Article

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

Faculté des Sciences Appliquées, Universté Libre de Bruxelles, CP165/63, Av. F. Roosevelt 50, 1050 Bruxelles, Belgium.
The Journal of Physical Chemistry A (Impact Factor: 2.77). 01/2009; 112(51):13452-7. DOI: 10.1021/jp8056674
Source: PubMed

ABSTRACT The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

0 Bookmarks
 · 
178 Views
  • [Show abstract] [Hide abstract]
    ABSTRACT: By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.
    Physical Chemistry Chemical Physics 12/2011; 13(45):20162-71. · 3.83 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This work presents a new experimental kinetic study at 39° and 50° of the iodine oxidation by hydrogen peroxide. The results allow us to obtain the temperature effect on the rate constants previously proposed at 25° for our model of the Bray-Liebhafsky oscillating reaction (G. Schmitz, Phys. Chem. Chem. Phys. 2010, 12, 6605.). The values calculated with the model are in good agreement with many experimental results obtained under very different experimental conditions. Numerical simulations of the oscillations observed formerly by different authors are presented, including the evolutions of the iodine, hydrogen peroxide, iodide ions and oxygen concentrations. Special attention is paid to the perturbing effects of oxygen and of the iodine loss to the gas phase.
    Physical Chemistry Chemical Physics 03/2011; 13(15):7102-11. · 3.83 Impact Factor

Full-text (3 Sources)

View
79 Downloads
Available from
May 23, 2014