Dielectric relaxation time, dependence

F. Ingrosso, B. Mennucci and J. Tomasi, Quantum mechanical calculations coupled with a dynamical continuum model for the description of dielectric relaxation time dependent Stokes shift of coumarin Cl53 in polar solvents, J. Mol. Liq., 108 (2003) 21 -6. 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found... 

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

This approximation requires that cos. This behavior in fact follows from a Debye dielectric continuum model of the solvent when it is coupled to the solute nuclear motion [21,22] and then xs would be proportional to the longitudinal dielectric relaxation time of the solvent indeed, in the context of time dependent fluorescence (TDF), the Debye model leads to such an exponential dependence of the analogue... 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

The expressions in brackets are the expansivities above and below Tg. The constant K3 is a function of bond type in chains and is really constant for every class of polymers. The physical interpretation of this equation may be consistent with the iso-free-volume concept. However, we believe that the introduction of this equality is in practise a denial of the concept. There are also other arguments against this concept. Kastner56 found, for example, that dielectric losses diminish during the isothermal volume contraction, which indicates a dependence of relaxation times on free-volume. However, if we assume that relaxation time depends exclusively on free-volume, the calculated reduction factor differs from the experimental one. 

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 analysis of the dynamics and dielectric relaxation is made by means of the collective dipole time-correlation function (t) = (M(/).M(0)> /( M(0) 2), from which one can obtain the far-infrared spectrum by a Fourier-Laplace transformation and the main dielectric relaxation time by fitting < >(/) by exponential or multi-exponentials in the long-time rotational-diffusion regime. Results for (t) and the corresponding frequency-dependent absorption coefficient, A" = ilf < >(/) cos (cot)dt are shown in Figure 16-6 for several simulated states. The main spectra capture essentially the microwave region whereas the insert shows the far-infrared spectral region. 

The VFT behavior of supercooled glycerol is well known from studies of liquid and supercooled glycerol [3,186-190], while the Arrhenius dependence of the dielectric relaxation time is more relevant for crystals. For example, the temperature dependence of the dielectric relaxation time of ice I also obey the Arrhenius law with the activation energy about 60 kJ moF1 [198,199]. 

Figure 48. Temperature dependence of dielectric relaxation time for water confined in sample C. The data were measured under different conditions and contain a different amount of water Unfilled circles correspond to the data presented early in Fig. 46 filled circles represent the experiment with reduced water content [78]. Full line is the best fit according to (133) In To = —17.8 0.5, ), = 39 1 kJmol 1, 7) = 124 7K, D — 10 2, C = 9 x 105 3 x 10s. The dashed line was simulated from (133) for the same In To, ), 7), and D, but with C divided by a factor 1.8 (explanation in the text). (Reproduced with permission from Ref. 78. Copyright 2004, The American Physical Society.)...

There are several complications in using this technique for a-Si H, first of which is the frequency dependence. The capacitance is measured by the response to a small alternating applied electric field. The depletion layer capacitance is obtained only when the free carriers within the bulk of the semiconductor can respond at the frequency of the applied field, dielectric relaxation time. 

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). 

Fig. 26. Temperature dependence of various properties of myoglobin crystals , frequency of the O-D band maximum (IR) —, dielectric relaxation time of water (schematic) ---—, Lamb-Mossbauer factor,/o, after subtracting the harmonic mode (sche-...

The plot shows a distribution closely around a slope of unity indicated by the solid line in Figure 2 except for the alcohols and nitrobenzene. Such anomaly in alcohols is also reported for other chemical processes and time-dependent fluorescence stokes shifts and is attributed to their non-Debye multiple relaxation behavior " the shorter relaxation components, which are assigned to local motions such as the OH group reorientation, contribute the friction for the barrier crossing rather than the slower main relaxation component, which corresponds to the longitudinal dielectric relaxation time, tl, when one regards the solvent as a Debye dielectric medium. If one takes account of the multiple relaxation of the alcohols, the theoretical ket (or v,i) values inaease and approach to the trend of the other solvents. (See open circles in Figure 2.)... 

The form of these dielectric dispersion curves is shown in Fig. 8 for a series of elongated ellipsoids of revolution of varying axial ratios. The magnitude of the contribution to the dielectric constant made by the two different portions of the curve, corresponding to the two different relaxation times, depends upon the components of the total... 

Figure 1 For pure bulk ice samples, (a) Temperature dependence of the dielectric relaxation time r and (b) Cole-Cole plots of pure ice crystal (parallel to the c-axis) at -10 °C. The dielectric dispersion is of the Debye type (a=0.99, p=1.00).

In this section, the melt viscosity, the dielectric relaxation time, and the DC conductivity are reviewed and summarized for DGEBA oligomers before crosslinking in terms of their temperature-dependent behavior. 

Resin system Type of relaxation Temperature dependence of dielectric relaxation time References... 

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