Heterogeneous dielectric systems

Heterogenous dielectric systems exhibit some special properties, among which most notable is interfacial polarization caused by hindered charge movement at the interfaces. This effect makes dielectric spectroscopy (AC and DC methods), in combination with other methods of structure determination, a usefol tool in studying the following phenomena in composite materials ... 

The basic outline of the heterogeneous dielectric media method is to divide the total system into two subsystems. The solvated molecule is encapsulated in a cavity C which is given by the surfaces and 2 . The cavity is surrounded by a heterogeneous environment given by two part Sm and St. The two dielectric media are in contact with the cavity through the surfaces Xm and 2,. Each of the two dielectric media is taken to be a linear, homogeneous and isotropic dielectric medium and is characterized by a scalar, optical, inertial or static dielectric constant. As an illustration, we consider two dielectric media, Sm and Sh characterized by the dielectric constants em and eh respectively, with the following spatial positions ... 

Next, we present the fundamental equations for determining the time-dependent electromagnetic properties of a molecular system interacting with a heterogeneous dielectric medium. For the heterogeneous dielectric media model we utilize the representation that is given in Equation (2.234), which makes it possible to rewrite the contributions due to the two dielectric media as... 

We observe that these contributions to the response equations have the same structure as the response equations for the molecule in vacuum [83]. We note that the implementation of these modifications to the vacuum MCSCF response equations gives us the possibility of investigating linear and nonlinear molecular properties of molecular systems interacting with heterogeneous dielectric media. 

The thermally stimulated relaxation in heterogeneous dielectrics, consisting of relaxing components and exhibiting interfacial relaxation, presents a special problem, which has been solved exactly only for bilayer systems [2]. Here, the accumulation of space charge at the interfaces may cause anomalous depolarization effects (currents of reversed polarity). The same is true for samples measured with air gap or with one-sided electrodes (this latter is frequently used for corona charged samples). 

You now have two methods for deriving the electrostatic potential from a given distribution of fixed electrical charges. First, >ou can use Coulomb s law. But this becomes unwieldy for complex constellations of charges or for systems with tw-o or more different dielectric media. Second, you can solve Poisson s equation. The second method is more general, and it can also be used for heterogeneous dielectric media (see page 401). 

Up to now it has been tacitly assumed that each molecular motion can be described by a single correlation time. On the other hand, it is well-known, e.g., from dielectric and mechanical relaxation studies as well as from photon correlation spectroscopy and NMR relaxation times that in polymers one often deals with a distribution of correlation times60 65), in particular in glassy systems. Although the phenomenon as such is well established, little is known about the nature of this distribution. In particular, most techniques employed in this area do not allow a distinction of a heterogeneous distribution, where spatially separed groups move with different time constants and a homogeneous distribution, where each monomer unit shows essentially the same non-exponential relaxation. Even worse, relaxation... 

Zhang X, Hayward DO (2006) Applications of microwave dielectric heating in environment-related heterogeneous gas-phase catalytic systems. Inorg Chim Acta 359 3421... 

Considerable progress has been made within the last decade in elucidating the effects of the microenvironment (such as electric charge, dielectric constant and lipophilic or hydrophilic nature) and of external and internal diffusion on the kinetics of immobilized enzymes (7). Taking these factors into consideration, quantitative expressions have been derived for the kinetic behavior of relatively simple enzyme systems. In all of these derivations the immobilized enzymes were treated as simple heterogeneous catalysts. 

The impedance for the study of materials and electrochemical processes is of major importance. In principle, each property or external parameter that has an influence on the electrical conductivity of an electrochemical system can be studied by measurement of the impedance. The measured data can provide information for a pure phase, such as electrical conductivity, dielectrical constant or mobility of equilibrium concentration of charge carriers. In addition, parameters related to properties of the interface of a system can be studied in this way heterogeneous electron-transfer constants between ion and electron conductors, or capacity of the electrical double layer. In particular, measurement of the impedance is useful in those systems that cannot be studied with DC methods, e.g. because of the presence of a poor conductive surface coating. 

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