Dipole loss functions

We have also measured the intensity of the optically allowed transition relative to the other valence excitations in the loss function. As q increases, the intensity decreases rapidly along [100], while the intensity along [110] changes little. This indicates that even the oscillator strength of the dipole-allowed transition is anisotropic. 

Fig. 8.11. Measured peak position of the dipole-allowed transition in the loss function versus the orientation angle of q relative to [100], for a fixed q of 0.38 in the x — 7 plane. The solid line is a fit of the data to —cos(2/) for the purpose of illustration.

To gain fmther insight into the crystallization mechanism of PDS, the shape and breadth of the relaxation spectrum were examined before and after crystallization. The comparison is made in Figure 9.11, where a normalized plot of dielectric loss as a function of frequency was constructed. Before the onset of crystallization (temperatures below 8°C), dipole loss curves superimpose quite well suggesting thermodielectric simplicity in the applied frequency interval between 100 Hz and 1 MHz.17 As crystalli-... 

These studies are based on the connection between the dielectric loss function and the dipole-dipole correlation function, Eq. 7.7, which on integration by parts shows... 

As shown in Fig. 7, a large increase in optical absorption occurs at higher photon energies above the HOMO-LUMO gap where electric dipole transitions become allowed. Transmission spectra taken in this range (see Fig. 7) confirm the similarity of the optical spectra for solid Ceo and Ceo in solution (decalin) [78], as well as a similarity to electron energy loss spectra shown as the inset to this figure. The optical properties of solid Ceo and C70 have been studied over a wide frequency range [78, 79, 80] and yield the complex refractive index n(cj) = n(cj) + and the optical dielectric function... 

Without loss of generality y = y can be assumed. If the dipole moment can be assumed to be a linear function of coordinate within the spread of the frozen Gaussian wave packet, the matrix element (gy,q,p, Pjt(r) Y,q, p ) can be evaluated analytically. Since the integrand in Eq. (201) has distinct maxima usually, we can introduce the linearization approximation around these maxima. Namely, the Taylor expansion with respect to bqp = Qq — Qo and 8po = Po — Po is made, where qj, and pj, represent the maximum positions. The classical action >5qj, p , ( is expanded up to the second order, the final phase-space point (q, p,) to the first order, and the Herman-Kluk preexponential factor Cy pj to the zeroth order. This approximation is the same as the ceUularization procedure used in Ref. [18]. Under the above assumptions, various integrations in U/i(y, q, p ) can be carried out analytically and we have... 

Material response is typically studied using either direct (constant) applied voltage (DC) or alternating applied voltage (AC). The AC response as a function of frequency is characteristic of a material. In the future, such electric spectra may be used as a product identification tool, much like IR spectroscopy. Factors such as current strength, duration of measurement, specimen shape, temperature, and applied pressure affect the electric responses of materials. The response may be delayed because of a number of factors including the interaction between polymer chains, the presence within the chain of specific molecular groupings, and effects related to interactions in the specific atoms themselves. A number of properties, such as relaxation time, power loss, dissipation factor, and power factor are measures of this lag. The movement of dipoles (related to the dipole polarization (P) within a polymer can be divided into two types an orientation polarization (P ) and a dislocation or induced polarization. 

Figure 8. Inelastic tunneling cross section, from the theory of Kirtley, Scalapino, and Hansma (KSH), for a point dipole as a function of position in a ISA thick barrier, for 3 different vibrational energy losses. One electrode is taken to be at OA,...

Here, r denotes the position vector of the charges qt with respect to the center of the sphere, and r, the distance from the center. By applying the dielectric scaling function for dipoles (Eq. (2.3)), which—as we have seen in Fig. 2.1—is also a good approximation for most other multipole orders, it was immediately clear that the idea of using a scaled conductor instead of the EDBC leads to a considerable simplification of the mathematics of dielectric continuum solvation models, with very small loss of accuracy. It may also help the finding of closed analytic solutions where at present only multipole expansions are available, as in the case of the spherical cavity. Thus the Conductor-like Screening Model (COSMO) was bom. 

Fig. 11a and b. Debye single relaxation time model for dipole orientation showing a) permittivity and b) loss factor as a function of the product of the angular frequency w and the dipole realxation time rd. The relaxed permittivity is e, and the unrelaxed permittivity is e ... 

Several distinct relaxation processes are usually present in a solid polymeric material, and these are dielectrically active if they incur significant orientation of molecular dipoles. The multiplicity of relaxation processes is seen most easily in a scan of dielectric loss at constant frequency as a function of temperature (Fig. 3.6). As the temperature is raised, molecular mobilities of... 

Detailed examination of the relaxations requires isothermal scans of relative permittivity and dielectric loss factor as a function of frequency/ so that effective dipole movements and activation energies of relaxation times may be obtained. A typical pair of plots of d and e" values against log/is shown in Fig. 3.7. Graphs of dielectric data of this kind are sometimes called, rather... 

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