Electric coefficient

Note A flexo-electric domain occurs when Ae< Anel/K where e is the flexo-electric coefficient and K is the elastic constant, assuming Ki = Kt, = K and e = -e = e (see Definitions 5.3 and 5.16). 

Thus the quadrupole mechanism yields very simple expressions for the flexo-electric coefficients, which are proportional to the nematic order parameter S in the first approximation (usually the parameter D is much smaller than S). In addition, the difference of the flexoelectric coefficients appears to be equal to zero, i.e. Ae = ei — 03 = 0 if the quadrupole contribution alone is taken into account. 

This chapter is concerned with experimental measurements of flexo-electric coefficients. After a brief introduction to flexoelectricity in nematic liquid crystaJs, some applications exploiting the flexoelectric effect and the influence of this effect on electrohydrodynamic instabilities are pointed out. Flexoelectricity axises in samples with a splay-bend distortion in the director field and as such its measurement is not as direct as for dielectric constants. The theoretical background needed to analyse electro-optic experiments and extract the flexocoefficients is outlined in Section 2.2. Various experimental techniques that have been developed are described in Section 2.3. These involve cells in which the alignment of the nematic director is homeotropic, or planar or hybrid. In the first case, the interdigitated electrode technique is particularly noteworthy, as it has been used to establish several features of flexoelectricity (1) the effect can arise purely from the quadrupolar nature of the medium, and (2) the dipolar contribution relaxes at a relatively low frequency. 

The dipolar mechanism is sensitive to the molecular shape. By dimensional considerations one can estimate the flexocoefficients due to dipolar mechanism as ei, 63 < /Xe/a, where /Xg 1-5 debye (1 D = 3.3x 10 Cm) is the molecular dipole moment and a 2-4 nm is the typical molecular dimension for a low molecular weight liquid crystal. This means that e and 63 are expected to be of the order of pCm. Assuming a random three-dimensional distribution of the centre of masses of the constituent bent-core (banana-shaped) molecules, Helfrich and Derzhanski and Petrov derived a more precise expression for the macroscopically testable bend fiexo-electric coefficient ... 

Another reason for the moderate popularity of the field among experimentalists is that fiexoelectricity-driven effects are rare their detection mostly requires unusual surface (anchoring) conditions, moreover, the flexo-electric coefficients are small (in the range of pC/m), thus are not easily measurable and the results are often contradictory. 

Piezoelectric Constitutive Relationships. The constitutive relationships that describe piezoelectric behavior in materials can be derived from thermodynamic principles (4). A tensor notation is adopted to identify the coupling between the various entities through mechanical and electrical coefficients. The common practice is to label directions as depicted in Figure 2. The stretch direction... 

The temperature gradient induced electric polarization allows us to estimate the order electricity coefficients ri, V2 in the expression (3.20) for the order polarization [202]. If a nonzero temperature gradient grad T 7 0 is installed the value of the order polarization could be rewritten as... 

The acconunodation coefficient for Kr on a carbon filament is determined experimentally as follows. The electrically heated filament at temperature 72 is stretched down the center of a cylindrical cell containing Kr gas at 7. Gas molecules hitting the filament cool it, and to maintain its temperature a resistance heating of Q cal sec cm is needed. Derive from simple gas kinetic theory the expression... 

Some electric properties of molecules are described in section Al.5.2.2 because the coefficients of the powers of Mr turn out to be related to them. The electrostatic, mduction and dispersion energies are considered m turn in section Al.5.2.3, section Al.5.2.4 and section Al.5.2.5, respectively. 

Figure A2.3.18 The excess energy in units of NkT as a fiinction of the concentration for the RPM and SEM 2-2 electrolyte. The curves and points are results of the EfNC/MS and HNC approximations, respectively, for the binding and the electrical interactions. The ion parameters are a = 4.2 A, and E = 73.4. The sticking coefficients = 1.6x10 and 2.44x 10 for L = all and a/3, respectively.

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

The reflection coefficients rP and r give the electric field in the reflected beam for each polarization. Since the intensity of light is proportional to the square of the electric field, the reflectances for s- and p-polarized... 

The application of a small external electric field A to a semiconductor results in a net average velocity component of the carriers (electrons or holes) called the drift velocity, v. The coefficient of proportionality between E and is known as the carrier mobility p. At higher fields, where the drift velocity becomes comparable to the thennal... 

Optical detectors can routinely measure only intensities (proportional to the square of the electric field), whether of optical pulses, CW beams or quasi-CW beams the latter signifying conditions where the pulse train has an interval between pulses which is much shorter than the response time of the detector. It is clear that experiments must be designed in such a way that pump-induced changes in the sample cause changes in the intensify of the probe pulse or beam. It may happen, for example, that the absorjDtion coefficient of the sample is affected by the pump pulse. In other words, due to the pump pulse the transparency of the sample becomes larger or smaller compared with the unperturbed sample. Let us stress that even when the optical density (OD) of the sample is large, let us say OD 1, and the pump-induced change is relatively weak, say 10 , it is the latter that carries positive infonnation. 

The electronic transitions which produce spectra in the visible and ultraviolet are accompanied by vibrational and rotational transitions. In the condensed state, however, rotation is hindered by solvent molecules, and stray electrical fields affect the vibrational frequencies. For these reasons, electronic bands are very broad. An electronic band is characterised by the wave length and moleculai extinction coefficient at the position of maximum intensity (Xma,. and emai.). 

The electronic configuration for an element s ground state (Table 4.1) is a shorthand representation giving the number of electrons (superscript) found in each of the allowed sublevels (s, p, d, f) above a noble gas core (indicated by brackets). In addition, values for the thermal conductivity, the electrical resistance, and the coefficient of linear thermal expansion are included. 

It resembles polytetrafiuoroethylene and fiuorinated ethylene propylene in its chemical resistance, electrical properties, and coefficient of friction. Its strength, hardness, and wear resistance are about equal to the former plastic and superior to that of the latter at temperatures above 150°C. 

The strain j Hes along the axis of the electric field, E, or most often along the axis of the induced polari2ation, P. The electrostrictive coefficients for the electric field and polari2ation are M and respectively. Electrostriction is a small effect. In contrast to pie2oeIectric materials, electrostrictive materials... 

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