KINETIC TRANSITIONS IN DIFFUSION-REACTION SPACE

In this paper we study how the strength and range of the potential function upsilon(r) governing the down-range motion of a diffusing coreactant A with respect to a stationary target molecule B influence the efficiency of the irreversible diffusion-reaction process: A+B-->C. This problem is translated into the lattice-statistical one of determining the mean walklength before trapping of the species A on a lattice of N sites of coordination nu and dimension d. Factors affecting the reaction efficiency are explored and quantified using a combination of analytical methods and numerical techniques rooted in the theory of finite Markov processes. Our results show that there exists a transition between two qualitatively different types of behavior in diffusion-reaction space, viz., a regime where the coreactant's motion is totally correlated with respect to the target species, and a regime where the coreactant's motion is totally uncorrelated. The transition between these two regimes is (relatively) abrupt, and we find that significant changes in the reaction efficiency can be induced by small changes in the strength and range of the correlations between coreactants, the temperature and/or the dielectric constant of the medium. This ''order-disorder'' behavior is characterized as a kinetic transition in diffusion-reaction space, and is explored as a function of system size and spatial dimension.