CO Oxidation

The catalytic oxidation of carbon monoxide is industrially relevant for automotive emission control, and the CO removal from large gas streams of the petrochemical industry. In research, it is considered as a model reaction for understanding fundamental concepts in heterogeneous catalysis [60].

𝐶𝑂 +1

2𝑂₂ → 𝐶𝑂₂ ∆_𝑅𝐻⁰ = −283 𝑘𝐽 𝑚𝑜𝑙⁻¹ ( 2.28 ) The reaction can be catalyzed by various metals. Commonly, noble metals are used:

for example, automotive exhaust catalysts contain Pt, Pd, and/or Rh, which are supported on monoliths; Ir could be also employed [61]. These noble metals require temperatures above 100 °C; but some catalysts are active at lower temperatures, e.g.

gold nanoparticles, Pt supported on tin(IV)oxide, or copper oxides [62]. Furthermore, tricobalt tetraoxide nanorods were found to be able to convert CO at temperatures as low as -77 °C[63].

Among all mentioned catalysts, CO oxidation on platinum is one of the most investigated reactions in literature. It can be divided into the following elementary steps [64]: respectively. Allian et al. [65] developed a Langmuir-Hinshelwood-Hougon-Watson (LHHW) mechanism by assuming Equation 2.32 as the rate-determining step, the adsorption of CO and O² as quasi-equilibrated (2.29, 2.31), Equation 2.33 and 2.34 are considered to be irreversible, and neglecting Equation 2.30 altogether; which results in the following expression for the overall reaction rate:

𝑟 = 𝑘₄⁺𝐾₃𝐾₁𝑝_𝐶𝑂𝑝_𝑂2 (1 + 𝐾₃𝑝_𝐶𝑂+ 𝐾₁𝑝_𝑂2)² ,

( 2.35 )

where 𝑝_𝐶𝑂 and 𝑝_𝑂2are the partial pressures of CO and O2, respectively, and 𝐾_𝑖 is the equilibrium constant defined as the ratio of 𝑘_𝑖⁺ and 𝑘_𝑖⁻ .

The CO oxidation over Pt occurs in a high- and a low-active regime. At low temperatures, i.e. the low active regime, 𝐾₃ becomes high, hence, the surface is predominantly covered with CO, and the reaction rate is proportional to 𝑝_𝑂2/𝑝_𝐶𝑂. The common assumption of quasi-equilibrated molecular and dissociative adsorption of O2 and subsequent reaction of 𝑂(𝑃𝑡) with 𝐶𝑂(𝑃𝑡), would result in CO oxidation rates proportional to 𝑝_𝑂2^0.5/𝑝_𝐶𝑂 in the low-active regime [65]. However, this is not in accordance with many experimental works in literature, since fitted LHHW mechanisms often have the form of Equation 2.35 (e.g. [32,33,65–67]).

The high-active regime occurs at higher temperatures. In literature, the surface at these conditions is intensively discussed. There is general agreement among researchers that the surface is nearly free of CO. However, it is not clear if either metallic platinum [68,69], chemisorbed oxygen [70], or a partially oxidized platinum surface [71] causes the high activity of the catalyst. In this regime, often strong external and/or internal diffusion limitations are observed [32]. These have not always been excluded in kinetic measurements, which might explain the wide range of activation energies for CO oxidation on Pt found in literature [32], ranging from 30 kJ mol^-1 [72] to 120 kJ mol^-1 [73].

Inside catalyst pellets, high- and low-active regimes can exist for the same external condition, resulting in two different steady state concentration profiles. This occurs when the diffusion resistance leads to significant concentration gradients inside the pellet. The shift from one to the other regime happens suddenly, by small changes in the boundary conditions (e.g. temperature, CO/O² ratio, velocity). It will be accompanied by a significant temperature change of the catalyst in adiabatic systems.

However, the opposite shift happens at different conditions, which lead to a hysteresis [67,74].

