Inhomogeneous dielectric constant

The difference between the electrostatic effect calculated using the bulk dielectric constant and that calculated taking account of local structural factors is sometimes called dielectric saturation, although it has been suggested that a better phrase would be inhomogeneous dielectric constant. We refer to the sum of these first-hydration-shell effects as the CDS term, representing structural rearrangements that entail cavitation, dispersion, and solvent disposition. 

Characteristic properties of SCFs include variable density, dielectric constant viscosity, and cage strength, local inhomogeneity, high diffusion rate, high miscibility with gaseous substances, and high sensitivity of all properties to added substances. All... 

The forced electric dipole mechanism was treated in detail for the first time by Judd (1962) through the powerful technique of irreducible tensor operators. Two years later it was proposed by Jorgensen and Judd (1964) that an additional mechanism of 4/-4/ transitions, originally referred to as the pseudo-quadrupolar mechanism due to inhomogeneities of the dielectric constant, could be as operative as, or, for some transitions, even more relevant than, the forced electric dipole one. 

The As calculations (Equation (3.95)) were based on the Poisson equation, solved for a five-zone model (Section 3.5.4, Inhomogeneous Media) in which the solute (zone 1) was surrounded by four dielectric zones (2-5). A simplified schematic picture is given in Figure 3.26, but in the actual calculations, the zone boundaries were based on structures obtained from classical molecular dynamics (MD) simulations (with inclusion of a few thousand TIP3P water molecules and Na+ counterions to neutralize the negative charge from the DNA). Each zone was assigned optical and static dielectric constants (sxk and e0k, k = 1, 5). For the solute (zone 1), = e0k = 1.0 was adopted. For zones 2,3,... 

The liquid-liquid interface formed between two immissible liquids is an extremely thin mixed-liquid state with about one nanometer thickness, in which the properties such as cohesive energy density, electrical potential, dielectric constant, and viscosity are drastically changing from those of bulk phases. Solute molecules adsorbed at the interface can behave like a 2D gas, liquid, or solid depending on the interfacial pressure, or interfacial concentration. But microscopically, the interfacial molecules exhibit local inhomogeneity. Therefore, various specific chemical phenomena, which are rarely observed in bulk liquid phases, can be observed at liquid-liquid interfaces [1-3]. However, the nature of the liquid-liquid interface and its chemical function are still less understood. These situations are mainly due to the lack of experimental methods required for the determination of the chemical species adsorbed at the interface and for the measurement of chemical reaction rates at the interface [4,5]. Recently, some new methods were invented in our laboratory [6], which brought a breakthrough in the study of interfacial reactions. 

We now turn attention to a completely different kind of supercritical fluid supercritical water (SCW). Supercritical states of water provide environments with special properties where many reactive processes with important technological applications take place. Two key aspects combine to make chemical reactivity under these conditions so peculiar the solvent high compressibility, which allows for large density variations with relatively minor changes in the applied pressure and the drastic reduction of bulk polarity, clearly manifested in the drop of the macroscopic dielectric constant from e 80 at room temperature to approximately 6 at near-critical conditions. From a microscopic perspective, the unique features of supercritical fluids as reaction media are associated with density inhomogeneities present in these systems [1,4],... 

The reason that chemical laws are not simply reduced to electrostatics is that the electrons behave under the influence of their own or applied electric fields, not according to classical mechanics, but according to quantum mechanics obeying the singular Pauli principle. In fact, electrostatics and dielectric constants are simpler applications of the electrical structure of molecules and use outside macroscopic homogeneous electric fields interacting with microscopic inhomogeneous fields. 

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

Blumenfeld, R., Bergman, D.J. Exact calculation to second order of the effective dielectric constant of a strongly nonlinear inhomogeneous composite. Phys. Rev. B 40, 1987-1989 (1989)... 

In order to calculate the effect quantitatively, explicit expressions are needed for the complex dielectric constant, e, in the presence and absence of an electric field the effects of thermal broadening and inhomogeneities in the electric field may be included at a later point in the theoretical development. 

Consider a spherical point dipole solute molecule with a dipole moment, p, at infinite dilution in a spherical container of supercritical fluid. With a continuum assumption, the fluid s electrical properties may be represented by a homogeneous dielectric constant, e. The inhomogeneous field of the dipole polarizes the fluid which reacts and gives rise to a field, R, at the dipole. R will be proportional to p as long as no saturation effects occur. 

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