Laser Diagnostics and Modeling

of the

Coupling between Heterogeneous Catalytic

and

Gas-Phase Oxidation of Hydrogen

Michael F�orsth

October 4, 1998

Abstract

The hydrogen oxidation process has been studied in the pressure range 1-150

torr by using a stagnation ow geometry. Both surface reactions, on a plat-

inum surface, and gas-phase reactions were included in the study which was

both experimental and theoretical. Experimental data of the OH concen-

tration outside the surface were measured with Planar Laser Induced Flu-

orescence, PLIF. Detailed simulations of surface chemistry, mass-transport

e�ects, and gas-phase chemistry, as well as the interaction between them,

were performed with the Chemkin software package using the application

code Spin, developed at Sandia National Laboratories.

It was found that for pressures up to 1 torr the OH molecules that desorb

from the surface are not in uenced by the gas-phase chemistry. At higher

pressures the desorbed OHmolecules are partially consumed in reactions with

gas-phase species, mainly hydrogen molecules. Increasing the pressure even

more will result in a reactive gas phase where water is produced. Simulations

show that with a catalytic surface the gas-phase production of water bypasses

the surface-phase production at a pressure of about 60 torr. By comparison

with an inert glass surface it is found that the catalytic surface strongly

inhibits the gas-phase ignition. The gas-phase ignition outside the inert

surface took place already at around 10 torr. The reason for this behaviour

is that gas-phase radicals adsorb onto the surface and react into less reactive

species, such as water. In this way the gas phase outside a catalytic surface

becomes depleted of reactive radicals, compared to the gas phase outside an

inert surface.

Keywords: catalysis, surface reactions, gas-phase chemistry, stagnation ow, hy-

droxyl, OH, platinum, planar LIF, ignition conditions, Chemkin

List of Papers

Paper 1 OH Gas Phase Chemistry outside a Pt Catalyst

Fredrik Gudmundson, John Persson, Michael F�orsth, Frank

Behrendt, Bengt Kasemo and Arne Ros�en.

Journal of Catalysis, in press.

Paper 2 The In uence of a Catalytic Surface on the Gas-Phase

Ignition and Combustion of H2+O2

Michael F�orsth, Fredrik Gudmundson, John Persson and Arne

Ros�en. Submitted to Combustion and Flame.

2

Contents

1 Introduction 5

2 Surface and Gas Reactions and their Interplay 7

2.1 High Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Low Vacuum . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3 Higher Pressures . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Hydrogen Oxidation Chemistry with Surface E�ects 29

3.1 Introduction to Heterogeneous Catalysis . . . . . . . . . . . . 29

3.2 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Reaction Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3.1 Gas-Phase Reactions . . . . . . . . . . . . . . . . . . . 35

3.3.2 Surface-Phase Reactions . . . . . . . . . . . . . . . . . 35

3.4 Numerical Solution Method . . . . . . . . . . . . . . . . . . . 39

3.4.1 The CHEMKIN Software Package . . . . . . . . . . . . 39

3.4.2 Mathematical Formulation . . . . . . . . . . . . . . . . 40

3.4.3 Structure of the CHEMKIN Package . . . . . . . . . . 43

3.4.4 Calculation of Total Water Production . . . . . . . . . 45

4 Experimental Setup and Methods 48

4.1 Molecular Structure and Transitions in the OH Molecule . . . 48

4.1.1 Energy Structure . . . . . . . . . . . . . . . . . . . . . 48

4.1.2 Transitions . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Laser Induced Fluorescence, LIF, Technique . . . . . . . . . . 56

4.2.1 Laser System . . . . . . . . . . . . . . . . . . . . . . . 56

4.2.2 Quenching . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2.3 Temperature Considerations . . . . . . . . . . . . . . . 57

4.3 Planar Laser Induced Fluorescence and Imaging Techniques . 61

4.3.1 Laser Optics Setup . . . . . . . . . . . . . . . . . . . . 63

4.3.2 CCD Optics Setup . . . . . . . . . . . . . . . . . . . . 64

3

5 Summary of Papers 65

5.1 Paper 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2 Paper 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6 Outlook 67

7 Acknowledgements 68

A Calculation of Total Water Production 69

References 71

4

Chapter 1

Introduction

Combustion processes are among the most important sources of energy in our

society. About 90% of all the energy supposedly released to serve mankind

comes from combustion processes [Warnatz et al., 1996]. In the ideal case

the products of hydrocarbon combustion are, besides the released heat en-

ergy, carbon dioxide, CO2, and water, H2O. Unfortunately a real combustion

process also yields di�erent amounts of emissions, such as CO, NOx and un-

burned hydrocarbons, which constitute a global threat to our environment.

This, together with the fact that the resources of fossil hydrocarbons are

limited, therefore makes it of utmost importance to study and develop tech-

niques which make the combustion as fuel-e�cient as possible and emissions

as low as possible.

Heterogeneous catalysis is a well-known method to reduce emissions in

secondary combustion processes, as in the three-way catalyst for example.

However, catalysis can also be used directly in the primary combustion

process. One example is the catalytically stabilized thermal (CST) com-

bustor. In the CST combustor, a heterogeneous catalyst is used to promote

gas-phase combustion at temperatures well below those possible in ame

combustors [Pfe�erle and Pfe�erle, 1987]. Decreasing the combustion tem-

perature is a very e�ective way of decreasing the NOx formation.

Reading the rich literature on the subject is quite interesting. The initial

interest of the subject was to avoid gas explosions in mines [Davy, 1840]:

\. . . the subject of explosions from in ammable air, and the modes

in which they may be prevented, as well as the collateral investiga-

tions to which they have given rise, with the hope of presenting

a permanent record on this important subject to the practical

miner, and of enabling the friends of humanity to estimate and

apply those resources of science, by which a great and perma-

nently existing evil may be subdued."

5

Davy also reported that

\. . . oxygen and coal-gas in contact with the hot wire combined

without ame, and yet produced heat enough to preserve the wire

ignited, and to keep up their own combustion."

Today the interest has shifted to avoiding gas explosions in a space-

craft, or avoiding early ignition in internal combustion engines, so-called

knock [Kim et al., 1997]. There are also other areas than catalytic combus-

tion where the interaction between surface- and gas-phase chemistry is im-

portant. One example is metal-organic chemical vapor deposition (MOCVD)

for growth of compound semiconductors. Therein, the surface stimulates a

decomposition reaction. Unwanted species desorb and the desired species

incorporate themselves into a solid material [Dupuis, 1984]. Another area

where the interaction between gas- and surface-chemistry is important is

growth of diamond �lms.

While the interest in the interaction between surface- and gas-phase chem-

istry has grown increasingly in the last decade, this does not mean that we

have the complete picture of pure surface-catalytic e�ects. For example,

there are still no satisfactory catalyst available for diesel engines, since the

three-way catalyst does not work in an oxygen-rich environment like that in

diesel exhaust gas.

The studies performed in this licentiate thesis are focused on the use and

development of Laser Induced Fluorescence, LIF, on combustion processes

near surfaces. The work is restricted to the reactants hydrogen and oxygen,

thus avoiding the very complex reaction schemes that have to be used when

hydrocarbons are involved. Although this may seem to be a very simple

system it contains the chemistry of the OH molecule, which is very important

in combustion processes. In Paper 1 of this work the transition from an inert

gas phase, where all chemical reactions take place on the catalyst in the form

of a Pt-foil, to an active gas phase, where the desorption radicals from the

catalyst are partly consumed in the gas phase, is studied. In Paper 2 the

pressure is further increased, giving rise to chain reactions in the gas phase.

The in uence of the surface on the gas-phase combustion is studied in detail.

6

Chapter 2

Surface and Gas Reactions and

their Interplay

Catalytic reactions as the oxidation of hydrogen can occur in quite di�erent

conditions, from high vacuum conditions to the conditions valid in an internal

combustion engine of a car, which is up to 50 bar. Increasing the pressure

will not only change the surface chemistry but we will also have to take into

account the interplay with gas-phase chemistry and uid dynamics.

In this chapter the literature on the interaction between surface and gas-

phase chemistry will be surveyed. We will go from low to high pressures p.

Starting with the theoretical case of pure surface phenomena, p = 0, and

continuing up to the all too realistic case of a knocking car engine, p � 50

atmospheres, via friction problems at the re-entry of the Space Shuttle in

the upper atmosphere, p � 10�6 atmospheres. Since the experiments and

simulations of the two papers in this report have been done in the pressure

range 1-150 torr, the literature survey is most detailed in this range.

2.1 High Vacuum

Properties of the Surface

In order to understand the interaction of a surface with a surrounding gas it

is important �rst to understand the properties of a clean surface, that is, the

interphase between the bulk of a material and vacuum.

A surface at thermodynamic equilibrium has the geometry that corre-

sponds to the lowest energy. However, to �nd the geometry that minimizes

the total energy is complicated for a bulk system with periodicity in three

directions, and it becomes immensely more di�cult for a surface where the

periodicity disappears in one direction. Therefore, with very few exceptions,

7

it is di�cult to determine surface crystal structure by purely theoretical

means [Zangwill, 1988].

Nevertheless, surface geometries are well known today because of an

important arsenal of experimental techniques. The standard experimen-

tal tool for determining a surface's crystal structure is low-energy elec-

tron di�raction, LEED. The method was invented by Davisson and Ger-

mer [Davisson and Germer, 1927, Scheibner et al., 1960]. In LEED, elec-

trons with energies in the range of 20-500 eV that are elastically backscat-

tered from a crystal surface will form a Fraunhofer di�raction pattern that

is the Fourier transform of the surface atom arrangement. Direct microscopy

methods give the surface structure in real space and in particular the scan-

ning tunneling microscope, STM, gives very detailed information about the

surface structure on the atomic level [Binnig et al., 1982].

The surface can be of two types, either polycrystalline or single crystal.

A polycrystalline surface is what we normally see as a metal surface in our

everyday life. The polycrystalline bulk consists of several crystals, grains,

and what we see as a surface is the di�erent faces of the di�erent grains.

A single crystal surface on the other hand is what is obtained if a single

crystal is cleaved along one of its planes. Depending on along which plane

the cleavage is performed, for example (100), (110) or (111) [Kittel, 1986],

the surface will exhibit di�erent properties as for example surface site density,

symmetry order, and eventually the existence of di�erent types of sites.

In this work we have used a polycrystalline platinum surface. However,

due to the interaction between the platinum atoms and the adsorbed species

during the catalytic process the platinum surface atoms have a tendency

to relax into the geometry that minimizes their potential energy. For plat-

inum this is the (111) surface and it is often assumed that the surface is a

multigrain surface where all the grains exhibit the Pt(111) facet towards the

surface [Shigeishi and King, 1976].

The Sticking Coe�cient

The probability that a gas molecule hitting the surface will be adsorbed

is called the sticking coe�cient, s, and will be discussed in more detail in

section 3.3.2. This is a very important parameter and much work have

been done to calculate the sticking coe�cients for various gases and sur-

faces. However, theoretical predictions of the sticking coe�cient are not

easily obtained [Clougherty and Kohn, 1992, Gross et al., 1995].

In general, the sticking coe�cient decreases with increasing coverage of

the surface. This is because more and more of the molecules hitting the

surface will hit a surface site which is already covered by an adsorbate. This

8

is often expressed as:

s(�) = s(0)f(�) = s(0)(1 � �)i (2.1)

where � is the coverage and i is the order of adsorption. From the form of

Eq. 2.1, it has been assumed that it is the average coverage that is important,

the e�ect of inhomogeneous coverage having been omitted. This is called the

mean-�eld approximation. Di�erent adsorption mechanisms have di�erent

adsorption order. For example, adsorption of a single atom is assumed to

be of �rst order, i = 1, since the atom requires only one free surface site

for its adsorption. In contrast, a diatomic molecule such as the O2 molecule

requires two neighboring free sites for its adsorption. Therefore, dissociative

adsorption of oxygen is usually considered to be of second order, i = 2.

Langmuir-Hinshelwood versus Eley-Rideal Reactions

Heterogeneous catalytic reactions can occur either via adsorbate-adsorbate

reactions or via an adsorbed particle and an impinging particle from the

gas. These two cases are denoted Langmuir-Hinshelwood reactions and Eley-

Rideal reactions, respectively [Zangwill, 1988]. A classic example is the cat-

alytic oxidation of CO into CO2. The question is whether the reaction follows

a Langmuir-Hinshelwood scheme:

Langmuir-Hinshelwood

CO ! COa (2.2)

O2 ! 2Oa (2.3)

COa +O

a ! CO2; (2.4)

or an Eley-Rideal scheme:

Eley-Rideal

O2 ! 2Oa (2.5)

Oa + CO ! CO2; (2.6)

where an \a" means adsorbed on the surface. [Campbell et al., 1980] solved

the question by using Modulated Molecular Beam Relaxation Spectroscopy,

MMBRS. In MMBRS information about surface reactions is obtained by

measuring the phase di�erence between an incident molecular beam imping-

ing on the surface and the molecules desorbed from the surface. Analysis

9

of the experimental data showed that the catalytic CO oxidation proceeded

according to the Langmuir-Hinshelwood reaction scheme 2.2, 2.3 and 2.4.

Most heterogeneous reactions are considered to be of Langmuir-Hinshelwood

type, as the hydrogen oxidation process studied in this work for example,

but there are cases where Eley-Rideal reactions may also be important, see

section 2.2 and [Deutschmann et al., 1995] for examples.

Studies Made at Pressures below 1 mbar

At pressures below 1 mbar the molecules move relatively freely and gas-phase

reactions are assumed to be unimportant.

In a study by [Fujimoto et al., 1983] mixtures of water and argon were

passed through a microwave discharge to produce a mixture containing OH

radicals. The gas then passed over a heated spiral platinum wire and the

relative OH concentration after the wire was measured by LIF. It was found

that the more the wire was heated, the smaller was the OH concentration,

since the OH removal by the wire became more e�ective with increasing

temperature. However, above 950 K the OH concentration increased abruptly

due to the desorption of OH from the wire. It is this e�ect that has been

used in Papers 1 and 2 in this work, and in many other studies. Hence,

if the concentration of desorbed OH molecules is to be probed by LIF the

foil temperature must be above 900 K; otherwise the desorption rate will be

under the detection limit. [Fujimoto et al., 1983] suggest that the reaction

OHa +O

a ! O2 +Ha (2.7)

is not e�ective in reducing the concentration of OHa even in the presence of

a large amount of oxidants. The authors also propose an Eley-Rideal process

where a gas-phase species reacts directly with a surface-adsorbed species:

OH +Ha ! H2O (2.8)

for the removal of gaseous OH, which was the subject of their study.

