Relative permittivity dispersion

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. 

The commonest case to have been analysed is that of 3-0 systems. James Clerk Maxwell (1831-1879) deduced that the permittivity m of a random dispersion of spheres of permittivity ei in a matrix of relative permittivity e2 is given by... 

Figure 4.53 shows the dispersion spectra of hydrated Ca-HC, K-HC, and Na-HC at 300K [120], They are plotted in the x-axis, and the natural logarithm of the frequency (Hz) versus the natural logarithm of the real part of the relative permittivity in the y-axis. This experiment shows once more the higher mobility of monovalent cations in comparison with divalent cations and the higher mobility of Na+ with respect to K+. The cause of this effect is due to the inferior cationic radius of Na+ in comparison with that of K+. 

In most cases, the propagation equations discussed in this chapter do not require a specific form of material response. However, for the sake of concreteness, as well as for discussion of numerical methods, we want to describe a generic model of nonlinear material response. We consider a nonmagnetic, dispersive medium with relative permittivity e that is a function of the transverse coordinates x, y and of the angular frequency u>... 

In this expression, q> is the volume fraction of water, Ct is the capacitance after some exposure time t, C0 is the capacitance of a dry film, which is usually measured at the outset of an exposure experiment. The relative permittivity of water at 25°C is reflected in the denominator of the expression. This expression applies only when water is homgeneously dispersed in the polymer, no water-... 

An apolar aprotic solvent is characterized by a low relative permittivity (sr < 15), a low dipole moment [ju < 8.3 10 Cm = 2.5 D), a low value ca. 0.0... 0.3) cf. Table A-1, Appendix), and the inability to act as a hydrogen-bond donor. Such solvents interact only slightly with the solute since only the non-specific directional, induction, and dispersion forces can operate. To this group belong aliphatic and aromatic hydrocarbons, their halogen derivatives, tertiary amines, and carbon disulfide. 

As the data for the Menschutkin reactions indicate, the character of the solute-solvent interactions is more complex than described by Eq. (5-87). It is evident that functions of relative permittivity alone, as given in Eq. (5-87), are not useful for describing the solvent effect on reactions between dipolar reactants, except in certain special cases, such as when a mixture of two solvents is used. In addition to electrostatic forces, non-electrostatic interactions, such as dispersion forces and hydrogen-bonding, must also be involved in Menschutkin reactions. 

Consider a dilute suspension of Np spherical soft particles moving with a velocity U exp(—/fflf) in a symmetrical electrolyte solution of viscosity r] and relative permittivity r in an applied oscillating pressure gradient field Vp exp(—imt) due to a sound wave propagating in the suspension, where m is the angular frequency 2n times frequency) and t is time. We treat the case in which m is low such that the dispersion of r can be neglected. We assume that the particle core of radius a is coated... 

The polarizability of a species is a measure of the degree to which it may be distorted, e.g. by the electric field due to an adjacent atom or ion. In the hard sphere model of ions in lattices, we assume that there is no polarization of the ions. This is a gross approximation. The polarizability increases rapidly with an increase in atomic size, and large ions (or atoms or molecules) give rise to relatively large induced dipoles and, thus, significant dispersion forces. Values of a can be obtained from measurements of the relative permittivity (dielectric constant, see Section 8.2) or the refractive index of the substance in question. 

The molecular origin of these relaxations has been established for dipolar molecular liquids by Debye [122] who has shown that the applied electric field perturbs the orientational distribution function for the dipolar molecules, leading to a static relative permittivity So greater than n, where n is the optical refractive index, and a dispersion for c (/) accompanied by a peak in c" f). 

The mechanical and dielectric loss methods are based on the different mobilities of the chain segment or dipoles bound to them in the solid state and in the melt. These differences lead to an anomalous dispersion of the modulus of elasticity (see Section 11.4.4) or the relative permittivity (see Section 13.1.2) and to corresponding losses in the mechanical or the electrical alternating fields. 

Figure 3.5 Debye single dispersion relaxation, relative permittivity. Values are found in the text.

In Eq. (72) the second term on the right-hand side is a coulombic potential, sq is the permittivity of vacuum, and ZjBQ are the charges on ions i and j, and is the relative permittivity of pure solvent. The first term, u j(r), is the short-range noncoulombic part of the direct potential, including repulsion, dispersion, or induction forces. 

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