Electric dipole torque

Ferraro and coll, used canonical transformation of the Hamiltonian to resolve the average optical rotatory power of a molecule into atomic contributions, based on the acceleration gauge for the electric dipole, and/or the torque formalism [151], This method has been applied to the study of the conformational profile of the optical rotatory poser of hydrogen peroxide and hydrazine [152]. 

The surface potential is easily predicted to alter the retention behavior of zwitterions. The molecular electrical dipole is subjected to a torque moment that... 

The dielectric constant at angular frequent w is e (tu) = e (.dielectric constants are Su (sometimes written ) and (sometimes written f,). In Debye s model the relaxing element (which represents a polar molecule) is a sphere of radius a containing an electric dipole of dipole moment p-qd (see Figure 4.36). The sphere is immersed in a liquid of viscosity i). Under an electric field E the torque on the dipole is pE sin d. The rotation of the dipole under this torque is resisted by the Stokes firictional torque The dipole will follow the field for... 

Furthermore, in FLCEs the macroscopic electric dipole moment provides a handle to apply a strong torque onto the director (see Fig. 14a). The resulting switching occurs on the cone of the so-called c-director, the projection of the director on the smectic layer plane (see Fig. 14a). Soon after the discovery of the potential of chiral smectic-C phases, the search for LC polymers with these phases started [130-132]. However, as ferroelectric switching is the final proof for the assignment of the phase, the more closely studied ferroelectric LC polymers were limited to several LC polysiloxanes, which have a low Tg and a relatively high switching speed [25, 66, 133-136] (see Scheme 1). These polymers form the basis for most of the FLCEs discussed here. 

The linear chain models evidently have no immediate relevance for relaxation of simple polar molecules in liquids but to the writer at least the results suggest strongly the importance particularly at low temperatures of cooperative interactions of molecules with their neighbors %diich may but need not involve electric dipoles as the source of intermolecular torques. When the energies involved are appreciable relative to k T it seems important to develop and study more realistic but still tractable models for analytic and simulation calculations. There have not yet been many serious attempts or promising results in analytical two and three dimensional theories except for diffusion-like models discussed by other contributors to this volume but a few developments which have some relevance can be mentioned. 

Forces on an electric dipole in an electric field E. The dipole moment p is the product of the charge and the separation or qd. The E-field produces a torque given by p x E = pE sinS that tends to align the dipole with the field. The work required to rotate the dipole through angle d is the integral of the torque from 0 to 0, or —pE cos 6 (assuming U = 0 at 0 = tt/2). 

It has been shown experimentally that a beam o circularly-polarized light exerts a torque on any optical component, such as a quarter- or half-wave plate, which changes the state of polarization of the light. This corresponds to a transfer of angular momentum from the radiation fields to the material system. To calculate the rate at which angular momentum is radiated by an electric dipole... 

The K quantum number can not change because the dipole moment lies along the molecule s C3 axis and the light s electric field thus can exert no torque that twists the molecule about this axis. As a result, the light can not induce transitions that excite the molecule s spinning motion about this axis. 

Objects having a dipole can be set into rotational motion by applying a torque by means of an electric field [95], Electrorotation is the rotation of particles as a consequence of the induction of dipole moments and torque exertion by a rotating electric field. Coupled electrorotation (CER) uses static external fields which are spatially fixed to induce dipoles in two or more adjacent particles. This creates oscillating components of the electric field, finally resulting in a rotating electric field (for more details, refer to the original literature [95]). 

Here V(<(), t) = pF(t) cos 4> is the potential arising from an external applied electric field F(f). Here, just as with the translational diffusion equation treated in Ref. 7, we consider subdiffusion, 0 < ct < 1 phenomena only. Here, the internal field effects are ignored, which means that the effects of long-range torques due to the interaction between the average moments and the Maxwell fields are not taken into account. Such effects may be discounted for dilute systems in first approximation. Thus, the results obtained here are relevant to situations where dipole-dipole interactions have been eliminated by extrapolation of data to infinite dilution. 

Contrary to the results of performance property, initial phase tendencies of life-time were well corresponded with the dipole moment values. As showed in Fig. 16, the rate of an initial luminance was decreased in the order of ETl, ET2, ET3, and ET4, which is contrary to the direction of the dipole moment increase in Fig. 9. ETl that can form a robust deposited layer through strong dipole-dipole interactions showed moderate luminance decrease tendency. It can stack regularly in order to form intermolecular network through localized charge distribution in the molecules. It is supvposed that an electrically polarized material located under electric field is torqued by an apvplied electric force and tends to rotate (Fig 17). 

The forces and torques on the polarizability tensors can be evaluated with the induced dipoles (as if they were permanent) and the total electric fields af fhe polarizability tensors. Once the induced dipoles have been determined, the exact polarization energy gradients can be evaluated analytically at a very low cost [16]. 

Electric held seeks to orient dipoles along E, with the torque t and dipole energy proportional to the dipole moment p. If x is directed along E, the angle between E and p is and... 

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