Electric field effect linear

Quadratic Response (3rd rank tensors) (1) electric field effects Linear electrooptic (Pockels) effect, three-wave mixing, SHG. (2) radiation/magnetic field Faraday Effect. 

The discussion above has been more or less empirical and descriptive. However, considerable effort has been made to interpret 3-SCS on a more physical basis. Electric-field effects (71-75) were invoked to explain signal shifts of 3-carbon atoms induced by protonation of amines (157,158) (cf. Section II-B-3). This approach was later extended to other functionalities by Schneider and coworkers, who assumed that the SEF component (E2) rather than inductive properties of the substituents should be responsible for 3-SCS (113). They found fairly linear correlations of 3-SCS(X ) and 3-SCS(X ) in cyclohexyl derivatives (76) and attributed the difference between these for a given X to a widening of the C -Cp-Cv bond angle by 2.2° in the axial conformer (114,159). The decrease of 3-SCS in the order primary Cp —> secondary Cp — tertiary Cp — quaternary Cp was explained by electron-charge polarization in the Cp-C" bond(s) induced by the LEF component of the C -X dipole, which is already of significance at this distance, though ( 2) still dominates (160). Such an electron flow toward the 3 carbon is expected to be much more pronounced in C-C than in C-H bonds because of the polarizability difference (aCH = 0.79 acc = 1.12) (150,151,160). 

Nonlinear effects are characterized by new components of the -field generated from the acceleration of charges as the nonlinear polarization P [second, third, and higher terms in Equation (4.1)] drives the electric field. When linear absorption... 

Calculations of the external electric field effect on the escape probability in multipair clusters [18] have shown that significant deviations from the results of the single-pair theory are expected at high electric fields. At low fields, the escape probability is a linear... 

From the foregoing discussion of electric field effects In Ionic equlibria It Is clear that a solution of a weak electrolyte shows a non-linear behavior In conductance (or resistance) at high field strengths. With an Interdisciplinary look at the field of electronics we note that such nonlinearities are at the heart of all modern electronic circuits and devices. We therefore can use a solution of a weak electrolyte subjects to high electric fields as an electronic device, which Is the basic Idea of the Field Modulation Tecnnlque, the general principles we will discuss now. 

Where Cz characterizes Xe-surface collisions and p, is the probability factor depending only on the particular structure under consideration. The importance of Eq. (27) lies in the fact that its various terms can be determined separately. For example, ds + SE is obtained by extrapolation of the plot of chemical shift to zero pressure. It is found that 8B is negligible in zeolites Na-Y and H-Y, possibly because of motional averaging of electric field effects on the large faujasite supercages, but it becomes important in alkaline earth-exchanged forms. Zeolites Ca-A, Na-X, Na-Y, H-Y Ca-Y, L, mordenite, and ZSM-5 have been studied using the method because of the aperture size, xenon is not sorbed on zeolite Na-A. In synthetic faujasites, the chemical shift is a linear function of pressure and varies between 58 to 110 ppm (from Xe gas... 

ESR-active clusters will be oxidized 3Fe, oxidized HiPIP, reduced 2Fe and reduced 4Fe (Fd). Further distinction may be made by consideration of the dependence on magnetic fields of the shift in g value induced by an externally applied electric field (linear electric field effect). This effect is similar for 3Fe and 4Fe ferredoxins, but is considerably different for both 2Fe and HiPIP clusters, which also differ from each other. Thus, all four classes of iron-sulfur protein (2Fe, 3Fe, Fd and HiPIP) may be distinguished by a combination of ESR and LEFE properties.814 ... 

Kama recently reported an ab initio study of linear electric field effects on the g-tensor and on the hyperfine splitting constant (the Bloembergen effect) of the silyl radical ( SiH3)13. TDUHF calculations predict an increase in hyperfine splitting in "SiH3 due to the Bloembergen effect, predictions which have yet to be verified experimentally. 

Mims, W. B. The Linear Electric Field Effect in Paramagnetic Resonance, Oxford, Clarendon 1976... 

If coherent radiation with a very high intensity is applied continuously or as pulse, non-linear effects can be observed which produce coherent Raman radiation. This is due to the quadratic and cubic terms of Eq. 2.4-14, which describe the dipole moment of a molecule induced by an electric field. Non-linear Raman spectroscopy and its application are described in separate chapters (Secs. 3.6 and 6.1), since this technique is quite different from that of the classical Raman effect and it differs considerably in its scope. 

This feature has frequently been introduced in various ad hoc empirical fashions in dielectric discussions. One analytically explicit form was used by Piekara (1939) to account for the non-linear electric field effects, e.g. in liquid nitrobenzene. The importance of these effects is in part precisely because they allow a sensibly direct appraisal of dipole inter-correlations (see Chapter 7). 

Permittivity variations in a strong electric field non-linear and saturation behaviour progress of e gperimental methods molecular behaviour and various theoretical models molecular correlations complete dielectric saturation electrostriction and electrocaloric effect. 

It is to Piekara and his collaborators that we owe almost all the currently available significant data on non-linear electric field effects in condensed molecular systems, including at least three different forms of molecular response. See Ann. Reports (,A), 1970, 67, 87— 96. (Note by Senior Reporter.)... 

