shock tube measurements of elementary oxidation … · iv 306 nm, respectively. ch radicals were...

SHOCK TUBE MEASUREMENTS OF ELEMENTARY OXIDATION AND

DECOMPOSITION REACTIONS IMPORTANT IN COMBUSTION USING OH,

CH AND NCN LASER ABSORPTION

By

Venkatesh Vasudevan

Report TSD-173

September 2007

High Temperature Gasdynamics Laboratory

Mechanical Engineering Department

Stanford University

Stanford, California 94305

ii

© Copyright by Venkatesh Vasudevan 2007

All Rights Reserved

iii

Abstract

The kinetics of several elementary chemical reactions that are important in

fuel-combustion and pollutant-formation have been studied using laser absorption

spectroscopy and shock tubes. The measurements made in this study can be broken

into four categories: (a) Toluene [C6H5CH3] oxidation, (b) Formaldehyde [CH2O]

chemistry, (c) Methyl [CH3] decomposition, and (d) Prompt-NO initiation.

OH concentration profiles and ignition delay times were measured in

toluene/oxygen mixtures behind reflected shock waves. These measurements provide

a data-set useful for evaluating and refining comprehensive kinetic mechanisms on

toluene oxidation. The reaction between toluene and OH, (1) C6H5CH3 + OH

Products, was found to be crucial to capturing the measured ignition times and OH

profiles. The rate coefficient of this reaction was accurately determined in shock tube

experiments using OH laser absorption at 306 nm.

High-sensitivity laser absorption measurements of OH were also used to study

several important chemical reactions in the formaldehyde decomposition and

oxidation systems. Experiments were designed to isolate the chemical reaction of

interest, with interference from secondary chemistry kept to a minimum. Tert-butyl

hydroperoxide [(CH3)3-CO-OH] and 1,3,5 trioxane [(CH2O)3] were used as precursors

to generate OH and CH2O, respectively, behind the reflected shock. The reactions

studied include: (2) CH2O + OH HCO + H2O, (3a) CH2O + Ar HCO + H + Ar,

(3b) CH2O + Ar H2 + CO + Ar, and (4) CH2O + O2 HCO + HO2. The low-

scatter rate coefficient measurements provide accurate kinetic data for modeling

natural gas combustion and reliable targets for theory.

The two-channel thermal decomposition of methyl radicals in argon, (5a) CH3

+ Ar CH + H2 + Ar and (5b) CH3 + Ar CH2 + H + Ar, was studied in high-

temperature shock tube experiments using CH and OH laser absorption at 431 nm and

iv

306 nm, respectively. CH radicals were generated by shock-heating highly dilute

mixtures of ethane [C2H6], or methyl iodide [CH3I], in an argon bath, while OH was

produced by shock-heating dilute mixtures of C2H6 or CH3I and excess O2 in argon.

Detailed chemical kinetic mechanisms were used to model the measured CH and OH

time-histories and to infer k5a and k5b. Theoretical master equation/RRKM calculations

were carried out and are in reasonable agreement with experiment.

The prompt-NO initiation reaction, (7) CH + N2 Products, was investigated

behind reflected shock waves using CH and NCN laser absorption at 431 nm and 329

nm, respectively. The overall rate coefficient of the CH+N2 reaction was measured

using a CH perturbation approach. CH profiles recorded upon shock-heating dilute

mixtures of ethane in argon and acetic anhydride [(CH3CO)2O] in argon were

perturbed by the addition of nitrogen. The perturbation in the CH concentration is due

principally to the reaction between CH and N2. Rate coefficients for the overall

reaction were inferred by kinetically modeling the perturbed CH profiles. At high

temperatures, there are two possible product channels for the reaction between CH and

N2, (7a) CH + N2 HCN + N, and (7b) CH + N2 H + NCN. The branching ratio of

reaction (7), k7b/(k7b+k7a), was determined by CH laser absorption in experiments in a

nitrogen bath. The measurements establish NCN and H as the primary products of the

CH+N2 reaction. NCN was also detected by laser absorption at 329 nm, and was used

to infer the rate coefficient of the reaction between H and NCN, H + NCN HCN +

N, and to estimate an absorption coefficient for the NCN radical.

v

Acknowledgements

I have had the pleasure of knowing several people at Stanford whose

enthusiastic support was crucial to the successful completion of this work.

I would like to thank my primary research advisor Prof. Ron Hanson for giving

me the opportunity to pursue research under his supervision. It has been a tremendous

privilege and pleasure to have interacted and worked with Prof. Hanson these past five

years. I would like to express my sincere gratitude to my co-advisors Prof. Tom

Bowman and Prof. Dave Golden. It was a unique opportunity to be advised by three

experts in the field of combustion – our weekly meetings and many discussions on

science will be missed. Their constant encouragement and advice helped surmount

many an obstacle in the current research.

I would like to acknowledge the contribution of Dr. Dave Davidson to this

work. It has been a lot of fun and a great experience working with Dave. I thank him

not only for the lessons in science but also for the lessons in life – he has been a

wonderful mentor, supervisor and friend. I would like to thank Dr. Jay Jeffries for his

support and help. Thanks also to Prof. Richard Zare for chairing my oral defense

panel, and Prof. Reggie Mitchell and Prof. Mark Cappelli for serving as examiners on

my defense committee.

A special thanks to all my friends and colleagues (current and former) in the

Hanson research group. I am grateful for their friendship and support. In particular, I

would like to thank John Herbon for his mentorship – I am grateful to John for guiding

me when I started off as a new student at Stanford, and for introducing me to laser

diagnostics and shock tubes. Thanks also to Rob, Ethan, Greg, Zach, Hejie, Brian,

Subith, Matt, Dan, Zekai and others in the Hanson group for their friendship – the

softball games, movies and discussions over lunch will be sorely missed.

vi

I have been very fortunate to have had several great friends at Stanford and

elsewhere. I would like to thank Varun, Chetan, Neelabh, Ankur, Madhu, Senthil,

Pankaj, Karan and several others for having made this journey a truly memorable one

and for all the wonderful memories. Their friendship I will cherish life-long.

Most importantly I would like to thank my loving parents, grandparents and

family for their encouragement and support. I am truly indebted to them for the

sacrifices they have made and for the tremendous source of inspiration they have been

over the years.

This research was sponsored by the U.S. Department of Energy, the National

Science Foundation and the U.S. Army Research Office.

vii

Contents

Abstract ............................................................................................................................ iii

Acknowledgements ............................................................................................................v

Contents............................................................................................................................vii

List of Tables.....................................................................................................................xi

List of Figures ................................................................................................................ xiii

Chapter 1: Background and Motivation.....................................................................1

1.1 Introduction ......................................................................................................1

1.2 Background and Motivation.............................................................................2

1.2.1 Toluene Oxidation ...............................................................................2

1.2.2 Formaldehyde Chemistry ....................................................................3

1.2.3 Methyl Decomposition ........................................................................6

1.2.4 Prompt-NO Initiation...........................................................................8

1.3 Scope and Organization of Thesis..................................................................11

Chapter 2: Experimental Apparatus and Diagnostics.............................................19

2.1 Shock Tubes ...................................................................................................19

2.2 OH Laser Absorption Diagnostic ...................................................................20

2.3 CH Laser Absorption Diagnostic ...................................................................20

2.3.1 CH Spectroscopic Model...................................................................21

2.4 NCN Laser Absorption Diagnostic ................................................................24

Chapter 3: Toluene + OH Products......................................................................35

3.1 Introduction ....................................................................................................35

3.2 Experimental Set-up.......................................................................................37

3.3 Kinetic Measurements....................................................................................38

3.3.1 OH Precursor Kinetics.......................................................................39

3.3.2 Toluene + OH Kinetics......................................................................39

viii

3.3.3 Acetone + OH Kinetics .....................................................................43

3.4 Comparison with Earlier Work ......................................................................44

3.5 Conclusions ....................................................................................................46

Chapter 4: CH2O + OH Products.........................................................................59

4.1 Introduction ....................................................................................................59


4.3 Kinetic Measurements....................................................................................60

4.3.1 Precursor Species Kinetics ................................................................60

4.3.2 CH2O + OH HCO + H2O..............................................................61

4.3.3 (CH3)3-CO-OH (CH3)3CO + OH..................................................63

4.4 Comparison with Earlier Work ......................................................................64

4.5 Transition State Theory Calculations .............................................................66

4.6 Conclusions ....................................................................................................67

Chapter 5: CH2O + Ar Products and CH2O + O2 Products........................79

5.1 Introduction ....................................................................................................79


5.3 Kinetics Measurements ..................................................................................80

5.3.1 CH2O + Ar Products .....................................................................80

5.3.2 CH2O + O2 HCO + HO2 ...............................................................82

5.4 Results and Discussion...................................................................................83

5.4.1 CH2O + O2 HCO + HO2: Discussion and Theory ........................85

5.5 Conclusions ....................................................................................................87

Chapter 6: CH3 + Ar Products..............................................................................95

6.1 Introduction ....................................................................................................95


6.3 Kinetics Measurements ..................................................................................96

6.3.1 CH3 + Ar CH + H2 + Ar ...............................................................96

6.3.2 Reaction Mechanism to Model CH Formation and Removal ...........97

6.3.3 Pressure and Temperature Dependence of CH Time-History ...........99

6.3.4 CH3 + Ar CH2 + H + Ar .............................................................100

ix

6.4 Results and Discussion.................................................................................101

6.5 Master Equation/RRKM Analysis ...............................................................104

6.6 Conclusions ..................................................................................................105

Chapter 7: Prompt-NO Initiation: CH + N2 Products......................................123

7.1 Introduction ..................................................................................................123

7.2 Experimental Set-up.....................................................................................124

7.3 Overall Rate Coefficient, CH + N2 Products ...........................................125

7.3.1 High-Temperature (T > 2500 K) Measurements of k7 ....................125

7.3.2 Low-Temperature (T < 2500 K) Measurements of k7.....................127

7.3.3 Effect of Vibrational Cooling on Reflected Shock Temperature ....130

7.3.4 Effect of N2 Vibrational State on CH+N2 Kinetics .........................131

7.4 Branching Ratio Measurements ...................................................................132

7.5 NCN Time-History Measurements ..............................................................137

7.5.1 H + NCN HCN + N ....................................................................137

7.5.2 NCN Absorption Coefficient...........................................................138

7.6 Results and Discussion.................................................................................139

7.6.1 Overall Rate Coefficient for CH+N2 ...............................................139

7.6.2 Branching Ratio for CH+N2 ............................................................141

7.6.3 H + NCN HCN + N ..................................................................141

7.6.4 Implications of Current Study to NO Modeling in Flames .............142

7.7 Conclusions ..................................................................................................143

Chapter 8: Conclusions ............................................................................................171

8.1 Summary of Results .....................................................................................171

8.1.1 Toluene Oxidation ...........................................................................171

8.1.2 Formaldehyde Chemistry ................................................................172

8.1.3 Methyl Decomposition ....................................................................174

8.1.4 Prompt-NO Initiation.......................................................................176

8.1.5 Archival Publications ......................................................................177

8.2 Recommendations for Future Work.............................................................177

8.2.1 NCN Kinetics ..................................................................................177

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8.2.2 Decomposition and Oxidation of Oxygenates.................................178

8.2.3 Peroxy Chemistry ............................................................................179

Appendix A: OH Time-Histories during Toluene Oxidation...............................181

A.1 Introduction ..................................................................................................181

A.2 Experimental Set-up.....................................................................................182

A.3 Results and Discussion.................................................................................183

A.3.1 Ignition Times .................................................................................183

A.3.2 OH Concentration Profiles ..............................................................185

A.4 Early-Time OH Chemistry ...........................................................................187

A.5 Recommendations & Suggestions for Future Work ....................................188

A.6 Conclusions ..................................................................................................189

Appendix B: Ab Initio Study of CH2O + O2 Products......................................201

B.1 Introduction ..................................................................................................201

B.2 Ab Initio Calculations...................................................................................202

B.3 Transition State Theory................................................................................203

References ......................................................................................................................211

xi

List of Tables

Table 3.1: C6H5CH3 + OH Products: Rate coefficient data.........................................47

Table 3.2: CH3COCH3 + OH CH3COCH2 + H2O: Rate coefficient data....................47

Table 3.3: Reactions describing C6H5CH3 + OH experiments.........................................48

Table 3.4: Reactions describing C6H4CH3 chemistrya .....................................................49

Table 4.1: CH2O + OH HCO + H2O: Rate coefficient data ........................................68

Table 4.2: (CH3)3-CO-OH (CH3)3CO + OH: Rate coefficient data.............................68

Table 4.3: Principal moments of inertia and ab initio vibrational frequenciesa ...............69

Table 5.1: CH2O + Ar Products: Rate coefficient data................................................88

Table 5.2: CH2O + O2 HCO + HO2: Rate coefficient data..........................................89

Table 6.1: Rate parameters for reactions sensitive during CH formation and

removal.........................................................................................................107

Table 6.2: Summary of experimental results, k5a ...........................................................108

Table 6.3: Summary of experimental results, k5b ...........................................................109

Table 6.4: Thermochemical and structural parameters ..................................................110

Table 6.5: Parameters for Multiwell calculations at 2800 K ..........................................111

Table 6.6: Comparison of calculated and experimental values at 2800 K and 1

atm................................................................................................................111

Table 7.1: Summary of k7 measurements at high temperatures .....................................144

Table 7.2: Summary of k7 measurements at low-to-moderate temperatures..................145

Table 7.3: Rate parameters for reactions important in CH perturbation

experiments in ethane/N2/Ar ........................................................................146

Table 7.4: Rate parameters for reactions important in CH perturbation

experiments in acetic anhydride/N2/Ar ........................................................147

Table 7.5: Rate parameters for reactions important in branching ratio and NCN

time-history measurements ..........................................................................148

xii

Table 7.6: Summary of branching ratio experiments .....................................................149

Table 7.7: Rate parameters for NCN reactions in kinetic model....................................150

Table 7.8: Summary of rate coefficient data: H + NCN HCN + N ..........................151

Table A.1: Summary of toluene OH absorption data .....................................................191

Table B.1: Ab initio vibrational frequencies..................................................................204

Table B.2: Experimental vibrational frequencies [186] ................................................205

Table B.3: Electronic energies.......................................................................................206

Table B.4: Energy barrier and heat of reaction ..............................................................208

xiii

List of Figures

Figure 1.1 Previous high-temperature rate coefficient data for C6H5CH3 + OH

Products. .................................................................................................... 13

Figure 1.2 Primary oxidation pathways in natural gas combustion, adapted from

Ref. [62]. ...................................................................................................13

Figure 1.3 Previous high-temperature rate coefficient data for CH2O + OH

Products: solid square, Peeters and Mahnen [18]; solid circle,

Westenberg and Fristom [65]; open triangle, Bott and Cohen [17];

dashed black line, Tsang and Hampson [66]; dash-dotted line,

D’Anna et al. [20a]; dash-dot-dot line, Vandooren et al. [19]; dotted

line, Dean et al. [64]; crossed squares, de Guertechin et al. [63]. .............14

Figure 1.4 Previous rate coefficient data for CH2O + M Products: (a) 1,

Kumaran et al. [21]; 2, Friedrichs et al. [28]; 3, Just [22]; 4, Saito et al.

[23]; 5, Eiteneer et al. [27]; 6, Irdam et al. [25] (b) open circles,

Kumaran et al. [21] data; 1, Kumaran et al. [21] fit; 2, Just [22]. .............15

Figure 1.5 Previous rate coefficient data for CH2O + O2 Products: open circles,

Michael et al. [34]; open triangles, Srinivasan et al. [33] from O-atom

traces; open squares, Srinivasan et al. [33] from OH traces; solid gray

line, Baulch et al. [11]. ..............................................................................16

Figure 1.6 Previous rate coefficient data for CH3 + M Products: (a) solid black

line, Dean and Hanson [35], 0.5-1.3 bar; dashed black line, Röhrig et

al. [36], 1.2 bar; dash-dotted line, Markus et al. [37], 1.1-1.8 bar; solid

gray line, Baulch et al. [11] (b) open circles, Eng et al. [43]; dash-

dotted line, Kiefer and Kumaran [67]; dashed line, Markus et al. [37];

solid black line, Lim and Michael [42]; solid gray line, Baulch et al.

[11]. ........................................................................................................... 17

xiv

Figure 1.7 Primary chemical pathways to prompt-NO................................................ 18

Figure 1.8 Previous high-temperature rate coefficient data for CH + N2

Products: open squares, Dean et al. [48]; dashed line, Lindacker et al.

[49]; solid gray line, Matsui et al. [51]; dotted line, Moskaleva and

Lin [56] RRKM theory; solid squares, Moskaleva and Lin reanalysis

of the Dean et al. data as measurements of k7b; solid circles,

Moskaleva and Lin reanalysis of the Lindacker et al. data as

measurements of k7b. .................................................................................18

Figure 2.1 (a) Layout of 306.7 nm OH absorption system (b) Example

absorption signal at 306.7 nm after two-beam common-mode

rejection; RMS noise is ~0.10%................................................................ 27

Figure 2.2 (a) Layout of 431.1 nm CH laser absorption system (b) Example

absorption signal at 431.1 nm; upper panel: output of Coherent 699

ring-dye laser cavity, RMS noise is ~0.9%; lower panel: after two-

beam common-mode rejection, RMS noise is ~0.05%. ............................28

Figure 2.3 (a) LIFBASE simulation of the CH absorption feature near 23194.80

cm-1 (431.1311 nm) at 2800 K and 7.25 atm: dashed black line, 2γCH-

Ar = 0.023 cm-1 atm-1, solid gray line, 2γCH-Ar=0.034 cm-1atm-1, solid

black line, 2γCH-Ar = 0.034 cm-1atm-1 shifted -0.015 cm-1; open

squares, experimental data from peak CH absorption during the

pyrolysis of 20 ppm ethane dilute in argon; numbers in parenthesis

correspond to the number of experiments performed at that

wavelength; vertical error bars: ±10%, horizontal error bars: ±0.02

cm-1 (b) Comparison of current absorption coefficient calculation at

431.1311 nm (23194.80 cm-1) with previous work: solid black line,

this work 1 atm; dashed black line, taken from Dean and Hanson [70]

1 atm; solid gray line, this work 4 atm; dashed gray line, taken from

Dean and Hanson [70] 4 atm.....................................................................29

Figure 2.4 (a) Layout of 329.1 nm NCN laser absorption system (b) Example

absorption signal at 329.1 nm; upper panel: output of Spectra Physics

xv

Wavetrain doubling cavity, RMS noise is ~2.0%; lower panel: after

two-beam common-mode rejection, RMS noise is ~0.10%...................... 30

Figure 2.5 NCN absorption spectrum mapped out via repeated single-frequency

experiments at different wavelengths; peak absorption was recorded:

(a) Measurements between 2215 K and 2260 K (frozen T) at ~0.82

atm; pre-shock reaction mixture: 253 ppm diketene, balance N2;

temperature at peak ~2250 K (b) Measurements between 2751 K and

2802 K (frozen T) at ~0.59 atm; pre-shock reaction mixture: 112.9

ppm ethane, balance N2; temperature at peak ~2640 K (c) Example

NCN absorption time-history, wavelength is 329.1301 nm (30383.12

cm-1); pre-shock reaction mixture: 253 ppm diketene, balance N2;

T(frozen) = 2273 K, T(equilibrated) = 1976 K, P~0.8 atm.......................32

Figure 2.6 LIF excitation spectrum for NCN from 326.9 nm to 329.8 nm; Upper

panel: low-pressure microwave discharge [87]; Lower panel: 30 torr

rich CH4-O2-N2 flame [60]; band head positions for hot bands, 010-

010, and 000-000 excitations, based on Refs. 86 and 87, are marked in

rows on the top of the lower panel; note that the 010Δ - 010Π (328.6

nm) and 000Π - 000Σ (329.13 nm) heads observed in Figure 2.5a are

seen at approximately the same wavelengths; above figure was taken

from Ref. 60. .............................................................................................33

Figure 3.1 Initial reflected shock conditions: 1586 K, 1.9 atm; 0.1% C6H5CH3,

0.9% O2, balance Ar, φ=1 (a) Typical OH concentration time-history

during toluene oxidation (b) OH sensitivity, S = (dXOH/dki)(ki), where

ki is the rate coefficient for reaction i. Note that S is not normalized

by XOH. ......................................................................................................50

Figure 3.2 Initial reflected shock conditions: 1115 K, 2.44 atm; 12 ppm TBHP,

120 ppm C6H5CH3, balance Ar (a) OH concentration time-history (b)

OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient

for reaction i. .............................................................................................51

xvi

Figure 3.3 Initial reflected shock conditions: 1344 K, 2.15 atm; 11.25 ppm

TBHP, 120 ppm C6H5CH3, balance Ar (a) OH concentration time-

history (b) OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate

coefficient for reaction i. ...........................................................................52

Figure 3.4 Initial reflected shock conditions: 1093 K, 2.48 atm; 12 ppm TBHP,

240 ppm C6H5CH3, balance Ar (a) OH concentration time-history (b)

OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient

for reaction i. .............................................................................................53

Figure 3.5 Uncertainty analysis for rate coefficient of C6H5CH3 + OH

Products; Initial reflected shock conditions: 1115 K, 2.44 atm;

Individual error sources were applied separately and their effect on

ktoluene+OH was determined..........................................................................54

Figure 3.6 Initial reflected shock conditions: 1048 K, 1.8 atm; 29.3 ppm TBHP,

486 ppm CH3COCH3, balance Ar (a) OH concentration time-history

(b) OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate


Figure 3.7 Arrhenius plot for C6H5CH3 + OH Products at temperatures greater

than 500 K; uncertainty in current data ~±30%. .......................................56

Figure 3.8 Arrhenius plot for CH3COCH3 + OH Products: (a) at all

temperatures (200 – 2000K) (b) at moderate to high (500 – 2000 K)

temperatures; uncertainty in current data ~±25%. ....................................57

Figure 4.1 HCO rate of production (ROP) analysis: 1% CH4, 4% O2, 1800 K, 1.2

atm. ............................................................................................................ 70


TBHP, 80 ppm (CH2O)3, balance Ar (a) OH concentration time-

history (b) OH sensitivity, S = (dXOH/dki)(ki), where ki is the rate


Figure 4.3 Uncertainty analysis for rate coefficient of CH2O + OH HCO +

H2O; Initial reflected shock conditions: 1229 K, 1.64 atm; Individual

error sources were applied separately and their effect on the rate of

xvii

reaction (2) was determined; Uncertainties were combined to yield an

overall uncertainty estimate for k2. ...........................................................72

Figure 4.4 Initial reflected shock conditions: 934 K, 2.1 atm; 14.50 ppm TBHP,

80 ppm (CH2O)3, balance Ar (a) OH concentration time-history (b)

OH sensitivity, S = (dXOH/dki)(ki), where ki is the rate coefficient for

reaction i. ...................................................................................................73

Figure 4.5 Uncertainty analysis for rate coefficient of (CH3)3-CO-OH

(CH3)3CO + OH; Initial reflected conditions: 934 K, 2.1 atm. .................74

Figure 4.6 Arrhenius plot for (CH3)3-CO-OH (CH3)3CO + OH; uncertainty in

current data ~±25%. .................................................................................. 75

Figure 4.7 Arrhenius plot for CH2O + OH HCO + H2O: (a) at high

temperatures (800 – 2500 K); uncertainty in current data ~±15% at

1229 K and ~±25% at 1595 K (b) at all temperatures (200 – 2500 K). ....76

Figure 4.8 (a) Potential energy surface for the (abstraction) reaction between OH

and CH2O, not to scale, adapted from Ref. 20b; barrier calculated in

this study is 0.22 kcal/mol, Xu et al. [20b] report -1 kcal/mol at a

different level of theory and basis-set (b) Structure of complex and

TS1, image taken from Ref. 20b; optimized geometries were obtained

at the CCSD/6-311++G(d,p) and B3LYP/6-311+G(3df,2p) (in

parenthesis) levels (c) Comparison of experimental measurements of

k2 and current TST calculations with and without a hindered rotor

treatment; energetics are from the theoretical calculations performed

in this study at CCSD(T)/6-311++G(d,p)//CCSD/6-311++G(d,p); note

that ±25% error bars are shown.................................................................78


trioxane, 0.5% O2, balance Ar (a) OH concentration time-history;

solid black line, fit to data by adjusting the overall decomposition

rate, k3a+k3b, and branching ratio, α; solid gray lines, variation of

k3a+k3b by ±50%; dashed black lines, variation of α by ±25% (b) OH

xviii

sensitivity analysis, S = (dXOH/dki)(ki/XOH), where ki is the rate



trioxane, 10% O2, 12% He, balance Ar (a) OH concentration time-

history; solid black line, fit to data by adjusting k4; dashed black lines,

variation of k4 by factor of 2 (b) OH sensitivity analysis, S =

(dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.............91


trioxane, 10% O2, 11.9% He, balance Ar (a) OH concentration time-

history; solid black line, fit to data by adjusting k4; dashed black lines,

variation of k4 by factor of 2 (b) OH sensitivity analysis, S =

(dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.............92

Figure 5.4 Comparison of current measurements of k3a and k3b with previous

work: (a) solid squares, this work (± 25% error bars); solid black line,

this work fit; 1, Kumaran et al. [21]; 2, Friedrichs et al. [28]; 3, Just

[22]; 4, Saito et al. [23]; 5, Eiteneer et al. [27]; 6, Irdam et al. [25]

(b) solid squares, this work (± 25% error bars); solid black line, this

work fit; open circles, Kumaran et al. [21] data; 1, Kumaran et al. fit;

2, Just [22]. ................................................................................................93

Figure 5.5 Comparison of current measurements of k4 with previous work: (a)

solid squares, this work (±35% error bars); solid black line, this work

fit; open circles, Michael et al. [34]; open triangles, Srinivasan et al.

[33] from O-atom traces; open squares, Srinivasan et al. [33] from

OH traces; solid gray line, Baulch et al. [11] (b) solid squares, this

work; solid black line, this work fit; solid gray line, this work

modified fit (see text); dashed black line, Michael et al. theory [34]........94

Figure 6.1 (a) Sensitivity to maximum of CH concentration in shock tube

oxidation of methane; CH4/O2/Ar (80ppm-100ppm-99.982%) phi =

1.6, P = 1.8 atm, T = 2800 K; adapted from Ref. 111 (b) Potential

energy surface for methyl decomposition [43], not to scale. ..................112

xix

Figure 6.2 Example CH data, modeling, and sensitivity: (a) CH concentration

time-history (b) CH sensitivity at early times, S = (dXCH/dki)(ki/XCH),

where ki is the rate coefficient for reaction i. ..........................................113

Figure 6.3 Example CH data, modeling, and sensitivity at high-pressure: (a) CH

concentration time-history (b) CH sensitivity at early times, S =

(dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i. ..........114

Figure 6.4 Example CH data, modeling, and sensitivity at high-temperature: (a)

CH concentration time-history (b) CH sensitivity at early times, S =

(dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i. ..........115

Figure 6.5 Comparison of CH time-histories calculated using different

hydrocarbon pyrolysis mechanisms; Initial reflected shock conditions:

3400 K, 1 atm; 20 ppm C2H6, balance Ar. ..............................................116

Figure 6.6 CH concentration time-history: (a) Pressure dependence (b)

Temperature dependence.........................................................................117

Figure 6.7 Example OH data, modeling, and sensitivity: (a) OH concentration

time-history (b) OH sensitivity at early times, S = (dXOH/dki)(ki/XOH),

where ki is the rate coefficient for reaction i. ..........................................118

Figure 6.8 Example OH data, modeling, and sensitivity at high-pressure: (a) OH

concentration time-history (b) OH sensitivity at early times, S =

(dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i...........119

Figure 6.9 (a) Comparison of current measurements of k5a with previous work:

open squares, this work (±25% error bars), 0.7-1.1 bar; solid black

line, Dean and Hanson [35], 0.5-1.3 bar; dashed black line, Röhrig et

al. [36], 1.2 bar; dash-dotted line, Markus et al. [37], 1.1-1.8 bar; solid

gray line, Baulch et al. [11] (b) Pressure dependence of k5a: solid

squares, 0.7-1.1 atm data; open circles, 1.8-2.9 atm data; solid

triangles, 3.6-4.2 atm data; solid black line, least-squares fit to data......120

Figure 6.10 (a) Comparison of current measurements of k5b with previous work:

solid squares, this work (±50% error bars); open circles, Eng et al.

[43]; dash-dotted line, Kiefer and Kumaran [67]; dashed line, Markus

xx

et al. [37]; solid black line, Lim and Michael [42]; solid gray line,

Baulch et al. [11] (b) Pressure dependence of k5b: solid squares, 1.09-

1.41 atm data; open circles, 1.42-1.75 atm data; solid triangles, 2.99-

3.89 atm data; solid black line, least-squares fit to data..........................121

Figure 6.11 Branching ratio for the unimolecular decomposition of methyl

radicals: (a) Temperature dependence: solid black line, this work;

open circles, Eng et al. [43] ( ρ(Ar)=1.8x10-6 mol cm-3 ); solid stars,

Fulle and Hippler [44] (high-pressure limit); dashed line, Markus et al.

[37] (1.1-1.8 bar); solid gray line, Baulch et al. [11] (b)

Pressure dependence at T=2750 K: solid black line, this work; open

circles, Eng et al. [43]; solid star, Fulle and Hippler [44] at high-

pressure limit; solid triangle, Markus et al. [37]; solid gray line,

Baulch et al. [11] (c) Effect of higher branching ratio on the modeled

CH time-history and comparison with experiment; a branching ratio

of ~0.70 was reported by Eng et al. [43] at a comparable temperature

and pressure (see Figure 6.11b)............................................................... 122

Figure 7.1 High-temperature CH perturbation experiment: upper CH trace is

obtained from the pyrolysis of 10 ppm ethane, balance Ar at 3348 K

and 1.08 atm; lower CH trace is from a similar experiment at 3348 K

and 0.95 atm, but with 10.1% added N2; addition of N2 causes the

peak CH mole fraction to be perturbed by ~35%; the solid black and

dashed lines are model simulations without and with N2, respectively;

k7=2.13 x 1011 cm3 mol-1 s-1 yields a best-fit between the perturbed CH

trace and the corresponding numerical simulation..................................152

Figure 7.2 CH rate of production (ROP) at high-temperatures: (a) experiment

with no N2: 10 ppm ethane, balance Ar at 3348 K and 1.08 atm

(b) experiment with added N2: 10 ppm ethane 10.1% N2, balance Ar

at 3348 K and 0.95 atm; the only additional CH removal path in the

experiment with added N2 is the reaction between CH and N2...............153

xxi

Figure 7.3 CH sensitivity at low-temperatures: 25.77 ppm acetic anhydride,

balance Ar, no N2; initial reflected shock conditions: 2278 K and 1.35

atm; Sensitivity, S = (dXCH/dki)(ki/XCH), where ki is the rate

coefficient for reaction i. .........................................................................154

Figure 7.4 Rate coefficient data for CH2CO + M CH2 + CO + M: open

squares, this work, 1.4 atm; solid black line, Frank et al. [162], 1.8

atm; solid gray line, Wagner and Zabel [161], 9.8 atm; dashed line,

Friedrichs and Wagner [160], 0.45 atm...................................................155

Figure 7.5 Low-temperature CH perturbation experiment: upper CH trace is

obtained from the pyrolysis of 25.77 ppm acetic anhydride, balance

Ar at 2278 K and 1.35 atm; lower CH trace is from a similar

experiment at 2233 K and 1.35 atm, but with 10.16% added N2;

addition of N2 causes the peak CH mole fraction to be perturbed by

~40%; the solid black and dashed lines are model simulations without

and with N2, respectively; k7=3.88 x 1010 cm3 mol-1 s-1 yields a best-fit

between the perturbed CH trace and the corresponding numerical

simulation. ...............................................................................................156

Figure 7.6 CH rate of production (ROP) at low-temperatures: (a) experiment with

no N2, 25.77 ppm acetic anhydride, balance Ar at 2278 K and 1.35

atm (b) experiment with added N2, 25.38 ppm acetic anhydride,

10.16% N2, balance Ar at 2233 K and 1.35 atm; the only additional

CH removal path in the experiment with added N2 is the reaction

between CH and N2. ................................................................................157

Figure 7.7 Effect of the vibrational state of nitrogen on k7; experiment with

helium in the reaction mixture: 9.95 ppm ethane, 5.72% He, 9.98% N2,

balance Ar; T(frozen) = 2684 K, T(equilibrated) = 2607 K, P ~1.06

atm; temperature change, due to vibrational relaxation, over 50 μs is

2.4% or 65 K; the best-fit k7 is unchanged due to helium addition,

which indicates that the vibrational state of N2 does not influence

CH+N2 kinetics. ......................................................................................158

xxii

Figure 7.8 (a) Rate coefficients of reactions (-7a) and (-7b) for the same rate in

the forward direction (b) Effect of the branching ratio of reaction (7)

on CH: reaction mixture is 101 ppm ethane, balance N2; T(frozen) =

2548 K, T(equilibrated) = 2185 K, P ~0.67 atm; temperature drops

from 2548 K to 2372 K due to vibrational relaxation in 250 μs. ............159

Figure 7.9 Example CH data, modeling, and sensitivity to infer the branching

ratio for CH+N2: (a) CH absorption time-history (b) CH sensitivity, S

= (dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i (c)

Effect of rate coefficient of CH3+M CH+H2+M; 101.39 ppm

ethane, balance N2; T(frozen) = 2634 K, T(equilibrated) = 2249 K,

P~0.64 atm; temperature drops from 2634 K to 2470 K due to

vibrational relaxation in 175 μs; data is presented in % absorption to

demonstrate the excellent sensitivity of the CH laser absorption

diagnostic, minimum detectable absorption is less than 0.1%. ...............161

Figure 7.10 Example CH data and modeling to infer the branching ratio for

CH+N2 with helium in the reaction mixture: (a) 101.6 ppm ethane,

5.02% He, balance N2 ; T(frozen) = 2611 K, T(equilibrated) = 2241 K,

P~0.57 atm; temperature drops from 2611 K to 2275 K due to

vibrational relaxation in 200 μs (b) 101.09 ppm ethane, 10.02% He,

balance N2; T(frozen) = 2671 K, T(equilibrated) = 2297 K, P~0.55

atm; temperature drops from 2671 K to 2302 K due to vibrational

relaxation in 200 μs. ................................................................................162

Figure 7.11 Example CH data and modeling to infer the branching ratio for

CH+N2 at high-pressure; 102.69 ppm ethane, balance N2; T(frozen) =

2531 K, T(equilibrated) = 2172 K, P~2.3 atm; temperature drops from

2531 K to 2329 K due to vibrational relaxation in 100 μs......................163

Figure 7.12 Example NCN absorption data, sensitivity, and rate of production: (a)

NCN absorption time-history, wavenumber is 30383.12 cm-1 (b) NCN

sensitivity, S = (dXNCN/dki)(ki/XNCN), where ki is the rate coefficient

for reaction i (c) NCN rate of production (ROP); 102.23 ppm ethane,

xxiii

balance N2; T(frozen) = 2587 K, T(equilibrated) = 2214 K, P~0.65

atm; temperature drops from 2587 K to 2380 K due to vibrational

relaxation in 300 μs. ................................................................................165

Figure 7.13 Example experiment to infer k34: (a) Normalized NCN time-history,

wavenumber is 30383.06 cm-1 (b) Temperature profile; test-gas is

almost completely relaxed in 100 μs (c) NCN sensitivity, S =

(dXNCN/dki)(ki/XNCN), where ki is the rate coefficient for reaction i;

105.3 ppm ethane, 9.8% He, balance N2; T(frozen) = 2930 K,

T(equilibrated) = 2492 K, P~0.45 atm. ...................................................167

Figure 7.14 (a) Example experiment to infer the absorption coefficient of NCN;

NCN absorption time-history at 30383.06 cm-1; kNCN was adjusted to

match NCN decay (best-fit value: 58 cm-1 atm-1); 105.3 ppm ethane,

9.8% He, balance N2; T(frozen) = 2930 K, T(equilibrated) = 2492 K,

P~0.45 atm (b) NCN absorption coefficient as a function of

temperature; all data inferred with a branching ratio of 1 for reaction

(7) in the kinetic mechanism; uncertainty in kNCN is estimated to be a

factor of two. ...........................................................................................168

Figure 7.15 Rate coefficient data for CH + N2 Products: open squares, this

work data; dash-dotted black line, this work fit; solid squares, Dean et

al. [48] data; solid black line, Dean et al. fit; dashed black line,

Lindackers et al. [49]; solid gray line, Matsui et al. [51]; dash-dotted

gray line, Blauwens et al. [50]; dotted line, Moskaleva and Lin [56]

RRKM theory for k1b; dashed gray line, GRI-Mech 3.0 [111];

uncertainty limits at ~2100 K and ~3350 K are ~±35% and ~±25%,

respectively.............................................................................................. 169

Figure 7.16 Rate coefficient data for H + NCN HCN + N: open squares, this

work; solid black line, Moskaleva and Lin [56] RRKM theory; dashed

line, Glarborg et al. [153] estimate; uncertainty in current data

estimated to be a factor of 2. ...................................................................170

xxiv

Figure A.1 Example OH concentration time-history; Reflected shock conditions:

φ=1, 0.1% C6H5CH3, 0.9% O2, balance Ar at 1689 K, 1.796 atm;

Ignition delay time defined as the time to 50% peak OH concentration

with zero time defined as arrival of reflected shock; tign = 209 μs..........192

Figure A.2 Variation of ignition delay time with temperature; Reflected shock

conditions: φ=1, 0.1% C6H5CH3, 0.9% O2, balance Ar at P=1 atm;

solid squares, current experimental results; Simulations are: dotted

line, Dagaut et al. [7]; dashed line, Pitz et al. [6]; dash-dot line,

Lindstedt et al. [5]. ..................................................................................193

Figure A.3 Variation of ignition delay time with fuel mole fraction; Reflected

shock conditions: φ=1, 1600K, P=1 atm; solid squares and solid line,

current experimental results; crossed squares, Burcat et al. [10]

experiments; Simulations are: dotted line, Dagaut et al. [7]; dashed

line, Pitz et al. [6]; dash-dot line, Lindstedt et al. [5]. .............................194

Figure A.4 Normalized ignition times: various shock tube studies; all data

normalized to φ=1, 1% C6H5CH3, 9% O2, 1 atm using equation 2;

solid circles, current study; crossed circles, Burcat et al. [10]; open

squares, Pitz et al. [6]; open circles, Burcat et al. [9]. ............................. 195

Figure A.5 OH concentration profiles; Reflected shock conditions: φ=1, 0.025%

C6H5CH3, 0.225% O2, balance Ar at 1648 K, 2.03 atm; solid line,

current study; dashed line, Pitz et al. [6]; dotted line, Dagaut et al. [7];

dash-dot line, Lindstedt et al. [5]; dash-dot-dot line, modified Pitz et

al; short dot line, Pitz [182]. ....................................................................196


C6H5CH3, 0.225% O2, balance Ar; solid line, current study; dashed

line, modified Pitz et al.; upper trace, 1783 K; lower trace, 1607 K.......197


C6H5CH3, 0.9% O2, 1586 K, balance Ar at 1.9 atm; solid line, current

study; dashed line, Pitz et al. [6]; dash-dot-dot line, modified Pitz et

xxv

al. ; dotted line, Dagaut et al. [7]; dash-dot line, Lindstedt et al. [5];

short dash line, modified Pitz et al. with 3 x k10b. ...................................198

Figure A.8 Early-time OH chemistry: a qualitative comparison between n-alkanes

(n-heptane, 2), branched chain alkanes (iso-octane, 1), and aromatics

(toluene, 3). .............................................................................................199

Figure B.1 Potential energy surface for the reaction between CH2O and O2; not to

scale; energies shown are from a CCSD(T)/cc-pVTZ// B3LYP/6-

31++g** calculation................................................................................209

Figure B.2 Comparison of theory with experiment: solid squares, this work

experiment (~±35% error bars); solid black line, this work least-

squares fit; dashed gray line, this work transition state theory. ..............209

1

Chapter 1: Background and Motivation

1.1 Introduction Combustion is characterized by phenomena such as heat transport, chemistry

and fluid dynamics. Combustion models include differential equations to describe

these different processes. These predictive models play a crucial role in the design and

optimization of combustion systems and devices. An important component of any

combustion model is the reaction mechanism that describes the chemistry of the

combustion event. The mechanism consists of elementary chemical reactions that are

characterized by rate coefficients which are a function of temperature and pressure. In

several advanced combustion systems, like homogenous charge compression ignition

(HCCI) engines, these elementary chemical reactions play a central role in controlling

overall system performance. For example, combustion chemistry can influence auto-

ignition properties of the fuel-oxidizer mixture, exhaust gas composition (pollutants

like nitrogen oxides, unburnt hydrocarbons, etc.) and heat release rates. Therefore, a

fundamental understanding of the chemistry of combustion is crucial to developing

advanced combustion devices and controlling pollutant-formation.

