Characteristic Dielectric Parameters

The useful properties of a dielectric ceramic material-that is, their figures of merit, and in particular for microwave applications (see Section 8.4)-can be described by  

When an electric field is applied to a dielectric ceramic material, the electrical charges within the material will shift, and a polarization is induced that is 

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Hence, strategies are required to balance e, Tj, and Q by grain boundary engineering. Several routes towards materials with improved characteristic dielectric parameters are outlined in Section 8.4.1 (see also Wersing, 1996). 

Extensive DR studies of rod-like polymers in solution covering the isotropic, biphasic and nematic states of solution have been carried out only for two different PAICs in toluene a 1/1 copolymer of n-butyl- and n-nonyl isocyanate (PBNIC) and homopoly(n-hexyl isocyanate) (PHIC). The relaxation process was studied as a function of both concentration and temperature. Only one relaxation process, with a broad distribution of relaxation times, was observed in the isotropic and nematic phases up at relatively low frequencies (10" --10 Hz) (see Fig. 4.15). The most important results are summarized in Fig. 4.16. All three characteristic dielectric parameters—the dielectric increment A8, the maximum of the loss factor 8, and the logarithm of the mean relaxation rate /c—undergo significant changes across the isotropic-biphasic-nematic concentration range. 

A method which circumvents many of the disadvantages of the transmission line and cavity perturbation technique was pioneered by Stuchley and Stuchley (1980). This technique calculates the dielectric parameters from the microwave characteristics of the reflected signal at the end of an open-ended coaxial line inserted into a sample to be measured. This technique has been commercialized by Hewlett Packard with their development of a user-friendly software package (Hewlett Packard 1991) to be used with their network analyzer (Hewlett Packard 1985). This technique is outstanding because of its simplicity of automated execution as well as the fact that it allows measurements to be made over the entire frequency spectrum from 0.3 MHz to 20 GHz. 

Three dielectric parameters are characteristic of the electrical and viscous properties of tissue water a) the conductance of ions in water, b) the relaxation frequency fc, and c) the static dielectric permittivity eQ observed at f fc =... 

Various organic solvents were used as reactionary medium at nonequilibrium polycondensation in solution realization [96]. The solvent type influence on the synthesis reaction main characteristics (conversion degree Q and molecular weight MM) is well known and is explained usually by solvent various characteristics (dielectric constant, solubility parameter, heat of dissolution and so on) [96]. However, up to now the indicated effects general theoretical explanation is not obtained. Besides, at the solvent type influence analysis its correlation with polycondensation process quantitative characteristics (the same Q and MM) is usually considered, but any changes of polymer structure or reaction mechanism are not assumed, although the possibility of side reactions is noted repeatedly [96]. The authors [71, 127] studied the solvent influence on the enumerated above characteristics on die example of the rules of chloranhydride of terephthalic acid and phenolfthaleine low-temperature polycondensation (polyarylate F-2), performed in 8 different solvents [128]. 

Electrostatic fields, local hydrogen ion concentration, ionic strength, dielectric constants, and strong macromolecular interactions have a marked effect on the characteristic kinetic parameters of enzymes. 

Study of dielectric parameters by the AC method is one of the earliest and commonly used techniques. The measurement of dielectric loss as a funetkm of temperature at fixed frequencies or vice versa shows maxima at a characteristic telaxatioo temperature/ frequency of the polymer. The dielectric constant shows dispershm regions corresponding to various types of polarization processes. Glass transition phenomena in several polymers have bwn investigated by AC dielectric studies [326327]. 

Parameters (ii)-(vii) depend on the dielectric, mechanical and optical properties of the mesogens. To optimize a dis compromise between different molecular characteristics is often required and mixtures of liquid crystals are usually commercial displays. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

Various theoretical and empirical models have been derived expressing either charge density or charging current in terms of flow characteristics such as pipe diameter d (m) and flow velocity v (m/s). Liquid dielectric and physical properties appear in more complex models. The application of theoretical models is often limited by the nonavailability or inaccuracy of parameters needed to solve the equations. Empirical models are adequate in most cases. For turbulent flow of nonconductive liquid through a given pipe under conditions where the residence time is long compared with the relaxation time, it is found that the volumetric charge density Qy attains a steady-state value which is directly proportional to flow velocity... 

Azo-bridged ferrocene oligomers also show a marked dependence on the redox potentials and IT-band characteristics of the solvent, as is usual for class II mixed valence complexes 21,22). As for the conjugated ferrocene dimers, 2 and 241 the effects of solvents on the electron-exchange rates were analyzed on the basis of the Marcus-Hush theory, in which the t/max of the IT band depends on (l/Dop — 1 /Ds), where Dop and Ds are the solvent s optical and static dielectric constants, respectively (155-157). However, a detailed analysis of the solvent effect on z/max of the IT band of the azo-bridged ferrocene oligomers, 252,64+, and 642+, indicates that the i/max shift is dependent not only on the parameters in the Marcus-Hush theory but also on the nature of the solvent as donor or acceptor (92). 

