Frequency regime

Figure Al.6.11. Idealized UV absorption spectrum of CO2. Note the regular progression of intemiediate resolution vibrational progression. In the frequency regime this structure is interpreted as a Franck-Condon...

These considerations can be extended to the full 3-D system where scarring is once again a relevant feature (R.V. Jensen, et.al., 1993 F. Benvenuto, et.al., 1994). For those concerned by the large field strengths used in the illustrative cases, it should be noted that these results can be scaled to other frequency regimes and also to excited state initial conditions, where an experimental realization is more likely (R.R. Jones, et.al., 1991). However, our simple example is sufficient to... 

Fig. 6.19 Frequency dependence of the conductivity at different temperatures for a micro PS film (5 U cm p-type, 30 mA cmf2, ethanoic HF). The transition from a frequency regime...

Bendow, B., 1978. Multiphonon infrared absorption in the highly transparent frequency regime of solids, Solid State Phys., 33, 249-316. 

Fig. 3. Phase Locked IR Pulses Time domain interferometry. (A) Output IR pulses from two tunable OPA-DFGs in the 4-pm frequency regime. (B) Three examples of interferograms generated by these IR pulses. (C) Linear IR absorption spectrum of acetic acid overlapped with the output of two OPAs. (D) Photon echo signal from acetic acid upon t-scan. The x-axis is the delay of the translation stage and the insert is a blow-up of a small region.

The experimental data shown in Figs. 15.3 and 15.5 were obtained with a microwave frequency oj/2ji > lit where r is the time or duration of the collision and 1/r is the linewidth. In this case the resonances corresponding to the absorption or emission of different numbers of photons are resolved. Here we describe radiative collisions starting from the high frequency regime, oj/2ji > 1/r and progressing to the low frequency regime, a> 2n < 1/r. 

In addition to the fact that the (f> = nil trace shows interference peaks, we note that they occur at approximately the same static field as the = 0 peaks, although they are narrower. As the rf frequency is raised, the phase dependence slowly disappears, until at 4 MHz it is undetectable, and we are in the high frequency regime described by the dressed state picture. 

The total frequency-dependent friction calculated from the MCT, (z), is plotted against the Laplace frequency (z) in Fig. 14. In the same figure the Enskog friction (e and the binary contribution (z) are also shown. Note here that in the high-frequency regime the frequency-dependent total friction is much less than the Enskog friction and is dominated entirely by the binary... 

For a deeper understanding of structure-property relationships it is useful to consider the effect of carbon black grade and concentration as well as polymer type on the dielectric properties more closely. In Fig. 29 the real part of the a.c.-conductivity o at 20 °C of a series of rubber composites, consisting of the more polar statistical co-polymer NBR and the fine black N220, is depicted for various filler concentrations in the high frequency regime up to 1 GHz. For the lower carbon black concentrations, a power law behavior with exponent around 0.6 is observed, while the highly filled com-... 

This behavior becomes more transparent in Fig. 30a,b, where the a.c.-con-ductivity a and relative dielectric constant (permittivity e ), respectively, for a series of less polar S-SBR-samples filled with various amounts of the coarse black N550 are show at 20 °C in a broader frequency range up to 107 Hz. For filler concentrations below the percolation threshold (O<0.15), the conductivity behaves essentially as that of an isolator and increases almost linearly with frequency. Above the percolation threshold (5>>0.2), it shows a characteristic conductivity plateau in the small frequency regime. Since at low frequencies the value of the conductivity a agrees fairly well with the d.c.-con-ductivity, the plateau value exhibits the characteristic percolation behavior considered above. In the high frequency regime the conductivity depicted in... 

There are some difficulties we should be aware of just the same. The maximum that is supposed to appear at co = 0 shows up in the INM calculations as a full-blown divergence (43,44). Indeed this infinity is just one instance of the fundamental problems with INMs at zero frequency. It probably should not be a surprise that a theory that pretends that basic liquid structure does not change with time is going to be ill-suited to studying behavior at the lowest frequencies. The same level of theory predicts liquid diffusion constants to be identically zero, for example. Fortunately, realistic molecular vibrational frequencies tend to be well outside this low-frequency regime, so the effects on predicted Tis are likely to be minimal. Still, as we shall note in Section VI, not every aspect of vibrational spectroscopy will be quite so insulated from this basic issue. 

---