Permittivity of a Medium

The permittivity of a medium, denoted e, expressed in farad per meter (F.m ), is defined by Coulomb s law applied to the medium. Actually, the modulus of the electrostatic force, in newtons (N) between two point electric charges in a medium q or q, in coulombs (C), separated by a distance in meters (m), is given by the following equation  

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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. 

The dielectric permittivity of a medium measures the polarization of the medium per unit applied electric field. The permittivity of free space, e, has the value 8.85 x 10 14 Farads/cm. Throughout this paper, we shall express the dielectric properties of a medium relative to e0. That is, the permittivity of a medium is written e eq, where e is the relative permittivity, also referred to as the dielectric constant of the medium (but remember that the dielectric constant changes with temperature and cure). 

The relative permittivity of a medium, K=Kr-iKi, is in general a complex quantity whose real part k, (also known as the dielectric constant) is associated with the increase in capacitance due to the introduction of a dielectric. The imaginary component tq is associated with mechanisms that contribute to the energy dissipation in the system, due to viscous damping of the rotational motion of the molecules in alternating fields this effect is frequency dependent. The experimental setup consisted of a parallel plate capacitor of... 

The dielectric permittivity of a medium (relative to the permittivity of free space, 8q = 8.85 X 10 F/m) is given by e and measures the polarization of the medium per unit applied electric field. The dielectric loss factor arises from energy loss during time-dependent polarization and bulk conduction. The loss factor is written as a". The loss tangent or dissipation of the medium, tan<5 is defined by e"/e. The orientation of molecular dipoles has a characteristic time r. Typically is short early in the cure but grows large at the end of the cure. 

Relative dielectric constant Ratio of the dielectric permittivity of a medium to the permittivity of free space... 

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. 

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. 

When the same procedure takes place in a medium such as liquid water, the vacuum permittivity in equation (1.2) is replaced by the permittivity of the medium. Normally the permittivities for a variety of solvents are expressed as relative permittivities, r, at given temperatures. Some typical values of relative permittivites are given in Table 1.4. 

A further problem is that ion association, that is, the tendency of oppositely charged ions to form pairs or larger aggregates in solution, becomes increasingly important as the temperature rises unless the density is kept constant this is because ion association is inversely related to the dielectric constant (relative permittivity) of the medium, which is correlated with density for a given solvent. Helgeson and co-workers have attacked these problems theoretically for aqueous solutions up to 1000 °C.28 For our purposes, it is enough to note that quantitative treatment of ionic reactions in sub- and supercritical aqueous solutions is extremely difficult at present, and likely to remain so for some time. 

There are several physical properties of a solvent that are of importance in determining its behavior. Two of the most important from a pragmatic point of view are the melting and boiling points. These determine the liquid range and hence the potential range of chemical operations. More fundamental is the permittivity (dielectric constant). A high permittivity is necessary if solutions of ionic substances are 10 form readily. Coulombic attractions between ions are inversely proportional to the permittivity of the medium ... 

Here e is the dielectric permittivity of the medium (since electron polarization is a rapid process taking about 10 15s, one should take the high-frequency value of e) and r+ is the effectve radius of the ion, the experimental values of which can be found only indirectly. Messing and Jortner192 have done more detailed calculations of the polarization energy, making allowance for the electrostatic interaction between the ion and its surrounding, which they considered as a continuum. Their final... 

The solvent is supposed to be continuous and we took the permittivity of the medium to be constant. This is certainly a rough approximation because polar molecules are hindered from rotating freely in the strong electric field at the surface. In addition, the high concentration of counterions in the proximity of the surface can change the permittivity drastically. 

The effective medium theory consists in considering the real medium, which is quite complex, as a fictitious model medium (the effective medium) of identical properties. Bruggeman [29] had proposed a relation linking the dielectric permittivity of the medium to the volumetric proportions of each component of the medium, including the air through the porosity of the powder mixture. This formula has been rearranged under a symmetrical form by Landauer (see Eq. (8), where e, is the permittivity of powder / at a dense state, em is the permittivity of the mixture and Pi the volumetric proportion of powder / ) and cited by Guillot [30] as one of the most powerful model. 

The method used in determining the dense dielectric permittivity of a definite material consists in defining a fluid in which the material cannot dissolve and further to measure the effective permittivity of various particulate media/fluid mixtures corresponding to various porosity. The interception point of the curves representing the variation of the permittivity of the material with porosity (through the effective medium equation, see section 3.2) gives the dense state permittivity. 

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