Dielectric relaxation time constant

Assuming that the diode has low forward resistance and the source impedance of (t) is also low, the cell voltage (t) will easily reach in a rather short time, e.g. in 60 jjls for television application (Fig. 51a—c). Neglecting diode leakage, i.e. assuming the reverse resistance of the diode to be large compared to the resistance of the liquid crystal cell, (t) decays with the dielectric relaxation time constant of the liquid crystal material which may typically be about 10 ms or 30 ms (Fig. 51c). 

When a constant electric field is suddenly applied to an ensemble of polar molecules, the orientation polarization increases exponentially with a time constant td called the dielectric relaxation time or Debye relaxation time. The reciprocal of td characterizes the rate at which the dipole moments of molecules orient themselves with respect to the electric field. 

Here td is the so-called Debye dielectric relaxation time. One could view td as a phenomenological time constant which applies to dielectric relaxation measurements, or alternatively for simple causes, involving dielectric relaxation of weakly interacting dipoles, tD is related to the reorientation time constant of the solvent dipole in the laboratory frame. 

As expected, the capacitance of the cell increases when the frequency is decreased (Figure 1.25a) below the knee frequency, the capacitance tends to be less dependent on the frequency and should be constant at lower frequencies. This knee frequency is an important parameter of the EDLC it depends on the type of the porous carbon, the electrolyte as well as the technology used (electrode thickness, stack, etc.) [20], The imaginary part of the capacitance (Figure 1.25b) goes through a maximum at a given frequency noted as/0 that defines a time constant x0 = 1 lf0. This time constant was described earlier by Cole and Cole [33] as the dielectric relaxation time of the system, whereas... 

The dielectric constants used for the solvents were values estimated at 158 MHz from literature values of the low-frequency dielectric constant and the dielectric relaxation time r. 

Here r is a characteristic time constant, usually called the dielectric relaxation time. To conform to analogous theories of visco-elastic behaviour we should really use the term dielectric retardation time, because it refers to a gradual change in a strain (the polarisation or resulting electric displacement) following an abrupt change in stress (the applied field). Dielectric relaxation time is, however, still most commonly used in spite of this inconsistency. By integration of Equation (3.12) ... 

Fig. 13. Hydration dependence of protonic conduction. The dielectric relaxation time, Ts, is shown versus hydration, h, for lysozyme powders. The relaxation time is proportional to the reciprocal of the conductivity. (A) H20-hydrated samples solid curve, lysozyme without substrate , lysozyme with equimolar (GlcNAc)< at pH 7.0 , with 3x molar (G1cNAc)4 at pH 6.5. The relaxation time is nearly constant between pH 5.0 and 7.0. (B) HjO-hydrated samples solid curve, lysozyme without substrate 9, lysozyme with equimolar (GlcNAcb at pH 7.0. From Careri etal. (1985). 

Electroreduction and electrooxidation of salene (7V,N -bis(salicylidene)-ethyledi-amine) complexes of cobalt and copper studied by Kapturkiewicz and Behr [147] in eight aprotic solvents obey these conditions. These authors were the first to demonstrate experimentally the significant influence of the dielectric relaxation time of solvents on the electrode kinetics. They found earlier [171] that the mechanism of electrode reactions of salene complexes is independent of the solvents applied. No correlation with the prediction of the Marcus theory was found, but the kinetic data correlated well with the viscosity of the solvents and their dielectric relaxation time. However, because the ohmic drop was not well compensated, their rate constants are likely to be too low, as was shown in DMSO by Lasia and coworkers [172]. 

The spectral position of absorption and fluorescence are influenced by the dielectric properties of the medium in which observations are made. Figure 5 shows that the vapour phase 0-0 bands in absorption and fluorescence of a molecule are identical, whereas in solution with solvent of static dielectric constant e, refractive index n, the bands are no longer coincident. The differences can be rationalized as follows. From Onsager theory, a solute molecule of dipole moment ju in a spherical cavity of radius a polarizes the dielectric of the solvent, producing a reaction field. This is given for the ground-state of the solute molecule (of dipole moment iiq), by (22). Upon excitation, and invoking the Franck-Condon principle, the electronic excitation is much more rapid than the dielectric relaxation time of... 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

In order to demonstrate convincingly that this is a general experimental fact of glass-formers, experimental data for many different materials and (for a particular material) experimental data for several dielectric relaxation times are presented herein. The glass-formers include both molecular liquids and amorphous polymers of diverse chemical structures. All show the property of temperature-pressure superpositioning of the dispersion of the structural a-relaxation at constant xa. 

