A simplified stochastic description for the A+B2 surface reaction including A diffusion

Infinitely fast diffusion in single-file systems

We have used dynamic Monte Carlo(DMC) methods and analytical techniques to analyze single-file systems for which diffusion is infinitely fast. We have simplified the master equation removing the fast reactions, and we have introduced a DMC algorithm for infinitely fast diffusion. The DMC method for fast diffusion give similar results as the standard DMC with high diffusion rates. We have investigated the influence of characteristic parameters, such as pipe length, adsorption, desorption, and conversion rate constants on the steady-state properties of single-file systems with a reaction, looking at cases when all the sites are reactive and when only some of them are reactive. We find that the effect of fast diffusion on single-file properties of the system is absent even when diffusion is infinitely fast. Diffusion is not important in these systems. Smaller systems are less reactive and the occupancy profiles for infinitely long systems show an exponential behavior.

Transient behavior in single-file systems

We have used Monte Carlo methods and analytical techniques to investigate the influence of the characteristics, such as pipe length, diffusion, adsorption, desorption, and reaction rates on the transient properties of single-file systems. The transient or the relaxation regime is the period in which the system is evolving to equilibrium. We have studied the system when all the sites are reactive and also when only some of them are reactive. Comparisons between mean-field predictions, cluster approximation predictions, and Monte Carlo simulations for the relaxation time of the system are shown. We outline the cases where the mean-field analysis gives good results compared to dynamic Monte Carlo results. For some specific cases we can analytically derive the relaxation time. Occupancy profiles for different distributions of the sites both for the mean field and simulations are compared. Different results for slow and fast reaction systems and different distributions of reactive sites are discussed.