Charged particles induced dipole moment

The effect of cationic polyacrylamide adsorption on the stability of aqueous cellulose suspension has been electro-optically studied by Khlebtsov et al. [19,20], The variations in transmitted light modulation in low-frequency (3-45 Hz) square-pulsed a.c. fields have been found to correlate well with the adsorption isotherm. The influence of sodium carboxymethylcellulose adsorption on the electro-optical behavior of negatively charged Si02 (ani-sometric aggregates, consisting of monodisperse spherical particles) has also been studied, and an increase of the particle induced dipole moment and its time of relaxation has been found [21,22],... 

This section provides the fundamental equations for the quantum mechanical and molecular mechanical approach for determining the energies of molecules interacting with a structured environment. We can illustrate the QM/MM procedure as indicated in Figure 13-1 for a system where one part is described by quantum mechanics (QM) and the other part is described by classical mechanics or molecular mechanics (MM). The electrons and the nuclei of the QM system are treated separately at positions r7 and Rm, respectively. We represent the particles in the MM part by effective charges positioned at the atomic sites, Rs, and induced dipole moments located at (R ). 

A proper solvated electron is a particle localized in the potential well of a polar medium, the well being created by the interaction of electron charge with the permanent and induced dipole moments of the nearest as well as remote neighbours. This notion of the nature of a solvated electron, based on the idea that the Landau-Pekar theory initially advanced for solid bodies can be applied also to liquid systems, was advanced in 1948 since then considerable efforts have been made to develop it and verify it experimentally. In most liquid systems, localization of an electron is followed by the formation of a cavity where most of the density of the solvated electrons is concentrated. The cavity is surrounded by the orientated dipoles of the solvent. Usually, the radius of this cavity equals about 3-3.5 A which conforms to a solvated-electron molar volume of 70-100 cm . This is the reason why solutions with large concentrations of solvated electrons have a lower density. 

For a homogeneous solid dielectric sphere (a particle with a radius of R) in a homogeneous dielectric medium, charges will accumulate at the interface between the particle and the medium. This results in an effective or induced dipole moment across the particle. The potential of the effective dipole moment Pg can be considered as an increment to the potential distribution of the applied field, which is given by ... 

Let us consider a system of N spherical particles, molecules or ions, of polarizability a,- and charge The potential energy due to the short-range contributions of the dispersion and repulsion forces is supposed to be independent of the electrostatic long-range forces. In a given spatial configuration, described by a set of position vectors r = rj,r2,. . ., r,v, the induced dipole moment of the particle i is... 

First, let us consider the measurement of CVR When the density of the particles Pp differs from that of the medium Pjjj, the particles move relative to the medium under the influence of an acoustic wave. This motion causes a displacement of the internal and external parts of the double layer (DL). The phenomenon is usually referred to as a polarization of the DL (6). This displacement of opposite charges gives rise to a dipole moment. The superposition of the electric fields of these induced dipole moments over the collection of particles gives rise to a macroscopical electric field which is referred to as the colloid vibration potential (CVP). Thus, the fourth mechanism of particles interaction with sound leads to the transformation of part of the acoustic energy to electrical energy. This electrical energy may then be dissipated if die opportunity for electric current flow exists. 

In general, because of the differences between the permittivities and conductivities of the dispersed phase and the medium, the induced dipole moment of the particle in an electrolyte solution consists of two contributions. One is due to the polarization (orientation) of the molecular dipoles of both phases, and the other is due to the process of accumulation of charges of different signs on opposite poles of the particle. Thus, at very high frequencies (in practice, several MHz) ionic motions in the electrolyte solution and in the double layer toward and around the particle are too rapid for charge accumulation to proceed. Hence, only orientation of dipoles in both the particle and the liquid medium can participate in the dipole. 

Since the dielectric constants of particle and the dispersing medium are different, the excess amount of charge appears on the particle surfaces under an electric field. The induced dipole moment p can be expressed as [34] ... 

Table 1. A - Coulomb repulsion between partly charged particles as the origin of electrostatic stabilization. B - Distribution of the surface charge and geometry of the electric field of the neutral metal sphere of radius R, when the adsorbate is a single external charge in the distance L from the centre. The electric potential of this system is equivalent to the superposition of the potential of an external point charge C[ and the induced dipole moment d.C- Attractive dipole-dipole interaction between electrically neutral metal particles.

After discovery of the combined charge and space parity violation, or CP-violation, in iT°-meson decay [7], the search for the electric dipole moments (EDMs) of elementary particles has become one of the most fundamental problems in physics [6, 8, 9, 10, 1]. A permanent EDM is induced by the weak interaction that breaks both the space symmetry inversion and time-reversal invariance [11]. Considerable experimental effort has been invested in probing for atomic EDMs induced by EDMs of the proton, neutron and electron, and by P,T-odd interactions between them. The best available restriction for the electron EDM, de, was obtained in the atomic T1 experiment [12], which established an upper limit of de < 1.6 X 10 e-cm, where e is the charge of the electron. The benchmark upper limit on a nuclear EDM is obtained in atomic experiment on i99Hg [13], ]dHgl < 2.1 X 10 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 " e-cm, was also recently obtained by Dmitriev Sen kov [14] (the previous upper limit on the proton EDM was obtained in the TIE experiment, see below). 

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