Dipole moment in the field

Imagine a spinning top which is a magnet. If you make it spin (with angular momentum I) and leave it in space without any external torque t, then due to the fact that space is isotropic, its angular momentum will stay constant, because = t = 0 (t is time), i.e. the top will rotate about its axis with a constant speed and the axis will not move with respect to distant stars. Fig. 12.9.a. 

The situation changes if a magnetic field is switched on. Now, the space is no longer isotropic and the vector of the angular momentum is no longer conserved. However, the conservation law for the projection of the angular momentum on the direction of the field is still valid. This means that the top makes a precession about the 

that the energy level splitting is proportional to the magnetic field intensity. Fig. 12.10. 

We see (Fig. 12.10) that for nuclei with y 0, lower eneigy corresponds to m/ = 2, i.e. to the spin moment along the field (forming an angle B = 54°44 with the magnetic field vector, see p. 28). 

Joseph Larmor (1857-1942), Irish physicist, professor at Cambridge University. 

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The quantity of interest to us is the average behavior of the component of the dipole moment in the field direction, namely () (we postulate an assembly of such rotating spheres). Since... 

An obvious aim of simulations and theoretical studies is to understand the mechanisms by which the structures observed in experiment (or simulations) evolve. A first explanation of how chains can attract each other in ER fluids was provided by Halsey and Toor [257,297,298]. These authors remark that once chains have grown sufficiently large to span the electrodes, they behave effectively as infinite chains, due to the image charges. If these chains were perfectly ahgned touching spheres with fixed dipole moments in the field direction (no thermal effects) two such (infinite) chains would repel each other if in register and attract each other when offset by one radius in the field direction. However, the electric field created by the perfect chain... 

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

The question arises whether an external electric field will have any large influence on the direction of these proton transfers. In the NH3 molecule all three protons are situated in one hemisphere of the electronic cloud, and so give to the molecule a dipole moment. In the (NH4)+ ion, on the other hand, it is generally accepted that the four protons are placed symmetrically at the corners of a tetrahedron. Accordingly, the (NH4)+ ion will have no dipole moment. 

The concept of hyperconjugation arose from the discovery of apparently anomalous electron-release patterns for alkyl groups. By the field effect alone, the order of electron release for simple alkyl groups connected to an unsaturated system is fert-butyl > isopropyl > ethyl > methyl, and this order is observed in many phenomena. Thus, the dipole moments in the gas phase of PhCHa, PhC2Hs, PhCH(CHa)2, and PhC(CHa)a are, respectively, 0.37, 0.58, 0.65 and 0.700. ... 

The second procedure, several aspects of which are reviewed in this paper, consists of directly computing the asymptotic value by employing newly-developed polymeric techniques which take advantage of the one-dimensional periodicity of these systems. Since the polarizability is either the linear response of the dipole moment to the field or the negative of the second-order term in the perturbation expansion of the energy as a power series in the field, several schemes can be proposed for its evaluation. Section 3 points out that several of these schemes are inconsistent with band theory summarized in Section 2. In Section 4, we present the main points of the polymeric polarization propagator approaches we have developed, and in Section 5, we describe some of their characteristics in applications to prototype systems. 

Although most solids do not have a dipole moment in the absence of an electric field, the classes of solids that do are commercially important, and so form the subject matter of the rest of this chapter. 

If the electric and magnetic dipole moments in the presence of frequency-dependent electric and static magnetic fields are expanded in a series, the leading terms give the following expression for (9)... 

This description of antennas may seem more appropriate to a discussion of radio or television waves. We must realize, however, that at the molecular level dipoles behave exactly like antennas. Since molecules are made up of charged parts, a dipole moment /x is induced by the electric field of the radiation in any material through which radiation passes. In this discussion, the dipole moment equals the product of the effective charge displaced by the field and its distance of separation from the opposite charge. In SI, pi has units C m. We consider isotropic materials characterized by a polarizability a. As the name implies, this property measures the ease with which charge separation —polarity —is induced in a molecule by an electric field. For isotropic substances, the dipole moment and the field are related by the expression... 

