Nonideal dielectric

The piezoelectric response investigation also provides direct evidence that significant inelastic deformation and defect generation can occur well within the elastic range as determined by the Hugoniot elastic limit. In quartz, the Hugoniot elastic limit is 6 GPa, but there is clear evidence for strong nonideal mechanical and electrical effects between 2.5 and 6 GPa. The unusual dielectric breakdown phenomenon that occurs at 800 MPa under certain... 

Other considerations aside, the use of dilute reagents minimizes effects of nonideality. This allows the use of concentrations in place of activities. Of course, the time scale, the sensitivity of the analytical method at different concentrations, and the use of other reaction components introduce additional considerations. Tied closely to this decision is the choice of solvent. Reaction rates may (or may not) be affected by such variables as polarity, dielectric constant, hydrogen-bonding ability, donor capacity, and viscosity. A change in solvent may change not only the rate but also the mechanism and possibly even the products. One cannot even assume that the net reaction is the... 

Capacitance as a function of charge was calculated.79 The capacitance curves showed a single hump, near qM = 0, and leveled off for qM about 10 /xC/cm2 on either side of the potential of zero charge, due to the dielectric saturation of the dipole system. The limiting values of the capacitance increased with increasing electron density of the metal. The nonideality of the metal was shown to... 

As previously discussed, silicon dioxide appeared to be a nonideal gate dielectric to be used with silicon carbide in UMOS configuration. Different design solutions used to protect SiO gate dielectric from a high electric field in SiC UMOSFETs resulted in dramatically complicated transistor structure. Because of the problems with SiC UMOSFET, the classical vertical double-diffused MOSEET (VDMOS)... 

Examination of complexation in such systems through spectroscopic means seems appropriate. The author believes that with such an approach a comparison of complexation properties in the solution and exchanger phases would be most useful and informative. All spectral peaks common to both phases were expected to permit a meaningful comparison of nonideality terms in the resin and solution phases to show the influence of dielectric change " in the exchanger phase introduced by the organic content of the ion-exchanger three-dimensional matrix. 

The complete theory of the field quantization in media with moving nonideal boundaries is not available at present. The field quantization in spatially inhomogeneous, but nonabsorbing dielectrics has been studied [292,293], and the same problem for nonabsorbing media with time-dependent parameters has also been considered [217-219,222]. The case of absorbing media has been analyzed [294-297]. The theory of the field quantization in leaky cavities has been developed [298-300]. However, in all those studies the boundaries were fixed. Because of the complexity of the problem, only a few of the simplest models have been considered up to now in the case of moving walls. 

The above approaches to treatments of nonideal surface films rely upon empirical adjustable parameters to produce waves with the shapes of experimental ones. By taking into account the interfacial potential distribution (related to such factors as the dielectric constants of film and solution, the concentrations of electroactive adsorbate and supporting electrolyte, and the film thickness) the shape of the cyclic voltammetric curves can also be modeled without the need for such parameters (39). 

The total current in the dielectric is thus made up of two components that are 90° out of phase with each other and have to be added vectorially. as shown in Fig. 14.4. The total current in a nonideal dielectric will thus... 

In a nonideal dielectric, however, the loss current and voltage are in phase, and... 

Figure 14.5 (a) Apparatus for measuring the dielectric constant of a material L is the inductance of the coil, h) The actual response of a nonideal dielectric to an applied voltage is such that the angle between the current and voltage is not 7t/2, but 7t/2 — (c) Equiva-... 

Useful exploratory studies of acid-base behaviour in solvents of low dielectric constant have been made by conductance " and potentio-metric " titrations. Association constants are usually obtained from spectrophotometric measurements. The strengths of various bases can be compared by means of their association with an indicator acid like 2,4-dinitrophenol. If both acid and base are colourless, a competition for the base can be established between the acid and an indicator acid like bromophthalein magenta In solvents like benzene, other reactions than simple 1 1 association between B and RX may occur. Self-association of the acid or base is one such auxiliary reaction. A classic example is the dimerisation of carboxylic acids in benzene. If allowance is not made for this, constant values of the quotient [BRX]j[B][RX] will not be obtained. (Variations in the quotient cannot be attributed to interionic forces or other nonideal behaviour BRX is scarcely dissociated into ions at all and in spectrophotometric work very low concentrations of B and RX can be used.) Evidence for association ratios other than 1 1 can be obtained from indicator studies. The method developed by Kolthoff and Bruckenstein for studying reactions in anhydrous acetic acid fails for reactions in benzene and similar solvents because more than one acid molecule reacts with the indicator to give complexes of the form/w J r"(HX)yi. In such studies it is generally a good approximation... 

