Frohlich expression

Frohlich and Platzman (1953) developed a detailed electromagnetic theory for the rate of energy loss of a subexcitation electron in a polar medium due to dielectric loss. Their final result may be expressed as... 

We shall call the frequency at which t = —2em and t" — 0 the Frohlich frequency coF the corresponding normal mode—the mode of uniform polarization—is sometimes called the Frohlich mode. In his excellent book on dielectrics, Frohlich (1949) obtained an expression for the frequency of polarization oscillation due to lattice vibrations in small dielectric crystals. His expression, based on a one-oscillator Lorentz model, is similar to (12.20). The frequency that Frohlich derived occurs where t = —2tm. Although he did not explicitly point out this condition, the frequency at which (12.6) is satisfied has generally become known as the Frohlich frequency. The oscillation mode associated with it, which is in fact the lowest-order surface mode, has likewise become known as the Frohlich mode. Whether or not Frohlich s name should be attached to these quantities could be debated we shall not do so, however. It is sufficient for us to have convenient labels without worrying about completely justifying them. 

In the preceding paragraphs we considered a homogeneous sphere. Let us now examine what happens when a homogeneous core sphere is uniformly coated with a mantle of different composition. Again, the condition for excitation of the first-order surface mode can be obtained from electrostatics. In Section 5.4 we derived an expression for the polarizability of a small coated sphere the condition for excitation of the Frohlich mode follows by setting the denominator of (5.36) equal to zero ... 

Next, use is made of the simple hypothesis that all the positions of the molecules and segments are equally probable, and, following tradition, we shall formulate an expression for the internal field as a field within a spherical cavity (Vleck 1932 Frohlich 1958)... 

The expression in square brackets in the above formnla is nothing but the screening factor at the Frohlich resonance frequency, and hence, the gain factor in core-shell nanocrystals is equal to the square of the Frohlich gain factor, Gcore-seii= [GFrohUdJ -... 

Frohlich, 1958). For other liquids, % can be estimated from dynamic simulations and usually lies in the range 1-500 ps. The rate constant is then expressed as... 

An electron in a solid behaves as if its mass [CGS units are used in this review the exception is for the tabulation of effective masses, which are scaled by the mass of an electron (m0), and lattice constants and radii associated with trapped charges, which are expressed in angstroms (1A = 10 8 cm)] were different from that of an electron in free space (m0). This effective mass is determined by the band structure. The concept of an effective mass comes from electrical transport measurements in solids. If an electron s motion is fast compared to the lattice vibrations or relaxation, then the important quantity is the band effective mass (mb[eff]). If the electron moves more slowly (most cases of interest) and carries with it lattice distortions, then the (Frohlich) polaron effective mass (tnp[eff]) is appropriate [11]. The known band effective and polaron effective masses for electrons in the silver halides are listed in Table 1. The polaron and band effective masses are related to a... 

This very general result is due to Frohlich and may be specialized, as we shall see presently, to give other well-known expressions. Before we do this, however, let us look briefly at the quantity m. If there is no interaction between molecular dipoles then m = m and indeed this can also be shown to hold if each molecule can be treated as a point dipole or as a uniformly polarized sphere. The deviation of [Pg.204]

The problem of the interaction of dipoles was treated by Kirkwood (1939, 1940, 1946) and Frohlich (1958). Starting point is the statistical mechanics (Bbttcher 1973 Landau and Lifschitz 1979) where the contribution of the orientation polarization to the dielectric permittivity is expressed by... 

For polymer chains a complicating feature is the presence of cross-correlation terms due to the angular correlations of dipole vectors along a chain (1,6,8). The dielectric increment Ae is a time-averaged (equilibrium) property of a system and may be expressed in terms of the fluctuations of the macroscopic dipole moment TJ(t) of a sphere of volume V according to the Kirkwood-Frohlich relation (1). 

A molecular theory of the local field factors appearing in the expression for the dielectric permittivity has been considered by Madden and Kivelson(56). They have shown how the introduction of an idealised distribution function leads to the Frohlich formula for the permittivity, ie. 

The interlayer model represents an extension of van der Pool s theory derived from works by Frohlich and Sack devoted to viscosity of suspension by a shell-model. Van der Poel obtained expressions for G and K (bulk modulus). In his model, the filler sphere of a radius, a, is supposed to be sturounded by the sphere of the matrix material with radius 1. The sphere in sphere obtained in this way is sturotmded by the great sphere of radius, R, consisting of material with macroscopic properties of heterogeneous composition. The residts of calculations according to the equations proposed by van der Poel are very close to those obtained using the Kemer equation. Detailed description of this approach can be found elsewhere. ... 

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