Application of singularity theory to modeling of steady-state multiplicity: propylene oxidation on platinum

Abstract

Two types of steady-state multiplicity patterns were observed during the isothermal oxidation of propylene over platinum wires. These patterns differ in the nature of the Ignition or extinction induced by slowly changing the propylene concentration. Changes in either the inert diluent, the wire temperature, or oxygen concentration caused a shift from one multiplicity pattern to the other. This information can be used to discard classes of kinetic models which cannot admit such a transition and to suggest the functional form of an appropriate rate expression. The process of model discrimination is greatly facilitated by the observation that the simplest model predicting this transition must have a pitchfork singularity. This information is utilized to develop the simplest rate expression which predicts the surprising shift in the multiplicity pattern. IntroductionMultiple steady states were observed in several isothermal catalytic reacting systems. When the reaction rate in these systems was determined as a function of an operating (bifurcation) variable, different types of multiplicity patterns (bifurcation diagrams) were obtained. For ex-

The Catalytic Mechanics of Dynamic Surfaces: Stimulating Methods for Promoting Catalytic Resonance

“…(76,77,78) Other examples include hydrogen oxidation on Ni, Pd, Pt, and Rh, nitrogen oxide reduction on Pd, Pt, and Rh, and CO hydrogenation on Fe and Pd, among many other passively oscillatory catalytic systems summarized by Schmidt, Schüth, and Henry (79) and Ertl and Imbihl (80) . These dynamic systems exhibit significant complexity such as the emergence of Hopf bifurcations (81,82) , the coexistence of limit cycles and multiple steady states (81,83) , and the possibility for chaotic chemical behavior (84) .…”

“…Due to the competitive adsorption of CO and oxygen, the metal catalysts transition sharply between two reactive states, a highly active saturated oxygen phase followed by a relatively inactive saturated CO phase. − Other examples include hydrogen oxidation on Ni, Pd, Pt, and Rh, nitrogen oxide reduction on Pd, Pt, and Rh, and CO hydrogenation on Fe and Pd, among many other passively oscillatory catalytic systems summarized by Schmidt, Schüth, and Henry and Ertl and Imbihl . These dynamic systems exhibit significant complexity such as the emergence of Hopf bifurcations, , the coexistence of limit cycles and multiple steady states, , and the possibility for chaotic chemical behavior …”

“…78−80 Other examples include hydrogen oxidation on Ni, Pd, Pt, and Rh, nitrogen oxide reduction on Pd, Pt, and Rh, and CO hydrogenation on Fe and Pd, among many other passively oscillatory catalytic systems summarized by Schmidt, Schuẗh, and Henry 81 and Ertl and Imbihl. 82 These dynamic systems exhibit significant complexity such as the emergence of Hopf bifurcations, 83,84 the coexistence of limit cycles and multiple steady states, 83,85 and the possibility for chaotic chemical behavior. 86 The complexity of chemical reactor dynamics further increases in response to forced oscillations in pressure, temperature, flow, or composition yielding a periodic, quasiperiodic, or chaotic chemical reactor response.…”

Analysis and modeling of multiplicity features. 2. Isothermal experiments

“…(c) Atmospheric oxidation of H2 on Pt (Volodin et al, 1982). (d) Atmospheric oxidation propylene on Pt (Sheintuch and Luss, 1983).…”

Modelling concentration oscillations in the oxidation of carbon-monoxide/propene mixtures over supported platinum catalysts

“…Isotherm al reaction rate oscillations have been described in the oxidation of propene over a P t wire by Scheintuch & Luss (1981) in the tem perature range 175-228 °C. Multiple steady states were also reported, and have been analysed using singularity theory w ith particu lar atten tio n being paid to th e interaction between m ultiple steady states, sym m etry breaking and the in terp retatio n of kinetic m easurem ents (Scheintuch & Luss 1983;Scheintuch et 1989). R ate oscillations have also been observed during th e sim ultaneous oxidation of CO and one or more alkenes, when th e alkene is 1-butene, ethene, 2-butene and a m ixture of propene and ethene (Capsaskis 1985).…”