Electric field effect square

The electric field effect on the fluorescence yield of the primary donor ip reflects the competition between the radiative rate and the field modulated rate k or k, respectively. For isotropically distributed RCs, the lowest term in the expansion for the field dependence of the fluorescence change = (E)- (O) is proportional to (/lE), since any linear contribution cancels due to mirror symmetry with respect to the electric field. In fact a quadratic dependence of was observed (see [12] and Fig.l), which holds up to external fields of about S-IO V/cm. At such fields an electric field induced fluorescence increase of ci 80% is observed. A least square fit of the data in Fig.l gives an exponent of 1.98 0.02 for... 

Piezoelectrics. AH ceramics display a slight change ia dimension, or strain, under the appHcation of an electric field. When the iaduced strain is proportional to the square of the field iatensity, it is known as the electrostrictive effect, and is expressed by ... 

According to this approximation, the drift velocity is proportional to the square of the electric field. This is a clear indication of the importance of the electric field inside an electrostatic precipitator. Equation (13.60) is a valid approximation for large particles [dp > 0.5 m), provided that particle charge is close to the saturation level. In the case of small particles, the effect of diffusion charging must be taken into account. 

The contribution to the stress from electromechanical coupling is readily estimated from the constitutive relation [Eq. (4.2)]. Under conditions of uniaxial strain and field, and for an open circuit, we find that the elastic stiffness is increased by the multiplying factor (1 -i- K ) where the square of the electromechanical coupling factor for uniaxial strain, is a measure of the stiffening effect of the electric field. Values of for various materials are for x-cut quartz, 0.0008, for z-cut lithium niobate, 0.055 for y-cut lithium niobate, 0.074 for barium titanate ceramic, 0.5 and for PZT-5H ceramic, 0.75. These examples show that electromechanical coupling effects can be expected to vary from barely detectable to quite substantial. 

FIG. 10 Effect of an electric field (Eg) on the mean-squared displacement perpendicular to the plane of the membrane for a 4.67 mole percent aqueous LiCl solution at 25°C and 1 bar [25]. 

Thus the IR active modes will be determined by the matrix elements of the polarlsablllty matrix and not by a combination of the surface selection rule and the normal IR selection rules l.e. all of the Raman active modes could become accessible. This effect has been formalized and Its significance assessed In a discussion (12) which compares Its magnitude for a number of different molecules. In the case of acrylonitrile adsorption discussed In the previous section, the Intensity of the C=N stretch band appears to vary with the square of the electric field strength as expected for the Stark effect mechanism. 

The value of the matrix element of the operator in Eq.(42) is determined principally by contributions from the regions in and around the nuclei, where both the electric field and the small component (relativistic effect) of the wavefunctions are largest. In the absence of screening Eij), the nuclear electric field diminishes with the square of the distance from the center of a nucleus screening further accelerates the decline of the electric field with distance. The electrons of each constituent atom have completely screened their nuclei at the location of any other nucleus, for which reason, and to a very good approximation, the problem is uncoupled for the various nuclear regions. 

The fourth term is a polarisation term. Here E(z) = di/z/dz is the electric field at position z. In previously published SCF results for charged bilayers, this last term is typically absent. It can be shown that the polarisation term is necessary to obtain accurate thermodynamic data. We note that all qualitative results of previous calculations remain valid and that, for example, properties such as the equilibrium membrane thickness are not affected significantly. The polarisation term represents relatively straightforward physics. If a (united) atom with a finite polarisability of erA is introduced from the bulk where the potential is zero to the coordinate z where a finite electric field exists, it will be polarised. The dipole that forms is proportional to the electric field and the relative dielectric permittivity of the (united) atom. The energy gain due to this is also proportional to the electric field, hence this term is proportional to the square of the electric field. The polarisation of the molecule also has an entropic consequence. It can be shown that the free energy effect for the polarisation, which should be included in the segment potential, is just half this value... 

Sc, carbon chemical shift, referred to tetramethylsilane (8 = 0) (cf. Sect. I) SCS, substituent-induced chemical shift, or substituent effect difference between S s of a given carbon atom in a monosubstituted and the respective unsubstituted parent molecule (cf. Sect. Ill) NAE, nonadditivity effect nonadditivity of individual SCSs in disubstituted molecules (cf. Sect. IV) ICS, intramolecular-interaction chemical shift = NAE (cf. Sect. IV) A, polarization effect difference in S s of sp2 carbon atoms in a double bond (cf. Sect. IV-C) LEF, linear electric field (cf. Sect. II-B-3) SEF, square electric field (cf. Sect. II-B-3). 

The second contribution in eq. [8] is the square-electric-field (SEF) effect, where (E2) is the time-averaged square of the electric field E (76) ... 

Similar splitting can occur in the presence of an electric field typically of strength > 10s volts cm-1 (Stark effect). The extent of splitting of energy terms is proportional to the square of the electric field strength. (ii) Interaction between p and d electron /i== 1 and /s = 2 L = 3,2,h... 

While the nuclei 3H and 13C relax predominantly by the DD mechanism, relaxation of a quadrupole nucleus such as deuterium essentially involves fluctuating fields arising from interaction between the quadrupole moment and the electrical field gradient at the quadrupole nucleus [16]. If the molecular motion is sufficiently fast (decreasing branch of the correlation function, Fig. 3.20), the 2H spin-lattice relaxation time is inversely proportional to the square of the quadrupole coupling constant e2q Q/H of deuterium and the effective correlation time [16] ... 

Finally, use of square (Lee et al., 2002b) or half (Lee et al., 2003) wave-pulsed electric fields of given frequency was found to be effective to mitigate anionic membrane fouling in presence of sodium humate. 

All materials undergo a small change in dimensions when subjected to an electric field. If the resultant strain is proportional to the square of the field it is known as the electrostrictive effect. Some materials show the reverse effect - the development of electric polarization when they are strained through an applied stress. These are said to be piezoelectric (pronounced pie-ease-oh ). To a first approximation the polarization is proportional to the stress and the effect is said to be direct . Piezoelectric materials also show a converse effect, i.e. the development of a strain x directly proportional to an applied field. 

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