Non-Arrhenius temperature dependence of bimolecular reaction rates at very high temperatures

Question

Once I have read that in some cases bimolecular reactions can exhibit a maximum as a function of temperature due to the short lifetime of the activated complex at very high temperatures.

At low temperatures the rate is increasing because the reaction is limited by diffusion or by the encounter rate. At high temperatures the rate is decreasing because the lifetime of the bimolecular complex is very short, so that there is no time to overcome the barrier for bond breaking or making. This means the reactants have lots of encounters but they do not have time to react each time they encounter, so that the effective rate is small.

Could any one please indicate any piece of reference or useful terminology for this ? I have read this a while ago from a couple of papers and I can only remember the phenomenology, without any precise information.

Answer 1

The cases you describe are

(a) In reactions with a low activation barrier with respect to thermal energy ($k_BT$) the rate constant will be limited by diffusion together of the two species since they react on first collision. The rate constant is thus limited by the viscosity of the solvent.

(b) If there is a large activation barrier vs $k_BT$ the species still collide just as often as in the diffusion limited case, but most collisions are ineffective because they do not have enough energy to surmount the barrier and so the rate constant is small.

(c) It is a fundamental assumption in transition state theory that reactants and products are maintained in Maxwell-Boltzmann equilibrium. This means that relaxation of products and reactants must be faster than reaction rate, but if the temperature is extremely high this may not be achievable and the reaction rate could drop, vs. that at a lower temp, since there is not time for the product to be stabilised before it recrosses the barrier to form reactants. (This could probably also happen in a low pressure gas where stabilising collisions are rare or effectively absent)