Dielectric position-dependent

Marchi and co-workers [27,28] have applied Equation (1.79) in the context of classical MD by using a Fourier pseudo-spectral approximation of the polarization vector field. This approach provides a convenient way to evaluate the required integrals over all volume at the price of introducing in the extended Lagrangian a set of polarization field variables all with the same fictitious mass. They also recognized the cmcial requirement that both the atomic charge distribution and the position-dependent dielectric constant be continuous functions of the atomic positions and they devised suitable expressions for both. 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

Fig. 2.1 Calculated emission energies of PRODAN as a function of its position with respect the cyclohexane/water interface, z is the coordinate perpendicular to the interface. The position-dependent value of the dielectric constant is also reported...

Static dielectric constant depends on the displacement of ions from their regular positions in an applied electric field. 

Approaches have been developed which modify the traditional double-layer theory by assuming that the dielectric constant depends upon position. This dependence is considered to occur because the dielectric constant is affected by the electric field [9-12]. However, the dielectric constant can also be changed by the presence of hairs on the surface. Indeed, hairy chains on the surface constrain the orientation of the water molecules nearby, and, as a result, in the region near the surface the dielectric constant becomes lower... 

To propagate the solvent-structuring effect induced by the presence of the hydrophobic spheres, we replace the position-dependent dielectric by an integral kernel convoluted with the electric field at position r to represent the correlations with the field at neighboring positions r. This prompts us to replace the classical Poisson equation by the rigorous relation (see Chap. 14) ... 

This is given by g = gexdex, where gex is the exciton generation rate and /ex the exciton dissociation probability. The position dependence of gex can be found by solving Maxwell s equations for light absorption in the thin, layered device structure. Because of the low thicknesses and low dielectric permittivity, absorption is strongly influenced by optical interference. In an effective medium, tj x can be treated as a... 

This is the so-called random stopping power, which i.s also obtained as the average over impact parameters of the position-dependent stopping power of equation (44). For simple metals like Al the diagonal elements of the inverse dielectric matrix A g,g(Q) rather isotropic, in which case there is little... 

In Eq. 12.28 p and y (0 < P, py < 1) are fractional shape parameters which describe the symmetric and asymmetric broadening of the complex dielectric function. Thn is characteristic relaxation time. The maximum position of the dielectric loss depends on the shape parameters according to (Diaz-Calleja 2000 Boersema et al. 1998 Schroter et al. 1998)... 

It is known that the value of dielectric constant is a function of the local electric field. Since the electric field near the interface is not a constant, but a function of distance from it, the further refinement of EDL theory and potential profile at the BLM interface should include this positional dependency of dielectric coefficient. The local value of this coefficient is of course a measure of the influence of uncharged species such as water or lipid molecules on the interaction between charges in their vicinity. The dielectric coefficient of bulk aqueous electrolyte at... 

From Equation (6.27), for a non-polar compound, fi 0 and its dielectric anisotropy is very small (Ae < 0.5). In this case, Ae is determined mainly by the differential molecular polarizability, i.e. the first term in Equation (6.27). For a polar compound, the dielectric anisotropy depends on the dipole moment, angle 0, temperature (T) and applied frequency. If an LC has more than one dipole, then the resultant dipole moment is their vector summation. In a phenyl ring, the position of the dipole is defined as... 

The lower energy fluorescence band is clearly a CT band, since its position depends on the dielectric constant of the solvent. 

This equation with a position-dependent dielectric constant is most easily solved by first applying to... 

Charging step - a cell was considered as a spherical shell with a dielectric membrane and with external and internal (cytoplasmic) conducting buffers. As a spherical dielectric, a position-dependent transmembrane potential was induced when the cell is submitted to an external field. This was a fast process. 

The detailed analysis of light propagation in the cholesteric helix is quite complex. It consists in the search for eigenmodes of Maxwell equations in a medium with the position-dependent dielectric permittivity tensor. 

They concluded that ionizable groups on the surface, where they tend to be found, do not contribute significantly to the protein dielectric constant deep in the interior of the protein. This is partly because these surface residues tend to be well hydrated, thereby weakening their electrosatic interaction with points deep in the protein. Effects of ionized residues are more likely to be highly position dependent. That is, for points close to an ionized residue, the effective protein dielectric constant would be predicted to be higher than points farther in the interior of the protein. 

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