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Bifurcation analysis on Pt and Ir for the reduction of NO by CO.



INTRODUCTION

Automotive emissions are a major contributor to air pollution. The main atmospheric pollutants from vehicles are nitrogen oxides ([NO.sub.x]), unburned hydrocarbons (HC) and carbon monoxide carbon monoxide, chemical compound, CO, a colorless, odorless, tasteless, extremely poisonous gas that is less dense than air under ordinary conditions. It is very slightly soluble in water and burns in air with a characteristic blue flame, producing carbon dioxide;  (CO). To control these emissions, catalytic reduction of NOx with different reductants like carbon monoxide, hydrocarbon and hydrogen is being explored. Current catalytic converters provide a high level of emission control The selective and controlled use of electromagnetic, acoustic, or other emitters to optimize command and control capabilities while minimizing, for operations security: a. detection by enemy sensors; b. mutual interference among friendly systems; and/or c.  by the removal of NO, CO and HC under stoichiometric stoi·chi·om·e·try  
n.
1. Calculation of the quantities of reactants and products in a chemical reaction.

2. The quantitative relationship between reactants and products in a chemical reaction.
 condition in gasoline engines. The NO-CO reaction plays a prominent role in the catalytic converter catalytic converter: see internal-combustion engine.
catalytic converter

In automobiles, a component of emission control systems used to reduce the discharge of noxious gases from the internal-combustion engine.
, as the exhaust from automobiles contains sufficient amount of CO. First reported literature (Kobylinski and Taylor, 1974) and as well as the more recent articles (Chambers et al., 2001; Granger et al., 2002) on the NO-CO reaction indicate good activity of Pt group catalysts.

Oscillations oscillations See Cortical oscillations.  and bistability in heterogeneous catalytic reactions are well known. Oxidation of CO by [O.sub.2] on a Pt surface is the renowned example in this category. Extensive literature is available for the NO-CO reaction specially related to oscillation Oscillation

Any effect that varies in a back-and-forth or reciprocating manner. Examples of oscillation include the variations of pressure in a sound wave and the fluctuations in a mathematical function whose value repeatedly alternates above and below some
 and bistability at low pressure conditions on the Pt catalyst surface. Detailed reaction mechanisms have been proposed for the NO-CO reaction on Pt(100), which shows bifurcations, kinetic oscillations, and multiple steady states under ultra high vacuum Ultra high vacuum (UHV) is the regime characterised by pressures lower than about 10−7 pascal or 100 nanopascals (~10−9 torr). UHV requires the use of special materials, extreme cleanliness, and baking the entire system to remove water and other  ([10.sup.-6]-[10.sup.-7] bar) conditions due to complex surface dynamics (Fink fink   Slang
n.
1. A contemptible person.

2. An informer.

3. A hired strikebreaker.

intr.v. finked, fink·ing, finks
1. To inform against another person.
 et al., 1992; Makeeva and Kevrekidis, 2004). It was found that oscillations are observed when [C.sub.NO]/[C.sub.CO] is greater than one and in the temperature range of 100-250[degrees]C (Frank et al., 1997; Sadhankar and Lynch, 1997). Cobden et al. (2000) observed that Ir(110) shows bifurcations for the NO-[H.sub.2] reaction at 200[degrees]C under [10.sup.-7] bar pressure when [C.sub.NO]/[C.sub.H2] = 0.05. Recently, oscillatory oscillatory

characterized by oscillation.


oscillatory nystagmus
see pendular nystagmus.
 behaviour has been observed on Ir(110) in the temperature range 100-104[degrees]C for the [N.sub.2]O-CO reaction under ultra high vacuum conditions (Peskov et al., 2005). Janssen et al. (1997) report in a review paper that rate oscillations have been observed only on Pt(100). The Pt(111) and Pt(110) surfaces do not show any oscillatory behaviour for the NO-CO reaction under ultra high vacuum conditions, due to low NO* dissociation dissociation, in chemistry, separation of a substance into atoms or ions. Thermal dissociation occurs at high temperatures. For example, hydrogen molecules (H2  (a critical step in the NO-CO reaction) ability on these surfaces compared to Pt(100) (Janssen et al., 1997; Schwartz and Schmidt, 1988). Some experimental work on supported Pt group catalysts under atmospheric conditions, available in literature is shown in Table 1.

Despite so much literature on the experiments and modelling of bifurcation Bifurcation

A term used in finance that refers to a splitting of something into two separate pieces.

