Inhomogeneous dielectric medium

Computing Induced Charges in Inhomogeneous Dielectric Media Application in a Monte Carlo Simulation of Complex Ionic Systems. 

Ma M, Xu Z Seltconsistent field model for strong electrostatic correlations and inhomogeneous dielectric media, J Chem Phys 141(24) 244903, 2014. 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

Let us study the derivation of the FDTD-PML expressions under a Maxwellian manner. Unfortunately, such complicated curvilinear environments create highly dispersive reflections that form bands of transmitted modes growing spatially instead of being damped in the layer. For the goals of the approach, an inhomogeneous, isotropic, and lossless dielectric medium is examined in the frequency domain. Thus,... 

Figure 5 Thermodynamic cycle illustrating the standard numerical procedure for calculating the energy of two solutes at distance R. When R is varied, this method can construct a potential of mean force. The steps are (1) association of solutes in a medium with a homogeneous dielectric, (2) transfer of the isolated solutes from a homogeneous dielectric into solution with an inhomogeneous dielectric, (3) association of the solutes in a medium with an inhomogeneous dielectric, and (4) transfer of the associated solutes from a homogeneous dielectric into solution with an inhomogeneous dielectric.

Note that the distinction between Eq. (19) and Eq. (12) lies in the term containing I/sq, i.e. in the term which makes a maximum contribution to the reorganization energy. The difference between the two approaches considered is most essential in the cases where there exist inhomogeneities in a dielectric medium, in particular, for processes at the interface between the two immiscible liquids, as well as when the finite sizes of ions are taken into account in the absence of a spherical symmetry. In these cases the second approach may give rise to considerable errors, whereas Eqs. (12)-(13) remain valid here as well. 

The notion of homogeneity is not absolute all substances are inhomogeneous upon sufficiently close inspection. Thus, the description of the interaction of an electromagnetic wave with any medium by means of a spatially uniform dielectric function is ultimately statistical, and its validity requires that the constituents—whatever their nature—be small compared with the wavelength. It is for this reason that the optical properties of media usually considered to be homogeneous—pure liquids, for example—are adequately described to first approximation by a dielectric function. There is no sharp distinction between such molecular media and those composed of small particles each of which contains sufficiently many molecules that they can be individually assigned a bulk dielectric function we may consider the particles to be giant molecules with polarizabilities determined by their composition and shape. 

We take as our model of an inhomogeneous medium a two-component mixture composed of inclusions embedded in an otherwise homogeneous matrix, where e and are their respective dielectric functions. The inclusions are identical in composition but may be different in volume, shape, and orientation we shall restrict ourselves, however, to ellipsoidal inclusions. The average electric field (E) over a volume V surrounding the point x is defined as... 

Inhomogeneity of the field-induced change in the characteristics of the medium, the complex dielectric permittivity esc = ei + >n particular (here e1>2 are real quantities), is a distinguishing feature of electrooptic effects in the space-charge region. The ranges of such inhomogeneities (10 4-10 5 cm)... 

Dielectrophoretic forces depend on the polarizibility of species, rather than on movement of charges [99]. This allows the movement of any type of droplet being immersed by a dielectrically distinct immiscible carrier medium. Since dielectric forces are generated by spatially inhomogeneous fields, no mechanical actuation is required. In addition to this, dielectrophoretic droplet movement benefits from the general advantages given by droplet microfluidic, i.e. discrete, well-known very small volumes, no need for channels, avoidance of dead volumes and more. 

This Section examines the dielectric and conduction mechanisms in bulk materials, assuming that the medium is linear (at the applied electric field strength) and homogeneous. Effects of interfaces and inhomogeneities are discussed in Section 3.2. Additional discussion can be found in basic texts 21 23). 

In the following section the power of the fractional derivative technique is demonstrated using as example the derivation of all three known patterns of anomalous, nonexponential dielectric relaxation of an inhomogeneous medium in the time domain. It is explicitly assumed that the fractional derivative is related to the dimension of a temporal fractal ensemble (in the sense that the relaxation times are distributed over a self-similar fractal system). The proposed fractal model of the microstructure of disordered media exhibiting nonexponential dielectric relaxation is constructed by selecting groups of hierarchically subordinated ensembles (subclusters, clusters, superclusters, etc.) from the entire statistical set available. 

Chylek, P., Srivastava, V. Dielectric constant of a composite inhomogeneous medium. Phys. Rev. B27, 5098-5106(1983)... 

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