High Electric Field Effects.—Determination of Variations in Electric Permittivity. The electric permittivity e of an isotropic dielectric is usually measured by means of a dowly varying dectric field, of a field strength Eoo so small as to cause only linear polarization of the medium ... 

The Onsager Model in the Non-linear Electric Field Effect. The non-linear dectric field theory of Debye disagrees with most of the measurements of Ac in liquids and thdr solutions. To Van Vleck is due the atten t to reduce the discrepandes by applying Onsager s local electric field model in the treatment of the field effect. Aiming at simplidty, he considered only the influence of reorientation of ri d (not polarizable) electric dipoles p,... 

A variety of spectroscopic and physical techniques have been used to investigate the nature of these redox centers. EPR, Fe Mossbauer spectroscopy, and Mo and Fe X-ray absorption spectroscopy Mo, Fe, and H electron-nuclear double resonance (ENDOR) linear electric field effect and magnetic circular dichroism (MCD) have provided information about the environment of the Mo and Fe nuclei and their interaction with the unpaired spin of electrons in paramagnetic species of the MoFe proteins. 

The linear response function [3], R(r, r ) = (hp(r)/hv(r ))N, is used to study the effect of varying v(r) at constant N. If the system is acted upon by a weak electric field, polarizability (a) may be used as a measure of the corresponding response. A minimum polarizability principle [17] may be stated as, the natural direction of evolution of any system is towards a state of minimum polarizability. Another important principle is that of maximum entropy [18] which states that, the most probable distribution is associated with the maximum value of the Shannon entropy of the information theory. Attempts have been made to provide formal proofs of these principles [19-21], The application of these concepts and related principles vis-a-vis their validity has been studied in the contexts of molecular vibrations and internal rotations [22], chemical reactions [23], hydrogen bonded complexes [24], electronic excitations [25], ion-atom collision [26], atom-field interaction [27], chaotic ionization [28], conservation of orbital symmetry [29], atomic shell structure [30], solvent effects [31], confined systems [32], electric field effects [33], and toxicity [34], In the present chapter, will restrict ourselves to mostly the work done by us. For an elegant review which showcases the contributions from active researchers in the field, see [4], Atomic units are used throughout this chapter unless otherwise specified. 

The linear electrooptic effect is tlie change in the index of refraction of a medium due to the presence of a dc or low-frequency electric field, in such a manner that the change in the index of refraction depends linearly in the strength of the low-frequency electric field. The linear electrooptic effect is tlie mechanism behind optical intensity modulators that are used in optical switching and fiber-optics communications, where the optical signal is modulated at high frequencies (out to 110 GHz) [7-9],... 

Note Ring-current (anisotropy) effects 60-85% (orientation dependent). Linear electric field effects 15-40% (orientation dependent) complexation-induced shifts in ppm. 

The two derivatives Ag Cu and CU2CU2SOD [the latter obtained through semireduction of Cu Cu SOD] show quite similar visible absorption and EPR spectra 244, 252). The spectra are characteristic of Cu(II) in the zinc site without interference from paramagnetic ions in the copper site. The h3q)erfine coupling constant of 105 X 10 cm" is typical of copper(II) tetrahedral complexes 244, 252). Experiments based on linear electric field effect (LEFE) in pulsed EPR also support the conclusion that Cu(II) in the zinc site retains the pseudotetrahe-dral coordination geometry. Furthermore, ENDOR and ESEEM experiments on Ag 2Cu2 SOD pointed out that Cu(II) forms inequivalent bonds to the three coordinated imidazoles 289). 

C chemical shifts of stearic, oleic, linoleic, a-linolenic and arachidonic acids have been assigned (Stoffel et al., 1972) and the data are presented in Table 21. Electric field effects associated with the dipolar head groups have been shown to be effective in influencing the 1 3C chemical shifts of unsaturated fatty acids (Batchelor et al., 1973). This electric field effect (Horsley and Sternlicht, 1968, McFarlane, 1970), predicted to be linear and dependent on distance and orientation, can be applied to problems of conformational analysis. A nondestructive technique utilizing l3Cnmr to determine the relative concentrations of the unsaturated fatty acids present in soyabeans has recently been developed (Schaefer and Stejskal, 1974). 

The upper lim cone conformed calix[4]arene-zinc porphyrin (ZP) conjugate 180 derivatized at ZP with a p5u-omellitimide (PI) electron acceptor at the distal position on calixarene with a carotenoid unit was designed and S5mthesized for stud5ung the electric field effect of photogenerated ion pair on an adjacent chromophore. The photoinduced charge separation within a ZP-PI electron donor-acceptor pair having an 8.4 A center-center distance in a linear orientation has been found to... 

Several spectroscopic techniques have been used to study nitrogenase proteins both in the isolated forms and during enzymatic activity. These include electron paramagnetic resonance (epr) spectroscopy, Mossbauer spectroscopy, uv-visible spectrophotometry, circular dichroism. X-ray absorption edge and fine structure spectroscopy (EXAFS), and linear electric field effects (LEFE). 

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