In the first row the relative dielectric constant for the compound is given. In the second row the valency of the unit is given. The other rows give the values for the various FH parameters. Remaining parameters the characteristic size of a lattice site 0.3 nm the equilibrium constant for water association K — 100 the energy difference for a local gauche conformation with respect to a local trans energy it/ 8 — 0.8 A T the volume fraction in the bulk (pressure control) of free volume was fixed to (pbv = 0.042575... 

The electrochemical etch-stop technology that produces the silicon island is rather complex, so that an etch stop directly on the dielectric layer would simplify the sensor fabrication (Sect. 4.1.2). The second device as presented in Fig. 4.6 was derived from the circular microhotplate design and features the same layout parameters of heaters and electrodes. It does, however, not feature any sihcon island. Due to the missing heat spreader, significant temperature gradients across the heated area are to be expected. Therefore, an array of temperature sensors was integrated on the hotplate to assess the temperature distribution. The temperature sensors (nominal resistance of 1 kfl) were placed in characteristic locations on the microhotplate, which were numbered Ti to T4. 

The data were fitted to a stretched exponential function (Eq. 4.9) setting the stretching parameter to its dielectric value. The solid lines included in Fig. 6.3 display the resulting curves. These fits lead to the Q-dependent characteristic relaxation times TKww(Q)> hich are converted to average relaxation times by Eq. 5.25 (see Fig. 6.4). 

Dielectric Characteristics. Fig. 30 reveals that at low frequency (10 kHz-100 Hz) the permittivities obey the trend PVC < PVC-DMG-Cu(II) < PVC-DMG-Ni(II) < PVC-DMG-Co(II). The permittivities fall monotonously with the applied frequency. The dielectric loss (tan 8) parameter also falls steadily with the applied frequency. However, PVC-DMG-Co(II) exhibits a comparatively large fall in tan 8 from 2.5 to 0.2 in the frequency range (100 KHz-10 MHz), while... 

In all the above three polymers only a single process is apparently observed in the time window for PCS (10-6 to 100 s). The shape of the relaxation function is independent of temperature. The temperature dependence of (r) follows the characteristic parameters observed for mechanical or dielectric studies of the primary (a) glass-rubber relaxation. Relaxation data obtained by many techniques is collected together in the classic monograph of McCrum, Read and Williams41. The data is presented in the form of transition maps where the frequencies of maximum loss are plotted logarithmically... 

The frequency dependence of e and e" and their magnitudes control the extent to which a substance is able to couple with the microwave radiation and therefore are fundamental parameters for interpreting the dielectric heating phenomenon. Although tan 8 is a helpful parameter for comparing the heating rates of a series of dielectrics with similar physical and chemical characteristics, for more complex mixtures expressions, which take into account the complexity of the electric field pattern, the heat capacity of the compound and the density, have been proposed. 

Modeling of High-Speed Interconnections. Modeling the electrical behavior of an interconnection involves two steps. First, the transmission line characteristics, such as the characteristic impedance, propagation constant, capacitance, resistance, dielectric conductance, and coupling parameters, must be calculated from the physical dimensions and material properties of the interconnection. In addition, structures, such as wire bonds, vias, and pins, must be represented by lumped resistance (R), inductance (L), and capacitance (C) elements. 

Early work using microwaves as a diagnostic tool relied upon measuring a secondary effect of the dielectric properties of the material under interrogation, i.e., reflection, absorption and transmission. The two fundamental microwave parameters, e and e" are related to the food or material composition. These two fundamental parameters also determine the reflection, absorption and transmission of the materials exposed to a microwave signal. Thus by measuring the amplitude and phase of the reflected or transmitted wave, or the characteristics of absorption of a wave through the material, one is able to empirically establish a relationship to the constituency of the product. 

The magnitude of the dissociation constant A plays an important role in the response characteristics of the sensor. For a weakly dissociated gas (e.g., CO2, K = 4.4 x 10-7), the sensor can reach its equilibrium value in less than 100 s and no accumulation of CO2 takes place in the interior layer. On the other hand, SO2, which is a much stronger acid (K = 1.3 x 10-2), accumulates inside the sensor and its rep-sonse time is in minutes. The detection limit and sensitivity of the conductometric gas sensors also depend on the value of the dissociation constant, on the solubility of the gas in the internal filling solution, and, to some extent, on the equivalent ionic conductances of the ions involved. Although an aqueous filling solution has been used in all conductometric gas sensors described to date, it is possible, in principle, to use any liquid for that purpose. The choice of the dielectric constant and solubility would then provide additional experimental parameters that could be optimized in order to obtain higher selectivity and/or a lower detection limit. 

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