the two dashed lines show the complex dielectric permittivity fitted by the Havriliak-Negami equation ... 

Xie et al. [2005] studied the influence of BT 100-nm particles on the dielectric properties of polyimide (PI) matrix. BT is commonly used, due to its high dielectric permittivity. The dielectric permittivity (e ) of PI/BT composites versus / increases... 

Fig. 9. Reciprocal dielectric permittivity 1/e versus volume fraction of lignocellulosic material derived from hemp and flax (Markiewicz et al., 2009)...

FIGURE 20.16 Dielectric permittivity e (a) and dissipation factor tanS (b) versus temperature of P4FST homopolymer at various frequencies [88]. 

FIGURE 20.19 Dielectric permittivities of various block copolymers and PVDF versus the... 

Figure 6.30. Schematic plots of (a) the real part e of dielectric permittivity and (b) the loss factor e" versus frequency with cure time (tc) as a parameter (Tcure = constant). The higher the frequency /i, the shorter the time at which the dipolar component (a relaxation) appears as a drop in e (f) and as a maximum in "(/). Experimental evidence of the low-frequency shift of the a relaxation with the increase of U is provided by Eloundou et al. (2002).

Fig. 2.39 Transmission coefficient of omnidirectional stacks with 8 layer pairs versus incident angle for different wavelengths, TM mode. Material parr is Si/Si02 (dielectric permittivity 11.958/ 2.1316), thickness 174 and 75 nm, respectively...

FIGURE 3.31 Permittivity versus dc field for doped PMN, ST, and CT dielectrics. ... 

Broadening of the distribution of relaxation times is also found to be caused by interactions between the mesogenic units. Haase et al and Parneix et al compared the dielectric properties of two poly acrylic scLCPs with slightly different mesogenic units PA/6/-/CN and PA/6/COO/CN. Both materials demonstrate a profound difference in the quasi-static dielectric permittivity and dielectric anisotropy gJ (PA/6/ -/CN) 12 versus 8 (PA/6/COO/CH) 19, and (a — i) 65 for the former versus 12 for the latter. Consequently, the strength of the... 

The results are reported of a study of the effects of fillers and vulcanising agents on the physicomechanical and dielectric properties of EPDM. Fillers employed were kaolin, quartz, PVC and talc and the vulcanising agents were TMTD and sulphur/N-cyclohexyl-2-benzothiazyl sulphenamide. The permittivity and dielectric loss versus temperature for the vulcanisates are illustrated and the effects of thermal ageing on the physicochemical properties of the vulcanisates are discussed. 25 refs. EGYPT... 

Figure 15.14 (a) The permittivity (s ) versus the frequency (log f) for EPDM containing different concentrations of EPDM-g-MAH as compatibilizer (b) dielectric loss (e") versus the frequency (log/) for EPDM containing different concentrations of EPDM-g-MAH as compatibilizer. (Prom Reference 66 with permission from Sage publications Etd.)... 

These books remain the reference works in measuring dielectric and magnetic constants of homogeneous materials. Methods used at that time were limited in frequency band measurements, permitting only the determination of the complex permittivity and permeability at fixed frequencies and sometimes versus temperature variations. 

Figure 13.7b shows the imaginary part of the dielectric modulus, M", versus/of a PA-11/BT 700-nm nanocomposite at 72°C for volume fractions / = 0.03,0.1, and 0.2. The maximum of M" decreases when the filler content increases, due to the increase in permittivity e. The filler content does not affect the frequency dependence of the three relaxations. However, the ratio between the maximum value of the a -mode versus the maximum value of the a-mode increases with increasing filler content, indicating the interphase effects between the polymer and the nanoparticles. The low-frequency relaxation associated with the MWS phenomena become more pronounced with increasing volume filler fraction compared to the other relaxations. This evolution is attributed to the increase in interfacial effects around the particles. 

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