Sinusoidal electric field

Figure 4.20 A sinusoidal electric field of angular frequency u> in a second-order nonlinear optical medium creates a polarization with component at 2tn( second-harmonic) and a steady (dc) component...

A simple thin film technique has been developed to measure the electrical properties of polyelectrolyte solutions under sinusoidal electric fields of 100-500 v/cm at frequencies of. 10-10 KHz. Ohmic heating is largely avoided by the rapid transfer of heat to the electrodes and by the high surface to volume ratios. The resulting temperature is not sufficient to damage the medium. Current and voltage wave forms are monitored directly so that dispersion and nonlinear phenomena of the medium can be viewed directly as functions of frequency, voltage, and concentration of the solution. Possible mechanisms for the observed phenomena are discussed. 

In a simple one-dimensional ansatz for a hydrogen atom in a sinusoidal electric field the Hamiltonian (4) reduces to... 

In impedance spectroscopy [IS also referred to as dielectric spectroscopy (DS)], a sinusoidal electric field is applied across a sample, and the resulting polarization (or electric displacement) is determined as a function of frequency. The frequency sweep typically ranges from about 1 MHz down to about 1 mHz, but measurement may be performed at higher frequencies by using special equipment. 

Localized fluorescence during application of a Sinusoidal Electric Field. Top, - 0° middle, - 90° bottom, - 180°. 

Fluorescence in Sinusoidal Electric Fields. Fluorescein is an indicator whose fluorescence intensity changes with pH. Consequently, it is reasonable to interpret fluorescence response to applied AC voltage in terms of electrochemical reactions that alter the local pH. This AC-response of local fluorescence intensity exhibits classic relaxation behavior. At high frequencies, electrochemical reactions do not proceed long enough during each half-cycle to produce any appreciable pH change consequently, specimens exhibit time-... 

The ITs described in Section 2.3.2 operate with a sinusoidal electrical field in the rf region (Frf) and the ions are ejected from the trap by increasing the VTi value. 

The colloid particle or polyelectrolyte molecule may possess a permanent dipole moment. Considerable influence of this moment on the magnitude and the sign of the electro-optical effect is expected in the range of particle rotation. Discrimination between the induced and the rotational relaxation of the particles can be reached, however, since the electro-optical response to a sinusoidal electric field is the sum of a time-independent term adc and a term a2rjJ that is sensitive to the particle rotation [24,45]. The critical frequency of the alrjJ relaxation depends on the rotational diffusion coefficient Dr of the particle, while the critical frequency of relaxation of the time-independent term adc depends on the translational diffusion coefficient of the ions moving on the particle surface. 

For linear dielectrics, it is assumed that P is linearly related to E, with the proportionality constant related to k. When a sinusoidal electric field of frequency ui is applied to a dielectric, some of the bound charges move in phase with the applied field and contribute to k. Another set of bound charges oscillate out of phase with the applied field, result in energy dissipation, and contribute to the dielectric loss factor k". In addition to these bound charges, there will always be a dc component to the total current which contributes to the total conductivity of the sample and is a loss current. 

The complex permittivity is given by s (o)= C (o) /Co, analogous to equation (1) for the static case, where Co= A.Bold is the vacuum capacitance of a parallel-plate capacitor ( =area of the plate, So the vacuum permittivity and d the plate separation (A/d) must have dimensions in cm) and C is the complex capacitance of the same capacitor filled with the material under study. Under the influence of a sinusoidal electric field, the complex permittivity relates to the impedance through ... 

In this technique the sample is subjected to an oscillating sinusoidal electric field. The applied voltage produces a polarisation within the sample and causes a small current to flow which leads the electric field by a phase dilference (5) (Figure 4). Two fundamental electrical characteristics, conductance and capacitance, are determined from measurements of the amplitude of the voltage (V), current (/) and S. These are used to determine the admittance of the sample (T) given by ... 

For a weak sinusoidal electric field E(t) = Eq sin cot. Equation (3.11) gives... 

When a steady-state sinusoidal electric field is applied, the polarizability of the particle and solvent becomes complex and the force in Eq. 3 can be generalized as... 

The dielectric relaxation spectroscopy can effectively measure the relaxation processes of dipoles in the polymers. Like the dynamic mechanical spectroscopy, the sinusoidal electric field is the imposing stimulation, and again in a complex form. 

When a polymer is subject to an intense sinusoidal electric field such as that due to an intense laser pulse, Fourier analysis of the polarization response can be shown to contain not only terms in the original frequency co, but also terms in 2(0 and 3nonlinear response depends on the square of the intensity of the incident beam for 2co, and the third power for 3 . For the second-order effects, the system must have some asymmetry, as discussed previously. For poling, this means both high voltage and a chemical organization that will retain the resulting polarization for extended periods of time. Polymeric systems investigated have been of three basic types ... 

The polarizability tensor a(a ) for a molecule in electronic state 0> subjected to a sinusoidal electric field with circular frequency co has components... 

If a sinusoidal electric field with a dc bias component 3 - DC + Eq cos( f) is applied to an irreversible electrostrictive material, such as relaxor PLZT, equation (2) becomes ... 

Co i ui eoE((v) where Cq is the vacuum capacitance of the arrangement E(cv) is the sinusoidal electric field applied (within the linear response)... 

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