Non-linear dielectric effect

The relative permittivity of a solvent depends also on the electric field E, but ordinary fields employed in the laboratory are rarely strong enough to cause an appreciable change of s. The phenomenon is called the non-linear dielectric effect. A relevant expression (Grahame 1953) is ... 

Sliwinska-Bartkowiak, M., Szurkowski, B., and Hilczer, T. 1984. Chem. Phys. Lett. Non-linear dielectric effect in critical and far pre-critical solutions of nitrotoluene. 94 609. 

Introduction. Books, monographs, and review articles available on dielectrics and their molecular aspects scope of present review the variety of non-linear field effects. 

As we see, the parameter 1 results from Langevin reorientation of the polarizability ellipsoid and is always positive. The second of the above parameters, 2, corresponds to Bom s term in the Kerr effect and can be positive or negative, depending on the electric structure of the molecule. The third, the Debye parameter 3, has no counterpart in other phenomena of molecular orientation, and is specific to the non-linear dielectric behaviour of dipolar substances. 

As deduced from thermal expansion measurements, a polarization is still present for temperatures greater than T j, but fluctuating in time and in space with a zero mean no pyroelectric effect can be detected. These fluctuations persist for temperamres much above T j, for example in the case of PMN up to 200-300°C (T = -15°C). The relationship P(E) is strongly non-linear. Dielectric susceptibility measured shows significant differences with respect to the Curie-Weiss law. 

The dielectric susceptibility x is related to the relative dielectric constant er by x = er — 1 Equations (1.4) are only valid for small fields. Large amplitudes of the ac field lead to strong non-linearities in dielectrics, and to sub-loops of the hysteresis in ferroelectrics. Furthermore, the dielectric response depends on the bias fields as shown in Figure 1.4. From the device point of view this effect achieves the potential of a tunable dielectric behavior, e. g. for varactors. 

What is of interest here is the description of nonlinear dielectric effects with a linear procedure. Nonlinear dielectrics were introduced in the theory of liquids by Dogonatze and Kornyshev in the 1970s [21] the reformulation of the theory in more recent years by Basilevsky [22] permits its insertion in the whole machinery of the PCM version of the CS method. The reader is also referred to the contribution of Basilevsky and Chuev dedicated to non-local dielectric solvation models. 

The inclusion of the environment effects for non-linear optical (NLO) properties is presented within the PCM (Cammi Mennucci) and the multipolar expansion (Agren Mikkelsen) solvation models. In the first contribution the attention is focused on the connection between microscopic effective properties and macroscopic NLO susceptibilities, whereas in the latter contribution the analysis is extended to treat heterogeneous dielectric media. 

However, the linear response of a dielectric to an applied field is an approximation the actual response is non-linear and is of the form indicated in Fig. 8.6. The electro-optic effect has its origins in this non-linearity, and the very large electric fields associated with high-intensity laser light lead to the non-linear optics technology discussed briefly in Section 8.1.4. Clearly the permittivity measured for small increments in field depends on the biasing field E0, from which it follows that the refractive index also depends on E0. The dependence can be expressed by the following polynomial ... 

This feature has frequently been introduced in various ad hoc empirical fashions in dielectric discussions. One analytically explicit form was used by Piekara (1939) to account for the non-linear electric field effects, e.g. in liquid nitrobenzene. The importance of these effects is in part precisely because they allow a sensibly direct appraisal of dipole inter-correlations (see Chapter 7). 

Permittivity variations in a strong electric field non-linear and saturation behaviour progress of e gperimental methods molecular behaviour and various theoretical models molecular correlations complete dielectric saturation electrostriction and electrocaloric effect. 

The effect consisting in a change in magnetic pmneability under the influ ice of an electric field still awaits detection, although considered theoretically for paramagnetics by Van Vleck, as wdl as for diamagnetics. Non-linear Electro- and Magneto-optical Effects, Optical saturation in an electric field. When an optically isotropic dielectric is placed in a very... 

Up to the present, studied aspects of non-linear effects include the influence of various solvents and temperatures," " hydrostatic pressure, and the behaviour of solid dielectrics. ... 

The expressions simplify considerably if the solution is chosen so that the solvent (e.g. CCI4, CbHo) under the influence of the electric field becomes endowed with a weak non-linearity, negligible by comparison with the non-linearity of the solute (e.g. nitrobenzene). If, moreover, the solute is strongly dipolar, one is justified in considering only the effect of reorientation of the permanent electric dipoles and omitting other mechanisms contributing to dielectric saturation. The molar saturation constant of the solute (302) now becomes ... 

Available theoretical and experimental results on electric field induced non-linearities in isotropic dielectrics prove that we have here an effective method for the study of the dectric structure of molecules, as well as of their mutual interactions in dense states, i.e. of the structure of near ordering in liquids. 

The primary concern of this chapter is to provide an introduction to the theory of the macroscopic properties of dielectric bodies. Attention is restricted to isotropic materials and it is assumed that the external electric field is always sufiSciently weak to allow any non-linear effects which might arise to be ignored. 

An Outline of Non-linear Effects in Dielectrics. Constitutive Relations in Linear Media. We shall be considering homogeneous and isotropic dielectrics, the electric, magnetic, and optical properties of which, in the absence of external fields, are described by the following three scalar quantities, characteristic of the material of which the medium consists e = electric permittivity /X = magnetic permeability n = refractive index. 

To show the influence of various microscopic and structural factors on linear and non-linear effects in dense dielectrics, it is convenient to apply first a semi-macroscopic treatment of the theory, and then to proceed to its molecular-statistical interpretation, assuming appropriate microscopic models. The semi-macroscopic method was initially applied by Kirkwood and modified by Frohlich in the theory of linear dielectrics, and has beat successfully used in theories of non-linear tUelectrics. "... 

General Treatment of Fluctuational Processes. The previous treatment is good only as long as we deal with strongly dipolar substances and all other polarizational effects remain negligible. In the majority of substances, besides reorientation of permanent dipoles, one has to consider reorientation of the polarizability ellipsoids as well as statistical-fluctuational processes. In calculating the electric polarization (277), one has to include the term accounting for linear distortional polarizability of the dielectric (non-linear polarizabilities are dealt with below) ... 

Kauffman and coworkers118 119 tried to fit the solvatochromic shifts of l-(9-anthryl)-3-(4-/V,/V-dimcthylanilino)propanc (83), relative to the hydrocarbon homomorph with the dimethylamino group replaced by H, to the dielectric non-ideality of solvent mixtures involving hexane with ethanol, tetrahydrofuran and dichloromethane. The shifts were not linear with the mole fraction of the polar component, and Suppan s theory of dielectric enrichment was applied to the data. It was found that the dielectric enrichment that can be calculated from the relative permittivities of the components and of the mixtures is not sufficient to account for the observed solvatochromic shifts, but that preferential solvation of the probe by the polar component is superimposed on this dielectric effect. Earlier,... 

Fig. 10. Effective charge values, Z = Kon(v)/Sp(v)] for and Kr ions in carbon targets, obtained from energy loss calculations using the dielectric function (DF) and the non-linear (NL) models described in the text. The dotted lines separate the regions where Z > q and Z < q.

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