Phenomenological approach to thermally assisted tunneling

Most of low-temperature reactions proceed faster than would be predicted by an Arrhenius-type extrapolation from the high-temperature regions. The def initions of low- and high-temperature regions are quite conditional, depend ing strongly on the properties of the host matrix for a given reactant. The transition from the low-temperature region to the high-temperature region, manifested by a break in an Arrhenius plot, is accompanied by the marked d ecrease of reaction dispersivity. In the low-temperature region, the specif ic reaction rates depend on time. For a time-dependent specific reaction ra te, using the concept of the energy profile along the reaction path, one fi nds the potential energy barrier separating reactants from products to evol ve in time during the reaction course. This evolution, in the Gamov picture for a simple rectangular barrier of constant height, is described in terms of a distribution function for the tunneling distance, related directly to the distribution function of logarithms of lifetimes calculable from the k inetic equation with a time-dependent specific reaction rate. In the high-t emperature region, classical kinetics with a constant specific reaction rat e provides a good approximation. This is rationalized in terms of the stoch astic model of reaction kinetics in the renewing environment. In the model, the structural relaxation of the host matrix is included by imposing upon the static disorder model the additional assumption that at random the rein itialization occurs. The reinitialization consists of random reassignment o f guest hopping rates with the values having the same initial distribution. Therefore, the breaks in Arrhenius plots might be taken to be an indicatio n of the onset of thermal assistance for tunneling, not necessarily of the change from quantum mechanical under barrier transition to thermally activa ted over barrier transition. As an example, the reactions of excess electro ns in aqueous systems are discussed.