Reaction Kinetics in Fractals

Kinetic Scaling Behavior of the Two-Species Annihilation Reaction with Input

“…This is a remarkable advantange in view of the fact that, particularly in lowdimensional media, diffusion-controlled reactions may be anomalous in the sense that the effective reaction order could be different than that expected according to the classical rate theory. 3 Equation 6 can be solved for both the LCK and GCK cases. For the case of independent A and B inputs (GCK), the quantity of interest is the standard deviation of the particle number difference γ 2 (r,t), 14 which in the case of an infinite volume is expected to behave as…”

“…This result also validates the analytical calculations performed in ref because by working with the difference in the concentration of species, as already discussed in the context of eqs and , the theoretical results become independent of the reaction order. However, the exponent X = 3 is the well-known anomalous reaction order of the diffusion-controlled reaction of the same type of species, i.e., A + A → 0, see e.g., ref . On the basis of the assumption that the type of particle, either A or B , is irrelevant when the coarsening process becomes stabilized, it is possible to outline some heuristic arguments in order to explain the obtained reaction order.…”

“…The study and understanding of heterogeneous reactions is a challenging topic in several branches of science, including chemical kinetics, surface and solid state physics, surface physical chemistry, biological and ecological systems, etc. − Within this broad context, the behavior of even simple reactions, involving only few species, is still not very well understood. A typical example is the annihilation reaction between different species that leads to inert products, e.g., the two-species diffusion-limited reaction of the type − ,− A + B → 0 which is also of interest in chemical kinetics and solid-state reactions: e.g., electron–hole, soliton-antisoliton, and defect–antidefect recombination . Further potential interest arises for the understanding of matter–antimatter annihilation in the early universe , and catalytic reactions .…”

“…19 Also, this type of reaction occurring in low-dimensional and fractal media exhibits a rich physical behavior including segregation of the reactants 5,6 and anomalous reaction orders. 3 The usefulness of the two-species diffusion-limited reaction model is greatly increased when one relaxes the restriction that the reaction must be irreversible. By allowing for back reactions, the model becomes suitable for the description of other systems where the onset of stationary states and the kinetic approach to that regime are relevant features of interest.…”

“…Further potential interest arises for the understanding of matter–antimatter annihilation in the early universe , and catalytic reactions . Also, this type of reaction occurring in low-dimensional and fractal media exhibits a rich physical behavior including segregation of the reactants , and anomalous reaction orders …”