In this thesis, elementary chemical reactions important in the combustion and

oxidation of commercial fuels like natural gas and gasoline have been studied. The

measurements made can be broken into four categories: (a) Toluene oxidation, (b)

Formaldehyde chemistry (decomposition and oxidation), (c) Methyl decomposition,

and (d) Prompt-NO initiation. The underlying theme that relates all these

measurements is that they facilitate improved modeling and understanding of

combustion and pollutant-formation at elevated temperatures. While toluene is a major

constituent of gasoline, formaldehyde is a key intermediate that lies along the primary

oxidation pathway for alkane-based hydrocarbon fuels like natural gas. Methyl

2

decomposition plays an important role in the high-temperature oxidation of natural gas

and is also of interest from a theoretical perspective. Nitrogen oxides (NOx) are

atmospheric pollutants that are largely formed via combustion; an understanding of the

various NO-formation routes is central to developing NOx mitigation schemes. In all

the studies carried out in this work, advanced laser-based absorption sensors have been

used to monitor trace quantities of transient species; the resulting concentration time-

history measurements were used to infer rate and mechanistic information on the

reaction system being investigated. The subsequent sections of this chapter describe in

detail past work that has been reported in the literature for the chemical reactions

studied in the current research.

1.2 Background and Motivation

1.2.1 Toluene Oxidation

Aromatics have desirable properties such as a high energy density [1] and a

high knock rating [2], and have, therefore, become important constituents of fuels like

gasoline. For example, aromatics can constitute up to 35% by weight of commercial

gasoline, with greater than 10% by weight of toluene. Therefore, toluene ignition

chemistry needs to be understood well to model the combustion of real fuels like

gasoline.

Many of the high-temperature studies of toluene that have been reported in the

literature involved monitoring the concentration profiles of reactants, stable

intermediates and final products in a flow reactor using GC analyses [see, for example,

Ref. 3]. However, the ignition process of hydrocarbons is, to a large extent, controlled

by the transient radical pool (H, OH, CH3 etc.), and very little information concerning

radical concentration profiles during the ignition process is available in the literature.

Detailed measurements of radical time-histories are needed. These measurements

would provide important targets for chemical kinetic model development, leading to

improved detailed models and improved predictions of global kinetic parameters like

ignition delay time. It is surprising to note that, in spite of the significance of toluene

3

in the combustion of commercial fuels, only a limited number of shock tube ignition

time [6, 8-10] and full modeling [3-7] studies of this aromatic have been carried out to

date.

Also, only a few direct kinetic studies of reactions that are important in toluene

ignition have been reported in the literature. Therefore, there is much uncertainty

associated with the rate coefficients of several of the key reactions that are rate-

controlling in toluene oxidation [11] at elevated temperatures. One of these reactions

is that between toluene and OH,

(1) C6H5CH3 + OH C6H5CH2 + H2O

The current estimate on the uncertainty of reaction (1) is relatively large [11], a factor

of 3. While the reaction of OH radicals with toluene has been studied at low

temperatures [12-15] because of its importance in tropospheric pollution, extensive

kinetic measurements of k1 have not been made at elevated temperatures. To the best

of our knowledge, there has been only one direct kinetic investigation of this reaction

at temperatures greater than 500 K [13], and none at temperatures greater than 1050 K;

Figure 1.1 summarizes these previous measurements of reaction (1). Investigations at

higher temperatures are warranted.

1.2.2 Formaldehyde Chemistry

Formaldehyde (CH2O) and the formyl radical (HCO) both lie on the primary

oxidation pathway of natural gas and other alkane-based hydrocarbon fuels. Under

radical rich conditions, CH3 reacts with O2 forming formaldehyde, and subsequent

abstraction reactions with H, OH, O and CH3 yield formyl radicals. CO and CO2 are

then formed by reaction of HCO with H, OH and O2, and also via the unimolecular

decomposition of HCO [16]. Figure 1.2 presents the important reaction pathways in

natural gas oxidation. In spite of the importance of HCO and CH2O reactions in the

overall hydrocarbon oxidation process, there still exist large uncertainties in the high-

temperature rate coefficients of several of the key oxidation and decomposition

reactions of these species. Accurate measurements of these critical rates at elevated

temperatures are needed to develop and refine detailed chemical kinetic mechanisms

4

of combustion chemistry. In this study, we have investigated the reactions of

formaldehyde with OH and O2 and the unimolecular decomposition of formaldehyde.

CH2O + OH Products

The reaction between OH and CH2O, (2), is an important HCO formation

pathway and also a major channel for the removal of CH2O in the hydrocarbon

oxidation process.

(2) CH2O + OH HCO + H2O

There has been only a single direct high-temperature measurement of the abstraction

reaction, (2), made at 1205 K, in a shock tube [17]. While estimates exist from flame

studies [18, 19], there is considerable scatter in the published data [11], see Figure 1.3;

high-temperature (> 1000 K) experimental data for this reaction are clearly needed.

D’Anna et al. [20a] have recently reported TST calculations for the rate

coefficient of reaction (2). The rates were computed based on results from

CCSD(T)//MP2 calculations using the aug-cc-pVDZ basis set. The computations

indicate that the H-abstraction reaction proceeds via a weak, but stable adduct in

which the H atom of the OH radical is bonded to the oxygen atom of the carbonyl

group in CH2O. The possibility of an OH-addition pathway, reaction (2a), forming

HCOOH was also considered,

(2a) OH + CH2O = HCOOH + H

The activation energy for the addition process was calculated to be 27.8 kJ mol-1, as

against -5.8 kJ mol-1 for the H-abstraction reaction. Further, the pre-exponential factor

for reaction (2a) was found to be 8 times smaller than for reaction (2). It was

concluded that the addition pathway is insignificant at combustion temperatures [20a].

Therefore, the only products considered in this study for CH2O+OH are HCO and

H2O.

CH2O + Ar Products and CH2O + O2 Products

There have been numerous studies [21-28] of the thermal decomposition of

CH2O, see Figure 1.4. The dissociation proceeds via two channels,

(3a) CH2O + M HCO + H + M

5

(3b) CH2O + M H2 + CO + M

Recent studies [Ref. 29 and references cited therein] have shown that reaction (3b)

occurs by two distinct mechanistic pathways: (1) a molecular-elimination channel,

CH2O + M H2 + CO + M, and (2) an intramolecular-hydrogen-abstraction channel,

CH2O + M H---HCO H2 + CO + M.

Most of the studies of CH2O pyrolysis that have been reported in the literature

[24-28] have been carried out using high CH2O concentrations, and at these

conditions, the measurements are insensitive to reaction (3b). However, recent work

has shown [21] that reaction (3b) is the dominant channel at combustion-relevant

conditions. To the best of our knowledge, there have been only two prior studies [21,

22] of k3b and the branching ratio of reaction (3). The Arrhenius expressions for k3a

and k3b in Just [22] yield rate coefficients that are about 65% higher and 30% lower,

respectively, than Kumaran et al. [21] in the 2000 – 2200 K temperature range.

Therefore, the relative importance of reactions (3a) and (3b) is not yet fully resolved.

There is, similarly, a large uncertainty in the rate coefficient of the reaction

between CH2O and O2, reaction (4),

(4) CH2O + O2 HCO + HO2

The scatter in the rate coefficients reported for this reaction is large, about an order-of-

magnitude at high temperatures, see Figure 1.5. A shock tube study by Hidaka et al.

[30] suggests an activation energy that is substantially higher than a linear

extrapolation of lower temperature measurements [31] of reaction (4). Michael et al.

[32] invoked a large rate coefficient for reaction (4), 2.5 to 5 times greater than GRI-

Mech 3.0, to describe their O-atom ARAS profiles in studies to measure the rate

coefficient of the reaction CH3 + O2 Products. In more recent work on the CH3+O2

reaction system, Michael and coworkers [33] indirectly inferred rate data for

CH2O+O2 by fitting OH and O-atom measurements to detailed model simulations –

the data reduction was complicated by the presence of competing reaction

sensitivities, in particular from the reaction between CH3 and O2. Michael et al. [34]

also studied reaction (4) directly using shock tube O-atom ARAS experiments – but

the measured rate coefficients show a higher activation energy than current

6

evaluations [11]. High-temperature measurements of CH2O + Ar and CH2O + O2 are

needed.

1.2.3 Methyl Decomposition

The thermal decomposition of methyl radicals proceeds via two competing

reaction pathways,

(5a) CH3 + M CH + H2 + M

(5b) CH3 + M CH2 + H + M

Reactions (5a) and (5b) play an important role in the high-temperature combustion and

pyrolysis of hydrocarbon fuels such as natural gas.

The rate coefficient of reaction (5a) has been measured by Hanson and co-

workers [35, 36] and Markus et al. [37], see Figure 1.6a. Dean and Hanson [35] and

Markus et al. [37] monitored CH by ring-dye laser absorption near 431.1 nm and

determined k5a from the measured CH profiles. Over nearly the same temperature

range, significantly different rate coefficients (~5x) were reported in the two studies.

This was subsequently attributed by Markus et al. [38, 39] to a large, unexplained

pressure dependence for CH formation between 0.3 and 3.5 bar. Values for k5a have

also been obtained in a shock tube study of the CH+O2 reaction system [36] by fitting

measured CH concentration time-histories using a detailed chemical kinetic

mechanism. The inferred rate coefficient data were found to be consistent with the

measurements of Dean and Hanson [35] at ~1 bar. However, the pressure dependence

of k5a remained unresolved.

Several experimental studies of reaction (5b) have been reported in the

literature [37, 40-43], see Figure 1.6b. All of these studies have involved shock tube

measurements of time-dependent H-atom concentration profiles via atomic resonance

absorption spectrometry, and span the 1700 – 4000 K temperature range. While

Bhaskaran et al. [40] monitored H-atoms in a shock tube study of C2H6/O2 mixtures,

Roth and coworkers [37, 41] detected H-atoms in shock-heated C2H6/Ar mixtures. At

high temperatures, the ethane in the initial reaction mixture rapidly decomposes to

yield CH3 which generates H-atoms via reaction (5b). The thermal reactions of CH3

7

were also investigated by Lim and Michael [42] by detecting H-atoms in reflected

shock wave experiments using CH3I/Kr mixtures. In the 2150 – 2520 K temperature

range, methyl decomposition to CH2 + H was found to dominate H-atom formation;

using detailed model simulations, Lim and Michael inferred rate coefficients for

reaction (5b). Most recently, H-atoms were monitored by Eng et al. [43] in incident

and reflected shock wave experiments at pressures ranging from 0.1 to 4.8 bar,

between 2000 and 4000 K, using highly dilute CH3N2CH3/Ar and CH3COCH3/Ar

mixtures to generate CH3. Values for k5b were obtained from the initial slope of the H-

atom profiles. At temperatures below 2500 K, H-atom formation was dominated by

secondary reactions, resulting in k5b values much higher than found in earlier work by

Lim and Michael, Roth and coworkers and Bhaskaran et al.

There is little direct experimental information on the branching ratio of methyl

decomposition [11]. Markus et al. [37] measured both k5a and k5b in a single study but

there were uncertainties due to pressure effects in their measurements. Dean and

Hanson [35] report Arrhenius expressions for both k5a and k5b, however, their CH

measurements were not particularly sensitive to k5b. Eng et al. [43] observed that the

H-atom concentration approaches a stationary level, [H]∞, at long-times. They

obtained the branching ratio, k5b/(k5a+k5b), by dividing this stationary H-atom

concentration by the initial methyl radical concentration. Unexpectedly high H-atom

yields of up to 70% were observed at pressures of ~1 bar; this could not be reconciled

with the 25-45% high-pressure-limit branching ratio estimate of Fulle and Hippler [44]

determined via studies of the reverse reaction.

There have been several theoretical studies of methyl decomposition [see Ref.

43 and references cited therein]. Two-dimensional, two-channel master equation

calculations were recently reported by Eng et al. [43]. These authors point out that the

decomposition of methyl radicals must be in the fall-off regime at ~1 bar since both

channels have been observed in experiments at this pressure (at the low-pressure limit,

only reaction (5a), the energetically favored channel, should be accessible via

collisions) [43]. Therefore, there is expectation of possible pressure dependence in

methyl decomposition at ~1 bar, which needs to be investigated.

8

Clearly, direct high-temperature measurements of methyl decomposition are

needed to provide accurate data on the overall rate and branching ratio, k5b/(k5a+k5b).

Also, uncertainty regarding the possible effect of pressure on methyl decomposition

needs to be resolved.

1.2.4 Prompt-NO Initiation

The oxides of nitrogen, NO and NO2 [NOx], are major atmospheric pollutants.

NOx compounds contribute to acid rain and the destruction of stratospheric ozone and

act as facilitators in the production of tropospheric ozone. The primary source of NOx

pollution is through combustion, forming NO, which is then partly converted to NO2

in the atmosphere. A fundamental understanding of the chemical pathways through

which NOx is produced is important since it is crucial to developing NOx reduction

strategies. There are three major chemical routes to NO formation in combustion: (a)

the oxidation of molecular nitrogen, called thermal-NO, (b) the oxidation of nitrogen-

containing compounds in the fuel, and (c) NO initiated by the reaction of hydrocarbon

fuel fragments with molecular nitrogen, called prompt-NO (Figure 1.7). A detailed

description of NO formation via routes (a) and (b) is available elsewhere [46]. In the

current study, we have made kinetic measurements of the initiation reactions that lead

to prompt-NO.

The first observation of prompt-NO was made by Fenimore [47] in

hydrocarbon flames. In his experiments, Fenimore found that NO formation in the

primary reaction zone exceeds that predicted by the thermal-NO mechanism.

Fenimore attributed this additional NO formation to the reaction of molecular nitrogen

with hydrocarbon fragments,

(7a) CH + N2 HCN + N

(57) C2 + N2 CN + CN

The products of reactions (7a) and (57) are oxidized to form NO by the following

reaction sequence: CN, HCN NCO NH NO. In their review paper on nitrogen

chemistry, Miller and Bowman [46] conclude that the primary initiation pathway in

9

the prompt-NO mechanism is reaction (7a), with minor contribution from reaction

(58) at high temperatures,

(58) C + N2 CN + N

Two high-temperature shock tube studies of reaction (7) have been reported in

the literature. In an earlier study from this laboratory, Dean et al. [48] monitored CH,

generated via the pyrolysis of methane [CH4] or ethane [C2H6] dilute in argon

(C2H6/CH4 CH3 CH), using narrow-linewidth ring-dye laser absorption at

431.1 nm. The perturbation in the CH profile upon adding N2 to the initial reaction

mixture was used to infer the rate coefficient of reaction (7a) in the 2500 – 3800 K

temperature range. Lindackers et al. [49] monitored N-atoms generated behind

reflected shock waves in C2H6/N2/Ar mixtures between 2600 and 2900 K using ARAS

at 119.9 nm. The N-atom profiles were fit to a detailed mechanism to infer k7a. The

rate coefficients measured in the two studies agree moderately at ~2600 K, Figure 1.8,

but diverge at higher temperatures. The measured activation energies are quite

different – Dean et al. inferred 22 kcal/mol, while Lindackers et al. report 14 kcal/mol.

Due to the difference in the activation energies, an extrapolation of the Arrhenius fits

reported in these two studies to flame temperatures leads to rate coefficients that differ

by up to about a factor of two. Rate coefficients for reaction (7a) have also been

inferred indirectly [50, 51] from flame experiments. These studies yield higher values

of k7a and lower activation energies than the shock tube studies described above.

While there appears to be a consensus in the literature that the CH+N2 reaction

is the primary initiation step to prompt-NO, there is debate over the products of this

reaction. Fenimore [47] originally postulated the products to be HCN and N, and this

was supported by NO measurements in flames [50, 51] and limited high-temperature

shock tube data [48, 49]. However, the formation of HCN and N from CH+N2 is a

spin-forbidden process that requires a potential surface crossing. Several theoretical

studies of the spin-forbidden CH + N2 HCN + N reaction (7a) have been reported

in the literature [52-55]. The calculated thermal rate coefficients [53] are much smaller

than measured in experiment. Wada and Takayanagi [52] conclude that other

10

mechanisms of prompt-NO formation might be needed to reconcile the serious

disagreement between experiment and theory.

Moskaleva and Lin [56] have suggested that the spin-conserved reaction,

(7b) CH + N2 H + NCN

is the initiation step in prompt-NO formation at high temperatures, rather than the

spin-forbidden reaction (7a). The NCN radical is expected to rapidly react with H, O,

OH and O2 to form intermediates CN, HCN, NH, and NCO that are oxidized to NO.

Therefore, the reactions of NCN present additional routes to previously established

prompt-NO formation pathways. Moskaleva and Lin have calculated k7b using ab

initio methods. At high temperatures, their RRKM rate coefficient expression (dotted

line in Figure 1.8) disagrees with the experimental data of Dean et al. [48] and

Lindackers et al. [49].

It is possible to re-interpret existing shock tube measurements of reaction (7a)

and of the overall reaction rate k7 as measurements of reaction (7b), as Moskaleva and

Lin [56] have done. The results of this analysis, which reflect the current state of rate

coefficient measurements for reaction (7b), k7b, are shown in Figure 1.8. It is evident

that there is still wide variation in k7b, and further work is needed to establish this rate

coefficient, especially because of the importance of this reaction in the formation of

NO in flames [57].

At low temperatures (< 1000 K), an association/stabilization channel can exist

for the CH+N2 reaction,

(7c) CH + N2 HCNN

At the temperatures of interest to prompt-NO formation in combustion (>1500 K), and

in the temperature and pressure regime where shock tube measurements of the CH +

N2 reaction have been made (1900 – 4000 K, 0.5 – 2 atm), this collisionally stabilized

process is unimportant, and reactions (7a) and (7b) are expected to dominate.

Measurements of the CH+N2 reaction have been performed at low temperatures and

high pressures where the stabilization path is significant and are described elsewhere

[see Refs. 58 and 59, and references cited therein].

11

Efforts have recently been made to confirm the existence of the spin-allowed

NCN channel. Smith [60] and Sutton et al. [61] have detected NCN using LIF in low-

pressure hydrocarbon flames. The spatial distribution of the measured NCN LIF

signal, its dependence on stoichiometry, its correlation to CH and NO concentration,

and its insensitivity to NO addition, all are consistent with the premise that it is

produced by reaction (7b). Yet even with these studies, no high-temperature rate

coefficient measurements based on NCN data have been performed to date.

Measurements of the reaction product NCN in isolated kinetic experiments

would offer stronger evidence for reaction (7b) – evidence that is not available by

measuring only the reactants, as is evident from the reanalysis of previous shock-tube

data (see Figure 1.8). Also, there are no direct measurements of the CH+N2 rate

coefficient at flame temperatures. The uncertainty and scatter in the limited high-

temperature data available in the literature is relatively large; this makes a reliable

extrapolation of these measurements to flame temperatures difficult. Therefore, the

objectives of this work are: (a) perform accurate rate coefficient measurements of

reaction (7) over a broad temperature range, and (b) establish the product pathways

and measure the branching ratio for CH+N2 Products.

1.3 Scope and Organization of Thesis The primary objective of the current work was to study elementary chemical

reactions that are important in the high-temperature combustion of commercial fuels

like natural gas and gasoline. Several reactions were studied in shock-tube

experiments using absorption spectroscopy. Narrow-linewidth, continuous-

wavelength, laser absorption diagnostics were developed to detect ppm-levels of

transient radical species [OH, CH, NCN] at high temperatures. Studies of (1) Toluene

ignition and oxidation, (2) Formaldehyde chemistry (decomposition and oxidation),

(3) Methyl radical decomposition, and (4) Prompt-NO initiation have been carried out.

Chapter 2 describes the experimental apparatus and laser diagnostics used in

this study. The 306 nm OH laser absorption diagnostic, which was used to make

measurements in the toluene and formaldehyde reaction systems, is described. The

12

431 nm CH laser absorption diagnostic, which was used to study methyl

decomposition and prompt-NO initiation, is also discussed. Spectroscopic

measurements of the CH collision-width in argon and nitrogen are described, along

with the spectroscopic model that was developed to determine the absorption

coefficient of CH as a function of temperature and pressure. NCN, a key precursor to

prompt-NO formation, was monitored by laser absorption at 329 nm. The diagnostic

that was assembled for this purpose is described here.

Chapter 3 presents measurements of the rate coefficient of the reaction

between toluene and OH, while Chapter 4 describes high-temperature measurements

of the reaction between formaldehyde and OH. Transition state theory calculations of

the CH2O+OH rate are also detailed in Chapter 4. Chapter 5 describes kinetic studies

of the decomposition of formaldehyde and the reaction of formaldehyde with oxygen.

Chapter 6 presents measurements of methyl decomposition, along with RRKM/master

equation calculations to model these measurements. Kinetic studies of prompt-NO

initiation are presented in Chapter 7 – measurements of the overall rate coefficient and

branching ratio of the reaction between CH and N2 are described. Experiment-design,

kinetic modeling and detailed uncertainty analyses are presented for all the kinetic

measurements made in this study. Chapter 8 concludes by summarizing the key

contributions of the current research and also presents suggestions and direction for

future work. Measurements of toluene + OH were motivated by toluene ignition-delay

time experiments, described in detail in Appendix A. Appendix B details ab initio,

theoretical calculations for the reaction of formaldehyde with oxygen.

13

Figure 1.1 Previous high-temperature rate coefficient data for C6H5CH3 + OH Products.

Figure 1.2 Primary oxidation pathways in natural gas combustion, adapted from Ref. [62].

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

1012

1013

Experiments Tully et al. [13]

Evaluation Baulch et al. [11]

500 K

k 1 [cm

3 m

ol-1 s

-1]

1000/T [K-1]

1250 K

14

Figure 1.3 Previous high-temperature rate coefficient data for CH2O + OH Products: solid square, Peeters and Mahnen [18]; solid circle, Westenberg and Fristom [65]; open triangle, Bott and Cohen [17]; dashed black line, Tsang and Hampson [66]; dash-dotted line, D’Anna et al. [20a]; dash-dot-dot line, Vandooren et al. [19]; dotted line, Dean et al. [64]; crossed squares, de Guertechin et al. [63].

0.25 0.50 0.75 1.00 1.25

1013

1014

k 2 [cm

3 mol

-1 s

-1]

1000/T [K-1]

1600 K 900 K4x1012

15

Figure 1.4 Previous rate coefficient data for CH2O + M Products: (a) 1, Kumaran et al. [21]; 2, Friedrichs et al. [28]; 3, Just [22]; 4, Saito et al. [23]; 5, Eiteneer et al. [27]; 6, Irdam et al. [25] (b) open circles, Kumaran et al. [21] data; 1, Kumaran et al. [21] fit; 2, Just [22].

0.3 0.4 0.5 0.6106

107

108

109

1010

1850 K2850 K

(4)(1)

(3)

(5)

(2)

k 3a [c

m3 m

ol-1

s-1]

1000/T [K-1]

(6)

(a)

(b)

0.40 0.45 0.50 0.55

108

109

1010

1900 K2350 K

(1)

k 3b [c

m3 m

ol-1

s-1]

1000/T [K-1]

(2)

16

0.4 0.5 0.6 0.7107

108

109

1010

1011

1500 K2500 K

1000/T [K-1]

k 4 [cm

3 mol

-1 s

-1]

Figure 1.5 Previous rate coefficient data for CH2O + O2 Products: open circles, Michael et al. [34]; open triangles, Srinivasan et al. [33] from O-atom traces; open squares, Srinivasan et al. [33] from OH traces; solid gray line, Baulch et al. [11].

17

0.25 0.30 0.35 0.40 0.45107

108

109

1010

1011

k 5a [c

m3 m

ol-1 s

-1]

1000/T [K-1]

3400K 2500K

0.25 0.30 0.35 0.40 0.45 0.50106

107

108

109

1010

1011

2200 K4000 K

k 5b [c

m3 m

ol-1 s

-1]

1000/T [K-1]

Figure 1.6 Previous rate coefficient data for CH3 + M Products: (a) solid black line, Dean and Hanson [35], 0.5-1.3 bar; dashed black line, Röhrig et al. [36], 1.2 bar; dash-dotted line, Markus et al. [37], 1.1-1.8 bar; solid gray line, Baulch et al. [11] (b) open circles, Eng et al. [43]; dash-dotted line, Kiefer and Kumaran [67]; dashed line, Markus et al. [37]; solid black line, Lim and Michael [42]; solid gray line, Baulch et al. [11].

(a)

(b)

18

0.25 0.30 0.35 0.40 0.45 0.50 0.55109

1010

1011

k CH

+N2 [

cm3 m

ol-1 s

-1]

1000/T [K-1]

4000K 1900K

Figure 1.7 Primary chemical pathways to prompt-NO.

Figure 1.8 Previous high-temperature rate coefficient data for CH + N2 Products: open squares, Dean et al. [48]; dashed line, Lindacker et al. [49]; solid gray line, Matsui et al. [51]; dotted line, Moskaleva and Lin [56] RRKM theory; solid squares, Moskaleva and Lin reanalysis of the Dean et al. data as measurements of k7b; solid circles, Moskaleva and Lin reanalysis of the Lindacker et al. data as measurements of k7b.

CH + N2

NCN

HCN NCO NH N NO +O +H +H +OH +H

forbidden?

19

Chapter 2: Experimental Apparatus and Diagnostics

This chapter describes the shock tubes and laser absorption diagnostics utilized

for the experiments performed in this study.

2.1 Shock Tubes All experimental measurements were carried out behind reflected shock waves,

in two high-purity, stainless steel, helium-driven shock tubes with inner diameters of

15.24 cm and 14.13 cm, respectively. The shock tube test section was evacuated

before each run with a turbo-molecular pump to pressures on the order of 10-6 torr.

Incident shock velocity measurements were made using five PZT pressure transducers

(PCB) and four programmable timer counters (Fluke PM6666), and linearly

extrapolated to the endwall. Average attenuation rates were between 0.5-1.5% per

meter. Reflected shock conditions were determined using ideal shock relations. Non-

ideal and boundary layer effects are not expected to be significant for the large-

diameter shock tubes and relatively short test-times utilized in this study. All optical

measurements in this work were performed 2 cm from the end wall of the shock tube

using 0.75” diameter UV fused silica or CaF2 windows flush mounted to the inner

radius of the shock tube. Signals were monitored using silicon photodetectors (700

kHz bandwidth) from Thorlabs (PDA55 or PDA36A, 3.6mm2 active area). For

measurements in the UV, PDA55s with UV-enhanced photodiodes from Hamamatsu

(S1722-02, 4.1 mm2 active area) were used. Pre-shock reaction mixtures were

prepared manometrically in a 14L (or a 12L) stainless steel mixing chamber equipped

with a magnetic stirrer assembly, and allowed to mix thereafter (2-12 hours) to ensure

homogeneity and consistency. Before shock heating, some of the mixture samples

were analyzed in a gas chromatograph (SRI GC 8160-C), providing a check on the

20

possible decomposition of mixture constituents in the gas phase in the mixing

chamber. Further details of the shock tube set-up can be found elsewhere [68].

2.2 OH Laser Absorption Diagnostic OH absorption was measured using the well-characterized R1(5) line of the OH

A2Σ+-X2Π (0,0) band at 306.6871 nm (32606.52 cm-1). A schematic of the OH

absorption system is presented in Figure 2.1a. Visible light at 613.4 nm (25-30 mW)

was generated in a Spectra-Physics 380 ring-dye laser cavity by pumping Rhodamine

6G dye with a 5 W, 532 nm, cw beam produced by a Coherent Verdi laser. UV light

(1-2 mW) at 306.7 nm was generated by intra-cavity frequency doubling the visible

light beam using a temperature tuned AD*A crystal. A Burleigh WA-1000 wavemeter

was used to monitor the visible wavelength. Uncertainty in the wavemeter reading is

estimated to be 0.01 cm-1, and this was taken into account when setting uncertainty

estimates for our rate measurements. A part of the UV beam was split off and common

mode rejection of laser intensity fluctuations was performed by balancing the two

beams (transmitted and reference) prior to each run. The minimum absorption

detection limit was ~0.1%, see Figure 2.1b, and this allowed for ppm-level

detectivities at time scales on the order of microseconds. The beams were aligned and

balanced as described in Herbon et al. [68]. Quantitative OH concentration profiles

were generated from the raw traces of fractional transmission using Beer’s law, (I/Io)ν

= exp(-kv P X L), where I is the intensity of the transmitted laser beam, Io is the

intensity of the reference beam, kv is the absorption coefficient (atm-1cm-1) at

frequency ν, P is the total pressure (atm), X is the mole fraction of the absorbing

species, OH, and L is the laser path length. The absorption coefficient of the OH

radical is well established [68, 69, 71] and known to within 5%. Further details of the

OH ring-dye laser absorption diagnostic may be found in Herbon et al. [68, 69].

2.3 CH Laser Absorption Diagnostic CH radicals were detected by cw, narrow-linewidth ring-dye laser absorption

at 431.1311 nm (23194.80 cm-1). This wavelength corresponds to the overlapping

21

Q1d(7) and Q2c(7) rotational lines of the CH A2Δ-X2Π (0,0) band [70]. Narrow-

linewidth radiation was generated by pumping a Coherent 699 ring-dye laser, with

Stilbene 3 dye, with the multi-line UV output from a Coherent Innova-200 Ar-ion

laser. Single mode operation of the laser was verified using a Spectra-Physics 470

scanning interferometer. A multi-line UV beam of ~2.5 W generated ~100 mW of

visible power at 431 nm. Neutral density filters were used to reduce the power of the

beam propagating through the diagnostic section of the shock tube to 1-5 mW. The

nominal laser wavelength was determined to within 0.01 cm-1 using a Burleigh WA-

1000 wavemeter. The laser beam was split into diagnostic and reference beams. The

two beams were balanced prior to each experimental run – this leads to effective

common-mode rejection of laser intensity fluctuations and a minimum absorption

detection limit of less than 0.1%. Figure 2.2a shows a schematic of the CH laser

absorption diagnostic, while Figure 2.2b presents the output of the Coherent 699 ring-

dye laser before (upper panel) and after (lower panel) common-mode rejection. An

improvement of about a factor of 20 in %RMS noise (0.9% to 0.05%) is achieved with

two-beam common-mode rejection. As in the OH measurements, Beer’s law was used

to convert the raw traces of fractional transmission to quantitative CH concentration

profiles. The CH absorption coefficient was determined as described below.

2.3.1 CH Spectroscopic Model

A spectroscopic model, based on previous work by Dean and Hanson [70], was

used to establish the absorption coefficient of the CH radical. The CH absorption

coefficient may be expressed as follows,

kCH(ν) = (πe2/mec2) x Σ [fB x (NA/RT) x fJ”J x Φ(ν) ] Eq. 1

where fJ”J is the rotational oscillator strength, fB is the Boltzmann fraction of the

population in the lower energy state, NA is the Avagadro number, R is the universal

gas constant, and Φ(ν) is the lineshape factor (cm). The Boltzmann fraction may be

calculated using,

fB=(2J”+1) x exp[-(hc/kT)F(J”)] x exp[-v”(hcωe/kT)]/Q Eq. 2

22

where F(J”) is the rotational energy of the lower energy state, ωe is the vibrational

frequency, and Q is the total internal partition function. The total partition function is

evaluated as a product of the rotational, vibrational and electronic partition functions,

Q = Qrot x Qvib x Qelec = (kT/hcB”) x (1- exp[-(hcωe/kT)])-1 x Qelec Eq. 3

where B” is the rotational constant. The electronic partition function is Qelec = Σ ge(n)

x exp(-Te(n)hc/kT), where ge(n) and Te(n) are the degeneracy and the electronic term

energy of the nth electronic state. The electronic term energy of the ground doublet

state Te(X2Π) = 0 cm-1, while for the lowest-lying excited quartet state Te(a4Σ−) = 5844

cm-1 [72]. Higher electronic states (for example, A2Δ) do not contribute to the

electronic partition function, even at temperatures as high as 5000 K. Populating the

a4Σ− quartet state would need to occur via collisions with argon, a spin-forbidden

process that is not likely to occur in the time-scale of our experiments (rate

coefficients were typically inferred at t < 50 μs in the current work) [73]. In the event

that the system does thermalize rapidly, the contribution of the low-lying quartet state

to Qelec is only ~6% at 3000 K. This was included as an uncertainty in our absorption

coefficient calculation where the electronic partition function was taken to be equal to

the degeneracy of the ground state, Qelec ~ ge(X2Π) = 4 [43, 70].

