Complex polarizability

The high conductivity observed at low frequencies would overlap the existence of another new relaxation (Fig. 2.78) what is very similar to that found for transfer complexes [243, 244] in which some of them have a pronounced semiconductor character. In this kind of compounds, the observation of dielectric relaxations over room temperature is inhibited by the high conductivity observed. To avoid this problem and to detect the conductivity effect, it is possible to use the complex polarizability a defined by equation [182], The transformation defined by equation (2.45), has been applied with good results in the case of dielectric relaxation peaks in terms of a" or tan 8 . 

The complex polarizability, oc, measured along the axis of symmetry of a prolate spheroid, of volume V and unit eccentricity, may be expressed in terms of e and of by tbe equations... 

We have related the dissipative part of the frequency-dependent complex polarizability to the spectral density of the spontaneous fluctuations in the... 

In Eq.6, is the unit vector from the rth to the jth particle and a is the complex polarizability tensor (which for the case of isotropic particles is a complex constant). Ay and By are the interaction coefficients whose expression is in [10],... 

In the linear response regime, however, the nonlinearity of the kinetic equation is not important because there Dr can be replaced by Dr since the change in Dr appears only in the higher order perturbation. Therefore the linear response function is given by the same form as that in dilute solution except that Dr is much smaller than Z>,o- For example, consider a rodlike polymer which has permanent dipole moment p and isotropic polarizability (an = a = a ). The complex polarizability and the dynamic Kerr constant (per polymer) are given in the same form as eqns (8.94) and (8.104),... 

The calculation is tedious, but straightforward. Here we only quote the results. The complex polarizability is given by... 

Figure 1.16 Imaginary part of the complex polarizability a o)) for an Na cluster with N = 198 in units of Effective single-pair excitations, as well as the surface plasmon and the volume plasmon, are clearly resolved. For comparison the result of the local Drude theory is also given. In this case there is only one mode of excitation, the classical surface-plasmon polariton or Mie-resonance at coply/3. Because the frequency is scaled with this frequency the Drude curve peaks trivially at 1. For more explanation see text. Reproduced with permission from Reference [5]. Copyright 1985 by the American Physical Society...

The linear response of a system (initially in the ground state 0)) to a periodic one-body perturbation Q(o)) = Q[exp(icot) -h c.c.] is fully described by the complex polarizability a(co), given by the well-known time-dependent perturbation-theory expression... 

Figure 11 Scaife plots of the complex polarizabilities for three temperatures of liquid methyl chloride.

Results of ab initio calculations for the polarizability tensor components of the CH4-N2 complex are shown at Fig. 4.10. As expected, the dependence of the polarizability tensor components of this complex on intermolecular distance R has the usual form. However, it is also seen that the polarizability of the complex is affected by the orientation of the N2 molecule due to its big anisotropy of the polarizability. The orientation of highly symmetric molecule CH4 in the complex affects significantly smaller on the complex polarizability and becomes noticeable only at small intermolecular separations. It should be pointed out that for configurations 4 and 5 (symmetry Cj) the small nondiagonal component a y (ccxy 0.005 a.u. at R = 3.5 A) is appeared in the coordinate system used (Fig. 3.6a). 

Scaife proposed that the Cole-Cole plot method of analyzing dielectric data should be replaced by the use of the polarizability plot in which the imaginary coordinate of the complex polarizability, p ([Pg.226]

Equation (1.193) represents the complex polarizability of a small sphere of sub-wavelength diameter in the quasi-static approximation. Note that it shows the same functional form as the Clausius-Mossotti polarizability [1]. 

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