Dielectric orientation

The electroclinic effect is a result of the coupling between tilt and polarization. The polarization Pe, which is induced by an external field E in the smectic- phase of chiral molecules, consists of a part Po which is present in every dielectric (orientation and electronic polarization), and a part Pg which is due to the P-6 coupling and should show a similar behavior as the induced tilt angle 9. While it is difficult to separate Pg and Pq exactly, measurements of the total polarization in the smectic- phase and around the smectic- -smectic-C transition indicate at least qualitatively that Pg and 9 show very similar behavior [65]. 

Strong covalent binding potentials determine the distance and direction of atomic binding. Changes in conformation of molecular groups are possible if barriers of rotational potentials can be overcome. The latter determine the intrinsic stiffness of molecular chains or segments. Weak interchain forces arise mainly from dipole interactions. Quantum-mechanical dipolar exchange forces are the main contributors even for nonpolar polymers. For polar polymers, permanent or induced dipoles are also involved they are responsible for dielectric orientational polarization (4). Mechanical loads in polymers are transmitted by covalent and by dipole forces. Electrical loads act directly on dipolar moments. 

The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

The most important materials among nonlinear dielectrics are ferroelectrics which can exhibit a spontaneous polarization PI in the absence of an external electric field and which can spHt into spontaneously polarized regions known as domains (5). It is evident that in the ferroelectric the domain states differ in orientation of spontaneous electric polarization, which are in equiUbrium thermodynamically, and that the ferroelectric character is estabUshed when one domain state can be transformed to another by a suitably directed external electric field (6). It is the reorientabiUty of the domain state polarizations that distinguishes ferroelectrics as a subgroup of materials from the 10-polar-point symmetry group of pyroelectric crystals (7—9). 

Fig. 3. Crystal structure and lattice distortion of the BaTiO unit ceU showiag the direction of spontaneous polarization, and resultant dielectric constant S vs temperature. The subscripts a and c relate to orientations parallel and perpendicular to the tetragonal axis, respectively. The Curie poiat, T, is also shown.

Some electrical properties are shown in Table 3. Values of other parameters have been pubflshed (146). Polymorphism of the PVDF chains and the orientation of the two distinct dipole groups, —CF2— and —CH2—, rather than trapped space charges (147) contribute to the exceptional dielectric properties and the extraordinarily large piezoelectric and pyroelectric activity of the polymer (146,148,149). 

The physical picture in concentrated electrolytes is more apdy described by the theory of ionic association (18,19). It was pointed out that as the solutions become more concentrated, the opportunity to form ion pairs held by electrostatic attraction increases (18). This tendency increases for ions with smaller ionic radius and in the lower dielectric constant solvents used for lithium batteries. A significant amount of ion-pairing and triple-ion formation exists in the high concentration electrolytes used in batteries. The ions are solvated, causing solvent molecules to be highly oriented and polarized. In concentrated solutions the ions are close together and the attraction between them increases ion-pairing of the electrolyte. Solvation can tie up a considerable amount of solvent and increase the viscosity of concentrated solutions. 

The dielectric constant is a measure of the ease with which charged species in a material can be displaced to form dipoles. There are four primary mechanisms of polarization in glasses (13) electronic, atomic, orientational, and interfacial polarization. Electronic polarization arises from the displacement of electron clouds and is important at optical (ultraviolet) frequencies. At optical frequencies, the dielectric constant of a glass is related to the refractive index k =. Atomic polarization occurs at infrared frequencies and involves the displacement of positive and negative ions. 

At lower frequencies, orientational polarization may occur if the glass contains permanent ionic or molecular dipoles, such as H2O or an Si—OH group, that can rotate or oscillate in the presence of an appHed electric field. Another source of orientational polarization at even lower frequencies is the oscillatory movement of mobile ions such as Na". The higher the amount of alkaH oxide in the glass, the higher the dielectric constant. When the movement of mobile charge carriers is obstmcted by a barrier, the accumulation of carriers at the interface leads to interfacial polarization. Interfacial polarization can occur in phase-separated glasses if the phases have different dielectric constants. 

Ferroelectrics. Ferroelectrics, materials that display a spontaneous polarization ia the abseace of an appHed electric field, also display pyroelectric and piezoelectric behavior. The distinguishing characteristic of ferroelectrics, however, is that the spontaneous polarization must be re-orientable with the appHcation of an electric field of a magnitude lower than the dielectric breakdown strength of the material. 

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

The dielectric constant of unsymmetrical molecules containing dipoles (polar molecules) will be dependent on the internal viscosity of the dielectric. If very hard frozen ethyl alcohol is used as the dielectric the dielectric constant is approximately 3 at the melting point, when the molecules are free to orient themselves, the dielectric constant is about 55. Further heating reduces the ratio by increasing the energy of molecular motions which tend to disorient the molecules but at room temperature the dielectric constant is still as high as 35. 

For films on non-metallic substrates (semiconductors, dielectrics) the situation is much more complex. In contrast with metallic surfaces both parallel and perpendicular vibrational components of the adsorbate can be detected. The sign and intensity of RAIRS-bands depend heavily on the angle of incidence, on the polarization of the radiation, and on the orientation of vibrational transition moments [4.267]. 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

In the second type of interaction contributing to van der Waals forces, a molecule with a permanent dipole moment polarizes a neighboring non-polar molecule. The two molecules then align with each other. To calculate the van der Waals interaction between the two molecules, let us first assume that the first molecule has a permanent dipole with a moment u and is separated from a polarizable molecule (dielectric constant ) by a distance r and oriented at some angle 0 to the axis of separation. The dipole is also oriented at some angle from the axis defining the separation between the two molecules. Overall, the picture would be very similar to Fig. 6 used for dipole-dipole interaction except that the interaction is induced as opposed to permanent. 

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]).

In the plus-x orientation, the region behind the plastic wave is treated as a conductor. Accordingly, in the electrical model, the left electrode is moving with the velocity of the plastic wave. Otherwise, the analysis proceeds as in the case of the elastic-dielectric. For convenience it is assumed that 3 = 2 = i. The thicknesses of the two dielectric regions are = I and I2 — ([/, — U2)t. Solution for the current is then... 

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