Dielectric-experimental parameters Relaxation time

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. 

It has already been mentioned that the properties of a dielectric sample are a function of many experimentally controlled parameters. In this regard, the main issue is the temperature dependence of the characteristic relaxation times—that is, relaxation kinetics. Historically, the term kinetics was introduced in the field of Chemistry for the temperature dependence of chemical reaction rates. The simplest model, which describes the dependence of reaction rate k on temperature T, is the so-called Arrhenius law [48] ... 

In the analysis of experimental kinetic data, more attention should be paid to a careful determination of the longitudinal relaxation times. In the literature there are discrepancies between permittivities used for calculation of that parameter from the Debye relaxation time. Static dielectric permittivities and, to some extent, the Debye relaxation times exhibit a dependence on the electrolyte concentration. Therefore, in any analysis of the kinetic data, carefully measured and selected values fo the above parameters should be used. 

Similar heterogeneous model has been used to develop a relaxation function by Chamberlin and Kingsbury (1994), who consider the localized normal modes to be involved in the relaxation process. Localized (domains) regions are assumed to be present between Tg and T. They are described as dynamically correlated domains (DCD). A Gaussian distribution of the domain sizes has been assumed, with each domain characterized by a Debye relaxation time. Expressions for the dielectric susceptibility have been derived and used to fit the experimental susceptibilities of salol, glycerol and many other substances with remarkable agreement over 13 decades of frequency (even when only one adjustable parameter is employed). 

The principal characteristics of the triboelectret state in polymers recorded experimentally are i) the efficient surface charge density (ESCD) value and ii) the thermally stimulated depolarization (TSD) current spectrum, i.e. the discharge current dependence of the electret on its heating temperature. The analysis of TSD spectra helped to estimate the parameters of the triboelectret state, including the homo- to heterocharge relation in a dielectric, activation energy of the charge relaxation processes, relaxation time and others. 

For most of the systems being studied such a rela tion does not sufficiently describe the experimental results. This makes it necessary to use empirical rela tions which formally take into account the distribution of relaxation times with the help of various parameters (a,P) (3). In the most general way such nonDebye dielectric behavior can be described by the so called Havriliak-Negami relationship (3, 4, 6) ... 

The measurements of physical properties can be categorized as direct or indirect. In the former are included measurements of stress relaxation, creep compliance, and dielectric relaxation. In these experiments an excitation is applied which induces a direct change of mechanical parameters, and a response is observed as a result of this change. In these direct e q>eriments the contribution from stress concentrations is inevitable. The indirect mefhod may entail the measurement of fluctuations. For example, NMR spin-lattice relaxation time (Ti) is a fluctuation quantity. No change is induced in the mechanical properties during the indirect measurement this analysis is therefore free from the stress concentrations. If the information from direct measurement is equivalent to that from indirect measurement, we can estimate the former through the measurement of the latter without the influence of the stress concentrations. The equivalence of these two measurements is guaranteed by the "fluctuation-dissipation theorem" (1,2). In the next section we will try an experimental verification of the theorem for fresh fiber san les. 

The relaxation time constant 0 would also influence the parameter A, finally p substantially. From either Eq.(73) and (75), one will find that p increases as 0 increases, that is, the ER effect will be stronger if the dielectric relaxation is slower. However, too slow relaxation time (tlien the slow response time) would make FR fluids useless. Generally, the FR response time around 1 millisecond is favorable, thus requiring the relaxation time be of the same time scale, i.e., the dielectric relaxation frequency around lO llz. Block presumably thought the polarization rate would be important in the ER response process, and too fast or too slow polarization is unfavorable to the ER effect [7J. Ikazaki and Kawai experimentally found that the FR fluids of the relaxation frequencies within the range 100-10 Hz would exhibit a large ER effect [21,31], supporting the derivation from Eq. (69). 

The effective correlation times for an approximately isotropic motion, tr, ranged from 40.3 ps in methanol to 100.7 ps in acetic acid for 5a, and from 61.6 ps to 180.1 ps for 5b in the same solvents. Neither solvent viscosity nor dielectric constant bore any direct relationship to the correlation times found from the overall motion, and attempts to correlate relaxation data with parameters (other than dielectric constant) that reflect solvent polarity, such as Kosover Z-values, Win-stein y-values, and the like, were unsuccessful.90 Based on the maximum allowed error of 13% in the tr values derived from the propagation of the experimental error in the measured T, values, the rate of the overall motion for either 5a or 5b in these solvents followed the order methanol N,N-dimethylformamide d2o < pyridine < dimethyl sulfoxide. This sequence appears to reflect both the solvent viscosity and the molecular weight of the solvated species. On this basis, and assuming that each hydroxyl group is hydrogen-bonded to two molecules of the solvent,137 the molecular weights of the solvated species are as follows in methanol 256, N,N-dimethylformamide 364, water 144, pyridine 496, and dimethyl sulfoxide 312. 

From the experimental point of view, all relevant parameters like the relaxation rate (or time), the dielectric strength, and the shape parameters can be estimated by fitting the HN function to the data (for details see references Schlosser and Schihihals 1989 Schonhals and Kremer 2003). As an example Fig. 12.5 gives the dielectric loss for poly(vinyl acetate) at the dynamic glass transition versus frequency at a temperature of T = 335.6 K. Only the HN function is able to describe the data correctly. 

---