Vibrational-translational relaxation

It is interesting that vibration-translation relaxation phenomena in liquids, where the molecules can be regarded as in continual close association, show the same general features as for the corresponding gases energy transfer would appear to occur in binary collisions with the same transfer probability per collision... 

That the carbon—metal or carbon—metalloid bonds are preserved at all in these reactions is quite surprising. With tetramethylgermanes, for example, this free radical reaction must be a 24 step process. The success in preserving carbon-germanium bonds must arise from very rapid molecular vibrational, rotational, and translational relaxation processes occurring on the cryogenically cooled surfaces such that the energy from the extremely exothermic reaction is smoothly dissipated. 

If a relaxing gas, A, is mixed with a non-relaxing gas, B, such as helium, there are two collision processes by which vibration-translation energy transfer may occur... 

If both A and B are polyatomic relaxing gases, there will also be two collision processes, corresponding to (1) and (2), for vibration-translation energy transfer from B in homomolecular and heteromolecular collisions. In addition there can be a vibration-vibration transfer between A and B, making five transfer processes in all... 

Alternatively, when process (3) is slower than (4) or (5), but faster than (1) or (2), A will again relax by the route (3) followed by (4) or (5), but now (3) will be rate determining. This will give a linear variation of 1// A with x. B will relax independently, and more rapidly, via (4) and (3), with linear dependence of 1// B on x. There will thus be a double relaxation phenomenon with two relaxation times, PA involving only the vibrational heat capacity of A, and / B only that of B, both showing linear concentration dependence. This mechanism is analogous to the relaxation behaviour discussed in Section 3.1 for pure polyatomic gases, which show double dispersion because vibration-vibration transfer between modes is slower than vibration-translation transfer from the lowest mode. 

The mixtures of the second section in Table 6, which were investigated earlier (when erroneous conclusions were drawn)77, all show double dispersion. The details for one mixture, SF6+C2F4, are shown in Fig. 16. There is near-resonance between the lowest (344 cm-1) mode of SF6 and the first harmonic of the lowest (190 cm-1) mode of C2F4. C2F4 shows very efficient homomolecular vibration-translation transfer, and the estimated vibration-vibration transfer rate (ZAB=70) falls between this and the slower vibration-translation transfer rate of SF6 (ZAA = 1005). Double dispersion is observed, and the predicted linear variation with concentration of the two relaxation times. The remaining mixtures in this section, all of which involve B components whose homomolecular relaxation is very rapid, behave similarly. 

A number of experimental measurements have been made on the vibrational relaxation of oxygen, which demonstrate the powerful catalytic effect of small quantities of various additives. The experimental data do not extend to sufficiently high concentrations of additive to make detailed interpretation possible in terms of vibration-vibration and vibration-translation transfers. The molecules involved are all simple enough to enable ssh calculations to be made with reasonable prospect of success. The results of a priori calculations by the procedures described by Stretton33 are presented in Table 782. They show clearly the striking efficiency... 

Whether rotation-vibration transfer occurs, and how important it is, are questions of considerable dispute. The experimental observation by Millikan106,107, that vibrational deactivation of CO in collision with p-H2 is more than twice as efficient as in collision with o-H2, seems to provide some evidence that rotational energy participates in vibrational relaxation. The only significant difference between o- and p-H2 in the context of this experiment would appear to be the difference in rotational energy states, as illustrated by the fact that at 288 °K (the temperature of the experiment) the rotational specific heat of o-H2 is 2.22, while that of p-H2 is 1.80 cal.mole-1.deg-1. Cottrell et a/.108-110 have measured the vibrational relaxation times of a number of hydrides and the corresponding deuterides. On the basis of SSH theory for vibration-translation transfer the relaxation times of the deuterides should be systematically shorter than those of the hydrides. The... 

This chapter is concerned with how energy deposited into a specific vibrational mode of a solute is dissipated into other modes of the solute-solvent system, and particularly with how to calculate the rates of such processes. For a polyatomic solute in a polyatomic solvent, there are many pathways for vibrational energy relaxation (VER), including intramolecular vibrational redistribution (IVR), where the energy flows solely into other vibrational modes of the solute, and those involving solvent-assisted processes, where the energy flows into vibrational, rotational, and/or translational modes of both the solute and the solvent. 

In this chapter we have reviewed the general theory of vibrational energy relaxation for a single oscillator coupled to a bath, and we have discussed the application of these results to three specific systems iodine in xenon, neat liquid oxygen, and W(CO)6 in ethane. In the first case the bath is the translations of the solute and solvent molecules, in the second case it is the translations and rotations of solute and solvent molecules, and in the third case it is the solute s other intramolecular vibrations and the translations of solute and solvent molecules. 

Data for vibrational-translational energy transfer are usually presented as a relaxation-time-pressure product pr, where r refers to the e-folding time... 

This asymptotic form is plotted in Fig. 5. A feature of BBM(d>) is that it decreases asymptotically with frequency to zero. If the atom B is involved in vibrational motion at frequency oo (Oq, the coupling with the bath through binary collisions is small and the slow dissipation is the stochastic manifestation of slow vibrational relaxation. The most significant feature of Eq. (3.17) is that the dependence in the exponent of Eq. (3.17) is equivalent to an exponent This is just the form of the Landau-Teller theory of vibration-translation (V-T) energy transfer in atom-diatom collisions, and this form is almost universally used to fit vibrational relaxation rates in such systems. This will be dealt with in more detail in Section V C. The utility of BBM(d>) is that it pertains to atom-atom collisions in which the atom B is bonded to the other atoms by arbitrary potentials. No assumptions have been made about the intramolecular motions, although the use of BBM(d)) implies linear coupling to the displacements of atom B. Grote et al. have alluded to the form of Eq. (3.20) for di = 0 in a footnote. 

Even these time resolutions of the Dens.G signal are not fast enough to trace the elementary step of the vibrational energy relaxation. In order to investigate the energy-transfer processes to the translational freedom from the vibrational freedom, we need a further fast detection system such as the Temp.G. The highest time resolution for the thermal detection reported so far is about 3 ps [63]. Ultimate intrinsic temporal response of the Temp.G has not been determined experimentally (Section IV). 

A basic assumption, which is made when writing such equations, is that the chemical relaxation time is much longer than other characteristic times in the system, such as internal (vibrational, rotational) or translational relaxation times. One might inquire about the generalization of the rate law when such a time-scale separation is not satisfied. From a theoretical point of view, a convenient generalization of (2.8) is ... 

Several excellent reviews in related and parallel areas have appeared recently. " Though much early work in the field concentrated on vibration-translation/rotation relaxation phenomena using ultrasonic methods, a remarkable resurgence of interest in the area occurred with the advent of infrared lasers and their application to laser-induced infrared... 

As a result of these measurements the authors conclude that the vibration-translation/rotation (V-T/R) relaxation time in CH4 is 0.69 ms ... 

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