Notes:
Generally, this term is used to refer to the splitting of a security into two separate pieces for the purpose of complex taxation advantages.
 behaviour of the NO-CO reaction on Pt catalysts, several questions are unanswered. The detailed reaction mechanisms do not consider the [N.sub.2]O formation step, which is relevant at both UHV UHV Ultra High Vacuum
UHV University of Houston-Victoria (Texas)
UHV Ultra-High Voltage
UHV Upper Huallaga Valley (drug trafficking area in Peru)
UHV Ultra High Viscosity
 and atmospheric conditions. Also, the simulated results are not validated against relevant experiments. The bifurcation behaviour in experiments has not been captured quantitatively in simulations. Finally, a detailed, coherent analysis of the bifurcation and oscillations phenomena occurring at atmospheric pressure atmospheric pressure
 or barometric pressure

Force per unit area exerted by the air above the surface of the Earth. Standard sea-level pressure, by definition, equals 1 atmosphere (atm), or 29.92 in. (760 mm) of mercury, 14.70 lbs per square in., or 101.
 (which is what is industrially relevant) is missing. The aim of this paper is to address this issue, with an emphasis on Pt and Ir catalysts, and for the (111) surface and supported catalysts.

We have already proposed a detailed surface reaction mechanism for the NO-CO system on Pt catalysts and found good agreement with literature experimental results on supported Pt catalysts (Mantri and Aghalayam, 2007a). An important improvement over other reaction mechanisms is that we include the [N.sub.2]O formation in an explicit set of reactions, and are able to quantitatively capture the change in selectivity from [N.sub.2]O at lower temperatures, to [N.sub.2] at higher temperatures.

In this work, first, the validity of our proposed detailed reactions mechanism under atmospheric conditions, by comparison with literature experiments, is demonstrated for a Pt catalyst. Then, this validated reaction mechanism is incorporated in an isothermal i·so·ther·mal
adj.
Of, relating to, or indicating equal or constant temperatures.



isothermal, isothermic

having the same temperature.
 perfectly stirred reactor (PSR PSR Pulsar
PSR Poster
PSR Physicians for Social Responsibility
PSR Psychosocial Rehabilitation
PSR Pacific School of Religion
PSR Policy and Survey Research
PSR Project Study Report
PSR Pre-Sentence Report
PSR Pressure-State-Response
PSR Puget Sound Region
) model with the continuation software CONTENT 1.5. Considering different operating conditions, the bifurcation features for the NO-CO system on Pt are mapped out. Furthermore, detailed comparisons with the Ir catalyst, which also shows promise for automotive emission control, are made. Effect of temperature, inlet CO and NO concentrations, and activation energy activation energy, in chemistry, minimum energy needed to cause a chemical reaction. A chemical reaction between two substances occurs only when an atom, ion, or molecule of one collides with an atom, ion, or molecule of the other.  of NO* dissociation on the NO reduction activity and bifurcation behaviour are examined.

SURFACE REACTION MECHANISM

Surface reaction mechanisms based on elementary steps describe the reaction on a molecular level, thus this approach to reaction kinetics kinetics: see dynamics.
Kinetics (classical mechanics)

That part of classical mechanics which deals with the relation between the motions of material bodies and the forces acting upon them.
 is more widely applicable than globally fitted kinetics (which is only relevant at certain sets of operating conditions due to empirical fitting). This "microkinetic approach" helps in understanding the complex interactions between different surface species and the surface chemistry of the catalyst which is essential to realize bifurcation behaviour. Several surface reaction mechanisms (for Pt and Rh catalysts) are proposed in the literature for the reduction of NO by CO (Hecker and Bell, 1983; Oh et al., 1986; Fink et al., 1992; Granger et al., 2002; Sarkar Sarkar could mean:
  • Government in Urdu/Persian/Hindi. Colloquially in India, it is a Metonymy for the incumbent government. The Persian wordSarkar is derived from two words; 'Sar' meaning Head and 'Kar' meaning Work.
 and Khanra, 2004). However, a reliable, quantitative reaction mechanism capable of capturing experimentally observed features is not available for the NO-CO reaction. Our proposed elementary reactions mechanism for the NO-CO system on Pt and Ir catalysts mainly consists of molecular NO adsorption adsorption, adhesion of the molecules of liquids, gases, and dissolved substances to the surfaces of solids, as opposed to absorption, in which the molecules actually enter the absorbing medium (see adhesion and cohesion). , dissociation of adsorbed NO to form adsorbed N and O species, formation of [N.sub.2] and [N.sub.2]O and the oxidation of molecularly adsorbed CO to form C[O.sub.2] (Mantri and Aghalayam, 2007a). Most of the activation energy values for Pt(111) are from various literature sources, while semi-empirical Unity Bond Index-Quadratic Exponential Potential (UBI-QEP) (Shustorovich and Sellers, 1998) calculations are performed to obtain the corresponding numbers for the Ir(111). Pre-exponential factors are estimated based on transition state theory as in earlier work (Aghalayam et al., 2000b). Our proposed elementary surface reaction mechanism with the kinetic data for Pt(111) and Ir(111) is shown in Table 2.

