Spherical dielectric

Purcell, E. M. and Permypacker, C. R. (1973) Scattering and absorption oflightby non-spherical dielectric grains. Astrophys. J., 186, 705-714. 

P. Chylek, V. Ramaswamy, A. Ashkin, and J. M. Dziedzic, Simultaneous determination of refractive index and size of spherical dielectric particles from light scattering data, Appl. Opt. 22, 2302-2307 (1983). 

S. D. Druger, S. Arnold, and L. M. Folan, Theory of enhanced energy transfer between molecules embedded in spherical dielectric particles, J. Chem. Phys. 87, 2649-2659 (1987). 

Astratov, V.N., Franchak, J.P., and Ashili, S.P., 2004, Optical coupling and transport phenomena in chains of spherical dielectric microresonators with size disorder, Appl. Phys. Lett. 85(23) 5508-5510. 

Spillane, S.M., Kippenberg, T.J., and Vahala, K. J., 2002, Ultralow-threshold Raman laser using a spherical dielectric microcavity, Nature 415 (6872) 621-623. 

Boundary effects on the electrophoretic mobility of spherical particles have been studied extensively over the past two decades. Keh and Anderson [8] applied a method of reflections to investigate the boundary effects on electrophoresis of a spherical dielectric particle. Considered cases include particle motions normal to a conducting wall, parallel to a dielectric plane, along the centerline in a slit (two parallel nonconducting plates), and along the axis of a long cylindrical pore. The double layer is assumed to be infinitely thin... 

For an isotropic spherical dielectric sample, formula (336) yields ... 

The diffusion equation for long-range energy transfer by the dipole-dipole interaction mechanism which is accompanied by material diffusion has been solved numerically . The theory of enhanced energy transfer between molecules embedded in spherical dielectric particles has been developed for application to dipole-dipole energy transfer taking place between molecules embedded in aerosol droplets. The experimental systems studied involved the use of the dyes coumarin as donor and rhodamine 6G as acceptor. 

A dielectric sphere of dielectric coefficient e embedded in an infinite dielectric of permittivity 82 is an important case from many points of view. The idea of a cavity formed in a dielectric is routinely used in the classical theories of the dielectric constant [67-69], Such cavities are used in the studies of solvation of molecules in the framework of PCM [1-7] although the shape of the cavities mimic that of the molecule and are usually not spherical. Dielectric spheres are important in models of colloid particles, electrorheological fluids, and macromolecules just to mention a few. Of course, the ICC method is not restricted to a spherical sample, but, for this study, the main advantage of this geometry lies just in its spherical symmetry. This is one of the simplest examples where the dielectric boundary is curved and an analytic solution is available for this geometry in the form of Legendre polynomials [60], In the previous subsection, we showed an example where the SC approximation is important while the boundaries are not curved. As mentioned before, using the SC approximation is especially important if we consider curved dielectric boundaries. The dielectric sphere is an excellent example to demonstrate the importance of curvature corrections . 

Figure 1. Real part of the Clausius-Mossotti factor for a solid spherical dielectric particle at various medium conductivities (for Sp = 2.55, o, = 0.01 S/m, and = 78.5). Switch of the sign of Re. K indicates switch between positive and negative dielectrophoresis.

Mie scattering - The scattering of light by spherical dielectric particles whose diameter is comparable to the wavelength of the light. 

Here we describe in some detail the basis of optical diffraction in spherical dielectric particles as a probe of material homogeneity in polymer composites, and discuss limitations on domain size (in multi-phase composites), and dielectric constant. We show how this measurement technique can be used to recover information on drying kinetics, inter-polymer dynamics, and material properties. In the following chapter, we describe some results of detailed molecular dynamics modeling that can be used to connect... 

The simplest simulated system is a Stockmayer fluid structureless particles characterized by dipole-dipole and Lennard-Jones interactions, moving in a box (size L) with periodic botmdary conditions. The results described below were obtained using 400 such particles and in addition a solute atom A which can become an ion of charge q embedded in this solvent. The long range nature of the electrostatic interactions is handled within the effective dielectric environment seheme. In this approach the simulated system is taken to be surrounded by a continuum dielectric environment whose dielectric constant e is to be chosen self consistently with that eomputed from the simulation. Accordingly, the electrostatic potential between any two partieles is supplemented by the image interaction associated with a spherical dielectric boundary of radius (taken equal to L/2) placed so that one of these... 

The theoretical analysis presented above assumes a solid homogeneous spherical dielectric particle, e.g., a polystyrene bead. Biological cells are neither perfect spheres nor completely homogenous dielectrics. However, their DEP properties can be... 

Fig.4.3. Schematic drawing of a spherical dielectric particle showing the dipole location within it. The exciting radiation is incident upon the particle along the +z direction...

Charging step - a cell was considered as a spherical shell with a dielectric membrane and with external and internal (cytoplasmic) conducting buffers. As a spherical dielectric, a position-dependent transmembrane potential was induced when the cell is submitted to an external field. This was a fast process. 

Let us consider a spherical dielectric particle (phase 1), which is immersed in a nonpolar medium (phase 2), near its boundary with a third dielectric medium (phase 3) see the inset in Figure 4.26. The interaction is due to electric charges at the particle surface. The theoretical problem has been solved exactly, in terms of Legendre polynomials, for arbitrary values of the dielectric constants of the three phases, and expressions for calculating the interaction force, F, and energy, W, have been derived [350] ... 

Thin lens focal length/(f > 0, converging /< 0, diverging) Dielectric interface refractive indices W] and Wj Spherical dielectric interface radius R Spherical mirror radius of curvature R... 

From Equation 6.10 in O Brien s dynamic mobility paper [13], it can be shown that the average tangential field around a spherical dielectric particle is given by ... 

E.M. Purcell, C.R. Pennypacker, Scattering and absorption of light by non-spherical dielectric grains, Astrophysical J. 186, 705 (1973)... 

The energy of reorganization of the external medium by a charge, transferred inside a spherical dielectric, was calculated by Kharkats[491,492]. The corresponding formula has the form... 

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