In [Hellsing et al., 1987], LIF and calorimetric experimental data for the

catalytic hydrogen oxidation process on a heated, 1100 K, platinum foil were

compared with kinetic model calculations. The reaction was assumed to be

of Langmuir-Hinshelwood type with sequential addition of adsorbed atomic

hydrogen to O and OH, according to the scheme:

H2*) 2Ha (2.9)

O2 ! 2Oa (2.10)

Ha +O

a ! OHa (2.11)

10

Ha +OH

a ! H2Oa ! H2O (2.12)

OHa ! OH: (2.13)

It was found that this model �ts with experimental data relatively well. The

mixing ratio � = pH2=(pH2

+ pO2), where the maximum water production

occurs was found to depend on the hydrogen and oxygen sticking coe�cients.

The OH production was found to depend relatively strongly on the di�erence

between the activation energies for OH and H2O formation. The authors

identify the need of reliable information about sticking coe�cients at high

temperatures.

The experiments in [Hellsing et al., 1987] were extended to a wider

pressure range, 2-200 mtorr, and temperature range, 900-1300 K,

in [Ljungstr�om et al., 1989]. The concentration of OH molecules 1-2 mm

below the heated platinum foil was probed by LIF. In order to �nd out

whether the OH molecules were produced by the Oa+Ha !OHa reaction

(as was believed), or by the reaction H2Oa+Oa !2OHa by readsorption of

water, a liquid nitrogen-cooled shield was mounted close to the catalyst as a

sorption pump for water in order to block the latter reaction. It was found

that the reaction Oa+Ha !OHa accounted for at least 95% of the detected

OH around the mixing ratio �OH = 3 � 8% which gave the maximum OH

desorption. However, at higher � the water decomposition reaction could

not be ruled out with certainty. Since the experiments were conducted at

such high temperatures, the authors wanted to make sure that gas-phase

reactions did not occur to such a degree that the experimental results were

a�ected. This was tested by several methods whereof one was to replace

the platinum foil with a gold foil. Since gold is believed to be catalytically

inert for the studied reaction, the calorimetric measurements should not in-

dicate any released chemical power from either surface reactions or gas-phase

reactions. This was also the case. The calorimetric measurements were per-

formed by measuring the electric power required to keep the foil at a certain

temperature. Released chemical energy was detected via a decrease in the

required electric power. While the mixing ratio for maximal OH desorption

was �OH = 3�8% the mixing ratio for maximal water production was found

to be �H2O= 15 � 22%. This is a very important observation since it gives

information about the relative importance of the two reaction paths

Ha +OH

a ! H2Oa (2.14)

OHa +OH

a ! Oa +H2O

a: (2.15)

If path 2.15 were the dominant one, the water production would have its

maxima when the coverage of OHa had its maxima. However, when the

11

coverage of OHa has its maxima the desorption rate of OH is also biggest.

Hence, if path 2.15 were dominant we would have �OH = �H2O. Since this

was not the case it was rather believed that path 2.14 was the dominant one,

since this reaction depends not only on the OHa coverage but also on the Ha

coverage.

The maximum in water production occurs when

� Ka

H2fH2

(�)

Ka

O2fO2

(�)= 2; (2.16)

where Ka is the product of the sticking coe�cient at zero coverage and

the impingement rate for the respective molecule. Since the coverage � is

very low at the water production maximum, the coverage dependence factors

fH2(�) = 1 � � and fO2

(�) = (1 � �)2 are approximately unity and we can

write

� Ka

H2

Ka

O2

=�H2� sH2

(0)

�O2� sO2

(0)� 2: (2.17)

Since the impingement rate � is proportional to the partial pressure p and

inversely proportional to the molecular mass for a certain species, this can

be written as

� �H2� sH2

(0)

�O2� sO2

(0)� 2) sH2

(0)

sO2(0)

=1

2

pH2

pO2

(2.18)

or, using � =pH2

pO2+pH2

,

sH2(0)

sO2(0)

=1

2� 1 � �H2O

�H2O

: (2.19)

With �H2O= 0:17 at T = 1100 K, [Ljungstr�om et al., 1989] obtain the ratio

sH2(0)=sO2

(0) = 2:4. In order to obtain absolute values the calorimetrically

determined absolute water production was used. The authors arrived at the

result sH2(0) = 0:04 and sO2

(0) = 0:02. Concerning the sticking coe�cients,

it is emphasized that they are e�ective sticking coe�cients in the sense that

possible e�ects of surface roughening, grain boundaries, steps, etc. are in-

cluded.

The model used to analyze the experimental data

of [Wahnstr�om et al., 1989] is explained in detail in [Hellsing et al., 1991].

The model is called the HKZ model after the authors: Hellsing, Kasemo and

Zhdanov. According to the HKZ model, the hydrogen/oxygen reaction on

platinum is assumed to contain the following steps:

H2*) 2Ha (2.20)

12

O2*) 2Oa (2.21)

Ha +O

a *) OHa (2.22)

Ha +OH

a *) H2Oa (2.23)

OHa +OH

a *) H2Oa +O

a (2.24)

OHa ! OH (2.25)

H2Oa ! H2O: (2.26)

The authors point out that the gas ow, or pumping speed, must be suf-

�ciently high in order to keep the partial pressure of water low; other-

wise reaction 2.26 must be made reversible. For this reason and also in

order to avoid concentration gradients a Roots pump with high pumping

speed was used in [Wahnstr�om et al., 1990]. In [Hellsing et al., 1991] the

sticking coe�cient for H2 is assumed to be coverage-independent, in con-

trast to [Hellsing et al., 1987] where it is assumed to be linear in coverage,

fH2(�) = 1 � �. It is also pointed out that reaction 2.24 might be the

dominant water production path despite the fact that �OH 6= �H2O. This

would require that the activation energy for OH desorption would be strongly

coverage-dependent due to adsorbate-adsorbate interaction:

Ed

OH(�) = E

d

OH(0)�B�: (2.27)

In order to make the model agree with experimental data of the OH des-

orption measurements if path 2.24 were the only water production path, a

value of B = 0:7 eV would be required. It is found that reaction 2.24 can

be the dominant path at low temperatures. However, the HKZ model is less

reliable at low temperatures since island formation e�ects may have to be

taken into account. The HKZ model is a mean-�eld model and the reason

why island formation is not taken into account is that, at the high temper-

atures which it is conceived for, T � 1000 K, the adsorbates are expected

to be randomized on the surface. The HKZ model has been used to predict

the reaction kinetics at pressures up to 105 torr. A noticeable e�ect at high

pressures is an eventual hydrogen poisoning of the surface for stoichiometric

and hydrogen rich mixtures. According to the calculations this should start

at a pressure of about 104 torr at 1000 K. The reason for this poisoning, if

it exists, would be that the coverage dependence of the sticking coe�cient

for oxygen is stronger than that for hydrogen, which would favor hydrogen

adsorption when the coverage � is large. However, since the HKZ model

only takes surface reactions into account the gas-phase reactions, which are

important at high pressures, are neglected. The HKZ model is therefore best

suited for low pressure calculations.

13

[Anton and Cadogan, 1990] used MMBRS to study the water formation

reaction on Pt(111). The principal aim of the study was to investigate the

mechanism and kinetics of the catalytic water formation reaction on Pt(111)

in the limit of low oxygen coverage, thereby circumventing the di�culties

associated with coverage-dependent rate parameters and island e�ects. The

surface temperatures were in the range 373 to 723 K. With the results from

the MMBRS measurements, the authors constructed a potential energy dia-

gram that accounted for the energetics of nearly all elementary steps in the

overall reaction.

The question of how reliable the detected OH LIF intensity is, as a mea-

sure of OH desorption rate, is adressed in [Gudmundson et al., 1993]. If

chemical gas-phase reactions can be neglected, the measured OH LIF signal

for a certain transition will depend on the following properties:

1. The desorption rate of OH molecules.

2. Di�usional transport and/or ow of OH molecules in and out of the

volume probed by the laser beam.

3. Rotational redistribution of the laser-excited OH molecules due to gas-

phase collisions, also called rotational quenching.

4. The laser-excited OHmoleculesmay fall back into the ground electronic

state via gas-phase collisions as described above. This means that the

molecules will not uoresce, and thus will not contribute to the OH

LIF signal. This e�ect is called electronic quenching and is further

described in section 4.2.2.

The �rst property is the studied one whilst the others can be looked

upon as unwanted interferences to the measurements. A major topic

in [Gudmundson et al., 1993] is mass transport e�ects, which become more

and more important as the pressure is increased. By analysis of the mea-

sured OH LIF signal with an equation, derived by V. P. Zhdanov, for the

di�usion caused by concentration gradients, it is shown that the results can

be improved. Other suggestions for improvement of experiments are:

1. To minimize the mass transport e�ect it is best to perform the exper-

iment at constant pressure. However, when variations in pressure are

necessary, it is best to keep the mass ow constant while the pump-

ing speed is varied. Furthermore the signal should be measured as

close to the surface as possible. Alternatively a set of points closer and

closer to the surface can be used to extrapolate the signal at zero dis-

tance. The use of a diode or CCD array, as used in [Fridell et al., 1991]

and [Gudmundson et al., 1993], is ideal for this purpose.

14

2. The mass ow should be large enough to minimize reactant gradients.

3. Rotational quenching should be accounted for. However, there is of-

ten a transition whose relative population is fairly insensitive to the

rotational redistribution; see also section 4.2.3.

4. Electronic quenching should be accounted for. It is often the depen-

dence of the quenching on partial pressures of di�erent species that

causes most di�culties. The temperature dependence is often less im-

portant.

In [Fridell et al., 1994] the decomposition of water from a Pt foil is stud-

ied. The desorption of OH from a platinum foil at 900-1300 K in H2O/O2,

H2O/H2 and H2O/O2+H2 mixtures was investigated by LIF. Deuterium, D2,

was also used in some experiments. The decomposition of water is an issue

that, besides its contribution to the understanding of hydrogen oxidation ki-

netics, is of general interest in the search for reaction schemes to produce H2

from water. The complications of gradients in the reactant concentrations

are eliminated in the water decomposition as compared to water formation.

As was pointed out in [Gudmundson et al., 1993] water decomposition is

a reversible reaction leading to equilibrium between gas-phase and surface-

phase species, which has the e�ect that no reactant gradients are formed.

The HKZ model was used to analyze the experimental data. However, as

opposed to [Hellsing et al., 1991], reaction 2.26 was made reversible with a

coverage-independent sticking coe�cient set to sH2O= 0:7. An analysis of

the equations showed that it was impossible to discriminate between reac-

tions 2.23 and 2.24 by studying the desorption of OH. However, a combination

of the analysis of the forward reaction, water formation [Hellsing et al., 1991],

and backward reaction, water decomposition, shows that the hydroxyl dis-

proportionation path 2.24 cannot be the dominant reaction path, in either

direction. The experimental data from the water decomposition experiments

in [Fridell et al., 1994] show that the coverage-dependent activation energy

for OH desorption in Eq. 2.27 would have to possess a value B < 0:05 eV in

order to �t the model. This is in con ict with the value B = 0:7 eV which

was required to �t with the forward reaction data. Furthermore, the fact

that OH desorption was detected even with pure water strongly supports the

unimolecular decomposition path, that is, the backward reaction 2.23.

Both formation and decomposition of water on a Pt(111) surface were

studied in [Fridell et al., 1995]. The measurements with Pt(111) agree with

the corresponding previous measurements on polycrystalline foils. This may

be because polycrystalline Pt has a tendency to crystallize to (111) facets.

15

In [Fridell et al., 1995] the enthalpy diagram for hydrogen oxidation is dis-

cussed in detail. It was observed in [Hellsing et al., 1991] that the di�erence

between the activation energies for hydroxyl desorption and for water forma-

tion, Ed

OH�Ef1

H2O, is not uniquely determined. E

f1

H2Ois the activation energy

for water formation through path 2.23; path 2.24 is neglected. The reason

why the experimental data are not su�cient to determine these activation

energies independently is that the desorption of OH, which is probed by the

LIF experiments, depends on the ratio between the expressions for OH des-

orption and H2O formation since a high H2O formation will decrease the

OH coverage. With the experimental data the authors arrive at a di�erence

Ed

OH� Ef1

H2O= 1:9 eV at 1200 K.

2.2 Low Vacuum

At 1 mbar pressure and a temperature of 300 K, the distance that a molecule

travels before it collides with another molecule is about 0.1 mm. This means

that in a container which is typically 10 cm in diameter the molecules will

hit each other many times before they hit the vessel surface. This gives rise

to an interaction between the molecules that is known as viscosity, and a

ow where viscosity e�ects come into play is called viscous ow; we then

speak of uids instead of single molecules. This is in contrast to molecular

ow, present at pressures up to around 10�2 mbar, where the molecules more

often interact with the walls than with each other. In the viscous ow region

it is important which ow geometry is being used. It is common to divide

the ow geometries into the following categories: (1) Closed vessel, where

there is no forced gas ow. However, di�usion and convection can occur.

(2) Wire ow geometry in which a gas ows against a wire. (3) Stagnation

ow against a foil. And �nally (4) boundary layer ow, where the gas ows

parallell to a surface. The ow condition used in Papers 1 and 2 of this work

is the stagnation ow against a foil.

One of the earliest observations of the catalytic e�ect on ammable gas

mixtures was made by [Davy, 1840] as mentioned in the introduction of this

licentiate thesis. A critical examination of the experimental and theoretical

work until 1982 concerned with methane/air ignition by hot surfaces is given

in [Laurendeau, 1982].

Closed Vessel

An example of a closed vessel is the condition valid in an Otto engine, which

will be discussed in coming works.

16

One of the �rst studies of the in uence of a hot surface on gas-

phase chemistry was made to study the risks of gas explosions in coal

mines [Coward and Guest, 1927]. Di�erent mixtures of natural gas1 and air

in a closed vessel were exposed to heated bars of platinum or nickel. The

authors noticed that the platinum bars had to be much hotter than the nickel

bars in order to ignite the gas. Furthermore, the required temperature for

the platinum to ignite the gas had a clear peak for mixtures close to the sto-

ichiometric, that is, 9.09% natural gas in the natural-gas/air mixture. The

authors found that the most probable explanation of the apparent paradox

that catalytic action of a solid surface tends to raise the ignition temperature

of a gaseous mixture is that the mixture immediately surrounding the heated

surface is consumed by surface reactions, thereby depleting the reactants to

such low levels that ame propagation is inhibited.

In a later study [Adomeit, 1965] a relation for the ignition conditions of

owing gases at hot bodies [Adomeit, 1963] was extended to conditions of

nonsteady state, for example the ignition delay from the sudden heating to

the gas-phase ignition. This type of process occurs, for example, in ignition

by electrical sparks in Otto internal combustion engines. This application

describes the great importance of the subject. Ignition delay is characteristic

for radical-chain explosions. During the ignition delay, radicals are created

through chain-branching reactions at an exponential rate while the temper-

ature is relatively constant. When the radical density suddenly reaches the

ignition limit, a signi�cant fraction of the reactants are consumed and ig-

nition takes place [Warnatz et al., 1996]. In the study, the heating source

consisted of a chromium-nickel rod coupled to electrical conductors. The

self-inductance of the discharge circuit was kept low enough that all the elec-

tric energy was converted into heat energy of the rod in a time interval much

shorter than the ignition delay. In this case the time from discharge to max-

imum temperature of the rod was 10�4s. The ignition took place in a vessel

�lled with hydrogen-air, pentane-air or propane-air at di�erent mixture de-

grees. The temperature of the chromium-nickel rod was between 700�C and

1200�C. A small section of the heated rod surface was focused on a photo-

multiplier, to measure the rod temperature and also the light output of the

combustion reaction. They also imaged the temperature of the rod plus the

surrounding gas with a Mach-Zehnder interferometer. It was observed that

the initial temperature rise in the gas is slow, determined essentially by heat

conduction. Thereafter a rapid transition occurs to a process where the tem-

perature rise is quick and determined essentially by exothermic reactions.

