Linear permittivity

The starting point is Maxwell s equations. We consider a non-magnetic medium (/i = fj,o) with a linear permittivity e(u>, x, y) that doesn t depend on the propagation coordinate z. 

The symbol A has the same meaning as before and stands for either constant finite strain V or stress t. It describes the field dependence of the conventional linear permittivity. Usually, the factor sq is extracted, and the third-order permittivity written as sqkkim but this would involve yet additional symbols, also for the impermittivities, and really makes only limited sense as it fails to render kklm dimensionless. Similar considerations also hold for the notation of all sorts of electrostriction coefficients. 

The above technique has successfully been applied to the ferroelectric copolymer P(VDF-TrFE) by Heiler and Floss (1994), who studied the linear permittivity 8i along with the second- and third-order permittivities 82 and 83 for poled and unpoled samples (cf Fig. 8). While 81 reveals the ferroelectric to paraelecfric transition including the typical Curie-Weiss behavior for T > Tq, the second-order permittivity appears to be sensitive to the state of poling. Combining 81 and 83 gives even... 

Fig. 4.7. The dielectric permittivity of impact-loaded dielectrics can be determined from current pulse measurements on disks biased with a voltage V. The magnitudes of the normalized current pulse values shown for two crystallographic orientations of sapphire are linear change with applied strain (after Graham and Ingram [68G05]).

Tantalum and niobium are added, in the form of carbides, to cemented carbide compositions used in the production of cutting tools. Pure oxides are widely used in the optical industiy as additives and deposits, and in organic synthesis processes as catalysts and promoters [12, 13]. Binary and more complex oxide compounds based on tantalum and niobium form a huge family of ferroelectric materials that have high Curie temperatures, high dielectric permittivity, and piezoelectric, pyroelectric and non-linear optical properties [14-17]. Compounds of this class are used in the production of energy transformers, quantum electronics, piezoelectrics, acoustics, and so on. Two of... 

Bu4NBr in AN/PC in the temperature range 75 °C>6>- 35°C a linear correlation /rmax 41) is found [209], independent of temperature and solvent composition. The use of high-permittivity solvents belonging to the same class suppresses the effects due to strong selective solvation or changing association. 

In contrast to points (l)-(3) of discussion, the effect of ion association on the conductivity of concentrated solutions is proven only with difficulty. Previously published reviews refer mainly to the permittivity of the solvent or quote some theoretical expressions for association constants which only take permittivity and distance parameters into account. Ue and Mori [212] in a recent publication tried a multiple linear regression based Eq. (62)... 

It has been pointed out321-324 that the two groups of solvents differ by some definite structural features. In particular, ED, 1,2-BD, and 1,3-BD possess vicinal OH groups that can form intramolecular hydrogen bonds. For these solvents, the ability of the organic molecule to interact with neighboring molecules is reduced. This results in the possibility of a different orientation at the interface because of different interactions of the OH groups with the Hg surface.323 The different molecular structure leads to different dipolar cooperative effects. As a result, the dependence of C on the bulk permittivity follows two different linear dependencies. 

The growth of an anodic alumina film, at a constant current, is characterized by a virtually linear increase of the electrode potential with time, exemplified by Fig. 10, with a more or less notable curvature (or an intercept of the extrapolated straight line) at the beginning of anodization.73 This reflects the constant rate of increase of the film thickness. Indeed, a linear relationship was found experimentally between the potential and the inverse capacitance78 (the latter reflecting the thickness in a model of a parallel-plate capacitor under the assumption of a constant dielectric permittivity). This is foreseen by applying Eq. (38) to Eq. (35). It is a consequence of the need for a constant electric field on the film in order to transport constant ionic current, as required by Eqs. (39)-(43). 

