Systematics of Vibrational Relaxation

A large number of data points for the vibrational relaxation time (pτ_v in atm sec) of simple systems have been logarithmically plotted vs (T°K)^—⅓. It appears that each system is well represented by a straight line, and that most of these straight lines when extended to higher temperatures intersect near the point [pτ_v=10^—8 atm sec, (T°K)^—⅓=0.03]. Systems with a small reduced mass μ are exceptions to such a simple convergence, and in an improved scheme, the location of the convergence point is dependent on the reduced mass. Such a presentation has lead to an empirical equation correlating available measurements of vibrational relaxation times: ${\log }_{10}{\mathrm{(p\tau }}_v{\text{)=(5.0×10}}^{\text{−4}}{\mathrm{)\mu }}^{\frac{1}{2}}{\theta }^{\frac{4}{3}}{\mathrm{[T}}^{-\frac{1}{3}}{\text{−0.015μ}}^{\frac{1}{4}}\text{]−8.00}$ , where θ is the characteristic temperature of the oscillator in K deg. This equation reproduces the measured times within 50% for systems as diverse as N₂, I₂, and O₂–H₂. In the worst case thus far, O₂–Ar near 1000°K, it is off by a factor of 5.