Permittivity of medium

A fourth correction term may also be required, depending upon the medium that surrounds the sphere of simulation boxes. If the surrounding medium has an infinite relative permittivity (e.g. if it is a conductor) then no correction term is required. However, if the surrounding medium is a vacuum (with a relative permittivity of 1) then the following energy must be added ... 

It is necessary to use the bulk permittivity of the solvent in the equation, instead of the unknown but more correct effective permittivity of the medium between the charges in the transition state. 

Heuristic Fxplanation As we can see from Fig. 22-31, the DEP response of real (as opposed to perfect insulator) particles with frequency can be rather complicated. We use a simple illustration to account for such a response. The force is proportional to the difference between the dielectric permittivities of the particle and the surrounding medium. Since a part of the polarization in real systems is thermally activated, there is a delayed response which shows as a phase lag between D, the dielectric displacement, and E, the electric-field intensity. To take this into account we may replace the simple (absolute) dielectric constant by the complex (absolute) dielectric... 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

On the assumption that = 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric field around an ion. Combined with the above-mentioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene-water and 1,2-dichloroethane-water interfaces. 

In isotropic media 0 and S are related by = < , where the scalar parameter a is now referred to as the permittivity. In the international (SI) system it is given by s = erso. where o is the permittivity of vacuum (see Appendix fl) and e, is a dimensionless permittivity that characterizes the medium. Furthermore, according to Ohm s law the current is given by 7 = cr< , where a is the electrical conductivity. The relation V S3 = 0 is a mathematical statement of the observation that isolated magnetic poles do not exist. 

When nonnegligible concentrations of the electrolyte are present in the organic solvent, ion-ion interactions superimpose on the ion-solvent ones, or the secondary medium ejfect. Although an equation similar to Eq. (2.43) may be used for determining the activity coefficient in the new medium, it is necessary to employ the appropriate value of A in this equation that depends on the relative permittivity of the medium A(org) = A(aq)(eaq/e ,g) Unless very water-rich mixed solvents are used, different numerical values of the parameters in the denominator and the second term on the right-hand side of Eq. (2.43) have to be employed. 

A further complication that sets in when organic or mixed aqueous-organic solvents are used, which is aggravated when the relative permittivity of the medium, e, falls below 40, is ion pairing. This phenomenon does occur in purely aqueous solutions, mainly with higher-valence-type electrolytes 2 2 and higher, and with 2 1 or 1 2 electrolytes only at high concentrations. Ion pairs may also form in aqueous solutions of some 1 1 electrolytes, provided the ions are poorly hydrated and can approach each other to within <0.35 nm. Such ion pairs are of major importance in solvents that are relatively poor in water or that are nonaqueous. 

In this expression, e is the dielectric permittivity of the suspending medium, is the electric surface potential, and k is the inverse Debye length [17], defined as ... 

The relationship describing the interaction, in terms of mutual force (F), between two electrostatic point charges F = QiQ2/(4 ned ) where <2i and Qi are the respective point charges, d is the distance separating them, and e is the permittivity of the medium. 

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