Kinetics of diffusion-limited reactions in confined domains: Spatio-temporal studies with experiments and numerical calculations

The kinetics laws of diffusion-controlled chemical reactions are drastically different from the conventional rate laws found in standard chemistry textbooks. The anomaly comes from the inhomogeneous, non-random distribution of reactant particles in the reaction domain. A dimensional dependence of the rate laws is the usual consequence for diffusion-controlled reactions, as the geometry strongly affects the particle distribution.; This work focuses on exploring the experimental evidence for the anomalous, non-classical kinetics of diffusion-controlled reactions in low dimensions. In the study of the trapping system, the anomalous growth of the depletion zone around a trap was observed using a laser photobleaching experiment in one- and two-dimensional geometries. The anomalous asymptotic t &thgr;/2 behavior of the &thgr;-distance [defined as the size of the depletion zone in which the reactant has been depleted to below a certain fraction &thgr; of its original concentration] has been confirmed by experiments. The imperfect bleaching of the laser phototrap generated a new kind of fast, early-time growth of the depletion zone. The results are supported by analytical equations and numerical calculations. When the trapping reaction occurred in a rectangular capillary, a non-classical dimensional crossover from two dimensions to one dimension was observed. In studies on reaction front systems, two reaction fronts were observed for a system of competing reactions. By changing the relative initial concentrations of reactants, two split fronts could be controlled to move in unison or in opposite directions. The crossover behavior for the reaction front system was studied using an analytical method and Monte Carlo simulations. Also, for the reaction front, we demonstrated that a diffusion-controlled environment can be achieved without gel by miniaturizing the reaction vessel.; The experiments not only confirmed recent theoretical predictions, such as one dimensional t1/2 and two dimensional t&thgr;/2 asymptotic time scaling for the &thgr;-distance in the trapping problem, but also triggered extensions or modifications of the simplified theoretical models, which often neglect the complex nature of the real life experimental systems, such as the imperfect trapping strength or the finite trap size in trapping problem. The interplay between experiments and theory provided a better understanding of the phenomena.