Particles dielectric

Let us first consider the role of electrostatic forces. To do this, we will start with the simplest case of a spherical, uniformly charged, dielectric particle on a grounded, conducting planar substrate. 

J. E. and Chu, S. (1986) Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett., 11, 288-290. 

Wolny, A., and Opalinski, I., Electric charge neutralization by addition of fines to a fluidized bed composed of coarse dielectric particles, J. Electrostat., 14 279-289(1983)... 

Gersten J., Nitzan A., Spectroscopic Properties of Molecules Interacting With Small Dielectric Particles,/. Chem. Phys. 1981 75 1139-1152. 

Dielectric particles show a reduced tendency for bubbling and a larger range of velocities over which particulate expansion occurs when an alternating electrical field is applied. 

Folan etal Z) recently investigated energy transfer in micron-sized dielectric particles. They found that the transfer was enhanced by as much as a factor of 100 in the particles compared to the transfer observed in bulk quantities of the same material. An interesting aspect of this work is that the concentrations used in the experiment place the average separation between molecules at over 1000 A. Thus, no nearfield model such as the dyadic used by Forster (Eq. 8.17) or the electrostatic approach used by Gersten and Nitzan is applicable. In what follows, we will attempt in a simple manner to show how such an effect might take place. Following this, we will review the experiments and present a more comprehensive model for the effect. 

For the present, let us suppose that a donor molecule is sitting on the surface of a particle with its emission moment (pd) perpendicular to the surface, as shown in Figure 8.19. Only one acceptor molecule is available, and it is also on the surface with its absorption moment (pj perpendicular to the particle surface. For a typical dielectric particle 5 pm in radius, the maximum distance between the donor and acceptor would be 100,000 A. We would now like to calculate the effect which this sphere has on the energy transfer rate. In other words, we would like to calculate the ratio of the transfer rate with the sphere present to that without the sphere present. This ratio zl(a>) 2is... 

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). 

J. I. Gersten and A. Nitzan. Spectroscopic properties of molecules interacting with small dielectric particles, J. Chem. Phys. 75, 1139-1152 (1981). 

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). 

The interaction between the electric dipole of light and the polarisability of molecules or dielectric particles produces a force of the order of piconewtons. By using one or more tightly focussed laser beams, this tiny force can be exploited to move molecules or nanoparticles and arrange them into particular structures. Presently, building up a structure in this way is too slow to be technologically useful. 

This dielectrophoresis (DEP) mixer, specially designed for mixing of dielectric particles was made with a rectangular chamber having one inlet and outlet [48], Pairs of micromachined electrodes generate the electric field. 

Dielectrophoresis is the translational motion of neutral matter owing to polarization effects in a non-uniform electric field. Depending on matter or electric parameters, different particle populations can exhibit different behavior, e.g. following attractive or repulsive forces. DEP can be used for mixing of charged or polarizable particles by electrokinetic forces [48], In particular, dielectric particles are mixed by dielectrophoretic forces induced by AC electric fields, which are periodically switched on and off. 

The optical trapping method uses a highly focused laser beam to trap and manipulate particles of interest in a medium (illustrated in Figure 3). The laser is focused on a dielectric particle (e.g., a silica microscopic bead), the refractive index of which is higher than the suspension medium. This produces a light pressure (or gradient force), which moves the particle towards the focal point of the beam, that is, the beam waist (Lim et al., 2006). 

Figure 3 Optical trapping of a dielectric particle (simplified from Lim et al., 2006).

DEP is based on a force exerted on a dielectric particle by a nonuniform electric field. The strength of the force depends on the electrical properties... 

Another type of intrinsic property is derived from the theory of light scattering in particles. The phenomenon of Raman and fluorescent scattering from molecules suspended in small dielectric particles exemplifies such prop-... 

The Mie equation also holds for absorbing or reflecting particles, which have complex refractive indices. The graphs of Cj (s,e) for such particles are similar to those for dielectric particles except that the amplitudes of the oscillations are generally smaller. 

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... 

The small particle limit x 1. In electromagnetic theory it is shown that the absorption and scattering cross-sections of small dielectric particles are (e.g. Bohren Huffman 1983) ... 

FIG. 19-55 Schematic representation of charging mechanisms. (A) Contact electrification. (B) Conductive induction. (C) Ion bombardment. Cond. = conductor particle diel. = dielectric particle = high-voltage dc electrode 0 = ions from corona discharge at high-voltage electrode. 

Figure 3.85. Dielectric particle in an external field, (a) non-conducting double layer, (b) conducting double layer.

See fig. 4.5. Three regions can be distinguished the (dielectric) particle, the double layer and the far field. As double layer polarization is ignored, there is no polarization field and = E. the applied field. The border between the... 

The problem may be stated as finding the function f In (4.3.6]. For reasons discussed earlier we shall only consider dielectric particles. Figure 4.4 gave Henry s solution. In which electrophoretic retardation was accounted for. but not yet double layer polarization. If polarization Is properly included, surface conduction beyond the slip plane Is automatically taken Into account, with Du = Du , given by [4.3.65, 66 or 67]. However, Du s 0 for "rigid particles". 

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