Polarizability dielectric particles

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. 

Although metal nanoparticles experience strong radiation pressure and scattering forces due to their high absorption and polarizability, stable trapping of such particles has been demonstrated in both two and three dimensions [74, 85, 86]. As for cells and dielectric particles, a NIR laser is usually used to trap metal nanoparticles while a separate laser, or the trapping laser itself, excites the... 

Almost all the formalism and the approximation schemes of Sections II and III have a natural extension to systems of polarizable dipolar particles, but the precise details of the extension depend on the way polarizability is introduced into the Hamiltonian. We refer to the two quite distinct Hamiltonian models that have been most thoroughly developed in this context as the constant-polarizability model and the fluctuating-polarizability model. The dielectric behavior of the former was first systematically investigated from a statistical mechanical viewpoint by Kirkwood and by Yvon, who considered the model almost exclusively in the absence of permanent dipole moments. (Kirkwood S subsequently pioneered an exact formulation of the statistical mechanics of polar molecules, but largely as a separate enterprise that did not attempt to treat the polarizability exactly.) The general case of polar-polarizable particles remained only very partially developed ... 

Direct current (DC) dielectrophoresis (DEP) is an efficient means to move and thus separate particles or cells with the force of a stationary electric field. This is accomplished with a spatially nonuniform electric field shaped around insulative objects as obstacles in the path of the DC field. DC-DEP is then the induced motion of polarizable, dielectric objects of micron and smaller size, in a DC electric field that is modified by lab-on-a-chip geometry (or other means) to be spatially nonuniform. 

Dielectrophoresis, Fig. 2 Schcanatic diagram of how different dielectric particles polarize if they have a much highra- (a) or much lower (b) polarizability than the suspending fluid medium. If the polarizability is higher, more charges are produced on the inside of the particle/ fluid interface and there is a net dipole araoss the particle that is parallel to the applied field. If the polarizability is lower, mme charges are produced on the outside of the interface and the net dipole points in the opposite direction, against the field... 

Dielectrophoresis (DEP) refers to the motion of polarizable particles or cells suspended in an electrolyte subjected to a nonuniform electric field. Dielectric particles, including cells, can be categorized into two types depending on their behavior within the nonuniform electric field, i. e., positive and negative DEP. Positive DEP occurs when the particle is more polarizable then the surrounding media so the particles or cells are attracted toward areas of high elec-... 

Dielectrophoresis is the electrokinetic motion of particles that occurs when a polarizable particle is placed in nonuniform electric fields, and the particle motion is influenced by the ambient electric field and by the properties of the dielectric particles or solutions (Lee et al., 2016 Song et al., 2012 Alshareef et al., 2013). Separation of particles and cells can also be achieved by microfiltration, which uses the size of micropores and the gap between microposts for the separation of particles and cells (Lee et al., 2016 Kang et al., 2014 Rodrigues et al., 2015). 

Formal Theory A small neutral particle at equihbrium in a static elecdric field experiences a net force due to DEP that can be written as F = (p V)E, where p is the dipole moment vecdor and E is the external electric field. If the particle is a simple dielectric and is isotropically, linearly, and homogeneously polarizable, then the dipole moment can be written as p = ai E, where a is the (scalar) polarizability, V is the volume of the particle, and E is the external field. The force can then be written as ... 

A parameter used to characterize ER fluids is the Mason number, which describes the ratio of viscous to electrical forces, and is given by equation 14, where 8 is the solvent dielectric constant T 0, th solvent viscosity 7, the strain or shear rate P, the effective polarizability of the particles and E, the electric field (117). 

The notion of homogeneity is not absolute all substances are inhomogeneous upon sufficiently close inspection. Thus, the description of the interaction of an electromagnetic wave with any medium by means of a spatially uniform dielectric function is ultimately statistical, and its validity requires that the constituents—whatever their nature—be small compared with the wavelength. It is for this reason that the optical properties of media usually considered to be homogeneous—pure liquids, for example—are adequately described to first approximation by a dielectric function. There is no sharp distinction between such molecular media and those composed of small particles each of which contains sufficiently many molecules that they can be individually assigned a bulk dielectric function we may consider the particles to be giant molecules with polarizabilities determined by their composition and shape. 

