Macroscopic dielectric function

The absorption spectrum is proportional to the imaginary part of the macroscopic dielectric function. Adopting the same level of approximation that we have introduced to obtain GW quasiparticle energies, i.e. neglecting the vertex correction by putting T = 55, we get the so called random phase approximation (RPA) for the dielectric matrix. Within this approximation, neglecting local field effects, the response to a longitudinal field, for q 0, is ... 

Optical thin-fihn theory is essentially based on the Maxwell theory (1864) [8], which summarizes all the empirical knowledge on electromagnetic phenomena. Light propagation, absorption, reflection, and emission by a film can be explained based on the concept of the macroscopic dielectric function of the film material. In this section, we will present the results of the Maxwell theory relating to an infinite medium and introduce the nomenclature used in the following sections dealing with absorption and reflection phenomena in layered media. The basic assertions of macroscopic electrodynamic theory can be found in numerous textbooks (see, e.g.. Refs. [9-16]). 

The expressions (7) and (8) have been used to calculate the macroscopic dielectric function of Si [5],... 

The macroscopic dielectric function of Silicon in the Hartree and in the Slater approximation is given in... 

In figure 2 the macroscopic dielectric function in the Hartree and Slater approximations is given for Germanium. For a comparison of our inverse dielectric function of Germanium with other calculations see the paper by K. Kune in these proceedings. 

The satisfactory result shown in Table 12 suggests that one might give a more detailed and quantitative discussion of the variation with temperature. If we are to do this, we need some standard of comparison with which to compare the experimental results. Just as wq compare an imperfect gas with a perfect gas, and compare a non-ideal solution with an ideal solution, so we need a simple standard behavior with which to compare the observed behavior. We obtain this standard behavior if, supposing that. /e is almost entirely electrostatic in origin, we take J,np to vary with temperature as demanded by the macroscopic dielectric constant t of the medium 1 that is to say, we assume that Jen, as a function of temperature is inversely proportional to . For this standard electrostatic term we may use the notation, instead of... 

The reflectivity of bulk materials can be expressed through their complex dielectric functions e(w) (i.e., the dielectric constant as a function of frequency), the imaginary part of which signifies absorption. In the early days of electroreflectance spectroscopy the spectra were often interpreted in terms of the dielectric functions of the participating media. However, dielectric functions are macroscopic concepts, ill suited to the description of surfaces, interfaces, or thin layers. It is therefore preferable to interpret the data in terms of the electronic transitions involved wherever possible. 

In Fig. 4.24, we plot the experimental free energies W(l, 1) as a function of the proton-proton distance Rjfu. We also plot the theoretical curve for the Coulombic interaction between the two protons, as modified by the macroscopic dielectric constant of water D = 78.54. It is clear that the values of W(l, 1) for the larger molecules follow closely the theoretical curve with a fixed value of D. Large... 

Macroscopic models have been developed that describe the protein and the water as macroscopic dielectric materials. In their simplest form these models use a distance-independent dielectric function, i.e. a simple Coulomb interaction. Others may apply a distance-dependent dielectric function. The more detailed implementatiorrs include a descriptions of the protein-solvent botmdary in terms of solvent accessibihty and ionic-strength effects (Gilson and Honig, 1988). 

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]

Fluctuations in the dielectric properties near the interface lead to scattering of the EW as well as changes in the intensity of the internally reflected wave. Changes in optical absorption can be detected in the internally reflected beam and lead to the well-known technique of attenuated total reflectance spectroscopy (ATR). Changes in the real part of the dielectric function lead to scattering, which is the main topic of this review. Polarization of the incident beam is important. For s polarization (electric field vector perpendicular to the plane defined by the incident and reflected beams or parallel to the interface), there is no electric held component normal to the interface, and the electric field is continuous across the interface. For p polarization (electric field vector parallel to the plane defined by the incident and reflected beams), there is a finite electric field component normal to the interface. In macroscopic electrodynamics this normal component is discontinuous across the interface, and the discontinuity is related to the induced surface charge at the interface. Such discontinuity is unphysical on the molecular scale [4], and the macroscopic formalism may have to be re-examined if it is applied to molecules within a few A of the interface. 

Coming to the present volume, one aim has been to provide a basis on which the student and researcher in molecular science can build a sound appreciation of the present and future developments. Accordingly, the chapters do not presume too much previous knowledge of their subjects. Professor Scaife is concerned, inter alia, to make clear what is the character of those aspects of the macroscopic dielectric behaviour which can be precisely delineated in the theoretical representations which rest on Maxwell s analysis, and he relates these to some of the general microscopic features. The time-dependent aspects of these features are the particular concern of Chapter 2 in which Dr. Wyllie gives an exposition of the essentials of molecular correlation functions. As dielectric relaxation methods provided one of the clearest models of relaxation studies, there is reason to suggest that dipole reorientation provides one of the clearest examples of the correlational treatment. If only for this reason, Dr. Wyllie s chapter could well provide valuable insights for many whose primary interest is not in dielectrics. 

As the existence of a resonance behaviour can be explained by pure electromagnetic considerations, using as only ingredients macroscopic quantities that are the dielectric functions of the different media, the local field amplification phenomenon is often said to originate from dielectric confinement. 

THE SOLVATION FORCE. The electrostatic and van der Waals disj>ersion forces retain the common attribute of depending on the nature of liquid water in the aqueous solution phase only through the macroscopic dielectric constant. In the case of the electrostatic force as exemplified in Eq. 6.16, the only dependence on the properties of liquid water comes through the parameter k, which, as shown in connection with Eq. 5.11, is a function of the bulk (zcro>frequency) dielectric constant, D. Similarly, for... 

Effective medium theories characterize the frequency-dependent transport in systems with large-scale inhomogeneities such as metal particles dispersed in an insulating matrix [118,119]. An IMT in the effective medium model represents a percolation problem where a finite a c as T 0 is not achieved until metallic grains in contact span the sample. To understand the frequency dependence of the macroscopic material, an effective medium is built up from a composite of volume fraction /of metallic grains and volume fraction 1 — / of insulator grains. The effective dielectric function semaCw) and conductivity function (Tema(w) are solved self-consistently. 

The present authors have used the dielectric screening method for all their ab-initio computations of the macroscopic dielectric constant and phonon frequencies of Si and Ge. For the calculation of the electron energies and wave functions needed in the expression of the electron density response matrix they apply the local density approximation in the Hamiltonian. The advantage and shortcomings of this approximation are treated at length in the papers by J.T. Devreese, R. Martin, K. Kune, S. Louie, A. Baldereschi and R. Resta in these proceedings. 

Besides frequency, time is another critical parameter for the description of dielectric phenomena in polymers. The mathematical analysis of the time-dependent response is based largely on the (macroscopic) relaxation function 0(r), which describes the change of the system after the removal of an applied stimulus (in the present case, the electric field, in the case of DMA, the stress). Dipole orientation, which follows the application (at time r = 0) of a static... 

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