Updated molecular and spectroscopic parameters [74-77] were used to

calculate the absorption coefficient as a function of temperature and pressure.

Rotational and vibrational constants (ωe and B”) and rotational term energies (F(J”))

were taken from a recent study by Zachwieja et al. [74], while rotational oscillator

strength values were taken from Luque and Crosley [76]. The positions of the two

lines that are of interest in this work, Q1d(7) and Q2c(7), have been accurately

measured by Brazier and Brown [77]. The lineshape factor was evaluated using a

Voigt profile for each CH transition.

Dean and Hanson [70], in calculating the CH lineshape, assumed the collision-

broadening coefficient of CH in Ar, 2γCH-Ar, to be equal to that of NH in Ar, 2γNH-Ar

(0.023 cm-1atm-1 at 2800 K), the latter having been measured accurately by Chang and

Hanson [78]. This assumption is reasonable at ~1 atm, the pressure at which Dean et

al. [79] performed all of their kinetic measurements, since the broadening is largely

23

Doppler and the 2γCH-Ar value has only a small effect on the absorption coefficient at

line-center. To the best of our knowledge, there have been no direct measurements of

the pressure broadening of CH A-X transitions in argon. Takubo et al. [80] used a

collision width of 0.07 cm-1 for CH A-X (0,0) for a propane/air flame, based on

emission measurements by Rank et al. [81] and Harned and Ginsburg [82] in an

oxyacetylene flame, while Luque et al’s [83] examination of the CH A-X spectra of

Peterson and Oh [84] suggests a collision width of < 0.1 cm-1.

In this study, the collision-broadening coefficient, 2γCH-Ar, was inferred by

measuring the absorption at discrete positions across the convolved CH lineshape

(overlapping Q1d(7) and Q2c(7) rotational lines) via repeated single-frequency

experiments in the ethane pyrolysis system at 2800 K and 7.25 atm. The initial

mixture was 20-21 ppm ethane in argon. The measured profile was simulated using

LIFBASE [75] with the broadening coefficient as the only free parameter. Note that

LIFBASE calculates the CH lineshape using a Voigt profile, where the Voigt line is

obtained by convolving the Gaussian (Doppler) and Lorentzian (Collision) profiles. At

2800 K, a 2γCH-Ar value of 0.034 cm-1atm-1 leads to a reasonable fit between the

measured and simulated lineshapes (see Figure 2.3a); the measured 2γCH-Ar is about a

factor of 1.5 larger than the value used by Dean and Hanson [70]. In order to reconcile

the measurements, a small collision-shift of -0.01 to -0.02 cm-1 needed to be included

in the simulation. This collision-shift is of the same order of magnitude and in the

same direction as measured for other radical species like OH in Ar (at 2800 K and

7.25 atm, recent measurements by Herbon [68] suggest a collision-shift of -0.04 cm-1

in the OH Q1(3) line). It is pertinent to note that this shift borders on the ± 0.01 cm-1

resolution of the Burleigh WA-1000 wavemeter used in the current study.

Selected kinetic measurements were also made in a nitrogen bath (see Chapter

7), necessitating a measurement of the collision broadening coefficient of CH in N2.

2γCH-N2 was measured via repeated single-frequency experiments in shock-heated

mixtures of 203.6 ppm ethane in N2. The measured CH lineshape at 2312 K and 4.18

atm was fit to a spectroscopic simulation using LIFBASE; 2γCH-N2 was used as the

fitting parameter, and was measured to be 0.044 cm-1 atm-1 at 2312 K. The uncertainty

24

in the collision-broadening coefficient measurements (2γCH-Ar and 2γCH-N2) is

conservatively estimated at ~±20%. In the absorption coefficient calculation, the

temperature dependence of the collision-broadening coefficient was taken to be the

same as that measured for 2γCH-OH by Rea et al. [85].

Figure 2.3b presents a comparison of the current absorption coefficient

calculation (for CH in an argon bath) with previous work by Dean and Hanson [70].

Agreement at 1 atm is good, as expected, because the higher 2γCH-Ar has only a small

effect on the absorption coefficient magnitude at this pressure, but at 4 atm the present

absorption coefficient calculation differs from that calculated by Dean and Hanson

[70] by 10-15%.

At 2800 K and 4 atm, the overall uncertainty in the CH absorption coefficient

is about ±10%. This uncertainty is due to uncertainty in: (a) CH oscillator strength

(±3%); (b) collision-broadening coefficient (±20%); (c) electronic partition function

(±5%); (d) temperature (±1%); and (e) pressure (±1%). A 3% change in the oscillator

strength results in a ~3% change in kCH(ν), while a 20% change in the broadening

coefficient changes k(ν) by ~8%. The absorption coefficient is not particularly

sensitive to uncertainty in temperature and pressure; a 1% change in temperature and

pressure results in changes of 2% and 0.4% in the absorption coefficient, respectively.

Our uncertainty estimate for kCH(ν) is conservative since the collision broadening

coefficient, the electronic partition function and the temperature are likely known to

better than ±20%, ±5% and ±1%, respectively. The combined uncertainty decreases

at lower pressures, where most of the current experiments were carried out, due to the

reduced influence of collision broadening.

2.4 NCN Laser Absorption Diagnostic Although NCN has been observed spectroscopically since the 1960s (see

Herzberg and Travis [86]), there has been renewed interest in this radical since the late

1980s because of its appearance in hydrocarbon flames, rockets, and fuel-bound

nitrogen combustion. Recent studies by Moskaleva and Lin [56], Smith [60] and

25

Sutton et al. [61] have indicated that NCN likely plays an important role in the kinetics

of prompt-NO formation. Spectroscopic studies have been made of the A3Π-X3Σ− transition near 329 nm

via laser induced fluorescence in microwave discharges [87, 88] and flames [60, 61].

However, to the best of our knowledge, laser absorption measurements of NCN have

not been performed to date. We have monitored NCN at the A3Π-X3Σ− (000,000) band

head at 329.13 nm via narrow-linewidth ring-dye laser absorption. Ultraviolet light

near 329 nm was generated using an external-cavity frequency doubler with a BBO

non-linear optical crystal. A schematic of the experimental setup is shown in Figure

2.4a. 658 nm radiation (~200 mW) was generated in a Coherent 899-21 ring-dye laser

cavity, with DCM dye, pumped by a 5 watt, 532 nm solid-state Spectra-Physics

Millenia laser. The visible beam was doubled in an external cavity, Spectra-Physics

Wavetrain, outfitted with a BBO crystal, generating UV light at 329 nm (~15 mW).

The UV beam is split into diagnostic and reference beams that are balanced prior to

each experiment. This facilitates common-mode rejection of laser intensity

fluctuations, leading to a minimum absorption detection limit of ~0.1%. Figure 2.4b

presents the output of the Wavetrain (upper panel) and the noise characteristics of the

balanced absorption signal (lower panel).

The 000Π - 000Σ head in the A-X system was located and the NCN absorption

spectrum was mapped out, both at high and low temperatures, via repeated single-

frequency experiments over the 328.5 to 329.5 nm wavelength range. NCN was

generated by heating mixtures of diketene/N2 and ethane/N2 behind reflected shock

waves. These measurements are shown in Figures 2.5a and 2.5b, while Figure 2.5c

presents an example NCN absorption time-history measurement. For comparison,

Figure 2.6 presents NCN LIF excitation spectra measured in a microwave discharge

[87] and in a low-pressure methane flame [60]. The 010Δ - 010Π (328.6 nm) and

000Π - 000Σ (329.13 nm) heads observed in the shock tube measurements (see Figure

2.5a) are seen at approximately the same wavelengths. The observation of the 010Δ -

010Π and 000Π - 000Σ heads at 328.6 nm and 329.13 nm, respectively, the absence of

absorption when nitrogen is replaced with argon and the qualitative agreement with

26

the NCN LIF excitation spectra of Smith and co-workers [60, 87] confirms that the

measured absorption is due to the NCN radical. These experiments also confirm that

NCN is a product of the reaction between CH and N2 since it is formed via the

following reaction paths,

ethane → CH3 → CH (+N2) → NCN

diketene → CH2CO → CH2 → CH (+N2) → NCN

In Chapter 7 of this thesis, we will demonstrate via careful kinetic experiments and

modeling that NCN + H is the dominant (and possibly the only) path of the CH+N2

reaction.

27

0 50 100 150 200 250 300

-0.4

-0.2

0.0

0.2

0.4

% A

bsor

ptio

n

Time [μs]

after two-beam common-mode rejection

Figure 2.1 (a) Layout of 306.7 nm OH absorption system (b) Example absorption signal at 306.7 nm after two-beam common-mode rejection; RMS noise is ~0.10%.

(a)

(b)

28

Figure 2.2 (a) Layout of 431.1 nm CH laser absorption system (b) Example absorption signal at 431.1 nm; upper panel: output of Coherent 699 ring-dye laser cavity, RMS noise is ~0.9%; lower panel: after two-beam common-mode rejection, RMS noise is ~0.05%.

(a)

(b)

0 50 100 150 200 250 300-0.1

0.0

0.1 after two-beam common-mode rejection

% A

bsor

ptio

n

Time [μs]

Coherent 699 output (431.1 nm)

0.0

0.5

1.0

1.5

I [vo

lts]

29

2600 2800 3000 3200 3400 3600

200

300

400

500

600

k CH(ν

) [cm

-1 a

tm-1]

Temperature [K]

23194.0 23194.5 23195.0 23195.5

0.0

0.4

0.8

1.2

% R

elat

ive

Abso

rptio

n

Wavelength [cm-1]

(2)

(5)

Figure 2.3 (a) LIFBASE simulation of the CH absorption feature near 23194.80 cm-1 (431.1311 nm) at 2800 K and 7.25 atm: dashed black line, 2γCH-Ar = 0.023 cm-1 atm-1, solid gray line, 2γCH-Ar=0.034 cm-1atm-1, solid black line, 2γCH-Ar = 0.034 cm-1atm-1 shifted -0.015 cm-1; open squares, experimental data from peak CH absorption during the pyrolysis of 20 ppm ethane dilute in argon; numbers in parenthesis correspond to the number of experiments performed at that wavelength; vertical error bars: ±10%, horizontal error bars: ±0.02 cm-1 (b) Comparison of current absorption coefficient calculation at 431.1311 nm (23194.80 cm-1) with previous work: solid black line, this work 1 atm; dashed black line, taken from Dean and Hanson [70] 1 atm; solid gray line, this work 4 atm; dashed gray line, taken from Dean and Hanson [70] 4 atm.

(b)

(a)

30

0 50 100 150 200 250 300

-0.4-0.20.00.20.4

after two-beam common-mode rejection

% A

bsor

ptio

n

Time [μs]

0.0

0.3

0.6

0.9

1.2

I [vo

lts]

SP WaveTrain output (329.1 nm)

Figure 2.4 (a) Layout of 329.1 nm NCN laser absorption system (b) Example absorption signal at 329.1 nm; upper panel: output of Spectra Physics Wavetrain doubling cavity, RMS noise is ~2.0%; lower panel: after two-beam common-mode rejection, RMS noise is ~0.10%.

(a)

(b)

31

328.4 328.6 328.8 329.0 329.2 329.40.0

0.2

0.4

0.6

0.8

1.0

1.2

010Δ - 010Π head

000Π - 000Σ head

Rel

ativ

e A

bsor

ptio

n

Wavelength [nm]

329.08 329.10 329.12 329.14 329.160.0

0.2

0.4

0.6

0.8

1.0

1.2000Π - 000Σ head

Rel

ativ

e Ab

sorp

tion

Wavelength [nm]

offline experiment

(a)

(b)

Low-temperature NCN absorption spectrum, ~2250 K

High-temperature NCN absorption spectrum, ~2640 K

32

-50 0 50 100 150 200 250-1

0

1

2

3

4

5

NC

N %

Abs

orpt

ion

Time [μs]

Figure 2.5 NCN absorption spectrum mapped out via repeated single-frequency experiments at different wavelengths; peak absorption was recorded: (a) Measurements between 2215 K and 2260 K (frozen T) at ~0.82 atm; pre-shock reaction mixture: 253 ppm diketene, balance N2; temperature at peak ~2250 K (b) Measurements between 2751 K and 2802 K (frozen T) at ~0.59 atm; pre-shock reaction mixture: 112.9 ppm ethane, balance N2; temperature at peak ~2640 K (c) Example NCN absorption time-history, wavelength is 329.1301 nm (30383.12 cm-1); pre-shock reaction mixture: 253 ppm diketene, balance N2; T(frozen) = 2273 K, T(equilibrated) = 1976 K, P~0.8 atm.

(c)

33

Figure 2.6 LIF excitation spectrum for NCN from 326.9 nm to 329.8 nm; Upper panel: low-pressure microwave discharge [87]; Lower panel: 30 torr rich CH4-O2-N2 flame [60]; band head positions for hot bands, 010-010, and 000-000 excitations, based on Refs. 86 and 87, are marked in rows on the top of the lower panel; note that the 010Δ - 010Π (328.6 nm) and 000Π - 000Σ (329.13 nm) heads observed in Figure 2.5a are seen at approximately the same wavelengths; above figure was taken from Ref. 60.

Image from Smith, Chem. Phys. Lett. 36 (2003), 541 [60]

35

Chapter 3: Toluene + OH Products

3.1 Introduction Toluene, owing to desirable properties such as a high energy density and a

high knock rating, is a major constituent of commercial fuels like gasoline. In spite of

toluene’s importance as a key fuel-component, the high-temperature combustion of

this aromatic is not well understood (see Chapter 1). There is much uncertainty

associated with the rate coefficients of several of the key reactions that are rate-

controlling in toluene ignition and oxidation [11].

Toluene chemistry [91] was studied in this laboratory by carrying out detailed

measurements of OH radical time-histories during toluene oxidation, with the

objective of providing kinetic targets for chemical model development and validation

(see Appendix A). The performance of three currently available toluene oxidation

mechanisms [5-7] was analyzed by comparing the measured ignition time and OH

time-history data to model predictions. While these measurements and analyses are

described in detail in Appendix A, an example OH concentration time-history

measurement, along with detailed model calculations using the Pitz et al. toluene

oxidation mechanism [6], is presented in Figure 3.1a. An OH radical sensitivity

analysis, for the conditions of this experiment, 1586 K and 1.9 atm, is shown in Figure

3.1b. As is evident, the reactions with the greatest sensitivity at early times are,

(8) H + O2 O + OH

(9) C6H5CH3 + H C6H5CH2 + H2

(1) C6H5CH3 + OH Products

(10a) C6H5CH3 C6H5CH2 + H

(10b) C6H5CH3 C6H5 + CH3

36

The differences between simulation and experiment, with regard to OH plateau levels,

ignition delay, and early-time behavior may be attributed, in part, to discrepancies in

the rate coefficients of the above reactions.

Reaction (8) is by far the most sensitive reaction over the entire time-frame of

the experiment shown in Figure 3.1. There have been several studies of reaction (8)

reported over the years, and recent publications [92] estimate an uncertainty of just 9%

for this rate coefficient over the 1336 – 3370 K temperature range.

Reaction (9), the abstraction of a hydrogen atom from the methyl group in

toluene by H, was recently measured in this laboratory by laser absorption at 266 nm

and is known to ~±25% [95b]. The current estimate on the uncertainty of reaction (1)

is relatively large [11], a factor of 3. There have been no measurements of this reaction

at elevated temperatures – previous studies [11, 13] of reaction (1) are described in

Chapter 1, see Figure 1.1. There have been numerous measurements of reactions (10a)

and (10b) [see, for example, Refs. 93, 94 and references therein], and rate coefficients

for these reactions are reasonably well established at their high-pressure limits; but,

there has been only one shock tube study of this reaction system at low pressures [93].

Shock tube measurements of toluene decomposition are described elsewhere [95a]; in

this chapter we describe direct, high-temperature measurements of the reaction

between toluene and OH radicals.

OH radicals were generated by shock heating tert-butyl hydroperoxide

[(CH3)3-CO-OH], and monitored by narrow-linewidth ring-dye laser absorption at

306.7 nm. A comprehensive toluene oxidation mechanism [6] was used to model the

OH time-histories. The mechanism was assembled by adding to the C1-C4 mechanism

of Curran et al. [100], the toluene and benzene reaction mechanisms of Zhong et al.

[101-103]. Further details on the mechanism are available elsewhere [6]. Rate

coefficients for the reaction between C6H5CH3 and OH were inferred by varying this

rate in the mechanism to achieve a match between modeled and measured OH

concentration time-histories behind reflected shocks, over the 911 – 1389 K

temperature range.

37

The reaction between OH radicals and acetone [CH3COCH3], reaction (6), was

one of the secondary reactions encountered in the toluene + OH experiments.

(6) CH3COCH3 + OH CH3COCH2 + H2O

Even though the kinetics of OH radical attack on acetone is of importance in

combustion systems, there is scarcity of high-temperature data on reaction (6). There

has been only a single, direct high-temperature measurement of this reaction rate

coefficient, made at 1200 K, in a shock tube [96]. The uncertainty estimate for the rate

coefficient of this reaction is relatively large, about a factor of 3 at high temperatures

[110]. Due to this large uncertainty, even a small secondary interference due to

reaction (6) can have a large effect on the uncertainty in the toluene+OH rate

coefficient; accurate rate coefficient measurements at elevated temperatures are

therefore needed. Here, we report rate coefficient data for this reaction at temperatures

ranging from 982 K to 1300 K.

A total of 19 kinetic measurements (see Tables 3.1 and 3.2) were carried out to

ascertain rate coefficients for the reactions of OH with C6H5CH3 and CH3COCH3.

Modeled OH traces were fit to the measurements over a time window of ~75 μs. In

this time-frame the OH profiles show maximum sensitivity to reactions (1) and (6),

and hence yield rate data under conditions where the reactions of interest are almost

completely isolated chemically. In all the modeling carried out in this work, the

recently revised value for the standard heat of formation of OH was used [69].

Computations were performed using the CHEMKIN software package from Reaction

Design.

3.2 Experimental Set-up Experiments were carried out in the reflected shock region of a high-purity,

stainless steel, helium-driven shock tube with inner diameter of 15.24 cm. Research

grade argon (99.999%) was supplied by Praxair Inc. A commercially available

solution of 70% TBHP in water from Sigma Aldrich was used in the experiments

conducted. Research grade toluene (>99.5%) and acetone (>99.5%) were supplied by

Aldrich Chemical Co., Inc. and purified before use by a freeze-thaw procedure.

38

Mixtures were prepared manometrically in a 14L stainless steel mixing chamber

equipped with a magnetic stirrer assembly, and mixed for about two hours to ensure

homogeneity and consistency. Before shock heating, mixture samples were analyzed

in a gas chromatograph (SRI GC 8160-C), providing a check on the possible

decomposition of TBHP in the gas phase in the mixing chamber. It was found that less

than 0.30 ppm TBHP decomposes in the mixing tank to form acetone [97]. Modeling

the reaction system with the decomposition taken into account showed that this has no

discernible affect on our rate measurements.

Measurements of OH radicals were made behind reflected shock waves using

the diagnostic described in Chapter 2. Temperature and pressure behind the reflected

shock were calculated using ideal shock relations and thermodynamic data from the

Sandia database [98], assuming frozen chemistry. The database was updated with

properties for toluene, acetone and TBHP [6]. In-situ measurements of toluene

concentration in the shock tube, providing a check on possible wall adsorption and

condensation effects, were carried out using a 3.39 μm laser absorption diagnostic

[99,180]. A three pass optical set-up was necessary because of the low absorption

coefficient of toluene. Our measurements indicate that less than 10% of the initial

toluene test gas is lost due to adsorption and condensation on the walls of the mixing

assembly, manifold and shock tube; this uncertainty in the initial toluene concentration

was accounted for when determining error limits for our rate measurements. Evidence

was also found for significant loss of TBHP in the mixing assembly and shock tube –

these observations are described in the next section.

3.3 Kinetic Measurements The reaction of toluene with hydroxyl radicals was studied at temperatures

ranging from 911 K to 1389 K, and at total pressures between 2.07 atm and 2.82 atm.

Nominal mixtures with 100 ppm TBHP (and water) and 120-240 ppm toluene dilute in

argon were prepared.

39

3.3.1 OH Precursor Kinetics

Several molecules, such as H2O2, HNO3 and HNO2, have been attempted as

OH- precursors in the past [104, 105]. Major disadvantages of these species include

complex handling and preparation methods. Tert-butyl hydroperoxide [TBHP] as an

OH radical precursor was first used by Bott and Cohen [106] to measure the reaction

of OH with propane. OH radical reactions with various other species were measured

using this strategy [17, 96, 107]. A major advantage of TBHP over other OH-

precursors is that it rapidly dissociates at low temperatures of ~1000 K [108]. It is also

relatively stable on metals such as stainless steel, and is easy to handle. That TBHP is

stable on metal surfaces is evident from the results of the GC analyses that were

described earlier in the chapter.

TBHP falls apart almost instantaneously upon shock heating to form an OH

radical and a tert-butoxy radical [(CH3)3CO]. The tert-butoxy radical rapidly

decomposes to form acetone and a methyl radical. The decomposition reactions are as

given below,

(11) (CH3)3-CO-OH (CH3)3CO + OH

(12) (CH3)3CO (CH3)2CO + CH3

TBHP was chosen and used as the OH precursor in all the experiments carried out to

measure the rate for reaction (1). Reactions (11) and (12) were added to the Pitz et al.

mechanism; rate coefficients suggested by Vasudevan et al. [97] and Benson

[108,109] were used for these reactions. Measurements of the rate coefficient of

reaction (11) were made and are described in Chapter 4 of this thesis.

3.3.2 Toluene + OH Kinetics

A sample OH concentration time-history recorded on shock heating a mixture

of 100 ppm TBHP (and water) and 120 ppm toluene in argon is shown in Figure 3.2a.

It should be noted that the spike in the OH trace at time-zero corresponds to the arrival

of the reflected shock front at the diagnostic location. The diagnostic beam is

temporarily steered off the detector surface resulting in the observed spike. Numerical

simulations of the reaction system reveal that water in the initial mixture has no

40

discernible effect on the measured OH profiles in our experimental range. For the

conditions of the experiment shown, 1115 K and 2.44 atm, the measured peak OH

mole fraction is ~12 ppm (see Figure 3.2a). A 70% by weight solution of TBHP in

water in the liquid phase corresponds, on applying Raoult’s law, to ~69% water and

~31% TBHP in the vapor phase. Hence, 100 ppm of the TBHP-water mixture should

contain ~31 ppm TBHP. The measured peak mole fraction is substantially lower than

the potential maximum of 31 ppm. The lower than expected OH yield is attributed to

condensation and adsorption of TBHP onto the walls of the mixing tank and shock

tube. The measurement of OH provides a check on the actual concentration of TBHP

in the shock tube. The assumption that condensation and adsorption reduce the mole

fraction of TBHP from its nominal value is reasonable, especially because GC

analyses indicate that there is little or no decomposition of TBHP in the gas phase in

the mixing chamber. In model simulations, an initial TBHP mole fraction that resulted

in the measured peak OH mole fraction was used. For example, for the experiment

presented in Figure 3.2a, an initial TBHP mole fraction of 12 ppm in the model leads

to good agreement between the measured and modeled OH peaks.

An OH radical sensitivity analysis, presented in Figure 3.2b, clearly shows that

the reactions between toluene and OH are the most sensitive over the entire time-

frame of the experiment. The chemistry is almost first order, with only slight

interference from the following reactions,

(6) CH3COCH3 + OH CH3COCH2 + H2O

(13) CH3 + OH CH2(S) + H2O

(14) CH3OH (+M) CH3 + OH (+M)

Measured and modeled OH time-histories for one of our higher temperature

experiments at 1344 K and 2.15 atm are presented in Figure 3.3a, while Figure 3.3b

presents an OH sensitivity analysis for this experiment. It is evident that secondary

chemistry is minimal – as with the lower temperature experiment presented above,

interference is primarily due to reactions (6), (13) and (14), with slight, additional

interference from reaction (15),

(15) C6H5CH2 + OH C6H5CH2OH

41

A short discussion on the product pathways possible for the reaction between

toluene and OH is pertinent here. In this study, three product channels were

considered,

(1a) C6H5CH3 + OH C6H5CH2 + H2O

(1b) C6H5CH3 + OH C6H4 CH3 + H2O

(1c) C6H5CH3 + OH C6H5OH + CH3

Tully et al. [13] assessed the relative importance of reactions (1a) and (1b) by

assuming a ring-H abstraction rate coefficient, k1b, that is five-sixth of the

corresponding best-fit hydrogen abstraction rate coefficient for benzene. A point-by-

point subtraction of k1b from experimental measurements of the overall rate, k1, was

carried out. This yielded data on k1a, the rate coefficient for side-chain hydrogen

abstraction. Tully et al. found that k1b/k1a ≤ 0.5 for all T < 1500 K, and this is

consistent with the relatively high bond energy for C-H in the aromatic ring.

Investigations of the reactions of OH with four isotopically substituted toluenes also

suggested that side-chain H abstraction, reaction (1a), is the dominant pathway for the

reaction between OH and toluene at elevated temperatures [13]. In the present work,

no attempt was made to determine quantitative rate expressions for the individual

product channels. When fitting modeled traces to experiment, the dominant reaction

pathway, assumed to be reaction (1a), was iteratively adjusted to yield a best fit, while

the rate coefficients recommended by Tully et al. [13] and Pitz et al. [6] were used for

the minor channels yielding phenylmethyl (reaction 1b) and phenol (reaction 1c).

Reactions that are essential for the description of the toluene+OH experiments are

summarized in Table 3.3 along with their rate parameters.

For the experiments shown in Figures 3.2a and 3.3a, overall rate coefficients

(k1a+k1b+k1c) of 4.54 x 1012 cm3 mol-1 s-1 and 6.19 x 1012 cm3 mol-1 s-1, respectively, for

reaction (1) lead to excellent agreement between modeled and measured OH time-

histories. To confirm that our modeling is consistent, experiments were conducted

with a higher toluene concentration in the initial mixture. An OH concentration profile

obtained on shock heating a nominal mixture of 100 ppm TBHP and 240 ppm toluene

dilute in argon is presented in Figure 3.4a, while Figure 3.4b shows an OH radical

42

sensitivity analysis for the conditions of this experiment (1093 K and 2.48 atm). We

note, from Figure 3.4b, that even with the higher fuel concentration mixture,

interference from secondary reactions is minimal. Furthermore, the k1 that leads to a

best fit between the simulated and measured OH traces, 4.42 x 1012 cm3 mol-1 s-1, is

consistent with measurements made at comparable temperatures of 1069 K and 1115

K at a lower initial toluene concentration. Table 3.1 summarizes the current

measurements of the rate coefficient of C6H5CH3 + OH Products.

A detailed error analysis was carried out to set uncertainty limits on the

measured rate coefficients. The following uncertainty categories were considered:

uncertainty in [a] wavemeter reading in the UV; [b] absorption coefficient of OH; [c]

mixture concentrations; [d] reflected shock temperature, primarily due to uncertainty

in the shock velocity determination; [e] rate coefficients of secondary reactions

[reactions (6), (13), and (14)]; [f] fitting the modeled trace to the experimental profile;

and [g] locating time zero. The major uncertainty categories and their effect on the

target reaction rate, for the experiment at 1115 K and 2.44 atm (Figure 3.2), are shown

in Figure 3.5. The effect of each of the above uncertainty categories on the rate

coefficient of C6H5CH3 + OH was ascertained and combined using a root-mean-square

summation to yield an overall uncertainty estimate of ~±30% at 1115 K and 2.44 atm.

A slightly higher uncertainty of ~±35% is estimated for our highest temperature

measurements; this increase in the uncertainty comes about mainly due to interference

from the reaction between benzyl and OH at elevated temperatures (see Figure 3.3b).

It should be noted that ensuing secondary chemistry of the products formed via

reactions (1a)-(1c) could potentially interfere with an overall rate measurement for

reaction (1). The Pitz et al. model already includes benzyl [C6H5CH2] and phenol

[C6H5OH] chemistry – secondary reactions due to these species are insignificant in our

experimental regime (this is evident from Figure 3.2b), except for our highest

temperature measurements where, as pointed out earlier, the reaction between benzyl

and OH is slightly interfering (Figure 3.3b). Phenylmethyl [C6H4CH3] yields are

expected to be small in our experiments; the phenylmethyl that is formed via reaction

(1b) will likely react with toluene and H atoms, with both reactions recycling toluene

43

[110]. Hence, these two reactions would not discernibly affect our modeled OH traces.

As one of the decomposition products of TBHP is acetone, the reaction between

phenylmethyl and acetone is also expected to occur. But estimates of the rate

coefficient for this reaction [110] indicate that it is much too slow to be of any

importance in our experiments. Another possible interfering reaction is that between

phenylmethyl and OH. Using C6H5 + OH as a model we find that this reaction also is

unlikely to have any perceptible effect on our measurements. We hence conclude that

phenylmethyl chemistry does not affect our determination of the rate coefficient for

reaction (1) – C6H4CH3 reactions were therefore disregarded in this study. To confirm

this conclusion, we added to the Pitz et al. mechanism C6H4CH3 reactions from the

recent toluene oxidation modeling study by Bounaceur et al. [90] (see Table 3.4) and

remodeled our experimental OH profiles. As expected, there was no discernible effect

on the simulated OH time-histories, which indicates that phenylmethyl chemistry does

not interfere with our measurements of k1.

3.3.3 Acetone + OH Kinetics

The reaction between acetone and OH, reaction (6), was one of the secondary

reactions encountered in the toluene + OH study. There has been just one kinetic study

of this reaction at elevated temperatures [96]. The scarcity of high-temperature data,

combined with the fact that the reaction shows pronounced non-Arrhenius behavior,

results in a relatively high uncertainty estimate of a factor of 3 in its rate coefficient

[110]. This, in turn, contributes to an uncertainty of about 25% in the rate coefficient

of reaction (1), leading initially to an overall uncertainty of ~±40% for k1 at ~1100 K.

As the kinetics of OH radical attack on acetone are of general importance in

combustion systems, we carried out kinetic measurements of reaction (6) at elevated

temperatures.

The reaction was studied at temperatures ranging from 982 K to 1300 K, and

total pressures between 1.52 atm and 1.80 atm. Reaction rate coefficients were once

again inferred by matching modeled and measured OH time-histories in the reflected

shock region. The GRI-Mech 3.0 mechanism (325 reactions, 53 species) [111] was

44

used to model the OH measurements. Acetone chemistry was incorporated into the

mechanism from the detailed LLNL hydrocarbon oxidation model (a total of 23

reactions involving CH3COCH3, CH3COCH2, and CH3CO were added) [6, 100]. The

only product channel considered in the modeling is the one leading to CH3COCH2 and

H2O because it has been shown [113] that these are the dominant products formed at

temperatures greater than about 450 K. Nominal mixtures with 200 ppm TBHP (and

water) and 480-505 ppm acetone in argon were prepared and used.

A typical OH concentration time-history recorded for a mixture of 200 ppm

TBHP (and water) and 486 ppm acetone in argon is shown in Figure 3.6a. Figure 3.6b,

an OH radical sensitivity analysis, shows that there is strong isolation of the target

reaction. There is, as expected, slight interference from the CH3 + OH reaction system.

For the experiment shown (1048 K and 1.77 atm), a rate coefficient of 3.35 x 1012 cm3

mol-1 s-1 results in good agreement between model and experiment. A detailed error

analysis was carried out to set uncertainty limits on the current measurements. Overall

uncertainty bars of ~±25% are estimated. Table 3.2 summarizes our measurements of

CH3COCH3 + OH CH3COCH2 + H2O.

The toluene + OH measurements were remodeled with the new acetone + OH

data. There was no discernible effect on the rate coefficient of reaction (3), and this is

because the rate coefficient for reaction (6) in the Pitz et al. model is in reasonable

agreement (at high temperatures) with the current measurements (see Figure 3.8b).

The new experimental data did allow us to lower the uncertainty estimate on reaction

(6) from a factor of three, to ~±30%. This, consequently, resulted in lower uncertainty

bars of ~±30% on the rate coefficient of the reaction between toluene and OH (see

Figure 3.5).

3.4 Comparison with Earlier Work Figure 3.7 presents the current data along with earlier evaluations and

measurements of reaction (3) at temperatures greater than about 500 K. Only a limited

number of studies of this key reaction have been reported at elevated temperatures [13,

112]. In Tully et al. [13], OH radicals were generated by flash photolysis of H2O at

45

165-185 nm, and the resulting fluorescence was monitored. Temperature and pressure

ranged between 500-1050 K and 27-133 mbar, respectively. Studies of dueterated

toluenes were also carried out to elucidate the variations of the reaction mechanism

with temperature. In the Baldwin et al. study [112], small amounts of toluene were

added to H2 + O2 mixtures – measurements of the consumption of toluene and H2 by

gas chromatography facilitated the evaluation of rate coefficients for the reactions of

toluene with OH, H, and O.

As is evident from Figure 3.7, the current high-temperature measurements of

k1 (k1a+k1b+k1c) are consistent and in good agreement with the overall rate coefficient

measurements of Tully et al. and Baldwin et al. The present data were fit with the

lower temperature measurements of Tully et al. to the following two-parameter form,

applicable over 570 – 1389 K,

k1 = 1.62x1013 x exp (-1394 / T [K]), [cm3 mol-1 s-1]

From Figure 3.7, we note that there appears to be slight non-Arrhenius behavior at

temperatures greater than ~1000 K. But since this curvature is within experimental

uncertainty and scatter, we decided not to use a three-parameter form for k1 – a two-

parameter expression fits the current measurements with the Tully et al. data very

well.

The reaction between acetone and OH radicals, like reaction (1), has not been

extensively studied at elevated temperatures. In the only other direct, high-temperature

measurement reported for this reaction [96], resonance absorption detection of OH

was used to measure the rate coefficient of reaction (6) under pseudo-first order

conditions at 1200 K. Resonance radiation at 309 nm was produced by a microwave-

powered discharge through a mixture of helium and water vapor flowing at 70 torr

through a quartz lamp. There have been several studies of this reaction at low to

moderate temperatures though [113-118]. Figure 3.8 summarizes our and earlier

measurements of reaction (6). Within experimental uncertainty, the current

measurements agree very well with the Bott and Cohen data-point [96]. It is pertinent

to note that, while at lower temperatures the curvature in the Arrhenius plot is marked,

46

at moderate-to-high temperatures, the experimental data points more or less lie along a

line. A two-parameter fit of the current data, valid over the 982 – 1300 K temperature

range, yields the following rate expression,

k6 = 2.95x1013 x exp (-2297 / T [K]), [cm3 mol-1 s-1]

The current high-temperature measurements were also fit with lower temperature data

reported in the literature [113-118]. A least-squares multi-parameter fit for the overall

reaction rate coefficient of CH3COCH3 + OH, valid over the temperature range of 200

–1300 K, is given below,

k6 = 8.0x1010 + 6.08x108 x T1.41 x exp (-1289 / T [K]), [cm3 mol-1 s-1]

Not included in this empirical, multi-parameter fit are the measurements of Yamada et

al. [113], because the authors state in their paper that there could exist a small,

systematic error in their rate measurements, possibly due to loss of acetone during

transport through the reactor used in their experiments. However, the Yamada et al.

measurements appear to be reasonably consistent with other work and with our multi-

parameter fit, see Figure 3.8a.

3.5 Conclusions The reaction between toluene and OH was studied in reflected shock wave

experiments by monitoring OH using narrow-linewidth ring-dye laser absorption at

306.7 nm. OH radicals were generated by the rapid thermal decomposition of tert-

butyl hydroperoxide behind the reflected shock front. Our high-temperature

measurements are consistent with the lower temperature measurements of Tully et al.

[13]. The kinetics of OH radical attack on acetone was also studied at elevated

temperatures. There is good agreement between the present work, and the only other

high-temperature measurement reported in the literature by Bott and Cohen [96].

47

Table 3.1: C6H5CH3 + OH Products: Rate coefficient data

T [K] P [atm] k1 [cm3mol-1s-1]

100 ppm TBHP (and water), 120 ppm C6H5CH3 , balance Ar

911 2.82 3.14 x 1012 972 2.74 3.35 x 1012 1069 2.49 4.29 x 1012 1115 2.44 4.54 x 1012 1174 2.39 4.86 x 1012 1277 2.22 5.23 x 1012 1344 2.15 6.19 x 1012 1389 2.07 7.10 x 1012

100 ppm TBHP (and water), 240 ppm C6H5CH3 , balance Ar 1093 2.48 4.42 x 1012 1281 2.18 5.84 x 1012

Table 3.2: CH3COCH3 + OH CH3COCH2 + H2O: Rate coefficient data


200 ppm TBHP (and water), 504 ppm CH3COCH3 , balance Ar

1093 1.57 3.46 x 1012 1159 1.61 4.14 x 1012 1188 1.58 4.31 x 1012 1201 1.52 4.05 x 1012 1297 1.80 5.42 x 1012 1300 1.54 4.98 x 1012

200 ppm TBHP (and water), 486 ppm CH3COCH3 , balance Ar 982 1.85 2.87 x 1012 1048 1.77 3.35 x 1012 1260 1.57 4.55 x 1012

48

Table 3.3: Reactions describing C6H5CH3 + OH experiments

Rate Coeff. [cm3 mol-1 s1] Reaction

A n E, cal/mol

Ref.

