Systematics of Vibrational Relaxation

TLDR

A large number of vibrational relaxation times for simple systems have been plotted logarithmically against T⁻¹/3. The study finds that these times follow straight lines converging near pτv = 10⁻⁸ atm·s, with low‑mass systems deviating; a mass‑dependent empirical equation predicts times within 50 % for N₂, I₂, and O₂–H₂, though it underestimates O₂–Ar at ~1000 K by a factor of five.

Abstract

A large number of data points for the vibrational relaxation time (pτv 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 [pτv=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: log10(pτv)=(5.0×10−4)μ12θ43[T−13−0.015μ14]−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.