Relaxation time dielectric measurements

Studies of the dispersion of the dielectric constant, especially those of Oncley 81), 83), 84), have yielded most of the data now available on the relaxation times of proteins. Measurements already obtained, expressed as T values in water at 25°, range from about tO" sec. for insulin, to about 250 10 sec. for the longer relaxation times of edestin and horse serum y-pseudoglobuKn. Relaxation times between 10 and 10" sec. have been determined for a nmnber of peptides and amino acids. Thus a range of more than 10 in relaxation times has been covered in studies already reported. Further extension of the method to longer relaxation times, involving measurements at lower frequencies, is now being carried on by Dr. Oncley and his associates. 

S. Yoshioka, Y. Aso, T. Otsuka, and S. Kojima, Water mobility in polyethylene glycol-, polyvinylpyrrolidone)-, and gelatin-watersystems, as measured by spin-lattice relaxation time, dielectric relaxation time, and water activity, J. Pharm. Sci. 84, 1072-1077(1995). 

Figure 9 Correlation of the segmental relaxation time ts measured in dilute solution and the glass transition temperature of the dense system. The data were taken from Adachi, K. Dielectric Spectroscopy of Polymeric Materials, American Chemical Society Washington, DC, p 261 and represent different chain structures. The line is a linear regression to the data.

In FIGURES 4 and 5 the available experimental data for the dielectric relaxation times are collected for 7CB and 8CB, respectively. The general behaviour is very similar in the two cases. In the isotropic phase a single relaxation time is measured, corresponding to the rotational (fynamics of the molecules about their short axes. However, the relaxation becomes bimodal for tempo-atures lower than Tni. In the nematic phase, dielectric data sets have been collected with the electric field parallel (8 ) and perpendicular (ij ) to the nematic director. In the parallel geometry a single relaxation process is observed, characterised by a relaxation time which increases rapidly at low temperatures. A second relaxation process appears in the perpendicular geometry its characteristic time is only... 

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

FIGURE 24.1 Local segmental relaxation times for pol3miethyltolylsiloxane (PMTS) measured dielectrically as a function of temperature at constant pressure (circles) and as a function of pressure at fixed temperature (triangles). (From Paluch, M., Pawlus, S., and Roland, C.M., Macromolecules, 35, 7338, 2002.)... 

Time Constant Analysis, r is the relaxation time of the corrosion process and is dependent on the dielectric properties of the interface. r is given by r = R P, but can be measured independently r = wz"max Since and P vary with surface area in exactly opposite fashion, r (or wzBmax) should be independent of surface area. To verify that this is indeed the case, we examined the corrosion of N80 steel in uninhibited 15% HC1 at 65 C. With increasing exposure time, we observed a continuous decrease in R (hence an increase in corrosion rate) and a concomitant increase in P. And, as expected, wz"max did not vary at all (see Figure 8). 

Using the Onsager model, the function Av-l(t) can be calculated for all time domains of dielectric relaxation of solvents measured experimentally for commonly used liquids (see, for example, [39]). Such simulations, for example, give for alcohols, at least, three different time components of spectral shift during relaxation, which are due to appropriate time domains of solvents relaxation. 

Roudaut et al. (1999a) used low-frequency pulsed-proton NMR and dielectric dynamic mechanical spectroscopies to study molecular mobility in glassy bread (<9%) as a function of temperature. Based on NMR results, they reported that some (if not all) of the water molecules were much more mobile than the polymer matrix whose relaxation time could not be measured within the 20-p,s dead time of the RF probe. 

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

Fig. 4.10 a Characteristic relaxation times determined from dielectric measurements [137] (diamonds), and from NSE spectra at (triangles) for triol (open symbols) and PU (solid symbols). The full lines correspond to Vogel-Fulcher and the dotted lines to Arrhenius descriptions, b Relaxation times from NSE spectra have been arbitrarily multiplied by a factor 6 for triol and 40 for PU to build a normalized relaxation map. (Reprinted with permission from [127]. Copyright 2002 Elsevier)... 

