Dielectric constant, defined

Before running a molecular dynamics simulation with solvent and a molecular mechanics method, choose the appropriate dielectric constant. You specify the type and value of the dielectric constant in the Force Field Options dialog box. The dielectric constant defines the screening effect of solvent molecules on nonbonded (electrostatic) interactions. 

Ref. (2)]. While a dependence of e" on solvent dipole moment or dielectric constant has been refuted for numerous experimental adsorption systems [c.g.. Ref. (7)], the belief that dielectric constant defines both solvent strength and sample adsorption energy continues to find support by many workers. The dependence of e values on solvent dielectric constant is tested in Fig. 8-13 for adsorption on alumina. There is a tendency for solvent strength to follow solvent dielectric constant, but the exceptions to this relationship are both numerous and large (e.g., dioxane, e = 0.56 and dielectric constant = 2.2, versus methylene chloride, e = 0.42 and dielectric constant = 9.1). Consequently, the dielectric constant of the solvent is quite limited in its ability to predict solvent strength. The data of Fig. 8-13 do not support any fundamental relationship between solvent strength and dielectric constant. 

Explicit solvent model The easiest way of incorporating discrete solvent is to include only a shell of solvent molecules surrounding the solute in molecular simulations. With this method, the solute-vacuum interface is replaced by a solvent-vacuum interface. A more realistic model involves placing the solute in a solvent box with periodic boundary conditions (Jorgensen et al, 1983) where solvent molecules leaving one side of the box reappear at the opposite side so that the density of the systan is maintained at a constant value. The dielectric constant defines the screening effect of solvent... 

Having obtained values of A and p for the electrode/solution interface of interest, or more commonly detected changes as the electrode potential is varied, the next step is to relate these values to the properties of the interface. As with all reflection techniques, this is usually done in terms of a three layer model consisting of bulk substrate/interfacial region/bulk solution as shown in Fig. 10.10. Assuming the optical constants of the substrate and solution and the film thickness are known, it is possible to obtain unique values of the effective optical constants of the interphase from A and p [15]. The optical characteristics of any phase are simply defined by p, the magnetic permeability (usually equal to unity) and either the wavelength dependent complex dielectric constant defined by Equation (10.11)... 

This shows that the dielectric constant e of a polar solvent is related to the cavity fimction for two ions at large separations. One could extend this concept to define a local dielectric constant z(r) for the interaction between two ions at small separations. 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

Dielectric Constant. Dielectric constant or specific inductive capacity (SIC) is both defined and measured by the ratio of the electric capacity of a condenser having that material as the dielectric to the capacity of the same condenser having air as the dielectric. The dielectric constant of vacuum is unity. Dry air has a constant slightly higher but for most practical purposes it is considered as unity. 

Dielectric Film Deposition. Dielectric films are found in all VLSI circuits to provide insulation between conducting layers, as diffusion and ion implantation (qv) masks, for diffusion from doped oxides, to cap doped films to prevent outdiffusion, and for passivating devices as a measure of protection against external contamination, moisture, and scratches. Properties that define the nature and function of dielectric films are the dielectric constant, the process temperature, and specific fabrication characteristics such as step coverage, gap-filling capabihties, density stress, contamination, thickness uniformity, deposition rate, and moisture resistance (2). Several processes are used to deposit dielectric films including atmospheric pressure CVD (APCVD), low pressure CVD (LPCVD), or plasma-enhanced CVD (PECVD) (see Plasma technology). 

The observed dielectric constant M and the dielectric loss factor k = k tan S are defined by the charge displacement characteristics of the ceramic ie, the movement of charged species within the material in response to the appHed electric field. Discussion of polarization mechanisms is available (1). 

For many years the petroleum industry has defined nonconductive liquids as having conductivities less than 50 pS/m. A higher value of 100 pS/m is used here to address the higher dielectric constants of certain flammable chemicals in relation to petroleum products. For example the dielectric constant of ethyl ether is 4.6 versus 2.3 for benzene from Eq. (2-3.2), ethyl ether therefore has the same relaxation time at a conductivity of 100 pS/m as benzene at a conductivity of 50 pS/m. It is the relaxation time, not the conductivity alone, that determines the rate of loss of charge hence the same logic that makes 50 pS/m appropriate for identifying nonconductive hydrocarbons makes 100 pS/m appropriate for identifying nonconductive chemical products. 

The influence of a particular dielectric on the capacitance of a condenser is conveniently assessed by the dielectric constant, also known as the relative permittivity or rarely specific inductive capacity. This is defined as the ratio of the relative condenser capacity, using the given material as a dielectric, to the capacity of the same condenser, without dielectric, in a vacuum (or for all practical intents and purposes, air). 

