Relaxation vibration-translation

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... 

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... 

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

As discussed in Secs. 3.6.1.3 and 3.6.2.4 in photoacoustic Raman spectroscopy (PARS) the energy deposited in the sample by excitation of e. g. a vibration by the stimulated Raman process leads to pressure increases through relaxation to translational energy and can therefore be detected by a sensitive microphone. 

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. 

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 ... 

The equihbrium distribution of diatomic molecules over vibrationally excited states follows the Boltzmann formnla (3-12). Vibrational excitation in non-thermal plasma can be much faster than vibrational-translation (VT)-relaxation therefore, the vibrational temperature Tv can significantly exceed the translational temperature Tq. The vibrational temperature in this case is nsnally defined in accordance with (3-10) as... 

This mechanism is the most effective channel for CO2 dissociation in plasma. First of all, the major portion of the discharge energy is transferred from plasma electrons to CO2 vibration at electron temperature typical for non-thermal discharges (7 1 eV) (see Fig. 5-5). The rate coefficient of CO2 vibrational excitation by electron impact in this case reaches maximum values of about ev = 1-3 x 10 cm /s. Vibrational energy losses through vibrational-translational (VT) relaxation at the same time are mostly related to symmetric vibrational modes and they are relatively slow ... 

Non-adiabatic NO synthesis proceeds through the formation and decay of the intermediate complex (see Fig. 6-6). The probability of complex formation is described by (6-24)-(6-26) decay of the complex will now be considered using the statistical theory of monomolecular reactions (Nikitin, 1970). Such an approach is acceptable because the characteristic time of vibrational energy exchange inside N20 ( S+) is much shorter than the lifetime of the complex, and vibrational-translational (VT) relaxation of N20 ( E+) is much longer than the lifetime of the complex (Rusanov, Fridman, Shohn, 1978). According to the statistical theory, the direct decomposition frequency (marked + ) of the complex N2O NO + N, and reverse decomposition frequency (marked - ) N2O N2 + O can be expressed as... 

The chain of reactions can be accelerated by vibrational excitation of molecules. The typical reaction time is about 0.1 ms and is much faster than ion-ion recombination (1-3 ms), which determines the termination of the chain. As the negative cluster size increases, the probability of reactions with the vibrationally excited molecules decreases because of an effect of vibrational-translational (VT) relaxation on the cluster surface. When the particle size reaches a critical value (about 2 nm at room temperature) the cliain reaction of cluster growth becomes much slower and is finally stopped by the ion-ion recombination process. The typical time for 2 nm particle formation by this mechanism is about 1 ms at room temperature. A critical temperature effect on particle growth is partially due to VT relaxation, which depends exponentially on translational gas temperature according to the Landau-Teller effect (Section 2.6.2). Even a small increase of gas temperature results in a reduction of the vibrational excitation level and decelerates the cluster growth. 

Study of ultrasonic relaxation in pure liquids provides an useful means to observe vibration-translation (v-t) energy transfer in polyatomic molecules, but it is almost blind to vibration= vibration (v-v) transfer process. If experiments are made in mixtures, however, one can obtain the speed of v-v process between different molecules since the contribution of v-v coupling to the whole relaxation process would be dependent on the concentration. For this purpose, it is required to carry out measurement over a wide frequency range and to determine relaxation frequency at each concentration. 

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