Charge relaxation time

Charge relaxation time The time required for a charge in a liquid or on a solid material to dissipate to 36.8 percent of its initial value when the material is grounded. 

Consider now the frequency dependence of the third cumulant. We will be interested in the case of a good conductor where the charge-relaxation time tq is much shorter than the dwell time td- Unlike the second cumulant of current, the third cumulant P3(wi,w2) in general exhibits a strong dispersion at wy2 1/td [11], For symmetry reasons, this dispersion vanishes for symmetric cavities and cavities with two tunnel or two ballistic contacts. The shape of P3(wi, w2) essentially depends on the parameters of the contacts. In particular, for a cavity with one tunnel and one ballistic contact with equal conductances Gl = Gr = G it exhibits a non-monotonic behavior as one goes from lv1 = uj2 = 0 to high frequencies. A relatively simple analytical expression for this case may be obtained if td 3> tq and one of the frequencies is zero ... 

Fig. 9. A rotation spectrum is produced by observing the motion of a cell in a rotating electric field of constant amplitude and plotting the rotation speed of the cell against frequency of the field. In solutions of low conductivity, the cell rotates in the opposite direction to the field (anti-field rotation) at low frequencies. This rotation reaches a peak when the field frequency corresponds to the charge relaxation time of the membrane. The position of this peak therefore contains information about membrane permittivity and conductivity. As the frequency increases further, the rate of cell spinning falls, becoming zero at about 1 MHz. Above this frequency, the cell starts to spin with the field (co-field rotation) and a second peak is reached. The frequency at which this peak occurs depends in practice mainly on the conductivity of the interior of the cell. It may be used for non-destructive determination of cytosolic electrolyte concentration.

The propensity of charge accumulation can also be expressed by the charge relaxation time, which is defined as the time required for a charge on a material to decay to a certain percentage (typically 37% (=e ) ) of its initial value. For conductive and semiconductive materials the charge relaxation time is typically less than 1 sec. 

Table IV. Charge Relaxation Times ofExplosives at 25°C and 40-50% Relative Humidity...

The fundamental measurements of dielectric constant and resistivity in multiphase systems follow directly from methods used for solid systems (Curtis, 1915). The material resistivity (or electrical conductivity) together with the permittivity are useful parameters for calculating the charge relaxation time of the material. 

An alternative expression for the charge relaxation time can be approximated for a multiphase system by an extension of continuum theory of solids. Applying conservation of charge V-J + dpqldt = 0, the equation of Poisson... 

However, the formation of monodisperse aqueous or organic drops in liquid-liquid systems is easily possible by the use of electrostatic fields [81]. Here, the applied voltage and thus the electric field at the capillary tip is the most significant parameter. This again is markedly influenced by the electrode and capillary geometry, as also by the electric properties (conductivity, permittivity, and charge relaxation time) of the liquids. 

On the other hand, since for the sine-form field dE/dt oc caE the role of permanent conductivity ct decreases with increasing frequency, in the high frequency limit (0 >> 1/tm = 47ta/ a material can be considered as non-conductive. The time Tm = /4tict is called Maxwell dielectric relaxation time. Later we shall meet it again under another name space charge relaxation time . 

We can see that relaxation time Tm is independent of the sample dimensions and includes only material parameters, namely, specific COTiductivity a and dielectric constant (real part s = s ). This time is called space charge relaxation time. It is the same Maxwell dielectric relaxatimi time we met in Section 7.2.1. Note that time Tm has no relation to the dispersion frequency of ionic conductivity (Ti) neither to Debye dipole relaxation time. 

Maxwell space charge relaxation time, 8 and a are dielectric permittivity (real part) and conductivity. 

The formation of space charges requires a certain time. We define a space charge relaxation time r as the time which is necessary to allow the material to reach the electrostatic equilibrium after applying an electric field, r is given by... 

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