Fig. 4.20 Temperature dependence of the average relaxation times of PIB results from rheological measurements [34] dashed-dotted line), the structural relaxation as measured by NSE at Qmax (empty circle [125] and empty square), the collective time at 0.4 A empty triangle), the time corresponding to the self-motion at Q ax empty diamond),NMR dotted line [136]), and the application of the Allegra and Ganazzoli model to the single chain dynamic structure factor in the bulk (filled triangle) and in solution (filled diamond) [186]. Solid lines show Arrhenius fitting curves. Dashed line is the extrapolation of the Arrhenius-like dependence of the -relaxation as observed by dielectric spectroscopy [125]. (Reprinted with permission from [187]. Copyright 2003 Elsevier)...

The electrical properties of materials are important for many of the higher technology applications. Measurements can be made using AC and/or DC. The electrical properties are dependent on voltage and frequency. Important electrical properties include dielectric loss, loss factor, dielectric constant, conductivity, relaxation time, induced dipole moment, electrical resistance, power loss, dissipation factor, and electrical breakdown. Electrical properties are related to polymer structure. Most organic polymers are nonconductors, but some are conductors. 

Chapter E is devoted to the mean-square dipole moment and mean rotational relaxation time derived from dielectric dispersion measurements. Typical data, both in helieogenic solvents and in the helix-coil transition region, are presented and interpreted in terms of existing theories. At thermodynamic equilibrium, helical and randomly coiled sequences in a polypeptide chain are fluctuating from moment to moment about certain averages. These fluctuations involve local interconversions of helix and random-coil residues. Recently, it has been shown that certain mean relaxation times of such local processes can be estimated by dielectric dispersion experiment. Chapter E also discusses the underlying theory of this possibility. 

Dielectric dispersion measurements also provide a means of determining rotational diffusion coefficients or mean rotational relaxation times of solute molecules. In principle, data for these hydrodynamic quantities can be used for a... 

For positive lit electrodes one can register the drift of holes, and for negative ones- the drift of the electrons. The photosensitizer (for example Se) may be used for carrier photoinjection in the polymer materials if the polymer has poor photosensitivity itself. The analysis of the electrical pulse shape permits direct measurement of the effective drift mobility and photogeneration efficiency. The transit time is defined when the carriers reach the opposite electrode and the photocurrent becomes zero. The condition RC < tlr and tr > t,r should be obeyed for correct transit time measurement. Here R - the load resistance, Tr -dielectric relaxation time. Usually ttras 0, 1-100 ms, RC < 0.1 ms and rr > 1 s. Effective drift mobility may be calculated from Eq. (4). The quantum yield (photogenerated charge carriers per absorbed photon) may be obtained from the photocurrent pulse shape analysis. 

Dielectric relaxation measurements define an operational correlation time for the decay of the correlation function (P cosO)). For alcohols, the monomer rotation time, r2, increases from 18ps for n-propanol at 40°C to 44 ps for n-dodecanol at 40°C [83], A small measure of saturation in the dielectric relaxation time of alkyl bromides with increasing chain length has been noted by Pinnow et al. [242] and attributed to chain folding. 

G. R. Fleming In simple liquids such as methanol and ethanol there is no evidence for relaxation times slower than expected from dielectric measurements. Glasses at room temperature clearly show time scales that are infinite on our measurement time scale. In complex liquids such as glycerol-water mixtures and ethylene glycol, we may observe time scales that are longer than dielectric relaxation, but further studies are required to confirm this. 

Dielectric relaxation measurements for the adsorbed water have been reported by Jansen (44) the dielectric relaxation time is essentially 3r where r is the rotational jump time of the water molecule. From Figure 5 it can be seen that the dielectric and NMR mobility estimates agree rather well. All is not quite in order, however, for Jensen estimates from relaxation strength that he sees only one-third of the water molecules. 

The dielectric tensor e in a viscoelastic medium is a function of the frequency at which it is measured. It can be represented in terms of a real and imaginary part e (co) = e (co) -ie"(a>). If the frequency dependence of e is determined by a single relaxation time, then the relationship between e and r is... 

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