(CH3)3-CO-OH (CH3)3CO + OH

2.50x1015 0.0 42998

97*

(CH3)3CO (CH3)2CO + CH3 1.30x1014 0.0 15300 108, 109* C6H5CH3 + OH C6H5CH2 + H2O see text this work C6H5CH3 + OH C6H4CH3 + H2O C6H5OH + CH3 C6H5CH3 + OH CH3 + OH CH2 (S) + H2O CH3 + OH CH2O + H2O CH3COCH3 + OH CH3COCH2 + H2O CH3COCH3 CH3CO + CH3 C6H5CH2 + OH C6H5CH2OH O + H2O OH + OH

1.20x1013 0.0 4491 5.42x1014 -0.83 12100 2.65x1013 0.0 2186 2.25x1013 0.0 4300 see text 1.22x1023 -1.99 83950 2.00x1013 0.0 0 2.96x106 2.02 13400

13 6 6 6

this work 6* 6 6

2CH3 (+M) C2H6 (+M) Low pressure limit 0.113x1037 Troe centering 0.405 CH3OH (+M) CH3 + OH (+M) Low pressure limit 0.295x1045 Troe centering 0.414

9.21x1016 -5.24 0.112x104 1.90x1016 -7.35

0.279x103

-1.17 0.170x104 0.696x102 0.0 0.954x105 0.546x104

635.8 0.1x1016 91730 0.1x10101

6

6

* rate coefficient units s-1

49

Table 3.4: Reactions describing C6H4CH3 chemistrya

Rate Coeff. [cm3 mol-1 s1] Reaction

A n E, cal/mol

C6H5CH3 + C6H4CH3 C6H5CH2. + C6H5CH3

7.9x1013

0.0

12000

C6H5CH3 + H C6H4CH3 + H2 6.0x108 1.0 16800 C6H5CH3 + O C6H4CH3 + OH 2.0x1013 0.0 14700 C6H5CH3 + HO2 C6H4CH3 + H2O2 4.0x1011 0.0 28900 C6H5CH3 + CH3 C6H4CH3 + CH4 2.0x1012 0.0 15000 C6H4CH3 + O2 O C6H4CH3 + O 2.6x1013 0.0 6100 C6H4CH3 + O2 OC6H4O + CH3 3.0x1013 0.0 9000 C6H4CH3 + H C6H5CH3 1.0x1014 0.0 0 C6H4CH3 + O OC6H4CH3 1.0x1014 0.0 0 C6H4CH3+ OH HO C6H4CH3 1.0x1013 0.0 0 C6H4CH3+ CH3 xylene 1.2x106 1.96 -3700 C6H4CH3+ HO2 O C6H4CH3+ OH 5.0x1012 0.0 0 C6H4CH3+ H C6H5CH2. + H 1.0x1013 0.0 0 a all rate parameters from Bounaceur et al. [90]

50

Figure 3.1 Initial reflected shock conditions: 1586 K, 1.9 atm; 0.1% C6H5CH3, 0.9% O2, balance Ar, φ=1 (a) Typical OH concentration time-history during toluene oxidation (b) OH sensitivity, S = (dXOH/dki)(ki), where ki is the rate coefficient for reaction i. Note that S is not normalized by XOH.

-200 0 200 400 600 800 1000-6

-3

0

3

6

9

12

15

18

OH

Sen

sitiv

ity x

10-6

Time [μs]

H+O2=O+OH C6H5CH3+OH=Products C6H5CH3+H=C6H5CH2.+H2 C6H5CH3=C6H5+CH3 C6H5CH3=C6H5CH2.+H

0 200 400 600 800 1000

0

100

200

300

400

500 Experiment Pitz et al. model

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

(a)

(b)

51

Figure 3.2 Initial reflected shock conditions: 1115 K, 2.44 atm; 12 ppm TBHP, 120 ppm C6H5CH3, balance Ar (a) OH concentration time-history (b) OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

-15 0 15 30 45 60 75

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

OH

Sen

sitiv

ity

Time [μs]

Toluene+OH = Products C6H5CH3+OH=C6H5CH2.+H2O C6H5CH3+OH=C6H4CH3+H2O C6H5OH+CH3=C6H5CH3+OH

Secondary Chemistry

CH3OH(+M)=CH3+OH(+M) CH3COCH3+OH=CH3COCH2+H2O CH3+OH=CH2(S)+H2O

0 15 30 45 60 75

0

5

10

15

20

25

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experiment 4.54x1012 cm3mol-1s-1

(a)

(b)

52

0 15 30 45 60 75

0

5

10

15

20O

H M

ole

Frac

tion

[ppm

]

Time [μs]

Experiment 6.19x1012 cm3mol-1s-1

-15 0 15 30 45 60 75

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

OH

Sen

sitiv

ity

Time [μs]

Toluene+OH=Products

C6H5CH3+OH=C6H5CH2.+H2O C6H5CH3+OH=C6H4CH3+H2O C6H5OH+CH3=C6H5CH3+OH

Secondary Chemistry

CH3OH(+M)=CH3+OH(+M) CH3COCH3+OH=CH3COCH2+H2O CH3+OH=CH2(S)+H2O C6H5CH2.+OH=C6H5CH2OH

Figure 3.3 Initial reflected shock conditions: 1344 K, 2.15 atm; 11.25 ppm TBHP, 120 ppm C6H5CH3, balance Ar (a) OH concentration time-history (b) OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

(a)

(b)

53

Figure 3.4 Initial reflected shock conditions: 1093 K, 2.48 atm; 12 ppm TBHP, 240 ppm C6H5CH3, balance Ar (a) OH concentration time-history (b) OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

0 15 30 45 60 75

0

5

10

15

20

25

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experiment 4.42 x 1012 cm3mol-1s-1

-15 0 15 30 45 60 75-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

OH

Sen

sitiv

ity

Time [μs]

Toluene+OH=Products C6H5CH3+OH=C6H5CH2.+H2O C6H5CH3+OH=C6H4CH3+H2O C6H5OH+CH3=C6H5CH3+OH

Secondary Chemistry CH3OH(+M)=CH3+OH(+M) CH3COCH3+OH=CH3COCH2+H2O CH3+OH=CH2(S)+H2O C6H5CH2+OH=C6H5CH2OH

(b)

(a)

54

Figure 3.5 Uncertainty analysis for rate coefficient of C6H5CH3 + OH Products; Initial reflected shock conditions: 1115 K, 2.44 atm; Individual error sources were applied separately and their effect on ktoluene+OH was determined.

-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

Fitting Uncertainty

Absorption coefficient, kv

(+/- 3%)

Wavemeter reading (+/- 0.01 cm-1 in UV)

Mixture Uncertainty(+/- 10%)

ΔT5 (+/-1.0%)

CH3OH (+M) = CH3 + OH (+M) (uncert. factor = 2)

CH3COCH3 + OH = CH3COCH2 + H2O (+/- 30%)

CH3 + OH = CH2 (S) + H2O (uncert. factor = 2)

1115 K, 2.44 atmCombined uncertainty on ktoluene + OH: +20.2% / - 31.4%

% Uncertainty in ktoluene+OH

55

Figure 3.6 Initial reflected shock conditions: 1048 K, 1.8 atm; 29.3 ppm TBHP, 486 ppm CH3COCH3, balance Ar (a) OH concentration time-history (b) OH sensitivity, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

0 15 30 45 60 75

0

10

20

30

40

50

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experiment 3.35 x 1012 cm3mol-1s-1

-15 0 15 30 45 60 75-0.3

-0.2

-0.1

0.0

0.1

0.2

OH

Sen

sitiv

ity

Time [μs]

CH3COCH3+OH=CH3COCH2+H2O OH+CH3=CH2(s)+H2O OH+CH3(+M)=CH3OH(+M) C2H6(+M)=2CH3(+M)

(b)

(a)

56

Figure 3.7 Arrhenius plot for C6H5CH3 + OH Products at temperatures greater than 500 K; uncertainty in current data ~±30%.

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

1012

1013

1014Experiments

This work Tully et al. [13] Stanford + Tully et al. fit Baldwin et al. [112]

Evaluation Baulch et al. [11]

500 K

k 1 [cm

3 mol

-1 s

-1]

1000/T [K-1]

1250 K

57

Figure 3.8 Arrhenius plot for CH3COCH3 + OH Products: (a) at all temperatures (200 – 2000K) (b) at moderate to high (500 – 2000 K) temperatures; uncertainty in current data ~±25%.

1 2 3 4 5

1011

1012

1013

250 K1000 K

k 6 [cm

3 mol

-1 s-1

]

1000/T [K-1]

This work This work, fit (see text) Multi-parameter fit (see text) Bott & Cohen [96] Gierczak et al. [114] Yamada et al. [113]a

Wallington et al. [117] Le Calve et al. [118] Yamada et al. [113]b

Tranter et al. [116] Wollenhaupt et al. [115]

see Figure 3.8b

a - HONO as OH precursorb - H2O/N2O as OH source

0.50 0.75 1.00 1.25 1.50 1.75 2.001011

1012

1013

570 K1300 K

k 6 [cm

3 mol

-1 s

-1]

1000/T [K-1]

Experiment This work This work, fit (see text) Bott & Cohen [96] Tranter et al. [116] Yamada et al. [113]

Model Pitz et al. [6]

(a)

(b)

59

Chapter 4: CH2O + OH Products

4.1 Introduction Formaldehyde [CH2O] and the formyl radical [HCO] are key intermediates in

the combustion of natural gas and alkane-based hydrocarbons, see Figure 1.2. The

major HCO formation and removal pathways in the high-temperature oxidation of

natural gas are shown in Figure 4.1, which presents a rate of production (ROP)

analysis for the formyl radical in the stoichiometric combustion of methane at 1800 K

and 1.2 atm. Calculations were carried out using the detailed GRI-Mech 3.0 natural

gas combustion mechanism [111]. As is evident, the major HCO production channels

are,

(16) H + CH2O HCO + H2

(2) CH2O + OH HCO + H2O

while the major HCO removal channels are,

(17) HCO + M H + CO + M

(18) HCO + O2 HO2 + CO

Reactions (16) and (17) were recently measured in this laboratory [119-121]. In this

chapter, we describe direct high-temperature measurements of reaction (2), CH2O +

OH HCO + H2O.

Previous measurements of reaction (2) are described in Chapter 1, see Figure

1.3. Based on ab initio calculations by D’Anna et al. [20a], we conclude that H-

abstraction to yield HCO and H2O is the only important product pathway for the

reaction between CH2O and OH at combustion temperatures. Other channels leading

to the formation of HCOOH+H, HO2+CH2, CH3+O2, O+CH3O, and O+CH2OH were

60

considered; however, model calculations [111] show that these reactions are

unimportant in our experimental range.

Measurements of k2 were made behind reflected shock waves using narrow-

linewidth OH laser absorption. OH radicals were generated by shock-heating tert-butyl

hydroperoxide [(CH3)3-CO-OH], while 1,3,5 trioxane [(CH2O)3] was used as a

precursor to produce CH2O. Rate coefficient data for reaction (2) were inferred by

matching the measured OH time-histories with profiles modeled using the GRI-Mech

3.0 mechanism [111]. Kinetic model simulations were performed using the

CHEMKIN software package from Reaction Design. Rate coefficients were also

calculated using ab initio quantum chemical methods and transition state theory, and

were compared with the experimental measurements.

4.2 Experimental Set-up All experimental measurements were carried out in the reflected shock region

of a high-purity, stainless steel, helium-driven shock tube with inner diameter of 15.24

cm (see Chapter 2). Research grade argon (99.999%) was supplied by Praxair Inc. A

commercially available solution of 70% TBHP in water was obtained from Sigma

Aldrich; 1,3,5 trioxane (>99% pure) was also supplied by Sigma Aldrich. As

described in Chapters 2 and 3, mixtures were prepared manometrically and analyzed

prior to shock heating in a gas chromatograph (SRI GC 8160-C). The decomposition

of TBHP in the gas phase was small and has no discernible affect on our rate

coefficient measurements.

OH absorption was measured using the well-characterized R1(5) line of the OH

A-X (0, 0) band near 306.7 nm. The diagnostic used is described in Chapter 2.

4.3 Kinetic Measurements

4.3.1 Precursor Species Kinetics

The first step to carrying out a direct and an accurate measurement of reaction

(2) is to identify suitable precursor species to generate reproducible levels of OH

61

radicals and CH2O in a shock tube experiment. TBHP was chosen and used as the OH

precursor in the experiments carried out to measure the rate of reaction (2). TBHP was

also used as an OH precursor in this laboratory to study the reaction between toluene

and OH [122], see Chapter 3. The advantages of using TBHP as an OH source have

already been highlighted in Chapter 3. The decomposition pathways for TBHP are,

(11) (CH3)3-CO-OH (CH3)3CO + OH

(12) (CH3)3CO (CH3)2CO + CH3

Measurements of the rate coefficient of reaction (11), the decomposition of TBHP,

were made and are described later in this chapter.

1,3,5 trioxane [(CH2O)3] was used to generate reproducible and known

amounts of CH2O in the shock tube [17]. One mole of 1,3,5 trioxane rapidly

decomposes on shock heating to form three moles of CH2O [108].

4.3.2 CH2O + OH HCO + H2O

The reaction of hydroxyl radicals with formaldehyde was studied at

temperatures ranging from 934 K to 1670 K, and total pressures between 1.3 atm to

2.1 atm. Mixtures with 100-200 ppm TBHP (and water) and 50-100 ppm 1,3,5

trioxane in argon were used. Model simulations were performed using the GRI-Mech

natural gas combustion mechanism [111]. Updating the mechanism with the recent

measurements of reactions (16) and (17) by Friedrichs et al. [119-121] did not

influence our determination of the rate coefficient of reaction (2). This is because the

measured OH time-histories are insensitive to these reactions in our experimental

regime (see Figure 4.2b). As pointed out earlier, one of the decomposition products of

TBHP is acetone (see reaction (12)). Acetone chemistry, which is not a part of the

GRI-Mech 3.0 model, was incorporated into the mechanism from the detailed LLNL

hydrocarbon oxidation model (a total of 23 reactions involving CH3COCH3,

CH3COCH2, and CH3CO were added) [6, 123]. The TBHP decomposition pathways,

reactions (11) and (12), were also added to the model; rate coefficients suggested by

Benson and co-workers [108, 109] were used for these reactions. As for the

62

decomposition of 1,3,5 trioxane, the rate expression of Irdam and Kiefer [124] was

used.

A typical raw OH concentration time-history recorded on shock heating a

mixture of 100 ppm TBHP (and water) and 80 ppm 1,3,5 trioxane in argon is shown in

Figure 4.2, along with an OH sensitivity plot generated using the GRI-Mech

mechanism. A peak OH yield of about 13 ppm is observed (see Figure 4.2a), lower

than the potential maximum value of ~31 ppm estimated using Raoult’s law. As GC

analyses indicate that TBHP decomposes only slightly in the mixing tank, we attribute

the low OH yields, as in the experiments described in Chapter 3, to condensation and

adsorption of TBHP onto the mixing tank and shock tube walls. For model

simulations, initial TBHP mole fractions were set at values that resulted in the

measured peak OH yields. For instance, for the experiment shown in Figure 4.2a, an

initial TBHP mole fraction of 13.25 ppm in the model led to good agreement between

the measured and modeled OH peaks. Model simulations show that water in the initial

reaction mixture has no discernible effect on the measured OH time-histories.

From Figure 4.2b, it is easily seen that reaction (2) is the most sensitive

reaction over the entire time-frame of the experiment, with a slight interference from

reaction (13), CH3 + OH CH2(S) + H2O. The chemistry is almost first order, and

this is a preferred condition at which to carry out the measurement. For the conditions

of Figure 4.2a, 1229 K and 1.64 atm, a rate coefficient of 1.32 x 1013 cm3 mol1 s-1 for

reaction (2) results in excellent agreement between the modeled and measured OH

time-histories.

It is instructive to identify the reactions that control OH decay when there is no

1,3,5 trioxane present in the initial mixture. An OH sensitivity analysis reveals that in

the absence of trioxane, the sensitive reactions are: (13) CH3 + OH CH2(S) + H2O,

and (6) CH3COCH3 + OH CH3COCH2 + H2O. Other reactions that are sensitive,

though to a much smaller extent, are: (19) CH3 + CH3(+M) C2H6(+M), and (20) OH

+ OH O + H2O.

A detailed error analysis was carried out to fit uncertainty limits on the

measured rate coefficient. The approach is similar to that adopted for reaction (1) and

63

is described in Chapter 3. The major uncertainty categories considered and their effect

on the rate coefficient of reaction (2) are shown in Figure 4.3. The individual

contributions were combined using a root-mean-square summation. Based on this

analysis, we estimate uncertainty bars of ~±15% on our measurement at 1229K and

1.64 atm. This is a marked improvement over the factor of 2 uncertainty at high

temperatures currently recommended in the literature for this reaction [11].

At reflected shock temperatures greater than about 1300 K, OH radicals are

formed behind the incident shock front itself (T2>900 K). This necessitated modeling

the OH traces in the incident shock region. However, OH formation and removal in

the incident shock did not affect the sensitivity profiles in the reflected; reaction (2)

was still by far the most sensitive reaction with respect to OH concentration. Hence,

even at these high temperatures, we could infer rate coefficient data for reaction (2) by

matching modeled and measured OH time-histories in the reflected shock region. A

detailed uncertainty analysis was carried out for a high-temperature experiment (1595

K, 1.37 atm). Uncertainty limits were estimated to be ~±25%, the increase coming

about mainly due to increased interference from the reaction CH3 + OH CH2(S) +

H2O and its associated uncertainties. Rate coefficients for reaction (2), over our

experimental range (934 – 1670 K), are summarized in Table 4.1.

4.3.3 (CH3)3-CO-OH (CH3)3CO + OH

At low temperatures (900-1000 K), an OH sensitivity analysis reveals that at

very early times (< 20 μs), TBHP decomposition, reaction (11), is the most sensitive

reaction (see Figure 4.4b). This suggests the possibility of inferring the rate coefficient

for reaction (11) by fitting the early-time, modeled OH traces with the experimental

time- histories. This is illustrated in Figure 4.4a for an experiment at 934 K and 2.1

atm. Reducing Benson and O’Neal’s [108] rate coefficient for reaction (11) by about

35% results in improved agreement between model and experiment at early times. It

should be noted that the OH decay (>20 μs) is still governed primarily by reaction (2),

and adjusting the rate coefficient of reaction (11) does not markedly affect the

subsequent decay. A detailed error analysis was carried out to set uncertainty limits on

64

this measurement. The various uncertainty categories considered, and their effects on

the rate coefficient of reaction (11) are shown in Figure 4.5. Overall uncertainty bars

of ~±25% are estimated.

Experiments carried out in pure TBHP mixtures at comparable reflected shock

conditions yielded the same rate data, indicating that the presence of CH2O does not

affect discernibly our determination of k11. Furthermore, measurements of this rate

were also made in low-temperature studies of the reaction of toluene with OH, and are

consistent with the measurements made in pure TBHP and TBHP/CH2O mixtures.

These data are presented in Table 4.2. Fitting the current measurements (average

pressure ~2.3 atm) to a two-parameter form, we get the following rate expression for

reaction (11) applicable over 900 – 1000 K,

k11 = 2.50 x 1015 exp (-21640 / T [K]), [s-1]

4.4 Comparison with Earlier Work Figure 4.6 summarizes our and earlier measurements [125-128] of reaction

(11). There is excellent agreement between all the studies on the temperature

dependence of this rate coefficient. The current measurements are slightly lower than

Benson and Spokes [128], the only other experimental data reported for this reaction

in the 900 – 1000 K temperature range. It is pertinent to note that the recommended

uncertainty on the most recent, direct measurement of this reaction by Sahetchian et al.

[126] (at 443-473 K) is a factor of 3.2. The current work therefore substantially

reduces the uncertainty of this rate coefficient.

Figure 4.7 presents the current data, along with earlier measurements and

evaluations of reaction (2). At high temperatures (see Figure 4.7a), we found two

shock tube studies of reaction (2), one direct [17] and one indirect [64]. Bott and

Cohen [17] used resonance absorption detection of OH to measure the rate coefficient

of reaction (2) under pseudo-first order conditions at 1205 K. The resonance radiation

at 309 nm was produced by a microwave-powered discharge through a mixture of

helium and water vapor flowing at 70 torr through a quartz lamp. Within estimated

65

experimental uncertainty limits, our data agree very well with the Bott and Cohen

data. Dean et al. [64] modeled CH2O oxidation in shock tube experiments by

employing a linear extrapolation of low-temperature OH + CH2O kinetic

measurements. It is evident from Figure 4.7b that there is strong curvature in the

Arrhenius plot, with the rate coefficient varying by almost an order of magnitude from

low to high temperatures. As a consequence of this curvature, the Dean et al. [64]

estimate is much lower than the current measurements. Amongst the high-temperature

estimates from flame experiments, there is good agreement with the Peeters and

Mahnen [18] value at 1600 K, while a two-parameter fit of the Vandooren et al. [19]

data provides some support. The Tsang and Hampson [66] evaluation, which is

currently used in the GRI-Mech 3.0 model, is about 30% higher and shows weaker

curvature than the current measurements (see Figure 4.7a).

There have been several direct kinetic studies of reaction (2) at low

temperatures [129-135, 139], and these data are presented in Figure 4.7b. The interest

in this reaction at low temperatures stems from the critical role that CH2O plays in

atmospheric chemistry. The reaction of CH2O with OH is one of the major

atmospheric sinks of CH2O, especially in the lower troposphere [131]. The most

recent low-temperature measurements of this reaction are those by Sivakumaran et al.

[131], where pulsed laser photolytic generation of OH radicals coupled with detection

by pulsed LIF was employed to measure absolute rate coefficients for reaction (2) over

the temperature range 202 – 399 K. The JPL 2004 evaluation [136] for this rate, which

takes into account several low-temperature studies [130-133, 135] reported for this

reaction, more or less coincides with the Sivakumaran et al. data. We hence fit our

high-temperature measurements with Sivakumaran et al. – considered to be the most

reliable measurements in the low-temperature regime – to yield the following three-

parameter fit applicable over 200 – 1670 K,

k2 = 7.82 x 107 T1.63 exp (531 / T [K]), [cm3 mol-1 s-1]

The above fit not only reconciles the most recent low-temperature data on reaction (2)

[131, 136] with our high-temperature experiments, but also fits reasonably well (to

66

within 15%) some of the available experimental data [132, 139] at intermediate

temperatures (400 – 600 K).

4.5 Transition State Theory Calculations The reaction of OH with CH2O was studied using quantum chemical methods

at the CCSD(T) level of theory using the 6-311++G(d,p) basis set. Ab initio

calculations were performed using the Gaussian 98 suite of programs [140].

Geometry optimization was carried out at CCSD/6-311++G(d,p), and a frequency

calculation was performed at that level of theory and basis set. A single point energy

calculation was then done at CCSD(T)/6-311++G(d,p) at the previously optimized

geometry. A barrier of 0.22 kcal/mol was obtained. The computed vibrational

frequencies and moments of inertia are summarized in Table 4.3. An IRC analysis was

not performed in this study. Recent IRC calculations by Xu et al. [20b] indicate that

the reaction between CH2O and OH occurs via a complex, OH---OCH2, in which the

hydrogen atom in the hydroxyl group forms a weak bond with the oxygen atom in the

carbonyl group (see Figure 4.8a). The abstraction then proceeds via the transition state

TS1 – our calculations at CCSD(T)/6-311++G(d,p)//CCSD/6-311++G(d,p) yield an

energy of 0.22 kcal/mol for TS1 relative to the reactants, while Xu et al. report -1

kcal/mol with calculations performed at CCSD(T)/6-311++G(3df,2p)//CCSD/6-

311++G(d,p). The potential energy surface for the OH+CH2O reaction is presented in

Figure 4.8a, while Figure 4.8b shows the geometries of the complex and the transition

state calculated by Xu et al. [20b].

Transition state theory calculations were carried out using the CSEO Kinetics

software [141]. In the current calculations, the effect of the OH---OCH2 complex was

not considered. The calculated rate coefficients are presented in Figure 4.8c, and agree

well with the current high-temperature measurements. It is evident from the figure that

a hindered rotor treatment (about the forming O-H bond) of the low-frequency mode

at 189 cm-1 helps improve agreement between theory and experiment. Our intention

here was not to carry out an exhaustive quantum chemical study of the title reaction,

but rather to show that at high temperatures, a simple H-atom abstraction treatment of

67

reaction (2), with a hindered rotor model for the appropriate transition state low-

frequency mode, yields values that are in good agreement with experiment. An

exhaustive theoretical study of reaction (2) was recently performed by Xu et al. [20b]

– the calculated rate coefficients are in excellent agreement with the current

measurements at high temperatures and with Sivakumaran et al. [131] at low

temperatures.

Shown in Figure 4.7 are the results of a recent TST calculation by D’Anna et

al. [20a]. We note that at moderate-to-high temperatures (500 – 2000 K), the

activation energy of the D’Anna et al. fit agrees reasonably well with our three-

parameter fit, but the calculated rate coefficient is about 2-3 times larger than the

current measurements. This could, in part, be on account of the harmonic oscillator

approximation that was adopted in that study to treat the low-frequency vibrational

modes.

4.6 Conclusions The reaction between hydroxyl radicals and formaldehyde was studied at

elevated temperatures in reflected shock wave experiments. The use of tert-butyl

hydroperoxide as an OH precursor, in conjunction with the sensitive detection of OH

using narrow-linewidth ring-dye laser absorption, facilitated accurate, direct

measurements of this reaction over a wide range of temperatures (934 – 1670 K). The

rate coefficient data agree well with an earlier study by Bott and Cohen [17]. The

reaction between CH2O and OH was also studied using quantum chemical methods

and transition state theory. The calculated rates were found to agree well with the

current measurements, especially with a hindered rotor treatment of the low-frequency

mode at 189 cm-1.

Early-time OH concentration profiles (in low-temperature experiments) were

employed to infer a rate coefficient for the decomposition of tert-butyl hydroperoxide

to a tert-butoxy radical and an OH radical. The measurements are in good agreement

with Benson and Spokes [128], the only other experimental data reported for this

reaction in the 900 – 1000 K temperature range.

68

Table 4.1: CH2O + OH HCO + H2O: Rate coefficient data


100 ppm TBHP (and water), 80 ppm (CH2O)3, balance Ar

934 2.10 1.02 x 1013 964 1.98 1.05 x 1013 1023 1.89 1.07 x 1013 1045 1.79 1.13 x 1013 1113 1.73 1.20 x 1013 1178 1.72 1.27 x 1013 1229 1.64 1.32 x 1013

200 ppm TBHP (and water), 160 ppm (CH2O)3, balance Ar 1250 1.70 1.35 x 1013 1444 1.41 1.64 x 1013


1492 1.50 1.70 x 1013 1595 1.37 1.90 x 1013 1670 1.31 2.10 x 1013

Table 4.2: (CH3)3-CO-OH (CH3)3CO + OH: Rate coefficient data

T [K] P [atm] k11 [s-1]


934 2.10 2.2 x 105 964 1.98 4.4 x 105

100 ppm TBHP (and water), Ar 923 2.07 1.7 x 105

100 ppm TBHP (and water), 120 ppm C6H5CH3, balance Ar

911 2.82 1.2 x 105 972 2.74 5.4 x 105

69

Table 4.3: Principal moments of inertia and ab initio vibrational frequenciesa

Species Ia Ib Ic ν [cm-1]

CH2O 1.78 13.04 14.81 1206, 1284 1563, 1816, 2961,

3027

OH 0.89 0.89 3780

TS

8.99

101.58

110.57 774i, 116, 120, (189)b, 731,

1152, 1209, 1246, 1536, 1868, 2969, 3792

a CCSD / 6-311++G (d,p) b treated as a hindered rotor

70

Figure 4.1 HCO rate of production (ROP) analysis: 1% CH4, 4% O2, 1800 K, 1.2 atm.

0 100 200 300 400-15

-10

-5

0

5

10H

CO

RO

P x

10-4

[mol

cm

-3 s

-1]

Time [μs]

1% CH4, 4% O2

1800 K, 1.2 atm H+CH2O<=>HCO+H2 OH+CH2O<=>HCO+H2O HCO+M<=>H+CO+M HCO+O2<=>HO2+CO

71

Figure 4.2 Initial reflected shock conditions: 1229 K, 1.64 atm; 13.25 ppm TBHP, 80 ppm (CH2O)3, balance Ar (a) OH concentration time-history (b) OH sensitivity, S = (dXOH/dki)(ki), where ki is the rate coefficient for reaction i.

0 10 20 30 40 50 60 70 80

0

5

10

15

20 Experiment 1.32x1013 cm3mol-1s-1

2kCH2O+OH

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

kCH2O+OH/ 2

0 10 20 30 40 50 60 70 80-2.0

-1.5

-1.0

-0.5

0.0

OH

Sen

sitiv

ity x

10-6

Time [μs]

OH+CH3<=>CH2(S)+H2O OH+CH2O<=>HCO+H2O

(b)

(a)

72

Figure 4.3 Uncertainty analysis for rate coefficient of CH2O + OH HCO + H2O; Initial reflected shock conditions: 1229 K, 1.64 atm; Individual error sources were applied separately and their effect on the rate of reaction (2) was determined; Uncertainties were combined to yield an overall uncertainty estimate for k2.

-10 -8 -6 -4 -2 0 2 4 6 8 10 12

Time Zero Uncertainty (+/- 0.25 μs)

Fitting Uncertainty

Mixture Uncertainty

Absorption coefficient, kv(+/- 3%)


ΔΤ5

(+/- 1.0%)

1229 K, 1.64 atmCombined uncertainty on k2: +13.3% / - 15.2%

% Uncertainity in k2

OH + CH3 = CH2(S) + H2O(Uncer. factor = 2)

73

Figure 4.4 Initial reflected shock conditions: 934 K, 2.1 atm; 14.50 ppm TBHP, 80 ppm (CH2O)3, balance Ar (a) OH concentration time-history (b) OH sensitivity, S = (dXOH/dki)(ki), where ki is the rate coefficient for reaction i.

0 20 40 60 80 100

0

5

10

15

20 Experiment k2=1.40 x1013 [66] ; k11=3.46 x 105 [108] k2=1.02 x 1013 [this work] ; k11=3.46 x 105 [108] k2=1.02 x 1013 [this work] ; k11=2.16 x 105 [this work]

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

0 5 10 15 20 25-1.2-0.8-0.40.00.40.81.21.62.02.4

OH

Sen

sitiv

ity x

10-6

Time [μs]

(CH2O)3=3CH2O TBHP=(CH3)3CO+OH OH+CH3<=>CH2(S)+H2O OH+CH2O<=>HCO+H2O

(b)

(a)

74

Figure 4.5 Uncertainty analysis for rate coefficient of (CH3)3-CO-OH (CH3)3CO + OH; Initial reflected conditions: 934 K, 2.1 atm.

-25 -20 -15 -10 -5 0 5 10 15 20 25

Time Zero Uncertainty (+/- 0.25 μs)

Fitting Uncertainty

Absorption coefficient, kv(+/- 3%)


ΔΤ5

(+/- 1.0%)

934 K, 2.1 atmCombined uncertainty on k11: +24.2 / - 24.1%

% Uncertainty in k11

75

Figure 4.6 Arrhenius plot for (CH3)3-CO-OH (CH3)3CO + OH; uncertainty in current data ~±25%.

0.75 1.00 1.25 1.50 1.75 2.00 2.2510-6

10-4

10-2

100

102

104

106

1.00 1.05 1.10 1.15

105

106

k 11 [s

-1]

1000/T [K-1]

Experiment This work Mulder & Louw [125] Sahetchian et al. [126] Kirk & Knox [127] Benson & Spokes [128]

Evaluation Benson & O'Neal [108]

1000 K 500 K

76

Figure 4.7 Arrhenius plot for CH2O + OH HCO + H2O: (a) at high temperatures (800 – 2500 K); uncertainty in current data ~±15% at 1229 K and ~±25% at 1595 K (b) at all temperatures (200 – 2500 K).

0.25 0.50 0.75 1.00 1.25

1013

1014

k 2 [cm

3 mol

-1 s

-1]

1000/T [K-1]

1600 K 900 K

(a)

4x1012

0 1 2 3 4 5

1013

1014

250 K

This work Stanford fit, this work Zabarnick et al. [139] Sivakumaran et al. [131] Bott & Cohen [17] Peeters & Mahnen [18] Atkinson & Pitts [132] Vandooren et al. [19] de Guertechin et al. [63] Dean et al. [64] Westenberg & Fristom [65] D'Anna et al. [20a] Tsang & Hampson/ GRI [66] Baulch et al. [11]

k 2 [cm

3 mol

-1 s

-1]

1000/T [K-1]

1000 K

(a)

(b)

77

Reaction Coordinate

Pote

ntia

l Ene

rgy

CH2O+OH

OH---OCH2

HCO+H2O

TS1

H2O---HCO

0.22 kcal/mol* (-1 kcal/mol**)

*, this work **, Xu et al. [20b]

(a)

(b)

Image from Xu et al., Intl. J. Chem. Kinet. 38 (2006), 322 [20b]

78

Figure 4.8 (a) Potential energy surface for the (abstraction) reaction between OH and CH2O, not to scale, adapted from Ref. 20b; barrier calculated in this study is 0.22 kcal/mol, Xu et al. [20b] report -1 kcal/mol at a different level of theory and basis-set (b) Structure of complex and TS1, image taken from Ref. 20b; optimized geometries were obtained at the CCSD/6-311++G(d,p) and B3LYP/6-311+G(3df,2p) (in parenthesis) levels (c) Comparison of experimental measurements of k2 and current TST calculations with and without a hindered rotor treatment; energetics are from the theoretical calculations performed in this study at CCSD(T)/6-311++G(d,p)//CCSD/6-311++G(d,p); note that ±25% error bars are shown.

0.5 0.6 0.7 0.8 0.9 1.0

1x1013

2x1013

3x1013

4x1013

5x1013

1000 K

k 2 [cm

3 mol

-1s-1

]

1000/T [K-1]

Experiment, this work TST Calculation, harmonic oscillator TST Calculation, hindered rotor

2000 K

(c)

79

Chapter 5: CH2O + Ar Products and CH2O + O2 Products

5.1 Introduction Even though CH2O decomposition and oxidation chemistry are of importance

in the overall hydrocarbon oxidation process, there still exists much uncertainty in the

high-temperature rate coefficients of several of the key reactions involving CH2O. In

this chapter, we describe measurements of two of these reactions, the two-channel

thermal decomposition of CH2O and the reaction between CH2O and O2.

Previous studies [21-29] of the thermal decomposition of CH2O are described

in Chapter 1. The dissociation proceeds via two competing reaction pathways, (3a)

and (3b):

(3a) CH2O + M HCO + H + M

(3b) CH2O + M H2 + CO + M

As pointed out earlier, the relative importance of the two decomposition paths is not

fully established in the literature.

Similarly, there is large uncertainty in the rate coefficient of the reaction

between CH2O and O2, reaction (4),

(4) CH2O + O2 HCO + HO2

Data that have been reported to date [30-34] for k4 have disparate activation energies

and order of magnitude scatter, see Figure 1.5.

In this study, measurements of the rate coefficients of reactions (3) and (4)

were made behind reflected shock waves using narrow-linewidth OH laser absorption.

OH radicals, generated upon shock heating trioxane-O2-Ar mixtures, were monitored

behind the reflected shock front. Initial mixture compositions were chosen so that the

80

measured OH traces showed dominant sensitivity to the title reactions. Rate

coefficients were inferred by matching the experimental OH concentration time-

histories with profiles modeled using the GRI-Mech 3.0 mechanism [111]. In all the

modeling (the CHEMKIN software package from Reaction Design was used), the

recently revised value for the standard heat of formation of OH was used [69].