MODEL EQUATIONS

A simple model is obtained consisting of differential equations for each of the gas and surface species. The surface reactions are included by incorporating mass balance of gas species for an isothermal perfectly stirred reactor (PS R). The balance equations for the surface species are as follows:

[GAMMA]/[N.sub.A][sup.d[theta Theta

A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option.
]NO/dt = ([r.sub.1]-[r.sub.2]-[r.sub.3]-[r.sub.5]) (1)

[GAMMA]/[N.sub.A][sup.d[theta]]N/dt = (r.sub.3]-2*[r.sub.4]-[r.sub.5]) (2)

[GAMMA]/[N.sub.A][sup.d[theta]]O/dt = ([r.sub.3] - [r.sub.9] (3)

[GAMMA]/[N.sub.A][sup.d[theta]]CO/dt = ([r.sub.7] - [r.sub.8] - [r.sub.9]) (4)

[GAMMA]/[N.sub.A][sup.d[theta]][N.sub.2]O/dt = ([r.sub.5] - [r.sub.6] (5)

where as catalyst site conservation gives:

[theta]* = 1 -[[theta].sub.NO] -[[theta].sub.CO] -[[theta].sub.[N.sub.2]O] -[[theta].sub.N] -[[theta].sub.O] (6)

The mass balance equations for the perfectly stirred reactor model for gaseous gas·e·ous
adj.
1. Of, relating to, or existing as a gas.

2. Full of or containing gas; gassy.
 species are given below:

[sup.dC]NO/dt = ([C.sup.0.sub.NO] - [C.sub.NO]) + [a.sub.v] * ([r.sub.2] - [r.sub.1]) (7)

[sup.dC]CO/dt = (C.sup.0.sub.CO] - [C.sub.CO]/[tau] + [a.sub.v] *([r.sub.8]-[r.sub.7]) (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. .] (9)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11)

where [GAMMA] is the active site density (1.25 x [10.sup.19] molecules/[m.sup.2]) of the catalyst and [N.sub.A] is the Avogadro number Avogadro's number also Avogadro number
n.
The number of molecules in a mole of a substance, approximately 6.0225 × 1023.

Noun 1.
. [C.sub.i] denotes outlet concentration of gas phase species i, [C.sup.0.sub.i] refers to the inlet concentration of species i, [tau], [a.sub.v] and [[theta].sub.k] are the space time, surface area/ volume of catalyst and fractional surface coverage of surface species k, respectively.

The reaction rates for adsorption are calculated as [R.sub.j] = [k.sub.j][C.sub.i][theta]*, where [k.sub.j] is the rate constant of reaction j, [C.sub.i] is the concentration of gas species i (NO or CO in this case) and [theta]* refers to the fractional coverage of vacant catalyst sites. The rate constant for adsorption of the species i (NO, CO) based on kinetic theory of gases is given as;

[k.sub.j] = [s.sub.j] [[RT/2[pi][M.sub.i]].sup.0.5] (12)

where, [s.sub.i] is the sticking coefficient Sticking coefficient is the term used in surface physics to describe the ratio of the number of adsorbate atoms (or molecules) that do adsorb, or "stick", to a surface to the total number of atoms that impinge upon that surface during the same period of time.  for gas species i and R is the universal gas constant universal gas constant: see gas laws.  in (g*[m.sup.2])/([s.sup.2]*mol*K). [M.sub.i] is the molecular weight of species i in g/mole and T is the temperature in K.

The reaction rate for desorption Desorption

A process in which atomic and molecular species residing on the surface of a solid leave the surface and enter the surrounding gas or vacuum.
 and surface reactions is given as [R.sub.j] = [k.sub.j][[theta].sub.k1][[theta].sub.k2], where [k.sub.1] and [k.sub.2] are the participants in the reaction j. The rate constants for desorption and surface reaction are of Arrhenius type:

[k.sub.j] = [k.sub.0] [GAMMA]/[N.sub.A] exp exp
abbr.
1. exponent

2. exponential
 (-Ea/RT) (13)

where, [k.sub.0] and Ea are the pre-exponential factor and activation energy, respectively.

RESULTS

Validation of Proposed Reaction Mechanism

Simulations are performed with the isothermal PSR model, considering the proposed reaction mechanism. These simulation results are compared with the experiments carried out by Chambers et al. (2001) for the NO-CO reaction on a 1.1 wt.% Pt/Si[O.sub.2] catalyst, with a standard NO-CO mixture (3000 ppm NO + 3400 ppm CO) and a flow rate of 100 cm3/min. Space time and surface area/volume of catalyst are taken as 0.105 s and 0.47 x [10.sup.6] [m.sup.2]/[m.sup.3], respectively, based on (Chambers et al., 2001).

