The principle of critical simplification in chemical kinetics

Yablonsky, Grigoriy; Mareels, Iven; Lazman, Mark

doi:10.1016/j.ces.2003.08.004

Cited by 19 publications

(12 citation statements)

References 4 publications

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“…A phenomenon of the bifurcational parametric simplification was presented as a generalization and a justification of the critical simplification principle described in [16]. The parametric simplification was applied to the Langmuir model using its transformation to the slow-fast dynamic system based on the concept of singularly perturbed vector fields [5].…”

Section: Discussionmentioning

confidence: 99%

“…The bifurcational parametric simplification was first described in papers of Yablonsky et al [15], [16] under the name of "critical simplification" for the famous Langmuir absorption model of heterogeneous catalytic kinetics. They observed an essential simplification of the kinetics at extinction and ignition points that permitted them to find simple connections between the values of "bifurcation parameters" and kinetic constants [16], [19]. As "bifurcation parameters" were used the maximal kinetic rate R 3 , is an observable quantity.…”

Section: Conjecture 1 the Maximal Bifurcational Simplification Number...mentioning

confidence: 99%

“…It means that the third row of the matrix is a linear combination on the first and second rows, Row 3 = −(Row 1 + Row 2 ). This relation gives us the existence of a well known linear integral which relates to catalyst mass conservation low [16] x + y + z = 1.…”

Section: Kernel Of the Stochiometric Matrixmentioning

confidence: 99%

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About Bifurcational Parametric Simplification

Gol’dshtein¹,

Krapivnik²,

Yablonsky³

2015

Preprint

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A concept of "critical" simplification was proposed by Yablonsky and Lazman in 1996 [15] for the oxidation of carbon monoxide over a platinum catalyst using a Langmuir-Hinshelwood mechanism. The main observation was a simplification of the mechanism at ignition and extinction points. The critical simplification is an example of a much more general phenomenon that we call a bifurcational parametric simplification. Ignition and extinction points are points of equilibrium multiplicity bifurcations, i.e., they are points of a corresponding bifurcation set for parameters.Any bifurcation produces a dependence between system parameters. This is a mathematical explanation and/or justification of the "parametric simplification". It leads us to a conjecture that "maximal bifurcational parametric simplification" corresponds to the "maximal bifurcation complexity."This conjecture can have practical applications for experimental study, because at points of "maximal bifurcation complexity" the number of independent system parameters is minimal and all other parameters can be evaluated analytically or numerically.We illustrate this method by the case of the simplest possible bifurcation, that is a multiplicity bifurcation of equilibrium and we apply this analysis to the Langmuir mechanism. Our analytical study is based on a coordinate-free version of the method of invariant manifolds (proposed recently [5]). As a result we obtain a more accurate description of the "critical (parametric) simplifications."With the help of the "bifurcational parametric simplification" kinetic mechanisms and reaction rate parameters may be readily identified from a monoparametric experiment (reaction rate vs. reaction parameter).

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Section: Discussionmentioning

confidence: 99%

Section: Conjecture 1 the Maximal Bifurcational Simplification Number...mentioning

confidence: 99%

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About Bifurcational Parametric Simplification

Gol’dshtein¹,

Krapivnik²,

Yablonsky³

2015

Preprint

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“…However, it was shown that a relatively simple equation can be obtained for the rate of catalytic CO oxidation at the saddle-node bifurcation point. 19 A combination of bifurcation theory and singular perturbation simplifies the mathematical description of critical behavior and results in relatively simple rate equations. This notion of 'principle of critical simplification' (PCS) has the advantage of being capable of system description by competing processes without isolation of limiting steps typically used in classical quasi-stationary treatments.…”

Section: Introductionmentioning

confidence: 99%

Frequency of negative differential resistance electrochemical oscillators: theory and experiments

Kiss

Pelster

Wickramasinghe

et al. 2009

Phys. Chem. Chem. Phys.

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An approximate formula for the frequency of oscillations is theoretically derived for skeleton models for electrochemical systems exhibiting negative differential resistance (NDR) under conditions close to supercritical Hopf bifurcation points. The theoretically predicted omega infinity (k/R)1/2 relationship (where R is the series resistance of the cell and k is the rate constant of the charge transfer process) was confirmed in experiments with copper and nickel electrodissolution. The experimentally observed Arrhenius-type dependence of frequency on temperature can also be explained with the frequency equation. The experimental validity of the frequency equation indicates that 'apparent' rate constants can be extracted from frequency measurements of electrochemical oscillations; such method can aid future modeling of complex responses of electrochemical cells.

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“…It has been commonly accepted in heterogeneous catalysis that CO reaction with O 2 over a Pt surface proceeds via the Langmuir-Hinshelwood (LH) Mechanism, i.e., both reactants adsorb on Pt surface prior to their reaction to yield CO 2 [6,11]. Oscillations occurred between two LH reaction branches, one of which the Pt surface is mainly covered by dissociative adsorbed oxygen (O ads ) and the other, by molecular adsorbed carbon monoxide (CO ads ).…”

Section: Discussionmentioning

confidence: 99%

Pd modified CO sensors with oscillatory response

Li¹,

Włodarski²,

Akolekar³

et al.

Proceedings of IEEE Sensors, 2004.

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In this paper, oscillatory changes in the conductance of Pd modified SnO 2 bead and Pd modified Pt coil in the presence of CO were investigated and compared. Changes in frequency were found for both sensors with varied CO concentrations. For the Pd modified SnO 2 sensor, the frequency of the waveform increased with increasing CO concentration, while for the Pd modified Pt coil, the frequency decreased. Influences of the surface temperature to CO responses were examined. The selectivity against H 2 was also tested.

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The principle of critical simplification in chemical kinetics

Cited by 19 publications

References 4 publications

About Bifurcational Parametric Simplification

About Bifurcational Parametric Simplification

Frequency of negative differential resistance electrochemical oscillators: theory and experiments

Pd modified CO sensors with oscillatory response

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