Strong-collision Models

At higher pressures only Raman spectroscopy data are available. Because the rotational structure is smoothed, either quantum theory or classical theory may be used. At a mixture pressure above 10 atm the spectra of CO and N2 obtained in [230] were well described classically (Fig. 5.11). For the lowest densities (10-15 amagat) the band contours have a characteristic asymmetric shape. The asymmetry disappears at higher pressures when the contour is sufficiently narrowed. The decrease of width with 1/tj measured in [230] by NMR is closer to the strong collision model in the case of CO and to the weak collision model in the case of N2. This conclusion was confirmed in [215] by presenting the results in universal coordinates of Fig. 5.12. It is also seen that both systems are still far away from the fast modulation (perturbation theory) limit where the upper and lower borders established by alternative models merge into a universal curve independent of collision strength. 

The simple fitting procedure is especially useful in the case of sophisticated nonlinear spectroscopy such as time domain CARS [238]. The very rough though popular strong collision model is often used in an attempt to reproduce the shape of pulse response in CARS [239]. Even if it is successful, information obtained in this way is not useful. When the fitting law is used instead, both the finite strength of collisions and their adiabaticity are properly taken into account. A comparison of... 

Fig. 6.7. The first-order (curve 1), second-order (curve 2) and third-order (curve 3) approximations to the exact dependence x x ) in the strong collision model (curve 4).

Q-branch rotational structure 179-82 spectra of nitrogen in argon 180 spectral collapse theory 150 spectral width 107 strong collision model 188 cumulant expansions 85-91... 

Maxwellian distribution 129 infinite-order sudden (IOS) approximation 155-6 semi-classical calculation 136-7 Sack s model rotational relaxation 19 strong collision model 219 scattering see isotropic scattering spectra ... 

The thermal rate is then computed as a function of collision frequency, a. When a strong collision model is assumed [85], the thermal rate is given by... 

The rate of vibrational energy flow in the reactant and product conformer is influenced by the rate of collisions with the solvent environment. Using a strong collision model, the microcanonical rate is still given by k(E) = K(E)kKKKM(E), where the IVR rate that enters into the transmission coefficient in Eq. (9) incorporates a collision frequency, a ... 

An interesting question is whether the large fluctuations in the quantum mechanical decay rates have an influence on the temperature and pressure dependent unimolecular rate constant P) defined within the strong collision model, in Eq. (2). In the state-specific quantum mechanical approach the integral over the smooth temperature dependent rate k E) is replaced by a sum over the state-specific rates fc,-. Applications have been done for HCO [93], HO2 [94-96], and HOCl [97]. The effect of a broad distribution of widths is to decrease the observed pressure dependent rate constant as compared to the delta function-like distribution, assumed by statistical theories [98,99]. The reason is that broad distributions favor small decay rates and the overall dissociation slows down. This trend, pronounced in the fall-of region, was clearly seen in a study of thermal rate constants in the unimolecular dissociation of HOCl [97]. The extremely... 

Fig. 21. Zero-field dynamic Gaussian Kubo-Toyabe functions for different field fluctuation times. The curves are labeled by the value of t A (in rad). The calculation used the strong-collision model. In the Gaussian-Markovian approach G t) decays minimally slower.

Third, we must know something about the collisional transition rates between the grains, and many models have been explored in the past, particularly those known as the step-ladder and the exponential models [72.R 73.F 77.T1] I will confine myself almost exclusively in this discourse to the strong collision model, equation (2.26), and for the time being, at least, the apparent rate constant p for the relaxation of the total internal energy can be regarded as an adjustable parameter. 

Thus, unlike all model calculations dted in Section 3.3, the strong collision model gives the result that all states below threshold are in... 

Small Step Rotational Diffusion and Strong Collision Models... 

Small Step Rotational Diffusion and Strong Collision Models 183 the expansion coefficients are found to obey... 

Thus, the Debye model for isotropic rotation behaves like the strong collision model. 

Small Step Rotational DiflFusion and Strong Collision Models 187... 

Now the result given in Eq. (7.54) is very similar to the corresponding expression in the strong collision model given by Eq. (7.30) except the correlation times r rnM( = different for different... 

The small step rotational diffusion model has been extensively applied to interpret ESR linewidth [7.4, 7.9], dielectric relaxation [7.2], fluorescence depolarization [7.19], infrared and Raman band shapes [7.24], as well as NMR relaxation in liquid crystals [7.14, 7.25]. When dealing with internal rotations in flexible mesogens, they are often assumed to be uncoupled from reorientation to give the so-called superimposed rotations model. Either the strong collision model or the small step rotational diffusion model may be used to describe [7.26, 7.27] molecular reorientation. 

The strong collision model has been used in several studies to interpret spectral densities of motion 5CB-di5 [7.15], 50.7-d4 [7.7], and discotic hexa-hexyloxytriphenylene (THE6) [7.46]. The spectral densities can be obtained from Eq. (7.30). In the fast motion limit,... 

---