The concentration profile with respect to reactor temperature for the above experiment is shown in Figure 1 (experimental results are shown by symbols). It was found that at lower temperatures (< 250[degrees]C), there is no reduction of NO. NO conversion starts at 250[degrees]C and reaches 100% at 420[degrees]C. At lower temperatures, selectivity to [N.sub.2]O was found to be higher than to [N.sub.2] and a peak was observed at 330[degrees]C for N2O N2O Nitrous Oxide (dinitrogen oxide)  concentration. At temperatures > 330[degrees]C, N2 selectivity was found to increase sharply with further increase in temperature. The concentration of CO was found to decrease with temperature and remain constant at high temperatures.

[FIGURE 1 OMITTED]

The excellent match between our simulations (shown in Figure 1 as lines) and the experimental results of Chambers et al. (2001) serves as a validation of our surface reaction mechanism. Thus, the agreement between experiments and simulations at each temperature for all the species indicates that the proposed surface reaction mechanism on Pt(111) is capable of capturing the observed trends for the NO-CO system on supported Pt catalysts. The kinetic data in our reaction mechanism has been obtained from independent theoretical formulas applicable to Pt(111), as discussed in the Surface Reaction Mechanism section, and is not fitted in any way to the experiments. We believe that for this reaction, the trends observed in supported catalysts are captured well by models for the (111) surface. This feature is reported earlier in the literature for Rh(111) and supported Rh catalysts (Belton and Schmieg, 1993; Peden et al., 1995). In other work, we have demonstrated reaction mechanisms for Rh and Ir catalysts as well, similar to the one shown here for the Pt catalyst (Mantri and Aghalayam, 2007b).

Bifurcation Analysis

The bifurcation behaviour of the system is studied by solving the model equations using the continuation software CONTENT 1.5. Simulations are performed on both Pt and Ir, with different operating conditions (temperature, inlet CO concentration and inlet NO concentration). Though multiplicity and kinetic oscillatory regimes are obtained for Pt(111), for [C.sub.NO]/[C.sub.CO] >1, no evidence of multiple steady states (MSS MSS - maximum segment size ) and oscillations are seen for Ir(111), in our simulations. It is observed that the dissociation of adsorbed NO is a key elementary step for NO reduction by CO on Pt and Ir (Mantri and Aghalayam, 2007b), considering this fact, the effect of the NO* dissociation activation energy on the bifurcation behaviour is also examined.

Effect of temperature at constant inlet CO concentration

The model is simulated for both the Pt and Ir catalysts at a fixed initial NO concentration of 3000 ppm (0.1227 mol/[m.sup.3]) and bifurcation diagrams are generated using temperature (150-500[degrees]C) as a bifurcation parameter and varying the CO concentration from 1400 ppm to 5000 ppm.

Bifurcation behaviour on Pt catalyst

The NO and CO conversions and [N.sub.2] selectivity obtained from our simulations are plotted in Figure 2, as a function of the reactor temperature, for the Pt catalyst. When the inlet [C.sub.NO]/[C.sub.CO] [less than or equal to] 1 (e.g. see the curve corresponding to [C.sub.NO]/[C.sub.CO] = 0.6), a single stationary solution is obtained at all temperatures. The same behaviour is observed for the inlet [C.sub.NO]/[C.sub.CO] = 0.88 and [C.sub.NO]/[C.sub.CO] = 1 (as shown in Figure 2). The general features seen here, such as, low conversions at temperatures < 250[degrees]C, low selectivity to [N.sub.2] at lower temperatures, and so on, quantitatively match with literature experimental results (Chambers et al., 2001) as shown in the previous section.

From our simulations, we note that the bifurcation behaviour changes as the inlet [C.sub.NO]/[C.sub.CO] ratio is changed. When [C.sub.NO]/[C.sub.CO] >1, multiple steady states (MSS) and oscillations are observed. In Figure 2, the limit points (saddle node bifurcation points) are marked as LP(*), and Hopf bifurcation In bifurcation theory a Hopf or Andronov-Hopf bifurcation is a local bifurcation in which a fixed point of a dynamical system loses stability as a pair of complex conjugate eigenvalues of the linearization around the fixed point cross the imaginary axis of the complex plane.  points are marked as H([]). Upon crossing a limit point, the solution changes from a stable to an unstable one (or vice-versa). The region between the Hopf bifurcation points is the region where oscillations occur while the region bounded by the limit points is the region where multiple solutions exist (Seydel, 1994). The limit points and the Hopf bifurcation points are automatically indicated by the CONTENT software, based on analysis of eigenvalues eigenvalues

statistical term meaning latent root.
.

