Inhomogeneous dielectric mechanisms

However, neither the inhomogeneous dielectric mechanism nor its equivalent, the dynamic-coupling mechanism, makes allowance for the polarizability of the outer shells of the rare-earth or actinide ion. For an external quadrupole field to penetrate to the f electrons, we must include a screening factor (1- o ) the same factor must be introduced if we take the point of view of dynamic coupling and ask what reduction the quadrupole field of the f electrons experiences as it penetrates out to the ligands. For a... 

Some correlation can be established between and hypersensitivity. Thus, for a nearly planar molecule Ndl, we find is roughly 6, while for the crystal NdCl, it is only 0.9. Intense hypersensitive transitions occur in the molecule but not in the crystal. Jowever, the pyramidal Ndl produces an electric field at the Nd site, while the crystal does not so the intensity correlation does not establish the predominance of the inhomogeneous-dielectric mechanism. The issue is further clouded by the vibronic contributions that undoubtedly occur in the molecule. 

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

Dielectrophoretic forces depend on the polarizibility of species, rather than on movement of charges [99]. This allows the movement of any type of droplet being immersed by a dielectrically distinct immiscible carrier medium. Since dielectric forces are generated by spatially inhomogeneous fields, no mechanical actuation is required. In addition to this, dielectrophoretic droplet movement benefits from the general advantages given by droplet microfluidic, i.e. discrete, well-known very small volumes, no need for channels, avoidance of dead volumes and more. 

This Section examines the dielectric and conduction mechanisms in bulk materials, assuming that the medium is linear (at the applied electric field strength) and homogeneous. Effects of interfaces and inhomogeneities are discussed in Section 3.2. Additional discussion can be found in basic texts 21 23). 

Molecules for which a temperature-dependent dielectric susceptibility is observed in gas phase are commonly called polar. Polar molecules have microwave spectra with transitions corresponding to AJ= 1 and are deflected by inhomogeneous electric fields. In the conventional approach, these phenomena are attributed to the presence of permanent dipole moments in such molecules. In contrast, the notion of permanent dipole moments (which are zero for spectroscopic states) plays no role at all in the fully quantum-mechanical treatment outlined above. The temperature-dependent component of x arises from the existence of low-lying spectroscopic states for which... 

The reason that chemical laws are not simply reduced to electrostatics is that the electrons behave under the influence of their own or applied electric fields, not according to classical mechanics, but according to quantum mechanics obeying the singular Pauli principle. In fact, electrostatics and dielectric constants are simpler applications of the electrical structure of molecules and use outside macroscopic homogeneous electric fields interacting with microscopic inhomogeneous fields. 

An early survey of the possible sources for the hypersensitivity concluded that the most likely candidate was a mechanism based on the inhomogeneities of the dielectric surrounding the rare-earth or actinide ion (4). It runs as follows. The radiation field induces sinusoidally fluctuating dipole moments in the ligands surrounding the ion. These induced dipoles necessarily radiate, and the emitted fields impinge on the rare-earth or actinide ion. Because of the proximity of source and receiver, the plane-wave condition no longer applies the wave fronts are sufficiently distorted to produce substantial quadrupole components. 

Work is being carried out in collaboration with Dr. W.T. Carnall in an effort to connect hypersensitivity to the structures of the crystal lattices where it is exhibited. The mechanism based on an inhomogeneous dielectric leads to an expression for the intensities of hypersensitive lines that is proportional to (12)... 

In these expressions, p is an arbitrary coefficient that measures the strength of the electric-field mechanism compared to qne based on an inhomogeneous dielectric. The values of CK can be worked out once the polar angles of any one of the three igands is specified. For example, ell - cos. The components for which M = 1 are mixed with those for which M = T 2 in C v symmetry, but if the relative mixtures are known (as they could be from Zeeman-effect data), a measurement of the three intensities would, in principle, determine p and also check the expressions above for consistency. 

We have recently started to explore a type of calculations in which DFT treatment of the quantum mechanical (QM) site is combined with either continuum electrostatics treatment of the protein, or with microscopic molecular mechanics/dynamics treatment of the protein, or with a combined molecular mechanics and continuum electrostatics treatment of the protein in a truly multiscale type of calculations. All these calculations have a spirit of QM/MM (quantum mechanics combined with molecular mechanics) method, which is currently in wide use in protein calculations. The DFT and the solvation energy calculations are performed in a self-consistent way. The work aims at both improving the QM part of p/ calculations and the MM or electrostatic part, in which of the protein dielectric properties are involved. In these studies, an efficient procedure has been developed for incorporating inhomogeneous dielectric models of the proteins into self-consistent DFT calculations, in which the polarization field of the protein is efficiently represented in the region of the QM system by using spherical harmonics and singular value decomposition techniques [41,42]. 

Manipulating fluids in a two-phase flow system is much more complicated than in single-phase systems. Fluid flows can be actuated spontaneously, nonmechanically, or mechanically. The most frequently used flow actuation method, till now, is still pressure-driven pumps due to their availability and versatility. Especially, for a two-phase flow system, the naturally existing inhomogeneity makes other methods much more difficult to be applied. Electroosmosis, for instance, resulting from the force exerted on a space-charge region in the liquid by an electric field, will not work if the conductivity continuum in the fluid is interrupted by an entrapped dielectric liquid droplet or gas bubble. 

A more striking example is that of symmetry, which has been discussed by Reid and Richardson (1983a). If we adopt the mechanism of the inhomogeneous dielectric, each polarizability tensor a for ligand L at leads to the contribution (o< ) induced dipole moment produced by the electric field E of the radiation field. The potential at a 4f electron at tj is given by... 

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