Order electricity

Meyer s idea of flexoelectricity has been generalized to include a contribution due to the gradient of the orientational order parameter. The polarization in this case arises not from the curvature distortion of the director but from the spatial variation of the degree of orientational order of the molecules. In a simple first order theory, one may take P oc V5, where s is the order parameter as defined in 2.3.1. This effect has been termed as order electricity . 

Order electricity may be expected to manifest itself at the nematic-isotropic (or air) interface where, as discussed in 2.7, the order parameter changes rapidly across the transition zone from one phase to the other. Let us make the simple assumption that at the N-I interface the gradient of the order parameter sj, where is a coherence length. If is the component of the polarization normal to the interface created by the order parameter gradient, and the director at the interface is tilted at an angle 6 with respect to z, the dielectric energy due to order electricity will be proportional to  

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Data Required When Ordering Electric Motors... 

Thornton, D. P, Jr., How to Get What You Need When You Order Electric Motors, Petroleum Processing, p. 1318, Sept. (1953). 

The region from the Helmholz plane into the solution, across which the potential varies exponentially attaining a value of zero at some distance in this region the ions are subjected to both ordering electrical forces and disordering thermal forces. 

We assume that the double bonds in 1,3-butadiene would be the same as in ethylene if they did not interact with one another. Introduction of the known geometry of 1,3-butadiene in the s-trans conformation and the monopole charge of 0.49 e on each carbon yields an interaction energy <5 — 0.48 ev between the two double bonds. Simpson found the empirical value <5 = 1.91 ev from his assumption that only a London interaction was present. Hence it appears that only a small part of the interaction between double bonds in 1,3-butadiene is a London type of second-order electrical effect and the larger part is a conjugation or resonance associated with the structure with a double bond in the central position. 

The ENBO method, which is a method for incorporating polarization and higher order electric field-molecule interaction terms into the theory, is discussed in Section IV. Nearly all OCT experiments actually use laser pulses that give rise to strong electric fields that are sufficiently strong to significantly... 

Five large basis sets have been employed in the present study of benzene basis set 1, which has been taken from Sadlej s tables [37], is a ( ()s6pAdl6sAp) contracted to 5s >p2dl >s2p and contains 210 CGTOs. It has been previously adopted by us in a near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38]. According to our experience, Sadlej s basis sets [37] provide accurate estimates of first-, second-, and third-order electric properties of large molecules [39]. 

These findings imply that our basis sets are definitely more reliable than those adopted in Ref. 16 and Ref. 18 for studying second-order electric properties. Accordingly, it seems quite difficult to understand that theoretical obtained via... 

Antiparallel dipole ordering to produce an antiferroelectric crystal is also commonly encountered. Other ways of ordering electric dipoles are not so well characterized, but parallels with the situation in magnetic materials occur. 

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

On matrix form the non-unitary transformations (27) and (30) of the previous section are easily extended to the complete Hamiltonian and have therefore allowed relativistic and non-relativistic spin-free calculations of spectroscopic constants and first-order properties at the four-component level (see, for instance. Refs. [45 7]). In this section, we consider the elimination of spin-orbit interaction in four-component calculations of second-order electric and magnetic properties. Formulas are restricted to the Hartree-Fock [48] or Kohn-Sham [49] level of theory, but are straightforwardly generalized. 

We then turn to the question of how to eliminate the spin-orbit interaction in four-component relativistic calculations. This allows the assessment of spin-orbit effects on molecular properties within the framework of a single theory. In a previous publication [13], we have shown how the spin-orbit interaction can be eliminated in four-component relativistic calculations of spectroscopic properties by deleting the quaternion imaginary parts of matrix representations of the quaternion modified Dirac equation. We show in this chapter how the application of the same procedure to second-order electric properties takes out spin-forbidden transitions in the spectrum of the mercury atom. Second-order magnetic properties require more care since the straightforward application of the above procedure will extinguish all spin interactions. After careful analysis on how to proceed we... 

Applying the first-order electric dipole transition rate expressions... 

Awq, in terms of interactions of the lowest-order electrical multipoles is often... 

Stern Combination of Parallel-Plate and Diffuse-Charge Models 9m = -9S = "[9h + J t 1 1 C Qi Qi maV=waVhaV Pole r R 1 of ,ial. linear variation V, ions are under the combined influence of the ordering electrical and the disordering thermal forces. Agrees with the experiment only for ions nonspecificaHy adsorbed on the electrode (e g. NaF). 

C(2)(t,q) can be related to the normalized first-order electric field time correlation function g (t,q) by [9,10]... 

In dynamic LLS [45,46], the intensity-intensity time correlation function G(2 t, q) in the self-beating mode was measured. For a Poisson distribution of the number of photons, G 2)(f, q) can be related to the normalized first-order electric field time correlation function g (f, q) as [46]... 

One can measure the dielectric constant e of gases, liquids and solids by placing the sample in a capacitance cell. From measuring e as a function of temperature, one routinely gets the scalar first-order electric dipole susceptibility... 

B. Direct Fifth-Order Electrically Nonresonant Scattering... 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

Here Pind is the induced dipole moment per unit volume, and X X and X are the first-, second-, and third-order electric susceptibilities of the sample, where the order refers to the power of electric field (not of X). Equation (1) represents the macroscopic (bulk) form for the polarization in terms of single molecule properties, the induced dipole moment per molecule is written as... 

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