Distribution frequency-dependent electric-field

In the present study we have used a relatively new technique to study the morphology of these systems. Application of an alternating electric field to a multiphase morphology results in a frequency-dependent electric-field distribution due to the different permittivities and conductivities of dissimilar phases. Measured permittivity increases with decreasing frequency v = 0)/2ir, approaching a low frequency limit eQ as the field distribution transits from permittivity dominated to conductivity dominated. 

Acoustophorometer is a measurement technique based on an electroacoustic effect which occurs when a high frequency alternate electric field (1 MHz) is applied to two electrodes immersed in a suspension of charged particles. The field applied periodically deforms the distribution of the mobile charges of the double electric layer of each particle and produces an acoustic pressure variation of the same frequency as the applied electric field. Its amphtude depends on the displaced charges and can be related to the zeta potential [O BR 88]. 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

The solute particles are held at the accumulation wall by a DEP force which depends on the dielectric properties of the particles and the surrounding medium, the frequency and magnitude of the electrical field, and the electrode geometry. DEP-FFF is an unconventional FFF technique in that the DEP force is inherently non-uniformly distributed over the channel, not only in the plane of the electrodes/channel wall, but also across the channel above the electrodes [282]. Since solute particles themselves are a source of local field non-uniformities, mutual attraction occurs due to DEP forces between the particles which in extreme cases can lead to what is called pearl-chain formation. As a consequence, DEP-FFF can be considerably disturbed by interparticular interactions [57]. 

Dependent on the interaction between the quadrupole moment of the nucleus and the electric-field gradients at the nucleus arising from the charge distribution in a solid. Resonant absorption of radio-frequency energy occurs when nuclei are excited to various higher-energy states related to these interactions. It is this resonant absorption that is studied... 

The results we have obtained provide a reinterpretation of IR absorption along the following lines the IR radiation is a dynamic electric field which causes oscillations in the electronic cloud. The perturbed electrons, in turn, induce an additional dynamic electric field at the nuclei via a feedback effect. The latter are hence acted upon by the effective electric field (145), that is, by a frequency-dependent Lorentz force that is responsible for changes of nuclear vibrational motion. Accordingly, the electron distribution of a molecule plays a fundamental role in determining the general features of nuclear vibrations and the magnitude of IR parameters. 

To obtain hyperpolarizabilities of calibrational quality, a number of standards must be met. The wavefunctions used must be of the highest quality and include electronic correlation. The frequency dependence of the property must be taken into account from the start and not be simply treated as an ad hoc add-on quantity. Zero-point vibrational averaging coupled with consideration of the Maxwell-Boltzmann distribution of populations amongst the rotational states must also be included. The effects of the electric fields (static and dynamic) on nuclear motion must likewise be brought into play (the results given in this section include these effects, but exactly how will be left until Section 3.2.). All this is obviously a tall order and can (and has) only been achieved for the simplest of species He, H2, and D2. Comparison with dilute gas-phase dc-SHG experiments on H2 and D2 (with the helium theoretical values as the standard) shows the challenge to have been met. 

The polarizability of an atom or molecule describes the response of the electron cloud to an external field. The atomic or molecular energy shift KW due to an external electric field E is proportional to i for external fields that are weak compared to the internal electric fields between the nucleus and electron cloud. The electric dipole polarizability a is the constant of proportionality defined by KW = -0(i /2. The induced electric dipole moment is aE. Hyperpolarizabilities, coefficients of higher powers of , are less often required. Technically, the polarizability is a tensor quantity but for spherically symmetric charge distributions reduces to a single number. In any case, an average polarizability is usually adequate in calculations. Frequency-dependent or dynamic polarizabilities are needed for electric fields that vary in time, except for frequencies that are much lower than electron orbital frequencies, where static polarizabilities suffice. 

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