Spectroscopy dielectric relaxation

Here the number of HN terms N=2 and the number of KWW terms M=0 or 1 depending of the spectrum shape. The presence of the conductivity term in Equation 10.67 was determined from the ( ) function shape at low frequencies as the corresponding decay. 

Nuclear Magnetic Resonance Studies of Interfacial Phenomena 

The dielectric loss can be written using the distribution function of relaxation time /(logx) (or fix)) assuming the Debye-type relaxations for simplicity of the kernel  

The experimental e (co,T) functions have an incomplete maximum at high co values because in our experiments the maximal co value was 1.88 x 10 Hz (i.e., boundary X, =5.32x 10 s). However, the used regularization procedure can retrieve a complete shape of a boundary maximum on 

Assuming that each relaxation process obeys the Arrhenius law l/x=(l/Xo)exp(- /KgT), the dependence of relaxation on temperature can be written using the distribution function of the activation energy/( )  

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Chemical models of electrolytes take into account local structures of the solution due to the interactions of ions and solvent molecules. The underlying information stems from spectroscopic, kinetic, and electrochemical experiments, as well as from dielectric relaxation spectroscopy. The postulated structures include ion pairs, higher ion aggregates, and solvated and selectively solvated ions. 

Smith et al. [1.127] reviewed the dielectric relaxation spectroscopy (DRS) as a method for structural characterization of polymers and proteins providing, among others, information about the water content and states of water. 

Rotational Mobility in a Crystal Studied by Dielectric Relaxation Spectroscopy 120... 

During the last two decades, studies on ion solvation and electrolyte solutions have made remarkable progress by the interplay of experiments and theories. Experimentally, X-ray and neutron diffraction methods and sophisticated EXAFS, IR, Raman, NMR and dielectric relaxation spectroscopies have been used successfully to obtain structural and/or dynamic information about ion-solvent and ion-ion interactions. Theoretically, microscopic or molecular approaches to the study of ion solvation and electrolyte solutions were made by Monte Carlo and molecular dynamics calculations/simulations, as well as by improved statistical mechanics treatments. Some topics that are essential to this book, are included in this chapter. For more details of recent progress, see Ref. [1]. 

Static solution permittivity, e(c), and static solvent permittivity, es(c), for solutions of various electrolytes at various concentrations (c) have been obtained by dielectric relaxation spectroscopy [44]. Ion-pairs contribute to permittivity if their lifetime is longer than their relaxation time. However free ions do not contribute to permittivity. Thus,... 

Ishida, T., Makino, T. and Wang, C. (2000) Dielectric-relaxation spectroscopy of kaolin-ite, montmorillonite, allophone, and imogolite under moist conditions, Clays and Clay Minerals 48 Suppl. 1, 75-84... 

A. Kyritsis, P. Pissis, and J. Grammatikakis, Dielectric relaxation spectroscopy in poly(hydroxyethy acrylate)/water hydrogels, J. Poly. Sci. B 33, 1737-1750 (1995). 

Wachter, W., Buchner, R., and Hefter, G. Hydration of tetraphenylphosphonium and tetraphenylborate ions by dielectric relaxation spectroscopy. 7. Phys. Chem. B. 2006, 110,5147-5154. 

Figure 4. Dependence of capacity C on 7 for CCI4 in multi-walled caibon nanotubes with average pore diaineter of 5 nm (10 nm average external diameter), from dielectric relaxation spectroscopy. Symbols represent results obtained at different fiequencies circles, 30 IcHz squares, 100 kHz and triangles, 600kHz. The signals are for both bulk and confined CCI4.

G Williams. Dielectric relaxation spectroscopy of amorphous polymer systems The modern approaches. In E Riande, ed. Keynote Lectures in Selected Topics of Polymer Science. Madrid CSIC, 1995 page 1. 

Dielectric relaxation spectroscopy has been utilized as a very sensitive tool to detect photo-oxldatlon of PS (4,5) by the appearance of a relaxation process at 230 K when measured at 24 KHz. Our measurements (Figure 3) Inldlcate a similar relaxation process Is occurlng at 27O K when measured at 100 kHz. In addition a portion of a large relaxation process that appears to be at or below 115 K Is apparent In the ozone treated PS. The origin of this relaxation process Is presently unclear but may be due to a molecular charge transfer complex similar to that formed... 

Polystyrene and polybutadiene homopolymers as well as random and block copolymers of these mers have been studied via dielectric relaxation spectroscopy and tensile stress-strain measurements. The results suggest that some block copolymer systems studied have styrene rich surfaces which appear to partially crosslink upon initial exposure to ozone even though surface oxygen concentrations are not significantly affected. After continued exposure these samples appear to then undergo chain scission. Complex plane analysis implies that after degradation... 

Table 7.5 Average Relaxation Times from Time-Dependent Stokes Shifts (TDSS) for Coumarin Cl 52 in Various Solvents Together with the Longitudinal Relaxation Time Determined by Dielectric Relaxation Spectroscopy [20]...

The rates of change (slopes of the curves) of many important properties (such as the refractive index, surface tension, and gas permeabilities) as a function of temperature, the value of the dielectric constant, and many other optical and electrical properties, often change considerably at Tg. These changes enable the measurement of Tg by using techniques such as refractometry and dielectric relaxation spectroscopy. Refractometry provides results which are similar to those obtained from dilatometry, because of the correlation between the rates of change of the specific volume and of the refractive index with temperature. Dielectric relaxation spectroscopy is based on general physical principles which are similar to those in dynamic mechanical spectroscopy, the main difference being in its use of an electrical rather than a mechanical stimulus. 

Secondary relaxations are usually measured either by mechanical methods such as dynamic mechanical spectroscopy or (somewhat less often) by electrical methods such as dielectric relaxation spectroscopy [159], The existence of Tp is generally ascribed to the onset of a significant amount of some kind of motion of the polymer chains and/or the side groups attached to them, on a much smaller and more localized scale than the large-scale cooperative motions of chain segments associated with Ta. These motions are usually inferred from the results of measurements using methods such as nuclear magnetic resonance spectroscopy. See... 

In the previous section, drug stability was shown to depend on the physical state of water in excipients. Detailed information on the physical state of water can be obtained by measuring the dynamics or the mobility of water molecules. The effect of water mobility on drug stability has been studied by determining water mobility in mixtures of water and polymers used as pharmaceutical excipients. Methods used include the measurement of spin-lattice relaxation time and spin-spinrelaxation time by nuclear magnetic resonance (NMR) spectroscopy as well as of dielectric relaxation time by dielectric relaxation spectroscopy. 

Smith, G., etal. (1995) Dielectric relaxation spectroscopy and some applications in the pharmaceutical sciences, J. Pharm. Sci., 84, 1029-1044. 

Andjelic, S. and Fitz, B. D., Study of reorientational dynamics during real-time crystallization of absorbable poly(p-dioxanone) by dielectric relaxation spectroscopy,. Polym. Sd. Polym. Phys. Ed., 38, 2436, 2000. 

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