Polar dielectric response

The treatment of electrostatics and dielectric effects in molecular mechanics calculations necessary for redox property calculations can be divided into two issues electronic polarization contributions to the dielectric response and reorientational polarization contributions to the dielectric response. Without reorientation, the electronic polarization contribution to e is 2 for the types of atoms found in biological systems. The reorientational contribution is due to the reorientation of polar groups by charges. In the protein, the reorientation is restricted by the bonding between the polar groups, whereas in water the reorientation is enhanced owing to cooperative effects of the freely rotating solvent molecules. 

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. 

Indeed, things are slightly more complicated, because the electrons of the solvent can respond on the timescale of the absorption. Thus, in discussing solvent effects, it is helpful to separate the bulk dielectric response of the solvent, which is a function of s, into a fast component, depending on where n is the solvent index of refraction, and a slow component, which is the remainder after the fast component is removed from the bulk. The initially formed excited state interacts with the fast component in an equilibrium fashion, but with the slow component frozen in its ground-state-equilibrium polarization. The fast component accounts for almost the entire bulk dielectric response in very non-polar solvents, like alkanes, and about one-half of the response in highly polar solvents. 

The high-frequency dielectric constant is determined by the effects of electronic polarization. An accurate estimate of this property lends confidence to the modeling of the electronic polarization contribution in the piezoelectric and pyroelectric responses. The constant strain dielectric constants (k, dimensionless) are computed from the normal modes of the crystal (see Table 11.1). Comparison of the zero- and high-frequency dielectric constants indicates that electronic polarization accounts for 94% of the total dielectric response. Our calculated value for k (experimental value of 1.85 estimated from the index of refraction of the P-phase of PVDF. ... 

The situation is very different for polar solvents, i.e., solvents that have a relevant permanent dipole moment. In such solvents the greatest part of the dielectric response originates from the slight reorientation of the applied external field, and only a small part from electronic polarization. For water, with s = 78.4 (at 25 °C), the electronic polarizability contribution is only... 

The relationship (139), of course, is not rigorous, but it is based on an elementary macroscopic consideration [41] of the internal-field correction. Being widely used (GT, VIG), such a relationship is sufficient for an accurate description of the low-frequency dielectric response of strongly polar fluids. We return to this problem later in this section. 

This section presents a fundamental development of Sections V and VI. Here a linear dielectric response of liquid H20 is investigated in terms of two processes characterized by two correlation times. One process involves reorientation of a single polar molecule, and the second one involves a cooperative process, namely, damped vibrations of H-bonded molecules. For the studies of the reorientation process the hat-curved model is employed, which was considered in detail in Section V. In this model a hat-like intermolecular potential comprises a flat bottom and parabolic walls followed by a constant potential. For the studies of vibration process two variants are employed. 

For a pure dielectric response of the matter the polarization is proportional to the electric field in a linear approximation by... 

In general, there are five different mechanisms of polarization which can contribute to the dielectric response [3],... 

Domain wall polarization plays a decisive role in ferroelectric materials and contributes to the overall dielectric response. The motion of a domain wall that separates regions of different oriented polarization takes place by the fact that favored oriented domains with respect to the applied field tends to grow. 

Dielectric response data were taken on a Czochralski-grown very pure crystals of sisniCc (size 0.5 x 5 x 5 mm3) with probing electric-field amplitudes of 200 V/m applied along the polar c axis. A wide frequency range, 10-5 < / < 106 Hz, was supplied by a Solartron 1260 impedance analyzer with a 1296 dielectric interface. Different temperatures were chosen both... 

Here we describe the theory for detecting polarization and the technique for nonlinear dielectric response and report the results of the imaging of the ferroelectric domains in single crystals and thin films using sndm. Especially in a measurement of pzt thin film, it was confirmed that the resolution was sub-nanometer order. We also describe the theoretical res-... 

Eq. (62) can take account of the dielectric response of a boundary (electrode, grain boundary) but would not be sufficient to describe bulk polarization phenomena (appearing at longer times or lower frequencies) induced by strongly selectively blocking electrodes or grain boundaries (see below). The latter effect will be touched upon in the next section. 

The origin of the effect here represented by x0) can be derived from modelistic considerations. Solvent molecules are mobile entities and their contribution to the dielectric response is a combination of different effects in particular the orientation of the molecule under the influence of the field, changes in its internal geometry and its vibrational response, and electronic polarization. With static fields of moderate intensity all the cited effects contribute to give a linear response, summarized by the constant value e of the permittivity. This molecular description of the dielectric response of a liquid is... 

In this section, I will discuss some of the more recent developments in continuum solvation dynamics in polar solvents. Some of these deal with incorporation of realistic models for chromophores [8,43 16] used in fluorescence-upconversion experiments, others with improvements in modeling of the solution dielectric properties [47,48], including incorporation solvent dielectric response over a wide frequency range [43,44, 46,48] into theories of SD. 

R. F. Loring and S. Mukamel, Molecular theory of solvation and dielectric response in polar fluids, J. Chem. Phys., 87 (1987) 1272-83. 

It should be noticed that nonpolar solvents exhibit solvation dynamics, which are qualitatively similar to what has been said about polar solvents. Modeling these effects is not trivial, because the dielectric response of solvents cannot be used as an empirical input [104]. 

The relaxation of the polarization in response to a change of the field applied to a material is not due directly to the pull of the field, as suggested by the naive imagination. It is brought about by thermal motion, and fields of the magnitude relevant to dielectric relaxation perturb the thermal motion only slightly. 

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