Hertz dipole

Figure 3. A) Electrical fields for a Hertz dipole (E dipole moment p) B) Electrical and magnetic field vectors in the propagation of electromagnetic radiation...

Whereas in gases or liquids the particles are disordered and cause random. scattering, atoms or molecules in the surface layer of solids (especially crystals and metals) are very highly ordered. Especially metals exhibit extremely polarizable electron density distributions. The many Hertz dipoles show constructive interference in certain directions. At solid surfaces this leads to directional reflection, which encloses the same angle with the optical normal to the surface as the incident radiation [11], [20] (Fig. 5). Reflectance R is given by the Fresnel equation, which, for the simplest case of normal incidence and a transparent medium. is [II], [13]... 

While the clathrate model is attractive, it is not correct to assume that the water is organized in some long-lived structure the observation that the self-diffusion coefficient for co-sphere water is larger than that for the solute rules this out. However, the rotational correlation time is shorter for ethanol and t-butyl alcohol in water (in the clathrate cage ) than in the pure liquid (Goldammer and Hertz, 1970 Goldammer and Zeidler, 1969). Nmr experiments show that in water the solvent dipole moments point away from the apolar groups (Hertz and Radle, 1973). 

Not all large molecules are spherical they can also be long random coils with a certain degree of flexibility along the chain. If the chain is flexible, there are rapid local fluctuations between monomers and the dipole-dipole interactions are effectively averaged. An example of this is polyuridylic acid (poly U), which has a molecular weight of 100,000 daltons but is nonetheless very flexible. The line widths for poly U as a random coil are only a few hertz. If the chain is incorporated into a rigid double or triple helix, these local motions are lost and the resonances are broadened beyond detection (see Section 14.7.2). 

Figure 15.1 shows a pair of protons in the magnetic field B0. Because each spin possesses a magnetic moment, each is surrounded by a magnetic field that is experienced by the other. This is the direct, or through-space, dipole-dipole (or dipolar) coupling. The equation that describes the direct splitting Av (in hertz) in the spectrum is... 

There are two conceptually different theories for quadrupolar relaxation of ionic nuclei in solution. Deverell (22) rationalized the electric field gradients at the site of the nucleus as arising from distortions of the closed-shell orbitals in the ion due to collisions with solvent molecules and, at higher concentrations, also counter-ions. In another theory developed by Valiev (23) and by Hertz and his coworkers (24) it is assumed that the electric field gradients are caused by the electric dipoles of the surrounding solvate molecules. It is certainly Hertz to whom we owe the detailed understanding of ionic quadrupole relaxation, and because of the fundamental implications that his work has on ionic solvation the important results are briefly summarized here. 

Holz et al. (47) have recently presented a relaxation model for mixed ionic solvation in binary solvent mixtures. The model, which is an extension of the Hertz electrostatic relaxation theory for ionic quadrupole relaxation at infinite dilution, is based on partial field gradients produced by a single solvent dipole. In a single solvent the quadrupole relaxation rate may be formulated as ... 

Both AP and Ga have a tightly bound hydrate shell in aqueous solution and both are prone to hydrolysis. In terms of the Hertz electrostatic model for quadrupolar relaxation of ionic nuclei in electrolyte solution (see Section III.C) one therefore expects effective quenching of the electric field gradient caused by the surrounding water dipoles, due to a nearly perfect coordination symmetry. Any contribution to the e.f.g. should therefore arise from outer-sphere solvent dipoles. In terms of the fully orientated solvation (FOS) model this would correspond to a distribution width parameter approaching zero (/. -> 0) with the first term in equation (4) vanishing. This is indeed what Hertz (24) found for both AF" and Ga ", and the experimental infinite dilution relaxation rates ( AP" 7-5 s Ga 350 s ) are remarkably well matched by the computed ones... 

The first term is the Zeeman interaction with the applied field with a mean shielding o for nucleus i, which may differ somewhat from the value in isotropic solvents due to the anisotropy of the shielding tensor. The second term contains the well-known isotropic part of the indirect spin-spin coupling of nuclei i and /. For pairs of protons the Jq are a few hertz. The major contribution to the parameters Dq of the last term derives from the direct (dir) magnetic dipole interactions of pairs of nuclei, which will be denoted by Efjf1. The contribution from the indirect interactions is often negligible and will be discussed below. 

In order to calculate the coefficient of scattering we start from the familiar formulae for the radiation from a dipole antenna. According to Hertz, the field of a dipole of moment p is given by... 

When light is incident on a polymer sample the sample is subg ed to an alternating electric field with frequencies in the ran 10 to 10 Hertz. In response to this field the electrons in the sample move with a periodic motion and become themselves a source of secondary dipole radiation. Hence the induced electric dipole moment, Pj, in the i direction (i = x, y, z) may be expanded in terms of the electric field by the equation ... 

This is the through-space coupling between a pair of nuclear magnetic dipoles. It is a purely anisotropic interaction and is also symmetric about r-, the internuclear vector. It contributes a term to the Hamiltonian, in hertz, of... 

A considerable body of literature has been devoted to this question. We have mentioned already the collision model of Deverell (60) an efg occurs at each ion-solvent molecule collision, with attendant loss of spherical symmetry of the ion. In the solvent exchange model of the Russian school (73), migration of a solvent molecule from the first solvation sphere into the bulk solution creates a vacancy the efg arises from coordinative unsaturation. In the electrostatic model of Hertz, the efg at the nuclear site is caused by the electric point dipoles of the... 

---