The observation of kinetic oscillations in critical runaway episodes of CO removal reactors opened the evolution of the whole research field of nonlinear dynamics in surface science [60]. Oscillations for CO oxidation on Pt have been observed on clean Pt structures under ultra-high-vacuum (UHV) conditions [75,76], but also on monoliths [26], single catalyst particles [74,77], Pt nanoparticles [78], Pt gauzes [74], and in macroscopic flow reactors [39,79] under atmospheric pressure. They can be

explained by structural dynamic responses, ranging from surface reconstructions to subsurface state populations [60]. These mechanisms are quite specific, depending on the reaction conditions and the active component of the catalyst.

Fundamental CFD equations 2.2

For modeling a heterogeneous catalytic reactor, governing equations for conservation of mass and momentum (Navier-Stokes equations), conservation of each species, and conservation of energy need to be implemented. All simulations in this work were carried out assuming laminar flow and steady state. Therefore, no turbulence models and time dependent equations are required. The conservation of mass can be expressed as [80]:

∇ ⋅ (𝑢𝜌) = 0, ( 2.36 )

where 𝜌 is the mixture averaged density, and 𝑢 the velocity vector. Conservation of momentum means the following holds[80]:

𝜌(𝑢 ⋅ ∇)𝑢 + ∇ ⋅ 𝑝 + ∇ ⋅ 𝜏 = 0 ( 2.37 ) The viscous stress tensor 𝜏 can be calculated as:

𝜏 = −𝜇(∇𝑢 + (∇𝑢)^𝑇) +2

3𝜇(∇ ⋅ 𝑢)𝐼 ( 2.38 )

where 𝜇 is the dynamic viscosity of the mixture and 𝐼 is the identity matrix.

Conservation of species 𝑖 is defined as [81]:

𝜌(𝑢 ⋅ ∇)𝑤_𝑖 + ∇ ⋅ 𝑗_𝑖− ∑ 𝜈_𝑖,𝑗

𝑗

𝑅_𝑗𝑀_𝑖 = 0 𝑖 = 1, … , 𝑁_𝑔, 𝑗 = 1, … , 𝑁_𝑅 ( 2.39 )

Where 𝜈_𝑖,𝑗 is the stoichiometric coefficient of the species 𝑖 in the reaction 𝑗, 𝑤_𝑖 is the mass fraction, 𝑅_𝑗 is the net production rate, and 𝑀_𝑖 is the molar mass. The diffusion mass flux 𝑗_𝑖, with respect to the mass average velocity, is calculated as [82]:

𝑗_𝑖 = − (𝐷_𝑖,𝑚𝜌∇𝑤_𝑖 + 𝐷_𝑖,𝑚𝜌𝑤_𝑖∇𝑀_𝑛

𝑀_𝑛 ) ( 2.40 )

where the mean molar mass 𝑀_𝑛 is

and the mixture averaged diffusion coefficient 𝐷_𝑖,𝑚 is defined as follows [51]:

𝐷_𝑖,𝑚= 1 − 𝑤_𝑖 Wilke-Bosanquet model is applied which combines molecular and Knudsen diffusion to a diffusion coefficient 𝐷_𝑖,𝑀. To describe the diffusion inside the pellet accurately, the pore geometry and connectivity need to be accounted for. Therefore, an effective diffusion coefficient 𝐷_{𝑖,𝑒𝑓𝑓} is introduced, that accounts for all these parameters [51]:

𝐷_{𝑖,𝑒𝑓𝑓} = 1

(𝐷_𝑖,𝑚⁻¹+ 𝐷_𝑖,𝐾⁻¹) 𝜖

𝜏 = 𝐷_𝑖,𝑀𝜖

𝜏 ( 2.43 )

𝐷_𝑖,𝐾 is calculated according to Equation 2.13. Conservation of energy is calculated as follows [80]:

𝜌𝐶_𝑝𝑢 ⋅ ∇𝑇 − ∇ ⋅ (λ∇𝑇) − ∑(−∆𝐻_𝑟,𝑗)𝑅_𝑗

𝑗

= 0, ( 2.44 )

where 𝐶_𝑝 is the mixture averaged heat capacity at constant pressure and λ is the mixture averaged thermal conductivity. For the catalyst particle, 𝐶_𝑝 and λ are catalyst properties. Furthermore, the ideal gas law needs to be included:

𝑝 =𝜌𝑅𝑇

surface [83]. A schematic diagram with all major components of the apparatus is shown in Figure 2-4.

