Theory of thermal unimolecular reactions at low pressures. I. Solutions of the master equation

Abstract

The master equation for a thermal unimolecular reaction in gases at low pressures is formulated. Steady-state solutions are derived in analytical form with an exponential model of collisional transition probabilities, (i) for vibrational energy transfer in molecules with variable densities of states, and (ii) for combined rotational and vibrational energy transfer in molecules with variable heights of the centrifugal barriers. Other models of transition probabilities are treated numerically. The diffusion limit of energy transfer is discussed. In all cases, the nonequilibrium populations of excited states and the weak collision efficiency factors βc are calculated.