5.2 Experimental Set-up Experiments were carried out in the reflected shock region of a high-purity,

stainless steel, helium-driven shock tube with inner diameter of 14.13 cm. Further

details of the shock tube set-up can be found elsewhere, see Chapter 2. Commercially

available 1,3,5 trioxane (> 99% pure) from Sigma Aldrich was used as the CH2O

precursor in the current experiments. Research grade argon (99.9999%), helium

(99.999%) and O2 (99.999%) were supplied by Praxair Inc. Mixtures were prepared in

a 12L mixing chamber equipped with a magnetic stirrer assembly using a ‘double-

dilution’ strategy [68]. To ensure homogeneity and consistency, mixtures were

allowed to mix overnight. As a check on the possible loss of trioxane due to wall

adsorption and condensation, experiments were conducted with the mixing assembly

and shock tube driven section at: (a) room temperature, and (b) 40 °C. The measured

OH profiles, at comparable reflected shock conditions, with and without wall heating,

were indistinguishable – this clearly shows that there is no significant loss of trioxane

due to wall adsorption and condensation effects in the mixing tank and the shock tube.

OH radicals were monitored using a narrow-linewidth ring-dye laser tuned to

the center of the R1(5) absorption line in the OH A-X (0, 0) band near 306.7 nm using

the diagnostic system described in Chapter 2.

5.3 Kinetics Measurements

5.3.1 CH2O + Ar Products

Mixtures with 6-7 ppm trioxane and 0.5% O2 dilute in argon were employed to

study the decomposition of CH2O. The formaldehyde precursor used in this study,

81

trioxane, instantaneously decomposes upon shock heating to yield three CH2O

molecules [108],

(21) (CH2O)3 3CH2O

Measurements were carried out over the 2258 – 2687 K temperature range at an

average total pressure of ~1.6 atm. In this experimental regime, formaldehyde

dissociates via reactions (3a) and (3b). The HCO formed in reaction (3a) subsequently

dissociates to give H and CO. Thus, the pyrolysis of each CH2O molecule yields two

H-atoms, which then rapidly react with O2 to form two OH radicals. If secondary

chemistry is neglected, the following reaction scheme represents the chemistry

prevailing in our experiments,

(3a) CH2O+Ar HCO + H + Ar

(3b) CH2O+Ar H2 + CO + Ar

(17) HCO + Ar H + CO + Ar

(8) H + O2 OH + O (x 2)

Since the rate of HCO decomposition, reaction (17), is much faster than CH2O

decomposition, OH formation is almost exclusively controlled by reactions (3) and

(8). As pointed out elsewhere in this thesis (Chapter 3 ‘Introduction’ and Appendix

A), the rate coefficient of reaction (8) is very well established, with an uncertainty of

just 9% over a broad temperature range [92]. The rate expression recently

recommended by Dryer and co-workers [142] for k8 is in excellent agreement (within

10%) with the GRI-Mech 3.0 expression [111], used here, over the temperature range

of the present study. An uncertainty of ~±10% in this rate coefficient was used when

setting error limits for our measurements.

Rate coefficients for the two decomposition pathways were inferred by

matching measured and modeled OH traces behind the reflected shock. To take into

account secondary interference from reactions such as O + H2 H + OH, CH2O + O2

HCO + HO2 and OH + OH O + H2O, a detailed kinetic mechanism [111] was

used to simulate the OH measurements.

A sample OH profile, for an experiment at 2687 K and 1.52 atm is presented in

Figure 5.1a, while Figure 5.1b is a sensitivity analysis for this experiment. The

82

sensitivity to OH is defined as (dXOH/dki)(ki/XOH), where XOH is the OH mole fraction

and ki is the rate coefficient for reaction i. The OH traces were fit in terms of the

overall decomposition rate coefficient, k3a+k3b, and the branching ratio (α) =

k3a/(k3a+k3b). The time dependence of the OH sensitivity to the overall decomposition

rate coefficient and the branching ratio allows for the separation of these two

parameters. The overall rate of decomposition is determined by fitting the early-time

behavior of the OH profile. At longer times, sensitivity to k3a+k3b decreases, and OH is

primarily sensitive to the branching ratio – this facilitates a simple determination of α.

5.3.2 CH2O + O2 HCO + HO2

Two sets of experiments were carried out to measure the rate coefficient of

reaction (4): (a) Mixtures with 5-7 ppm trioxane and 10% O2 dilute in argon were used

to determine k4 over the 1631 – 2367 K temperature range; (b) Mixtures with ~33 ppm

trioxane dilute in O2 were employed to measure k4 between 1480 K and 1665 K. In

both cases OH radicals were monitored behind reflected shock waves. Reflected shock

pressures ranged from 0.9 atm to 1.9 atm.

The measurement strategy is straightforward (see reaction scheme below).

CH2O in the initial mixture reacts with O2 to produce HCO and HO2. The HCO and

HO2 decompose rapidly via reactions (17) and (22) to form H-atoms that react with O2

generating OH radicals. HCO may also react with O2 to yield HO2 via reaction (18);

the HO2 decomposes to form H-atoms that, once again, yield OH by reaction with O2.

(4) CH2O + O2 HCO + HO2

(17) HCO + M H + CO + M

(22) HO2 + M H + O2 + M

(8) H + O2 OH + O

(18) HCO + O2 HO2 + CO

OH formation is thus controlled primarily by reaction (4) since it is, by far, the slowest

step in the reaction system; therefore, the measured OH time-histories show strong

sensitivity to the rate coefficient of CH2O + O2 HO2 + HCO (see Figure 5.2b).

83

At elevated temperatures, the decomposition of CH2O influences the OH

measurements. Secondary effects, although small, due to reactions such as: CH2O +

OH HCO + H2O, CH2O + H HCO + H2, OH + HO2 O2 + H2O, OH + OH

H2O + O and H + O2 + M HO2 + M also need to be accounted for. Hence, as in the

CH2O decomposition measurements, the detailed GRI-Mech 3.0 model [111] was

used to simulate the experimental traces.

A typical OH concentration time-history recorded for a mixture of 6.98 ppm

trioxane, 10% O2, and 12% He dilute in argon is shown in Figure 5.2a. Figure 5.2b, an

OH radical sensitivity analysis, shows that there is strong isolation of the target

reaction. Helium was added to the initial reaction mix to minimize the vibrational

relaxation time (τvib) of O2 – for example, for the experiment at 2068 K and 1.26 atm

(see Figure 5.2), the addition of 12% He reduced τvib from 14.8 μs to 2.6 μs, calculated

using correlations from Millikan and White [143].

At temperatures lower than ~2050 K, updating the base GRI mechanism with

our new fits for CH2O + M (k3a and k3b) had little or no effect on k4. However, at

higher temperatures, interference from formaldehyde decomposition is larger – hence

the new CH2O decomposition measurements were used in the model when inferring

rate data for reaction (4) at elevated temperatures. A typical high-temperature

experiment (at 2331 K and 1.16 atm), for a mixture of 6.67 ppm trioxane, 10% O2, and

11.9% He dilute in Ar, is shown in Figure 5.3. The reaction between CH2O and O2

still has dominant sensitivity (see Figure 5.3b), although there is, as expected,

increased interference from reaction (3b) at long times.

5.4 Results and Discussion A total of 43 kinetic experiments were carried out to measure k3a, k3b and k4 –

these data are summarized in Tables 5.1 and 5.2 and compared with earlier work in

Figures 5.4 and 5.5.

Figure 5.4a presents a comparison of the current measurements of k3a with

earlier evaluations and measurements, and a comparison of the current k3b results with

earlier work is shown in Figure 5.4b. All the previous work shown in Figure 5.4 was

84

carried out either in argon or krypton in the 0.4 – 2 bar pressure range. At these

pressures, reaction (3) proceeds close to the low-pressure limit [29] and this allows for

a direct comparison of the reported rate data. The current k3a data are in good

agreement with a linear extrapolation of the recent Friedrichs et al. [28]

measurements, and in reasonable agreement with Just [22] and Kumaran et al. [21]. As

for k3b (see Figure 5.4b), our measurements agree very well with Just [22], and extend

the temperature range over which this rate coefficient is known. Within experimental

uncertainty, a linear extrapolation of the Just fit is in excellent agreement with our

elevated temperature measurements. Two-parameter fits for k3a and k3b, applicable

between 2258 K and 2687 K, are,

k3a= 5.85x1014 exp (-32100 / T [K]), [cm3 mol-1s-1]

k3b= 4.64x1014 exp (-28700 / T [K]), [cm3 mol-1s-1]

The standard deviations of the k3a and k3b fits are 0.059 and 0.024 while the

correlation coefficients are -0.98 and -0.99, respectively. Based on a systematic error

analysis, uncertainty limits for k3a and k3b were estimated to be about ~±25%.

This study and earlier work by Just [22] and Kumaran et al. [21] confirm that

the branching ratio in formaldehyde decomposition favors molecular product

formation. At 2258 K, the lowest temperature CH2O decomposition experiment

conducted in this study, a branching ratio of 0.23 was measured. Using reported fits

for k3a and k3b from Just yields a branching ratio of 0.22 at 2258 K, in excellent

agreement with our measurement. The branching ratios reported by Kumaran et al. are

about 50% lower than the current measurements. We conservatively estimate the

uncertainty in our branching ratio measurements to be ~35% which is comparable to

that reported by Kumaran et al. [21]. While the Kumaran et al. results were obtained

under conditions of chemical isolation, the rate data exhibit larger scatter than the

current measurements (see Figure 5.4b). Within the scatter and uncertainty of the

Kumaran et al. data and the uncertainty in the current measurements, agreement

between the two studies is quite reasonable.

85

Our measurements of k4, along with previous results and evaluations, are

shown in Figure 5.5a. The current rate coefficient data agree very well with the recent

evaluation of Baulch et al. [11]. The Baulch et al. preferred expression is an optimum

fit to the low-temperature data of Baldwin et al. [31] and the high-temperature data of

Michael and co-workers [32, 33]. At temperatures lower than ~2000 K, there is

reasonable agreement with the direct measurements of Michael et al. [34]. It is evident

from Figure 5.5a that the rate coefficients from this study have lower scatter than

previous direct [34] and indirect [33] measurements of reaction (4). Also, our

experiments suggest a smaller activation energy than the Michael et al. study [34]. A

two-parameter, least-squares fit of the current data, valid over the 1480 – 2367 K

temperature range, yields the following rate expression,

k4= 5.08x1014 exp (-23300 / T [K]), [cm3 mol-1s-1]

The standard deviation and the correlation coefficient of the above fit are 0.10 and -

0.99, respectively. The uncertainty in our k4 measurements is estimated to be ~±35%.

The primary contributors to this uncertainty are uncertainty due to: (a) initial mixture

composition, and (b) interfering chemistry.

5.4.1 CH2O + O2 HCO + HO2: Discussion and Theory

The least-squares fit of the present data yields an activation energy, Ea, of 46.3

kcal/mol and an A-factor of 5.08x1014 cm3 mol-1 s-1. This A-factor is high when

compared to the Lennard Jones (LJ) collision frequency for reaction (4) at 2000 K,

~3.8x1014 cm3 mol-1 s-1. Transition state theory can be used to analyze A and Ea in

terms of the entropy of activation, ΔS#, and the enthalpy of activation, ΔH#,

respectively. It can be easily shown [144] that,

Ea (T) = ΔH# (T) + RT

Since the reverse reaction, HO2 + HCO CH2O + O2, is barrierless, Ea (0K) = ΔHo

(0K), where ΔHo (0K) is the standard enthalpy of reaction. The experimental ΔHo

(0K) can be determined using bond energy data, and equals 39.1 ± 0.8 kcal/mol [34].

86

At the average temperature of the current experiments, 1975 K, the activation energy,

calculated using the above equation, is 43 kcal/mol. With this Ea, the A-factor was

adjusted to best fit our experimental data; the modified two-parameter Arrhenius

expression, applicable over the 1480 – 2367 K temperature range, is,

k4= 2.15x1014 exp (-21640 / T [K]), [cm3 mol-1s-1]

The original and modified two-parameter fits are presented in Figure 5.5b. The change

in slope of ~7% is compensated for by the modified A-factor – clearly, the current

experiments can be fit with more moderate values for A and Ea. The original least-

squares fit for k4 is, however, recommended since it fits the experimental data better.

Michael et al. [34] have evaluated rate data for reaction (4) using variational

transition state theory, and these calculated rate coefficients are shown in Figure 5.5b.

The uncertainty in the calculated rate coefficient is ±30% (gray error bars, see Figure

5.5b) due to uncertainty in the theoretical energy barrier. Theory and experiment are in

relatively good agreement within the uncertainty range of the measurements and the

calculations. The theoretical, ab initio activation energy is ~6% higher than the least-

squares fit for k4 and ~12% higher than our modified fit for k4. The theory, however,

supports the lower experimental activation energy observed in this study vis-à-vis the

high activation energy observed in the Michael et al. [34] experiments (see Figure

5.5a).

We have studied the reaction of O2 with CH2O using quantum chemical

methods at the CCSD(T) level of theory using the 6-311++g** basis set (see

Appendix B). Ab initio calculations were performed using the Gaussian suite of

programs [140]. Geometry optimization and frequency calculations were carried out

at the B3LYP/6-311++g** level. Single point energy calculations were then done at

CCSD(T)/6-311++g** for the previously optimized geometries. Transition state

theory calculations were carried out using the CSEO Kinetics software [141]. Our

calculations are in good agreement with the VTST calculation carried out by Michael

and co-workers [33, 34] and with the current experimental data (see Figure B.1 in

Appendix B). Also, calculations have been carried out at various levels of theory and

87

with different basis sets to gauge the accuracy of different method-basis set

combinations. The calculations are described in detail in Appendix B.

5.5 Conclusions The two-channel thermal decomposition of CH2O and the reaction between

CH2O and O2 were studied in reflected shock wave experiments by monitoring OH

using narrow-linewidth ring-dye laser absorption at 306.7 nm. The new rate data for

CH2O decomposition are in good agreement with earlier work but have improved

uncertainty limits and extend the temperature range over which these rate coefficients

are known. Our measurements of the rate coefficient of CH2O + O2 are in moderate

agreement with an earlier study by Michael et al. [34] at T< 2000 K but suggest a

lower activation energy; this lower activation energy is consistent with ab initio,

theoretical calculations for this reaction system.

88

Table 5.1: CH2O + Ar Products: Rate coefficient data

T [K] P [atm] k3a [cm3mol-1s-1] k3b [cm3mol-1s-1]

6.61 ppm trioxane, 0.5% O2, balance Ar

2258 1.63 4.73 x 108 1.54 x 109 2369 1.62 9.10 x 108 2.45 x 109 2446 1.58 1.02 x 109 3.50 x 109 2567 1.50 2.07 x 109 6.65 x 109 2641 1.46 3.78 x 109 8.89 x 109


2361 1.64 6.83 x 108 2.31 x 109 2411 1.61 8.40 x 108 3.33 x 109 2443 1.45 1.02 x 109 3.85 x 109 2604 1.55 2.45 x 109 8.05 x 109 2687 1.52 4.06 x 109 1.03 x 1010


2296 1.63 4.90 x 108 1.65 x 109 2440 1.71 1.02 x 109 3.50 x 109

89

Table 5.2: CH2O + O2 HCO + HO2: Rate coefficient data


6.67 ppm trioxane, 10% O2, 10% He, balance Ar

1873 1.96 1.25 x 109 1934 1.82 2.71 x 109 2089 1.76 6.23 x 109

6.67 ppm trioxane, 10% O2, 11.9% He, balance Ar

1817 1.29 1.32 x 109 1926 1.23 2.75 x 109 2006 1.21 3.65 x 109 2046 1.19 5.25 x 109 2123 1.23 6.60 x 109 2157 1.16 6.25 x 109 2161 1.12 6.50 x 109 2331 1.16 2.80 x 1010

5.05 ppm trioxane, 9.9% O2, 12% He, balance Ar

1631 1.43 4.75 x 108 1939 1.30 2.80 x 109 2055 1.23 7.00 x 109 2127 1.13 8.00 x 109

6.97 ppm trioxane, 10% O2, 12% He, balance Ar

2068 1.26 6.60 x 109 2138 1.17 1.15 x 1010 2149 1.19 1.20 x 1010 2231 1.19 1.50 x 1010 2275 1.09 2.50 x 1010 2287 1.18 2.50 x 1010 2367 1.11 3.70 x 1010

33.3 ppm trioxane, balance O2

1480 1.03 8.67 x 107 1540 1.01 1.37 x 108 1605 1.00 2.20 x 108 1640 1.04 3.62 x 108 1650 0.93 3.52 x 108 1745 0.94 6.15 x 108

33.3 ppm trioxane, 10% He, balance O2

1521 0.96 1.16 x 108 1591 0.91 2.40 x 108 1665 1.00 4.49 x 108

90

0 25 50 75 100 125 150

0

5

10

15

20

25

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experiment ktot = 1.44 x 1010 cm3 mol-1 s-1

α = 0.28

0 25 50 75 100 125 150-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

OH

Sen

sitiv

ity

Time [μs]

overall rate, k1a+k1b

branching ratio, α H+O2<=>O+OH O+H2<=>H+OH 2OH<=>O+H2O O2+CH2O<=>HO2+HCO

Figure 5.1 Initial reflected shock conditions: 2687 K, 1.52 atm; 6.53 ppm trioxane, 0.5% O2, balance Ar (a) OH concentration time-history; solid black line, fit to data by adjusting the overall decomposition rate, k3a+k3b, and branching ratio, α; solid gray lines, variation of k3a+k3b by ±50%; dashed black lines, variation of α by ±25% (b) OH sensitivity analysis, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

(b)

(a)

91

0 75 150 225-5

0

5

10

15

20

25

30

35

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experiment 6.60x109 cm3 mol-1 s-1

0 75 150 225

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

OH

Sen

sitiv

ity

Time [μs]

O2+CH2O<=>HO2+HCO H+O2<=>O+OH HCO+M<=>H+CO+M CH2O+M<=>H+HCO+M HCO+O2<=>HO2+CO 2OH<=>O+H2O H+O2+AR<=>HO2+AR CH2O+M<=>H2+CO+M

Figure 5.2 Initial reflected shock conditions: 2068 K, 1.26 atm; 6.98 ppm trioxane, 10% O2, 12% He, balance Ar (a) OH concentration time-history; solid black line, fit to data by adjusting k4; dashed black lines, variation of k4 by factor of 2 (b) OH sensitivity analysis, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

(a)

(b)

92

0 20 40 60 80 100 120

0

10

20

30

40

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experiment 2.80x1010 cm3 mol-1 s-1

0 20 40 60 80 100 120

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

OH

Sen

sitiv

ity

Time [μs]

O2+CH2O<=>HO2+HCO H+O2<=>O+OH CH2O+M<=>H+HCO+M 2OH<=>O+H2O HCO+M<=>H+CO+M CH2O+M<=>H2+CO+M HCO+O2<=>HO2+CO H+O2+AR<=>HO2+AR

Figure 5.3 Initial reflected shock conditions: 2331 K, 1.16 atm; 6.67 ppm trioxane, 10% O2, 11.9% He, balance Ar (a) OH concentration time-history; solid black line, fit to data by adjusting k4; dashed black lines, variation of k4 by factor of 2 (b) OH sensitivity analysis, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

(a)

(b)

93

0.35 0.40 0.45 0.50 0.55

108

109

1010

(1)

k 1b [c

m3 m

ol-1

sec

-1]

1000/T [K-1]

(2)

0.3 0.4 0.5 0.6106

107

108

109

1010

(4)(1)

(3)

(5)

(2)

k 1a (c

m3 m

ol-1

sec-1

)

1000/T [K-1]

(6)

Figure 5.4 Comparison of current measurements of k3a and k3b with previous work: (a) solid squares, this work (± 25% error bars); solid black line, this work fit; 1, Kumaran et al. [21]; 2, Friedrichs et al. [28]; 3, Just [22]; 4, Saito et al. [23]; 5, Eiteneer et al. [27]; 6, Irdam et al. [25] (b) solid squares, this work (± 25% error bars); solid black line, this work fit; open circles, Kumaran et al. [21] data; 1, Kumaran et al. fit; 2, Just [22].

k 3b [

cm3 m

ol-1

s-1

]

(a)

(b)

k 3a [

cm3 m

ol-1

s-1

]

2850 K 1850 K

2000 K 2500 K

94

0.4 0.5 0.6 0.7107

108

109

1010

1011

1000/T [K-1]

k 2 [cm

3 m

ol-1

sec-1

]

Figure 5.5 Comparison of current measurements of k4 with previous work: (a) solid squares, this work (±35% error bars); solid black line, this work fit; open circles, Michael et al. [34]; open triangles, Srinivasan et al. [33] from O-atom traces; open squares, Srinivasan et al. [33] from OH traces; solid gray line, Baulch et al. [11] (b) solid squares, this work; solid black line, this work fit; solid gray line, this work modified fit (see text); dashed black line, Michael et al. theory [34].

0.4 0.5 0.6 0.7

108

109

1010

1011

k 2 [cm

3 mol

-1 s

-1]

1000/T [K-1]

k 4 [c

m3 m

ol-1

s-1

]

(b)

(a)

k 4 [c

m3 m

ol-1

s-1

]

2500 K 1500 K

1500 K 2500 K

95

Chapter 6: CH3 + Ar Products

6.1 Introduction The thermal decomposition of methyl radicals proceeds via two channels,

(5a) CH3 + Ar CH + H2 + Ar

(5b) CH3 + Ar CH2 + H + Ar

Reactions (5a) and (5b) play an important role in the high-temperature combustion and

pyrolysis of hydrocarbon fuels such as natural gas. For example, rate coefficients of

both methyl decomposition pathways need to be well-established to correctly capture

CH peak height in elevated temperature methane oxidation experiments. This is

evident from the sensitivity plot shown in Figure 6.1a.

There have been several theoretical and experimental studies of methyl

decomposition, and these are described in Chapter 1. The potential energy surface has

been computed using ab initio methods and is presented in Figure 6.1b. Reaction (5a)

has a threshold that is 13 kJ/mol lower than reaction (5b) and is therefore energetically

favored. Both reactions proceed via “loose” transition states; i.e., they occur without

any energy barrier. While reaction (5b) follows the least-motion pathway with C2v

geometry, reaction (5a) follows a complicated non-least motion pathway [45]. As

described in Chapter 1, there is expectation of possible pressure dependence in methyl

decomposition at ~1 bar, which is investigated in this work.

In this study, measurements were made behind reflected shock waves using

narrow-linewidth CH and OH laser absorption near 431.1 nm and 306.7 nm,

respectively. Experiments were carried out at different pressures to study the effect of

pressure on the two methyl decomposition pathways. Rate coefficients were inferred

by matching the experimental CH and OH concentration time-histories with profiles

96

modeled using detailed chemical kinetic mechanisms. The modeling was performed

using the CHEMKIN software package from Reaction Design.

6.2 Experimental Set-up All experiments were carried out in the reflected shock region of a high-purity,

stainless steel, helium-driven shock tube with an inner diameter of 14.13 cm. The

shock tube facility has been described in Chapter 2 and Ref. 68. Ethane (99%) and

methyl iodide (>99.5%) were obtained from Specialty Chemical Products Inc. and

Sigma Aldrich, respectively. Research grade argon (99.9999%), helium (99.999%)

and O2 (99.999%) were supplied by Praxair Inc. Since all the mixtures used in the

methyl decomposition experiments were highly dilute, mixtures were prepared by

successive dilution [68] in a 12L magnetically-stirred mixing chamber. OH and CH

radicals were monitored at 306.7 nm and 431.1 nm, respectively, using the laser

absorption systems described in Chapter 2.

6.3 Kinetics Measurements

6.3.1 CH3 + Ar CH + H2 + Ar

The rate coefficient of reaction (5a) was measured by monitoring CH radicals

generated upon shock heating highly dilute mixtures of ethane, C2H6, or methyl

iodide, CH3I, in an argon bath. A detailed chemical kinetic mechanism was used to

model the measured CH time-histories and is described in greater detail in an ensuing

section of this chapter. Initial mixture compositions were chosen such that the

measured CH traces showed dominant sensitivity to reaction (5a) at early-times. The

rate coefficient of this reaction was adjusted in the mechanism to yield a best-fit

between model and experiment. Figure 6.2a presents measured and modeled CH

concentration profiles for an experiment conducted at 2944 K and 0.97 atm, while

Figure 6.2b is a sensitivity analysis for this experiment. Sensitivity is defined as

(dXCH/dki)(ki/XCH), where XCH is the local CH mole fraction and ki is the rate

coefficient of reaction i. Clearly, up to ~50 μs, the most sensitive reaction is methyl

97

decomposition to CH and H2. Note that in the sensitivity plot, the collision partner

M=Ar.

Experiments were also carried out at higher reflected shock pressures and

temperatures. The CH profiles were primarily sensitive to reaction (5a) at the earliest

times. This is evident from Figure 6.3, which presents measured and modeled CH

traces and the corresponding sensitivity plot for an experiment conducted at 3.9 atm

and 2982 K. When compared to the lower-pressure experiment shown in Figure 6.2a,

the time-window over which reaction (5a) has dominant sensitivity is shorter. Figure

6.4 presents a kinetic measurement performed at 3393 K and 1.039 atm; as expected,

the sensitive time-window is shorter at higher temperatures. Interference from

unimolecular dissociation reactions, such as (5b), (23), and (24), is somewhat higher at

elevated temperatures and pressures.

(23) CH + Ar C + H + Ar

(24) CH2 + Ar C + H2 + Ar

In summary, for both the high-temperature and high-pressure experiments, k5a could

be accurately and reliably ascertained by fitting the measured profiles to a model at the

earliest times (t < 20 μs).

6.3.2 Reaction Mechanism to Model CH Formation and Removal In previous work, different reaction schemes have been used to model CH

formation and removal in hydrocarbon pyrolysis systems. Dean and Hanson [35] used

a two-channel scheme for CH2 thermal decomposition with nearly equal rate

coefficients for the two decomposition pathways, reactions (24) and (25), to model

their CH and C-atom measurements.

(24) CH2 + Ar C + H2 + Ar

(25) CH2 + Ar CH + H + Ar

However, Kiefer and Kumaran [67] were able to successfully model Dean’s

experiments using a very different reaction mechanism consisting largely of rapid

bimolecular reactions. In the Kiefer and Kumaran mechanism, the rate coefficient used

for reaction (25) was about a factor of 10 smaller than Dean and Hanson [35],

effectively eliminating the role of this reaction in the mechanism. That CH2

98

decomposition favors reaction (24) was subsequently confirmed via measurements in

the ketene pyrolysis system by Roth and coworkers [146]. In the current work, we

have used a reaction scheme that is based on Kiefer and Kumaran, in which CH2

decomposition results primarily in the formation of C-atoms and H2. However, it is

important to note that the reaction scheme used has little or no effect on our rate

determination for reaction (5a). This is because at the earliest times CH is primarily

sensitive only to reaction (5a); see Figures 6.2b, 6.3b and 6.4b.

At later times the CH profile is sensitive to several reactions; these include,

(5b) CH3 + Ar CH2 + H + Ar

(23) CH + Ar C + H + Ar

(24) CH2 + Ar C + H2 + Ar

(26) H + CH C + H2

(27) C + CH C2 + H

(28) C +CH2 2CH

(29) C + CH3 H + C2H2

Even with the highly dilute reaction mixtures used in this study, it was not possible to

unambiguously relate the decay in CH to a single dominant reaction. Hence, while the

rate coefficients of the above reactions were constrained to match measured and

modeled CH time-histories over the temperature and pressure range of this study,

these do not necessarily represent a unique reaction rate coefficient set.

The mechanism and rate parameters used here are similar to those reported by

Kiefer and Kumaran [67], with some differences: (1) the rate coefficient for reaction

(5b) used by Kiefer and Kumaran was based on an RRKM calculation, while we have

used a value that is based on direct measurements that were concurrently carried out to

determine k5b. These experiments are described in an ensuing section of this chapter.

Note that we did adjust our k5b determination, within quoted uncertainty limits, to

provide a best-fit to each modeled and measured CH trace. (2) Minor adjustments

were made to the rate coefficients of CH2 + Ar C + H2 + Ar (~1.25 x Kiefer) and

CH + Ar C + H + Ar (~1.25 x Kiefer at T < 3000 K) to capture the measured CH

decay. (3) Rate parameters for several reactions (for example, C2H2 + Ar, C2H3 + Ar,

99

C2H4 + Ar, CH4 + Ar, H2 + Ar, H + CH4, H +CH3, H + CH2, H + CH, CH3 + CH, CH3

+ CH2, CH3 + CH3 etc) in the Kiefer and Kumaran mechanism were updated with

more recent values from evaluations such as GRI-Mech 3.0 [111] – all of these

changes, however, had only a small effect on the modeled CH time-histories. (4) The

rate coefficient inferred for reaction (5a) in this study was on average about 25%

lower than Kiefer and Kumaran over the 2800 – 3600 K temperature range, with

agreement being the poorest at low temperatures (~35% at 2800 K) and the best at

high temperatures (~15% at 3600 K).

Table 6.1 summarizes the rate parameters that were employed in this study for

the key reactions that control CH formation and removal in our experiments. That the

current mechanism is largely consistent and in good overall agreement, at high

temperatures, with earlier mechanisms developed by Dean and Hanson [35] and

Kiefer and Kumaran [67] is evident from Figure 6.5 which presents modeled CH

traces for an ethane pyrolysis experiment at 3400 K and 1 atm. The concentration

chosen, 20 ppm ethane dilute in argon, corresponds to that used by Dean and Hanson

[35] in their ethane pyrolysis study.

6.3.3 Pressure and Temperature Dependence of CH Time-History

Figures 6.6a and 6.6b show the pressure and temperature dependence of the

CH time-history, respectively. At higher pressures and temperatures, the rise and

decay in CH becomes faster. As temperature is increased, there is also a pronounced

increase in the CH peak height, see Figure 6.6b. Clearly, our mechanism is able to

capture the essential characteristics of the CH trace. Model performance, while

satisfactory over the entire temperature and pressure range of the current study, was

the poorest for experiments conducted at low temperatures and high pressures. In the

worst case, decay times differed by 10-20% from experiment. However, this has little

or no effect on the rate coefficients reported for reaction (5a) which were inferred

using only the early-time CH rise.

100

OH + O

6.3.4 CH3 + Ar CH2 + H + Ar

The rate coefficient of reaction (5b) was determined by shock-heating mixtures

of C2H6 or CH3I and excess O2 (0.1-0.5%) dilute in argon. During the course of

reaction, OH radicals were monitored using the well-characterized R1(5) line of the

OH A-X (0, 0) band near 306.7 nm. H-atoms generated via reaction (5b) rapidly react

with O2, present in excess, forming OH. In the absence of secondary chemistry, the

OH traces are primarily sensitive to reaction (5b) and (8) H + O2 OH + O. We used

a similar measurement approach in a recent study to infer the overall rate coefficient

and branching ratio for formaldehyde decomposition [145], see Chapter 5. The kinetic

strategy may be represented by the following simple reaction scheme,

C2H6 or CH3I CH3 + Ar CH2 + H + Ar

Rate data were inferred by adjusting the rate coefficient of reaction (5b) to

match modeled OH profiles with experiment. A detailed chemical kinetic mechanism

(GRI- Mech 3.0 with the Kiefer and Kumaran hydrocarbon pyrolysis model) was used

to simulate the OH measurements. An example experimental profile is presented in

Figure 6.7a, while Figure 6.7b shows the OH radical sensitivity analysis for this

experiment. At early times, the OH profile shows reasonably strong sensitivity to

reaction (5b). However, there is some secondary interference from reactions (5a), (8),

(30) and (31),

(5a) CH3 + Ar CH + H2 + Ar

(8) H + O2 OH + O

(30) CH3 + O2 OH + CH2O

(31) O + H2 H + OH

The rate coefficients of the three primary interfering reactions, (5a), (8) and

(30), are all relatively well-established. k5a was carefully measured in this study to

within ~±25% (the Arrhenius fit reported in this work was used in the current

modeling). As pointed out in Chapters 3 and 5, there have been several measurements

+ O2

101

of reaction (8) and the uncertainty in k8 is only 9% over a broad temperature range.

The GRI rate expression, used here, is also in good agreement with a recent

recommendation by Dryer and co-workers [142]. Reaction (30) was very recently

studied in our laboratory by Herbon et al. [71] and is known to within ~±35%; the

Arrhenius expressions recommended by Herbon et al. were used in the current

modeling. Besides reaction (31), minor secondary interference (not shown in Figure

6.7b) from 2OH O + H2O, CH + O2 O + HCO, CH2 + O2 OH + H + CO,

CH2(s) + O2 OH + H + CO, CH3 + O H + CH2O and CH2 + Ar C + H2 + Ar

was observed. Conservative uncertainty estimates were used for the rate coefficients

of these secondary reactions when setting error limits for our rate measurements. Note

that as temperature is reduced, sensitivity to reaction (5b) diminishes while sensitivity

to reaction (30) increases. This is because at lower temperatures, methyl radicals are

more likely to react with oxygen than decompose.

Experiments were also conducted to investigate the pressure dependence of

reaction (5b). A sample high-pressure measurement at 3.89 atm and 2587 K is shown

in Figure 6.8. As in the low-pressure experiment described earlier (see Figure 6.7),

early-time OH shows reasonable sensitivity to reaction (5b).

6.4 Results and Discussion Our measurements of k5a between 0.7 and 1.1 bar are presented in Figure 6.9a.

The k5a data are in good agreement with Dean and Hanson [35] and with a recent

evaluation by Baulch et al. [11]. The current high-temperature data are also consistent

with the lower temperature results of Röhrig et al. [36]. The effect of pressure on the

bimolecular rate coefficient is shown in Figure 6.9b. Within experimental uncertainty

and scatter, a pressure dependence could not be discerned for k5a in the 0.7-4 atm

pressure range. A least-squares, two-parameter fit of the current measurements, valid

over the 2706 – 3527 K temperature range, is given by the following expression,

k5a = 3.09 x 1015 exp (-40700/T [K]), [cm3 mol-1 s-1]

The correlation coefficient of the above fit is -0.997 and standard deviation is 0.038.

102

Figure 6.10a summarizes the current measurements of k5b and previous work

reported for this reaction rate coefficient. The k5b data agree very well with the H-atom

ARAS measurements of Eng et al. [43] at high temperatures and Lim and Michael

[42] at low temperatures. At temperatures lower than ~2500 K, our measurements are

in poor agreement with Eng et al. These authors inferred k1b using the initial slope of

measured H-atom ARAS profiles. However, at low temperatures, reactions (32) and

(33) contribute significantly to early-time H-atom formation, resulting in the observed

high rate coefficient values.

(32) CH3 + CH3 C2H5 + H

(33) C2H5 C2H4 + H

Note that the current laser absorption data exhibit lower scatter than H-atom ARAS

measurements reported in the literature. Pressure dependence could not be discerned

in the k5b measurements (see Figure 6.10b) between 1.1 and 3.9 atm. A two-parameter,

least-squares fit of the current data, valid over the 2253 – 2975 K temperature range,

yields the following rate expression,

k5b = 2.24 x 1015 exp (-41600/T [K]), [cm3 mol-1 s-1]

The correlation coefficient and standard deviation of the above fit are -0.992 and

0.071, respectively.

Even though pressure dependence could not be discerned for reactions (5a) and

(5b) between 1 and 4 atm, this does not necessarily imply that the reactions are at the

low-pressure limit because pressure-dependent fall-off might well be small and

embedded within the scatter of the experimental data. The current k5a and k5b rate

coefficient data are presented in Tables 6.2 and 6.3.

A detailed uncertainty analysis was carried out to set error limits for our

measurements. The uncertainty factors taken into account were: uncertainty in [a]

wavemeter reading; [b] absorption coefficient of CH and OH; [c] initial mixture

concentration; [d] reflected shock temperature, primarily due to uncertainty in shock

velocity determination; [e] rate coefficients of secondary reactions; [f] fitting the

modeled trace to the experimental profile; [g] locating time zero. The effect of each of

103

the above uncertainty categories on the rate coefficients of reactions (5a) and (5b)

were ascertained and combined to yield overall uncertainty limits for both reactions.

Based on this analysis, we conservatively estimate an uncertainty of ~±25% on our k5a

measurement at 2944 K and 0.974 atm, and ~±50% on our k5b measurement at 2843 K

and 1.198 atm. The uncertainty in k5a is expected to be larger for our high-temperature

(T>3200K) and pressure (P~4atm) experiments due to increased secondary

interference from unimolecular decomposition reactions such as CH2 + Ar C + H2

+ Ar and CH + Ar C + H + Ar, while the uncertainty in k5b is expected to be larger

for our lower temperature data due to increased interference from the CH3 + O2

reaction system and methyl radical recombination.