1The composition of the natural gas was approximately 93.2% CH4, 3.3% C2H6, 1.5%

C3H8, 0.5% C4H10, etc., and 1.5% N2.

17

One of the conclusions from the study is that in cross- ow it is the point, in

space and time, where the heat loss to the rod is smallest that determines

the ignition delay.

In the work of [Nagata et al., 1994] the rationale of studying gas-

phase ignition by a hot surface has shifted from security in coal

mines [Coward and Guest, 1927] to security on spacecraft. The ignition of

CH4/air and CH4/O2 mixtures by an electrically heated wire was studied

under normal conditions and during the 1.4 s long fall from an 11 m high

drop tower. The latter setup was used to achieve microgravity, which has

the advantage that the e�ect of convection is eliminated. It was found that

with high temperatures on the platinum wire, Tw > 1400 K, there is no im-

portant di�erence in the ignition delay for normal gravity and microgravity.

However, at lower temperatures the natural convection that occurs at normal

gravity cools the gas, thus delaying the ignition as compared to microgravity

conditions where no natural convection exists. Because of this, the CH4/air

mixture is less in uenced by gravity than the CH4/O2 mixture since the for-

mer requires wire temperatures above 1400K to ignite at all. In a later study

it is found, by numerical calculations and by experiments, that the wire tem-

perature required for ignition is higher for a catalytic wire than for an inert

wire [Kim et al., 1997]. The numerical results show that reactants near the

catalytic wire are consumed by catalytic reactions. Therefore a higher tem-

perature is required to ignite a mixture with a catalytic wire than with an

inert wire.

Wire Flow Experiments

Catalytic ignition of H2+O2+N2 mixtures on platinum wires was studied

by [Rinnemo et al., 1997a]. Catalytic ignition, in contrast to gas-phase igni-

tion by a (hot) catalytic surface, occurs when the heat release by chemical

reactions on the surface becomes higher than the heat transport from the

surface. This happens at a certain temperature because the heat transport

increases approximately linearly with temperature while the chemical power

release is almost exponential. The study contains a sensitivity analysis which

shows that it is the adsorption and desorption that are most important for the

ignition process. For example, one calculation was made where all activation

barriers for the surface processes were unrealistically set to zero. This did

not have any in uence on the numerical results for the ignition temperature.

In another work [Rinnemo et al., 1997b] CO+O2 mixtures were studied

and it was found that the ignition process is very similar to the one for

H2+O2+N2.

18

Stagnation Flow towards a Foil

In most cases the stagnation ow is achieved by a gas ow towards a surface.

This is the method used in Papers 1 and 2 in this licentiate thesis and the

geometry is shown in Fig. 4.6.

An analysis of the transient ignition of a combustible mixture by a hot,

isothermal body with non-catalytic surface inserted in a stagnant ow was

made by [Law, 1979]. It was found that the ignition process occurs close to

the surface and hence is minimally a�ected by the geometry of the surface.

This was particularly clear in the case where the body was a spherical par-

ticle. It was found that the ignition process, to �rst order of accuracy, was

identical for spherical particles and in�nite surfaces.

The study of spherical particles in [Law, 1979] was extended to parti-

cles with a catalytic surface in [Law and Chung, 1983]. The e�ect described

in [Coward and Guest, 1927] that a catalytic surface raises the ignition tem-

perature for a gas mixture was demonstrated analytically. It was also shown

that in certain circumstances an increased particle temperature could in fact

inhibit ignition. This would be because although the Arrhenius factors in-

crease with increasing temperature, the concentration of reactants decrease

so much that the ignition is inhibited by the increase in temperature.

Both catalytic and gas-phase ignition, and extinction, were studied at at-

mospheric pressure in [Song et al., 1990]. By increasing the temperature

of a resistively heated platinum foil it was observed that catalytic igni-

tion occurred at 500-600�C, depending on mixture ratio, for methane/air

mixtures, and near 200�C for propane/air mixtures. At ignition the tem-

perature of the foil increased considerably and the supplied electric power

could be decreased. When the power became too low, extinction occurred

at 800-900�C and around 400�C for the respective mixtures. For some mix-

tures, extinction never occurred even if the power supply to the foil was

cut o�; this was referred to as a self-sustained autothermal steady state.

Homogeneous ignition, where the ignition takes place in gas phase, was ob-

served at surface temperatures from 1220�C at 5% methane to 1513�C at

10% methane, and from 1000�C at 3% propane to 1200�C at 6% propane.

The maximum in homogeneous ignition temperature thus occurred at sto-

ichiometric mixtures, which as we have seen is typical for heated catalytic

surfaces [Coward and Guest, 1927], [Law and Chung, 1983]. Finally, the au-

thors point out that the results were relatively insensitive to geometry, as also

mentioned in [Law, 1979], and thus many of the qualitative features of the

results for a catalytic foil should be similar to those of more practical systems

like gauzes and monoliths; see also section 2.3.

[Williams et al., 1992] studied OH LIF over a polycrystalline platinum

19

foil exposed to mixtures of H2, O2 and H2O at surface temperatures be-

tween 1000 and 1800 K. The model used was essentially the same as

in [Hellsing et al., 1991] except that O2 was assumed to have a �rst-order

adsorption, sO2(�) = sO2

(0)(1 � �), and that reaction 2.26 was made re-

versible since both water formation and decomposition were studied. The

study ends up with an enthalpy diagram that complements the work

of [Anton and Cadogan, 1990] which was done at low and intermediate sur-

face temperatures. The authors emphasize that the studied reaction can be

used as a model for surface combustion in general. In particular, they made

the generalization that at low surface temperatures, reaction kinetics are lim-

ited by the availability of free surface sites, while at high surface temperatures

the reaction kinetics are limited by the availability of a reactant.

Numerical analysis of the catalyzed combustion of lean hydrogen-oxygen

mixtures in a stagnation ow over a platinum surface and in a at-plate

boundary layer was made in [Warnatz et al., 1994]. Both gas-phase and

surface-phase chemistry were taken into account. The mathematical for-

mulation is the same as described in section 3.4 and the solution is obtained

with the same software package, Chemkin, as was used in the work of this

licentiate thesis. The article is very generous with data and much of it has

been adopted in Papers 1 and 2 in this work. One important di�erence in

the surface reaction scheme is that, instead of considering the dissociative ad-

sorption of reactants as a single reaction, as done in most other works with a

detailed surface-reaction scheme, the adsorption occurs via a precursor state.

This means that the reactant �rst adsorbs as a diatomic molecule (H2 or O2)

and then, when adsorbed on the surface, dissociates into two surface atoms.

The sticking coe�cients are chosen as sO2(0) = 0:023 and sH2

(0) = 0:05

based on the work by [Ljungstr�om et al., 1989]. The authors �nd that the

ignition process is sensitive to the activation energy for the dissociation of

molecularly adsorbed hydrogen, and they emphasized the need for more de-

tailed experiments in order to �x the important parameters. However, with

the help of the experimental data from [Ljungstr�om et al., 1989], they man-

age to tune in a reasonable value for the above-mentioned activation energy

by �tting the calculations to the experimental results.

In [Behrendt et al., 1995] a numerical analysis of the heterogeneous oxi-

dation of a methane/air mixture in an atmospheric-pressure stagnation-point

ow onto a platinum foil is performed. The emphasis of the study is on sensi-

tivity analysis of the di�erent reaction steps. It is found that at steady state

conditions after the ignition has occurred, the system reaches a di�usion-

limited state and no surface reaction has any relevant in uence on the cov-

erage of the surface.

Experiments and numerical analysis on the hydrogen/oxidation process

20

on a polycrystalline platinum foil were also performed by [Ikeda et al., 1995].

Species concentration pro�les were measured with gas chromatography, and

temperature pro�les were measured with a thermocouple. From the study it

is concluded that the activation energy for reaction 2.23, Ha+OHa *)H2Oa,

is appreciably lower at the high coverages under which the measurements and

calculations were done, compared to the low-coverage case of previous low-

pressure and high-temperature studies.

The heat release by recombination of O and N atoms on a silicon-dioxide

surface was studied theoretically in [Deutschmann et al., 1995]. During re-

entry of the Space Shuttle, or any orbiter, in the upper atmosphere, a shock

wave forms in front of the vehicle and leads to a very high translational

temperature in the ow �eld. Nitrogen and oxygen molecules are dissoci-

ated, and a non-negligible part of the O and N atoms produced strike the

surface of the orbiter and recombine catalytically to molecules, generating

heat. This heat of recombination is responsible for a considerable part of the

increase of the orbiter surface temperature. The model for recombination

contains both Langmuir-Hinshelwood reactions, that is, adsorbate/adsorbate

reactions, and Eley-Rideal reactions, that is, adsorbate/gas-phase species re-

actions. It is found that at low temperatures, when the surface is well covered

by adsorbed N and O, the recombination is dominated by Eley-Rideal reac-

tions because the activation barriers, for this particular surface, are relatively

high for Langmuir-Hinshelwood reactions. As the temperature increases, the

latter reactions become increasingly important. Both a catalytic and an inert

model for the surface were used, and it was found that the surface temper-

ature increased and the concentrations near the surface were in uenced by

the catalytic surface model.

Flat-Plate Boundary Layer Combustor

The at-plate boundary layer geometry is interesting to study from

a fundamental viewpoint, but practical aspects such as ame stabi-

lization and accidental explosions are also relevant, as pointed out

by [Law and Law, 1981]. The authors study gas-phase ignition using a com-

bined perturbation/numerical procedure. In contrast to many other previous

studies, reactant consumption was taken into account, and was shown to be

an important factor for the ignition process.

In [Cattolica and Schefer, 1982] the development of a combustion bound-

ary layer formed by a lean hydrogen/air mixture over a at plate at tem-

perature T=1170 K was investigated. Platinum and quartz were used as

surface material. The OH concentration pro�les were measured by LIF and

the temperature pro�les were measured by Rayleigh scattering. It was found

21

that near the leading edge, that is, where the gas �rst hit the surface, the

OH pro�les indicated a net OH production for both the platinum and the

quartz surface. However, further downstream the development of the OH

pro�les di�ered. The OH concentration pro�le from the platinum surface

became higher and propagated faster into the unburned combustion gas.

Furthermore it displayed a negative slope into the surface, which indicated

a net sink e�ect. This was in marked contrast to the concentration from the

quartz surface, which did not show a net sink e�ect anywhere. An interesting

observation was that for the quartz surface the surface energy release was not

zero. This would mean that the quartz surface was not completely inert but

that some hydrogen oxidation took place on it. The authors also solved the

equations for the gas-phase chemistry and introduced the surface e�ects as

di�erent types of boundary conditions, depending on whether the surface was

modeled as noncatalytic, supported oxidation but not radical recombination,

or as fully catalytic where both oxidation and radical recombination on the

surface took place. The model failed to reproduce the experimentally mea-

sured OH concentration pro�les downstream of the combustor. The authors

claimed that in order to improve the model an improved surface-chemistry

model, which incorporates both �nite-rate radical production and recombi-

native reactions, would be needed.

[Brown et al., 1983] performed the same type of experiment for a plat-

inum surface but in the surface temperature range 450-1070 K and at various

lean hydrogen/air mixtures. The model used for the catalyst reaction was

the same as the one supporting oxidation but not radical recombination used

in [Cattolica and Schefer, 1982]. Signi�cant surface reaction was found to

occur at all temperatures studied.

[Warnatz et al., 1994] also simulated the at-plate boundary layer reac-

tive ow over a platinum and a quartz surface. Their results were compared

with the experimental results of [Cattolica and Schefer, 1982]. Signi�cant

di�erences were reported for the OH concentration pro�les between the two

articles. However, [Warnatz et al., 1994] noticed that if the surface temper-

ature is increased from 1170 K, as reported in [Cattolica and Schefer, 1982],

to 1210 K the agreement becomes good. It was therefore suggested that un-

certainty in the temperature measurement in [Cattolica and Schefer, 1982]

was relatively large. It was concluded that combustion under the studied

conditions should mainly be a gas-phase process.

An early study with planar OH LIF and a two-dimensional ar-

ray detector was made by [Pfe�erle et al., 1988, Pfe�erle et al., 1989a,

Pfe�erle et al., 1989b]. The process of gas-phase ignition in an atmospheric

pressure ethane/air boundary layer over heated catalytic and non-catalytic

surfaces was investigated. The experimental setup was meant to simulate

22

the entrance of a catalytically stabilized thermal (CST) combustor; see sec-

tion 2.3. Single point measurements of OH and O were also performed. The

oxygen atoms were probed by two-photon absorption. The radical concentra-

tion pro�les demonstrated that the platinum catalyst acted to promote gas-

phase oxidation of ethane for mixtures with an equivalence ratio � < 0:35 and

it inhibited gas-phase reactions for richer mixtures. � is the fuel-air equiv-

alence ratio, which is the actual fuel-air ratio divided by the stoichiometric

fuel-air ratio. It was believed that mass transfer-limited oxidation reactions

accounted for the inhibiting e�ect at rich mixtures. In [Gri�n et al., 1992]

the studies were extended to low pressures, 40-175 torr, and several fuels:

acetylene, hydrogen and methane. By decreasing the pressure, the length

scales increase and thereby the spatial resolution. From the studies it is con-

cluded that a platinum surface can stabilize gas-phase combustion both by

providing energy and by promoting the formation of reactive intermediates

important in fuel-air ignition.

A computational study of methane/air combustion over heated catalytic

and non-catalytic surfaces was made in [Markatou et al., 1993]. The e�ect of

di�erent surface-reaction boundary conditions on ame propagation and on

the development of radical pro�les in the gas phase was studied. The e�ect

of desorption of OH radicals from the surface on the radical pro�les and on

the ame propagation was also studied. It was shown that an accurately

measured temperature pro�le as temperature boundary condition was neces-

sary to decouple temperature e�ects and species boundary condition e�ects

on the development of radical pro�les.

2.3 Higher Pressures

The studies done at subatmospheric pressures are mostly con�ned to simple

model experiments. In this section we will focus on the applications at which

the studies done in the previous sections were aiming. Most of the material

is taken from [Hayes and Kolaczkowski, 1997]. In many cases, but not all,

the reason why heterogeneous combustion is preferred to conventional ho-

mogeneous combustion is the need of reducing emissions of NO and NO2,

commonly denoted NOx. Therefore this section is introduced with a brief

description of the ways in which NOx is formed.

