The model introduced by Ziff, Gulari, & Barshad (1986) (ZGB) for the oxidation of carbon monoxide (CO) on a catalytic surface has provided a source of continual fascination for students of nonequilibrium phase transitions. This manifestly irreversible system exhibits transitions from an active steady state into absorbing or ‘poisoned’ states, in which the surface is saturated by oxygen (O) or by CO. The transitions attracted wide interest, spurring development of numerical and analytical methods useful for many nonequilibrium models, and uncovering connections between the ZGB model and such processes as epidemics, transport in random media, and autocatalytic chemical reactions.

The literature on surface reactions continues to expand as variants of the ZGB scheme are explored. In this chapter we do not attempt to give even a partial survey; we define the model, examine its phase diagram, and describe mean-field and simulation methods used to study it.

The Ziff–Gulari–Barshad model

To begin, let us describe some facts about the oxidation of CO, a catalytic process of great technological importance; see Engel & Ertl (1979). (An immediate poison is converted into a global one!) The reaction, which is catalyzed by various platinum-group metals, proceeds via the Langmuir—Hinshelwood mechanism: to react, both species must be chemisorbed. CO molecules adsorb end-on, and require a relatively small area.