Dielectric spectra, high frequency

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

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. 

The High Frequency dielectric constant is measured at the frequencies faster than the vibrational motion of ions. It is applicable to the visible region of the spectrum. It determines refractive index which governs the transmission of light in transparent media. 

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.. 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

The far-infrared (FIR) absorption spectrum of low-viscosity liquids contains a broad peak of resonant character with a resonant frequency and intensity which decreases with increasing temperature [14,15]. Phis phenomenon is known as the Poley absorption. It takes its name from the work of Poley [16], who observed that the difference between the high-frequency dielectric permittivity... 

The TV-dielectric relaxation mechanism allows us to (i) remove the THz deficit of loss e" inherent in previous (see GT2) theoretical studies, (ii) explain the THz loss and absorption spectra in supercooled (SC) water, (iii) describe, in agreement with the experiment, the low- and high-frequency tails of the two bands of ice H20 located in the range 10-300 cm-1, and (iv) describe the nonresonance loss spectrum in ice in the submillimetric region of wavelengths. Specific THz dielectric properties of SC water are ascribed to association of water molecules, revealed in our study by transverse vibration of the HB charged molecules. 

Let us first discuss estimates fi om DR measurements that provide several important pieces of information. These experiments measure the frequency-dependent dielectric constant and provide a measure of a liquid s polarization response at different frequencies. In bulk water, we have two dominant regions. The low-frequency dispersion gives us the well-known Debye relaxation time, Tq, which is equal to 8.3 ps. There is a second prominent dispersion in the high-frequency side with relaxation time constant less than Ips which contains combined contributions from low-frequency intermolecular vibrations and libra-tion. Aqueous protein solutions exhibit at least two more dispersions, (i) A new dispersion at intermediate frequencies, called, d dispersion, which appears at a timescale of about 50 ps in the dielectric spectrum, seems to be present in most protein solutions. This additional dispersion is attributed to water in the hydration layer, (ii) Another dispersion is present at very low frequencies and is attributed to the rotation of the protein. 

Dielectric relaxation results are proven to be the most definitive to infer the distinctly different dynamic behavior of the hydration layer compared to bulk water. However, it is also important to understand the contributions that give rise to such an anomalous spectrum in the protein hydration layer, and in this context MD simulation has proven to be useful. The calculated frequency-dependent dielectric properties of an ubiquitin solution showed a significant dielectric increment for the static dielectric constant at low frequencies but a decrement at high frequencies [8]. When the overall dielectric response was decomposed into protein-protein, water-water, and water-protein cross-terms, the most important contribution was found to arise from the self-term of water. The simulations beautifully captured the bimodal shape of the dielectric response function, as often observed in experiments. 

Similar property distributions occur throughout the frequency spectrum. The classical example for dielectric liquids at high frequencies is the bulk relaxation of dipoles present in a pseudoviscous liquid. Such behavior was represented by Cole and Cole [1941] by a modification of the Debye expression for the complex dielectric constant and was the first distribution involving the important constant phase element, the CPE, defined in Section 2.1.2.3. In normalized form the complex dielectric constant for the Cole-Cole distribution may be written... 

The table presents oscillator parameters of five selected CH2 vibrations between 1200 and 1400 cm used to fit the Drude-Lorentz spectrum calculation to an experimental spectrum of random polycrystalline PEG. See ref. [15] for the meaning of Qq. Gp, and Q. Lor the high-frequency dielectric constant 00 = 2.10 was used, see text... 

Benzene is a non polar molecule and as such cannot exhibit dielectrically active reorientational relaxation. Investigation of the microwave and far infrared dielectric spectrum indicates that pure benzene exhibits a distinct loss feature. It is well known from ultrasonic studies that molecules with a high degree of symmetry can exhibit translational-vibrational relaxation "24 jp molecules collide inelasti-cally part of their momentum can be used to excite an internal vibrational mode to a higher state. In the case of benzene it is assumed that this is one of the low frequency ring vibrational modes . Deactivation of this excited mode is not readily... 

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