In this case, when [C.sub.NO]/[C.sub.CO] = 2.1, two LP and two H points are seen in Figure 2. Thus multiple steady states exist between the temperatures ~180 and 275[degrees]C, and an oscillatory regime occurs between the temperatures 180 and 220[degrees]C. As the temperature is increased from low values, the NO conversion increases slowly, starting at around 250[degrees]C. At a temperature of 275[degrees]C, a sharp and abrupt increase in the NO conversion from a value of ~40% to ~85% will be observed due to the presence of a LP. This LP is usually termed an "ignition" and represents a sharp increase in reaction rate. Starting with high conversions of NO (termed the "ignited branch"), if the reactor temperature is reduced, another abrupt change will occur at ~180[degrees]C. However, in this case, because of the presence of a Hopf bifurcation point, the system will start to oscillate To swing back and forth between the minimum and maximum values. An oscillation is one cycle, typically one complete wave in an alternating frequency. , ultimately resulting in a drop in conversion to insignificant values. This is termed an 'oscillatory extinction'. Several combinations of real and oscillatory ignitions and extinctions have been encountered in our simulations, at various operating conditions; we report here a representative result. The intermediate conversion (~40-80% in NO conversion) branch occurring between the two LPs is a set of unstable solutions, with part of it being also oscillatory (due to the Hopf bifurcation point at 220[degrees]C). Such types of ignitions and extinctions have been previously observed experimentally on supported Pt catalysts for the NO-CO reaction (Frank and Renken, 1998).

[FIGURE 2 OMITTED]

The fractional surface coverages of the important species are plotted as a function of reactor temperature in Figure 3. For [C.sub.NO]/ [C.sub.CO] [less than or equal to] 1, the CO* fractional coverage remains fairly high. However, when [C.sub.NO]/[C.sub.CO] = 2.1, while the "extinguished" branch (i.e., branch of low conversions) corresponds to a high fractional coverage of CO* (nearly one) on the surface, at the "ignition" point, the CO comes off the surface and the catalyst gets covered by N* and O* (obtained from the dissociation of adsorbed NO). This sudden phase-transition of the Pt surface from a CO covered one to N and O covered one is possibly the reason why the multiple steady states are observed.

With an increase in the inlet [C.sub.NO]/[C.sub.CO] ratio, the ignition temperature (temperature at which limit point observed), decreases. As we can see in Figure 2, for [C.sub.NO]/[C.sub.CO] = 1.2, 1.5 and 2.1, the ignition is observed at 322[degrees]C, 299[degrees]C and 275[degrees]C, respectively. At the ignition temperature, the CO* comes off the surface and N* and O* occupy the surface (due to NO* dissociation). The same behaviour is observed for CO-[O.sub.2] reaction on Pt catalyst (Aghalayam et al., 2000a), where the ignition temperature decreases with [O.sub.2]/CO ratio and CO* crossover with O* occurs at the ignition temperature.

[FIGURE 3 OMITTED]

In order to observe the nature of the oscillations obtained, we have performed time dependent simulations as well. In Figure 4, the variation of the fractional coverage of CO with time, for the [C.sub.NO]/[C.sub.CO] = 2.1, at a temperature of 180[degrees]C, on the ignited branch, is shown. Stable oscillations with amplitude of ~0.05 are observed.

Bifurcation behaviour on Iridium iridium (ĭrĭd`ēəm), metallic chemical element; symbol Ir; at. no. 77; at. wt. 192.22; m.p. about 2,410°C;; b.p. about 4,130°C;; sp. gr. 22.55 at 20°C;; valence +3 or +4.  catalyst

The behaviour of the NO-CO reaction on Ir is found to be different than on Pt. Figure 5 and Figure 6 show the effect of temperature on NO and CO conversions and fractional coverages at various inlet [C.sub.NO]/[C.sub.CO] ratios. No multiplicity or oscillations are observed on Ir at the [C.sub.NO]/[C.sub.CO] ratios and temperature ranges studied. NO and CO conversions increase monotonically and become constant at higher temperature. Nearly complete NO conversion is obtained at temperatures > 400[degrees]C which indicates higher temperature activity of Ir than Pt catalyst. The fractional coverage of CO* on Ir is lower than on Pt. Possibly the lack of multiple steady states for Ir is attributable to the lack of severe competition between CO*, N* and O* for the catalyst sites.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Selectivity to [N.sub.2]

In the NO-CO reaction, an important (and harmful) side product is [N.sub.2]O. One of the advantages of our reaction model is that the formation of [N.sub.2]O has been explicitly accounted for. Thus, an analysis of our results in terms of selectivity to [N.sub.2] is possible. In general we find selectivity of both catalysts to [N.sub.2]O at lower temperatures (see also Mantri et al. (2004) for detailed discussion on Pt and Mantri and Aghalayam (2007b) for detailed discussion on Ir), and selectivity to [N.sub.2] at higher temperatures. Furthermore, Ir has the edge over Pt, giving better selectivities to [N.sub.2] at comparable NO conversions. However, the reaction activity of Ir is at temperatures higher than Pt as also seen in Figures 2 and 5.

