Nonequilibrium velocity distribution and reaction rate in hot-atom reactions

The nonequilibrium velocity distribution and reaction rate in the hot-atom reactions are studied by solving the time-dependent Boltzmann equation with the Monte Carlo simulation. The explicit time-dependent velocity distribution, temperature, and rate constant of hot atoms from initial to steady states are obtained for a simple model system, where hot atoms are dispersed in the heat bath of surrounding molecules without internal degrees of freedom and the cross sections are chosen as a simple hard sphere model. The low- or high-temperature steady state exists in consistence with the prediction of Keizer with the Maxwell distribution approximation. The hot-atom velocity distribution for the high-temperature steady state is, however, different from the Maxwell distribution. The nonequilibrium velocity distribution yields a much smaller value of the lower limit of the ratio of reactive to elastic cross sections for the existence of the high-temperature steady state and a smaller rate constant than those of the Maxwell distribution approximation by Keizer