With current flow, an ideal resistor dissipates heat energy the energy is lost as electrical energy. However, an ideal capacitor stores electrical energy. In a nonideal capacitor, there are dielectric losses and perhaps losses from a DC current. The stored energy may be partially lost, and completely lost with time (relaxation). As long as a device, a black box or real tissue, has flie ability to store electrical energy, it contains some form of capacitors (or inductors). 

The reactive power Wr is pumped to and from the capacitor each quarter period, but the net supplied energy is zero. The capacitive, quadrature current just pumps electrons charging the plates. The quadrature current causes no heating of the dielectric, but the current in the wires is real and causes heat losses if the wires are nonideal. 

For polymeric systems in the most cases, the measured dielectric loss is much broader and in addition the loss peak is asymmetric. This is called non-Debye or nonideal relaxation behavior. Formally such a non-Debye-like behavior can be described by a supposition of Debye functions... 

FIGURE 11.10 Electrical circuit of the parallel mounting of a capacitive common phase element and a resistor representing the generalized Cole-Cole model of nonideal dielectric relaxation. 

It should be noted, though that defective semiconductors - for instance oxide layers on metals - typically do not show an ideal capacitive behavior which often leads to a strong frequency-dependence of the capacitance. There are many possible reasons for non-ideal behavior such as ionic participation , a frequency-dependent dielectric constant, contributions from the Helmoltz-layer or from surface states, non-ideal structure or nonideal donor distribution, as well as inhomogeneous depth distribution in the composition or structure of the oxide layer. Independent of the origin of the non-ideal behavior, the frequency dispersion can partially be corrected by replacing the capacitance in impedance fits by a so-called constant phase element (CPE), which takes into consideration the non-ideal nature of a capacitance. While the introduction of CPE may eliminate the... 

Theoretical modeling of the experiment was carried out using two approaches that led to the same solution. Simulations were also performed to include nonidealities like finite rise time that are exceedingly difficult to solve analytically. Time-of-flight measurement of drift mobility was performed in organic transistors with varying semiconductors and dielectrics that were produced by different methods of fabrication. 

While up to a certain degree solute-induced effects occur in all types of (nonideal) solutions, its manifestation in electrolyte systems deserves special attention. The presence of charged species in a dielectric solvent adds an important ingredient to the solvation phenomenon, i.e., the possible formation of neutral ion pairs. In fact, an outstanding property of water as a solvent at normal conditions is its intrinsic ability to solvate, and consequently dissolve, ionic and polar species, owing to its unusually large dielectric constant. This solvation process is typically described in terms of ion-solvent interactions, ion-induced solvent microstructural changes, solvent dielectric behavior, and their effects on the macroscopic properties of the solution. ... 

During the last 80 years, hundreds of papers have appeared on the attempts to analyze intermolecular forces in liquids. Entailed in these analyses are arguments carrying a bewildering variety of connotations of the terms polar, nonpolar, normal, abnormal, associated, nonassociated, physical interaction, chemical interaction, ideal, and nonideal. I need only refer to the relevant Discussions of the Faraday Society held in 1937, 1953, 1965, and 1967. Certain workers pin the distinction of polar from nonpolar to the relative magnitude of the dielectric constant. Others connect these terms with the possession or otherwise of a dipole moment. I can find no systematic correlation between solubility, expressed as a mole ratio, and the dipole moment, or dielectric constant. 

These relationships are known as the Debye formulae. The Debye process has a relaxation time distribution, which is symmetrical around /niax= niax/2n and has a full width at half-maximum of 1.14 decades in frequency for the dielectric loss. In most cases, the half width of measured loss peaks is much broader than the predicted by eqn [26] and in addition, their shapes are asymmetric and with a high-frequency tail. This is the non-Debye (or nonideal) relaxation behavior found in many glass formers. In the literature, several empirical model funaions, mostly generalization of the Debye function, have been developed and tested which are able to describe broadened and/or asymmetric loss peaks. Among these empirical model functions, the most important are the Kohlrausch-Williams-Watts (KWW), Cole-Cole (CC), Cole-Davidson (CD), and the Havriliak-Negami (HN) function. The HN function, with two shape parameters, is the most commonly used funaion in the frequency domain. 

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