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

It is important to note that the form effect is proportional to the square of the dielectric contrast, Ae, and will always be positive for prolate particles (Ll > L2), and negative for oblate shapes (L2 > Lx). The intrinsic contribution can change sign depending on the relative magnitudes of the principal values of the polarizability tensor of the particle. 

The molecule is often represented as a polarizable point dipole. A few attempts have been performed with finite size models, such as dielectric spheres [64], To the best of our knowledge, the first model that joined a quantum mechanical description of the molecule with a continuum description of the metal was that by Hilton and Oxtoby [72], They considered an hydrogen atom in front of a perfect conductor plate, and they calculated the static polarizability aeff to demonstrate that the effect of the image potential on aeff could not justify SERS enhancement. In recent years, PCM has been extended to systems composed of a molecule, a metal specimen and possibly a solvent or a matrix embedding the metal-molecule system in a molecularly shaped cavity [62,73-78], In particular, the molecule was treated at the Hartree-Fock, DFT or ZINDO level, while for the metal different models have been explored for SERS and luminescence calculations, metal aggregates composed of several spherical particles, characterized by the experimental frequency-dependent dielectric constant. For luminescence, the effects of the surface roughness and the nonlocal response of the metal (at the Lindhard level) for planar metal surfaces have been also explored. The calculation of static and dynamic electrostatic interactions between the molecule, the complex shaped metal body and the solvent or matrix was done by using a BEM coupled, in some versions of the model, with an IEF approach. 

In several examples for gases and dilute suspensions, we expand the dielectric response e around its vacuum value of 1 or around its pure-solvent value em, respectively, for the suspending medium. In those cases, the dimensionless x for the gas or for the suspension as a whole will be proportional to the number density of particles (units 1/length3), and the contribution to the polarizability from individual particles will have volume units (length3). 

Depending on the type of interaction between an adsorbed particle and a solid state surface there are cases, where adsorption enthalpies can be calculated using empirical and semi-empirical relations. In the case of atoms with a noble-gas like ground-state configuration and of symmetrical molecules the binding energy (EB) to a solid surface can be calculated as a function of the polarizability (a), the ionization potential (IP), the distance (R) between the adsorbed atom or molecule and the surface, and the relative dielectric constants (e) (Method 9) [58-61] ... 

Discrete dipole approximation. For particles with complex shape and/or complex composition, presently the only viable method for calculating optical properties is the discrete dipole approximation (DDA). This decomposes a grain in a very big number of cubes that are ascribed the polarizability a according to the dielectric function of the dust material at the mid-point of a cube. The mutual polarization of the cubes by the external field and the induced dipoles of all other dipoles is calculated from a linear equations system and the absorption and scattering efficiencies are derived from this. The method is computationally demanding. The theoretical background and the application of the method are described in Draine (1988) and Draine Flatau (1994). 

Where a is the polarizability, e is the frequency dependent dielectric function [4J], and V the volume of the dipole. The radius of each sphere is calculated using a/R=1.612 42, where a is the spacing between the particles, 40 nm... 

Casimir and Polder also showed that retardation effects weaken the dispersion force at separations of the order of the wavelength of the electronic absorption bands of the interacting molecules, which is typically 10 m. The retarded dispersion energy varies as R at large R and is determined by the static polarizabilities of the interacting molecules. At very large separations the forces between molecules are weak but for colloidal particles and macroscopic objects they may add and their effects are measurable. Fluctuations in particle position occur more slowly for nuclei than for electrons, so the intermolecular forces that are due to nuclear motion are effectively unretarded. A general theory of the interaction of macroscopic bodies in terms of the bulk static and dynamic dielectric properties... 

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