Substrate material Price per unit area (arb. units) Dielectric permittivity of insulator Maximum working temperature (K) Resistivity of dielectric layer (fl-cm) Density (g/cm3) Linear expansion coefficient x i[Pg.490]

The assumption of linear response played a prominent role in the derivation (given above) of the SCRF equations, and one aspect of the physics implied by this assumption is worthy of special emphasis. This aspect is the partitioning of Gp into a solute-solvent interaction part Gss and a intrasolvent part Gss The partitioning is quite general since it follows entirely from the assumption of linear response. Since classical electrostatics with a constant permittivity is a special case of linear response, it can be derived by any number of classical electrostatic arguments. The result is [114, 116-119]... 

According to the capacitor model of the double layer, assuming constant thickness and electric permittivity, the dependence of AG° on <7m should be linear. " Deviations from linearity can be viewed as resulting from changes of X2 and/or e in the inner part of the double layer. A linear plot ofAG° vs. is observed for adsorption of ions and thiourea. ... 

The nonlinear part of the susceptibility was introduced into the quasi-linear finite-difference scheme via iterations, so that at any longitudinal point, the magnitude of E calculated at the previous longitudinal point was used as a zero approximation. This approach is better than the split-step method since it allows one to jointly simulate both the mode field diffraction on irregular sections of the waveguide and the self-action effect by introducing the nonlinear permittivity into the implicit finite-difference scheme which describes the propagation of the total field. 

The fifth letter in the Greek alphabet hence, used to denote the fifth in a series (for example, the fifth methylene carbon in a fatty acid). 2. Symbol for molar absorption coefficient or extinction coefficient. 3. Symbol for permittivity (cq refers to permittivity of a vacuum refers to relative permittivity). 4. s, Symbol for degree of activation (lUB (1982) Eur. J. Biochem. 128, 281). 5. 8i, Symbol for degree of inhibition. 6. Symbol for efficiency. 7. Symbol for linear strain. 8. Symbol for emit-tance. 

In the above sections, we considered electrolytes that are ionophores.10 Iono-phores, like sodium chloride, are ionic in the crystalline state and are expected to dissociate into free ions in dilute solutions. In fact, in high-permittivity solvents (er>40), ionophores dissociate almost completely into ions unless the solutions are of high concentration. When an ionophore is completely dissociated in the solution, its molar conductivity A decreases linearly with the square root of the concentration c (<10 2 M) ... 

A summary of analytic expressions obtained in this manner for all the viscoelastic functions is presented in Table 4 and 5 for the linear and cubic arrays. The well-known phenomenological analogy (8) between dynamic compliance and dielectric permittivity allows the formal use of Eqs. (T 5), (T 6), and (T 11), (T 12) for the dielectric constant, e (co), and loss, e"(co), of the linear and cubic arrays, respectively (see Table 6). The derivations of these equations are elaborated in the next section and certain molecular weight trends are discussed. 

Fig. 2. Reduced loss compliance or analogous dissipative dielectric permittivity for the linear array as a function of molecular weight...

Equations (10.23) and (10.24) hold for the /3-phase as well and could be inserted into Eqn. (10.22). The additivity of pt with respect to the elastic and electric potential is based on 1) the assumption of linear elastic theory (which is an approximation) and 2) the low energy density of the electric field (resulting from the low value of the absolute permittivity e0 = 8.8x10 12 C/Vm). In equilibrium, V/i, = 0 and A V, = df-pf = 0. Therefore, in an ionic system with uniform hydrostatic pressure, the explicit equilibrium condition reads Aa/fi=A)... 

We employ the linear response theory based on a phenomenological molecular model of water. In the proposed composite HC-HO model the complex permittivity is represented as the sum... 

We shall remove an important drawback of the polarization model described in Section VI by considering another variant of a composite model than that described in previous Section VILA. We use again a linear-response theory to find the contribution of a vibrating dipole to the total permittivity . We split the total concentration N of polar molecules into the sum Nm and Nv b, where each term refers to rotation of a like rigid dipole (viz. with the same electric moment p) but characterized by different law of motion ... 

The theory of wideband complex permittivity of water described in the review drastically differs from the empirical double Debye representation [17, 54] of the complex permittivity given for water by formula (280b). Evolution of the employed potential profiles, in which a dipole moves, explored by a dynamic linear-response method can be illustrated as follows ... 

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