The Ziff–Gulari–Barshad (ZGB) model is a simple
Monte Carlo method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be determi ...
for
catalytic reaction
Catalysis () is the process of increasing the rate of a chemical reaction by adding a substance known as a catalyst (). Catalysts are not consumed in the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recyc ...
s of
oxidation
Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a d ...
of
carbon monoxide
Carbon monoxide (chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simple ...
to
carbon dioxide
Carbon dioxide (chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is transpar ...
on a surface using
Monte-Carlo methods which captures correctly the essential dynamics: the
phase transition
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of ...
between two poisoned states (either CO
2- or O-poisoned) and a
steady-state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p'' ...
in between. It is named after Robert M. Ziff, Erdogan Gulari, and Yoav Barshad, who published it in 1986.
Model definition
The model consists of three steps:
* ''Adsorption'' of the reacting species
CO and
O2
* The actual ''reaction step'' on the surface: CO + O → CO
2
* Desorption of the products.
The simplest implementation considers the catalyst as simple square two-dimensional
lattice, but one can also consider other kinds of underlying lattices. When a gas-phase molecule touches an empty site, adsorption occurs immediately and the chemical reaction is also instantaneous. Furthermore, assumes that the composition of the
gas phase remains constant.
Results and other work
The model belongs to the
universality class
In statistical mechanics, a universality class is a collection of mathematical models which share a single scale invariant limit under the process of renormalization group flow. While the models within a class may differ dramatically at finite s ...
of
directed percolation
In statistical physics, directed percolation (DP) refers to a class of models that mimic filtering of fluids through porous materials along a given direction, due to the effect of gravity. Varying the microscopic connectivity of the pores, these ...
. The model was modified several times.
References
Chemical physics
Monte Carlo methods
Statistical mechanics
Computational physics
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