A remark on the language is in place here. The expression catalytic

combustion is not well de�ned. For example [Hayes and Kolaczkowski, 1997]

refer to catalytic combustion as a process occurring on a surface. They

distinguish between:

23

� catalytic combustion, where combustion occurs primarily on the cat-

alytic surface and the aim is to minimize gas-phase combustion, and

� catalytically supported homogeneous combustion, or catalytically stabi-

lized combustion, where intermediates are formed at the surface and

then desorb into the gas. If this is accompanied by su�ciently high

temperature and/or pressure, then homogeneous combustion may be

initiated and sustained.

In [Pfe�erle and Pfe�erle, 1987] the term igneslytic is proposed for surface-

induced gas-phase combustion, that is, the second type above. It seems,

however, that this term has gained limited acceptance.

NOx Formation Mechanism

The two nitrogen oxides NO and NO2 are described by the generic formula

NOx. The molecule that is primarily formed in combustion is NO. NO2 may

also be formed, for example by oxidation of NO. The source of NOx emissions

is, however, NO and therefore this section will not include NO2 formation.

Thermal NO Thermal NO, also called Zeldovich NO [Zeldovich, 1946],

is initiated at temperatures above 1200�C by oxidation of molecular nitrogen

by oxygen atoms. It is signi�cant at temperatures higher than 1500�C. The

reaction scheme is:

O2 +M *) 2O +M (2.28)

N2 +O *) NO +N (2.29)

where M is an arbitrary molecule transferring energy.

Prompt NO Prompt NO, also called Fenimore NO [Fenimore, 1979],

is formed in combustion chambers that operate with hydrocarbon fuel-rich

ames. The molecular nitrogen reacts with the hydrogen radicals derived

from the fuel according to

N2 + CH *) HCN +N (2.30)

N +OH *) H +NO: (2.31)

Prompt NO, in contrast to thermal NO, is also produced at relatively low

temperatures, down to about 700�C.

24

NO Generated via N2O The N2O mechanism is analogous to the

thermal mechanism in that oxygen atoms attack molecular nitrogen. How-

ever, with the presence of a third molecule M, the outcome of this reaction

is N2O [Wolfrum, 1972]:

N2 +O +M ) N2O +M: (2.32)

The N2O may subsequently react with O atoms to form NO according to

N2O +O) NO +NO: (2.33)

Normally the N2O mechanism is negligible, but in lean premixed combustion

in turbines the N2O route is the major source of NO [Warnatz et al., 1996].

Fuel-bound NO Fuel-bound NO arises from the oxidation of nitrogen

compounds contained in the fuel. The oxidation process occurs via the for-

mation of intermediates, HCN being one of the most common intermediates

formed.

Catalytic Converters

Prior to the year 1966 emissions from vehicle exhaust systems were uncon-

trolled. In 1966, California required control of hydrocarbons and CO, and in

1968 the US Federal Government also introduced regulations governing the

acceptable level of harmful emissions. Following the introduction of the Clean

Air Act of 1970 in the USA, permissible limits were de�ned for concentration

levels of CO, HC and NOx in auto exhausts.

Evidently it is better to prevent harmful emissions from being formed in

the �rst place, but in the case of internal combustion engines for cars this

cannot yet be fully achieved. There are two basic types of auto catalysts,

the oxidation catalyst and the three-way catalyst. Both are typically made

of a porous catalyst material, washcoat, covered with noble metal in some

form. The oxidation catalyst consists of platinum and/or palladium, which

are good materials for oxidizing CO and HC in an oxygen-rich environment,

that is, when the engine is run on a slightly lean mixture. The three-way

catalyst, used in modern cars, manages the feat of oxidizing CO and HC at

the expense of the oxygen in NOx, thereby also reducing the NOx to N2.

In order to achieve this the engine should be operated near a stoichiometric

mixture. In three-way catalysts the catalyst material is a mixture of platinum

and rhodium particles, typically in a ratio of 5 to 1.

Another way of reducing NOx is by adding ammonia, NH3, to the exhaust

gas. Ammonia acts as a reducing agent and by reactions with oxygen the

25

products become N2 and H2O. This method is called Selective Catalytic

Reduction (SCR) and is mainly used to clean exhaust gas from fuel-�red

power plants.

Catalytic Combustors in Gas Turbines

In gas turbines the main emission concern is thermal NOx. There are two

ways of attacking the primary NOx problem inside the gas turbine, that is,

in the direct combustion process and not by cleaning the exhaust gases. The

di�erence between the two methods concerns in what way the surface should

modify the combustion process.

In the �rst type, called Catalytic Combustor with a Homogeneous Zone,

the primary purpose of the catalyst is to convert fuel to CO2 and H2O and, as

a result of the released heat energy, raise the temperature of the gas mixture

to a point at which homogeneous gas-phase reactions are initiated.

In the second type, the Catalytically Stabilized Thermal (CST) Combus-

tor [Pfe�erle and Pfe�erle, 1987], the catalyst converts the fuel to interme-

diates that may support homogeneous reactions at fuel/air ratios that would

otherwise be too lean to sustain a ame. This will lower the combustion

temperature and thereby decrease the production of thermal NOx. However,

as will be seen in Paper 2 of this work, the presence of a catalyst surface in

a region where gas-phase reactions are trying to be sustained may also be

counterproductive, as the surface may also quench radicals that have been

created in the gas phase.

Catalytic Process Heating

In the process industry there are many examples where combustion takes

place in order to heat uids or to provide the energy to support endothermic

reactions. In conventional homogeneous combustion of this type the ame

temperature is often above 1500�C, making NO production by the thermal

route important. This could be minimized if catalytic combustion were used.

However, as [Hayes and Kolaczkowski, 1997] point out, the commercializa-

tion of this type of catalytic combustors has been relatively slow. This is

mainly due to problems with extinguishing of the catalytic combustion by

the cold uids, and to problems with hot spots which damage the catalyst

or the support.

Catalytic Combustion inside Internal Combustion Engines

The purpose of internal combustion engines is the production of mechanical

power from the chemical energy contained in the fuel. In internal combus-

26

tion engines, as distinct from external combustion engines, this energy is

released by combustion inside the engine, that is, inside the cylinder. This

con�nement of the combustion process into a certain volume implies that the

container walls may play a role in the overall process. Furthermore, due to

the nature of a propagating ame, hot burned gas pushing colder unburned

gases in front of it, the surface may play an even greater role than one might

expect at �rst. Let us consider two-dimensional ame propagation in a circle

with the spark-plug in the centre. Some calculations show that when 50%

of the fuel mass has been consumed, the ame front has made 90% of its

way to the wall [Heywood, 1988]. This shows the importance of possible wall

e�ects. Half of the combustion process will take place at a distance from the

wall equal to or less than 10% of the container radius.

Studies show that the use of catalyst coatings inside the cylinder can be

both bene�cial, in aiding fuel ignition, and detrimental because of ame-front

quenching at the combustor chamber surfaces. [Jones, 1997] showed that sur-

face �lms of metal oxides exhibit catalytic activity, but rapidly become less

e�ective with successive tests. One application that is commonly used in

modern cars is Pt-tipped spark-plugs where, it is believed, they promote

ignition of lean mixtures [Jones, 1997].

[Beyerlein and Wojcicki, 1988] achieved catalytic prereaction by pass-

ing the fuel mixture through a platinum wire mesh in a prechamber. The

prechamber concept consists of an auxiliary combustion chamber above the

piston. The fuel (Diesel engine) or the fuel/air mixture (Otto engine)

passes the prechamber before entering the cylinder, where the main part

of the chemical energy is released into heat [Heywood, 1988]. The study

of [Beyerlein and Wojcicki, 1988] showed that the catalytic prechamber con-

cept can substantially increase mixture ame velocity and reduce ignition

energy requirements. If catalytic oxidation were extensive enough, it would

be possible to reduce the minimum ignition energy to zero, thereby inducing

an autoignition of the fuel/air mixture.

Catalytic Radiant Heaters

Radiant heaters range in performance from domestic or tent radiant heaters,

to heaters conceived for manufacturing processes such as drying wet paint

or curing materials. There are two types of catalytic radiant heaters: (1)

countercurrent convective di�usive radiant heaters where the fuel (most often

natural gas or propane) comes from a container into a catalytic pad, while

the air comes from outside the pad, and (2) co-current radiant heaters where

the fuel and air are premixed before they enter the catalytic pad. The aim

with catalytic radiant heaters is primarily to sustain a combustion process

27

at relatively low temperatures in order to make them comfortable to use, for

example, in a tent. The primary goal is not to minimize NOx production.

Finally we round o� this chapter by mentioning the catalytic curling

iron [Saint-Just and der Kinderen, 1995], heated by propane which is com-

busted over a catalytic surface. The purpose of the catalyst is to stabilize

complete combustion at a very low temperature, around 55�C.

28

Chapter 3

Hydrogen Oxidation Chemistry

with Surface E�ects

This chapter deals with how we imagine that the studied reaction takes place.

We start by giving an intuitive view of what heterogeneous catalysis really

is. With this in mind we attack the thermodynamic and reaction-kinetic

expressions that are relevant for the hydrogen oxidation process studied in

this work, on a surface and in gas phase. The chapter ends with the important

topic of how to simulate the exact results of the chemical process, according

to the model that we believe to describe it.

3.1 Introduction to Heterogeneous Catalysis

When hydrogen and oxygen gases are mixed in a container at ambient tem-

perature, not very much happens. However, if we compare the enthalpy of

H2+1/2O2 with the enthalpy of H2O, the water molecule lies 2.5 eV below

the gas mixture. The reason why the oxidation of hydrogen into water does

not take place spontaneously despite this enthalpy di�erence is that there is

an activation barrier that has to be surmounted. In the studied reaction, the

major barrier is the energy required to break the bond between the atoms in

the oxygen and hydrogen molecules.

The e�ect of a catalytic surface is to lower the activation barriers and/or

to open up new reaction channels. In the case of hydrogen oxidation on a Pt

surface, the most important aspect is the lowering of the energy required to

break the bond in an oxygen or a hydrogen molecule. The reason why, for

example, an oxygen molecule is stable is that there is an enhanced electron

density between the two positive nuclei. This acts as a negative glue keeping

the two nuclei together. However, if the molecule approaches the surface

29

it can be physisorbed, chemisorbed or dissociated by charge transfer into

atoms bonded to the surface. Consequently the molecule can separate into

two reactive atoms, and water is formed from adsorbed atomic oxygen and

hydrogen on the surface more easily than in the gas phase.

The stable oxygen and hydrogen molecules can however react if a match

is inserted into the container, the reaction will go o�: an ignition occurs.

What is really happening is that the heat from the match breaks the bond

in many molecules, which produces reactive radicals such as O and H atoms.

Then the atoms can react into water, and for each produced water molecule

there will be a heat release of 2.5 eV. The radicals and the produced energy

will promote the bond-breaking in other molecules and a chain reaction will

take place: an ignition occurs.

3.2 Thermodynamics

The �rst law of thermodynamics reads:

dU = �Q+ �W (3.1)

where dU is the change of internal energy, �Q is the heat transferred to the

system and �W is the work done on the system. The reason why a d is used

to indicate an in�nitesimal change in the internal energy U , while a � is used

for the heat and work, is that U is a state variable while Q and W are not.

This means that U is uniquely determined by the state of the system, that

is, by its pressure, volume, and temperature, while Q and W also depend on

the history of the system. If there is no other work than compression made

on the system we can write1 �W = �pdV and thus

dU = �Q� pdV : (3.2)

It is convenient to introduce a state variable, H, de�ned as

H = U + pV (3.3)

which implies

dH = �Q+ V dp; (3.4)

or

dH = �Q (3.5)

1To do positive work on a system, for example a balloon, one has to squeeze it, that is,

decrease its volume, and accordingly �V < 0) �W = �pdV > 0.

30

Ea

OH+H

Enthalpy [eV]

2.4

2.5

2.6

2.7

2.8

2.9

+H O2

Figure 3.1: Enthalpy diagram for the reaction H2 +O *) OH +H.

for constant pressure. The state variable H (which should not be confused

with the hydrogen atom H) is called the enthalpy and is extensively used in

chemistry. Let us study the elementary reaction

H2 +O *) OH +H: (3.6)

The enthalpy diagram for the reaction is shown in Fig. 3.1. What is the

enthalpy axis in Fig. 3.1 referring to? It is the heat of formation for the

molecule from the pure elements in their most stable form. Since H2 is the

most stable form of hydrogen, this means that the enthalpy of H2 is zero.

The enthalpy of OH on the other hand is higher than zero, since a positive

amount of heat energy is required to form OH radicals from stable O2 and H2

molecules. One should however keep in mind that the absolute enthalpy scale

is arbitrary, it is di�erences in enthalpy that matter. As is seen in Fig. 3.1

the enthalpy for H2 +O is lower than the enthalpy for OH +H. This gives

us an general idea of which direction the reaction \likes" to go in, as long

as there are no large entropy changes. The second law of thermodynamics

results from the observation that a process which only withdraws heat from

31

a cold system and transfers it to a warmer system is not possible; it is rather

the opposite that happens. If for example we look at a warm system, a

ame, and a colder system, the surrounding air, this means that there will

be a heat transfer from the ame to the surrounding air. The heat comes

from the combustion reactions in the ame. This does not mean that each

single reaction event gives up heat energy, that is, lowers the enthalpy of the

participating species; but averaged over many reaction events, they do. In

conclusion, the above reaction \likes" to go from right to left since it gives

up enthalpy into heat energy in this manner.

A way of quantifying the balance of a reaction at equilibrium is with the

equilibrium constant, Kp. Kp is de�ned as the product of the equilibrium par-

tial pressures of the reaction products divided by the partial pressures of the

reactants, with each species having the same exponent as its stoichiometric

coe�cient. Or, to be more speci�c, if we study the overall reaction

H2 +1

2O2

*) H2O (3.7)

this would mean that

Kp =pH2O

pH2� ppO2

(3.8)

since the stoichiometric coe�cient of O2 is 1/2.

The equilibrium constant can be calculated by statistical-

thermodynamics methods and spectroscopic data. For example, for

the overall water production reaction 3.7 above, the equilibrium constant is

found to be 1:6 � 1010 atm�1=2 at T=1000 K [McQuarrie, 1976, Zeise, 1937].

We get

Kp =pH2O

pH2� ppO2

) pH2O= pH2

� ppO2�Kp = 1:6 � 1010pH2

� ppO2: (3.9)

Imagine that we have a mixture of H2, O2 and H2O at equilibrium. If the

partial pressures of hydrogen and oxygen are the same, pH2= pO2

= 1:6�10�7atm, then the partial pressure of water vapor will be

pH2O= 1:6 � 1010 � 1:6 � 10�7 �

p1:6 � 10�7 � 1 atm. (3.10)

That is, the partial pressure of water is seven orders of magnitude higher than

the partial pressures of H2 and O2 at 1000 K. But this is not consistent with

our experience from high-school chemistry classes where we mixed hydrogen

and oxygen and nothing happened (before we lit the match, of course). It

could be argued that the gas mixture will self-ignite, but this is in fact not

the case at partial pressures of hydrogen and oxygen as low as those above.

