Vibration Transfer

To minimize resonance corrosion fatigue, reduce vibration and fluttering on stressed structures or equipment in corrosive environments  

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Kraijnovitch D J, Parmenter C S and Catlett D L Jr 1987 State-to-state vibrational transfer in atom-molecule collisions. Beams vs. bulbs Chem. Rev. 87 237-88... 

Similar measurements for Li and argon collisions have been performed by Ottinger et al. and for vibrational transfer in excited by Steinfeld et a/. 153). Exciting different (/, v) levels of the... 

The frame for the instrument always has vibrations transmitted from the ground and the air. The displacement of the frame is described by a function of time, X t). The STM is represented by a mass M, mounted on the frame. The problem of vibration isolation is to devise a proper mounting to minimize the vibration transferred to the mass, that is, to minimize its displacement of the mass M, x(t). The basic method for vibration isolation is to mount the mass to the frame through a soft spring, as shown in Fig. 10.1. The restoring force of the spring acting on the mass is... 

Vibrational-to-vibrational transfer tentatively has been identified in collisions of H2+ with H25 91, 951... 

Values of /JAB and AB have been calculated by applying equation (20), and often show striking catalytic effects of the additive i.e. very small amount of additive produces reductions in / A which are far greater than can be explained in terms of the ssh theory for vibration-translation transfer. Now that vibration-vibration transfer is better understood (see Section 5 below), it has become quite clear that many of these cases, where B is a polyatomic molecule, can be explained in terms of rapid vibration-vibration transfer from... 

Water vapour is a particularly effective catalyst for vibrational relaxation, as illustrated by the data given in Tables 4 and 7. For H20+02 (Table 7, p. 229) near-resonant vibration-vibration transfer between the fundamental frequency of 02, v = 1554 cm-1, and the bending frequency of H20, v = 1595 cm-1, accounts satisfactorily for the low value of Z. This is discussed in more detail in Section 5 below. For the H20+C02 and H20+N20 mixtures there are no near-resonant frequencies, as may be seen from Table 4 neither NzO nor C02 is polar, so that dipole-dipole interaction cannot be responsible, and some other explanation must be sought. It has been suggested both by Eucken and Kiichler70 and by Widom and Bauer71 that for C02 + H20, because of incipient chemical combination to H2C03, there will be a transition state... 

It was pointed out in Section 4.2 that most polyatomic molecules show only a single relaxation process, owing to rapid intramolecular vibration-vibration transfer between modes. This corresponds to a state of affairs where Vibrational energy enters the molecule via process (a), which is rate-determining,... 

Zi.jis the collision number for vibration-vibration transfer between i quanta of mode 1 (frequency and one quantum of mode 2 (frequency v,). 

Experimental observation of relaxation phenomena in binary mixtures of polyatomic gases affords much more information about vibration-vibration transfer. The nature of the vibrational relaxation process for a mixture of a relaxing gas, A, with a non-relaxing gas, B, has been discussed in Section 4.3. It involves two collision processes... 

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... 

If process (3), vibration-vibration transfer, does not occur, the mixture will show a double relaxation phenomenon, characterized by two relaxation times, / A and / B> which will both be related to molar composition by equations of type (20), each giving a linear plot of 1 // against composition. If vibration-vibration transfer does occur, the picture is completely altered. Supposing, for convenience, that pure A relaxes slowly, and pure B rapidly, so that processes (4) and (5) are both much faster than processes (1) and (2), there are now two alternative possibilities for the overall relaxation process. 

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. 

Direct information about the rate of vibration-vibration transfer between molecules with comparatively high vibrational frequencies can be obtained by... 

The theoretical treatment of vibration-vibration transfer was outlined in Section 3. Sufficient data for a priori theoretical calculations are only available for the simpler molecules. It is interesting first to discuss the general pattern revealed by the collision numbers in Tables 5 and 6 in terms of equations (18) and (19). 

Comparison of the collision numbers given above for vibration-vibration transfer with those for vibration-translation, given in Section 4, shows that in many cases vibration-vibration transfer between two resonant or near-resonant modes is much more efficient than vibration-translation transfer from either. This applies equally to homomolecular and heteromolecular collisions, and carries the interesting consequence that the quickest route for vibrational excitation of upper levels from the ground level by homomolecular collisions is an initial vibration-translation excitation to the v = 1 level, followed by successive vibration-vibration transfers to higher levels. Because of the selection rule, Av = 1,... 

The slowest process will be the vibration-translation activation to the (v = 1) level, which will be rate-determining, and the subsequent vibration-vibration transfers will occur at increasingly fast rates with increasing vibrational quantum number. (For harmonic oscillators 1 = n(m+ l) 1 .) Shock-tube experi-... 

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... 

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