Dielectric theory

As the metallic particles are assumed to be sufficiently large for macroscopic dielectric theory to be applicable, we can substitute for a the expression for the polarisability of metallic particle immersed in an insulator. The dipole moment is given by the integration of the polarisation over the volume V. Thus, if the polarisation is uniform ... 

McConnell J. Rotational Brownian Motion and Dielectric Theory. (Academic Press, New York) (1980). 

Hoye JS, Stell G (1980) Dielectric theory for polar molecules with fluctuating polarizability. J Chem Phys 73(l) 461-468... 

In a contrary to the DFT studies of isolated molecules, where there is a strong link between applications to biological systems and general developments in the theory of density functionals, approaches used for modeling properties of chemical molecules embedded in the biological microscopic environment combine developments in many fields. These fields include DFT, statistical physics, dielectric theory, and the theory of liquids. 

Marten, B., K. Kim, C. Cortis, R. A. Friesner, R. B. Murphy, M. N. Ringnalda, D. Sitkoff, and B. Honig. 1996. New Model for Calculation of Solvation Free Energies Correction to Self-consistent Reaction Field Continuum Dielectric Theory for Short-Range Hydrogen-Bonding Effects. J. Phys. Chem. 100, 11775. 

Marten B, Kim K, Cortis C, Friesner RA, Murphy RB, Ringnalda MN, Sitkoff D, Honig B. New model for calculation of solvation free energies correction of self-consistent reaction field continuum dielectric theory for short-range hydrogen-bonding effects, / Phys. Chem. 1996, 100, 11775-11788. 

The nature of the neutral or acidic hydrolysis of CH2CI2 has been examined from ambient temperature to supercritical conditions (600 °C at 246 bar). Rate measurements were made and the results show major deviations from the simple behaviour expressed by the Arrhenius equation. The rate decreases at higher temperatures and relatively little hydrolysis occurs under supercritical conditions. The observed behaviour is explained by a combination of Kirkwood dielectric theory and ab initio modelling. 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

DIELECTRIC THEORY. A dielectric is a material having electrical conductivity low in comparison to that of a metal. It is characterized by its dielectric constant and dielectric loss, both of which are functions of frequency and temperature. The dielectric constant is the ratio of the strength of an electric held in a vacuum to that in the dielectric for the same distribution of charge. It may also be defined and measured as the ratio of the capacitance C of an electrical condenser filled with the dielectric to the capacitance Cu of the evacuated condenser ... 

Liquid insulators are required for circuit breakers, transformers, and some cable applications. Natural hydrocarbon mineral oils are commonly-used, as well as chlorinated aromatic liquids (desirable because of nonflammability). For high-temperature situations, silicone fluids may be used. Permittivities range between 2 and 7. Insulating liquids function both as electrical insulators and heat-transfer media. See also Dielectric Theory. 

ONSAGER, LARS (1903-1976). A Norwegian chemist who won the Nobel pnze for chemistry in 1968. He studied and wrote on the theory of electrolytic conduction and theory of dielectrics. He also worked with stiperfluids and crystal statistics and reciprocal relations in irreversible processes. After receiving his doctorate in Norway, he came to the U.S. and became a citizen. See also Dielectric Theory. 

Other important works containing copious references on dielectric theory, measurement techniques and data tabulation have been published. Pioneering work was done by von Hippel (1954 a b and c). Buckley and Maryott (1958) have tabulated data on liquids. Nelson (1991) and with Trnga (Tinga and Nelson 1973) and El-Rays and Ulaby (1987) have tabulated dielectric information on agricultural as well as other materials. Ohlsson and Bengtsson (1975) and Kent (1987) have published data on foods. 

The results of the SCRF models depend strongly on the radius Rx used for the definition of the spherical interface between the solute and the solvent. Unfortunately, the dielectric theory does not provide an answer for the question of which value is appropriate for this radius. Owing to the implicit assumption of the dielectric continuum models that the electron density of the solute should be essentially inside the cavity, any value of Rx below a typical van der Waals (vdW) radius would not be meaningful. On the other hand, at least at the distance of the first solvent shell, i.e., typically at two vdW radii, we should be in the dielectric continuum region. However, there is no clear rationale for the right value between these two limits other than empirical comparison of the results with experimental data. Among others, the choice of spherical cavities which correspond to the liquid molar-solute volume has proved to be successful. 

Having recognized the theoretical inadequacy of the dielectric theory for polar solvents, I started to reconsider the entire problem of solvation models. Because the good performance of dielectric continuum solvation models for water cannot be a result of pure chance, in some way there must be an internal relationship between these models and the physical reality. Therefore I decided to reconsider the problem from the north pole of the globe, i.e., from the state of molecules swimming in a virtual perfect conductor. I was probably the first to enjoy this really novel perspective, and this led me to a perfectly novel, efficient, and accurate solvation model based upon, but going far beyond, the dielectric continuum solvation models such as COSMO. This COSMO for realistic solvation (COSMO-RS) model will be described in the remainder of this book. 

The dielectric theory may be expressed in a nonlocal form based on the definition of the susceptibility and permittivity in a form that makes these physical quantities the kernel of appropriate integral equations. 

The nonlocal dielectric theory has as a special case the standard local theory. Its fuller formulation permits the introduction in a natural way of statistical concepts, such as the correlation length which enters as a basic parameter in the susceptibility kernel For brevity we do not cite many other features making this approach quite useful for the whole field of material systems, not only for solutions. 

The remainder of this contribution is organized as follows In the next section, the connection between the experimentally observed dynamic Stokes shift in the fluorescence spectrum and its representation in terms of intermolecular interactions will be given. The use of MD simulation to obtain the SD response will be described and a few results presented. In Section 3.4.3 continuum dielectric theories for the SD response, focusing on the recent developments and comparison with experiments, will be discussed. Section 3.4.4 will be devoted to MD simulation results for e(k, w) of polar liquids. In Section 3.4.5 the relevance of wavevector-dependent dielectric relaxation to SD will be further explored and the factors influencing the range of validity of continuum approaches to SD discussed. 

As noted above, nonlocal dielectric theory provides the starting point for continuum approaches to SD. The derivation given below follows that presented by Song et al. [47], The solvation energy change due to solute electronic transition occurring at t = 0 is given by... 

Figure 3.17 Comparison between experiment (dashed curve) and calculations combining the polarizable continuum model for solute electronic structure and continuum dielectric theory of solvation dynamics in water. SRF(t) stands for S(t) in our notation. The calculations are for a cavity based on a space-filling model of Cl53, while the experiments are for C343. The two sets of theoretical results correspond to using water e(o>) from simulation (full curve) of SPC/E water and from a fit to experimental data (dash-dotted curve). (Reprinted from F. Ingrosso, A. Tani andJ. Tomasi, J. Mol. Liq., 1117, 85-92. Copyright (2005), with permission from Elsevier).

Another class of systems for which the use of the continuum dielectric theory would be unable to capture an essential solvation mechanism are supercritical fluids. In these systems, an essential component of solvation is the local density enhancement [26,33,72], A change in the solute dipole on electronic excitation triggers a change in the extent of solvent clustering around the solute. The dynamics of the resulting density fluctuations is unlikely to be adequately modeled by using the dielectric permittivity as input in the case of dipolar supercritical fluids. 

Figure 5. HREELS cross-section curves (peak height normalized to the elastic peak intensity) for the excitation of selected molecular vibrational bands of polyimide. The dielectric theory predicts a E 1 behaviour.

To summarize, for photon energies above the plasmon energies (and away from other excitation energies), the electromagnetic fields can be described adequately with macroscopic dielectric theory. 

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