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

EZEQUIEL V ALBANO

JOURNAL OF PHYSICAL CHEMISTRY C

AMER CHEMICAL SOC

Año: 2011 vol. 115 p. 24267 - 24273

1932-7447

We present an extensive simulation study of the kinetic behavior of thetwo-species annihilation reaction of the type A + Bf0, with input of species that takesplace immediately after each reaction event. Simulations are performed by using latticesof length L in d = 1 dimension. Two different types of processes are considered: (i) thelocally conservative kinetic (LCK) case, which involves the conservation of the densitiesof both types of particles during the whole reaction, and (ii) the so-called globallyconservative kinetic (GCK) case where the total density of particles still remainsconstant, but after each reaction event, the type of particle to be introduced into the system is selected at random with the sameprobability. By starting from a random distribution of particles, it is found that the reaction rate, given by the number of reactionevents per unit of time and length, decreases as a power law of the time according to Rate
t
β, with β = 1/2 and β = 1/4 for theGCK and LCK cases, respectively. It is found that the GCK never leads to the occurrence of a steady state, and the fluctuations of thedensity difference between different types of species in the lattice grow as Æγ2(t)æ
tδ, where δ = 1 is an exponent. However, for theLCK case, we observe that after a crossover time of the order of τ
Lz, where z = 2 is a dynamic exponent, the systems reachstationary regimes, such that Ratestat
FX, where F is the density of the species, and X = 3 is the (anomalous) reaction order. Oursimulation results not only confirm some existing analytical predictions but also, in many kinetic scaling aspects, go beyond thepresent knowledge addressing new and interesting theoretical challenges.