Effect of inlet CO concentration at constant temperature

As bifurcations are observed only on Pt, further simulations are performed only on Pt (not on Ir) to examine the MSS behaviour. The effect of inlet CO concentration on NO reduction activity and surface coverage is analyzed in order to examine the bifurcation behaviour of Pt for the NO-CO reaction. The main focus here is to determine the temperature and inlet CO feed concentrations for which the system displays bistability. We perform the simulations with step decrease in inlet CO concentration (0.25 to 0 mol/[m.sup.3]) at different temperatures with a fixed inlet NO concentration (0.12277 mol/[m.sup.3]) and observe the effect on the outlet NO concentration. In the temperature range studied here (190-400[degrees]C), unstable and oscillatory regions are observed at specific [C.sub.NO]/[C.sub.CO] ratios. When the [C.sub.NO]/[C.sub.CO]>1, the system exhibits limit points and Hopf bifurcation points, while for [C.sub.NO]/[C.sub.CO]<1 system shows a single stable solution at all the temperatures studied here.

The temperature 275[degrees]C has been chosen as an example. In Figure 7, the outlet NO concentration is plotted as a function of the inlet CO concentration, with the temperature fixed at 275[degrees]C. The inlet NO concentration is fixed at 0.12277 mol/[m.sup.3]. For these conditions, the NO conversion increases with decrease in CO concentration and the first limit point is observed at [C.sub.CO] = 0.05762 mol/[m.sup.3] ([C.sub.NO]/[C.sub.CO] = 2.13) and the next limit point is observed at [C.sub.CO] = 0.122747 ([C.sub.NO]/[C.sub.CO] = 1.00018), which means that multiple steady states (MSS) are found only between CO concentrations of 0.05762-0.122747 mol/[m.sup.3] (shaded area in Figure 7 at 275[degrees]C and inlet [C.sub.NO] = 0.122747 mol/[m.sup.3]). When the CO concentration <0.05762 mol/[m.sup.3], Hopf points are observed (not shown in Figure). At all other inlet concentrations, the system will exhibit a single steady state at this temperature. The same qualitative behaviour is observed at other temperatures also. Sadhankar and Lynch (1997) performed experiments on 0.5%Pt/[Al.sub.2][O.sub.3] with feed conditions of 0.45% NO (0.184 mol/[m.sup.3]) and by changing CO concentration from 0 to 1.2% CO (0-0.491 mol/[m.sup.3]) at 232[degrees]C. The experimental results of Sadhankar and Lynch (1997) are shown in Figure 7b. Our simulation results (Figure 7a) are qualitatively in good agreement with these experimental results (Figure 7b). A quantitative comparison is not attempted here as more details of the experiments are required in order to perform our simulations.

[FIGURE 6 OMITTED]

Simulations are performed in order to correlate the temperature and inlet CO concentration on the occurrence of MSS behaviour. Figure 7c shows the effect of temperature on outlet NO concentration when inlet CO = 0.05762 mol/[m.sup.3] (where we observed the limit point). The limit point is observed exactly at 275[degrees]C, as expected from Figure 2.

[FIGURE 7 OMITTED]

DISCUSSION

Detailed reaction mechanism models can assist in locating the set of parameter values where unstable solutions and oscillations occur. For the NO-CO reaction, several types of bifurcations are observed, among these fold bifurcations (LP) and Hopf bifurcations (H) are of prime importance. A fold bifurcation is also known as a turning point, limit point, and saddle node bifurcation. Basically, at the turning point, two solutions are created or two solutions annihilate an·ni·hi·late  
v. an·ni·hi·lat·ed, an·ni·hi·lat·ing, an·ni·hi·lates

v.tr.
1.
a. To destroy completely: The naval force was annihilated during the attack.
 each other. Hopf bifurcation is an oscillatory bifurcation that connects a branch of equilibria with a branch of periodic solutions. Mathematically one of the important reasons for oscillations is complex/non-linear terms in the model equations. From an engineering point of view, different reasons for the occurrence of multiple steady states and oscillations have been mentioned in the literature, including:

* Exothermicity of reaction;

* Defect sites/impurities on catalyst;

* Surface structural changes;

* Blocking of active metal by carbon or [O.sub.2];

* Catalyst aging;

* Inhibition effect by the presence of adsorbate ad·sor·bate  
n.
An adsorbed substance.

Noun 1. adsorbate - a material that has been or is capable of being adsorbed
;

* Coverage dependent activation energy.