Forty years after Kramers seminal paper on the effect of solvent dynamics on chemical reaction rates (Kramers, 1940), Zusman (1980) was the first to consider the effect of solvent dynamics on ET reactions, and later treatments have been provided by Friedman and Newton (1982), Calef and Wolynes (1983a, 1983b), Sumi and Marcus (1986), Marcus and Sumi (1986), Onuchic et al. (1986), Rips and Jortner (1987), Jortner and Bixon (1987) and Bixon and Jortner (1993). The response of a solvent to a change in local electric field can be characterised by a relaxation time, r. For a polar solvent, % is the longitudinal or constant charge solvent dielectric relaxation time given by, where is the usual constant field dielectric relaxation time... 

The origin of the terms transverse and longitudinal dielectric relaxation times lies in the molecular theory of dielectric relaxation, where one finds that the decay of correlation functions involving transverse and longitudinal components of the induced polarization vector are characterized by different time constants. In a Debye fluid the relaxation times that characterize the transverse and longitudinal components of the polarization are T ) and rp = (ee/eslfD respectively. See, for example, P. Madden and D. Kivelson, J. Phys. Chem. 86, 4244 (1982). 

Abstract The present study demonstrates, by means of broadband dielectric measurements, that the primary a- and the secondary Johari-Goldstein (JG) /3-processes are strongly correlated, in contrast with the widespread opinion of statistical independence of these processes. This occurs for different glassforming systems, over a wide temperature and pressure range. In fact, we found that the ratio of the a- and P- relaxation times is invariant when calculated at different combinations of P and T that maintain either the primary or the JG relaxation times constant. The a-P interdependence is quantitatively confirmed by the clear dynamic scenario of two master curves (one for a-, one for P-relaxation) obtained when different isothermal and isobaric data are plotted together versus the reduced variable Tg(P)/T, where Tg is the glass transition temperature. Additionally, the a-P mutual dependence is confirmed by the overall superposition of spectra measured at different T-P combinations but with an invariant a-relaxation time. 

A semiquantitative explanation of the 2-ns component may be as follows The static polarity or the dielectric constant of the water pool of the AOT microemulsions can be obtained from the position of the emission maximum of the probes (C480 and 4-AP) [165,166]. For both probes, the water pool resembles an alcohol-like environment with an effective dielectric constant of 30-40. If one makes a reasonable assumption that the infinite frequency dielectric constant of water in the water pool of the microemulsions is the same as that of ordinary water, i.e., 5, and that the dielectric relaxation time is 10 ns as obtained for the biological systems [18b], then the solvent relaxation time should be about 1.67 ns, which is close to the observed solvation time in AOT microemulsions. 

V. The curves in Figure 1 were calculated by using the static value of the dielectric constant for each liquid. However, the dielectric constant of a medium is time dependent, because it requires a certain amount of time for the medium to attain its new polarization equilibrium after the sudden application of an electric field. In a polar liquid the permanent molecular dipoles require a certain time to rotate to line up with the electric field. When the value of tgn is in the vicinity of or smaller than that of the dielectric relaxation time t of the liquid—i.e., when tgn S 10t,— then a time-averaged complex dielectric constant should be used in Equations II, IV, and V. At a time t after the instantaneous application of a d.c. electric field, the dielectric constant of the medium in the field is given approximately by... 

Figure 2. Effect of the assumed value of the dielectric relaxation time on the calculated spectrum of lifetimes of solvated electrons in ethyl alcohol. For Curve I, as in Figure I, e = ex was used for all values of y time-averaged complex dielectric constants were used for Curves 2, 3, and 4. For Curve 2, td = 1 X 10 11 sec. Curve 3, t = 3X 10 n sec. Curve 4, Tud = 1.4 X 10 10 sec. was used at all y...

It turns out that the water and acetone curves in Figure 1 are also not appreciably altered by the use of their respective complex dielectric constants, even if one uses rup for all ion separation distances. This is because the dielectric relaxation times of these liquids are so short that a negligible amount of ion neutralization occurs during an interval equal... 

T he dielectric constant of deoxyribonucleic acid (DNA) solution was first measured by Allgen (1) and Jungner, Jungner and Allgen (9), who reported that DNA exhibited an anomalous dispersion in the 100-kc. region with a large dielectric increment. They calculated the dipole moment and the dielectric relaxation time and observed a dipole moment of approximately 103 to 104 Debye units and a relaxation time of about 10-7 second. They attempted to account for the dielectric relaxation of DNA in terms of the Debye theory. 

For instance, dielectric relaxation times usually are close to, and scale simply with, the shear and bulk viscosity relaxation times, and t . Since the Stokes-Einstein equation connecting diffusivity with shear viscosity is generally valid, this implies that the structural relaxation time for a system could be estimated if the diffusivity were known. Indeed for a number of simple polar molecules the product seems experimentally to be roughly constant at 2X 10 cm, implying that perturbations of a liquid of diffusivity 1 X 10 cm /sec would require of the order 10 psec to be relaxed to 1/eth of their initial value. 

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