Dielectric spectra

Although the frequency dependence of the dielectric spectrum contains a (mostly orientational) response from all of the molecules (water, biomolecules, and ions) in the system, assignment to the orientational relaxation of individual species is possible when they are well separated in the frequency (or time) scales. 

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Application of the exact continuum analysis of dispersion forces requires significant calculations and the knowledge of the frequency spectmm of the material dielectric response over wavelengths X = 2irc/j/ around 10-10 nm. Because of these complications, it is common to assume that a primary absorption peak at one frequency in the ultraviolet, j/uv. dominates the dielectric spectrum of most materials. This leads to an expression for the dielectric response... 

These and other values [381,406] allow us to depict the dielectric spectrum of a bilayer, shown in Fig. 5.2. Given this view, one can think of the phospholipid bilayer as a dielectric microlamellar structure as a solute molecule positions itself closer to the center of the hydrocarbon region, it experiences lower dielectric field (Fig. 5.2). At the very core, the value is near that of vacuum. A diatomic molecule of Na+Cl- in vacuum would require more energy to separate into two distinct ions than that required to break a single carbon-carbon bond ... 

Dielectric measurements are carried out on PPOA and PPODG. The dielectric spectrum of PPOA in the bulk presents a prominent glass-rubber relaxation followed by a subglass absorption. The low-molecular-weight compound only exhibits a prominent glass-liquid absorption followed by a diffuse and weak subglass relaxation. This behaviour cannot be explained in terms of only intramolecular interactions, and therefore intermolecular interactions must play an important role in this process. 

The dielectric spectrum for polymers with bulky side chains are shown in Fig. 2.69 for PDIPI and PDIBI. In these cases beside the prominent a relaxations it is possible to observe conductive contributions at low frequencies and high temperatures. A relaxation map is summarized in Fig. 2.70. 

Relation (14) gives equivalent information on dielectric relaxation properties of the sample being tested both in frequency and in time domain. Therefore the dielectric response might be measured experimentally as a function of either frequency or time, providing data in the form of a dielectric spectrum s (co) or the macroscopic relaxation function [Pg.8]

The majority of cases of non-Debye dielectric spectrum have been described by the so-called Havriliak-Negami (HN) relationship [8,11,15] ... 

Figure 24. The imaginary parts of the dielectric spectrum for anhydrous glycerol in the supercooled state at 196 K [186]. The dotted and dashed line show descriptions of the main relaxation process by CD [Eq. (21)] with tcd = 2.61 s, Ae = 63.9, and Pq, = 0.51) and KWW [Eq. (23)] with iK — 1.23 s, As = 62.0, and (3 = 0.69) functions, respectively. (The half-width of the loss curve were fixed for both CD and KWW functions.) (Reproduced with permission from Ref. 208. Copyright 2005, American Chemical Society.)...

Figure 35. A typical fitting result by the function (114) for the dielectric spectrum (75 mol% at 224 K, both real and imaginary parts are shown) where parameters ft and A were fixed to be the same values obtained in the master plot of 75 mol% of glycerol (see Fig. 27b) with x = 25 ps and Ae = 64.1. (Reproduced with permission from Ref. 208. Copyright 2005, American Chemical Society.)...

The spectral profiles of solid-state resonances from small particles depends on both the shape and the size of the particles. This is particular true for the strong mid-infrared Si-0 stretching and O-Si-O bending modes, characteristic of circumstellar silicate dust. In the dielectric spectrum, the stretching mode is roughly centered on 10 pm, while the bending mode is centered on 18 pm. Both resonances are very broad and strongly dependent on the structure of the molecules in which the SiO ... 

It is now well understood that the static dielectric constant of liquid water is highly correlated with the mean dipole moment in the liquid, and that a dipole moment near 2.6 D is necessary to reproduce water s dielectric constant of s = 78 T5,i85,i96 holds for both polarizable and nonpolarizable models. Polarizable models, however, do a better job of modeling the frequency-dependent dielectric constant than do nonpolarizable models. Certain features of the dielectric spectrum are inaccessible to nonpolarizable models, including a peak that depends on translation-induced polarization response, and an optical dielectric constant that differs from unity. The dipole moment of 2.6 D should be considered as an optimal value for typical (i.e.. 

Dynamic properties, such as the self-diffusion constant, are likewise strongly correlated with the dipole moment. This coupling between the translational motion and the dipole moment is indicated in the dielectric spectrum. Models that are overpolarized tend to undergo dynamics that are significantly slower than the real physical system. The inclusion of polarization can substantially affect the dynamics of a model, although the direction of the effect can vary. When a nonpolarizable model is reparameterized to include polarizability, the new model often exhibits faster dynamics, as with polarizable versions of TIP4P, ° Reimers-Watts-Klein and reduced... 

The dielectric spectrum of water predicted by our model refined in this way exhibits some interesting features, in good agreement with those experimentally observed ... 

This improvement in evaluating the true dipole moment affects the calculation in the correct sense that is, the disagreemrat between the calculated band and the experimental one decreases. However, for a completely satisfactory model, one really allowing prediction of the observed dielectric spectrum of water, much work is still necessary. In this direction we mention two recent papers by Stillinger and Camie and Patey. In Table II we have listed all the data obtained from our model. 

It is a trite observation that our understanding of water is in many respects even less adequate than that of other liquids. Recent monographs have shown that the past decade has seen sigiuficant advances, but a satisfactory treatment of the dielectric spectrum is stfll elusive. Professor Hasted, who has long-developed interests in this problem, contributes his own assessment of the present situation in Oiapter 4. He includes an account of some computer-model calculations as well as a summary of recent far-i.r. observations which are of immediate relevance to the quantitative appreciation of the dielectric spectrum of water. 

S. J. Paddison, G. Bender, K.D. Kreuer, N. Nicoloso, and T.A. Zawodzinski. The microwave region of the dielectric spectrum of hydrated Nafion (R) and other sulfonated membranes. Journal of New Materials for Electrochemical Systems 3, 291-300 2000. 

The composite 6 relaxations appearing around -80°C in the dielectric loss spectrum of the precursor, that is 8 and 8", are identified with the motions of fluorocarbon backbone and ether side-chains respectively. The higher temperature 8" process is dominant in the dielectric spectrum as it originates from motions of the ether side-chains. 

The dielectric spectrum (DS), pertaining to the T-band region, arises also in a certain specific form in the low-frequency Raman spectrum (RS). Comparison of both spectra allows us to improve the parameterization of our molecular model. Namely, in view of recent works (Gaiduk et al. [24], Gaiduk [25], we may write down the following relationships for the so-called R(v) and Bose-Einstein (BE) representations of the RS, denoted, respectively, Ir(v) and /hi (v) ... 

The first process prevails at relatively low frequencies. The electric component E of radiation orients dipole moments p along the field direction, while chaotic molecular motions hinder this orientation p and E are the vectors, and the field E is assumed to vary harmonically with time t. Due to inertia of reorienting molecules the time dependence of the polarization lags behind the time dependence E(f), so that heating of the medium occurs (the heating effect is not considered in this work). The dielectric spectrum obeys the Debye relaxation, for which the absorption monotonically increases with frequency. 

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