However, in our model simulations, without considering coverage dependent activation energies, non-isothermal behaviour, change in morphological structure and catalyst aging, oscillations have been observed on Pt(111) for the NO-CO reaction. We believe that in addition to the above reasons, a strong competition for the catalyst sites can result in such phenomena. This was seen in the case of Pt catalysts in our results. On the contrary, when such strong competition is not present, as is the case of Ir, where the adsorption of NO and its subsequent dissociation are very dominant compared to the reactions of CO, MSS and oscillations do not occur.

Various experimental results available on Pt surface under ultra high vacuum conditions suggest that Pt(111) does not show any oscillation due to low NO* dissociation ability. Temperature Programmed Desorption Temperature programmed desorption (TPD), also known as thermal desorption spectroscopy (TDS), is a surface science technique used to quantitatively measure thermodynamic and kinetic parameters of gas/solid desorption processes and decomposition reactions on surfaces involving  (TPD TPD Tons Per Day
TPD Therapeutic Products Directorate
TPD Total and Permanent Disablement (insurance)
TPD Temperature Programmed Desorption
TPD Temporary Partial Disability (insurance) 
) experiments suggest that only ~2% NO* dissociation on Pt(111), ~15% on Pt(110) and ~50% on Pt(100) is possible (Park et al., 1984), however, our simulation results confirm that Pt(111) can also show an oscillatory behaviour, at atmospheric pressure conditions. We also perform simulations to find out the sensitive reaction that is responsible for oscillations. We observed that if we decrease the activation energy of NO* dissociation (from 13 kcal/mol to lower values), then the oscillatory behaviour disappears. This indicates that the activation energy for NO* dissociation is crucial for oscillatory behaviour.

CONCLUSIONS

The NO-CO reaction exhibits bifurcations at atmospheric pressure on Pt(111) but not on Ir(111). Results show that kinetic oscillations and multiple steady states are observed for a specified range of ratio of inlet concentrations. Competition for catalyst sites between the different surface species, activation energy for NO* dissociation, and reactor temperature are found to be crucial for multiple steady states on respective metal surfaces.

ACKNOWLEDGEMENTS

We are grateful to the Department of Science and Technology (DST (1) (DeSTination) Contrast with SRC, which is an abbreviation of "source."

(2) (Digital Signal Trust Company, Salt Lake City, UT, www.digsigtrust.com) An organization that sets up and manages PKI systems for companies and industry groups.
), Government of India The Government of India (Hindi: भारत सरकार [3]Bhārat Sarkār), officially referred to as the Union Government, and commonly as Central Government , for financial support through SERC SERC - Science and Engineering Research Council  (#03DS014). We are thankful to Sonal Patel and Saugata Gon for their valuable suggestions.

NOMENCLATURE nomenclature /no·men·cla·ture/ (no´men-kla?cher) a classified system of names, as of anatomical structures, organisms, etc.

binomial nomenclature
 

[a.sub.v] surface area/volume of catalyst ([m.sup.2]/[m.sup.3])

[C.sub.i] outlet concentration of gas species i (mol/[m.sup.3])

[C.sub.i.sup.0] inlet concentration of gas species i (mol/[m.sup.3])

Ea activation energy (kcal/mol)

[k.sub.0] pre-exponential factor ([s.sup.-1])

[k.sub.j] rate constant for reaction j

[M.sub.i] molecular weight of species i

[N.sub.A] Avogadro number (6.022 x [10.sup.23] molecules/mol)

[p.sub.i] partial pressure of gas species i

R gas constant ([m.sup.2]*gm/ ([s.sup.2]*mol*K))

[R.sub.j] rate of surface reaction j (mol/[m.sup.2]/s)

[s.sub.i] sticking coefficient for species i (dimensionless)

T temperature (K)

[GAMMA] number of active sites ([m.sup.-2])

[theta]* fractional coverage of vacant sites (dimensionless)

[[theta].sub.k] fractional coverage of surface species k (dimensionless)

[v.sub.ij] stoichiometric coefficient of species i in surface reaction j

[v.sub.kj] stoichiometric coefficient of species k in surface reaction j

[tau] space time (s)

Subscripts

i gas phase/surface species

j reaction number

* vacant site

k surface species

Manuscript received January 16, 2007; revised manuscript received March 15, 2007; accepted for publication March 16, 2007.

