Decay of metastable phases in a model for the catalytic oxidation of CO

Abstract

We study by kinetic Monte Carlo simulations the dynamic behavior of a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O $\to$ CO$_2$ on a catalytic surface. Finite-size scaling analysis of the fluctuations and the fourth-order order-parameter cumulant show that below a critical CO desorption rate, the model exhibits a nonequilibrium first-order phase transition between low and high CO coverage phases. We calculate several points on the coexistence curve. We also measure the metastable lifetimes associated with the transition from the low CO coverage phase to the high CO coverage phase, and {\it vice versa}. Our results indicate that the transition process follows a mechanism very similar to the decay of metastable phases associated with {\it equilibrium} first-order phase transitions and can be described by the classic Kolmogorov-Johnson-Mehl-Avrami theory of phase transformation by nucleation and growth. In the present case, the desorption parameter plays the role of temperature, and the distance to the coexistence curve plays the role of an external field or supersaturation. We identify two distinct regimes, depending on whether the system is far from or close to the coexistence curve, in which the statistical properties and the system-size dependence of the lifetimes are different, corresponding to multidroplet or single-droplet decay, respectively. The crossover between the two regimes approaches the coexistence curve logarithmically with system size, analogous to the behavior of the crossover between multidroplet and single-droplet metastable decay near an equilibrium first-order phase transition.