Vibrational relaxation in gases

The velocity of ultrasonic waves has been measured in a number of gases at 25°C and for values of the ratio, ultrasonic frequency/pressure, ranging from 2 x 10 5 to 2 x 10 7 c s -1 atm -1 . Dispersion, corresponding to a single vibrational relaxation process was shown by acetylene, CD 3 Br and hexafluoro-ethane; and, to a double relaxation process, by ethane. Incipient dispersion was shown by propane, ethyl chloride, ethyl fluoride and dimethyl ether. No dispersion was shown by 1.1-difluoro-ethane, n -butane, iso -butane, neo -pentane and ammonia. Correlation of these with previous results leads to the conclusion that: ( а ) For molecules with a distribution of fundamental frequencies, such that there is only a small gap between the lowest and the remaining frequencies, vibrational activation enters via the lowest mode and spreads rapidly to the other modes, giving rise to a single relaxation process involving the whole of the vibrational energy. The chief factors determining the probability of excitation of the lowest mode are its frequency and the presence or absence of hydrogen atoms in the molecule. Molecules containing two or more hydrogen atoms suffer translational-vibrational energy transfer very much more easily than other molecules. Deuterium has almost the same effect as hydrogen. ( b ) For molecules, in which there is a large gap between the lowest and the remaining fundamental frequencies, a double relaxation process occurs. The complex energy transfer probabilities involved do not fit the same quantitative functional relation with vibrational frequency as in ( a ) above. ( c ) Torsional oscillations due to hindered internal rotation behave similarly to other fundamental modes. For molecules in which there is a large gap between the torsional frequency and the other modes (e. g. ethane) a double relaxation process occurs as in ( b ). Where there is no such gap, vibrational energy enters all modes via the torsional mode as in ( a ).