32

The resolution of the problem is that the concept of an equilibrium constant

is not applicable, since the H2/O2 mixture is not at equilibrium. The reaction

goes very slowly, but if we were to let the mixture equilibrate, during a very

long time, almost all of the atoms would be bound in water molecules in the

end. One way of speeding up the reaction rate is with a catalyst, as described

in the introduction to this chapter, or to start a chain reaction with the help

of a match, where the radicals and heat released from one reaction promotes

the reaction of other molecules and so on.

3.3 Reaction Kinetics

Consider again reaction 3.6, H2+O*)OH+H. When H2 and O react into

OH and H they are assumed to do so via a transition state, also called an

activated complex. This is, as the name suggests, a very complex state which

occurs only during the transition of the reaction from H2 and O to OH and

H. An activated complex is not a reaction intermediate that can be isolated

and studied like ordinary molecules [Atkins, 1987]. The energy required to

create a transition state is called the activation energy, Ea, and is indicated

in Fig. 3.1. If the collision between the H2 molecule and the O atom occurs

at a lower energy than Ea the transition state cannot be formed and the two

reactants are just scattered against each other. If the system is at thermal

equilibrium at temperature T , the probability that the total kinetic energy

of the H2 molecule and the O atom is as high as Ea is proportional to the

Boltzmann factor exp(�Ea=kT ) where k is Boltzmann's constant.

The rate at which H2 and O react should be proportional to the amounts

of the reactants in the gas. Thus we write

reaction rate / kf [H2][O] (3.11)

where [H2] and [O] are concentrations of the respective reactants, and kf is

called the forward rate constant. Since the reaction rate should be propor-

tional to the Boltzmann factor exp(�Ea=kT ), as explained above, we write

kf = A exp(�Ea=kT ) (3.12)

where A is the constant of proportionality between the concentrations of re-

actants and the rate at which they collide. The expression 3.12 was found em-

pirically at the end of the nineteenth century by the Swedish chemist Svante

Arrhenius [Arrhenius, 1889] and is therefore called Arrhenius' expression in

his honour. A more general form for the rate constant is

kf = AT� exp(�Ea=kT ): (3.13)

33

This expression admits a more detailed description for the rate constant and

is used when the reaction in question is well studied and well understood.

For the particular reaction 3.6 the forward rate constant is

kf = 5:06 � 104T 2:7 exp(�3165=T ) (3.14)

where the temperature T is given in Kelvin. Thus the rate at which H2 and

O react into OH and H in reaction 3.6 is

reaction rate = 5:06 � 104T 2:7 exp(�3165=T ) � [H2][O] mole/cm3s: (3.15)

This however is only the forward reaction rate, that is, from left to right. The

reverse reaction rate is given by the reverse rate constant kr. If the forward

rate constant is known, as in Eq. 3.14, the reverse rate constant is given by

kr =kf

Kc

(3.16)

where Kc is the equilibrium constant given in concentration units, that is,

as a ratio of concentrations instead of a ratio of partial pressures as in Kp

used above. Kc can be derived from the equation for Kp by substituting

pi = ciRT , where pi and ci are the partial pressure and molar concentration

of the i:th species, respectively, and R is the universal gas constant R = NAk.

NA and k are Avogadro's constant and Boltzmann's constant, respectively.

By using statistical-thermodynamics methods the equilibrium constant Kc

can be obtained from thermodynamic data. In fact, Kc can be expressed as

Kc = exp(�(�U0

RT� �S0

R)) (3.17)

where �U0 and �S0 are the di�erences in standard-state internal energy and

entropy between products and reactants, that is, between the right-hand-side

species and the left-hand-side species. The standard state is de�ned at ptot=1

atm [Kee et al., 1996].

For gas-phase reactions whose thermodynamic properties are well known,

the use of Eq. 3.16 and the evaluation of Kc from thermodynamic data as

in Eq. 3.17 are the normal way of describing reverse reaction rates when the

forward reaction rate is known. However, when the thermodynamic proper-

ties are not well known, as is often the case for adsorbed species on a surface,

this method fails. Then an elementary reversible reaction can be split into

two irreversible reactions. A typical example is the adsorption/desorption of

a species, where the adsorption is de�ned as an irreversible reaction charac-

terized by a sticking coe�cient and the desorption reaction is characterized

by an Arrhenius expression.

34

3.3.1 Gas-Phase Reactions

As mentioned above, the gas-phase species and reactions are relatively well

known [Warnatz et al., 1994], especially for the hydrogen oxidation reaction.

Therefore a set of reversible reactions characterizes the whole gas-phase re-

action mechanism. The gas-phase reactions used in the simulations in Pa-

pers 1 and 2 are shown in Table 3.1. The parameters are taken mainly

from [Baulch et al., 1992] and have been obtained from several shock-tube

experiments, studies of ames, ow reactors and stirred reactors. Notice

that, with the units of Table 3.1, the forward rate constant is given by

kf = AT� exp(�Ea=RT ). The use of the universal gas constant R instead

of the Boltzmann constant k means that the activation energies are given in

Joules/mole instead of Joules/molecule. The reactions including a species

M on both sides, such as the G5 reaction H+H+M*)H2+M, are three-body

reactions. These reactions require a third body in order to occur. If for

example two hydrogen atoms hit each other, they would quickly dissociate

again if there were not a third body that could take up the surplus energy

from the collision and thus leave the hydrogen atoms in a state where a di-

atomic hydrogen molecule can be created. Some molecules are more e�cient

than others in taking up energy. In this reaction scheme, the water mole-

cule is believed to be 6.5 times more e�cient than an average molecule in

its energy adsorption capability. On the other hand, the oxygen molecule is

believed to be less e�cient than the average molecule, with an enhancement

factor 0.4. An important feature of three-body reactions is their pressure

dependence. At low pressures they are relatively slow since their reaction

rate is proportional to the third power of the pressure. As the pressure in-

creases, however, they become increasingly important, competing with the

other two-body reactions.

3.3.2 Surface-Phase Reactions

When surface chemistry is added to a system, not only surface reactions

are added but also a new type of process, the transport of species between

the two-dimensional surface and the three-dimensional gas phase. These

processes constitute the interface between surface and gas chemistry, except

for energy transfer that takes place without mass transport, such as radiation

from the surface. The common way to characterize transfer of a molecule

from the gas to the surface, that is, adsorption, is by a so-called sticking

coe�cient s. The sticking coe�cient is simply the probability that a molecule

hitting the surface will adsorb onto it and not bounce back into the gas.

However, when more and more atoms are adsorbed on the surface, there will

35

Table 3.1: Gas-phase reactions of hydrogen oxidation. Forward rate con-

stants are given in the form kf = AT� exp(�Ea=RT ).

Reaction A[depends on reaction] �[none] Ea[Joules/mole]

G1 O2+H*) OH+O 2:00 � 1014 0.0 70300.0

G2 H2+O*) OH+H 5:06 � 104 2.7 26300.0

G3 H2+OH*)H2O+H 1:00 � 108 1.6 13800.0

G4 OH+OH*)H2O+O 1:50 � 109 1.1 420.0

G5 H+H+M*)H2+M 1:80 � 1018 -1.0 0.0

G6 O+O+M*)O2+M 2:90 � 1017 -1.0 0.0

G7 H+OH+M*)H2O+M 2:20 � 1022 -2.0 0.0

G8 H+O2+M*)HO2+M 2:30 � 1018 -0.8 0.0

G9 HO2+H*)OH+OH 1:50 � 1014 0.0 4200.0

G10 HO2+H*)H2+O2 2:50 � 1013 0.0 2900.0

G11 HO2+H*)H2O+O 3:00 � 1013 0.0 7200.0

G12 HO2+O*)OH+O2 1:80 � 1013 0.0 -1700.0

G13 HO2+OH*)H2O+O2 6:00 � 1013 0.0 0.0

G14 HO2+HO2*)H2O2+O2 2:50 � 1011 0.0 -5200.0

G15 OH+OH+M*)H2O2+M 3:25 � 1022 -2.0 0.0

G16 H2O2+H*)H2+HO2 1:70 � 1012 0.0 15700.0

G17 H2O2+H*)H2O+OH 1:00 � 1013 0.0 15000.0

G18 H2O2+O*)OH+HO2 2:80 � 1013 0.0 26800.0

G19 H2O2+OH*)H2O+HO2 5:40 � 1012 0.0 4200.0

36

be less and less space for an impinging molecule to be adsorbed on. The

degree of coverage is called � and is de�ned as

� � adsorbed molecules per area

adsorption sites per area: (3.18)

For a hydrogen atom the sticking probability is assumed to decrease linearly

with coverage according to

sH(�) = sH(0)(1 � �) = sH(0) � fH(�) (3.19)

where sH(�) is the sticking coe�cient at coverage � and fH(�) is the functional

dependence of the sticking coe�cient on the coverage. In Table 3.2 where the

surface reactions are shown it is reactions S1, S3, S7, S9, S11 and S13 that

are adsorption reactions. They are characterized by the sticking coe�cient at

zero coverage. The coverage dependence f(�) is set to (1��) for all reactionsexcept the dissociative adsorption of oxygen, reaction S3. This is because

both oxygen atoms in the diatomic oxygen molecule need a free surface site

to adsorb on. Furthermore, these free sites must be located next to each

other and the probability for this is equal to the square of the number of free

sites, that is, proportional to (1 � �)2.The type of reaction where a molecule leaves the surface, desorption, is

characterized by a conventional Arrhenius expression as indicated for reac-

tions S2, S4, S8, S10, S12 and S14. Here the pre-exponential A is a measure

of the vibration frequency with which the molecule is vibrating on the sur-

face. The activation energy Ea is a measure of the strength of the bond

between adsorbate and surface.

Thermodynamic data for adsorbates are not as well known as thermo-

dynamic data for free molecules as discussed above. However, in the re-

action scheme for the hydrogen oxidation on a platinum surface given in

Table 3.2 the surface reactions S5 and S6, that is, Hads+Oads *)OHads and

Hads+OHads *)H2Oads are reversible. The thermodynamic data, that is, the

standard-state internal energy U0 and entropy S0 used in Eq. 3.17 to calcu-

late the equilibrium constant and thereby the reverse reaction rate, are taken

from [Warnatz et al., 1994].

The pre-exponential factor A, which should not be confused with the

sticking coe�cient for adsorption reactions, depends on the number of reac-

tants in the speci�c reaction. The pre-exponential factors are divided into

two groups. For reactions with only one reactant on the left-hand side,

A = 1:00 � 1013 which is of the order of the di�usion rate of hydrogen on the

surface [Elg, 1996], and for reactions with two reactants A = 3:7 � 1021. Thisdi�erence is equal to 1/�, where � = 2:72 � 10�9 is the number of platinumatoms per surface area on a Pt(111) surface.

37

Table 3.2: Surface reactions of hydrogen oxidation. Rate constants are given

either in Arrhenius form k = A exp(�Ea=RT ) or in terms of an initial sticking

coe�cient [Coltrin et al., 1996].

Reaction A[depends on reaction] Ea[Joules/mole]

S1 H2) 2Hads 0.046a 0

S2 2Hads) H2 3:70 � 1021 67542.0

S3 O2) 2Oads 0.023b 0

S4 2Oads)O2 3:70 � 1021 213240.0

S5 Hads+Oads*)OHads 3:70 � 1021 11579.0

S6 Hads+OHads*) H2Oads 3:70 � 1021 17368.0

S7 H2O)H2Oads 0.75c 0

S8 H2Oads)H2O 1:00 � 1013 42455.0

S9 OH)OHads 1c 0

S10 OHads)OH 1:00 � 1014 192977.0

S11 O)Oads 1c 0

S12 Oads)O 1:00 � 1013 365700.0

S13 H)Hads 1c 0

S14 Hads)H 1:00 � 1013 249700.0

aSticking coe�cient for zero coverage. For reaction S1 the coverage dependence of the

sticking coe�cient is linear in 1 � � as opposed to the Langmuirian (1 � �)2-dependence

that is expected for bimolecular dissociative adsorption. This linear dependence gives good

agreement with experimental data [Williams et al., 1992] and has been proposed to be due

to a physisorbed precursor state of H2 on the Pt surface [Harris et al., 1981, Ternow, 1996].bSticking coe�cient for zero coverage. The coverage dependence is of second order,

(1� �)2.cSticking coe�cient for zero coverage. The coverage dependence is of �rst order, 1� �,

since the H2O, OH, O and H molecules are assumed to occupy one Pt atom.

38

3.4 Numerical Solution Method

Thus far the chemistry of hydrogen oxidation in a heterogeneous environ-

ment, that is, an environment consisting of both gas and surface phases, has

been described. The fact that we can describe the reactions and reaction

mechanisms does not mean that we know everything about the system. In

order to calculate properties such as water production, ignition temperatures,

OH concentration and so on, we must formulate mathematical equations and,

not to forget, solve these equations. That is the subject of this section.

3.4.1 The CHEMKIN Software Package

The software that has been used in Papers 1 and 2 is the Chemkin software

package developed by Sandia National Laboratories in Albuquerque, New

Mexico and Livermore, California [Kee et al., 1989].

The Chemkin software package was developed to simulate complex chem-

ically reacting ow systems such as combustion, catalysis, chemical vapor

deposition and plasma processing. The core of the Chemkin codes consists

of �ve packages for dealing with gas-phase reaction kinetics, heterogeneous

reaction kinetics, species transport properties, thermodynamic data, and nu-

merical solution.

Chemkin [Kee et al., 1989] was developed to aid in the incorporation of

complex gas-phase chemical reaction mechanisms into numerical simulations.

The Chemkin interface allows the user to specify the necessary input through

a high-level symbolic interpreter, which interprets the information and passes

it to a Chemkin application code. To specify the needed information, the

user writes an input �le declaring the chemical elements in the problem, the

name of each chemical species, a list of chemical reactions (written in the

same fashion that a chemist would write them in, i.e., a list of reactants

converted to products), and rate constant information in the form of Ar-

rhenius coe�cients. The thermochemical information is normally obtained

from the data base described below. However, the user may also specify

thermodynamic data for species that do not exist in the data base.

The Surface Chemkin package [Coltrin et al., 1990] was designed for the

complementary task of specifying mechanistic and kinetic rate information

for heterogeneous chemical reactions. Surface Chemkin was designed to run

in conjunction with Chemkin, and execution of the Chemkin interpreter is

required before the Surface Chemkin interpreter may be run. The user inter-

face for Surface Chemkin is very similar to that of Chemkin, but is expanded

to account for the richer nomenclature and formalism required to specify

heterogeneous reaction mechanisms. Thermodynamic data must always be

39

supplied since there are no data on surface-adsorbed species in the thermo-

dynamic data base described below.

