Dipole moment, average induced electric

Dipole rotation refers to the alignment, by effect of the electric field, of molecules in the sample that have permanent or induced dipole moments. As the electric field of microwave energy increases, it aligns polarized molecules. As the field decreases, thermally induced disorder is restored. In fact, applied microwave fields cause molecules, on average, to temporarily spend very slightly more time pointing in one direction than in others. Associated with that very small fraction of preferred orientation there is another very small fraction of molecular order imposed and hence a tiny bit of energy. When the... 

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 anisometry of mesogenic molecules leads to anisotropic polarization in electric fields. If an electric field, E, is applied to a molecule, a dipole moment is induced. The dipole tends to orient in the direction of the field. The average dipole moment per unit volume defines the polarization, P, which is proportional to the electric field ... 

Equilibrium electrostatic interactions between a solute and a solvent are always nonpositive - tliey are zero if the solute is characterized by no electrical moments (e.g., a noble gas atom) and negative otherwise, i.e., attractive. It is easiest to visualize the electrostatic interactions as developing in a stepwise fashion. Consider a solute A characterized by electrical moments for simplicity, consider only die dipole moment. When A passes from the gas phase into a solvent, the solvent molecules, if diey have permanent moments of their own, reorient so that, averaged over thermal fluctuations, their own dipole moments oppose that of the solute. In an isotropic liquid with solvent molecules undergoing random thermal motion, the average electric field at any point will be zero however, the net orientation induced by the solute changes this, and the lield induced by introduction of the solute is sometimes called the reaction field . 

Polarizability (of a molecule) — There are numerous different mechanisms that contribute to the total polarizability of a molecule. The three most important of these are termed electron polarizability, molecular-distortion polarizability, and orientation polarizability. All these parameters are measured as statistical averages over large numbers of molecules present in the bulk phase. (1) -> Electron polarizability a is a measure of the ease with which electrons tend to be displaced from their zero-field positions by the applied -> electric field. Thus, the electron polarizability of a molecule is defined as the ratio of induced dipole moment pincj (coulomb meters) to the inducing electric field E (volts per meter) ... 

Molecular polarizability, a, is a measure of the ability of an external electric field, E, to induce a dipole moment, = aE, in the molecule. As such, it can be viewed as contributing to a model for induced dipole (dispersive) interactions in molecules. Because the polarizability is a tensor (matrix) quantity, there is the question of how to represent this in a scalar form. One approach is to use the average of the diagonal components of the polarizability matrix, (a x + otyy + Since the polarizability increases with size (and... 

In condensed media consisting of molecules, the intermolecular forces such as permanent and induced dipole interactions are generally small compared to intramolecular chemical binding forces. Therefore, the molecular identities and properties are conserved to a certain extent. They nevertheless differ significantly from those of an isolated molecule in the gas phase. Therefore, both in linear and non-linear optics the question arises of how to relate molecular to macroscopic properties. More specifically, how do the individual permanent and induced dipole moments of the molecules translate into the macroscopic polarization of the medium The main problem is to determine the local electric field acting on a molecule in a medium which differs from the average macroscopic field E (Maxwell field) in this medium. 

The application of an electric field always causes some physical changes in the medium even if the liquid molecules are non-polar, the electrons in the molecule will be affected by the electric field. The movement of electrons within the molecule results in an induced dipole, ft, and the alignment of the induced dipoles with the electric field gives induced polarization. For example, if a positive charge is placed above the plane of a neutral benzene molecule, the average positions of the electrons will shift upward, giving the benzene molecule a dipole moment whose direction is perpendicular to the molecular plane. In summary, when a non-polar molecule is subjected to an electric field, the electrons in the molecule are displaced from their ordinary positions so that the electron clouds and nuclei are attracted in opposite directions and a dipole is induced thus the molecule temporarily has an induced dipole moment, ft. 

However when a normal or low-frequency electric field is applied, for polar molecules, the of the medium is due to both permanent and induced dipoles in the molecule, and in order to measure the permanent dipole moment, the effect of the induced dipole moment must be evaluated. One molecular property helps us to solve this difficult problem the induced dipole moment, fd1 is independent of the temperature since if the position of the molecule is disturbed by thermal collisions, the dipole is immediately induced again in the field direction. However, the contribution of permanent dipoles, fd, is temperature-dependent and decreases with increasing temperature because the random thermal collisions of the permanent dipole molecules oppose the tendency of their dipoles to line up in the electric field. In order to discriminate between fi1 and fi, it is necessary to calculate the average component of a permanent dipole in the field direction as a function... 

The polarizability of an atom or molecule describes the response of the electron cloud to an external field. The atomic or molecular energy shift KW due to an external electric field E is proportional to i for external fields that are weak compared to the internal electric fields between the nucleus and electron cloud. The electric dipole polarizability a is the constant of proportionality defined by KW = -0(i /2. The induced electric dipole moment is aE. Hyperpolarizabilities, coefficients of higher powers of , are less often required. Technically, the polarizability is a tensor quantity but for spherically symmetric charge distributions reduces to a single number. In any case, an average polarizability is usually adequate in calculations. Frequency-dependent or dynamic polarizabilities are needed for electric fields that vary in time, except for frequencies that are much lower than electron orbital frequencies, where static polarizabilities suffice. 

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