High-frequency Dielectric Relaxation Spectroscopy

2 High-frequency Dielectric Relaxation Spectroscopy Earlier studies of dielectric relaxation times in aqueous alkali hahde solutions by Kaatze and coworkers [12, 130] were obtained from the complex permittivities as a function of the frequency, but at frequencies up to about 100 GHz only as noted by Buchner [131]. The complex permittivity of conducting solutions has to be corrected for the conductance. The remainder can be expressed as Debye equations  

As a generalization, high-frequency dielectric relaxation spectroscopy in dilute aqueous salt solutions is rather insensitive to the nature of the anion, provided it is not dipolar itself, but does respond to the cation that orients the water dipoles around it through its electric field, and affects the water reorientation times, manifested by the appearance of the so-called slow water.  

The apphcation of dielectric relaxation smdies to electrolytes in nonaqueous solvents has been rather sparse. The molecular rotational correlation time is related to the solvent relaxation time according to Barthel et al. [138] as  

In the first equality, is the static permittivity of the solvent, its infinite frequency permittivity, is the ratio of the dynamic coupling and the Kirkwood dipole 

The methodology was applied by Barthel et al. [138] to solutions of Nal and Bu NBr in acetonitrile, yielding solvent molecular rotational correlation times r l =2.5 to 3.Ops for the pure solvent, according to various assumptions regarding that increase with electrolyte concentration due to the increased viscosity. It was applied by Wurm et al. [139] to LiClO, NaClO, and Bu NClO in DMF and DMA. For the pure solvents DMF and DMA, r j=6.6 and 8.9 ps, respectively, corresponding to rotation volumes v Q /lO m =11.3 and 13.8. These volumes diminish by a factor of about 4 in the presence of the electrolytes, but the reasons for this were not provided. Application of the method to NaCFjCO, MglCFjCOj), and Ba(C10 )2 in DMF by Placzek et al. [140] yielded r j = 7.2 ps for pure DMF, somewhat different from the earlier value shown above. The effects of the salts on this rotation time were not discussed. 

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Figure 5 Ranges of some dielectric relaxation spectroscopy techniques (a) conventional transient methods (b) newer transient methods (c) low frequency impedance bridge (d) conventional impedance bridges and analyzers (e) high frequency impedance analyzers and time domain spectroscopy (f) microwave cavities, transmission lines ...

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

The dielectric response of biological tissue has long been assumed linear. Thus an enzyme is treated as a hard sphere which relaxes linearly in an a. c. field at all but high field strengths [128]. In a suspension of cells, the electric field cannot penetrate to the interior of the cell at the low frequencies currently of interest in nonlinear dielectric spectroscopy [129], and is dropped almost entirely across the outer membrane of the cell which is predominantly capacitive at these frequencies, as was shown in Fig. 4. 

Cerveny investigated the development of the dynamic glass transition in styrene-butadiene copolymers by dielectric spectroscopy in the frequency range from 10 to 10 Hz. Two processes were detected and attributed to the alpha- and beta-relaxations. The alpha relaxation time has a non-Arrhenius temperature behavior that is highly dependent on styrene content... 

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