The transport software package [Kee et al., 1986] provides a multicom-

ponent, dilute-gas treatment of the gas-phase transport properties. It also

includes the e�ects of such phenomena as thermal di�usion. It has the capa-

bility of calculating, as a function of temperature, the pure species viscosity,

pure species thermal conductivity, and binary di�usion coe�cients for every

gas-phase species in the mechanism.

The Chemkin thermodynamic data base [Kee et al., 1987] contains poly-

nomial �ts, with respect to temperature, to entropy, S, enthalpy, H, and

heat capacity, cp, at 1 atmosphere pressure.

The numerical solution is obtained with the Twopnt (pronounced \two

point") program [Grcar, 1991]. Twopnt is a computer program that �nds

steady-state solutions for systems of di�erential equations.

3.4.2 Mathematical Formulation

The stagnation- ow �eld simulated in this work is shown experimentally

in section 4.3 and theoretically in Fig. 3.2. At a distance x = L below

a surface, a uniform (independent of radius) upward velocity is imposed.

The inlet gas composition and temperature are also independent of radius,

and the radial velocity component is zero. By con�ning our attention to

the center of the surface, edge e�ects can be neglected, permitting use of

a one-dimensional analysis. The temperature of the surface is a boundary

condition in the calculations and is experimentally kept �xed by an adaptive

resistive heating. At low surface temperatures, the surface chemistry is slow

and no combustion occurs. As the surface temperature is increased a surface

ignition will take place, and if either the temperature or the pressure, or

both, become high enough gas-phase combustion will also take place. In

Papers 1 and 2 of this work, we study how the gas-phase chemistry evolves

when the pressure of a H2/O2 mixture is increased from 1 to above 100 torr

with a surface temperature of 1300 K. The main goal is to �nd out how the

surface in uences the gas-phase chemistry and to what extent the qualities

of the surface, catalytic or not, are a signi�cant parameter. The conservation

equations de�ning the reactive stagnation- ow �eld are the following:

Mixture continuity

1

�

@�

@t= �@u

@x� 2V � u

�

@�

@x= 0 (3.20)

40

Surface

stagnation point

Figure 3.2: Stagnation- ow �eld used in the simulations.

Radial momentum

�@V

@t=

@

@x(�@V

@x)� ��@V

@x� �V 2 � 1

r

@p

@r= 0 (3.21)

Thermal energy

�cp@T

@t=

@

@x(�@T

@x)� �cpu

@T

@x� (cpk�YkVk

@T

@x+

�

!k hk) + Sq(x) = 0 (3.22)

Species continuity

�@Yk

@t= �@�YkVk

@x� �u@Yk

@x+Mk

�

!k= 0 (k = 1; : : : ;Kg) (3.23)

Equation of state

ptot = �RT

KgXk=1

Yk

Mk

(3.24)

and

Surface species

d�k

dt=

�

sk

�= 0 (3.25)

wherex the distance from the surface, and

t the time

are the independent variables and

41

u the axial velocity,

V the reduced radial velocity, V = v=r,

T the temperature,

Yk the gas-phase mass fractions of species k, and

�k the surface species site fractions

are the dependent variables. The other symbols are� mass density,

cp speci�c heat capacity of the mixture,

Mk molecular mass of species k,

hk speci�c enthalpy of species k,

� viscosity,

� thermal conductivity,

ptot pressure,

R universal gas constant,

Vk di�usion velocity of species k,

Sq spatially distributed thermal energy source,�

!k chemical gas-phase production rate of species k,�

sk chemical surface-phase production rate of species k,

Kg number of gas-phase species,

� surface site density.

The surface boundary condition requires that the gas-phase mass ux of

each species k, denoted jk, is balanced by the creation or depletion rate of

the species by surface reactions:

Surface boundary condition: mass conservation

jk = �YkVk =�

sk Mk (k = 1; : : : ;Kg): (3.26)

The energy balance at the surface can be written as

Surface boundary condition: energy conservation

�@T

@x�

KgXk=1

�YkVkhk = ��(T 4� T 4

x) +

Kg+KsXk=Kg+1

�

sk Mkhk��

E (3.27)

where� is the Stefan-Boltzmann constant,

� the surface emissivity,

Tw the wall temperature to which the surface radiates, and

Ks the number of surface species.

42

The term�

E represents an energy source in the surface itself, such as

resistive heating.

The description of the reactive stagnation- ow �eld studied in this work

is thus far from trivial. Eqs. 3.20 to 3.27 are of course nothing else than a ter-

rible bunch of coupled partial di�erential equations. They are not presented

here in order to clarify the studied system but rather to show its complex-

ity! Eqs. 3.20 to 3.27 are formulated in [Warnatz et al., 1994] and are in

fact a simpli�cation of a system of more general nature, where the surface

has an angular velocity and therefore the equations become even more com-

plex. This general system can be solved by the Chemkin application code

Spin [Coltrin et al., 1991]. Spin was originally developed to solve chemical

vapor deposition (CVD) problems and the name comes from the spinning

disk on which the deposition takes place. However, in our case the rotation

of the disk is set to zero which leads to Eqs. 3.20 to 3.27 above. The only

thing we must do is to supply necessary parameters, such as surface temper-

ature, inlet temperature, inlet gas mixture, and so on. From the output we

get species pro�les, temperature pro�les and coverages among many things.

This shows the great importance that the Chemkin software package has had

in this work, since we did not have to solve the above equation system our-

selves. Therefore we will now give a somewhat detailed description on how

the Chemkin software package works with Spin as the application code.

3.4.3 Structure of the CHEMKIN Package

As mentioned above, the Chemkin software package consists of several pro-

gram modules. Some of them require input from the user and some of them

do not. Here we will give an overview of what input parameters are required

to the di�erent modules, what the di�erent modules do, and how the overall

information ow converges to the output �le that contains the information

we are looking for. This is schematically shown in Fig. 3.3.

Input to Chemkin When the word \Chemkin" is used alone, in con-

trast to the expression \Chemkin software package", it is a single program

module, handling gas-phase chemistry data, that is referred to. The input

from the user to Chemkin is:

� The elements that are included in the reactions, that is, H and O.

� The species, made up of the above mentioned elements. In this work

the gas-phase species are H, O, OH, HO2, H2O2, H2O, H2 and O2.

43

� The reactions and their reaction parametersA, � and Ea; see Table 3.1.

The enhancement factors for third bodies that were discussed in sec-

tion 3.3.1 are also included in the list of reaction parameters.

Input to Surface Chemkin

� The surface species, made up of the elements in the input to Chemkin

(therefore Chemkin must be run before Surface Chemkin). In this

work the surface species are Ha, Oa, OHa, H2Oa and Pta, where Pta

represents the platinum surface.

� The density, �, of surface sites on an empty surface. In our case this

is the same as the density of Pta when the coverage of other species is

zero. As mentioned in 3.3.1 we have used � = 2:72 � 10�9 mole/cm2

corresponding to a Pt(111) surface.

� The surface reactions and their reaction parameters. These can be

either Arrhenius parameters A, � (not used for the surface reactions in

this work) and Ea, or initial sticking coe�cients s0. In the latter case

the functional dependence of the sticking coe�cient on coverage, f(�),

is also given. See also Table 3.1.

� Since the thermodynamic data base does not contain any data about

the enthalpies of surface species, these must be provided to Surface

Chemkin by the user.

Chemkin and Surface Chemkin use the input to create �les readable for

the application code that will solve a particular problem. In our case it is the

application code Spin that solves the reactive stagnation- ow �eld. Chemkin

also uses, in addition to the input provided by the user, information from

the thermodynamic data base and from the transport software package.

Input to Spin Spin formulates a boundary-value problem based on

Eqs. 3.20 to 3.27. It uses the information fromChemkin and Surface Chemkin

in addition to input that must be provided by the user. These user-provided

input data are:

� Various parameters for the numerical method, such as convergence cri-

terion, grid spacing and so on.

� A keyword that determines if the temperature pro�le is to be calculated

by the program itself or if it is provided as a boundary condition by

the user.

44

� Temperature of the surface and at the inlet.

� Mole fractions X at the inlet. In this work we used XO2= 0:9 and

XH2= 0:1.

� Velocity of the gas at the inlet.

� Pressure.

� Initial guesses regarding surface coverage of the di�erent species and

regarding the gas-phase composition near the surface.

Spin formulates a (big) equation system which is solved by the boundary-

value solver Twopnt. The output from Spin, which is what we initially were

looking for, is:

Output from Spin (with assistance from Twopnt)

� Pro�les of molar fractions Xk of the di�erent gas-phase species.

� Pro�les of the axial and radial velocities.

� Temperature pro�le; this is either a calculated pro�le, or else the same

pro�le that was given as input to Spin.

� Total density pro�le.

� Coverage, �k, of the di�erent surface species.

� Detailed information about reaction rate for each surface reaction is

given, such as mass produced per unit area and time, or mass desorbing

from the surface per unit area and time.

3.4.4 Calculation of Total Water Production

The reaction rates in the gas phase are not given speci�cally in the output

for each point in space. However, Fig. 5 in Paper 2 of this work contains

the total gas-phase water production of the system. Since this is not directly

supplied by the Spin output it must be calculated in data postprocessing.

The details for the calculations are given in Appendix A. The �nal result is

that the average gas-phase water production per unit volume is given by:

Jgas(L) =1

L(Z

L

0

2ptotMH2O

XH2O(x)

RT (x)V (x)dx� �jH2O

) [kgm�3s�1]: (3.28)

45

All data on the right-hand side in the expression above are supplied by the

Spin output �le. A MATLAB program was used to calculate Jgas(L) from

these data.

46

Surface

Chemkin

Transport

package

Twopnt

solver

ChemkinThermo-

dynamic

data base

Spin

inlet gas velocity

pressure

(temperature profile)

numerics parameters

inlet mole fractions

surface and inlet temperature

Results:

etc.

molar fractions

coverages

velocities

(temperature profile)

elements, species, reaction parameters

surface species, surface site density

reaction rate parameters, thermodynamic data

elements

Figure 3.3: Information ow for the Chemkin software package

47

Chapter 4

Experimental Setup and

Methods

Laser-Induced Fluorescence, LIF, is a technique that involves many aspects

from an experimentalist's point of view. In this chapter we �rst discuss the

theoretical foundations for energy structure in diatomic molecules in general

and the OH molecule, studied in this work, in particular. Then, once we

know which energies are possible to use, we discuss which energies are best to

use for probing OH with LIF, and how to obtain these energies in the form

of photons from a laser system. Finally we discuss the optics used for the

laser beam and the optics used for the detection system, the camera.

4.1 Molecular Structure and Transitions in

the OH Molecule

4.1.1 Energy Structure

The energy structure for a molecule is obtained as the solutions of the time-

independent Schr�odinger equation:

H = E (4.1)

where H is the Hamiltonian operator and E are the energy eigenvalues of

the equation. For a molecule the energy consists of three parts, namely

electronic, vibrational and rotational energy:

E = Eel + Evib + Erot (4.2)

48

A2Σ+

X2Π

B Σ2 +D Σ2 -

C Σ2 +

X Σ3 -

0.5 1.0 1.5 2.0 2.5Internuclear distance [A]

0

50000

100000

150000

Pote

ntia

l ene

rgy

[cm

]-1

o

Figure 4.1: Schematic diagram for the electronic energy levels of the

OH molecule. The state X3�� is the ground state for the OH+ ion.

From [Elg, 1996].

Electronic Energy

The electronic energy is due to electrostatic potential energy between and

among the electron and nuclei, as well as the kinetic energy of the electrons.

Since the electrons are much lighter than the nuclei they are also moving

much faster. This implies that the nuclei can be regarded as �xed from the

electrons' point of view. Thus for a certain con�guration of nuclei we can

solve the Schr�odinger equation without taking the movement of the nuclei

into account. This method, where the nuclei are regarded as �xed with

respect to the electrons, is called the Born-Oppenheimer approximation. For

the OH molecule the method yields the potential energy curves shown in

Fig. 4.1. The energy curves are denoted X, A, B, C etc. in order of increasing

energy.

The position of the minima on the R-axis corresponds to the equilibrium

position, Re, of the nuclei for each potential energy curve. As there are

atomic wave functions with orbital angular momentum quantum number

l=0,1,2. . . denoted by s, p, d. . . there are molecular wave functions denoted

by �; �; �. . . . However, for cylindrically symmetric diatomic molecules, such

as OH, it is the orbital angular momentum around the molecular axis that

is determined by the Greek letter. This means that there is room for two

electrons in each � electronic state, one with spin up and one with spin down.

49

For a � wave function the orbital angular momentum around the internuclear

axis is one unit. This can be achieved by circulating the electron either in

one direction or in the other direction around the axis1. In each direction

there can be two electrons with opposite spin, and hence there is room for four

electrons in a � electronic state. This will give the ground state con�guration

for OH as:

1�22�23�21�3: (4.3)

Vibrational Energy

The energy levels in Fig. 4.1 are often described by the Morse potential:

u(R) = De[1� exp(�a(R�Re))]2 (4.4)

where De is the depth of the well, Re is the equilibrium separation of the

nuclei and a is an empirical constant. For small displacements, R-Re, from

the equilibrium position the Morse potential is well approximated by:

u(R) = C(R�Re)2 (4.5)

where C is a constant equal to a2De. Equation 4.5 describes a harmonic

oscillator. This is the same energy expression as that for a spring obeying

Hooke's law. Thus, for small displacements R-Re, the movement of the nuclei

against each other resembles the movement of a very small spring with spring

constant k = 2a2De. It is important to stress that the spring should be so

small that quantum e�ects come into play, since we are studying a molecule

on the microscopic scale. Solving the Schr�odinger equation for the nuclear

motion with the expression 4.5 for the potential yields the discrete vibrational

energy levels:

Evib = h�(n+1

2) (4.6)

where h is Planck's constant, � is the fundamental vibrational frequency of

the molecule in a given electronic state and n=0,1,2,. . . is the vibrational

quantum number.

Figure 4.2 shows the energy diagram for the OH molecule with the vibra-

tional levels included. As is clear from the �gure, the vibrational energy is

smaller than the electronic energy. While the di�erence between electronic

energy levels is of the order of 1 eV, the di�erence between vibrational levels

is of the order of 0.1 eV. Since the total energy is conserved, the kinetic energy

of the nuclei has its maximum when the potential energy has its minimum,

1This is not strictly correct. Using strict quantum mechanical notation the two \direc-

tions" correspond to the two linear combinations �x + i�y and �x � i�y.

50

0123

01

A Σ2

2X Π

2

n’’

n’

3

Energy

Figure 4.2: Schematic diagram for the electronic and vibrational energy levels

of the OH molecule.

that is, when R = Re. Note that even in the vibrational ground state, n=0,

the nuclei perform small oscillations. This is due to the zero-point energy

which is equal to h�=2 according to Eq. 4.6.

