Relaxational contribution reduced frequency

It should be noted that there is a considerable difference between rotational structure narrowing caused by pressure and that caused by motional averaging of an adiabatically broadened spectrum [158, 159]. In the limiting case of fast motion, both of them are described by perturbation theory, thus, both widths in Eq. (3.16) and Eq (3.17) are expressed as a product of the frequency dispersion and the correlation time. However, the dispersion of the rotational structure (3.7) defined by intramolecular interaction is independent of the medium density, while the dispersion of the vibrational frequency shift (5 12) in (3.21) is linear in gas density. In principle, correlation times of the frequency modulation are also different. In the first case, it is the free rotation time te that is reduced as the medium density increases, and in the second case, it is the time of collision tc p/ v) that remains unchanged. As the density increases, the rotational contribution to the width decreases due to the reduction of t , while the vibrational contribution increases due to the dispersion growth. In nitrogen, they are of comparable magnitude after the initial (static) spectrum has become ten times narrower. At 77 K the rotational relaxation contribution is no less than 20% of the observed Q-branch width. If the rest of the contribution is entirely determined by... 

Figure 4. Plot of the difference between experimental G (uaT) and its relaxational contribution versus the reduced frequency for six representative networks.

Fig. 7 Reduced storage modulus [G ( )1 plotted on double logarithmic scales versus the reduced frequency cotq for a 3-D topologically-regular cubic (40 x 40 x 40) network cross-linked from Rouse chains of 20 beads each (solid line). Also shown are the contributions to the [G (ffl)] that come from intrachain relaxation (solid line with circles) and interchain relaxation (solid line with stars)...

Alternating-current and frequency effects. With an AC rather than a DC voltage applied to the electrodes, the processes above reverse themselves with the period of the alternating voltage. But each process proceeds at a different rate (with a characteristic relaxation time) so that their relative contributions to energy dissipation vary with frequency. As the frequency is increased concentration-polarization can be reduced or eliminated, particularly if the electrode reaction is reversible (fast electron transfer in both directions). 

In compound C the static nuclear relaxation term is nearly seven times greater than the static electronic term, although in the frequency-dependent effects its value is greatly reduced while the electronic effect is expected to get substantially greater. Generally the correlated and HF vibrational values show similar trends the differences for the electronic contributions are much greater. 

Kirtman and Luis review some of the theoretical/computational methods which have been proposed over the past fifteen years for the calculation of vibrational contributions to the linear and NLO properties. They discuss (i) the time-dependent sum-over-states perturbation theory and the alternative nuclear relaxation/curvature approach, (ii) the static field-induced vibrational coordinates which reduce the number of n -order derivatives to be evaluated, (hi) tire convergence behavior of the perturbation series, (iv) an approach to treat large amplitude (low frequency) vibrations, (v) the effect of the basis set and electron correlation on the vibrational properties, and (vi) techniques to compute the linear and NLO properties of infinite polymers. 

Cl2 and CO2 and used the DID model for the induced polarizability. They showed that for CO2 the collision induced contribution to the depolarised Rayleigh intensity was 25% of the total intensity and that the second moment was increased by about 50% by induced effects. The timescale separation was examined in N2 and C02 In their terminology is the collision induced contribution it was found to relax in a very similar way to the orientational function <°M(t).°M> and the spectra of the two terms were indistinguishable for practical purposes. Furthermore the cross-term was quite large. The net effect of the non-orientational terms was to reduce the amplitude of the spectrum at low frequencies and to increase it in the wings. Frenkel and McTague s results on nitrogen have been carefully compared with experiment by Sampoli de Santis and co-workers(54). 

Although equation 3 was obtained from the Rouse theory, the application of reduced variables in Fig. 11-3 is based on a much more general hypothesis, namely, that the modulus contributions are proportional. opT and the relaxation times to whether or not the specific spectrum of times predicted by the Rouse theory is applicable. (In fact, the shape of the curve in Fig. 11-3 deviates considerably from the Rouse theory predictions.) This hypothesis is widely fulfilled but must be carefully examined each time it is used. An important criterion is that the shapes of the original curves at different temperatures must match over a substantial range of frequencies other criteria will be discussed in Section B. 

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