Dielectric relaxation parameters, table

Table 4.5 Dielectric Relaxation Parameters for Some Protic Solvents at 25°C [5, 9]...

Table 4 Microwave dielectric data and relaxation parameters deduced from constraint fitting program...

The behavior of the dielectric spectra for the two-rotational-degree-of-ffeedom (needle) model is similar but not identical to that for fixed-axis rotators (one-rotational-degree-of-fireedom model). Here, the two- and one-rotational-degree-of-freedom models (fractional or normal) can predict dielectric parameters, which may considerably differ from each other. The differences in the results predicted by these two models are summarized in Table I. It is apparent that the model of rotational Brownian motion of a fixed-axis rotator treated in Section IV.B only qualitatively reproduces the principal features (return to optical transparency, etc.) of dielectric relaxation of dipolar molecules in space for example, the dielectric relaxation time obtained in the context of these models differs by a factor 2. 

All protic solvents undergo multiple relaxation processes due to the presence of hydrogen bonding. In the case of water and formamide (F), the data can be described in terms of two Debye relaxations. For the alcohols and A-methyl-formamide (NMF), three Debye relaxations are required for the description. In all of these solvents, the low-frequency process involves the cooperative motion of hydrogen-bonded clusters. In the case of water and the alcohols the high-frequency process involves the formation and breaking of hydrogen bonds. The intermediate process in the alcohols is ascribed to rotational diffusion of monomers. Studies of dielectric relaxation in these systems have been carried out for the -alkyl alcohols up to dodecanol [8]. Values of the relaxation parameters for water and the lower alcohols are summarized in table 4.5. 

The dielectric parameters of the samples at 0° and 6° C are only suggestive because the relevant dielectric relaxation is not yet very well resolved. (Data from Table 1 of Buchet et al. )... 

Values of the jS parameter (Table 13.4) are relatively large for PVME compared to those measured for the blend and PS. This suggests that, while aging is dominated by the faster PVME component, blending causes a broadening of the distribution of relaxation times. The dielectric studies of PS/PVME blends of Roland and Ngai (1992) indicate that the coupling parameter n defined by... 

In order to compare frequencies of maximum loss to l/( r), the frequency dependent susceptibility corresponding to the WW function was calculated as a function of / . The values of ra>max and r/( z ) are listed as a function of P in Table 1. The frequency of maximum loss correlates much better with the parameter r and depends only weakly on p. The exact relationship presented in the Table should allow data obtained from PCS to be compared properly to dielectric or mechanical relaxation data. 

As a second example, we consider liquid fluoromethane CH3F, which is a typical strongly absorbing nonassociated liquid. For our study we choose the temperature T 133 K near the triple point, which is equal to 131 K. The relevant experimental data [43] were summarized in Table IV. As we see in Table VIII, which presents the fitted parameters of the model, the angle p is rather small. At this temperature the density p of the liquid, the maximum dielectric loss and the Debye relaxation time rD are substantially larger than they would be, for example, near the critical temperature (at 293 K). At such small (5 the theory given here for the hat-curved model holds. For calculation of the complex permittivity s (v) and absorption a(v), we use the same formulas as for water. 

If vdielectric permittivity in vacuum will then be equal to 80. This is the so-called static permittivity. The permittivity of the vaccum is 0.855x 10 C m. The static dielectric permittivity near the ion or the surface of the charged electrodes, however, will exhibit smaller values. For instance, in the case of water at the electrode surface is assumed to approach 6. When applying the Marcus theory [8] both static and optical permittivities are used in calculations. These parameters therefore are listed in Table 1. In other calculations and correlations of the rate constants of electrode reactions and the dynamic relaxation properties of the solvents, the relaxation time of the solvents is used (Thble 1). 

In equations (5)-(8), i is the molecule s moment of Inertia, v the flow velocity, K is the appropriate elastic constant, e the dielectric anisotropy, 8 is the angle between the optical field and the nematic liquid crystal director axis y the viscosity coefficient, the tensorial order parameter (for isotropic phase), the optical electric field, T the nematic-isotropic phase transition temperature, S the order parameter (for liquid-crystal phase), the thermal conductivity, a the absorption constant, pj the density, C the specific heat, B the bulk modulus, v, the velocity of sound, y the electrostrictive coefficient. Table 1 summarizes these optical nonlinearities, their magnitudes and typical relaxation time constants. Also included in Table 1 is the extraordinary large optical nonlinearity we recently observed in excited dye-molecules doped liquid... 

Table 1. Dielectric parameter of several polar solvents at 25 C showing one or two sex>arated relaxation processes...

Table 6. Results of DRS measurements for the a relaxation relaxation strength, shape parameter, (both at 263K), VTF parameters B and T, dielectric glass transition temperature, Tg dieb 4 kinetic free volume fraction at for selected samples of Table 5 [55]...

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