Recombination Kinetics in Low Dimensions

The laws of chemical reaction kinetics are seen that constant stirring produces the customarily used for recombination kinetics, classical result, the effects of partial This implies time—independent rate constants stirring are not yet clear, since partial (K). For instance, for the triplet exciton stirring is characterized, in part, by diffusion fusion process A + A + A 2 , leading to delayed and, in part, by classical behavior. This is fluorescence, one gets investigated in the current work. F = KP 2 K = constant (1) In Fig. 1 we compare the A + A + A 2±with the where F designates the delayed fluorescence and A + B + AB+ reactions for the 1-dim topology. P the phosphorescence. This relation has been We observe that trends of the A + A reaction are questioned 1 in experiments with isotopic mixed paralleled in the A + B reaction: The nonnaphthalene single crystals at low temperatures. constant K = K(t) in the diffusion-limited case Further corroboration is given by computer and the constant K in the well-stirred case. simulations, where a chemical reaction is In Fig. 2 we investigate the effect of simulated using random walk models for the stirring on the reaction rate. There is no reacting species,2 showing that K = K(t) goes conventional method of such stirring available down monotonically with time for low-dimensional and the consequences for the rate coefficient reaction spaces. This is the case when the are not immediately obvious. We tried several reacting-particle motion is diffusion-limited, models, covering the whole range from no stirWe monitor the diffusion limited process of ring (a), to the case of a well-stirred reaction reactions by introducing the idea of stirring (b), where all particles are stirred constantly, the reactants during the course of reaction. i.e. at each time-step. Intermediate mechanisms Stirring has an effect of breaking up the noninclude: (I) Stirring of all particles once random spatial and temporal distri-butions every 400 steps (c); (11) stirring of a fraction caused by the reaction. While it is easily (1%) of particles only (d), randomly chosen;