Figures 6.11a and 6.11b present the branching ratio, k5b/(k5a+k5b), as a function

of temperature and pressure, respectively. The branching ratio for methyl

decomposition is not well-established in the literature. Markus et al. [37] measured

both k5a and k5b in a single study. However, their k5a measurements are about a factor

of 5 lower than the current data set (see Figure 6.9), resulting in a substantially higher

branching-ratio value. In subsequent work, Markus et al. [39] report an average k5a for

pressures near 1 bar. When this expression for k5a is used in conjunction with the

Baulch et al. [11] recommendation for k5b (based on several previous studies of k5b, all

of which are in good agreement), the resulting branching ratio is in excellent

agreement with the current work. The current branching-ratio measurements show no

discernible dependence on pressure, unlike Eng et al. [43] who inferred branching

ratios of up to 70% (see Figure 6.11b) from measured, long-time H-atom plateaus. Our

branching-ratio data are in very good agreement with the recent evaluation of Baulch

et al.

If the branching ratio were ~70%, as measured by Eng et al., CH peak levels

would, based on detailed kinetic simulations, need to be about a factor of 2 lower than

observed, with an early-time CH rise that is substantially slower than experiment.

Note that in the simulation k5b was kept fixed, while k5a was adjusted to yield a

branching ratio of ~70%. The significant change in the temporal behavior of the CH

profile at early-times is illustrated in Figure 6.11c for an experiment at 2770 K and

104

1.871 atm. Such large differences cannot be explained by uncertainty in: (a)

experiment, and (b) spectroscopic calibration of the CH diagnostic. To address the

effect of pressure on the branching ratio, theoretical calculations using a Master

equation/RRKM analysis were carried out and are described in the next section of this

chapter.

6.5 Master Equation/RRKM Analysis Attempts were made to reproduce the experimental results with a master

equation RRKM analysis. This is in keeping with previous such attempts by Eng et al.

[43] and Hippler et al. [147]. The “Multiwell” suite [148, 149] was used for the

calculations. The potential energy surface for methyl decomposition is shown in

Figure 6.1. Calculations were performed at 2800K. The required parameters include

thermochemical values for CH3, CH2, CH, H2 and H. The values employed were the

same as Eng et al. [43] and are given in Table 6.4. These allow the calculation of the

equilibrium constants. The values obtained at 2800 K were

K-5b(CH2+H=CH3)/molecule cm-3 = 2.97x1016 and K-5a(CH+H2=CH3)/molecule cm-3 =

1.26x1017. The expressions in Fulle and Hippler [44] for the high-pressure limit rate

coefficients for the reactions as written above yield for 2800 K, k-5b∞/molecule cm-3s-1

= 4.5x10-10 and k-5a∞/ molecule cm-3s-1 = 2.8x10-10. Thus, k5b

∞/s-1 = 1.3x107 and k5a∞/s-

1 = 3.5x107.

Values for calculation of the sums and densities of states of the transition states

between CH3 and the two channels that yield CH2+H and CH+H2 were taken to

reproduce the high-pressure rate parameters for the reverse processes from Fulle and

Hippler [44] given above. The transitional modes were treated as hindered rotors in

the hindered Gorin method as employed for example in Golden [150]. All parameters

are given in Table 6.5.

The centrifugal barriers were computed from the moments of inertia as

explained in Golden [150]. Using a Morse potential, with the Morse β computed using

(for the CH2+H channel) the C-H stretching frequency in CH3, the C-H bond distance

and the appropriate masses, the position of the centrifugal maximum was obtained by

105

adding the rotational energy at the maximum, assumed to be kT, and finding the

maximum. This leads directly to a two-dimensional moment of inertia which can be

used in the calculation of transition state properties. For the transition state leading to

CH+H2, the potential is more complicated than a Morse function (see Mayneris et al.

[151]). The surface can be fit with a Morse potential at CH-H2 distances greater than

1.33 Å. This was used as the starting point for computing the moment of inertia for

that transition state. The probability for energy transfer was treated using the

exponential down function.

When calculations were performed at 1 atmosphere of Ar using the best inputs

determined as above, the CH+H2 channel did not appear. Since this is the channel

with the more complex potential energy surface, the value for the two dimensional

moment of inertia in the transition state was modified until the correct branching ratio

could be attained. This required a change from 11.0 to 12.89 AMU-Å2. This change

together with a value for ΔEdown of 150 cm-1 in the exponential down model could fit

our data reasonably well. The results of a representative calculation are compared with

the experimental values in Table 6.6. A pressure effect with a magnitude similar to

that reported by Eng et al. could not be discerned in our calculation. Note that many

parameter changes were tried (energy transfer was increased and decreased, Gorin

hindrance was varied, the parameters were not required to fit the Fulle and Hippler

reverse rate coefficient), none of which yielded a significant pressure dependent fall-

off.

6.6 Conclusions Sensitive, narrow-linewidth laser absorption diagnostics for CH at and OH have been

used to perform measurements in the methyl decomposition system. Rate coefficients

for the two methyl decomposition pathways, k5a and k5b, have been measured with

experimental conditions ranging from 2253 to 3527 K and 0.7 to 4.2 atm. Within

experimental uncertainty and scatter, no discernible dependence on pressure was

observed in the rate coefficients of either pathway in the pressure and temperature

range studied. The measurements are in very good agreement with the recent

106

evaluation of Baulch et al. [11]. Theoretical calculations carried out using a master

equation RRKM analysis fit the measurements reasonably well.

107

Table 6.1: Rate parameters for reactions sensitive during CH formation and removal

Rate Coeff. [cm3 mol-1 s1] Reaction A N E, kcal/mol

Reference

CH3 + M CH + H2 + M see text This work CH3 + M CH2 + H + M see text This work CH + M C + H + M 1.0x1014 0 64.0 67* CH2 + M C + H2 + M 1.15x1014 0 55.8 67* H + CH C + H2 1.65x1014 0 0.0 111 C + CH C2 + H 2.0x1014 0 0.0 67 C +CH2 2CH 1.0x1014 0 0.0 67 C + CH3 H + C2H2 5.0x1013 0 0.0 111

*see text; rate coefficients were adjusted slightly (≤ ±25%) to match each measured CH decay

108

Table 6.2: Summary of experimental results, k5a

T [K] P [atm] k5a [cm3 mol-1 s-1]

10 ppm C2H6, balance Ar

2837 1.042 2.14 x 109 2738 1.095 1.08 x 109 2984 1.005 4.49 x 109 3161 0.945 8.50 x 109


2858 0.976 2.39 x 109 2763 2.391 1.18 x 109 2845 2.637 2.03 x 109 2802 2.742 1.54 x 109

10.3 ppm C2H6, balance Ar

2789 1.883 1.36 x 109 2949 1.838 3.47 x 109 2861 1.907 1.90 x 109 2944 0.974 3.05 x 109 2717 3.829 8.12 x 108 2706 4.116 8.06 x 108

19.99 CH3I, balance Ar

2848 1.835 1.77 x 109 2770 1.871 1.29 x 109 2982 3.923 3.48 x 109 2783 4.208 1.25 x 109


3393 1.039 1.87x1010 3527 0.964 2.85x1010 3230 1.024 9.91x109 3198 1.072 9.19x1010 3273 1.013 1.25x1010 3527 1.005 2.85x1010 3472 1.040 2.35x1010 3348 1.079 1.49x1010

10.09 ppm C2H6, balance Ar

2709 1.087 9.11 x 108 3011 1.094 4.22 x 109 2925 3.580 2.63 x 109 2789 3.636 1.29 x109

109

Table 6.3: Summary of experimental results, k5b

T [K] P [atm] k5b [cm3 mol-1 s-1]

25.38 ppm CH3I, 0.106% O2, balance Ar

2780 1.425 8.82 x 108 2665 1.529 4.34 x 108 2562 1.600 2.66 x 108 2253 1.754 1.98 x 107 2747 1.488 6.93 x 108 2843 1.198 8.82 x 108 2698 1.242 3.73 x 108 2693 1.288 3.61 x 108 2550 1.285 2.45 x 108 2417 1.289 7.18 x 107 2375 1.370 5.61 x 107 2941 1.161 1.51 x 109 2276 1.409 2.43 x 107

24.98 ppm CH3I, 0.106% O2, balance Ar

2743 1.215 4.92 x 108 2765 3.698 5.61 x 108 2882 3.626 9.59 x 108 2587 3.898 2.03 x 108 2953 2.988 2.00 x 109 2635 2.991 3.42 x 108

5.11 ppm C2H6, 0.103% O2, balance Ar

2707 1.191 4.93 x 108 2975 1.091 2.25 x 109 2871 1.119 1.03 x 109 2790 1.170 7.32 x 108

110

Table 6.4: Thermochemical and structural parameters

CH3 Vibrational Frequencies/cm-1: 3184, 3184, 3002, 1383, 1383, 580 Moments of Inertia/AMU-A2: IA=IB=1.78, IC=3.60 Symmetry Number: 6 Enthalpy of Formation: ΔfH0/kJ mol-1= 149.7 Electronic Partition Function: Qel=2 CH2 Vibrational Frequencies/cm-1: 3123, 2954, 1056 Moments of Inertia/AMU-A2: IA=.231 (IBIC)=2.19 Symmetry Number: 2 Enthalpy of Formation: ΔfH0/kJ mol-1= 390.0 Electronic Partition Function: Qel=3+1exp(-3147cm-1hc/kbT) +1exp(-11497cm-1hc/kbT) CH Vibrational Frequencies/cm-1: 2861 Moments of Inertia/AMU-A2: I=1.18 Symmetry Number: 1 Enthalpy of Formation: ΔfH0/kJ mol-1= 390.0 Electronic Partition Function: Qel=2+2exp(-17.9cm-1hc/kbT) +4exp(-4500cm-1hc/kbT) H2 Vibrational Frequencies/cm-1: 4395 Moments of Inertia/AMU-A2: I=.281 Symmetry Number: 2 Enthalpy of Formation: ΔfH0/kJ mol-1= 0 Electronic Partition Function: Qel=1 H Symmetry Number: 1 Enthalpy of Formation: ΔfH0/kJ mol-1= 216.0 Electronic Partition Function: Qel=2

111

Table 6.5: Parameters for Multiwell calculations at 2800 K

CH3

Frequencies*/cm-1 3184, 3184, 3002, 1383, 1383, 580

(J-rotor)Adiabatic Moments of Inertia /AMU A2 1.78

(K-rotor) Active External Rotor/AMU A2 3.60

CH2--H (Transition State)

Critical Energy at 0K/kcal mole-1 109.1

Frequencies*/cm-1 3123,2954,1056



Moments of Inertia Active 2-D Rotors/ AMU A2 2.19

Hindrance: η(2800K) 90% Collisions: (σ/A2; ε/K;) CH3 Ar

3.8; 144 3.47; 114

<ΔΕ>d2800K/cm-1 150

CH—H2 (Transition State)

Critical Energy at 0K/kcal mole-1 106.2

Frequencies*/cm-1 4395, 2861



Moments of Inertia Active 2-D Rotors/ AMU A2 1.18(CH rotor);.281 (H2 rotor)

Hindrance: η(2800K) 98.7% Collisions: (σ/A2; ε/K;) CH3 Ar

3.8; 144 3.47; 114

<ΔΕ>d2800K/cm-1 150

Table 6.6: Comparison of calculated and experimental values at 2800 K and 1 atm

k5b(CH2+H) [cm3mol-1s-1] k5a(CH+H2) [cm3mol-1s-1] k5b/(k5a+k5b) Experiment 7.9x108 1.5x109 0.33 Calculated 9.8x108 1.8x109 0.39

112

Figure 6.1 (a) Sensitivity to maximum of CH concentration in shock tube oxidation of methane; CH4/O2/Ar (80ppm-100ppm-99.982%) phi = 1.6, P = 1.8 atm, T = 2800 K; adapted from Ref. 111 (b) Potential energy surface for methyl decomposition [43], not to scale.

CH+H2

CH2+H

CH3

457 kJ/mol444 kJ/mol

13 kJ/mol

Reaction Coordinate

Pote

ntia

l Ene

rgy

(b)

(a)

(5b)

(5a)

113

0 50 100 150 200 250 300-2

0

2

4

6

8 10.3 ppm C2H6, Ar2944 K, 0.974 atm

Experiment Model (k5a, best fit) Model (k5a x 0.5)

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Figure 6.2 Example CH data, modeling, and sensitivity: (a) CH concentration time-history (b) CH sensitivity at early times, S = (dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i.

0 10 20 30 40 50

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

CH

Sen

sitiv

ity

Time [μs]

CH3+M<=>CH+H2+M CH3+M<=>CH2+H+M CH+M<=>C+H+M C+CH2<=>2CH 2CH3(+M)<=>C2H6(+M)

(a)

(b)

114

-25 0 25 50 75 100 125 150-1

0

1

2

3

4

5

6 19.9 ppm CH3I/Ar2982 K, 3.923 atm


CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Figure 6.3 Example CH data, modeling, and sensitivity at high-pressure: (a) CH concentration time-history (b) CH sensitivity at early times, S = (dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i.

-5 0 5 10 15 20 25-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

CH

Sen

sitiv

ity

Time [μs]

CH3+M<=>CH+H2+M CH3+M<=>CH2+H+M C+CH<=>C2+H CH+M<=>C+H+M CH2+M<=>C+H2+M C+CH2<=>2CH

(a)

(b)

115

-20 0 20 40 60 80 100 120-2

0

2

4

6

8

10

12 10 ppm C2H6, Ar3393 K, 1.039 atm


CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Figure 6.4 Example CH data, modeling, and sensitivity at high-temperature: (a) CH concentration time-history (b) CH sensitivity at early times, S = (dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i.

0 5 10 15 20-0.6-0.4-0.20.00.20.40.60.81.01.2

CH

Sen

sitiv

ity

Time [μs]

CH3+M<=>CH+H2+M CH+M<=>C+H+M CH3+M<=>CH2+H+M CH2+M<=>C+H2+M C+CH2<=>2CH CH2+M<=>CH+H+M

(a)

(b)

116

0 25 50 75 100

0

2

4

6

8

10

12C

H M

ole

Frac

tion

[ppm

]

Time [μs]

20 ppm C2H6, Ar3400 K, 1 atm

Current mechanism Kiefer & Kumaran (1994) Dean & Hanson (1991)

Figure 6.5 Comparison of CH time-histories calculated using different hydrocarbon pyrolysis mechanisms; Initial reflected shock conditions: 3400 K, 1 atm; 20 ppm C2H6, balance Ar.

117

Figure 6.6 CH concentration time-history: (a) Pressure dependence (b) Temperature dependence.

0 50 100 150 200 250-2

0

2

4

6

8

(3)

(2)

Experiment solid bold lines: model

10.3 ppm C2H6/Ar(1) 2944 K, 0.974 atm(2) 2949 K, 1.838 atm

19.9 ppm CH3I/Ar (3) 2982 K, 3.923 atm

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

(1)

0 50 100 150 200 250-2

0

2

4

6

(2)

(1)

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experimentsolid bold lines: model

10.3 ppm C2H6, Ar(1) 2949 K, 1.838 atm(2) 2789 K, 1.883 atm

(a)

(b)

118

0 50 100 150 200 250 300

0

15

30

45

6025.38 ppm CH3I, 0.106% O2, Ar2941 K, 1.16 atm

Experiment Model (k5b, best fit) Model (k5b x 3)

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Figure 6.7 Example OH data, modeling, and sensitivity: (a) OH concentration time-history (b) OH sensitivity at early times, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

0 20 40 60 80 100 120

0.0

0.3

0.6

0.9

OH

Sen

sitiv

ity

Time [μs]

CH3+O2<=>OH+CH2O H+O2<=>O+OH CH3+M<=>CH2+H+M CH3+M<=>CH+H2+M 2OH<=>O+H2O O+H2<=>H+OH

(a)

(b)

119

-20 0 20 40 60 80 100 120

0

10

20

30

40

50

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

24.98ppm CH3I, 0.106% O2, Ar2587 K, 3.898 atm

Experiment Model (k5b, best fit) Model (k5b x 3)

Figure 6.8 Example OH data, modeling, and sensitivity at high-pressure: (a) OH concentration time-history (b) OH sensitivity at early times, S = (dXOH/dki)(ki/XOH), where ki is the rate coefficient for reaction i.

-10 0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

OH

Sen

sitiv

ity

Time [μs]

CH3+O2<=>OH+CH2O H+O2<=>O+OH CH3+M<=>CH2+H+M CH3+M<=>CH+H2+M O+CH3<=>H+CH2O CH2+O2=>OH+H+CO CH2O+M<=>H+HCO+M

(a)

(b)

120

Figure 6.9 (a) Comparison of current measurements of k5a with previous work: open squares, this work (±25% error bars), 0.7-1.1 bar; solid black line, Dean and Hanson [35], 0.5-1.3 bar; dashed black line, Röhrig et al. [36], 1.2 bar; dash-dotted line, Markus et al. [37], 1.1-1.8 bar; solid gray line, Baulch et al. [11] (b) Pressure dependence of k5a: solid squares, 0.7-1.1 atm data; open circles, 1.8-2.9 atm data; solid triangles, 3.6-4.2 atm data; solid black line, least-squares fit to data.

0.28 0.32 0.36 0.40

109

1010

1011

k 1a [c

m3 m

ol-1 s

-1]

1000/T [K-1]

0.25 0.30 0.35 0.40 0.45107

108

109

1010

1011

k 1a [c

m3 m

ol-1 s

-1]

1000/T [K-1]

3600K 2500K

(a)

(b)

k 5a [

cm3 m

ol-1

s-1

] k 5

a [cm

3 mol

-1 s

-1]

121

Figure 6.10 (a) Comparison of current measurements of k5b with previous work: solid squares, this work (±50% error bars); open circles, Eng et al. [43]; dash-dotted line, Kiefer and Kumaran [67]; dashed line, Markus et al. [37]; solid black line, Lim and Michael [42]; solid gray line, Baulch et al. [11] (b) Pressure dependence of k5b: solid squares, 1.09-1.41 atm data; open circles, 1.42-1.75 atm data; solid triangles, 2.99-3.89 atm data; solid black line, least-squares fit to data.

0.25 0.30 0.35 0.40 0.45 0.50105

106

107

108

109

1010

1011

k 1b [c

m3 m

ol-1 s

-1]

1000/T [K-1]

0.32 0.36 0.40 0.44 0.48107

108

109

1010

k 1b [c

m3 m

ol-1 s

-1]

1000/T [K-1]

(a)

(b)

k 5b [

cm3 m

ol-1

s-1

] k 5

b [cm

3 mol

-1 s

-1]

122

2000 2500 3000 3500 40000.0

0.2

0.4

0.6

0.8

1.0

k

1b/(k

1a+k

1b)

T [K]0.0 1.0x10-5 2.0x10-5 3.0x10-5

0.0

0.2

0.4

0.6

0.8

1.0

k1b

/(k1a

+k1b

)[Ar], mol cm-3

4 atm

-30 -15 0 15 30 45-1

0

1

2

3

4

5

619.9 ppm CH3I/Ar2770 K, 1.871 atm, ρ(Ar) = 8.2x10-6 mol cm-3

Experiment Model (k5a, best fit) Model (k5a x 0.30), corresponds to

a branching ratio, k5b/(k5a+k5b), of ~0.70

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Figure 6.11 Branching ratio for the unimolecular decomposition of methyl radicals: (a) Temperature dependence: solid black line, this work; open circles, Eng et al. [43] ( ρ(Ar)=1.8x10-6 mol cm-3 ); solid stars, Fulle and Hippler [44] (high-pressure limit); dashed line, Markus et al. [37] (1.1-1.8 bar); solid gray line, Baulch et al. [11] (b) Pressure dependence at T=2750 K: solid black line, this work; open circles, Eng et al. [43]; solid star, Fulle and Hippler [44] at high-pressure limit; solid triangle, Markus et al. [37]; solid gray line, Baulch et al. [11] (c) Effect of higher branching ratio on the modeled CH time-history and comparison with experiment; a branching ratio of ~0.70 was reported by Eng et al. [43] at a comparable temperature and pressure (see Figure 6.11b).

(b) (a)

(c)

k 5b /

(k5a

+k5b

)

k 5b /

(k5a

+k5b

)

123

Chapter 7: Prompt-NO Initiation: CH + N2 Products

7.1 Introduction The CH+N2 reaction is the initiation step to prompt-NO formation in

combustion. At high temperatures, there are two possible pathways for the reaction

between CH and N2,

(7a) CH + N2 HCN + N

(7b) CH + N2 H + NCN

Previous experimental measurements of reaction (7) are described in Chapter 1. The

overall rate coefficient has not been measured at temperatures lower than 2500 K and

there is considerable scatter in the limited high-temperature data reported in the

literature (see Figure 1.8). Also, there is debate regarding the products of reaction (7).

Recent theoretical work [52-56, 152] strongly supports the spin-conserved reaction

(7b) over the spin-forbidden reaction (7a). However, there have been no direct

experiment studies of reaction (7b) to date.

In this work, we have made measurements of the overall rate coefficient, k7,

and the branching ratio, k7b/(k7b+k7a), of reaction (7) behind reflected shock waves

using narrow-linewidth CH laser absorption at 431.1 nm. A CH perturbation approach

was used to infer k7 in the 1943 – 3543 K temperature range. Ethane [C2H6] was used

as a CH precursor for T > 2500 K, while acetic anhydride [(CH3CO)2O] was used to

generate CH for T < 2500 K. A total of 34 kinetic measurements (Tables 7.1 and 7.2)

were carried out to ascertain the overall rate coefficient of the reaction between CH

and N2. The effect of the vibrational state of nitrogen (v = 0 vs. v = 1) on the kinetics

of the CH+N2 reaction was also investigated. The branching ratio was inferred in the

124

2228 – 2905 K temperature range by shock-heating C2H6 dilute in helium and

nitrogen. Absorption by NCN was monitored at 329.1 nm and confirms the existence

of reaction (7b). In addition, we report rate coefficient data for the reaction between H

and NCN between 2378 K and 2492 K,

(34) H + NCN HCN + N

This reaction is thought to be one of the primary routes for NCN removal in

hydrocarbon flames. However, its rate coefficient is not well established, with no

previous measurements available in the literature. The rate coefficient was recently

calculated by Moskaleva and Lin [56] using ab initio methods. The calculated RRKM

rate coefficient is about a factor of three lower than an earlier estimate by Glarborg et

al. [153].

All the detailed kinetic model simulations were performed using the

CHEMKIN software package from Reaction Design. In experiments conducted in a

nitrogen bath, the bulk translational temperature changes due to vibrational relaxation.

The effect of vibrational cooling was taken into account in the kinetic modeling by

imposing a time-dependent temperature profile in CHEMKIN using vibrational

relaxation time correlations from Millikan and White [143, 154]. As a check on our

treatment of the effect of vibrational relaxation on the bulk translational temperature,

experiments with added helium were also performed. The addition of helium reduces

the vibrational relaxation time. These measurements are described in greater detail

later in this chapter. The heat of formation recently measured by Bise et al. [155] for

the NCN radical was used in the kinetic modeling.

7.2 Experimental Set-up All experiments were carried out behind reflected shock waves in a high-

purity, stainless steel, helium-driven shock tube with an inner diameter of 14.13 cm.

The shock tube facility is described in Chapter 2. Ethane (99%) was obtained from

Specialty Chemical Products Inc. and Praxair Inc.; acetic anhydride (99.5%) was

obtained from Sigma Aldrich. Argon (99.9999%), helium (99.999%) and nitrogen

(>99%) were supplied by Praxair Inc. CH and NCN were detected at 431.1 nm and

125

329.1 nm, respectively, using the continuous-wave narrow-linewidth laser absorption

diagnostics described in Chapter 2.

7.3 Overall Rate Coefficient, CH + N2 Products

A perturbation approach, similar to that used by Dean et al. [48], was used to

infer the overall rate coefficient for reaction (7), k7 (where k7 = k7a + k7b). CH was

generated by shock-heating different hydrocarbon precursors (ethane, acetic

anhydride) dilute in argon. Detailed kinetic mechanisms were developed to model the

measured, baseline (unperturbed, no N2 in the reaction mixture) CH concentration

time-histories. Upon adding nitrogen to the initial reaction mixture, the CH profiles

are perturbed. The perturbation in the CH concentration is due primarily to the

reaction between CH and N2. Therefore, rate data for reaction (7) could be inferred by

adjusting k7 in the mechanism to best-fit the perturbed CH profiles. The experiments

were designed so that the product path used in the mechanism for CH+N2 has no

discernible effect on the overall rate coefficient determination.

7.3.1 High-Temperature (T > 2500 K) Measurements of k7

At temperatures greater than 2500 K, CH was generated by heating C2H6/Ar

mixtures behind reflected shock waves. In recent work [156], see Chapter 6, we used

a reaction mechanism based on Kiefer and Kumaran [67] to model CH time-history

measurements in C2H6 and CH3I pyrolysis over a broad temperature and pressure

range. The mechanism used in this chapter to simulate the unperturbed, baseline CH

profiles is similar to that used in Ref. [156]. Reactions of nitrogen species were added

to the mechanism to model the perturbed CH concentration time-histories in the

presence of N2. However, as described below, the perturbation in the CH

concentration is almost entirely due to reaction (7), facilitating a relatively direct

measurement of k7. Table 7.3 summarizes the rate parameters of the reactions that are

important in the high-temperature overall rate coefficient measurements of reaction

(7).

126

An example unperturbed CH concentration time-history, resulting from the

pyrolysis of 10 ppm ethane dilute in argon, is the upper profile in Figure 7.1. That the

mechanism captures the measured CH profile is evident from the figure. CH is formed

primarily from methyl decomposition, reaction (5a),

(5a) CH3 + Ar CH + H2 + Ar

and is removed by the unimolecular decomposition of CH, reaction (23), and the self-

reaction of CH, reaction (-28),

(23) CH + Ar C + H + Ar

(-28) CH + CH C + CH2.

Upon adding 10.1% nitrogen to the initial reaction mixture, the CH profile is

perturbed. The perturbed CH time-history, with added N2, is the lower profile in

Figure 7.1. The peak CH mole fraction drops by ~35%. By varying the rate coefficient

of only reaction (7) in the mechanism, we can fit the perturbed CH profile (dashed line

in the figure). For the experiment shown, k7 = 2.13 x 1011 cm3 mol-1 s-1 fits the

measurement very well. CH rate of production (ROP) analyses without and with N2

are shown in Figures 7.2a and 7.2b, respectively. As is evident, the only additional CH

removal path when N2 is present is reaction (7). This clearly shows that the

perturbation in CH concentration is principally due to the CH + N2 reaction. It should

be noted that the rates of unimolecular reactions such as CH3+M and CH2+M change

with N2 addition because of the different third-body collision-efficiency of N2 relative

to Ar. However, these changes have no discernible effect on the perturbed CH profiles

since the bath gas is primarily argon (added nitrogen was limited to ~10%). The model

simulations shown in Figures 7.1 and 7.2 have been performed assuming that the only

products formed when CH and N2 react are NCN and H (that this is a good assumption

will be demonstrated later in the chapter). The choice of product path, however, has no

effect on our overall rate coefficient determination – if the products are taken to be

HCN and N in the kinetic mechanism, we still obtain the same k7. The current high-

temperature measurements of k7 are summarized in Table 7.1.

It is important to note that the reaction mechanism used is not unique;

however, uniqueness is not essential for a perturbation approach [48]. The only

127

requirement is that the mechanism be applicable both in the presence and absence of

the perturbing species, which in this case is nitrogen. To check this hypothesis, we

used a different set of rate coefficients to model the unperturbed CH profile. For

example, the rate coefficient of reaction (5a) was adjusted by 25%; to compensate for

this change, rate coefficients of other reactions in the base mechanism such as CH+M

and CH2+M were modified. The k7 that best fits the perturbed profile was unchanged

(with the modified base mechanism) – this is a direct consequence of the fact that

perturbation is due principally to reaction (7). The effect of all the other reactions

tends to cancel out across the unperturbed and perturbed CH profiles.

7.3.2 Low-Temperature (T < 2500 K) Measurements of k7

At temperatures lower than 2500 K, CH was generated by the pyrolysis of

acetic anhydride dilute in argon behind reflected shock waves. Akao et al. [157] have

studied the thermal decomposition of acetic anhydride behind incident and reflected

shock waves at temperatures between 750 K and 980 K. The decomposition process

was monitored by IR emission at 4.63 μm and vacuum-UV absorption at 174.5 nm.

The only products observed were acetic acid and ketene.

(35) (CH3CO)2O CH3COOH + CH2CO

The reaction was found to be at the high-pressure limit at pressures between 0.16 atm

and 1 atm, in the 750 – 980 K temperature range. The following Arrhenius expression

was reported by Akao et al.,

k35 = 6.3x1011 exp(-138 kJ mol-1/RT), [s-1]

The data are in good agreement with earlier measurements carried out in flow and

static systems [158, 159]. The above expression yields a characteristic decomposition

time of less than 6 μs at 1100 K, the typical temperature behind the incident shock in

the current experiments. Since the pressure in the present work was always greater

than ~0.2 atm, the decomposition proceeds at the high-pressure limit. Therefore, in our

experiments, the acetic anhydride is expected to rapidly decompose behind the shock

128

front to form acetic acid [CH3COOH] and ketene [CH2CO]. The acetic acid then

decomposes via two channels,

(36a) CH3COOH + Ar CH2CO + H2O + Ar

(36b) CH3COOH + Ar CH4 + CO2 + Ar

The ketene formed in reactions (35) and (36a) decomposes to form CH2 and CO,

(37) CH2CO + Ar CH2 + CO + Ar

CH is subsequently generated by the rapid reaction of CH2 and H,

(38) CH2 + H CH + H2

Primary CH removal pathways include the bimolecular reactions of CH with C2H2, H

and CH2,

(39) CH + C2H2 C3H2 + H

(40) CH + H C + H2

(41) CH + CH2 C2H2 + H

An acetic anhydride pyrolysis mechanism was assembled to model the

measured CH concentration time-histories. A ketene pyrolysis mechanism recently

reported by Friedrichs and Wagner [160] forms the basis of the current model. Since

methane is one of products formed following the initial decomposition of acetic

anhydride (reaction (36b)), reactions from the natural-gas oxidation mechanism, GRI-

Mech 3.0 [111], were added to the Friedrichs mechanism. The important reactions in

the mechanism and the rate coefficients used are summarized in Table 7.4.

A CH sensitivity analysis is presented in Figure 7.3 for one of the experiments

conducted in this study. The CH profile is most sensitive to reactions (37) and (38)

and the self-reactions of CH2,

(42) CH2 + CH2 C2H2 + 2H

(43) CH2 + CH2 C2H2 + H2

At later-times, the CH profile shows some sensitivity to reactions (39) and (40). The

rate coefficients used for reactions (37)-(43) are from Friedrichs and Wagner [160].

Small adjustments (< ±25%) were made to these rate coefficients to best-fit each

measured CH trace. For example, the rate coefficients used in this study for reaction

(37), ketene decomposition, are shown along with the Friedrichs and Wagner fit [160]

129

and previous work [161, 162] in Figure 7.4. The current rate coefficient data are just

20% lower than Friedrichs and Wagner.

As is evident from Figure 7.3, the CH concentration is also sensitive to the two

acetic acid decomposition pathways, reactions (36a) and (36b), at early times. Only a

few studies of acetic acid decomposition have been reported in the literature [163-

166]. Mackie and Doolan [163] studied the thermal decomposition of acetic acid dilute

in argon in the 1300 – 1950 K temperature range in a single-pulse shock tube. At a

total density of ~1.9x10-4 mol cm-3, the acetic acid was found to decompose

homogenously, with nearly equal rates, via reactions (36a) and (36b). These

measurements are relatively indirect; rate coefficients were inferred by fitting

concentration profiles of the residual acid, CH4, CO2 and ketene to a detailed kinetic

mechanism. Saito et al. [164] investigated the branching ratio of the two competing

acetic acid decomposition paths. In the 1300 –1800 K temperature range and at a

density of 1 x 10-5 mol cm-3, the ratio k36b/k36a was found to be unity. Saito et al.

report rate coefficient expressions at the high-pressure limit, whereas the

decomposition is expected to be in the fall-off at the temperatures and pressures that

are of interest here. The decomposition of acetic acid is therefore not well

characterized for the experimental conditions used in this work.

In the mechanism, we have used high-pressure limit rate coefficients for acetic

acid decomposition from a theoretical study by Duan and Page [165]. Fortunately, due

to the small sensitivity of the two acetic acid decomposition pathways and because a

perturbation approach was used to infer rate coefficient data for k7, large uncertainties

in k8 and k9 can be tolerated, with little or no effect on the overall rate coefficient

determination for CH+N2 (this also applies for other reactions in the mechanism such

as reactions (42) and (43)). This is just an alternate way of stating what was

highlighted earlier – for a perturbation approach, the mechanism used need not be

unique; the only requirement is that the mechanism fit the unperturbed CH profile and

be applicable both with and without the perturbing species. To confirm that this

assumption is valid, for selected experiments, we used a different base mechanism to

fit the unperturbed CH profiles. Instead of using acetic acid decomposition rates from

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Duan and Page [165], we used rate coefficient expressions from Mackie and Doolan

[163]. In the 1900 – 2500 K temperature range, the Duan and Page rate coefficients for

reactions (36a) and (36b) are 7x and 3.7x Mackie and Doolan, respectively. However,

since the CH profiles are only weakly sensitive to k36a and k36b, small changes (<

±20%) in the rate coefficients of reactions (37) and (38) were sufficient to compensate

for the large change in the acetic acid decomposition rates. Upon using the adjusted

base mechanism in the perturbation study, the inferred k7 is unchanged, confirming

that the mechanism need not be unique and only needs to fit the unperturbed CH

concentration time-history.

An example unperturbed CH concentration time-history, resulting from the

pyrolysis of 25 ppm acetic anhydride dilute in argon, is the upper profile in Figure 7.5.

The mechanism does a very good job of capturing the key characteristics of the CH

trace. Upon adding 10% N2 to the initial reaction mixture, the peak CH concentration

is perturbed by ~40%; the perturbed CH trace is the lower profile in Figure 7.5.

Figures 7.6a and 7.6b, CH rate of production (ROP) analyses without and with added

nitrogen, show that the perturbation in the CH concentration is primarily due to

reaction (7), see Figure 7.6b. This is because with added nitrogen, the only additional

CH removal path is reaction (7). Therefore, as in the high-temperature perturbation

experiments in ethane, k7 was adjusted in the mechanism to fit the perturbed CH

profile. In the modeling, NCN and H were assumed to be the only products of reaction

(7). The choice of product path has a small effect, < 15%, on the k7 determination at

low-temperatures, and was included as an uncertainty in our measurements. The

current low-temperature measurements of k7 are summarized in Table 7.2. The k7 data

are reported at frozen conditions since temperature change due to N2 relaxation is

small – this is described in greater detail in the next section.

7.3.3 Effect of Vibrational Cooling on Reflected Shock Temperature

The addition of nitrogen to the reaction mixture in the perturbation

experiments causes the test-gas to cool in the reflected shock region due to N2

vibrational relaxation (V-T energy transfer),

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(44) N2 (v = 0) + M N2 (v = 1) + M

The vibrational relaxation time can be calculated as a function of temperature and

pressure using correlations from Millikan and White [143]. For example, at 3348 K

and 1 atm (experiment shown in Figure 7.1), the 1/e relaxation time, τvib, for 10% N2

in argon is ~65 μs. At 2233 K and 1.35 atm (experiment shown in Figure 7.5), τvib is

substantially higher, ~460 μs. In all our experiments, we limited our data reduction

and analysis to a time-window over which temperature change due to relaxation is

small. For example, for the high-temperature perturbation experiment shown in Figure

7.1, the time-window of interest is 30 μs (ΔT0-30μs is 1.4%, 47 K), while for the low-

temperature perturbation experiment shown in Figure 7.5, it is 100 μs (ΔT0-100μs is

0.44%, 10 K). The change in the translational temperature of the test-gas over the

chosen experimental time-frame is small, less than 1.5% and 0.5% for the high- and

low-temperature experiments, respectively. Therefore, we report the current overall

rate coefficient measurements at frozen conditions (Tables 7.1 and 7.2).

The effect of the change in temperature on the CH concentration profiles was

also investigated. A time-dependent temperature profile T(t) was imposed in

CHEMKIN to simulate the effect of vibrational cooling. The temperature profile has

the following form,

T(t) = Te + (Tf – Te) exp(-t/ τvib)

where, Te is the vibrationally equilibrated temperature and Tf is the vibrationally

frozen temperature. The impact of the temperature-change on the CH profile was

found to be small (< 0.05% abs.). Therefore, the influence of vibrational relaxation on

the bulk translational temperature has no discernible effect on our k7 determination.