In the second type of interaction contributing to van der Waals forces, a molecule with a permanent dipole moment polarizes a neighboring non-polar molecule. The two molecules then align with each other. To calculate the van der Waals interaction between the two molecules, let us first assume that the first molecule has a permanent dipole with a moment u and is separated from a polarizable molecule (dielectric constant ) by a distance r and oriented at some angle 0 to the axis of separation. The dipole is also oriented at some angle from the axis defining the separation between the two molecules. Overall, the picture would be very similar to Fig. 6 used for dipole-dipole interaction except that the interaction is induced as opposed to permanent. 

The insulating property of any insulator will break down in a sufficiently strong electric field. The dielectric strength is defined as the electric strength (V/m) which an insulating material can withstand. For plastics the dielectric strength can vary from 1 to 1000 MV/m. Materials may be compared on the basis of their relative permittivity (or dielectric constant). This is the ratio of the permittivity of the material to the permittivity of a vacuum. The ability of a... 

The substituent constant cr is defined at a given temperature. If 8rA// and 8rAS are independent of temperature, p should be linearly related to 1/7" if all other conditions are held constant. (The constancy of other conditions is not strictly possible, however, because the dielectric constant is a function of temperature.) Data are in reasonable agreement with this prediction. 

Table 8-2 lists several physical properties pertinent to our concern with the effects of solvents on rates for 40 common solvents. The dielectric constant e is a measure of the ability of the solvent to separate charges it is defined as the ratio of the electric permittivity of the solvent to the permittivity of the vacuum. (Because physicists use the symbol e for permittivity, some authors use D for dielectric constant.) Evidently e is dimensionless. The dielectric constant is the property most often associated with the polarity of a solvent in Table 8-2 the solvents are listed in order of increasing dielectric constant, and it is evident that, with a few exceptions, this ranking accords fairly well with chemical intuition. The dielectric constant is a bulk property. 

One femily of models for systems in non-aqueous solution are referred to as Self-Consistent Reaction Field (SCRF) methods. These methods all model the solvent as a continuum of uniform dielectric constant e the reaction field. The solute is placed into a cavity within the solvent. SCRF approachs differ in how they define the cavity and the reaction field. Several are illustrated below. 

Although the LD model is clearly a rough approximation, it seems to capture the main physics of polar solvents. This model overcomes the key problems associated with the macroscopic model of eq. (2.18), eliminating the dependence of the results on an ill-defined cavity radius and the need to use a dielectric constant which is not defined properly at a short distance from the solute. The LD model provides an effective estimate of solvation energies of the ionic states and allows one to explore the energetics of chemical reactions in polar solvents. 

When a solute is added to an acidic solvent it may become protonated by the solvent. If the solvent is water and the concentration of solute is not very great, then the pH of the solution is a good measure of the proton-donating ability of the solvent. Unfortunately, this is no longer true in concentrated solutions because activity coefficients are no longer unity. A measurement of solvent acidity is needed that works in concentrated solutions and applies to mixed solvents as well. The Hammett acidity function is a measurement that is used for acidic solvents of high dielectric constant. For any solvent, including mixtures of solvents (but the proportions of the mixture must be specified), a value Hq is defined as... 

The common example of real potential is the electronic work ftmction of the condensed phase, which is a negative value of af. This term, which is usually used for electrons in metals and semiconductors, is defined as the work of electron transfer from the condensed phase x to a point in a vacuum in close proximity to the surface of the phase, hut heyond the action range of purely surface forces, including image interactions. This point just outside of the phase is about 1 pm in a vacuum. In other dielectric media, it is nearer to the phase by e times, where e is the dielectric constant. 

In this Section we want to present one of the fingerprints of noble-metal cluster formation, that is the development of a well-defined absorption band in the visible or near UV spectrum which is called the surface plasma resonance (SPR) absorption. SPR is typical of s-type metals like noble and alkali metals and it is due to a collective excitation of the delocalized conduction electrons confined within the cluster volume [15]. The theory developed by G. Mie in 1908 [22], for spherical non-interacting nanoparticles of radius R embedded in a non-absorbing medium with dielectric constant s i (i.e. with a refractive index n = Sm ) gives the extinction cross-section a(o),R) in the dipolar approximation as ... 

The electric field or ionic term corresponds to an ideal parallel-plate capacitor, with potential drop g (ion) = qMd/4ire. Itincludes a contribution from the polarizability of the electrolyte, since the dielectric constant is included in the expression. The distance d between the layers of charge is often taken to be from the outer Helmholtz plane (distance of closest approach of ions in solution to the metal in the absence of specific adsorption) to the position of the image charge in the metal a model for the metal is required to define this position properly. The capacitance per unit area of the ideal capacitor is a constant, e/Aird, often written as Klon. The contribution to 1/C is 1 /Klon this term is much less important in the sum (larger capacitance) than the other two contributions.2... 

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