Figure 2-4: Schematic diagram of a FIB with all major components. Adapted from [83].

FIB systems most commonly use a liquid-metal ion source, typically Ga⁺. A reservoir of heavy metal atoms is heated to near evaporation so that it starts flowing down a heat-resistant tungsten needle. At the tip, Ga forms a “Taylor cone”, caused by a potential difference between the needle tip and the extractor (~ -6 kV). The apex of the cone is only 5 nm, and therefore small enough that the extractor voltage can pull Ga from the tip and ionize it by field evaporation. This effect appears because the potential barrier preventing the Ga from evaporation is lowered by the electric field,

and it can only be crossed by the ionization of the evaporating Ga atom. The current emitted from the tip is controlled by both, the suppressor and the extractor. The suppressor maintains the beam current constant by applying an electric field of up to +2 kV.

These ions are subsequently accelerated by a potential down the ion column (~ 30 kV) and pass through the aperture. There, the beam is focused by electrostatic lenses, which have been proven to be more effective for ions than magnetic lenses.

Subsequently, the sample surface is scanned by the focused ion beam. On the surface, either elastic or inelastic ion-atom collisions occur. The inelastic scattering transfers some of the energy either to the surface atoms or electrons, releasing secondary electrons, which can be used for imaging. They are collected by a multi-channel plate or an electron multiplier depending on the apparatus. Furthermore, secondary ions are emitted following the secondary electrons. During the elastic scattering, surface atoms are excavated, resulting in a process called milling or sputtering. By injecting an organometallic gas just above the surface sample where the beam strikes, the material can be deposited. Almost any microstructure can be created by combining deposition and milling. For imaging purposes or milling fine structures, currents of less than 100 pA are applied to avoid surface damage. For rough structures, currents in the nA range are applied for a faster procedure [83].

Mass spectrometry 2.4

The mass spectrometer (MS) produces ions from neutral species and determines the mass of these ions based on the mass-to-charge ratio (m/z, z is the number of elemental charges) and/or the number of ions [84]. It consists of four main components (Figure 2-5): the sample inlet into the vacuum chamber (I, not shown in the Figure), an ion source (II), a mass analyzer (III), and an ion detector (IV). Various main components exist, the choice of which to use depends on the analyzing task.

Here, only components and physical concepts of the HALA EPIC Low Energy mass spectrometer, which was used in this work, are explained in detail.

Figure 2-5: Electrodes of the HALA EPIC Low Energy mass spectrometer, adapted from [85].

2.4.1 Electron impact ionization

Electron impact ionization (EI) is the most commonly used principle for ion generation today. Electrons are emitted from a cathode (a heated filament usually made from tungsten, rhenium, or thoriated iridium) and are accelerated towards an anode (IIa). The kinetic energy of the electrons must be larger than the ionization energy (IE) of the sample molecule (e.g. IE of Ar is 15.8 eV [86]). Most of the molecules have their respective maximum of the total ionization cross section around 70 eV, which is why this electron energy is usually applied [86]. The gaseous sample molecules enter the ion source perpendicular to the electron beam and start to form positively charged molecular ions. If these ions have sufficient internal energy, they will undergo further fragmentation within a few microseconds, and the signature molecule-dependent mass spectrum is obtained [84]. These ions are drawn out of the source by a focus electrode (IIb).

(II)

(III)

(IV)

(IIa)

(IIb)

(IIIa)

(IVa)

(IVb)

Im Dokument Spatially resolved probing of diffusion and reaction in porous catalyst pellets (Seite 27-35)