Electric relaxation time

Historically, temperature dependence of mechanical and electrical relaxation times were first examined by Williams, Landel and Ferry... 

Glassy and polymer electrolytes may be considered as liquids and AngelF has defined a decoupling index J , as the ratio of mechanical (viscosity tf) and electrical relaxation time i , = For some ionic... 

In the absence of concentration gradients, no space charge density can exist in the solution under steady state conditions. Moreover, if by any means some electrical charge density is generated at any position within the system, the time required for this charge to disappear (in fact, to migrate to the system boundaries) is of the order of nanoseconds. This time is the so-called electrical relaxation time of the system, Tg, and can be obtained from Eqs. (8, 13, and 156) as... 

Here s is the real part of the relative permittivity in the low-frequency bulk relaxation regime, S = d/ Dx where d is the film thickness, D the diffusion coefficient of the moving ions, and t= fbes/Odc is the electrical relaxation time. The density and mobility of the moving ions can be obtained from the high-frequency part of e immediately below the frequency range of bulk polarization ( s) by picking a frequency x, where (e>x) = X s. Provided that the approximation 1 + =... 

Because of the large conductivity in aqueous electrolytes, externally applied fields cannot approach such magnitudes and thus hardly disturb the electrical double layer equilibrium. Similarly, convection has a negligible effect as is seen by comparing the electrical relaxation time e/cT 84 ys to a liquid transport time where 1 is a... 

The cell design required to achieve a reliable measurement depends on the sample shape and conductivity," " although for most polymer electrolytes of interest a path length of about 1 mm and a cross-section of about 10 mm will suffice. Alternatively, provided stray capacitance and inductance are eliminated, a very short path length and a large area of cross-section can be used. This gives a measurement of the electrical relaxation time constant, which is the ratio of permittivity to conductivity, without a knowledge of the sample dimensions." " ... 

It is important to recognize the approximations made here the electric field is supposed to be sulficiently small so that the equilibrium distribution of velocities of the ions is essentially undisturbed. We are also assuming that the we can use the relaxation approximation, and that the relaxation time r is independent of the ionic concentration and velocity. We shall see below that these approximations break down at higher ionic concentrations a primary reason for this is that ion-ion interactions begin to affect both x and F, as we shall see in more detail below. However, in very dilute solutions, the ion scattering will be dominated by solvent molecules, and in this limiting region A2.4.31 will be an adequate description. 

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

We have next to consider the measurement of the relaxation times. Each t is the reciprocal of an apparent first-order rate constant, so the problem is identical with problems considered in Chapters 2 and 3. If the system possesses a single relaxation time, a semilogarithmic first-order plot suffices to estimate t. The analytical response is often solution absorbance, or an electrical signal proportional to absorbance or to another physical property. As shown in Section 2.3 (Treatment of Instrument Response Data), the appropriate plotting function is In (A, - Aa=), where A, is the... 

The several experimental methods allow a wide range of relaxation times to be studied. T-Jump is capable of measurements over the time range 1 to 10 s P-jump, 10 to 5 X 10" s electric field jump, 10 to 10 s and ultrasonic absorption, 10 to 10 " s. The detection method in the jump techniques depends upon the systems being studied, with spectrophotometry, fluorimetry, and conductimetry being widely used. 

Shown in Fig. 4a is the temperature dependence of the relaxation time obtained from the isothermal electrical resistivity measurement for Ni Pt performed by Dahmani et al [31. A prominent feature is the appearance of slowing down phenomenon near transition temperature. As is shown in Fig. 4b [32], our PPM calculation is able to reproduce similar phenomenon, although the present study is attempted to LIq ordered phase for which the transition temperature, T]., is 1.89. One can confirm that the relaxation time, r, increases as approaching to l/T). 0.52. This has been explained as the insufficiency of the thermodynamic driving force near the transition temperature in the following manner. 

Hultman, E. Sjoholm, H. (1983b). Electromyogram, force and relaxation time during and after continuous electrical stimulation of human skeletal muscle in situ. J. Physiol. 339, 33-40. 

NMR Spectroscopy. All proton-decoupled carbon-13 spectra were obtained on a General Electric GN-500 spectrometer. The vinylldene chloride isobutylene sample was run at 24 degrees centigrade. A 45 degree (3.4us) pulse was used with a Inter-pulse delay of 1.5s (prepulse delay + acquisition time). Over 2400 scans were acquired with 16k complex data points and a sweep width of +/- 5000Hz. Measured spin-lattice relaxation times (Tl) were approximately 4s for the non-protonated carbons, 3s for the methyl groups, and 0.3s for the methylene carbons. 

The addition of salts modifies the composition of the layer of charges at the micellar interface of ionic surfactants, reducing the static dielectric constant of the system [129,130]. Moreover, addition of an electrolyte (NaCl or CaCli) to water-containing AOT-reversed micelles leads to a marked decrease in the maximal solubihty of water, in the viscosity, and in the electrical birefringence relaxation time [131],... 

First, it is assumed that the EEDF is spatially uniform and temporally constant, which is allowed if the energy relaxation time of the EEDF is much shorter than the RF-cycle duration, and if the relaxation length is much smaller than the typical gradient scale length. This assumption implies a spatially and temporally constant electric field. It reduces the Boltzmann equation to a problem exclusively in the velocity space. 

Debye and Falkenhagen predicted that the ionic atmosphere would not be able to adopt an asymmetric configuration corresponding to a moving central ion if the ion were oscillating in response to an applied electrical field and if the frequency of the applied field were comparable to the reciprocal of the relaxation time of the ionic atmosphere. This was found to be the case at frequencies over 5 MHz where the molar conductivity approaches a value somewhat higher than A0. This increase of conductivity is caused by the disappearance of the time-of-relaxation effect, while the electrophoretic effect remains in full force. 

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