Polarization displacement

Since P = %E (Equation (10)), 4tuxE is the internal electric field created by the induced displacement (polarization) of charges. Usually, the induced polarization causes the spatial orientation of the internal electric field to differ from the applied electric field and, like ay (co), xij( ) is a tensor quantity that reflects the anisotropy of the internal electric field. 

The extensive jt-delocalized system of metal-dithiolene complexes is also responsible for the nonlinear optical properties (NLO) which have been recently reviewed . The interaction of radiation with the matter induces an instantaneous displacement (polarization Pq = /X = aE, where a is the linear polarizability) of the electronic density away from the nucleus at small field (linear optics). At high fields (laser light) the polarizability of the molecule can be driven beyond the linear regime and a nonlinear polarization is induced (NLO) = aE + fiE" + y E + and for the bulk material... 

When a metal body is exposed to an electric field, free electrons are displaced by electric forces until the field in the body vanishes. In an ideal dielectric (dc conductivity is zero), there exists only bound charges (electrons, ions) that can be displaced from their equilibrium positions until the field force and the oppositely acting elastic force are equal. This phenomenon is called displacement polarization (electronic or ionic polarization). A dipole moment is induced in every atom or between ion pairs. The molecular dipoles can only be rotated by an electric field. Usually, their dipole moments are randomly oriented. In an external held, however, an orientation parallel to the field direction is preferred so that a dipole moment is induced. This process is called orientational polarization. 

In an alternating electric field, the displacement polarization leads to electric oscillations. This is a resonant process with resonant frequencies of lO -lO " Hz for the electronic and of 10 -10 Hz for the ionic polarization. 

Because the four mechanisms of polarization have varying time responses, dielectric solid properties strongly depend on the frequency of the applied electric field. Actually, electrons respond rapidly to reversals of electric potential, and hence no relaxation of the electronic displacement polarization contribution occurs up to frequencies of 10 GHz. Secondly, ions. 

The first term represents the contribution of the polarizability (displacement polarization) and is always positive whereas the second term originates from the permanent dipole moment (orientation polarization) and is positive or negative depending on whether P is smaller or larger than 55°. 

Polarization processes are extremely important in HR lluicls. Generally, there are four kinds of polarizations in a non-aqueous system containing no electrolytes or ions. They are electronic, atomic, Debye and the interfacial polarizations (the Wagner-Maxwell polarization). If the particulate material is an ionic solid, ionic displacement polarization should also be considered. The Debye and the intcrfacial polarizations arc rather slow processes as compared with electronic and the atomic polarizations. Usually, the former two polarizations arc called the slow polarizations, appearing at low frequency fields, whereas the last two are termed fast polarizations, appearing at high frequencies. 

The ion displacement polarization usually takes place in an ER suspension having ionic solid particulate. If the conductivity of the solid material is not loo high, then the maximunn of the dielectric loss tangent, due to the ion displacement polarization, can be expressed [28,43]... 

Since the conductivity of most ER particle materials is comparatively low, one may assume that the particle dielectric loss just results from the ion displacement polarization. The dielectric loss due to the ion displacement polarization can be calculated from the absorption current. Assuming that the initial conductivity of an ER particle material is Oo, and the absorption... 

T is the relaxation time, thus under an oscillatory electric field E=Eothe induced current density d due to the ion displacement polarization can be expressed as [43]... 

Eq. (41) is a general expression for a solid material of a very low conductivity and marked ionic displacement polarization. Differentiating Eq. (41) with respect to o, one would find the tgS has a maximum value. 

The commonly used LCR meters offer quick and easily computerized measurements in many frequencies, usually up to about 10 MHz. At higher frequencies, up to about 2 GHz, microwave teclmologies are needed. At even higher frequencies, which would test the displacement polarization, absorption spectroscopy (IR intramolecular reorientation UV-VIS electronic polarization) techniques are used. 

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