The study of catalysis calls upon many disciplines: solid state chemistry,
organic and organometallic chemistry, physical chemistry, surface
science and theoretical chemistry; the CNRS "Institut de recherches
sur la catalyse" (Catalysis Research Institute) brings together
a wide range of knowledge and experience. The team from the "Theory
and Modeling" group has been studying systems that cannot be
described by algebraic equations and has succeeded in treating non-separable
systems using a 16,000-processor machine. With their results, they
made a CD-Rom containing more than 5,000 files of mathematical models
applied to catalytic experiments.
Heterogeneous
catalysis, in particular, is a hotbed of non-linear phenomena and
represents a substantial mathematical challenge. The team has used
a Monte-Carlo method to study the problems, generating random numbers
to calculate the differential equations required.
Examples
from the CD-ROM are:
Steady
State Isotopic Transient Kinetic Analysis: isotopic exchange in
C and O was studied to determine the residence time of labeled compounds
on a catalyst and calculate the kinetic constants and the different
sites of the catalyst.
The
Eley-Rideal mechanism, studied for upgrading natural gas: hetero-homogeneous
catalysis occurring on the catalyst surface and in the gas phase.
The
Langmuir-Hinschelwood mechanism: oxidation of adsorbed CO by adsorbed
oxygen in an automobile catalytic converter; change with increasing
poisoning.
The
Mars-Van Krevelen redox mechanism, applied to oxygen adsorption
onto MgO.
Using
the Monte-Carlo Metropolis method: diffusion of a sulfur adsorbate
onto the [100] face of a platinum catalyst.
Genetic
algorithms: The application of Darwinian theories to mathematics
and catalysis. The "optimal fitness" law was applied to
sets of equations representing catalytic kinetics and the results
compared with simulated experimental data.