Spectroscopy, dielectric

Dielectric spectroscopy, also known as impedance spectroscopy, has been used for process analysis for some time, as it offers the ability to measure bulk physical properties of materials. It is advantageous to other spectroscopic techniques in that it is not an optical spectroscopy and is a noncontact technique, allowing for measurement without disturbing a sample or process. The penetration depth of dielectric spectroscopy can be adjusted by changing the separation between the sensor electrodes, enabling measurement through other materials to reach the substrate of interest. Because it measures the dielectric properties of materials, it can provide information not attainable from vibrational spectroscopy. 

It has been shown that radio frequency impedance (RFI) is an effective tool for moifitoring cell density and cell growth of bioprocesses. The fermentation process, quite complex, is oftentimes difficult to sample and monitor. The RFI measurement could detect cell viability of Escherichia coli during the fermentation, serving as a qualitative measure of the metabolic load of the cell, and thus provide an in situ indicator of the optimal harvesting times. 

The dielectric spectroscopy of anisotropic fluids started in the 1970s by the extension of the Debye model from isotropic media (described in Appendix D) to uniaxial systems based on statistical mechanical Kubo formalism/ but no quantitative estimates about the critical frequencies or the susceptibilities were obtained. Quantitative estimates were given first on molecules with dipole moments along the long axis/ then for general dipole directions using the rotational Brownian picture in Maier-Saupe mean-field potential. This theory was subsequently refined in the 1990s.i  

The rotational diffusion coefficients for ellipsoids characterized by half axes of revolutions a, b, c, with respect to each axes can be given as  

Substituting parameters typical to uniaxial nematic liquid crystals, such as p 0.1, a = 2 nm, rj = 0.1 Pa-s, we get 2 x 10 Hz, D 1(F Hz, which correspond to half of the relaxation frequencies. 

Calculated imaginary part of the dielectric permittivity tvhen the electric field is parallel (a) and perpendicular (b) to the director.  

The rotational diffusion constant and relaxation frequency depend on temperature mainly through the temperature dependence of the viscosity which 

since the impedance of an equivalent circuit of a parallel connection between a resistance and a capacitor is [132,133] 

Consequently, (see Equations 4.30 and 4.31) when measuring the impedance, we are as well determining e0(co), since 

FIGURE 4.49 (a) Vacuum system and the equipment used for the measurements, (b) cylindrical capacitor 

The Physical Chemistry of Materials Energy and Environmental Applications 

Equation 4.48 was thoroughly tested using different capacitors in the range of 10 pF CX 200 pF [120], These capacitors are located in the sensor circuit in place of the cylindrical sample capacitor [120], With the help of this procedure, it was shown that Equation 4.48 is really adequate and can be used for the calculation of the capacity of the cylindrical sample capacitor at different frequencies in experiments carried out at a sample temperature T 200°C, where [HR]1 is negligible [120], 

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The presence of surface conductance behind the slip plane alters the relationships between the various electrokinetic phenomena [83, 84] further complications arise in solvent mixtures [85]. Surface conductance can have a profound effect on the streaming current and electrophoretic mobility of polymer latices [86, 87]. In order to obtain an accurate interpretation of the electrostatic properties of a suspension, one must perform more than one type of electrokinetic experiment. One novel approach is to measure electrophoretic mobility and dielectric spectroscopy in a single instrument [88]. 

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. 

Kremer F. and Schonhals, A., Eds., Broadband Dielectric Spectroscopy, Springer, Berlin, 2003. 

Williams, G. Dielectric Spectroscopy of Polymeric Materials, J.P. Runt and J.J. Fitzgerald, Eds., American Chemical Society, Washington, DC, 1997, Chapter 1. 

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. 

Rotational motion is spinning of the entire molecule around an axis in three-dimensional space. Figure 10 illustrates the rotational motion of a water molecule. Rotational motion occurs in liquid and gas phases of water and, to a limited extent, through defects in the solid phase (ice). Rotational motion of water molecules can be measured using NMR and dielectric spectroscopy (Belton, 1994). 

Dielectric spectroscopy, in silicone network characterization, 22 569 Dielectric stiffness, 11 93 Dielectric strength, of plastics, 19 587 of thermoplastics, 10 176... 

Fig. 1.3 Relaxation map of polyisoprene results from dielectric spectroscopy (inverse of maximum loss frequency/w// symbols), rheological shift factors (solid line) [7], and neutron scattering pair correlation ((r(Q=1.44 A )) empty square) [8] and self correlation ((t(Q=0.88 A" )) empty circle) [9],methyl group rotation (empty triangle) [10]. The shadowed area indicates the time scales corresponding to the so-called fast dynamics [11]...

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. 

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. 

In the case of polymers, the a-relaxation has been well characterized for many years, e.g. by dielectric spectroscopy and mechanical relaxation (see, e.g. [34, 111]).The main experimental features extracted from relaxation spectroscopies are ... 

Fig. 4.5 Scaling representation of the spin-echo data at Q nax- Different symbols correspond to different temperatures. Solid line is a KWW description (Eq. 4.8) of the master curve, a Polyurethane at Qmax=l-5 A L The shift factors have been obtained from the superposition of the NSE spectra. (Reprinted with permission from [127]. Copyright 2002 Elsevier), b Poly-(vinyl chloride) at Qmax=l-2 A L The shift factors have been obtained from dielectric spectroscopy. (Reprinted with permission from [129]. Copyright 2003 Springer, Berlin Heidelberg New York)...

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)...

The elastic contribution is also called elastic incoherent structure factor (EISF). It may be interpreted as the Fourier transformed of the asymptotic distribution of the hopping atom for infinite times. In an analogous way to the relaxation functions (Eq. 4.6 and Eq. 4.7), the complete scattering function is obtained by averaging Eq. 4.22 with the barrier distribution function g E) obtained, e.g. by dielectric spectroscopy (Eq. 4.5)... 

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. 

Arbe A, Colmenero J, Richter D (2002) In Kremer F, Schonhals A (eds) Polymer dynamics by dielectric spectroscopy and neutron scattering - a comparison in broadband dielectric spectroscopy... 

Braun et al. [341] investigated the molecular dynamics of the rigid polypeptide brush by means of dielectric spectroscopy and prepared patterned brushes by SIP from pCP SAM initiators [342]. 

I. Alig, D. Fischer, D. Lellinger and B. Steinhoff, Combination of NIR, Raman, ultrasonic and dielectric spectroscopy for in-line monitoring of the extrusion process, Macromol. Symp., 230, 51-58 (2005). 

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