Dielectric spectroscopy dependence

The attenuation of ultrasound (acoustic spectroscopy) or high frequency electrical current (dielectric spectroscopy) as it passes through a suspension is different for weU-dispersed individual particles than for floes of those particles because the floes adsorb energy by breakup and reformation as pressure or electrical waves josde them. The degree of attenuation varies with frequency in a manner related to floe breakup and reformation rate constants, which depend on the strength of the interparticle attraction, size, and density (inertia) of the particles, and viscosity of the Hquid. 

The fact that the dielectric constant depends on the frequency gives SPFM an interesting spectroscopic character. Local dielectric spectroscopy, i.e., the study of s(w), can be performed by varying the frequency of the applied bias. Application of this capability in the RF range has been pursued by Xiang et al. in the smdy of metal and superconductor films [39,40] and dielectric materials [41]. In these applications a metallic tip in contact with the surface was used. 

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. 4.9 Temperature dependence of the characteristic time of the a-relaxation in PIB as measured by dielectric spectroscopy (defined as (2nf ) ) (empty diamond) and of the shift factor obtained from the NSE spectra at Qmax=l-0 (filled square). The different lines show the temperature laws proposed by Tormala [135] from spectroscopic data (dashed-dotted), by Ferry [34] from compliance data (solid) and by Dejean de la Batie et al. from NMR data (dotted) [136]. (Reprinted with permission from [125]. Copyright 1998 American Chemical Society)...

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)...

It is noteworthy that the neutron work in the merging region, which demonstrated the statistical independence of a- and j8-relaxations, also opened a new approach for a better understanding of results from dielectric spectroscopy on polymers. For the dielectric response such an approach was in fact proposed by G. Wilhams a long time ago [200] and only recently has been quantitatively tested [133,201-203]. As for the density fluctuations that are seen by the neutrons, it is assumed that the polarization is partially relaxed via local motions, which conform to the jS-relaxation. While the dipoles are participating in these motions, they are surrounded by temporary local environments. The decaying from these local environments is what we call the a-process. This causes the subsequent total relaxation of the polarization. Note that as the atoms in the density fluctuations, all dipoles participate at the same time in both relaxation processes. An important success of this attempt was its application to PB dielectric results [133] allowing the isolation of the a-relaxation contribution from that of the j0-processes in the dielectric response. Only in this way could the universality of the a-process be proven for dielectric results - the deduced temperature dependence of the timescale for the a-relaxation follows that observed for the structural relaxation (dynamic structure factor at Q ax) and also for the timescale associated with the viscosity (see Fig. 4.8). This feature remains masked if one identifies the main peak of the dielectric susceptibility with the a-relaxation. 

Dielectric spectroscopy has been shown to be of great interest in dealing with transitions involving reorientation of permanent dipoles [93]. By monitoring the temperature and frequency dependence of the complex dielectric permittiv-... 

Dielectric spectroscopy or culture capacitance measurement is used as an on-line, non-invasive method for biomass estimation (see the chapter by Sonnleitner in this issue - the section on electrical properties) and responds mainly to living cells [43,44]. Observed difficulties in using the signal as a pure biomass concentration sensor, i.e. deviations from the simple correlation with cell density, were attributed to dependencies on the physiological state [43], and could be used to discriminate different populations in yeast cultures [45]. Connections with morphological features could be found for budding yeast... 

This chapter concentrates on the results of DS study of the structure, dynamics, and macroscopic behavior of complex materials. First, we present an introduction to the basic concepts of dielectric polarization in static and time-dependent fields, before the dielectric spectroscopy technique itself is reviewed for both frequency and time domains. This part has three sections, namely, broadband dielectric spectroscopy, time-domain dielectric spectroscopy, and a section where different aspects of data treatment and fitting routines are discussed in detail. Then, some examples of dielectric responses observed in various disordered materials are presented. Finally, we will consider the experimental evidence of non-Debye dielectric responses in several complex disordered systems such as microemulsions, porous glasses, porous silicon, H-bonding liquids, aqueous solutions of polymers, and composite materials. 

The classical approach to the fit parameter estimation problem in dielectric spectroscopy is generally formulated in terms of a minimization problem finding values of X which minimize some discrepancy measure S(, s) between the measured values, collected in the matrix s and the fitted values = [/(co,-, x(7 ))] of the complex dielectric permittivity. The choice of S(e,e) depends on noise statistics [132]. 

In dielectric spectroscopy the polarization response P(t) of a dipolar material is monitored, which is subject to a time-dependent electric field (Maxwell field), E t). For a linear and isotropic dielectric one can write (e.g., Ref. 34) ... 

Fig. 10. Transition map for the mixture of hydrophilic Aerosil with PDMS [27] the relaxation of chain units outside the adsorption layer is represented by symbol , anisotropic motion of chain units inside the adsorption layer is shown by symbol 0, the slowest chain motion related to adsorption-desorption processes in the adsorption layer is designated by symbol O the data of the fu t two relaxation processes are fitted by the WLF function, the tempoature dependence of the slowest relaxation shows the Arrhenius-like behavior for comparison data from previous h Ty and NMR experiments , mechanical , and dielectric spectroscopy are given...

CF3SQ3H H2O probed by temperature dependent dielectric spectroscopy. J. Chem. Soc. Faraday Trans. 94, 1953-1958 (1998). 

Figure 50. Temperature dependencies of the various relaxation times of OTP. Filled circles are a-relaxation times of bulk OTP obtained by photon correlation spectroscopy open diamonds are JG relaxation times obtained by dielectric spectroscopy open circles are the primitive relaxation times x0 of bulk OTP calculated by Eq. (10). The photon correlation spectroscopy relaxation times of OTP confined in 7.5-nm pores (A) 5.0-nm pores ( ) 2.5-nm pores ( ).

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... 

Corezzi, S., Lucchesi, M., Rolla P. A., Capaccioli, S., Gallone, G. (1999) Temperature and pressure dependences of the relaxation dynamics of supercooled systems explored by dielectric spectroscopy, Phil. Mag. B 79, 1953-1963... 

---