COLLISIONAL ENERGY-TRANSFER AT HIGH-TEMPERATURES FROM THE BIASED WALK MODEL

A new expression for the probability, P(E,E'), of collisional energy transfer for large polyatomics at high temperatures is deduced by using the assumptions of the biased random walk (BRW) model [Lim, K. F.; Gilbert, R. G. J. Chem. Phys. 1986, 84, 6124] and of a Gaussian equilibrium population distribution. The latter approximation is shown to be very accurate at sufficiently high temperatures. Simple analytic expressions are obtained for P(E,E'), which show the correct limiting weak- and strong-collision forms as the duration of a collision approaches zero and infinity, respectively. Expressions are found for the average energy-transfer quantities <DELTA-E(all)>, <DELTA-E(d)>, and <DELTA-E2>, as functions of initial energy E'. The expression for <DELTA-E(all)> explicitly shows the change of sign as E' is varied over a wide range of E'. The new BRW expression for P(E,E') can be accurately approximated as Gaussian. The derived expressions will be of use in modeling high-temperature processes such as combustion.