Collisional relaxation of transient vibrational energy distributions in a thermal unimolecular system. The variable encounter method

A method has been developed, called the Variable Encounter Method, for the study of the relaxation of an initial vibrationally cold ensemble of molecules into a vibrationally hot distribution by a known and variable number of successive collisions with a hot wall. The theory of the experiment is presented. The system studied was the isomerization of 1,1-cyclopropane-d₂ with a fused quartz wall temperature of 800 K to 1175 K, and average number of collisions from 2.3 to 22.3. Various modified gaussian and exponential models of energy transfer were found to give agreement with the data. The average down-step size was found to decline from ≤ 3500 cm^?1 at the lowest temperature to ≈ 2500 cm^? at the highest on the basis of a gaussian model. A mathematical analysis of the relation between mean first passage times and incubation times is given. Incubation times increase from ≈ 7 to ≈ 12 collisions with increasing temperature. Transient population distributions and the sequential reaction probabilities as a function of collision number are calculated.