Anisotropies dielectric constant

To obtain a measure of the dielectric constant and anisotropy of thin films, the refractive index of thin film samples was measured. It has been shown that the measured dielectric constant is approximately the square of the refractive index at 633 nm wavelength [the actual relationship is roughly e (refractive index) -i- 02.] and the anisotropy is obtained from the difference between the in-plane and out-of-plane refractive index [97]. The measured anisotropy of foamed polyimides is lower than that observed for non-foamed polyimides. In addition, a drop in refractive index of the samples was observed upon foaming. The polyimide PMDa/3FDA has a measured dielectric constant of ca. 2.9 at 70 °C. A foamed sample of PMDA/3FDA derived from copolymer 6f showed a drop in dielectric constant of 2.3 [97]. 

PFMB can be used to prepare aromatic polyimides that display solubility in ketone, ether, and polar aprotic solvents. This unusual solubility can be utilized in die facile preparation of thin films that display anisotropy in their structures and properties. The anisotropy in the optical properties of the films makes them promising candidates for use as compensation layers in liquid-crystal displays. Their low dielectric constants and CTEs in combination with their outstanding thennal and thermooxidative stabilities make diem candidates for dielectric layers in microelectronics applications. 

Other physical properties. Anisotropy of thermal and electrical conductivity, coefficient of thermal expansion, elasticity, and dielectric constant may also provide information on internal structure. These properties, however, have so far been little used in structure determination, because they are less easily measured than those already considered consequently not very much experimental evidence is available for the purpose of generalizing on the relations between such properties and structural features. For further information on these subjects, see Wooster (1938), Nye (1957). 

Ion-pairing between the paramagnetic [Co(tdt)2] monoanion and nine different cations was examined by Tsao and Lim.105 The cations belong to either of two classes, quaternary ammonium or substituted V-octylpyridinium ions. By recording the H NMR spectra as a function of concentration (nitrobenzene, 307 K), the concentration association constants (Kas) were obtained. Substituent effects were found to influence the ion-pair geometry, as deduced from the isotropic shifts of the cationic protons and their shift ratios. In low dielectric constant solvents, speculation consistent with the magnetic anisotropy and the relation between the cationic proton shifts and concentration was tendered for cylindrically shaped aggregates. 

For instance, for a nematic polymer with positive anisotropy of dielectric constant (Ae > 0) orientation of mesogenic groups along the applied field takes place (homeo-tropic orientation). The fact of orientation is illustrated in Fig. 25, which shows that under crossed polarizers the optical transmittance I of a film of nematic polymer with optically anisotropic texture (taken for 100%) falls practically to zero when a low-frequency field is switched on. 

With this background, we have proposed and developed a new purely electrical method for imaging the state of the polarizations in ferroelectric and piezoelectric material and their crystal anisotropy. It involves the measurement of point-to-point variations of the nonlinear dielectric constant of a specimen and is termed scanning nonlinear dielectric microscopy (sndm) [1-7]. This is the first successful purely electrical method for observing the ferroelectric polarization distribution without the influence of the screening effect from free charges. To date, the resolution of this microscope has been improved down to the subnanometer order. 

Among the first theories of form birefringence was the calculation of Peterlin and Stuart [58] who solved for the anisotropy in the dielectric tensor of a spheroidal particle with different dielectric constants e j and e2 parallel and perpendicular to its symmetry axis, respectively. If the spheroid is aligned along the z axis, and resides in a fluid of dielectric constant e, the contribution of a single particle to the difference between the principal values of the macroscopic dielectric tensor of the fluid is... 

The response of the director of a nematic phase to an applied electric field is dependent upon the magnitude of the dielectric permitivity (dielectric constants) measured parallel and perpendicular, and jl respectively, to the director and to the sign and magnitude of the difference between them, Le. the dielectric anisotropy, Aa, see Equation 9 and Figure 2.10. Since the dielectric permitivity measured along the x-axis is unique and the values of the dielectric permitivity measured parallel to the y- and z-axes are the same. 

The dielectric constants of an aligned nematic phase are dependent upon both the temperature and the frequency of the applied field at temperatures below the clearing point. The dielectric permitivity, j, measured parallel to all three axes above the clearing point in the isotropic liquid is the same. Therefore, the dielectric anisotropy of the same compound in the liquid state is zero, see Figure 2.10. The sign and magnitude of the dielectric constants and, therefore, the dielectric anisotropy are dependent upon the anisotropy of the induced molecular polarisability, Aa, as well as the anisotropy and direction of the resultant permanent molecular polarisation determined by permanent dipole moments. 

Table 3.13 Transition temperatures (°C) and some values for the dielectric anisotropy (Ae), the ratio of the dielectric anisotropy and dielectric constant measured parallel to the director fAe/ej. and the ratio of the bend (kjj) and splay (kjj) elastic constants for the nitriles 36, 41, 53, 39,49 and 50... 

Table 3.14 Transition temperatures (°C), elastic constants fk/y, k22 kjj, 10 N), dielectric anisotropy ( e), dielectric constant measured perpendicular to the molecular long axis (e ), birefringence ( n), refractive index measured perpendicular to the director (noJ, rotational viscosity (y. Poise) and bulk viscosity (r, Poise) for tr ns-l-(4-cyanophe-nyl)-4-pentylcyclohexane (41), iTSins-l-(4-cyanophenyl)-4-[(E)-pent-l-enyl]cyclohexane (74) andtra.ns-l-(4-cyanophenyl)-4-[(E)-pent-3-enyI]cyclohexane (78) extrapolated to 100% at 22°...

To study the N-1 phase transition, it is necessary to find some physical property proportional to 5(7) that can be measured accurately as a function of temperature. There are many possibilities, which include depolarization of Raman spectra, diamagnetic susceptibility anisotropy, NMR deuterium quadrupole splitting, dielectric constant... 

Fig. 17.3 Polarization anisotropy ratio as a function of reduced optical radius ka, where e is the dielectric constant of the material. Solid (broken) lines are the theoretical curves for Si (SiC) NWs. Circles (diamonds) are the experimental values for Si (SiC) NW optical phonon (TO) lines (With permission from reference [12]. Copyright (2006) by the American Physical Society)...

In deriving Eq. (48) one ignores the anisotropy of the linear part of the dielectric constant and one assumes that Kleinman s symmetry is valid. Under these conditions, using group theory to reduce the number of non-vanishing tensor elements, the electro-optic tensor for poled polymers is given by... 

Whereas the dielectric constant probes essentially the R-dependence of the isotropic polarizability, the collison induced depolarized Raman scattering depends on the increment in the anisotropy of the polarizability with varying R. Depolarized Raman scattering of noble gases has first been observed by MacTague and Bim-baum in 1968, and later investigated for many gases . Very recently also polarized Raman intensities have been measured for NCj and He ... 

To respond to an applied electric field, the liquid crystal must exhibit dielectric anisotropy (Ae = ey — e ), defined as the difference between the dielectric constant parallel and perpendicular to the director (n) of the nematic phase. The relationship between Ae on a supramolecular level and the physical characteristics of the single molecules is described by the Maier-Meier formula (Eq. 1) ... 

Kevlar fiber reinforced polyimide or epoxy CTE matched to ceramic, available from DuPont-Howe, dielectric constant = 3.6, moisture absorption reduced Relatively thick (over 4.5 mil), fiber anisotropy may produce non-uniform strains, microcracking problems... 

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