A careful study of Fig. 4.2 shows that the di�erence in energy between

adjacent vibrational levels di�ers among the di�erent electronic levels, X, A

and so on. This is due to the fact that each electronic level corresponds to

a certain distribution of the electrons. The electrons strongly in uence the

potential in which the nuclei are moving. Thus the spring constant k will be

di�erent for di�erent electronic con�gurations, and in that way the energy

separation between vibrational levels will di�er.

51

Rotational Energy

The rotational kinetic energy of the nuclei in a molecule is expressed by:

Erot;kin = hcBe;nJ(J + 1) (4.7)

where c is the speed of light, J is the rotational quantum number and Be;n is

the rotational constant. The rotational constant depends on the electronic

state as well as the vibrational state since these states govern the separation

between the nuclei, and Be;n is inversely proportional to the square of the

separation between the nuclei2.

However, there are other contributions to the rotational energy and these

come from coupling of di�erent angular momenta in the molecule. In a

diatomic molecule, such as the OH molecule, there are three contributions

to the total angular momentum3:

� Total orbital angular momentum of the electrons, denoted L.

� Total intrinsic angular momentum, spin, of the electrons, denoted S.

� Angular momentum due to the rotation of the two nuclei around the

molecule's center of mass, denoted R. This is the same movement as

what gives the energy in Eq. 4.7.

For diatomic molecules the conserved quantities of the orbital and in-

trinsic angular momenta of the electrons are their projections along the axis

between the nuclei. The notation is such that the projection of L, the or-

bital angular momentum, is given as an absolute value, �, which therefore

is always positive. The projection of S, the intrinsic spin, is signed and is

denoted �.

It is a fairly complicated matter to describe in detail how the rotation

of the OH molecule gives rise to energy levels. However, there are some

general features that can be stated �rst. The energy di�erence between ad-

jacent rotational energy levels is much smaller than the energy di�erence

between adjacent vibrational energy levels. This means that the energy di-

agram in Fig. 4.2 should be completed with a spectrum of rotational levels

for each vibrational level. The complicated matter comes in when we want

to describe quantitatively how the three types of angular momenta described

above interact, and ultimately how they give rise to the di�erent rotational

2In Eq. 4.7 the stretching of the bond due to the rotation, that is, the centrifugal

distortion e�ect, is neglected.3We neglect the in uence of the intrinsic spin of the nuclei, that is, the hyper�ne

structure.

52

energy levels. We will adopt a model where the angular momentum due to

the rotation of the nuclei, R, and the projection of the orbital angular mo-

mentum, �, couple to give a resultant angular momentum N=R+�. Here

we use the vector notation for the quantum number �. This is to stress the

fact that the angular momentum corresponding to � is directed along the

molecular axis while the angular momentum R is directed perpendicular to

the molecular axis. Thus N describes the total angular momentum except

the intrinsic spin. To obtain the total angular momentum we add the spin

and get J=N+S. Beware of the unfortunate notation! J is the total angular

momentum and is not the same thing as the rotational quantum number J .

This approach for coupling of angular momenta is called Hund's coupling

case (b) and can be summarized as:

N = R+� (4.8)

J = N+ S (4.9)

OH electronic spectroscopy is in fact more complicated than this, since

Hund's coupling case (b) applies only for higher rotational quantum numbers

J . At low J another coupling case, called Hund's coupling case (a), is valid

where the electronic orbital and intrinsic angular momentum couples to a

resultant and the coupling of the nuclear rotation with this resultant gives

the total angular momentum J. However, we will stick to the notation of

Hunds coupling case (b).

For the ground-state con�guration of OH, 1�22�23�21�3, the orbital an-

gular momentum around the internuclear axis is one unit. This is because

there are three � electrons. Two of them must circulate in opposite direc-

tions, thus cancelling each other's orbital angular momentum. The third one

gives the only contribution to the total orbital angular momentum. Since

a � electron contributes one unit of angular momentum, the total angular

momentum quantum number, �, will also be one. This is called a � state.

Thus N in Eq. 4.8 must be at least one. In the same way that two of the

three � electrons cancel each other's orbital angular momentum, they also

cancel each other's intrinsic spin. Thus only one electron contributes to the

total intrinsic spin, S, of the OH molecule in its ground-state con�guration.

Since the spin of an electron is half a unit, the total angular momentum

quantum number in Eq. 4.9 is either

J = N + 1=2 (4.10)

or

J = N � 1=2: (4.11)

53

Energy

1/23/25/2

7/2

9/2

11/2

13/2

3/25/27/2

9/2

11/2

13/2

15/2

N

1

2

3

4

5

6

7

J=N+1/2 J=N-1/2

Figure 4.3: Schematic diagram for the rotational energy levels in a 2� state,

such as the electronic ground state of OH. Note that the vibrational energy

level � has not been speci�ed.

The rotational energy diagram of the OH molecule in its ground-state con�g-

uration X can be described as in Fig. 4.3. The 2 in 2� is called the multiplicity

and is equal to 2S+1.

The �rst excited electronic state A of the OH molecule is obtained by

exciting one of the two 3� electrons to the 1� wave function, yielding the

con�guration 1�22�23�1�4. This means that the � wave function contains

four electrons which cancel each other's angular momenta. The only electron

contributing to the electronic angular momentum is the 3� electron, which

has zero orbital angular momentum since it is a � electron. The �rst excited

electronic state is thus denoted A2� since a state with � = 0 is called a �

state. Again beware of the notation! A � state is a state with the projection

of the total orbital angular momentum� = 0, and is not the same thing as the

quantum number � corresponding to the projection of the total intrinsic spin

54

J’ N’

X2Π

3/21

2

3

0

4

5

1

3/22

3

4

3/21/2

5/2

7/25/2

9/27/2

1/2

1/2

5/23/2

7/25/2

9/27/2

11/29/2

J’’ N’’

2Σ

Energy

A

n’=0

n’’=0

R 22

R 21

R

(4)

(4)

11(4

)

Figure 4.4: Schematic energy level diagram for transitions between a A2�

and a X2� state. The notation is according to Hund's coupling case (b).

The transitions used in this work are denoted R transitions and correspond

to the case where the rotational plus angular momentum,N, is one quantum

higher in the excited state than in the ground state.

of the electrons. Since �=0, Eq. 4.8 can give any integer value. Figure 4.4

shows the rotational levels in the vibrational levels n'=0 and n"=0 where

a prime denotes the �rst excited electronic level, A2�, and double prime is

used in the electronic ground state X2�. The transitions between di�erent

energy levels will be discussed next.

4.1.2 Transitions

The idea of LIF on OH is to excite the molecule from the electronic ground

state X2� to an excited state with the help of photons from a laser source.

In our case the excited state is the �rst excited state A2�. After a short

55

time the excited molecule will relax back to the ground state by emitting

a photon. This is the uorescence and it is the emitted photons that we

detect. There are several rules for how the transitions from the ground to the

excited state can take place. These rules are based on the fundamental law

of conservation of total angular momentum for the molecule+photon system.

For example it can be shown that the quantum number corresponding to the

rotational plus orbital angular momentum, N , can only change by �N =

N0 � N

00 = �2;�1; 0; 1; 2 when an incoming photon excites the molecule

from the ground to the excited level. The transitions used in this work are

denoted R transitions and correspond to the case where the rotational plus

angular momentum, N, is one quantum higher in the excited state than in

the ground state. R21(4) for example means a transition from the ground

electronic state X2� with N00=4 to the excited electronic state A2� with

N0=5. The subscript 21 means that the intrinsic spin S0 is in the opposite

direction to the rotational plus orbital angular momentumN0 in the excited

state, corresponding to the number 2, while in the ground state S00 is in the

same direction as N00, corresponding to the number 1. In other words we

have J 0=N 0-1/2=9/2 and J00=N 00+1/2=9/2; see Eqs. 4.10 and 4.11. The

transition R11(4) means that S and N are in the same direction in both the

excited and the ground state while the opposite is true for R22(4). R11 and

R22 are also denoted R1 and R2 transitions, respectively.

4.2 Laser Induced Fluorescence, LIF, Tech-

nique

4.2.1 Laser System

In order to select which of the transitions in Fig. 4.4 to induce, a laser system

with su�ciently well de�ned wavelength must be used. We have used a dye

laser (Lambda Physik FL2002 E) with the dye Rhodamine B/Rhodamine

610 (two di�erent names for the same dye). The dye laser was pumped by

an excimer laser (Lambda Physik EMG 102E) working on xenon chloride

excimers. This is a commonly used combination because the Rhodamine B

dye withstands the excimer light relatively well and because the achieved

light intensity from the dye laser is high.

The wavelength from the XeCl excimer laser is around 308 nm. When the

dye in the dye laser absorbs this light an inverted population can be obtained

in an energy region selected with a grating. In our case the wavelengths of

the dye laser were around 614 nm. This is not a useful wavelength for excit-

ing OH molecules. However, by letting the 614 nm laser beam pass a crystal

56

of KDP (meaning potassium dihydrogen phosphate) the light will partially

get a doubled frequency, that is �=307 nm. This method is called Second

Harmonic Generation (SHG). There may seem no point in this whole proce-

dure of going from the excimer laser light with �=308 nm to a wavelength

which does not di�er very much, �=307 nm. However, the light from the

dye laser has a narrow bandwidth, that is a well-de�ned energy, and can be

tuned to induce the transitions in Fig. 4.4 individually. By contrast, a direct

use of the excimer laser light would be like shooting blindly since the excimer

laser light cannot be tuned and since the bandwidth is not appropriate.

Thus we have a well-working laser system with wavelengths that can

be tuned around �=307 nm. This is the same wavelength region that is

required to induce transitions from the ground state X2� in its ground vi-

brational state n00=0 to the excited state A2� in its ground vibrational state

n0=0. These transitions (plural since there are transitions between di�erent

N numbers) are called (A2�(n0 = 0) X2�(n00 = 0)) transitions. The rea-

son why a transition from the ground vibrational state, n00=0, is used is that

almost all OH molecules are in this state (see also section 4.2.3); thus all

of them can be excited and contribute to a high intensity in the subsequent

uorescence. At the same time, the choice of n0=0 is rather due to the fact

that it suits to the available wavelength region of the laser system.

4.2.2 Quenching

If the excited molecule collides with a gas molecule, the de-excitation may

proceed via a radiationless collision energy transfer. In this case the OH

molecule will not uoresce. This process is called electronic quenching, and

the probability for quenching is denoted Q. Q depends on the partial pres-

sures of the species in the gas and on the temperature. As a consequence,

quenching will complicate the analysis of OH uorescence if the uorescence

is measured at di�erent pressures. Furthermore, the analysis of images of

OH uorescence will be complicated since the composition of species and

the temperature may vary in the image. The quenching can be handled by

measuring the lifetime of the excited molecules. The lifetime � is written

� = 1=(A + Q) where A is Einstein's coe�cient for spontaneous emission.

Since A is known, the quenching probability can be calculated if � is mea-

sured and the measured uorescence intensity can be corrected.

4.2.3 Temperature Considerations

The populations of OH molecules in the di�erent vibrational levels are pro-

portional to the Boltzmann factor exp(�Evib=kT ). For a light molecule such

57

as OH the vibrational quantum h� is relatively large; see Eq. 4.6. This means

that most of the molecules are in their ground vibrational state. In fact, even

at such a high temperature as T=1300 K less than two percent of the mole-

cules are in the �rst excited vibrational state. This is the reason why we

choose to excite the molecules from the ground vibrational state as discussed

above.

When considering the populations of the di�erent rotational states in a

particular (in our case the ground) vibrational state, the distribution is not

simply given by a Boltzmann factor exp(�Erot=kT ). We also have to take

into account the degeneracy of the di�erent rotational quantum states. The

degeneracy for a certain rotational quantum state with quantum number J

is equal to 2J+1. This means that the rotation of the two nuclei around the

center of mass has a certain frequency determined by J but that this rotation

can take place in 2J+1 directions in space. Thus there are 2J+1 quantum

states with the same energy hcBe;nJ(J + 1) as given by Eq. 4.74. Therefore

the rotational energy distribution is given not simply by the Boltzmann factor

but by its product with the degeneracy:

NJ / (2J + 1) exp(�Erot;kin=kT ): (4.12)

Minimizing the Temperature Dependence of the Fluorescence Sig-

nal

In this work we have measured the intensity of the OH uorescence at di�er-

ent distances from a hot surface. As discussed in section 4.2.3 the temper-

ature di�ers at di�erent distances from the surface. Hence the populations

among the rotational levels will di�er at di�erent distances from the surface.

This in its turn complicates the interpretation of the measured uorescence

intensity. If for example we tune the laser to a transition from an initial

state N 00=2 (see Fig. 4.4), and measure the same uoresence intensity at

two di�erent distances from the surface, this does not imply that the abun-

dance of OH is the same at the two distances. What we are measuring is

the abundance of OH molecules in the particular state N 00=2. Because of

the temperature di�erence between the two distances from the surface the

population in the level N 00=2 does not have the same proportion to the total

abundance of OH molecules, that is, to the abundance of molecules in all

initial states N 00. This is just what Eq. 4.12 is about: the proportionality of

the rotational energy levels to each other.

4This degeneracy is lifted if an electromagnetic �eld is present. In that case the energy

depends on which direction the molecule is rotating in.

58

From Eq. 4.7 we get the expression for Erot;kin and Eq. 4.12 becomes:

NJ / (2J + 1) exp(�BeJ(J + 1)hc=kT ): (4.13)

In order to replace the proportionality with an exact expression for the num-

ber of OH molecules that are in the state with quantum number J , we must

�rst sum up the expression in Eq. 4.13 for J=0,1,2,. . . , that is, for all values

of J . This is called the state sum Qr and is thus given by:

Qr = 1 + 3 exp(�2Behc=kT ) + 5 exp(�6Behc=kT ) + : : : (4.14)

The subindex r indicates that we are dealing with the state sum for rotational

states. The number of OH molecules that are in state J is now given by:

NJ =N

Qr

(2J + 1) exp(�BeJ(J + 1)hc=kT ) (4.15)

where N is the total number of OH molecules.

