Dielectric spectroscopy frequency determination

Dielectric Spectroscopy The determination of dielectric properties such as the loss factor and the dielectric constant as a function of frequency at different fixed temperatures. 

In impedance spectroscopy [IS also referred to as dielectric spectroscopy (DS)], a sinusoidal electric field is applied across a sample, and the resulting polarization (or electric displacement) is determined as a function of frequency. The frequency sweep typically ranges from about 1 MHz down to about 1 mHz, but measurement may be performed at higher frequencies by using special equipment. 

Dielectric spectroscopy is a technique which allows one to evaluate the complex dielectric permittivity e = e — ie" as a function of frequency and temperature, where e is the dielectric constant and e" is the dielectric loss [3,12]. A schematic view of a dielectric spectroscopy experiment is shown in Fig. 21.3. A dielectric sample of thickness d and area A is subjected to an alternating electric field of angular frequency w. Through measurements of the complex impedance of the sample it is possible to experimentally determine e [12,18-20]. Dielectric spectroscopy is a very suitable method to study molecular dynamics in polymers above Tg. In this case, segmental motions of the polymeric chains give rise to the so called cc-relaxation process, which can be observed as a maximum in e" and a step-Uke behavior in e as a function of frequency. Both, the intensity of the a relaxation, and the frequency of maximum... 

Samouillan et al. (2011) studied the dielectric properties of elastin at different degrees of hydration and specifically at the limit of freezable water apparition. The quantification of freezable water was performed by DSC. Two dielectric techniques were used to explore the dipolar relaxations of hydrated elastin dynamic dielectric spectroscopy (DDS), performed isothermally with the frequency varying from 10 to 3 x 10 Hz, and the TSDC technique, an isochronal spectrometry running at variable temperature, analogous to a low-frequency spectroscopy (10 to 10 Hz). A complex relaxation map was evidenced by the two techniques. Assignments for the different processes can be proposed by the combination of DDS and TSDC experiments and the determination of the activation parameters of the relaxation times. As already observed for globular proteins, the concept of solvent-slaved protein motions was checked for the fibrillar hydrated elastin (Samouillan et al. 2011). 

Natural rubber (NR) is a well studied elastomer. Of particular interest is the ability of NR to crystallize, specifically the strain-induced crystallization that takes place whilst the material is stretched. Moreover, in many elastomer applications, network chain dynamics under external stress/strain are critical for determining ultimate performance. Thus, a study on how the strain-induced crystallization affects the dynamics of a rubbery material is of outmost importance. Lee et al [1] reported their initial findings on the role of uniaxial extension on the relaxation behavior of cross-linked polyisoprene by means of dielectric spectroscopy. Nonetheless, to our best knowledge no in-depth study of the effects of strain induced crystallization on the molecular dynamics of NR has been undertaken, analyzing the relaxation spectra and correlating the molecular motion of chains with its structure. Broadband dielectric spectroscopy (BDS) has been chosen in order to study the dynamic features of segmental dynamics, because it is a comparatively simple technique for the analysis of the relaxation behaviour over a suitable frequency interval. This study is important from a basic and practical point of view, since an elongated crosslinked polymer at equilibrium may be considered as a new anisotropic material whose distribution of relaxation times could be affected by the orientation of the chains. 

To determine the movements of the whole chain and those of subchains, various techniques are accessible and available to the experimenter, including dielectric spectroscopy and mechanical spectrometry. Dielectric techniques are suitable for the study of polymers in a wide range of frequencies (between 10 Hz and 10 ° Hz), while the mechanical dynamic characterization of polymers provides access to long relaxation times (>10 s) through creep and stress relaxation tests. 

Dielectric Spectroscopy - Surface Characterization ofLiquid-borne Colloids When an oscillatory electric field is applied to a colloidal suspension, the electric double layer around the particle will be polarized. The complex dielectric properties of the suspension, the loss factor, and the relative permittivity are determined by performing several isothermal scans as a function of frequency in the range of 100-10 ° Hz. The dielectric relaxation of particles can be determined through the dielectric spectroscopy and the... 

It is not a trivial problem to obtain a complete characterization of a material responding over many decades of time. The brute force method would be to carry out experiments over many decades of time. More efficient is to employ more than one instrument, and cover a time span that includes high frequencies. This is now possible with broad dielectric spectroscopy, with which the frequency reuige from 10 to 10 can be attained by using different techniques - time domain spectroscopy, frequency response analysis using AC-bridges, and coaxial line reflectrometry. Of course, each isothermal experiment has to be repeated at various temperatures in order to determine the temperature dependence. 

A second use of microwave spectroscopy is the measurement of dipole moments. These are obtained by measuring the frequency shifts of lines in the applied electric field of a Stark-modulated spectrometer. This method of dipole-moment determination is superior to the older method of measuring dielectric constants. For example, impurities in the sample will not affect the dipole moment as measured by microwave spectroscopy. The dipole moment of a substance present to the extent of a few percent can be accurately measured if its microwave spectral lines can be assigned. The components of d can be determined, thus giving its orientation in the molecule, in addition to its magnitude. 

The method is based on the magnetorefractive effect (MRE). The MRE is the variation of the complex refractive index (dielectric function) of a material due to change in its conductivity at IR frequencies when a magnetic field is applied. A direct measure of the changes of dielectric properties of a material can be performed by determining its reflection and transmission coefficients. Hence, IR transmission or reflection spectroscopy can provide a direct tool for probing the spin-dependent conductivity in GMR and TMR [5,6]. 

Here, ve is the main electronic absorption frequency in the UV, typically around 3xl015s-1 [6], An analysis of the above equation shows some interesting consequences. A close match between the dielectric constants of the interacting bodies leads to diminishing values of the first term. The second term (determined by the refractive index values) shall then play the dominant role in the surface forces in this case. This effect can be utilized in force spectroscopy to maximize pull-off forces. On the other hand, interaction forces can also be minimized by a proper choice of the medium. Both these aspects will be important later for AFM-based force spectroscopy. 

The techniques of impedance spectroscopy, widely used in dielectrics (Jonscher, 1983 MacDonald, 1987) have been applied to magnetic materials. In this method, impedance measurements as a function of frequency are modelled by means of an equivalent circuit and its elements are associated with the physical parameters of the material. The complex permeability, p, is determined from the complex impedance, Z, by ... 

Literature reports on a variety of applications of dielectric measurements in different types of technical processes. The classical application is to determine water contents in process fluids by means of capacitance measurements. This technique has also been extended to higher frequencies by Wasan and coworkers (173, 174). In the following we present a technically very important problem that combines a controlled reaction inside a W/O emulsion and dielee trie Spectroscopy as a process on-line instrumentation. This problem concerns the formation and transport of gas hydrates in pipelines. 

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