Critical properties of the Ziff, Gulari, and Barshad (ZGB) model with inert sites

Abstract

We study the model proposed by Ziff, Gulari, and Barshad to mimic the oxidation of carbon monoxide (CO) in the presence of fixed impurities distributed over the catalytic surface. Our focus is on the continuous phase transition between the active phase, where occurs the production of carbon dioxide (CO2), and the inactive phase, where all the non inert sites become filled with oxygen molecules. We employ Monte Carlo simulations to calculate the different ratios between moments of the order parameter at the critical point, as well as, we determine the critical exponents β and ν⊥ as a function of the concentration of impurities. We show that the presence of impurities over the catalytic surface changes the critical behavior of the system. The critical exponents depend on the concentration of impurities and the model does not belong to the directed percolation universality class.

Dynamical critical behavior of the Ziff–Gulari–Barshad model with quenched impurities

“…We observed a very small variation of the critical value of y CO as we increase P d . Like as in our previous work [1] concerning the static critical properties of the model, we also found here that the dynamic critical exponents also depend on the concentration of the quenched inert sites. Particularly, the exponent η, which is the exponent associated to the mean number of empty sites n v (t) strongly depends on the concentration, decreasing as a function of P d .…”

“…We also investigated the change observed in the universality class of the ZGB model due to presence of fixed impurities over the lattice, so that some sites are forbidden for adsorptions. The net effect of these inert sites is to change the universality class of the model [1]. The static critical exponents change with the concentration of quenched impurities in agreement with the Harris criterion [35] for this model, since the presence of inert sites work as a weak disorder in the system.…”

“…In a recent work [1] we have investigated the static critical properties of the Ziff, Gulari, and Barshad (ZGB) model [2] in the presence of fixed impurities over a catalytic surface. Through Monte Carlo simulations [3] we have determined the coverages of species for different values of the density of impurities and calculated the static critical exponents associated with the order parameter and spatial correlation length, β and ν ⊥ , respectively.…”

Reversible Reshaping of Supported Metal Nanoislands Under Reaction Conditions in a Minimalistic Lattice Model

“…Also, these considerations provide an idea about the current place of such minimalistic models (considered as sub-networks of more involved realistic reaction networks) in the spectrum of existing approaches as a complement to ever developing experimental and first principle studies. Recent examples include surface oxide models [31,36], models of CO oxidation accompanied by surface reconstruction [30,32,34], in the presence of surface impurities [17] and gas phase impurities [1,2], distinguishing hollow and bridge surface sites [24].…”

Mapping the phase transitions of the ZGB model with inert sites via nonequilibrium optimizing methods

“…In this paper, we include to the original model the existence of inert sites (or impurities) over the surface (see, for example, Ref. [12]). So, our intent is to analyse the two phase transitions of the original model when the adsorption rate and the density of inert sites vary.…”