For su�ciently large temperatures T, or su�ciently small rotational con-

stants Be the state sum 4.14 can be approximated by an integral:

Qr;approx =Z1

0

(2J + 1) exp(�BeJ(J + 1)hc=kT )dJ =kT

hcBe

(4.16)

In fact, an exact calculation of the state sum in Eq. 4.14 at a temperature

T=1300 K gives the result:

Qr;exact = 48:21 : : : (4.17)

where the parameter Be=18.871 cm�1 for the OH molecule has been

used [Herzberg, 1950]. The value of the approximative state sum in Eq. 4.16

is:

Qr;approx = 47:88 : : : (4.18)

with the same values of Be and T. Thus for our purposes the approximation

is acceptable. Now we can express the population in quantum state J as:

NJ = NhcBe

kT(2J + 1) exp(�BeJ(J + 1)hc=kT ): (4.19)

In order to minimize the temperature dependence of the uorescence sig-

nal, we are now seeking the initial rotational level, denoted J�, that gives the

smallest dependence on the temperature [Eckbreth, 1996]. This is achieved

by calculating the derivative of NJ with respect to the temperature and re-

quiring the result to be zero:

@NJ

@T=NBehc

T 2exp(�BeJ(J + 1)hc=kT )(1 � BeJ(J + 1)hc

kT) (4.20)

59

and thus@NJ

@T= 0) 1� BeJ

�(J� + 1)hc

kT= 0: (4.21)

This yields the second-order equation

J�2 + J

� � kT

Behc= 0 (4.22)

where T is the average temperature in the studied region. The solution is

J� = �1

2

+

(�)

vuut kT

Behc+1

4(4.23)

where the plus sign is the only possible solution since J cannot be negative.

The average temperature is not well de�ned but has to be chosen in some

more or less subjective way. From the results in Papers 1 and 2 in this work

we estimate this temperature to be T � 700 K. Inserting the parameter

Be=18.871 cm�1 for the OH molecule we obtain:

J� = 4:6: (4.24)

Thus in Fig. 4.4 a transition with N 00=4 or 5 should be chosen in order to

achieve the smallest temperature sensitivity of the uorescence signal. In this

work the transition R1(4) has been used to probe the relative OH abundance

at di�erent distances from the surface.

Measuring Temperature Pro�les

The population of a certain rotational level is given by Eq. 4.12. Or, to be

more exact, it is given by

NJ / (2J + 1) exp(�Erot=kT ) (4.25)

where Erot is the total rotational energy, including the e�ects of the coupling

of angular momenta as discussed in section 4.1.1 above. The uorescence

intensity is proportional to the number of molecules that are excited by the

laser. However, this number is given not by Eq. 4.25 but by

IN 00!N 0 / SN 00

!N 0 exp(�Erot=kT ) (4.26)

where the SN 00!N 0 is called the H�onl-London factor, or the line

strength [Herzberg, 1950]. The H�onl-London factor is almost the same thing

as the degeneracy, but it also depends on the rotational quantum number

60

Erot

1kT

x

x

x

x

x

x

x

xx

x

The slope is equal to -

ln

N’’ N’S

I N’’ N’

Figure 4.5: An Arrhenius plot. The slope of the line is equal to - 1

kTas given

by Eq. 4.27.

in the excited state and on the quantum number �5. Dividing Eq. 4.26 by

SN 00!N 0 and calculating the logarithm we obtain

ln(IN 00

!N 0

SN 00!N 0

) = c� Erot=kT; (4.27)

where c is a constant. If the left-hand side, ln(IN 00!N 0

SN 00!N 0), is plotted versus the

energy in the initial state, Erot, a so-called Arrhenius plot is obtained; see

Fig 4.5. According to Eq. 4.27 the slope of the line is equal to - 1

kT. And since

k is a constant the temperature can be calculated.

4.3 Planar Laser Induced Fluorescence and

Imaging Techniques

A schematic overview of the studied system is shown in Fig. 4.6. The vac-

uum system consists of a roots-pumped stainless-steel vacuum chamber. The

5We neglect the fact that the intensity also depends on the frequency of the transition.

However, when studying the relative intensities of the R transitions, as has been done in

this work, the relative change ��=� is very small.

61

h w

Fluorescence

CCD

CAMERA

Lasersheet

GasInlet

VA

Figure 4.6: Experimental setup

reactant gases enter the chamber via a tube, 20 mm in diameter, which ends

30 mm below the sample, resulting in a directed gas ow towards the surface.

The ow of O2 and H2 was controlled by mass ow meters.

A platinum foil, of purity 99.95%, with the dimensions 20x3.8 mm and

thickness 0.025 mm, was resistively heated to 1300 K. The surface tempera-

ture was measured by a four-point resistance measurement and kept constant

by microcomputer control. In addition we used an inert surface in the form

of molten glass on a Nikrothal ribbon, 2x25 mm, heated to 1300 K. The tem-

perature of the glass surface was controlled with a thermocouple attached to

the back of the ribbon.

The gas mixture at the inlet was 10% H2 and 90% O2. This mixture

gives a high OH yield from the surface at the present pressure range, up to

120 torr, and temperature. The mass ow was 800 sccm (1 Standard Cubic

CentiMeter� 4:08�1017 molecules/s at T=300 K, which was the temperature

of the gas mixture at the inlet). Since the mass ow was kept constant, the

ow velocity decreased as the inverse of the pressure.

62

Figure 4.7: The Galilean telescope

4.3.1 Laser Optics Setup

As described in section 4.2.1 an excimer-pumped dye laser was tuned in the

wavelength region, 306.3 to 307.5 nm, which corresponds to the transitions,

used in this study, of the OH molecule.

The laser pro�le from the dye laser was only a few mm in diameter. Since

we wanted to probe the OH intensity from the surface and up to eight mm

out, the laser beam was expanded with a Galilean telescope. This telescope

setup is schematically shown in Fig. 4.7 and is useful as a laser beam ex-

pander, since it has no internal focal point where the laser otherwise would

ionize the surrounding air [Hecht, 1987]. The Galilean telescope is also less

sensitive to dust in the air, since dust particles ying around a focal point

could induce shot-to-shot variations in the beam quality.

After the laser beam was expanded to a diameter of about ten mm, it

had to be focused into a thin sheet. This was for two reasons. Firstly, the

area which is illuminated must be completely under the foil. The heated

part of the platinum foil was 3.8 mm wide while the heated glass surface

used in Paper 2 was only 2.0 mm wide. Thus in order to minimize edge

e�ects the laser beam should be narrower than 2.0 mm. Secondly, with the

high degree of magni�cation and the wide-open iris diaphragm used for the

ICCD camera optics (see below), the focal depth was relatively short. Thus

in order to avoid a blurred image the laser pro�le should be narrower than

the shallow focal depth. Therefore the laser beam was shaped in the form of

a sheet (10 � 0:1mm2) in the probed region outside the foil, using cylindrical

lenses and a telescope.

Before entering the vacuum chamber the laser beam was attenuated to a

level where the recorded uorescence was linear with the laser beam intensity

over the entire image.

63

4.3.2 CCD Optics Setup

The uorescence light was imaged with a standard lens (Nikon UV quartz

4.5, f=105 mm) mounted with a bellow extender for high magni�cation on

a gateable intensi�ed charge-coupled device (ICCD) camera (Princeton In-

struments). A magni�cation factor of 1.67 was obtained with this setup.

A bandpass �lter (Schott UG11) was used to eliminate the stray light and

black-body radiation from the heated foil. In order to capture as much uo-

rescence light as possible the iris diaphragm was completely open. The laser

beam pro�le was recorded as it exited the chamber on a thermo-electrically

cooled charge-coupled device (TE/CCD) camera (Princeton Instruments),

and the pro�les were used to normalize each uorescence image.

The ICCD camera captured the uorescence light from the excited mole-

cules. It should be noted that this is a broad-band detection, since not only

de-excitations of exactly the same transition wavelength as the laser light

were captured. In fact, when an OH molecule is excited via, for example,

an R1(4) transition, the uorescence light will contain a spectrum of equal

and longer wavelengths (less energy) since some de-excitations end up on a

higher N level than where they were initially; see Fig. 4.4.

For the measurements of OH concentration as a function of pressure in

Paper 2, the total uorescence has been integrated over a certain area as

indicated in Fig. 4.6. The area covers 1.4-3.5 mm outside the surface and

extends 2.8 mm along the middle of the foil, where the foil was evenly heated.

Thus, each point on the pressure axis in Figs. 3 and 4 in Paper 2 contains

the normalized OH concentration from a w � h = 2:8 � 2:1 mm2 area of the

laser sheet.

64

Chapter 5

Summary of Papers

5.1 Paper 1

In this paper we studied the OH LIF intensity outside a Pt foil at 1300 K

and at 1, 5 and 10 torr pressure. We used the stagnation ow geometry and

the reactant gas mixture was 10% H2 and 90% O2. The question that we

addressed was whether gas-phase chemistry had to be taken into account to

explain the OH concentration pro�les. It was found that at pressures up to

1 torr there is no signi�cant interaction between the desorbed OH molecules

and the gas phase. At higher pressures one must take into account the fact

that the desorbed OH molecules are destroyed by reactions in the gas phase,

mainly the reaction OH+H2 ! H2O+H. However, the simulations showed

that the production of OH in the gas phase at these conditions is negligible.

5.2 Paper 2

The experiments and simulations in this paper were done for the same tem-

perature, ow geometry and reactant mixture as in Paper 1. However, the

pressure was increased up to 150 torr. This was done because we wanted

to study in what way the catalytic surface in uenced the gas-phase ignition.

For comparison we also used a glass surface as an example of an inert surface.

It was found that the gas-phase ignition took place at around 40 torr for the

Pt surface. For the glass surface the ignition occurred already at 10 torr and

in a more abrupt way. Thus the catalytic surface inhibited the gas-phase

ignition. The simulations showed that this inhibition was due to the surface

acting as a sink for radicals. Gas-phase radicals adsorbed on the surface and

recombined into less reactive molecules, such as H2O. In this way the gas

phase was depleted of radicals and the pressure had to be higher than with

65

the glass surface in order to achieve gas-phase ignition. The simulations also

showed that the water production was crucial in this inhibition. If the water

formation reaction was blocked, and thus only allowed production of OH, the

inhibition e�ect still remained but was less important.

66

Chapter 6

Outlook

Learning more about the interplay between surface and gas-phase chemistry

will be of continued importance in the future. The area is very large and one

could say that it remains to explore all surface chemistry that corresponds

to all the gas-phase chemistry which has been studied in detail in the past.

In addition, there is a speci�c surface chemistry for each surface, material,

surface geometry and so on. This is more or less an intractable problem

and it is therefore also interesting to draw qualitative conclusions from the

studies that are done, which yield information of general character regarding

surface/gas interplay.

Regarding the work in Papers 1 and 2 of this report there are some points

that should be emphasized. Experimentally, we lack reliable quantitative

measurements of the OH concentration pro�le. Some types of absorption

spectroscopy, such as Cavity Ringdown Spectroscopy, CRS, or infrared spec-

troscopy, could be useful techniques for this purpose. There are also some

problems in obtaining precise temperature pro�les with LIF and the avail-

able laser system. This could be improved with, for example, some Raman

spectroscopic techniques, such as Coherent Anti-stokes Raman Spectroscopy,

CARS.

The simulations depend directly on the experimental data through the

obtained reaction parameters. In order to re�ne the quality of these parame-

ters, sensitivity analysis of the model should be done repeatedly, which points

out the parameters that most in uence the oxidation process and thereby are

most interesting to determine precisely.

67

Chapter 7

Acknowledgements

First of all I thank Prof. Arne Ros�en for accepting me as a graduate student

in the Molecular Physics Group. Arne's deep knowledge and enthusiasm

have been invaluable for me.

I also thank Dr. John Persson for introducing me to the �eld of ex-

perimental physics in general and to laser spectroscopy in particular. In

more or less all my work John has supported me with his great understanding

in physics and chemistry.

Thanks also to my previous room-mate Dr. Fredrik Gudmundson for

very fruitful cooperation. Good luck with your company, Fredrik!

A scienti�c atmosphere is made up of its participants and it is a plea-

sure to have come to know the people participating in the Molecular

Physics Group. Thanks to Dr. Mats Andersson, Dr. Alf-Peter Elg, Dr.

Frank Eisert, Eva Eriksson, So�a Grapengiesser, Dr. Henrik Gr�onbeck,

Gunner Haneh�j, Dr. Lotta Holmgren, Johan Mellqvist, Michael R�ossler,

Nils Tarras-Wahlberg, Jan Westergren, Dr. Erik Westin, Torbj�orn �Aklint

and Dr. Daniel �Ostling. Very special thanks go to Leif Johansson for his

invaluable help with computers, electronics, lasers, vacuum pumps and

whatever technical apparatus I used in my work.

Thanks also to my parents Lars and Gunnel, and to my brother Pe-

ter and his family Malin and Agnes, for being my family. Many thanks also

to my friends.

Finally I am grateful to the Combustion Engine Research Center, CERC,

and the Swedish Natural Science Research Council, NFR, for �nancial

support.

68

Appendix A

Calculation of Total Water

Production

Fig. 5 in Paper 2 of this work contains the total gas-phase water production

of the system. This is not supplied by the Spin output but must be calculated

in data postprocessing.

The output from the SPIN code contains the reduced radial velocity, V,

which is the radial velocity divided by the radius.

V =v(r)

r(A.1)

This reduced velocity is given for the di�erent grid points under the surface.

For a certain distance, x, from the surface the radial mass ow is

jradial;tot(x; r) = �(x)v(r) = �(x)V r [kgm�2s�1] (A.2)

and the mass ow from a circle a distance x from the surface will be

2�rjradial;tot(x; r) = 2��(x)V r2 [kgm�1s�1] (A.3)

Finally, the total mass ow out of a cylinder with radius r and height L

will be

J(r; L) =Z

L

0

2��(x)V r2dx [kgs�1]: (A.4)

If we consider just the water, the partial water density, �H2O(x), should be

used. We get �H2Ofrom the ideal gas law:

n(x) =ptot

RT (x)[moles �m�3] (A.5)

and

nH2O(x) =

ptotXH2O(x)

RT (x)[moles �m�3] (A.6)

69

where XH2O(x) is the molar fraction of water. We get the density by multi-

plying with the molar mass, MH2O:

�H2O(x) =MH2O

nH2O(x) =

ptotMH2OXH2O

(x)

RT (x)[kgm�3]: (A.7)

This gives us the total water mass ow out of the cylinder:

JH2O(r; L) =

ZL

0

2��H2O(x)V r2dx [kgs�1]: (A.8)

Thus, the average water production per unit volume will be

JH2O(L) =

JH2O(r; L)

�r2L=

ZL

0

2ptotMH2OXH2O

(x)

RT (x)Ldx [kgm�3

s�1]: (A.9)

Here we have assumed that there is no water- ow through the ends of the

cylinder. This is true at the inlet where according to the boundary condition

XH2O(L) � 0. At the other end, the surface, this need not be true. If the

ow of water from the surface into the cylinder is jH2O[kgm�2

s�1] then the

net gas-phase water production will be

Jgas(r; L) =Z

L

0

2��H2O(x)V r2dx� �r2jH2O

[kgs�1]: (A.10)

and the average gas-phase water production per unit volume will be

Jgas(L) =Jgas(r; L)

�r2L=

1

L(Z

L

0

2ptotMH2O

XH2O(x)

RT (x)V (x)dx��jH2O

) [kgm�3s�1]:

(A.11)

The expression for Jgas(L) was implemented in a MATLAB code and

the total gas-phase water production, that is, a measure of the gas-phase

combustion rate, was calculated for di�erent pressures.

70

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