Dipolar Electric Polarization

Linear Dipolar Electric Polarization. Even atoms and microsystems with symmetrically distributed charges are known to exhibit polarization under the influence of an external electric field or the internal (molecular) electric field of a neighbour. Such a system is said to become endowed with an induced electric dipole (or higher multipoles). In many a case it sufiSces to assume that the induced dipole moment p E) is proportional to the field strength inducing it ... 

Polypeptides are electrically polar, carrying permanent dipoles at the planar CO-NH groups of the backbone chain and generally at some atomic groups of the side-chains. Because of the vector nature of dipoles, we must speak of the mean-square dipole moment, averaged over all possible conformations of the backbone chain and all accessible orientations of the side-chains when the dipolar nature of a polypeptide in solution is considered. The of a polypeptide thus may depend on what conformation the molecule assumes in a given solvent. 

Dipolar Saturation. The vector of electric polarization of a macroscopic sample of volume in an electric field is ... 

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) ... 

Electric polarization, dipole moments and other related physical quantities, such as multipole moments and polarizabilities, constitute another group of both local and molecular descriptors, which can be defined either in terms of classical physics or quantum mechanics. They encode information about the charge distribution in molecules [Bbttcher et al, 1973]. They are particularly important in modelling solvation properties of compounds which depend on solute/solvent interactions and in fact are frequently used to represent the -> dipolarity/polarizability term in - linear solvation energy relationships. Moreover, they can be used to model the polar interactions which contribute to the determination of the -> lipophilicity of compounds. 

This term is a measure of the exoergic balance (i.e. release of energy) of solute-solvent and solute-solute dipolarity / polarizability interactions. This term, denoted by n, describes the ability of the compound to stabilize a neighbouring charge or dipole by virtue of nonspecific dielectric interactions and is in general given by -> electric polarization descriptors such as -> dipole moment or other empirical - polarity / polarizability descriptors [Abraham et al, 1988]. Other specific polarity parameters empirically derived for linear solvation energy relationships are reported below. 

In addition to the pear-shaped molecules, bent-shaped molecules were used to illustrate the dipolar origin of the flexoelectric effects in nematic liquid crystals. It was assumed that the constituent molecules of the nematic liquid crystals are free to rotate around their axes, and in the absence of electric fields, their dipole moments average out so the net polarization of the material is zero. However, when liquid crystals made from polar pear- or banana-shaped molecules are subjected to splay or bend deformations, respectively, they can become macroscopically polar, because the polar structures correspond to a more efficient packing of the molecules. It follows from symmetry considerations that the deformation-induced fiexo-electric polarization Pa can be written as ... 

The sketch of the experimental set-up is shown in Figure 1. A Q-switched Nd-YAG laser, operating at 1.06 ixm and a pulse repetition 2-12.5 Hz was used to provide the fundamental (pump) beam. The peak power was 200-300 kW. The beam was focused with a 43 cm lens so that the power density on the sample placed in a thermostate was about 100-200 MW-cm. " For investigation the field-induced SHG, short pulses (tp = 20 fxs) of high voltage Up = 4kV) were provided by an electrical generator. The pulse duration was chosen from the condition Trelaxation time for dipolar (Debye) polarization, and T is the director reorientation time. Under such a condition, molecular dipoles are oriented by the field but the Fredericks transition does not take place. The sensitivity of our set-up was about 30 photons of the optical second harmonic per single laser pulse. The cell temperature was stabilized with an accuracy of 0.1° K. 

FIGURE 3.5. (a) Ionic, (b) dipolar, and (c) quadrupolar mechanisms for the appearance of the surface electric polarization. 

The interactions between the dipoles and ions in biopolymen are important in many respects. The physiological significance trf piezoelectric and pyroelectric effects, if any. could be the influence of the electrical polarization of biopolymets on the behavior of ions. One possible example would be the interaction of the ion chaimel proteins with kms. The applied stress, mechanical or electrical, may change the molecular conformation, which is associated with the dipolar roiatioo. The adsorption and desorption of ions to the protein molecule could be affected by the conformational change of molecule. An enzymatic reaction accompanied by a change of mdecular conformatioo could be another example. 

In general, because of the complexity of the Hamiltonian Hq and the large number of energy levels involved, an analytical solution of Equation (10.3) is neither possible nor instmctive. On the other hand, we can solve Equation (10.4) in a pertuibative manner and obtain a solution for the induced dipole moment, and therefore the electric polarization, in a power series of the interaction -d E. This is valid if the dipolar interaction is of a small perturbation magnitude compared to /fo Accordingly, we attach a perturbation parameter A, (A= 1) to -d and rewrite Equation (10.3) as... 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

It is important to understand that the atomic charges refer to atoms that are not spherical. Consequently the centroid of electronic charge of an atom does not in general coincide with the nucleus, and each atom therefore has an electric dipole moment—or, more generally, an electric dipolar polarization (since only the dipole moment of electrically neutral atoms is origin independent). 

Relaxation processes are probably the most important of the interactions between electric fields and matter. Debye [6] extended the Langevin theory of dipole orientation in a constant field to the case of a varying field. He showed that the Boltzmann factor of the Langevin theory becomes a time-dependent weighting factor. When a steady electric field is applied to a dielectric the distortion polarization, PDisior, will be established very quickly - we can say instantaneously compared with time intervals of interest. But the remaining dipolar part of the polarization (orientation polarization, Porient) takes time to reach its equilibrium value. When the polarization becomes complex, the permittivity must also become complex, as shown by Eq. (5) ... 

Thermal effects (dielectric heating) can result from dipolar polarization as a consequence of dipole-dipole interactions of polar molecules with the electromagnetic field. They originate in dissipation of energy as heat, as an outcome of agitation and intermolecular friction of molecules when dipoles change their mutual orientation at each alternation of the electric field at a very high frequency (v = 2450 MHz) [10, 11] (Scheme 3.1). 

To answer this question, let us first consider a neutral molecule that is usually said to be polar if it possesses a dipole moment (the term dipolar would be more appropriate)1 . In solution, the solute-solvent interactions result not only from the permanent dipole moments of solute or solvent molecules, but also from their polarizabilities. Let us recall that the polarizability a of a spherical molecule is defined by means of the dipole m = E induced by an external electric field E in its own direction. Figure 7.1 shows the four major dielectric interactions (dipole-dipole, solute dipole-solvent polarizability, solute polarizability-solvent dipole, polarizability-polarizability). Analytical expressions of the corresponding energy terms can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres (Suppan, 1990). These four non-specific dielectric in-... 

An electric field induces a polarization of the charge within a single molecule by the instantaneous displacement of the electrons with respect to the nucleus. In this manner an induced dipole and, hence, a dipolar moment, p, are generated. When the applied field is weak, the induced charge displacement is proportional to the strength of the field ... 

On the basis of these formulae one can convert measurements of area, which equals the integral in the latter formula, under spectral lines into values of coefficients in a selected radial function for electric dipolar moment for a polar diatomic molecular species. Just such an exercise resulted in the formula for that radial function [129] of HCl in formula 82, combining in this case other data for expectation values (0,7 p(v) 0,7) from measurements of the Stark effect as mentioned above. For applications involving these vibration-rotational matrix elements in emission spectra, the Einstein coefficients for spontaneous emission conform to this relation. 

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