Summary

This chapter continues the theme of simulation of dynamic processes in zeolites, but concentrating on dynamical Monte Carlo (MC) methods, which are widely used in physics and engineering [1–6] and which were introduced in the previous chapter. They are useful to probe the kinetics of heterogeneously catalyzed reactions, e.g. which often exhibit very complex nonlinear dynamic behavior including multiple steady states, oscillations, chemical waves, bifurcation, and chaos. Mean field rate equations of chemical kinetics, on the other hand, typically neglect selfestablished correlations between the reactant species. A broad variety of surface reactions have been studied by MC methods. Reviews on this subject were published, e.g. by Albano [7], Kang and Weinberg [8], Gelten et al. [9], and Gelten [10]. A problem associated with MC simulations is the dynamic interpretation of the MC results. MC simulations use ‘jumps’ instead of the real time. Fichthorn and Weinberg [11] have demonstrated that within the theory of Poisson processes, both static and dynamic properties of Hamiltonian systems may be consistently simulated with the benefit that an exact correspondence between MC time and real time can be established in terms of the dynamics of individual species comprising the ensemble. Molecules should not all be moved at the same time during the simulations, one after the other, or according to some other fixed scheme, as this is not only unrealistic but may also lead to persistent errors in the asymptotically obtained results. Instead, one should think in terms of events that are Poisson-distributed in time. Reaction probabilities are replaced by rate constants. With an event-oriented method and knowledge of the times needed for each microscopic event, problems can be avoided, because the clock is advanced every time an event occurs, and the event-list is updated. In cases where the microscopic events are unknown, some reference time needs to be defined. There are different approaches to implement a dynamic MC simulation. Fichthorn and Weinberg [11] introduced the variable step-size method, and Gillespie [12] and Jansen [13] the discrete event simulation.