Local effective field

In a polycrystalline material each crystallite experiences its own effective field, which is determined in part by magnetic anisotropy. Therefore, because of the different orientations of the crystallites, there will be a distribution of resonant frequencies in consequence, narrow linewidths are associated with low anisotropies. Magnetic inhomogeneities - inclusions and pores - also disturb the local effective fields and so lead to line broadening. The effect of porosity on resonance linewidth can be expressed by the relationship... 

Nuclear spins are sensitive to the chemical environment of a nucleus. Electrons moving near the nucleus establish an internal magnetic field that modifies the local effective field felt by each proton to a value different from that of the externally applied field. The resulting chemical shift causes protons within different structural units of the molecule to show NMR peaks at different values of magnetic field. All protons in chemically equivalent environments will contribute to a single absorption peak in the spectrum. The relative area under each absorption peak is proportional to the number of protons within each equivalent group. In order to standardize procedures, chemical shift values are recorded relative to the selected reference compound tetramethylsilane (TMS) by adding a very small amount of... 

Equation (8.1.4) is rewritten in a reference frame oriented along the local effective field, which changes direction with the resonance offset from the rf excitation frequency (cf. Fig. 2.2.7),... 

The experimentally controlled variables which are explicit in equation (10.9.12) are the activity of the adsorbate and the temperature T. The experimentally observed quantity is the surface excess Fa. The dependence of the adsorption on the electrical state of the interface is expressed through the local effective field E perpendicular to the interface and the average dipole moments of the adsorbate (/7a) and water molecules p ) in the same direction. The contribution of the last term is much larger under most circumstance for adsorption at the electrode solution interface than at the solution air interface. As a result, further treatment of the two problems is quite different. 

The study considered in this paper models the mixture as a single micromorphic fluid. The theory presented does not model more complex changes in the shape of the bubbles than that considered here. However, the results obtained here are the simplest that would include the characterization of the local effects. Field equations derived in this study are more general then the equations derived by Van Wijngaarden [1]. The theory must be continued to describe more complex variations in the volume and shape in the local structure, and to model the phase change by introducing additionnal variables to formulate the constitutive theory. 

Attempts have also been made to separate non-specific effects of the local electrical field from hydrogen-bonding effects for a small group of ionic liquids through the use of the k scale of dipolarity/polarizability, the a scale of hydrogen bond donor acidity, and the (i scale of hydrogen bond basicity (see Table 3.5-1) [13, 16]. 

All nuclei in molecules are surrounded by electrons. When an external magnetic field is applied to a molecule, the electrons moving around nuclei setup tiny local magnetic fields of their own. These local magnetic fields act in opposition to the applied field so that the effective field actually felt by the nucleus is a bit weaker than the applied field. 

We consider first the polarizability of a molecule consisting of two or more polarizable parts which may be atoms, bonds, or other units. When the molecule is placed in an electric field the effective field which induces dipole moments in various parts is not just the external field but rather the local field which is influenced by the induced dipoles of the other parts. The classical theory of this interaction of polarizable units was presented by Silberstein36 and others and is summarized by Stuart in his monograph.40 The writer has examined the problem in quantum theory and finds that the same results are obtained to the order of approximation being considered. 

Figure 6.16. Different modes of adsorption of CHjOH on Pt under ultra-high vacuum (left) and in aqueous solutions (right) showing the effect of local electrostatic field and surface work function on the mode of adsorption.100 Reprinted with permission from the American Chemical Society.

Pyridones have not been considered previously because the reaction site can undergo resonance effects involving more than one type of interaction. Localized effects, assuming they are field effects, will not be affected. If the localized effect were an inductive effect, which seems very unlikely, then there would be two paths to the reaction site. Consider the pyridones for which data are available. Three sets are extant. They are the 3-substituted 4-pyridones, 33 the 5-substituted 2-pyridones, 34 and the 3-substituted 2-pyridones, 35. In each of these systems, the substituent is conjugated with the nitrogen atom by one path and in... 

M. (2006) Ahgned silver nanorod arrays for surface-enhanced Raman scattering. Nanotechnology, 17, 2(>70-2(>74, (b) Lu, Y, Liu, G.L., Kim, J., Mejia, Y.X. and Lee, L.P. (2005) Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect Nano Letters, 5, 119-124 ... 

The influence of structured electrodes or multipoint electrodes, which enhance the local electric field [20,21], as well as the effect of discharge polarity [20-22] and gap length [21,23,24], was investigated. 

The y-facior. The 0-factor takes into account the fact that the local magnetic field experienced by a particular atom in a molecule may not be the same as the applied field owing to the existence of local field effects. In the absence of such effects, g for any particular radical would simply have the same value as that of the free electron, 2.0023, and all radicals would come into resonance at the same applied field for a given microwave frequency. We can thus express the resonance condition (equation 2.173) as ... 

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