Local electric polarization

In addition, in any electrochemical component, at every interface between an electrode and the electrolyte, there is a spontaneous phenomenon of accumulation of opposite charges on both sides of that interface, which then constitutes a condenser, in the electrostatic sense of the term (Figure 1.2a). This phenomenon is referred to as a double electrochemical layer . As local electrical polarization occurs over a depth ranging from a few dozen to a few hundred nanometers around that interface, the equivalent condensers may have very large values if the electrodes have a very large surface per volume (they are therefore dubbed supercapacitors). This phenomenon plays an important role in the dynamic behavior of the component. 

The continuum electrostatic approximation is based on the assumption that the solvent polarization density of the solvent at a position r in space is linearly related to the total local electric field at that position. The Poisson equation for macroscopic continuum media... 

The influence of structured electrodes or multipoint electrodes, which enhance the local electric field [20,21], as well as the effect of discharge polarity [20-22] and gap length [21,23,24], was investigated. 

It is necessary to note that fluorescence characteristics demonstrate remarkable sensitivity to variations of physicochemical parameters of the environment. Therefore, such parameters as polarity, viscosity, temperature, electric potential, local electric field, pressure, pH, etc., can be registered successfully using the modem sensitive apparatus for fluorescence detection [1, 4—12]. As a consequence, fluorescent molecules are used successfully as molecular probes to study the local characteristics of physicochemical, biochemical and biological systems. 

Figure 8.16 Illustration of symmetry of Soto Bustamante-Blinov achiral antiferroelectric smectic LC with finite number of layers. Such systems can be studied using DRLM technique with thin freely suspended smectic films, (a) With even number of bilayers, film has local C2 symmetry, and therefore no net electric polarization, (b) With odd number of bilayers, film has local Cnv symmetry and is therefore polar, with net spontaneous electric polarization in plane of layers.

As reviewed above, when a solute is placed in a dielectric medium, it electrically polarizes that medium. The polarized medium produces a local electrostatic field at the site of the solute, this field polarizes the solute, and the polarized solute interacts with the polarized medium. The interaction is typically too large to be treated by perturbation theory, and some sort of self-consistent treatment of polarized solute and polarized medium is more appropriate. At this point several options present themselves. It promotes orderly discussion to classify these... 

Orientation polarization can occur in materials composed of molecules that have permanent electric dipole moments. The permanent dipoles tend to become aligned with the apphed electric field, but entropy and thermal effects tend to counter this alignment. Thus, orientation polarization is highly temperature-dependent, unlike the forms of induced polarization which are nearly temperature-independent. In electric fields of moderate intensity, the orientation polarization is proportional to the local electric field, as for the other forms of polarization... 

Here (r, 6) are polar coordinates, < (r, 9) is the normalized local electric potential, and integration is carried Over the region accessible for counterions. If the singularity in

positive line charge indeed were of... 

Equation (1) expresses the crystal polarization (P, C/iiF). as a function of the dipole moment (p, Cm) and the unit cell volume (V, iif). In PVDF, it suffices to express Eq. (1) in scalar form, where it is miderstood that P and p represent the components of the polarization and dipole moment vectors parallel to the ( -crystal axis. This arrangement of dipoles produces a significant local electric field in the... 

Equation (2) expresses the model of the crystal polarization used in the molecular modeling of PVDF reported in this chapter, where is the dipole of each repeat unit of the single chain in vacuum, Ap is the change in dipole moment of the repeat unit of the chain in going from the vacuum environment to the environment of the packed crystal and (cos tp) is the attenuation of the dipole moment of the repeat unit along the fe-axis due to thermally stimulated oscillations about thec-axis. Ap is directly related to the local electric field (Eioc, V/m) through the repeat unit polarizability (ot, m ) ... 

FERROELECTRIC EFFECT. The phenomenon whereby certain crystals may exhibit a spontaneous dipole moment twhich is called ferroelectric by analogy with ferromagnetic—exhibiting a permanent magnetic moment). The effect in the most typical case, barium manate. seems to he due to a polarization catastrophe, in which the local electric fields due lo the polarizuiion itself increase faster than die elastic restoring forces on the ions in Ihe crystal, thereby leading to an asymmetrical shift in ionic positions, and hence lo a permanent dipole moment. Ferroelectric crystals... 

A simple electrostatic model facilitates understanding the physical meaning of the Curie behavior of [Mn(taa)] in the HS phase. Electric polarization P produced by a number of reorienting molecular dipoles /r under a local field Eloc obeys a simple Curie law,... 

In order to find a correlation between the macroscopic polarization and the microscopic properties of the material a single (polarizable) particle is considered. A dipole moment is induced by the electric field at the position of the particle which is called the local electric field Eloc... 

Piezoresponse force microscopy (pfm) [11] and Kelvin probe force microscopy (kpfm) [9] were applied to deduce the polarization and local electric potential distribution over the whole cross section of the pzt sample (see Figure 12.3 and Figure 12.4) under static conditions as well as after switching. The details of our setup are described elsewhere [9,11],... 

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