Torques electric field

Electro-osmosis has been defined in the literature in many indirect ways, but the simplest definition comes from the Oxford English Dictionary, which defines it as the effect of an external electric held on a system undergoing osmosis or reverse osmosis. Electro-osmosis is not a well-understood phenomenon, and this especially apphes to polar non-ionic solutions. Recent hterature and many standard text and reference books present a rather confused picture, and some imply directly or indirectly that it cannot take place in uniform electric fields [31-35]. This assumption is perhaps based on the fact that the interaction of an external electric held on a polar molecule can produce only a net torque, but no net force. This therefore appears to be an ideal problem for molecular simulation to address, and we will describe here how molecular simulation has helped to understand this phenomenon [26]. Electro-osmosis has many important applications in both the hfe and physical sciences, including processes as diverse as water desahnation, soil purification, and drug delivery. 

As a result of the projection theorem [31], the expectation value of the EDM operator d, which is a vector operator, is proportional to the expectation value of J in the angular momentum eigenstate. This fact, in conjunction with Eq. (9), implies that the electric field modifies the precession frequency of the system because of the additional torque experienced by the system due to the interaction between the electric field and the EDM. It can readily be shown that the modified precession frequency is... 

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]). 

The application of an electric field above the threshold value results in a reorientation of the nematic liquid crystal mixture, if the nematic phase is of negative dielectric anisotropy. The optically active dopant then applies a torque to the nematic phase and causes a helical structure to be formed in the plane of the display. The guest dye molecules are also reoriented and, therefore, the display appears coloured in the activated pixels. Thus, a positive contrast display is produced of coloured information against a white background. The threshold voltage is dependent upon the elastic constants, the magnitude of the dielectric anisotropy, and the ratio of the cell gap to the chiral nematic pitch ... 

Kielictf has calculated the Langevin functions generated by this type of torque, where Eg is an electric field. The torque produces the results... 

The effect of the strong external field is to accentuate this difference— using the method first developed for achiral molecules described earlier in this review—that of aligning the molecules in the molecular dynamics cube with an externally applied torque.This may be used to simulate the effect of an electric field on an assembly of dipolar molecules using second-order... 

The operator representing the torque on the electrons due to the external electric field (Lorentz electric torque) is... 

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. 

We consider the rotational motion of a thin rod, or rotator, representing the linear polar molecule, which is subjected to an external electric field F [8,41]. We assume that the field F is parallel to the Z axis of the laboratory coordinate system OXYZ. In the molecular coordinate system oxyz rigidly connected to the rotator, the components of the angular velocity of the rotator and of the torques K produced by the field F are [41]... 

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). 

According to Eq. (20), the multipolar DEP force and ROT torque on a particle can be determined as long as the electric field distribution in the system is known. 

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