Permittivity field effects

For practical purposes, the very small signals generated by pyroelectric elements must be amplified. The most widely used first stage consists of a field effect transistor (FET) which responds to electric potential rather than to charge. In this case, it is advantageous for the material to have a low permittivity to match the low input capacitance of the FET. Therefore the compositions with high... 

Onsager model—reaction field effects. In the simplest form of this model a chosen molecule is represented by a spherical cavity of suitable volume filled with fluid of relative permittivity c , containing a rigid dipole of value fi. This p, is chosen so that if py is the measured vacuum dipole moment of the molecule, = (c , + 2)py/3. Correct calculation of the orienting couple on the dipole due to a given external field leads to the Onsager relation... 

High Electric Field Effects.—Determination of Variations in Electric Permittivity. The electric permittivity e of an isotropic dielectric is usually measured by means of a dowly varying dectric field, of a field strength Eoo so small as to cause only linear polarization of the medium ... 

Molecular Theory and Bectric Field Effects in Isotropic Dielectrics 335 obtaining the following formula for the change in electric permittivity ... 

Moleadar Theory and Electric Field Effects in Isotropic Dielectrics 357 the permittivity variation (318) reduces to ... 

However, in the ease of eolloidal semiconduetor nanoeiystals experiments show an essential depression of the decay compared to the valne determined by Eq. (2). To explain this depression, Wehrenberg, Wang, and Guyot-Sioimest" noted that the above expression, derived for point-like emitters, does not take into account the local field effect, or screening of the radiation field inside a nanociystal of finite size. If a spherical nanociystal of permittivity snc is embedded into a dielectric host of permittivity Shost and snc > e host, then the internal electric field (inside the nanociystal) int is weaker in comparison with the external field E xt in the host, Ei t = S E xt, where the screening factor S is found to be ... 

It should be mentioned that even in the absence of dipolar, polarizable, or ionic reaction partners, high electric fields may cause shifts in chemical distributions. Such a field effect requires, however, that the solvent phase has a finite temperature coefficient of the dielectric permittivity or a finite coefficient of electrostriction an additional condition is that the chemical reactions proceed with a finite reaction enthalpy (AH) or a finite partial volume change (A V). Electric field induced temperature and pressure effects of this type are usually very small they may, however, gain importance for isochoric reactions in the membrane phase. 

Besides electric field effects, ion association within the polymer films plays an important role in the dynamics of electron hopping within the films. (Extensive ion association might be expected due to the high ion content and the low dielectric permittivity that prevails in the interiors of many redox polymers.) According to the model that includes ion association, the sharp rise in the apparent diffusion coefiicient as the concentration of the redox couple in the film approaches saturation is an expected consequence of the shift in the ionic association equilibrium to produce larger concentrations of the oxidized form of the redox couple, which is related to rapid electron acceptance from the reduced form of the couple [176]. 

Equation (4) is valid with high accuracy because induced magnetic dipoles interact only weakly. By contrast, interaction between the induced electric dipoles is strong and produces substantial local field effects which do not allow one to express the dielectric permittivity of the nematic phase in terms of the molecular parameters in a simple way (see, for example, [4]). 

In this section we wish to consider all the possible contributions to the electric permittivity of liquid crystals, regardless of the time-scale of the observation. Conventionally this permittivity is the static dielectric constant (i.e. it measures the response of a system to a d.c. electric field) in practice experiments are usually conducted with low frequency a.c. fields to avoid conduction and space charge effects. For isotropic dipolar fluids of small molecules, the permittivity is effectively independent of frequency below 100 MHz, but for liquid crystals it may be necessary to go below 1 kHz to measure the static permittivity polymer liquid crystals can have relaxation processes at very low frequencies. 

Here, Ne is the number of electrons, N is the number of nuclei, me is the mass of the electron, e is the elementary charge, eg is the vacuum permittivity, r and p are the position and momentum operators of electron s, and R and Zk are the position and atomic number of nucleus K. Starting from the Schrodinger equation (O Eq. 5.1), relativistic effects as described by the Breit-Pauli Hamiltonian can be treated as perturbations on an equal footing with external fields. Effects of nuclear motion (vibrations and rotations) can be estimated once the electronic response functions have been calculated. 

The generated signal is low and must be amplified by a field effect transistor. For reasons of impedance matching, the capacitance must be of low value, i.e. a material of low relative permittivity. The sensitivity of the device will be greatly affected by the different noise sources. 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

This macroscopic theory justifies the complex nature of the dielectric permittivity for media with dielectric loss. The real part of the dielectric permittivity expresses the orienting effect of the electric field with the component of polarization which fol-... 

The fourth term is a polarisation term. Here E(z) = di/z/dz is the electric field at position z. In previously published SCF results for charged bilayers, this last term is typically absent. It can be shown that the polarisation term is necessary to obtain accurate thermodynamic data. We note that all qualitative results of previous calculations remain valid and that, for example, properties such as the equilibrium membrane thickness are not affected significantly. The polarisation term represents relatively straightforward physics. If a (united) atom with a finite polarisability of erA is introduced from the bulk where the potential is zero to the coordinate z where a finite electric field exists, it will be polarised. The dipole that forms is proportional to the electric field and the relative dielectric permittivity of the (united) atom. The energy gain due to this is also proportional to the electric field, hence this term is proportional to the square of the electric field. The polarisation of the molecule also has an entropic consequence. It can be shown that the free energy effect for the polarisation, which should be included in the segment potential, is just half this value... 

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