7.3.4 Effect of N2 Vibrational State on CH+N2 Kinetics

The vibrational state of N2 (v = 0, v = 1) could potentially influence the

kinetics of the reaction between CH and N2. At temperatures lower than 2400 K, most

of the N2 is in the v = 0 vibrational state in the CH perturbation experiments since the

vibrational relaxation time, τvib, is large in comparison to the time-frame of the

experiment, τexpt. Also, the population fraction of N2 in v = 1 after vibrational

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relaxation is fully complete (i.e. at equilibrium) is small, less than 20%. Therefore, it is

reasonable to assume that at low temperatures our measurements are of CH + N2 (v =

0) Products. At higher temperatures, we cannot make this assumption since

relaxation is faster and the population fraction in v = 1 is higher. Therefore, the effect

of the vibrational state of nitrogen on reaction (7) was investigated in experiments

with added helium.

An example measurement with helium is shown in Figure 7.7. Adding 5.7%

helium to the argon bath reduces the relaxation time at 2684 K and 1.1 atm from 190

μs to 25 μs. As a consequence, the fraction of N2 in v = 1 is higher when helium is

present in the reaction mixture. In the first 50 μs, the change in the bulk translational

temperature for the experiment shown is 2.4% or 65 K. Since temperature is changing

quite rapidly, a time-dependent temperature profile was imposed in CHEMKIN when

simulating the measurement. N2-N2 and N2-He relaxation data needed to calculate the

temperature profile were taken from Refs. 143 and 154.

When the experiment with helium was analyzed disregarding the effect of the

vibrational state of N2 on CH+N2 kinetics, the inferred k7 was comparable to that

measured in an experiment with no helium. This suggests that the vibrational state of

nitrogen does not affect the kinetics of the CH+N2 reaction, at least to within the

resolution of the current experiments. If the N2 vibrational state did have an effect on

k7, the rate coefficient measured in the experiment with added helium would have

been higher or lower than that measured in the experiment with no helium. A similar

approach was used in our laboratory to study the OH + CO (v = 0, 1) reaction system

[167]. In those measurements, the OH + CO reaction rate was found to be dependent

on the vibrational state of CO.

7.4 Branching Ratio Measurements The branching ratio of reaction (7), k7b/(k7b+k7a), was measured by CH laser

absorption in experiments in a nitrogen bath. We have taken advantage of the fact that

the equilibrium constants of reactions (7a) and (7b) are very different due to

differences in the thermochemical properties of the products formed. As a

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consequence, reaction (-7b), H + NCN CH + N2, is orders of magnitude faster than

reaction (-7a), N + HCN CH + N2. This is evident from Figure 7.8a which presents

a comparison of k-7a and k-7b for the same rate coefficient in the forward CH+N2

direction. The rate coefficient in the forward direction is fixed by the CH perturbation

measurements described earlier in this chapter. The large difference in the rate

coefficients of the reverse reactions results in a strong sensitivity to the branching

ratio. For example, the concentration of CH would clearly be higher for a branching

ratio of 1 (all NCN+H) than for a branching ratio of 0 (all HCN+N). This is because k-

7b >> k-7a, and therefore, more CH is formed when the branching ratio is higher (since

the reverse reaction (-7b) is faster).

The validity of this approach is demonstrated by kinetic modeling in Figure

7.8b. For the calculations shown, a branching ratio of 1 yields CH mole fractions that

are about a factor of two higher than a branching ratio of 0; the shape of the CH

profile also changes. To maximize the effect of the branching ratio on the CH trace,

the reverse reaction rates need to be as large as possible – therefore, the simulations

and experiments were performed in a nitrogen bath.

Since the branching ratio measurements were made in nitrogen, the bulk

translational temperature of the test-gas changes over the time-frame of the experiment

due to N2 vibrational relaxation. The change in temperature due to relaxation was

taken into account by imposing a time-dependent temperature profile in CHEMKIN.

To calculate the temperature profile, we used vibrational relaxation time correlations

from Millikan and White [143].

Dilute mixtures of ethane in nitrogen were shock-heated and CH was

monitored at 431.1 nm. The branching ratio was inferred by fitting the measured CH

time-histories to detailed kinetic model simulations using the branching ratio (BR) as a

fitting parameter. An example branching ratio measurement is presented in Figure

7.9a. We chose to present the measurement in terms of percentage absorption to

demonstrate the excellent sensitivity of the CH laser absorption diagnostic (minimum

detectable absorption is less than 0.1%). In the kinetic simulation, the concentration

profiles output by CHEMKIN were converted to percentage absorption using Beer’s

134

law (% absorption = [1 - exp (-kv P XCH L)] x 100). The temperature changes by ~145

K over 175 μs due to N2 vibrational relaxation and was taken into account in the

kinetic modeling. The effect of temperature on the CH absorption coefficient, kv, was

also accounted for.

The chemical kinetic mechanism that was used in the high-temperature

perturbation study in ethane was updated and used to model the CH branching ratio

measurements. The reactions that are important in the branching ratio experiments are

presented in Table 7.5. Rate coefficients for these reactions were chosen based on a

detailed survey of the literature. The rate coefficient used for reaction (7), CH + N2

Products, is from the perturbation experiments described earlier, while rate

coefficients for the two methyl decomposition pathways, reactions (5a) and (5b), are

from Vasudevan et al. [156], see Chapter 6. The methyl decomposition rates reported

in Ref. 156 are for M=Ar; therefore, the rate coefficients were adjusted to account for

the different third-body collision-efficiency of nitrogen relative to argon [1.10-1.15x at

~0.6 atm]. For reaction (38), CH2 + H CH + H2, a recent recommendation by

Friedrichs and Wagner [160] was used, while for reaction (45), CH2 + CH3 C2H4 +

H, we used the Baulch et al. [11] recommendation. Similarly, up-to-date rate

coefficients were chosen for the other reactions as well, see Table 7.5.

The rate coefficients in Table 7.5 have uncertainty limits, which were

determined from the literature. We analyzed all of our CH measurements using a

range of reasonable rate coefficients that spanned these estimated uncertainty bands.

We found that if the rate coefficients for reactions (38) and (34) are ~20% lower and

~50% higher than shown in Table 7.5, we can fit all our CH absorption profiles to a

branching ratio of 1; see, for example, Figure 7.9a. A branching ratio of 1 is consistent

with recent theoretical studies [52, 53, 56] of the CH+N2 reaction system. Also, the

above changes in k38 and k34 are well within the uncertainty limits estimated for these

reaction rate coefficients. It should be noted that if our CH measurements are analyzed

with the rate coefficients shown in Table 7.5 (i.e. k38 and k34 unchanged), the average

branching ratio inferred is 0.88, with estimated upper and lower bounds of 1 (since the

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branching ratio cannot be greater than 1) and 0.70 (determined using a systematic

uncertainty analysis), respectively.

A CH sensitivity analysis for the experiment shown in Figure 7.9a is presented

in Figure 7.9b. From the CH sensitivity plot, it is evident that the early-time ‘jump’ in

CH absorption (t < 15 μs) is controlled by the decomposition of methyl radicals to

CH+H2, reaction (5a), and the overall CH+N2 rate coefficient, k7. The collision-

efficiency of N2 was adjusted to match the ‘jump’ in CH absorption at early-times; for

the low-pressure experiments at ~0.6 atm, a collision efficiency of 1.10-1.15 for N2

relative to argon best fits the measured CH ‘jump’. At later-times, there is sensitivity

to reaction (38) CH2 + H CH + H2, reaction (5b) CH3 + M CH2 + H + M,

reaction (34) H + NCN HCN + N, and reaction (45) CH2 + CH3 C2H4 + H.

The CH profile shows good sensitivity to the branching ratio – kinetic model

simulations for branching ratios of 0 and 1 are shown in Figure 7.9a. We have limited

ourselves to times < 175 μs because the effect of interfering reactions like H+NCN

HCN+N and CH2+H CH+H2 become more pronounced at later times (see Figure

7.9b). Even though the CH profile shows large sensitivity to reactions (5a) and (7),

these reactions do not significantly affect our determination of the branching ratio.

This is because if either k5a or k7 is changed, the early-time CH ‘jump’ is not captured.

Consequently, the temporal shape of the later-time CH profile cannot be reconciled

with any branching ratio. This is demonstrated in Figure 7.9c, where, with 1.5 x k5a

even a branching ratio of 0 does not fit the measured CH trace. To confirm that the

rate coefficients of reactions (7) and (5a) do not have a significant effect on the

branching ratio, simulations were performed with different combinations of k7 and k5a.

We found that so long as the early-time “jump” is captured, the branching ratio

inferred is the same and not dependent on the (k7, k5a) combination used.

As a check on our treatment of the effect of vibrational relaxation on the bulk

translational temperature, experiments with added helium (5%, 10%) were performed.

The addition of helium significantly reduces the nitrogen vibrational relaxation time.

For example, at 2600 K and 0.6 atm, τvib with 5% helium is ~50 μs and with 10%

helium is ~30 μs, compared to 250 μs without helium. Example experiments with 5%

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and 10% helium are shown in Figures 7.10a and 7.10b, respectively. A branching

ratio of 1.0 fits both the measurements well.

The peak CH absorption in the measurements shown in Figures 7.9 and 7.10

are less than 0.5%. Higher pressures would increase both the peak absorption level

and the signal-to-noise ratio. Also, at higher pressures, the relaxation of nitrogen is

faster (since τvib scales as 1/P), serving as an additional check on our treatment of

vibrational relaxation. Experiments were conducted at reflected shock pressures of

~2.5 atm, with and without added helium. As in the lower pressure measurements, the

methyl decomposition rate coefficient, k5a, was adjusted to get the early-time ‘jump’ in

CH to match experiment. The adjusted k5a is within 35% of that used in the 0.6 atm

experiments – this suggests that pressure-dependent fall-off in reaction (5a) is small in

the 0.5-3 atm pressure range, in good agreement with our methyl decomposition

measurements [156], see Chapter 6. A sample high-pressure measurement at 2.3 atm

is shown in Figure 7.11. The peak CH absorption and signal-to-noise ratio are, as

expected, higher than the lower pressure measurements (at ~0.6 atm) shown in Figures

7.9 and 7.10. A branching ratio of 1 fits the experiment well; a simulation for a

branching ratio of 0 is also shown, and demonstrates the sensitivity of the

measurement to the branching ratio.

In summary, CH measurements were performed over a broad range of

conditions – pressure, temperature, precursor concentration, helium concentration and

vibrational relaxation time were all varied. The measurements were fit to the

branching ratio of reaction (7) using a detailed kinetic mechanism. A branching ratio

of 1 is consistent with the current measurements. It is important to note that varying

reaction rates within their estimated uncertainty limits can lead to lower branching

ratios, with a minimum, based on our current understanding of key reactions and rate

coefficient uncertainties, of 0.70. Even so we can conclude that CH+N2 NCN+H is

the principal pathway for the reaction between CH and N2. The conditions at which

the branching ratio experiments were conducted are summarized in Table 7.6.

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7.5 NCN Time-History Measurements NCN absorption time-histories were recorded in C2H6/N2 mixtures behind

reflected shock waves. NCN was detected at the A-X (000,000) head at 329.13 nm.

The experiments were carried out in a nitrogen bath to drive the CH+N2 reaction

forward and increase the amount of NCN formed. The kinetic mechanism that was

used to model the NCN data is the same as that used in the branching ratio

experiments. The reactions that NCN is sensitive to are identical to the ones that are

important in the branching ratio measurements described earlier, and are summarized

in Table 7.5.

An example NCN absorption trace obtained upon shock-heating ethane dilute

in nitrogen is presented in Figure 7.12a. NCN sensitivity and rate of production (ROP)

analyses for this experiment are shown in Figures 7.12b and 7.12c. It is evident from

Figure 7.12c that NCN is formed by the reaction between CH and N2, and is removed

by reaction with H-atoms,

(34) H + NCN HCN + N

While NCN formation and removal are principally due to reactions (7) and (34), a

complete NCN reaction subset was included in the kinetic model, see Table 7.7.

Since temperature is changing over the time-frame of the experiment due to

nitrogen vibrational relaxation (over 300 μs, the bulk translational temperature

changes by ~200 K) and because the absorption coefficient of NCN is not known, it is

not easy to infer kinetic data from these measurements. However, from Figure 7.12b it

is evident that the decay in NCN is sensitive principally to reaction (34). This suggests

that if we were to conduct experiments where temperature is a constant during the

decay period, the effect of the absorption coefficient could be normalized out,

facilitating a simple and relatively direct kinetic determination of the rate coefficient

of reaction (34). These measurements are described next.

7.5.1 H + NCN HCN + N

NCN formation and removal, upon shock-heating dilute mixtures of ethane in

helium and nitrogen, were measured via laser absorption at 30383.06 cm-1

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(329.1307 nm). A relative NCN absorption record (normalized at 100 μs) for an

experiment with 10% added helium is shown in Figure 7.13a. The addition of helium

reduces the vibrational relaxation time; the nitrogen relaxes almost completely in ~100

μs, see Figure 7.13b. Since at t > 100 μs, the temperature is approximately a constant,

the decay can be normalized by the NCN absorption-level at 100 μs. This removes the

effect of the NCN absorption coefficient during the decay-period. The various

reactions that NCN is sensitive to are shown in Figure 7.13c. During the decay-period,

it is evident that reaction (34) has strong sensitivity, with secondary interference from

reactions (7), (5) and (38). The rate coefficient of reaction (34) was adjusted in the

mechanism to fit the normalized NCN trace (at t > 100 μs). A rate coefficient of 3.45 x

1013 cm3 mol-1 s-1 yields an excellent fit between model and experiment. Normalizing

the modeled profile with respect to the peak, instead of 100 μs, does not affect our rate

coefficient determination.

Measurements for k34 were conducted over the 2375 – 2500 K temperature

range and are summarized in Table 7.8. At lower temperatures, sensitivity to reaction

(34) decreases and secondary chemistry becomes important. At higher temperatures, a

large portion of the NCN decay occurs before the test-gas has fully relaxed. Hence, it

is no longer possible to normalize out the effect of the absorption coefficient as

temperature is not a constant during the decay.

Our measurement strategy for H+NCN involved the use of normalized NCN

profiles. To model NCN absorption quantitatively, the absorption coefficient of NCN,

kNCN, is needed as a function of temperature. The absorption coefficient can be

inferred approximately from the NCN time-histories as described below.

7.5.2 NCN Absorption Coefficient

We can infer the NCN absorption coefficient, kNCN, in the C2H6/He/N2

experiments used to measure k34. Figure 7.14a presents an example measurement. The

absorption coefficient of NCN was adjusted to best-fit the absolute, constant-

temperature decay in NCN absorption; a simulation with 2kNCN is also shown. Over

the 2375 – 2500 K temperature range, at a pressure of ~0.42 atm, kNCN varies between

139

87 and 55 cm-1 atm-1. These values are reasonable and are comparable to previous

measurements made in our laboratory for other polyatomic species. For example, the

absorption coefficient of NCO varies between 50 cm-1 atm-1 and 15 cm-1 atm-1 in the

2000 – 2500 K temperature range at ~1 atm [187]. The current kNCN data are presented

as a function of temperature in Figure 7.14b. At early-times, the fit between model and

experiment is poor – this is because at t < 100 μs, temperature changes significantly

due to vibrational relaxation, and the effect of this temperature-change on kNCN was

not accounted for in the simulations shown in Figure 7.14a.

It is important to note that the kNCN measurements are only approximate. From

the sensitivity analysis presented in Figure 7.13c, it is evident that the absolute NCN

profile, and therefore the NCN absorption coefficient, is dependent on the rate

coefficients of reactions (7), (34), (5) and (38). The primary interfering reaction is that

between H and NCN, reaction (34); the uncertainty in the rate coefficient of this

reaction is about a factor of two (see ‘Results and discussion’ section). The absorption

coefficient is also influenced by the branching ratio of reaction (7). The simulations

and kNCN data shown in Figure 7.14 are for a branching ratio of 1. A branching ratio of

0.85 yields an absorption coefficient that is ~15% higher. Given that there are several

error sources (k7, k34, k5, k38, temperature, vibrational relaxation time, branching

ratio), an uncertainty estimate of a factor of 2 for kNCN is reasonable. The primary

contributors to the uncertainty are uncertainty in k34 and k38.

7.6 Results and Discussion In this section we compare our measurements of k7, k34 and the branching ratio with

previous work. Detailed uncertainty analyses for our measurements are also described.

7.6.1 Overall Rate Coefficient for CH+N2

Our measurements of the overall CH+N2 rate coefficient, k7, between 1943 K

and 3543 K in the 0.9-1.4 atm pressure range are presented in Figure 7.15. The current

rate coefficient data are in good agreement (to within ~35%) with Dean et al. [48] at

high temperatures and have substantially lower scatter and uncertainty. At

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temperatures lower than ~2500 K, there are no previous, direct measurements of k7.

Estimates from flame studies exist [50, 51] and are shown in Figure 7.15. The k7

values are higher, while the activation energies are lower than measured in this work.

All of these previous studies were interpreted as measurements of k7a, CH + N2

HCN + N.

The rate coefficient for reaction (7b) has been calculated by Moskaleva and

Lin [56] using RRKM theory. The calculated rate coefficients do not agree well with

the current measurements. At 2000 K, the calculation is about a factor of five smaller

than experiment. Recent studies [see, for example, Ref. 61] that have attempted to

model NO and NCN profiles in low-pressure hydrocarbon flames have found that

using the Lin rate coefficient expression leads to an under-prediction of NO and NCN

levels in the flame. This observation appears to be consistent with the RRKM rate

coefficient being too low.

A least-squares, two-parameter fit of the current measurements, valid over the

1943 – 3543 K temperature range, is given by the following expression,

k7 = 6.03 x 1012 exp (-11150 / T [K]), [cm3 mol-1 s-1]

The correlation coefficient of the above fit is -0.98 and standard deviation is 0.03.

A detailed uncertainty analysis was carried out to set error limits for our

measurements of k7. The uncertainty sources considered were: uncertainty in [a]

absorption coefficient of CH; [b] initial mixture concentration; [c] reflected shock

temperature, primarily due to uncertainty in shock velocity determination; [d] rate

coefficients of secondary reactions; [e] choice of product path for reaction (1) in the

kinetic modeling; [f] fitting the modeled trace to the experimental profile; [g] locating

time zero. The effect of each of the above uncertainty categories on the rate coefficient

of reaction (7) was ascertained and combined via a root-mean-square summation to

yield an overall uncertainty estimate for k7. Based on this analysis, we conservatively

estimate uncertainties of ~±25% and ~±35% on our k7 measurements at ~3350 K and

~2100 K, respectively. The primary contributors to the uncertainty are the uncertainty

in the reflected shock temperature and the CH absorption coefficient. At low

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temperatures, uncertainty in fitting the perturbed CH profile to the kinetic model

becomes important. This is because the CH profile is only weakly sensitive to the

overall rate coefficient at low temperatures.

7.6.2 Branching Ratio for CH+N2

There have been no previous measurements of the branching ratio of reaction

(7). A branching ratio of 1 fits all our CH absorption data, with no discernible

dependence on temperature or pressure. Since the branching ratio measurements were

made in a nitrogen diluent, the temperature changes in each experiment due to N2

vibrational relaxation. Table 7.6 summarizes the experimental conditions at which the

branching ratio measurements were made; also shown are the change in temperature

due to relaxation and the “average” temperature for each experiment. As pointed out

earlier, while a branching ratio of 1 is consistent with the current CH measurements,

varying key reaction rates within estimated uncertainty limits can lead to lower

branching ratios. A detailed and systematic error analysis, taking into account

experimental and mechanism-induced contributions, yields a conservative lower

bound of 0.70.

Our measurements clearly indicate that the dominant (and likely only) pathway

for the CH+N2 reaction is (7b), CH + N2 H + NCN, and confirms the NCN product

hypothesis made by Moskaleva and Lin [56]. The current study, in conjunction with a

previous flame study by Smith [60] and recent theoretical work on the CH+N2

reaction system [52, 53, 56, 152], establishes that NCN is a primary product of

reaction (7) and a key precursor to prompt-NO formation.

7.6.3 H + NCN HCN + N

The current measurements of k34 are presented in Figure 7.16. To the best of

our knowledge, this is the first experimental study of reaction (34). The rate data are in

excellent agreement with rate coefficients calculated by Moskaleva and Lin [56] using

ab initio methods. An estimate by Glarborg et al. [153] is about three times the current

measurements.

142

In the 2378 – 2492 K temperature range, the average rate coefficient measured

is k34 = 3.2 x 1013 cm3 mol-1 s-1. The uncertainty in k34 is estimated to be about a

factor of two. The primary contributors to this uncertainty are uncertainty in: (a) the

vibrational relaxation time (and hence, temperature), and (b) interfering chemistry

(here, CH + N2 Products, CH3 + M CH + H2 + M and CH2 + H CH + H2).

Since the temperature range of the current experiments is limited and because

uncertainty is relatively large, no definitive conclusions can be made regarding the

activation energy for reaction (34) based on the measured data.

7.6.4 Implications of Current Study to NO Modeling in Flames

Two studies [61, 190] have attempted to model NO profiles in low-pressure

hydrocarbon flames with mechanisms that incorporate NCN kinetics. El bakali et al.

[190] found that using the Moskaleva and Lin [56] rate coefficient for reaction (7b),

CH + N2 NCN + H, in detailed flame calculations leads to an under-prediction of

prompt-NO by more than a factor of six. Similarly, Sutton et al. [61] report that both

NO and NCN mole fractions are severely under-predicted with the Moskaleva and Lin

rate for reaction (7b). These observations are consistent with the current experiments

which indicate that the RRKM rate coefficient from Moskaleva and Lin is too low by

about a factor of 5 at ~2000 K (see Figure 7.15). Therefore, using the current

measurements of the rate coefficient of reaction (7) will likely lead to improved

model-predictions of NO and NCN in flames.

The current study establishes NCN and H as the primary products of the

CH+N2 reaction – this could have an impact on NO modeling in flames. This is

because the rate coefficients (and barriers) of the reverse reactions (-7a) and (-7b) are

very different (see Section 7.4). For HCN+N, the reverse reaction is unimportant

(Figure 7.8a) and since the reactions that oxidize HCN to NO (HCN NH NO)

are fast compared to CH+N2 at flame temperatures, it is the CH+N2 reaction which is

“rate controlling” [61]. However, the current experiments indicate that little, if any,

HCN is formed when CH and N2 react. With NCN and H as products, prompt-NO

formation need not necessarily be controlled by CH+N2 alone. This is because the

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reverse reaction rate, H + NCN CH + N2, is large and the fraction of NCN that

proceeds to NO could be influenced by the rate coefficients of NCN removal reactions

like H + NCN HCN + N and NCN + O Products. If the rates of these reactions

are fast compared to reaction (-7b) and NCN is rapidly converted to HCN/ NH/ CN

(which subsequently form NO), NCN kinetics would not significantly influence the

rate of prompt-NO formation, i.e., reaction (7) would still be “rate controlling”.

However, it is difficult to accurately gauge the effect of NCN on flame modeling since

the chemistry of this short-lived intermediate is not well known. Sutton et al. [61]

found that for a meaningful determination of the sensitivities of NO formation to NCN

kinetics to be made, accurate values for NCN removal rate coefficients are needed. In

this work we have studied reaction (34), H + NCN HCN + N – the rate coefficient

of this reaction is only slightly lower than the rate coefficient of reaction (-7b), which

implies that a part of the NCN formed in reaction (7b) is converted to HCN via

reaction (34). This might also suggest that subsequent NCN chemistry does not play

too significant a role in prompt-NO formation. Measurements of other NCN removal

reactions are currently planned (see Chapter 8, “Recommendations for Future Work”),

and will help ascertain the importance of NCN kinetics to prompt-NO formation in

flames.

7.7 Conclusions Sensitive, narrow-linewidth laser absorption diagnostics for CH and NCN have

been used to study the reaction between CH and N2. A CH perturbation approach was

used to measure the overall rate coefficient in the 1943 – 3543 K temperature range.

The branching ratio was measured between 2228 and 2905 K – the measurements

establish NCN and H as the principal products of the CH+N2 reaction. NCN was

detected for the first time by laser absorption, and confirms that NCN is a key

precursor to prompt-NO. The measured NCN time-histories were also used to infer the

rate coefficient of the reaction between H and NCN, and to estimate an absorption

coefficient for NCN.

144

Table 7.1: Summary of k7 measurements at high temperatures

T [K]* P [atm]* k7 [cm3 mol-1 s-1]

10.14 ppm C2H6 , 9.98% N2, balance Ar

2819 1.112 1.15 x 1011 2651 1.199 8.96 x 1010 2615 1.208 9.29 x 1010 2916 1.063 1.31 x 1011 3021 0.975 1.49 x 1011 3296 0.976 2.23 x 1011 3503 0.943 2.71 x 1011 3194 0.892 1.82 x 1011


3062 0.979 1.57 x 1011 3256 0.946 2.14 x 1011 3175 0.986 1.96 x 1011 3484 0.918 2.58 x 1011 3348 0.952 2.13 x 1011 3543 0.929 2.33 x 1011

9.9 ppm C2H6 ,10.1% N2, balance Ar

2778 1.173 1.08 x 1011 2816 1.121 1.14 x 1011 2589 1.237 8.11 x 1010


2910 1.034 1.30 x 1011 3080 1.027 1.60 x 1011


2901 1.033 1.28x1011

* frozen temperature and pressure, see text

145

Table 7.2: Summary of k7 measurements at low-to-moderate temperatures

T [K]* P [atm]* k7 [cm3 mol-1 s-1]

25.38 ppm acetic anhydride , 10.16% N2, balance Ar

2170 1.375 3.36 x 1010 2233 1.348 3.88 x 1010 1951 1.405 2.05 x 1010 2098 1.384 2.82 x 1010


2080 1.313 2.91 x 1010 1981 1.343 2.32 x 1010 1943 1.391 2.15 x 1010 2226 1.285 3.67 x 1010 2356 1.226 4.83 x 1010


2082 1.339 2.60 x 1010 2126 1.301 3.63 x 1010 2227 1.242 3.68 x 1010 2398 1.199 5.24 x 1010 2344 1.228 4.71 x 1010

* frozen temperature and pressure, see text

146

Table 7.3: Rate parameters for reactions important in CH perturbation experiments in ethane/N2/Ar

Rate Coeff. [cm3 mol-1 s1] Reaction A n E, kcal/mol

Reference

CH3 + M CH + H2 + M 3.09x1015 0 80.9 156* CH3 + M CH2 + H + M 2.24x1015 0 82.7 156* CH + M C + H + M 1.0x1014 0 64.0 67* CH2 + M C + H2 + M 1.15x1014 0 55.8 67* CH2 + M CH + H + M 5.60x1015 0 89.6 156 H + CH C + H2 1.65x1014 0 0.0 111 C + CH C2 + H 2.0x1014 0 0.0 67 C + CH2 2CH 1.0x1014 0 0.0 67 C + CH3 H + C2H2 5.0x1013 0 0.0 111 CH2 + H CH + H2 1.1x1014 0 0.0 160 C + CH4 CH + CH3 5.0x1013 0 0.0 67 CH + CH3 H + C2H3 6.0x1013 0 0.0 67 CH + N2 Products 6.0x1012 0 22.1 This work H + NCN HCN + N 1.89x1014 0 8.4 56** * rate coefficients were adjusted slightly (≤ ±25%) to match each measured baseline CH profile [156] ** agrees well with the measurements made in the current study

147

Table 7.4: Rate parameters for reactions important in CH perturbation experiments in acetic anhydride/N2/Ar


Reference

CH2CO + M CH2 + CO + M 9.5x1015 0 58.3 160* CH2 + H CH + H2 1.1x1014 0 0.0 160* CH2 + CH2 C2H2 + H2 3.8x1014 0 7.0 160* CH2 + CH2 C2H2 + 2H 3.8x1014 0 7.0 160* H + CH C + H2 1.65x1014 0 0.0 111 C2H2 + CH C3H2 + H 1.30x1014 0 0.0 160 CH3COOH CH2CO + H2O 2.95x1014 0 78 165# CH3COOH CH4 + CO2 7.08x1013 0 74.6 165# CH2 + CH C2H2 + H 1.00x1014 0 0.0 160 CH + N2 Products 6.0x1012 0 22.1 This work H + NCN HCN + N 1.89x1014 0 8.4 56**

* rate coefficients were adjusted slightly (≤ ±25%) to match each measured CH decay # rate coefficient units: s-1; also see text for explanation on rate coefficient choice ** agrees well with the measurements made in the current study

148

Table 7.5: Rate parameters for reactions important in branching ratio and NCN time-history measurements


Reference

CH3 + M CH + H2 + M see text 156* CH3 + M CH2 + H + M see text 156 H + CH C + H2 1.65x1014 0 0.0 111 CH2 + H CH + H2 1.1x1014 0 0.0 160# CH2(S) + H2 CH3 + H 7.0x1013 0 0.0 111 CH3 + CH3 C2H5 + H 3.16x1013 0 14.7 42 CH2 + CH3 H + C2H4 7.2x1013 0 0.0 11 CH + N2 Products 6.0x1012 0 22.1 This work H + NCN HCN + N 1.89x1014 0 8.4 56# * rate coefficient adjusted to match early-time CH ‘jump’ in branching ratio experiments # see text, a 20% lower rate coefficient for k38 (CH2 + H CH + H2) and a 50% higher rate coefficient for k34 (H + NCN HCN + N) was used in the branching ratio experiments

149

Table 7.6: Summary of branching ratio experiments

T(frozen) [K]

P(frozen) [atm]

T(equilibrated) [K]

P(equilibrated) [atm]

Temperature over fitting window

Average Temperature [K]

103.92 ppm C2H6 , balance N2

2429 0.703 2095 0.676 2429-2268 2349 2443 0.698 2105 0.671 2443-2278 2361


2548 0.667 2185 0.64 2548-2418 2483 2634 0.641 2249 0.614 2634-2484 2559 2396 0.733 2070 0.705 2396-2228 2312

101.6 ppm C2H6 , 5.02% He, balance N2

2611 0.598 2241 0.573 2611-2261 2436

101.09 ppm C2H6 ,10.02% He, balance N2

2671 0.571 2297 0.548 2671-2302 2487


2531 2.312 2172 2.22 2531-2289 2410 2628 2.182 2244 2.092 2628-2355 2492

24.88 ppm C2H6 ,10.2% He, balance N2

2905 2.822 2474 2.702 2905-2474 2690 2893 2.738 2465 2.622 2893-2465 2679

150

Table 7.7: Rate parameters for NCN reactions in kinetic model


Reference

CH + N2 NCN + H see text This work H + NCN HCN + N 1.89x1014 0 8.4 56 CH + N2 HNCN 1.65x1021 -3.62 14.2 56 HNCN + M H + NCN + M 1.79x1028 -3.44 64.5 56 NCN + M N + CN + M 3.25x1025 0 112.9 56 CH2 + NCN CH2CN + N 3.57x1013 0 -5.1 56 CH2 + NCN CH2NC + N 2.61x1013 0 4.0 56 CH2 + NCN H2CN + CN 7.99x1013 0 4.6 56 CH2 + NCN HNC + HCN 2.69x1012 0 4.6 56 CH + NCN HCCN + N 2.29x1014 0 5.1 56 CH + NCN HCN + CN 3.21x1013 0 -0.86 56 CN + NCN C2N2 + N 1.25x1014 0 8.0 56 CH3 + NCN CH3CN + N 8.06x1010 0 13.3 56 CH3 + NCN H2CNH + CN 1.37x107 0 -49.9 56 N + NCN N2 + CN 1.0x1013 0 0.0 56 C + NCN 2CN 1.0x1013 0 0.0 56

151

Table 7.8: Summary of rate coefficient data: H + NCN HCN + N

T [K] P [atm] k34 [cm3 mol-1 s-1]

105.3 ppm ethane, 9.8% He, balance N2

2492 0.447 3.45 x 1013 2455 0.437 3.36 x 1013 2420 0.413 3.28 x 1013

101.92 ppm ethane, 10.14% He, balance N2

2491 0.401 3.45 x 1013 2378 0.421 2.54 x 1013

152

Figure 7.1 High-temperature CH perturbation experiment: upper CH trace is obtained from the pyrolysis of 10 ppm ethane, balance Ar at 3348 K and 1.08 atm; lower CH trace is from a similar experiment at 3348 K and 0.95 atm, but with 10.1% added N2; addition of N2 causes the peak CH mole fraction to be perturbed by ~35%; the solid black and dashed lines are model simulations without and with N2, respectively; k7=2.13 x 1011 cm3 mol-1 s-1 yields a best-fit between the perturbed CH trace and the corresponding numerical simulation.

-30 -20 -10 0 10 20 30 40 50 60-2

0

2

4

6

8

10

12

10.1% N2, pertubed CH

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

0% N2, unpertubed CH

1.75% abs.

153

Figure 7.2 CH rate of production (ROP) at high-temperatures: (a) experiment with no N2: 10 ppm ethane, balance Ar at 3348 K and 1.08 atm (b) experiment with added N2: 10 ppm ethane 10.1% N2, balance Ar at 3348 K and 0.95 atm; the only additional CH removal path in the experiment with added N2 is the reaction between CH and N2.

-10 0 10 20 30 40 50 60

-1

0

1

2

3

4

5

CH

RO

P x

10-6

, mol

cm

-3 s

-1

Time [μs]

CH3+M=CH+H2+M CH+M=C+H+M C+CH2=CH+CH CH2+M=CH+H+M

-10 0 10 20 30 40 50 60

-1

0

1

2

3

4

CH

RO

P x

10-6

, mol

cm

-3 s

-1

Time [μs]

CH+N2=NCN+H CH3+M=CH+H2+M CH+M=C+H+M C+CH2=CH+CH CH2+M=CH+H+M

(b)

(a)

154

Figure 7.3 CH sensitivity at low-temperatures: 25.77 ppm acetic anhydride, balance Ar, no N2; initial reflected shock conditions: 2278 K and 1.35 atm; Sensitivity, S = (dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i.

0 50 100 150 200-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

1.5

1.8

CH

Sen

sitiv

ity

Time [μs]

CH2CO+M<=>CH2+CO+M CH2+H<=>CH+H2 2CH2<=>C2H2+2H H+CH<=>C+H2 CH+C2H2<=>C3H2+H 2CH2<=>C2H2+H2 CH3COOH<=>CH2CO+H2O CH3COOH<=>CH4+CO2

155

Figure 7.4 Rate coefficient data for CH2CO + M CH2 + CO + M: open squares, this work, 1.4 atm; solid black line, Frank et al. [162], 1.8 atm; solid gray line, Wagner and Zabel [161], 9.8 atm; dashed line, Friedrichs and Wagner [160], 0.45 atm.

0.3 0.4 0.5 0.6 0.7 0.8105

107

109

1011

k 37 [c

m3 m

ol-1 s

-1]

1000/T [K-1]

2500 K 1400 K

156

Figure 7.5 Low-temperature CH perturbation experiment: upper CH trace is obtained from the pyrolysis of 25.77 ppm acetic anhydride, balance Ar at 2278 K and 1.35 atm; lower CH trace is from a similar experiment at 2233 K and 1.35 atm, but with 10.16% added N2; addition of N2 causes the peak CH mole fraction to be perturbed by ~40%; the solid black and dashed lines are model simulations without and with N2, respectively; k7=3.88 x 1010 cm3 mol-1 s-1 yields a best-fit between the perturbed CH trace and the corresponding numerical simulation.

0 50 100 150 200-1

0

1

2

3

4

5

10.16% N2, perturbed CH

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

0% N2, unperturbed CH

2.0% abs.

157

Figure 7.6 CH rate of production (ROP) at low-temperatures: (a) experiment with no N2, 25.77 ppm acetic anhydride, balance Ar at 2278 K and 1.35 atm (b) experiment with added N2, 25.38 ppm acetic anhydride, 10.16% N2, balance Ar at 2233 K and 1.35 atm; the only additional CH removal path in the experiment with added N2 is the reaction between CH and N2.

0 50 100 150 200-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

CH

RO

P x

10-6

, mol

cm

-3 s

-1

TIme [μs]

CH2+H<=>CH+H2 CH+N2<=>NCN+H H+CH<=>C+H2 CH+C2H2<=>C3H2+H CH2+CH<=>C2H2+H

0 50 100 150 200

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

CH

RO

P x

10-6

, mol

cm

-3 s

-1

Time [μs]

CH2+H<=>CH+H2 H+CH<=>C+H2 CH+C2H2<=>C3H2+H CH2+CH<=>C2H2+H

(a)

(b)

158

-20 -10 0 10 20 30 40 50

0.0

0.5

1.0

1.5

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Experiment Model

Figure 7.7 Effect of the vibrational state of nitrogen on k7; experiment with helium in the reaction mixture: 9.95 ppm ethane, 5.72% He, 9.98% N2, balance Ar; T(frozen) = 2684 K, T(equilibrated) = 2607 K, P ~1.06 atm; temperature change, due to vibrational relaxation, over 50 μs is 2.4% or 65 K; the best-fit k7 is unchanged due to helium addition, which indicates that the vibrational state of N2 does not influence CH+N2 kinetics.