Given the lack of success with the phase-tailored UV pulse we tried a different approach a two-pulse scheme, where a weak-field ultrashort UV pulse is combined with a strong infrared (IR) field [7]. The strong IR field affects the nuclear dynamics such that the propagator AT, in Eq. (1) in this case describes the nuclear dynamics under the influence of Vt + fijEm (r), where fii is the dipole moment in the electronic state i. The idea that this approach may work is based on the fact that the nuclear dynamics no longer takes place on the pure Bom-Oppenheimer potentials and this may speed up the process. Various applications of IR+UV two-pulse schemes have been discussed recently [9-12]. 

The second thought experiment resembles transient solvation. At t = 0, a certain amount of charge is put on the capacitor plates. This charge jump (D field jump) is analogous to the photon induced change of the dipole moment in the fluorescence solvation experiment. Subsequently (t > 0), the decay of the voltage on the capacitor due to dielectric relaxation of the medium is measured. Note the capacitor in this experiment is not connected to an external power supply for t > 0. The characteristic relaxation time for the decay of the voltage (and electric field E) is t,. 

Separation of Electronic and Nuclear Motions. The polarizabilities of the ground state and the excited state can follow an electronic transition, and the same is true of the induced dipole moments in the solvent since these involve the motions of electrons only. However, the solvent dipoles cannot reorganize during such a transition and the electric field which acts on the solute remains unchanged. It is therefore necessary to separate the solvent polarity functions into an orientation polarization and an induction polarization. The total polarization depends on the static dielectric constant Z), the induction polarization depends on the square of the refractive index n2, and the orientation polarization depends on the difference between the relevant functions of D and of n2 this separation between electronic and nuclear motions will appear in the equations of solvation energies and solvatochromic shifts. 

We noted earlier (Section I. 1.) that the intensity of an absorption band is proportional to the square of the changing dipole moment in the molecule (i. e., transition moment) during the corresponding normal vibration. The intensity also depends upon the direction that the electric vector in the incident radiation makes with the transition moment. In particular, the intensity is proportional to the square of the scalar product of the transition moment and electric field vectors. This implies, for example, that if the electric field vector is perpendicular to the transition moment vector no absorption will occur. This fundamental relationship is the basis for the utilization of polarized infrared radiation as a powerful tool in the study of the spectra and structure of oriented polymers. We consider below some aspects of this technique. 

Fig. 6 (a) Cartoon of a nanoparticle with no electric dipole moment in the isotropic phase, (b) Cartoon of a ferroelectric nanoparticle with electric dipole moment, which produces an electric field that interacts with orientational order of the nematic phase [327], (Copyright 2009, American Physical Society)... 

To visualize the depolarization fields we may consider the following idea assume we find a molecule with its absorption dipole moment in the plane of the sample. We now adjust the polarization of the excitation beam such that the fluorescence is maximized. We may assume that this happens if the electric field vector in the focus is parallel to the dipole moment. Now, if we turn the incoming polarization by 90° the dominant electric field component will not be able to excite the molecule and the presence of other field components should become visible as weak, but distinctly non-circular spots. Figure 6 shows the result of such an experiment. In Fig. 6(b) the polarization has been turned by 90° as compared to (a) as indicated by the white arrows. The bright spots become dim and their symmetry changes to a four-lobed structure. These weak structures can be made visible if the excitation intensity is increased by a factor of five [see Figs. 6(c) and (d)]. 

The principle behind this investigation is electrochromism or Stark-effect spectroscopy. The electronic transition energy of the adsorbed chromophore is perturbed by the electric field at the electric double layer. This is due to interactions of the molecular dipole moment, in the ground and excited states, with the interfacial electric field induced by the applied potential. The change in transition frequency Av, is related to the change in the interfacial electric field, AE, according to the following ... 

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