Charged particles polarization field

Process Concept The application of a direct elecdric field of appropriate polarity when filtering should cause a net charged-particle migration relative to the filter medium (electrophoresis). The same direct electric field can also be used to cause a net fluid flow relative to the pores in a fixed filter cake or filter medium (electroosmosis). The exploitation of one or both of these phenomena form the basis of conventional electrofiltration. 

The second method of exploitation occurs when the electric field is of a polarity such that the charged-particle migration occurs away from the filter medium. The contribution to the net-particle velocity of the elec trqphoreticaUy induced flow away from the filter medium is generally orders of magnitude less than the contribution to the net-... 

One area where the concept of atomic charges is deeply rooted is force field methods (Chapter 2). A significant part of the non-bonded interaction between polar molecules is described in terms of electrostatic interactions between fragments having an internal asymmetry in the electron distribution. The fundamental interaction is between the Electrostatic Potential (ESP) generated by one molecule (or fraction of) and the charged particles of another. The electrostatic potential at position r is given as a sum of contributions from the nuclei and the electronic wave function. 

Process Concept The application of a direct electric field of appropriate polarity when filtering should cause a net charged-particle... 

As discussed previously, the presence of an electrostatic charge or force field results in a stress within the material. In the absence of polarization, this stress will always tend to rupture a particle. This tendency to rupture is resisted either by the action of surface tension or by the molecular bonds or tensile strength. 

Some piezoelectric crystals are electrically polarised in the absence of mechanical stress one example is gem-quality tourmaline crystals. Normally, this effect is unnoticed because the crystal does not act as the source of an electric field. Although there should be a surface charge, this is rapidly neutralised by charged particles from the environment and from the crystal itself. However, the polarisation decreases with increasing temperature and this can be used to reveal the polar nature of the crystal. If tourmaline is heated its polarisation decreases and it loses some of its surface charges. On rapid cooling it has a net polarisation and will attract small electrically charged particles such as ash. Such crystals are known as pyroelectric, and ferroelectric crystals are a special subclass of pyroelectric crystals. 

Of course, the presence of an electric field means dial a term accounting for the interactions of charged particles with this lield should be included in the solute Hamiltonian. When it is included, the effect is to increase the solute polarity in a fashion proportional to the solute polarizability and the strength of the external lield. Thus, die dipole moment of A increases. The solvent, seeing this increase, itself polarizes and moreover increases its own orientation to oppose A s dipole, and so on. 

Following from formula (4.54), the transfer of energy on excitation of molecules has a noticeable probability even in the case where the impact parameter is much greater than their size d. Since the intermolecular spacings in a condensed medium are of order of d, a charged particle interacts with many of its molecules. The polarization of these molecules weakens the field of the particle, which, in its turn, weakens the interaction of the particle with the molecules located far from the track. This results in that the actual ionization losses are smaller than the value we would get by simply summing the losses in collisions with individual molecules given by formula (5.1). This polarization (density) effect was first pointed out by Swann,205 while the principles of calculation of ionization losses in a dense medium were developed by Fermi.206... 

A Lagrangian for a collection of charged particles in an electromagnetic field can be written down directly using the polarization fields... 

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