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: 2.78). 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.

Download full-text


Available from: Željko D Čupić, Sep 03, 2015
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The kinetics of the iodine oxidation by hydrogen peroxide is a complicated function of the concentrations of iodine, hydrogen peroxide, perchloric acid and iodate. A proposed model in eight steps explains the new experimental results. It explains also the effect of the concentrations at the steady state of the hydrogen peroxide decomposition catalyzed by iodine and iodate. Without iodate added initially, the iodine oxidation by hydrogen peroxide is preceded by an induction period that depends on the oxygen concentration. A simple extension of the proposed model gives a semi-quantitative explanation of the oxygen effect and allows simulations of the Bray-Liebhafsky oscillations at 25 degrees C.
    Physical Chemistry Chemical Physics 04/2010; 12(25):6605-15. DOI:10.1039/b927432d · 4.20 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. DOI:10.1039/c1cp00006c · 4.20 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Isomeric structure of diphenyl urethane during synthesis from phenylisocyanate and phenol has been investigated by modeling the reaction extent as an inverse kinetic problem, using FT-IR difference spectroscopy, to obtain structural information on the formation of the isomeric structure. The aim of this study was to determine the primary algebraic structures (an inverse problem), which describe the chemical reaction system in terms of spectroscopic observables. Moreover, a conventional description of the evolution of chemical species and of the change of moles of the observable species, as a function of time, was explored, defined in terms of the extent of reaction ξ and the reaction stoichiometries ν, based on the Jouguet-de Donder equation, for an invariant system in batch experiments. Two processes for diphenyl urethane with hydrogen bonding and their free form were identified. Experimental input for the identification is a matrix of in situ spectroscopic data A (FT-IR/ATR spectra measured during the reaction process) and a matrix of initial moles (N(0)). Subsequently, (1) the number of observable reactions present, (2) the change of moles and their extent of reactions ξ, (3) the reaction stoichiometries v, (4) the concentration of all observable species (C), and finally (5) the kinetic rate constants were determined. Meaningful extraction of such algebraic system information (an inverse algebraic problem) is a mandatory prerequisite for the subsequent detailed kinetic modeling (an inverse kinetic problem). This research opens up the possibility of modeling the extent of the reaction and performing a kinetic analysis of the hydrogen bonding in an organic system. Important information could be extracted, for understanding of different functions and interactions of hydrogen bonding in a supramolecular system.
    The Journal of Physical Chemistry A 06/2011; 115(32):8832-44. DOI:10.1021/jp202227d · 2.78 Impact Factor
Show more