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External links
  • Combustion Institute
  • History
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* Author to whom correspondence may be addressed. E-mail address: preeti@iitb.ac.in

Dinesh Mantri, Viral Mehta and Preeti Aghalayam *

Department of Chemical Engineering, Indian Institute of Technology, Bombay, Mumbai, India 400 076
Table 1. Reported oscillations and bistability for the NO-CO reaction
on supported Pt group catalysts at atmospheric pressure

                                                             [C.sub.NO]
                                              Temp.          /
Authors              Catalysts                ([degrees]C)   [C.sub.CO]

Mergler and          0.4%Pt/29%Ce[O.sub.2]/   400            0.33
Nieuwenhuys, 1996    [Al.sub.2][O.sub.3]
Frank et al., 1997   0.5%Pt/3-4Mo[O.sub.3]/   360-460        1-2.5
                     [Al.sub.2][O.sub.3]
Sadhankar and        0.5%Pt/[Al.sub.2]        190-250        1-1.5
Lynch, 1997          [O.sub.3]
Subramaniam and      0.1%Pt/[Al.sub.2]        380-600        --
Varma, 1983          [O.sub.3]
Schueth and Wicke,   1-5%Pt/Si0z, Pt/         350-470        0.8-4
1989                 [Al.sub.2][O.sub.3]
Schueth and Wicke,   Pd/[Al.sub.2]            327            0.5-2
1989                 [O.sub.3]
Frank and Renken,    0.5%Pt/3-4% Mo           340-495        -1
1998                 [O.sub.3]/[Al.sub.2]
                     [O.sub.3]

Authors              Catalysts                Remarks

Mergler and          0.4%Pt/29%Ce[O.sub.2]/   Oscillation
Nieuwenhuys, 1996    [Al.sub.2][O.sub.3]
Frank et al., 1997   0.5%Pt/3-4Mo[O.sub.3]/   Oscillation, Bistability
                     [Al.sub.2][O.sub.3]      (PFR)
Sadhankar and        0.5%Pt/[Al.sub.2]        Bistability
Lynch, 1997          [O.sub.3]
Subramaniam and      0.1%Pt/[Al.sub.2]        Oscillation (NO + CO +
Varma, 1983          [O.sub.3]                [O.sub.2] + [H.sub.2]0)
Schueth and Wicke,   1-5%Pt/Si0z, Pt/         Oscillation
1989                 [Al.sub.2][O.sub.3]
Schueth and Wicke,   Pd/[Al.sub.2]            Oscillation
1989                 [O.sub.3]
Frank and Renken,    0.5%Pt/3-4% Mo           Bistability (CSTR)
1998                 [O.sub.3]/[Al.sub.2]
                     [O.sub.3]

Table 2. Elementary surface reaction mechanism with kinetic data for
Pt and Ir

No.   Elementary reactions        Rate expressions

 1    NO + * [right arrow] NO *   [r.sub.1] = [k.sub.1][C.sub.NO]
                                  [theta] *
 2    NO * [right arrow] NO + *   [r.sub.2] = [k.sub.2][[theta].sub.NO]
 3    NO * + * [right arrow]      [r.sub.3] = [k.sub.3][[theta].sub.NO]
      N * + O *                   [theta] *
 4    N * + N * [right arrow]     [r.sub.4] = [k.sub.4][[theta].sub.N]
      [N.sub.2] + 2 *             [theta]N
 5    NO * + N * [right arrow]    [r.sub.5] = [k.sub.5][[theta].sub.NO]
      [N.sub.2] O + *             [theta]N
 6    [N.sub.2] O * [right        [r.sub.6] = [k.sub.6][[theta].sub.N2]
      arrow] [N.sub.2] O + *      O
 7    CO + * [right arrow] CO *   [r.sub.7] = [k.sub.7][C.sub.CO]
                                  [theta] *
 8    CO * [right arrow] CO + *   [r.sub.8] = [k.sub.8][[theta].sub.CO]
 9    CO * + O** [right arrow]    [r.sub.9] = [k.sub.9][[theta].sub.CO]
      C[O.sub.2] + 2 *            [[theta].sub.O]

                                  Pre-exponential
                                  factor([s.sup.-1])   Activation
                                  /Sticking            energy
No.   Elementary reactions        coefficient          (kcal/mol)

                                                       pt(111)  Ir(111)

 1    NO + * [right arrow] NO *   #0.6/0.6              0        0
 2    NO * [right arrow] NO + *   1 x [10.sup.13]      26       30.7
 3    NO * + * [right arrow]      1 x [10.sup.11]      13        7.7
      N * + O *
 4    N * + N * [right arrow]     1 x [10.sup.11]      27       39.3
      [N.sub.2] + 2 *
 5    NO * + N * [right arrow]    1 x [10.sup.11]      21       28.71
      [N.sub.2] O + *
 6    [N.sub.2] O * [right        1 x [10.sup.13]      13       14
      arrow] [N.sub.2] O + *
 7    CO + * [right arrow] CO *   #0.89/0.92            0        0
 8    CO * [right arrow] CO + *   1 x [10.sup.13]      32       34
 9    CO * + O** [right arrow]    1 x [10.sup.11]      23.7     24.9
      C[O.sub.2] + 2 *

# the first and second value indicate sticking coefficient on
Pt(111) and Ir(111), respectively.
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Author:Mantri, Dinesh; Mehta, Viral; Aghalayam, Preeti
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