The Ziff-Gulari-Barshad (ZGB) model is a statistical model most commonly implemented to simulate catalytic reactions.[1]
The original paper presented ZGB as a deviation from the classical approach to catalyst kinetics, i.e. the tendency "to consider only average concentrations of the adsorbed species, and to write systems of differential equations of varying complexity with multiple parameters."
The oxidation of CO is an important process in automobile emission control and a "prime example of heterogeneous catalysis." The reaction occurs as follows:
In the reactions above, ads indicates a molecule that is adsorbed on the catalyst surface. When adsorbed, the O2 disassociates into two O atoms which occupy two separate catalyst surface sites. The CO molecule occupies a single surface site. In the final step, CO2 is produced and desorbs from the surface.
The ZGB model treats the catalyst in this reaction as a "simple square two-dimensional lattice" of active sites. In order to simplify the kinetics, the model also assumes that:
In the ZGB simulation, a trial begins with the random collision of a gas molecule on the square lattice that represents the catalyst surface. The probability of the colliding molecule being CO is expressed as yCO, while the probability of the colliding molecule being O2 is expressed as 1 - yCO.