Phase Diagrams of the YK Surface-Reaction Model on 2D lattices with Exchange Diffusion

TL;DR

This study investigates how exchange diffusion of CO and N atoms affects the YK surface-reaction model on square and hexagonal lattices using steady-state Monte Carlo simulations to map phase diagrams in the $(x,y)$ plane for several values of the nitric oxide dissociation rate $r_{NO}$. The results show that exchange diffusion enables a steady reactive state on square lattices and expands the active phase region on hexagonal lattices, with the transition structure comprising a continuous boundary and a discontinuous boundary between active and absorbing states; at $r_{NO}=1$, the continuous transition is suppressed except for very small $x$. The work demonstrates that diffusion processes and lattice geometry qualitatively alter non-equilibrium catalytic models and provides detailed phase diagrams for the YK model incorporating exchange diffusion. This first systematic analysis of exchange diffusion in the YK framework advances understanding of how particle mobility influences surface-catalyzed reactions with multiple adsorbates.

Abstract

In this work, we investigate the phase diagrams of the Yaldram and Khan catalytic surface model on square and hexagonal lattices when exchange diffusion is allowed for carbon monoxide (CO) and nitrogen (N) atoms. To reach our goal, we carried out steady-state Monte Carlo (MC) simulations over $4\times 10^5$ points, for both lattices, in order to obtain a framework of the steady reactive state of the model for different values of the nitric oxide dissociation rate, $r_{NO}$. The results show the emergence of steady reactive state for certain values of $r_{NO}$ and of exchange diffusion rate $x$ when the simulations take place on square lattices. Our findings on the hexagonal lattice also show that the diffusion of these species favors the appearance of the active phase for values of $r_{NO}$ lower than that found for the standard model. In addition, we observed that the system possesses a continuous phase transition and a discontinuous one separating the active phase from absorbing states for both lattices, except for $r_{NO}=1$ in which the continuous phase transition is destroyed and a steady reactive state emerges from the beginning since very small values of $x$.

Figures (6)

• Figure 1: Phase diagram of the YK model for (a) square and (b) hexagonal lattices for $r_{NO}=0.750$. Each figure shows $4\times 10^5$ points in $(x,\ y)$ space, each one representing the density of vacant sites, $\rho_V$. The black color stands for poisoned states, i.e., $\rho_V=0$.
• Figure 2: Phase diagram of the YK model for (a) square and (b) hexagonal lattices for $r_{NO}=0.800$. Each figure shows $4\times 10^5$ points in $(x,\ y)$ space, each one representing the density of vacant sites, $\rho_V$. Black color stands for poisoned states, i.e., $\rho_V=0$.
• Figure 3: (a) Phase diagram of the YK model for square lattices for $r_{NO}=0.900$. (b) Density of vacant sites, $\rho_V$, as function of the adsorption rate $y$ for square lattices and different values of $x$. The densities were estimated by considering $N=2\times 10^4$ MC steps.
• Figure 4: Densities $\rho_s$ of the species presented in the YK model for $r_{NO}=0.900$ as function of the adsorption rate $y$ for square lattices and different values of $x$: (a) $x=0$, (b) $x=0.001$, (c) $x=0.500$, and (d) $x=1.000$. The densities were obtained with $N=2\times 10^4$ MC steps.
• Figure 5: Phase diagram of the YK model for (a) square and (b) hexagonal lattices for $r_{NO}=1.000$. Each figure shows $4\times 10^5$ points in $(x,\ y)$ space, each one representing the density of vacant sites, $\rho_V$. The black color stands for poisoned states, i.e., $\rho_V=0$.