Electric field induced distortions

Ionic Polarisability Polarisability of an atom is the ability of the applied electric field to distort the electric cloud and thus induce an electric dipole moment. 

A CDW is a periodic modulation of the conduction electron density within a material. It is brought about when an applied electric field induces a symmetry-lowering lattice modulation in which the ions cluster periodically. The modulation mechanism involves the coupling of degenerate electron states to a vibrational normal mode of the atom chain, which causes a concomitant modulation in the electron density that lowers the total electronic energy. In one-dimensional systems, this is the classic Peierls distortion (Peierls, 1930, 1955). It is analogous to the JT distortion observed in molecules. 

In addition to orienting dipoles, electric fields induce dipole moments in molecules, since electrons and nuclei experience forces in opposite directions in the same electric field and since electrons, being less massive, move much more easily than nuclei in a field. The quantity that measures the ease with which the electron cloud in a certain molecule can be distorted is the molecular polarizability ccq. The magnitude of an induced dipole is given as... 

An external electric field can distort the electron density in both polar and nonpolar molecules and this results in an induced dipole moment that is proportional to the field. The constant of proportionality is called the polarizability. 

The electric field also distorts the partner s electronic cloud, and as a consequence of the Hellmann-Feynman theorem (Chapter 12) this creates a distortion of the nuclear framework. Thus, the multipole moments of a distorted molecule are a little changed ( induced moments ) with respect to the permanent ones. If we take the indueed moment interaction with the field into account, then apart from the eleetrostatie interaetion energy we obtain the induction energy contribution. ... 

For example, while the induced moment may be in the direction of the electric field, the distortion of the sphere may be perpendicular to the field. 

A polar molecule with dipole moment p, can induce a dipole moment in a polarizable molecule (which may itself be either polar or nonpolar) because the partial charges of the polar molecule give rise to an electric field that distorts the second molecule. That induced dipole interacts with the permanent dipole of the first molecule, and the two are attracted together (Fig. 11.26). The formula for the dipole-induced-dipole interaction energy is... 

At present, at least three types of steady-state dielectrically driven pattern are known for nematics. The electric-field-induced periodic bend distortion in the form of parallel stripes has been observed in a homeotropi-cally oriented layer of 5-CB ( a= 13) in the presence of a stabilizing magnetic field [75, 76]. The stripes with a wavevector q were parallel to the electric field E and stationary at low fields. It was shown that a stable periodic pattern of the director minimizes the free energy of the cell when the ela.stic moduli and A 33 are similar to each other. In these experiments the Frederiks transition is of first order, the nonde-formed and deformed areas coexist at a given voltage, and the front between them may propagate along the direction y perpendicular to both fields [77]. 

In this section we discuss electrohydrodynamic (EHD) instabilities, that is electric-field-induced phenomena that are caused by the flow of a liquid crystal (see also [8,219]. The reason for the flow is electrical conductivity, which has been disregarded in previous sections. The flow may arise either independently of the anisotropic properties of substance, as in isotropic liquids (isotropic modes of the electrohydrodynamic instability), or may be driven by the conductivity anisotropy, as in liquid crystals (anisotropic modes). The threshold for EHD instabilities depends on many parameters, such as the electrical and viscoelastic properties of substance, the temperature, and the applied field frequency. Due to flow distortion of the director alignment, the instability is usually accompanied by a characteristic optical... 

Dielectric fluids such as liquid crystals are leaky insulators, i.e., they have low electrical conductivity and polarize in the presence of an electric field E. This means that the electric field induces internal charge reorganization, or distortion such as a net electric dipole moment per unit volume P appears. This is the polarization with units C/m. The sign of the polarization is defined as P > 0 if the direction is pointing from negative to positive charges. 

Consider the interaction of a neutral, dipolar molecule A with a neutral, S-state atom B. There are no electrostatic interactions because all the miiltipole moments of the atom are zero. However, the electric field of A distorts the charge distribution of B and induces miiltipole moments in B. The leading induction tenn is the interaction between the pennanent dipole moment of A and the dipole moment induced in B. The latter can be expressed in tenns of the polarizability of B, see equation (Al.S.g). and the dipole-mduced-dipole interaction is given by... 

Now let us examine the molecular origin of Molecular polarity may be the result of either a permanent dipole moment p or an induced dipole moment ind here the latter arises from the distortion of the charge distribution in a molecule due to an electric field. We saw in Chap. 8 that each of these types of polarity are sources of intermolecular attraction. In the present discussion we assume that no permanent dipoles are present and note that the induced dipole moment is proportional to the net field strength at the molecule ... 

An electric dipole consists of two equal and opposite charges separated by a distance. AH molecules contain atoms composed of positively charged nuclei and negatively charged electrons. When a molecule is placed in an electric field between two charged plates, the field attracts the positive nuclei toward the negative plate and the electrons toward the positive plate. This electrical distortion, or polarization of the molecule, creates an electric dipole. When the field is removed, the distortion disappears, and the molecule reverts to its original condition. This electrical distortion of the molecule is caHed induced polarization the dipole formed is an induced dipole. 

Carbon atoms in free space have spherical symmetry, but a carbon atom in a molecule is a quite different entity because its charge density may well distort from spherical symmetry. To take account of the finer points of this distortion, we very often need to include d, f,. .. atomic orbitals in the basis set. Such atomic orbitals are referred to as polarization functions because their inclusion would allow a free atom to take account of the polarization induced by an external electric field or by molecule formation. 1 mentioned polarization functions briefly in Section 9.3.1. 

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