0.6% abs.

159

Figure 7.8 (a) Rate coefficients of reactions (-7a) and (-7b) for the same rate in the forward direction (b) Effect of the branching ratio of reaction (7) on CH: reaction mixture is 101 ppm ethane, balance N2; T(frozen) = 2548 K, T(equilibrated) = 2185 K, P ~0.67 atm; temperature drops from 2548 K to 2372 K due to vibrational relaxation in 250 μs.

0.2 0.3 0.4 0.5 0.61011

1012

1013

1014

2000 K

N+HCN CH+N2

k reve

rse [

cm3 m

ol-1 s

-1]

1000/T [K-1]

H+NCN CH+N2

3330 K

0 50 100 150 200 250

0.0

0.2

0.4

0.6

0.8

1.0

1.2 BR=0 BR=1

CH

Mol

e Fr

actio

n [p

pm]

Time [μs]

(a)

(b)

160

0 50 100 150-0.8

-0.4

0.0

0.4

0.8

1.2

Time [μs]

CH

Sen

sitiv

ity

CH3+M=CH+H2+M CH+N2=NCN+H CH2+H=CH+H2H+NCN=HCN+N

CH2+CH3<=>H+C2H4 CH3+M=CH2+H+M H+CH<=>C+H2

-50 0 50 100 150-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

CH

% A

bsor

ptio

n

Time [μs]

Experiment BR=1 BR=0

(a)

(b)

161

-50 0 50 100 150-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

CH

% A

bsor

ptio

n

Time [μs]

Experiment BR=1 1.5xk5a, BR=0

Figure 7.9 Example CH data, modeling, and sensitivity to infer the branching ratio for CH+N2: (a) CH absorption time-history (b) CH sensitivity, S = (dXCH/dki)(ki/XCH), where ki is the rate coefficient for reaction i (c) Effect of rate coefficient of CH3+M CH+H2+M; 101.39 ppm ethane, balance N2; T(frozen) = 2634 K, T(equilibrated) = 2249 K, P~0.64 atm; temperature drops from 2634 K to 2470 K due to vibrational relaxation in 175 μs; data is presented in % absorption to demonstrate the excellent sensitivity of the CH laser absorption diagnostic, minimum detectable absorption is less than 0.1%.

(c)

162

-50 0 50 100 150 200-0.2

0.0

0.2

0.4

0.6

0.8


CH

% A

bsor

ptio

n

Time [μs]

-100 -50 0 50 100 150 200-0.2

0.0

0.2

0.4

0.6

0.8

Time [μs]

CH

% A

bsor

ptio

n


Figure 7.10 Example CH data and modeling to infer the branching ratio for CH+N2 with helium in the reaction mixture: (a) 101.6 ppm ethane, 5.02% He, balance N2 ; T(frozen) = 2611 K, T(equilibrated) = 2241 K, P~0.57 atm; temperature drops from 2611 K to 2275 K due to vibrational relaxation in 200 μs (b) 101.09 ppm ethane, 10.02% He, balance N2; T(frozen) = 2671 K, T(equilibrated) = 2297 K, P~0.55 atm; temperature drops from 2671 K to 2302 K due to vibrational relaxation in 200 μs.

(a)

(b)

163

-40 -20 0 20 40 60 80 100-0.5

0.0

0.5

1.0

1.5

2.0 Experiment BR=1 BR=0

Time [μs]

CH

% A

bsor

ptio

n

sdsdsd

Figure 7.11 Example CH data and modeling to infer the branching ratio for CH+N2 at high-pressure; 102.69 ppm ethane, balance N2; T(frozen) = 2531 K, T(equilibrated) = 2172 K, P~2.3 atm; temperature drops from 2531 K to 2329 K due to vibrational relaxation in 100 μs.

164

0 50 100 150 200 250 300-0.9

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

NC

N S

ensi

tivity

Time [μs]

CH+N2=NCN+H H+NCN=HCN+N CH3+M=CH+H2+M CH2+H=CH+H2 2CH3<=>H+C2H5 CH2(S)+H2<=>CH3+H CH2+CH3<=>H+C2H4 CH3+M=CH2+H+M H+CH<=>C+H2

-100 -50 0 50 100 150 200 250 300-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2N

CN

% A

bsor

ptio

n

Time [μs]

(a)

(b)

165

0 50 100 150 200 250 300-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Time [μs]

NC

N R

OP

x 1

0-6, m

ol c

m-3 s

-1 CH+N2=NCN+H H+NCN=HCN+N CH2+NCN=CH2CN+N

Figure 7.12 Example NCN absorption data, sensitivity, and rate of production: (a) NCN absorption time-history, wavenumber is 30383.12 cm-1 (b) NCN sensitivity, S = (dXNCN/dki)(ki/XNCN), where ki is the rate coefficient for reaction i (c) NCN rate of production (ROP); 102.23 ppm ethane, balance N2; T(frozen) = 2587 K, T(equilibrated) = 2214 K, P~0.65 atm; temperature drops from 2587 K to 2380 K due to vibrational relaxation in 300 μs.

(c)

166

0 100 200 300 400

2500

2600

2700

2800

2900

3000

Tem

pera

ture

[K]

Time [μs]

-50 0 50 100 150 200 250 300-1

0

1

2

3 Experiment Model fit, k34 Model fit, 3k34 (normalized at 100 μs) Model fit, 3k34 (normalized at peak)

Nor

mal

ized

NC

N

Time [μs]

(a)

(b)

Fitting normalized NCN decay to k34

167

0 50 100 150 200 250 300-0.9

-0.6

-0.3

0.0

0.3

0.6

0.9

1.2

Time [μs]

NC

N S

ensi

tivity

CH+N2=NCN+H H+NCN=HCN+N CH3+M=CH+H2+M CH2+H=CH+H2 2CH3<=>H+C2H5 CH2+CH3<=>H+C2H4 CH2(S)+H2<=>CH3+H CH3+M=CH2+H+M H+CH<=>C+H2

Figure 7.13 Example experiment to infer k34: (a) Normalized NCN time-history, wavenumber is 30383.06 cm-1 (b) Temperature profile; test-gas is almost completely relaxed in 100 μs (c) NCN sensitivity, S = (dXNCN/dki)(ki/XNCN), where ki is the rate coefficient for reaction i; 105.3 ppm ethane, 9.8% He, balance N2; T(frozen) = 2930 K, T(equilibrated) = 2492 K, P~0.45 atm.

(c)

168

2250 2300 2350 2400 2450 2500 25500

25

50

75

100

125

150

Temperature [K]

k NC

N [c

m-1

atm

-1]

Figure 7.14 (a) Example experiment to infer the absorption coefficient of NCN; NCN absorption time-history at 30383.06 cm-1; kNCN was adjusted to match NCN decay (best-fit value: 58 cm-1 atm-1); 105.3 ppm ethane, 9.8% He, balance N2; T(frozen) = 2930 K, T(equilibrated) = 2492 K, P~0.45 atm (b) NCN absorption coefficient as a function of temperature; all data inferred with a branching ratio of 1 for reaction (7) in the kinetic mechanism; uncertainty in kNCN is estimated to be a factor of two.

-50 0 50 100 150 200 250 300-0.5

0.0

0.5

1.0

1.5

2.0 Experiment Fitting decay to kNCN

2kNCN

NC

N %

Abs

oprti

on

Time [μs]

Fitting absolute NCN decay to kNCN

(a)

(b)

169

Figure 7.15 Rate coefficient data for CH + N2 Products: open squares, this work data; dash-dotted black line, this work fit; solid squares, Dean et al. [48] data; solid black line, Dean et al. fit; dashed black line, Lindackers et al. [49]; solid gray line, Matsui et al. [51]; dash-dotted gray line, Blauwens et al. [50]; dotted line, Moskaleva and Lin [56] RRKM theory for k1b; dashed gray line, GRI-Mech 3.0 [111]; uncertainty limits at ~2100 K and ~3350 K are ~±35% and ~±25%, respectively.

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

1010

1011k C

H+N

2 [cm

3 mol

-1 s

-1]

1000/T [K-1]

4000K 1900K

170

0.36 0.38 0.40 0.42 0.44 0.461012

1013

1014

2220 K

k 34 [c

m3 m

ol-1 s

-1]

1000/T [K-1]

2700 K

Figure 7.16 Rate coefficient data for H + NCN HCN + N: open squares, this work; solid black line, Moskaleva and Lin [56] RRKM theory; dashed line, Glarborg et al. [153] estimate; uncertainty in current data estimated to be a factor of 2.

171

Chapter 8: Conclusions

8.1 Summary of Results

8.1.1 Toluene Oxidation

Toluene + OH Products

The reaction of hydroxyl [OH] radicals with toluene [C6H5CH3] was studied at

temperatures between 911 K and 1389 K behind reflected shock waves at pressures of

~2.25 atm. OH radicals were generated by rapid thermal decomposition of shock-

heated tert-butyl hydroperoxide [(CH3)3-CO-OH], and monitored by narrow-linewidth

ring-dye laser absorption of the well-characterized R1(5) line of the OH A-X (0, 0)

band near 306.7 nm. OH time-histories were modeled using a comprehensive toluene

oxidation mechanism. Rate coefficients for the reaction of C6H5CH3 with OH were

extracted by matching modeled and measured OH concentration time-histories in the

reflected shock region. Detailed error analyses yielded an uncertainty estimate of

~±30% at 1115 K for the rate coefficient of this reaction. The current high-temperature

data were fit with the lower temperature measurements of Tully et al. [13] to the

following two-parameter form, applicable over 570 – 1389 K,

k1 = 1.62x1013 x exp (-1394 / T [K]), [cm3 mol-1s-1]

The reaction between OH radicals and acetone [CH3COCH3] was one of the

secondary reactions encountered in the toluene + OH experiments. Direct high-

temperature measurements of this reaction were carried out at temperatures ranging

from 982 K to 1300 K in reflected shock wave experiments at an average total

pressure of 1.65 atm. Uncertainty limits were estimated to be ~±25% at 1159 K. A

two-parameter fit of the current data yields the following rate expression,

172

k6= 2.95x1013 x exp (-2297 / T [K]), [cm3 mol-1s-1]

Toluene Ignition Chemistry

Ignition delay times and OH concentration profiles were measured in

toluene/O2/Ar mixtures behind reflected shock waves. Initial reflected shock

conditions spanned 1400 - 2000 K and 1.5 - 5.0 atm, with equivalence ratios of 0.5 -

1.875 and toluene concentrations of 0.025 - 0.5%. OH time-histories were monitored

using narrow-linewidth ring-dye laser absorption of the well-characterized R1 (5) line

of the OH A-X (0, 0) band at 306.7 nm. Ignition time data was extracted from the OH

traces and was found to compare very well with measurements using sidewall

pressure. The results of this study were compared to three detailed kinetic models: Pitz

et al. [6], Dagaut et al. [7] and Lindstedt et al. [5]. The ability of the mechanisms to

predict the measured ignition time data and OH concentration profiles was analyzed.

Suggestions to improve model performance were made, and key reactions that need to

be studied further were identified.

8.1.2 Formaldehyde Chemistry

CH2O + OH Products

The reaction of hydroxyl [OH] radicals with formaldehyde [CH2O] was

studied at temperatures ranging from 934 K to 1670 K behind reflected shock waves at

an average total pressure of 1.6 atm. OH radicals were produced by shock-heating tert-

butyl hydroperoxide [(CH3)3-CO-OH], while 1,3,5 trioxane [(CH2O)3] was used in the

pre-shock mixtures to generate reproducible levels of CH2O. OH concentration time-

histories were inferred from laser absorption using the well-characterized R1(5) line of

the OH A-X (0, 0) band near 306.7 nm. Detailed error analyses, taking into account

both experimental and mechanism-induced contributions, yielded uncertainty

estimates of ~±25% at 1595 K and ~±15% at 1229 K for the rate of the reaction

between CH2O and OH. These uncertainties are substantially lower than the factor of

two uncertainty currently used for this reaction at high temperatures. The rate

coefficients were fit with the recent low-temperature measurements of Sivakumaran et

173

al. [131] to the three-parameter form shown below; this fit reconciles experimental

data on the title reaction at low, intermediate and high temperatures (200 - 1670 K).

k2 = 7.82 x 107 T 1.63 exp (531 / T [K] ), [cm3 mol-1s-1]

The reaction of OH with CH2O was also studied using quantum chemical methods at

the CCSD(T) level of theory using the 6-311++G(d,p) basis set. The transition state

for the H-atom metathesis reaction was located, and reaction rate coefficients were

calculated. Reasonable agreement with the experimental measurements was obtained.

The decomposition rate of tert-butyl hydroperoxide to a tert-butoxy radical and

an OH radical was measured at an average pressure of ~2.3 atm, and fit to the

following form,

k11 = 2.50 x 1015 exp (-21640 / T [K] ), [ s-1]

Uncertainty limits for k11 were estimated to be ~±25% in the 900 – 1000 K

temperature range, a marked reduction from the factor of 2-3 uncertainty currently

recommended for this reaction in the literature.

CH2O + Ar Products

The two-channel thermal decomposition of formaldehyde [CH2O], (3a) CH2O

+ Ar HCO + H + Ar, and (3b) CH2O + Ar H2 + CO + Ar, was studied in shock

tube experiments in the 2258 – 2687 K temperature range, at an average total pressure

of 1.6 atm. OH radicals, generated on shock heating trioxane-O2-Ar mixtures, were

monitored behind the reflected shock front using narrow-linewidth laser absorption.

1,3,5 trioxane [C3H6O3] was used as the CH2O precursor in the current experiments.

H-atoms formed upon CH2O and HCO decomposition rapidly react with O2 to

produce OH via H + O2 O + OH. The recorded OH time-histories show dominant

sensitivity to the formaldehyde decomposition pathways. The second-order reaction

rate coefficients were inferred by matching measured and modeled OH profiles behind

the reflected shock. Two-parameter fits for k3a and k3b, applicable in this temperature

range, are,

174

k3a= 5.85x1014 exp (-32100 / T [K]), [cm3 mol-1s-1]

k3b= 4.64x1014 exp (-28700 / T [K]), [cm3 mol-1s-1]

Uncertainty limits for k3a and k3b were estimated to be ~±25%.

CH2O + O2 Products

The reaction between CH2O and O2, (4) CH2O + O2 HO2 + HCO, was

investigated by shock-heating trioxane/O2(~10%)/Ar mixtures. The rapid thermal

decomposition of HCO and HO2 generate H-atoms that react with O2 to produce OH.

Rate coefficients were, as in the CH2O decomposition experiments, inferred by

matching measured and modeled OH time-histories behind the reflected shock, under

conditions where interference from secondary chemistry is minimal. A two-parameter,

least-squares fit of the current data, valid over the 1480 – 2367 K temperature range,

yields the following rate expression,

k4= 5.08x1014 exp (-23300 / T [K]), [cm3 mol-1s-1]

The uncertainty in k4 was estimated to be ~±35%. Simple transition state theory was

used to analyze the A-factor and Ea in terms of the entropy and enthalpy of activation.

Ab initio calculations of k4 were performed using the Gaussian suite of

programs. Geometry optimization and frequency calculations were carried out at the

B3LYP/6-311++g** level. Single point energy calculations were done at CCSD(T)/6-

311++g** for the previously optimized geometries. Transition state theory was used

to determine k4 – the calculated rate coefficients are in excellent agreement with the

current experimental data.

8.1.3 Methyl Decomposition

The two-channel thermal decomposition of methyl radicals in argon, (5a) CH3

+ Ar CH + H2 + Ar and (5b) CH3 + Ar CH2 + H + Ar, was investigated in shock

tube experiments over the 2253 – 3527 K temperature range, at pressures between 0.7

and 4.2 atm. CH was monitored by cw, narrow-linewidth laser absorption at 431.1 nm.

The collision-broadening coefficient for CH in argon, 2γCH-Ar, was measured via

175

repeated single-frequency experiments in the ethane pyrolysis system behind reflected

shock waves. The measured 2γCH-Ar value and updated spectroscopic and molecular

parameters were used to calculate the CH absorption coefficient at 431.1311 nm

(23194.80 cm-1), which was then used to convert raw traces of fractional transmission

to quantitative CH concentration time-histories in the methyl decomposition

experiments. The rate coefficient of reaction (5a) was measured by monitoring CH

radicals generated upon shock-heating highly dilute mixtures of ethane, C2H6, or

methyl iodide, CH3I, in an argon bath. A detailed chemical kinetic mechanism was

used to model the measured CH time-histories. Within experimental uncertainty and

scatter, no pressure dependence could be discerned in the rate coefficient of reaction

(5a) in the 0.7-4.2 atm pressure range. A least-squares, two-parameter fit of the current

measurements, applicable between 2706 K and 3527 K, is,

k5a = 3.09 x 1015 exp (-40700/T [K]), [cm3 mol-1 s-1]

The rate coefficient of reaction (5b) was determined by shock-heating dilute

mixtures of C2H6 or CH3I and excess O2 in argon. During the course of reaction, OH

radicals were monitored using the well-characterized R1(5) line of the OH A-X (0,0)

band at 306.7 nm. H-atoms generated via reaction (5b) rapidly react with O2, which is

present in excess, forming OH. The OH traces are primarily sensitive to reaction (5b),

reaction (8): H + O2 OH + O, and reaction (30): CH3 + O2 Products, where the

rate coefficients of reactions (8) and (30) are relatively well-established. No pressure

dependence could be discerned for reaction (5b) between 1.1 and 3.9 atm. A two-

parameter, least-squares fit of the current data, valid over the 2253 – 2975 K

temperature range, yields the following rate expression,

k5b = 2.24 x 1015 exp (-41600/T [K]), [cm3 mol-1 s-1]

Uncertainty limits for k5a and k5b were estimated to be ~±25% and ~±50%,

respectively. Theoretical calculations carried out using a master equation-RRKM

analysis fit the measurements reasonably well.

176

8.1.4 Prompt-NO Initiation

The reaction between CH and N2, (7) CH + N2 Products, was studied in

shock tube experiments using CH and NCN laser absorption. CH was monitored by

continuous-wave, narrow-linewidth laser absorption at 431.1 nm. The overall rate

coefficient of the CH+N2 reaction was measured between 1943 K and 3543 K, in the

0.9-1.4 atm pressure range, using a CH perturbation approach. CH profiles recorded

upon shock-heating dilute mixtures of ethane in argon and acetic anhydride in argon

were perturbed by the addition of nitrogen. The perturbation in the CH concentration

is principally due to the reaction between CH and N2. Rate coefficients for the overall

reaction were inferred by kinetically modeling the perturbed CH profiles. A least-

squares, two-parameter fit of the current overall rate coefficient measurements is,

k7 = 6.03 x 1012 exp (-11150 / T [K]), [cm3 mol-1 s-1]

The uncertainty in k7 was estimated to be ~±25% and ~±35% at ~3350 K and ~2100

K, respectively.

At high temperatures, there are two possible product channels for the reaction

between CH and N2, (7a) CH + N2 HCN + N, and (7b) CH + N2 H + NCN. The

branching ratio of reaction (7), k7b/(k7b+k7a), was determined in the 2228 – 2905 K

temperature range by CH laser absorption in experiments in a nitrogen bath. The

collision-broadening coefficient for CH in nitrogen, 2γCH-N2, was measured via

repeated single-frequency experiments in the ethane pyrolysis system behind reflected

shock waves, and used to calculate the absorption coefficient of CH. The current CH

measurements are consistent with a branching ratio of 1, and establish NCN and H as

the primary products of the CH+N2 reaction. A detailed and systematic uncertainty

analysis, taking into account experimental and mechanism-induced contributions,

yields a conservative lower bound of 0.70 for the branching ratio. NCN was also

detected for the first time by continuous-wave, narrow-linewidth laser absorption at

329.13 nm. The measured NCN time-histories were used to infer the rate coefficient of

the reaction between H and NCN, (34) H + NCN HCN + N, and to estimate an

absorption coefficient for the NCN radical.

177

8.1.5 Archival Publications

The work described in this thesis has been published in the following journals,

• Vasudevan, V.; Davidson, D.F.; Hanson, R.K., “Shock Tube Measurements of

Toluene Ignition Times and OH Concentration Time Histories”, Proc.

Combust. Inst. 2005, 30, 1155.

• Vasudevan, V.; Davidson, D.F.; Hanson, R.K., “Direct Measurements of the

Reaction OH + CH2O HCO + H2O at High Temperatures”, Intl. J. Chem.

Kinet. 2005, 37, 98.

• Vasudevan, V.; Davidson, D.F.; Hanson, R.K., “High Temperature

Measurements of the Reactions of OH with Toluene and Acetone”, J. Phys.

Chem. A 2005, 109, 3352.

• Vasudevan, V.; Davidson, D.F.; Hanson, R.K.; Bowman, C.T.; Golden, D.M.,

“High-Temperature Measurements of the Rates of the Reactions CH2O + Ar

Products and CH2O + O2 Products”, Proc. Combust. Inst. 2007, 31, 175.

• Vasudevan, V., Hanson, R.K.; Golden, D.M.; Bowman, C.T.; Davidson, D.F.,

“High-Temperature Shock Tube Measurements of Methyl Radical

Decomposition”, J. Phys. Chem. A 2007, 111, 4062.

• Vasudevan, V., Hanson, R.K.; Bowman, C.T.; Golden, D.M.; Davidson, D.F.,

“Shock Tube Study of CH with N2: Overall Rate and Branching Ratio”, J.

Phys. Chem. A 2007 (in press).

8.2 Recommendations for Future Work

8.2.1 NCN Kinetics

In the current research, it was established that NCN is an important precursor

to prompt-NO. The kinetics of this short-lived intermediate is very poorly

characterized. Theoretical calculations of NCN reactions that are expected to be

important in combustion have recently been reported in the literature [168-171]. It is

thought that the reaction between H and NCN, reaction (34), is the primary removal

path for NCN in hydrocarbon flames (see Chapter 7 for measurements of k34). But

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high-temperature experimental measurements of other possible NCN removal

reactions are as yet unavailable in the literature. The sensitive 329.1 nm NCN laser

absorption diagnostic developed in this work could be used to study NCN kinetics at

high temperatures in a shock tube. The following reactions merit study,

(46) NCN + O Products

(47) NCN + NO Products

(48) NCN + O2 Products

An NCN perturbation approach (similar to the CH perturbation approach used

in the current work, see Chapter 7) could potentially be used to infer rate coefficients

for the above reactions. NCN profiles recorded upon shock heating dilute mixtures of

ethane (or acetic anhydride) in nitrogen can be perturbed by the addition of O

(generated by the pyrolysis of N2O) or NO or O2, and the perturbation can be related

to the NCN removal rate coefficient being measured.

8.2.2 Decomposition and Oxidation of Oxygenates

There is much interest in the kinetics of oxygenates like dimethyl ether (DME)

because of their ability to serve as fuel-additives that reduce soot and particulate

formation in diesel combustion [172]. The kinetic strategies developed in this thesis

can be used to study several important elementary chemical reactions involving

oxygenates. For example, the decomposition of DME is known to occur via reaction

(49),

(49) CH3OCH3 + M CH3 + CH3O + M

At elevated temperatures the CH3O rapidly decomposes to form CH2O and H,

(49a) CH3O + M CH2O + H + M

If excess oxygen is present in the reaction system, the H-atoms rapidly react with O2

to form OH via the H+O2 chain branching reaction. Experiments can be designed so

that the measured OH profiles are sensitive primarily to DME decomposition. This

approach is identical to that used to study formaldehyde decomposition in Chapter 5.

In Chapters 3 and 4, we described the use of TBHP as a convenient and

reliable OH-precursor. TBHP decomposition was studied and used to measure the rate

179

coefficients of the reactions of OH with toluene, formaldehyde, and acetone. A similar

experimental approach could be used to study the reaction of OH with various

oxygenates, for example: DME + OH, ethanol + OH etc. While TBHP is a reliable and

convenient OH source, it cannot be used at reflected shock temperature greater than

~1650 K. This is because at these conditions TBHP starts to decompose behind the

incident shock, making data analysis and reduction complicated. Therefore, other

high-temperature OH precursors need to be investigated; these include methanol

[CH3OH] and hydroxylamine [NH2OH], both of which rapidly dissociate to form OH

at elevated temperatures [189].

8.2.3 Peroxy Chemistry

Reactions involving hydroperoxyl (HO2) and peroxyl (RO2) radicals play an

important role in the intermediate temperature (800-1200 K) oxidation of alkane-based

hydrocarbon fuels. Two of these reactions are,

(50) C2H5 + O2 HO2 + C2H4

(51) C3H7 + O2 HO2 + C3H6

Reactions (50) and (51) have been studied at temperatures lower than ~700 K.

However, there is large scatter in the reported data [11], which makes a reliable

extrapolation to higher temperatures difficult and uncertain. The rate coefficients of

these reactions could be measured via the simultaneous UV detection of OH (at 306.7

nm; see Chapter 2 for a description of the OH diagnostic) and HO2 (at 215 nm). Light

at 215 nm for HO2 detection can be generated by doubling the 431 nm output of the

CH diagnostic (see Chapter 2) in an external-cavity wavetrain doubler. Kinetic

modeling shows that HO2 produced upon shock-heating 50 ppm C2H5 (generated

using a suitable ethyl precursor) and 1% O2 dilute in argon to 900 K and 1 atm is

sensitive primarily to reactions (50) and (52),

(52) C2H5 + HO2 C2H5O + OH

Measuring OH, in conjunction with HO2, would allow us to constrain the rate

coefficients of these reactions, facilitating a relatively direct measurement of both k50

and k52. Similar experiments can be performed to study reaction (51).

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HO2 and OH laser absorption can also be employed to study other important

hydroperoxyl radical reactions, such as,

(53) H2O2 + M 2OH + M

(54) OH + H2O2 HO2 + H2O

(55) HO2 + HO2 H2O2 + O2

The rate coefficient for reaction 53, k53, can be determined by shock heating mixtures

of hydrogen peroxide in argon and monitoring OH radicals. By using very dilute

mixtures of H2O2 (< 100ppm) in Ar, interfering chemistry can almost completely be

suppressed. Once k53 is known, OH measurements at a higher H2O2 concentration

(~1000 ppm) allow for an accurate determination of the rate coefficient of reaction

(54). The self reaction of HO2 radicals, reaction (55), can be measured by shock

heating chlorine atoms (generated via 308 nm Cl2 photolysis), O2 and methanol (to

generate HO2) dilute in argon, and monitoring HO2 absorption. Developing other

diagnostics, such as H-atom ARAS would allow for the measurement of other

important reactions in the hydroperoxyl system such as,

(56) H + H2O2 HO2 + H2

A better understanding of HO2 radical reactions is an important step towards

understanding low-temperature hydrocarbon oxidation where RO2 and HO2 chemistry

plays a crucial role.

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Appendix A: OH Time-Histories during Toluene Oxidation

A.1 Introduction In this appendix, we describe ignition time measurements in toluene/O2/Ar

mixtures behind reflected shock waves. A limited number of shock tube ignition time

and full modeling [5-10] studies of toluene have been reported in the literature. Of

importance to the present work are the two experimental studies by Burcat and

coworkers [9, 10] who measured ignition delay times of toluene-oxygen-argon

mixtures in reflected shock wave experiments, the experimental and modeling study

by Pitz et al. [6] who present shock tube ignition time data for toluene over a limited

range of conditions and a comparison of these data with predictions by a detailed

chemical kinetic model they developed, and the reaction mechanisms of Lindstedt et

al. [5] and Dagaut et al. [7]. Among the experimental studies, there is wide variation in

the reported ignition times.

The objectives of the present work are twofold: 1) to collect ignition delay time

data for the oxidation of toluene over a wide range of conditions and compare these

new data with those reported earlier and with calculations based on detailed kinetic

models, and 2) to compare OH concentration profiles, measured using narrow-

linewidth ring-dye laser absorption spectroscopy, with detailed model predictions.

This latter objective is particularly important as the aforementioned models have not

been validated using OH radical profiles as kinetic targets, simply because these data

have not been available for aromatics like toluene.

OH and ignition time measurements were made over the following ranges –

temperature: 1400-2000 K, pressure: 1.5-5.0 atm, equivalence ratio: 0.5-1.875, and

C6H5CH3 concentration: 0.025 - 0.5%. Sensitivity and contribution factor analyses

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were carried out to identify reactions to which the OH profile is most sensitive.

Suggestions have been made to improve agreement between model and experiment,

and reactions that need to be studied further have been identified.

A.2 Experimental Set-up All experimental measurements were carried out in the reflected shock region

of a high-purity shock tube with inner diameter of 15.24 cm (see Chapter 2). Research

grade argon and oxygen (99.999%) were supplied by Praxair Inc; research grade

toluene (>99.5%) was supplied by Aldrich Chemical Co. Pre-shock reaction mixtures

were prepared as described in Chapter 2. We have developed a number of techniques

to facilitate accurate mixture preparation for fuels that are in the liquid phase at room

temperature and these are discussed by Horning [173, 174]. OH measurements were

performed using the diagnostic described in Chapter 2.

Off-line measurements did not reveal any interference absorption, unlike that

observed in earlier studies on iso-octane [175] and JP10 [176, 177]. Figure A.1

presents a typical OH trace. There are numerous ways of defining ignition delay time.

In the present work, ignition time was defined as the time to 50% of the peak OH

concentration, with zero time being defined as the arrival of the reflected shock front

at the sidewall measurement location. This definition was found to correspond very

well with ignition delay defined as the time to the first rise in pressure after arrival of

the reflected shock front [10]. It is estimated that the uncertainty in the measured

ignition times is ~±10%, primarily due to a ~±1% uncertainty in the reflected shock

temperature.

In-situ measurements of toluene concentration at 3.39 μm [99, 180] were

performed and indicate a toluene loss of < 10% due to wall adsorption and

condensation, see Chapter 3.

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A.3 Results and Discussion

A.3.1 Ignition Times

Ignition times were measured over a wide range of temperatures, pressures,

fuel concentrations and stoichiometries and the results are summarized in Table A.1.

Ignition times were found to scale with pressure as P-0.69 (from a regression analysis of

all the present data), and this power law dependence has been applied to normalize our

data to P = 1 atm. The variation of ignition time with temperature and fuel

concentration are presented in Figures A.2 and A.3 along with modeling predictions of

Pitz et al. [6], Lindstedt et al. [5] and Dagaut et al. [7].

As is evident from Figure A.2, all the models predict the ignition time to

within a factor of two of the experimentally measured value for the 1000 ppm toluene

case. At low-to-moderate temperatures, both the Pitz et al. and Dagaut et al. models

agree well with experiment, while at higher temperatures, the Dagaut et al. model

follows the measured ignition time most closely. The activation energy (57.6

kcal/mol), for the conditions of Figure A.2, is predicted relatively well by all three

models.

Experiments indicate that the dependence of ignition time on equivalence ratio

follows a simple power law (figure not shown). The detailed models, on the other

hand, predict a roll-off in the ignition time at high equivalence ratios (φ=1.5). For still

richer mixtures (φ=1.875), the agreement between the measured and simulated traces

was poor; mechanistic predictions at high equivalence ratios is an area that requires

further study.

The dependence of ignition time on fuel concentration (see Figure A.3) allows

some interesting observations. The ignition time markedly falls off at high fuel

concentrations; this fall-off is also evident in the higher concentration data of Burcat et

al. [10]. The agreement in this trend between the current study and Burcat et al. [10] is

excellent. The marked fall-off in ignition time with increased concentration was also

observed in a recent study of iso-octane carried out in our laboratory [175]. To

account for this dependence of tign on the fuel (and oxygen) concentration, an

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exponential form for XO2 is needed instead of a simple power law to correlate the

ignition time data over the full concentration range. All three mechanisms correctly

predict this fall-off. The Lindstedt et al. profile best resembles the experimental trace,

though the predicted ignition delay is consistently lower. The Pitz et al. and Dagaut et

al. models do a good job at low concentrations, but at higher fuel concentrations,

longer ignition delays than measured are predicted.

The ignition time data of the present study was correlated into the form used

by Davidson et al. [175],

)/55240exp()92.41exp(1015.4 08.1694.052

RTXPxt Oign φ−= −− Eq. 1

where: tign is in μs, P is in atm, R is in cal/mol/K, T is in K. The computed activation

energy of 55.24 kcal/mol (see Equation 1) agrees very well with the activation energy

reported by Burcat et al. [10], 55.09 kcal/mol. As pointed out earlier, our low fuel

concentration data are consistent with the high concentration measurements of Burcat

et al. [10]. This suggests the possibility of developing a global correlation applicable

over a much wider range of conditions, by fitting data from the current study with

Burcat et al. [10]. Such a global regression analysis leads to the following correlation

that can be applied over the ranges: 1339 – 2000 K, 1.5 – 7.0 atm, equivalence ratio:

0.33-1.5 and C6H5CH3 concentration: 0.025% - 1.5%,

)/53112exp()16.3exp(1017.2 61.063.057.0622

RTXXPxt OOign φ−−− −= Eq. 2

Ignition times from the four shock tube studies, normalized using Equation 2

to 1% C6H5CH3, 9% O2 and 1 atm are shown in Figure A.4. Data from this study and

Burcat et al. [10] correlate well, while the ignition time data of Pitz et al. [6] and the

older Burcat et al. [9] data are shorter and show greater scatter. Possible reasons for

this disagreement include: (1) different ignition delay time definition (10% of max OH

emission) used in the Pitz et al. [6] study, and (2) possible uncertainties in reflected

shock temperature due to the small diameter (25 mm) of the shock tube used by Burcat

et al. [9].

185

A.3.2 OH Concentration Profiles

OH concentration profiles were measured over a wide range of conditions and

the results are summarized in Table A.1. An example OH concentration profile is

presented in Figure A.1. The trace may be divided into three distinct regions: region 1

- OH concentration increases rapidly due to toluene decomposition and at moderate-

to-low temperatures, evens out to form an intermediate plateau; region 2 - OH

concentration rises due to chain branching and propagation; and region 3 – net rate of

production of OH is close to zero. At high fuel concentrations (say 0.5% toluene), the

plateau in region 1 is not as well developed as the one shown in Figure A.1; instead,

the profile slopes gently in the upward direction before showing the steep rise

characteristic of region 2. On the other hand, for rich mixtures (say φ=1.5), the trace

slopes in the downward direction before transitioning to region 2. Details of the

structure of the OH concentration profiles are given in Table A.1. XOH (1st plateau)

and XOH (peak) correspond to the mole fractions of OH at the first plateau (or the

maximum mole fraction when the plateau is not properly defined) and peak

respectively. The ignition delay time, tign , is the time to XOH (50% peak) and t (first

plateau) is the time to XOH (1st plateau) (see Figure A.1).

A sample OH concentration profile is shown in Figure A.5 along with model

predictions for a stoichiometric 250 ppm C6H5CH3 mixture. The Pitz et al. model does

a good job of predicting the first OH plateau, while the Dagaut et al. model does an

excellent job of qualitatively matching the overall profile. The Lindstedt et al. model

fails to capture the first OH plateau, though it does a reasonable job of predicting the

ignition delay.

Sensitivity analysis using the Pitz et al. and Dagaut et al. models reveal that, as

expected, the OH concentration is most sensitive to the branching reaction: H + O2

O + OH. The H+O2 chain branching reaction has been extensively studied over the

years and recent publications [see, for example, Ref. 92] estimate an uncertainty of

only 9% over the 1336 – 3370 K temperature range. Even though extensive efforts

have been made to refine this critical rate coefficient, some mechanisms continue to

use an older rate recommended in 1992 by Baulch et al. [178]. This rate varies by over

186

40% over portions of the above temperature range from the Yu et al. [92] value

published in 1994. The Pitz et al. model uses a rate coefficient that is a slight variation

(by ~3-10%) of the Baulch et al. [178] value. Recent TST calculations [179] support

the Yu et al. and GRI-Mech [111] rates for the H+O2 chain branching reaction. Hence

we elected to update the Pitz et al. mechanism with the rate coefficient for this

reaction in GRI-Mech 3.0. The OH trace for this modified Pitz et al. mechanism is

also shown in Figure A.5. Agreement between model and experiment is now much

better, although the modified model underpredicts both OH plateau concentrations

slightly. Figure A.6 presents a comparison of measured OH time-histories, with traces

modeled using the modified Pitz et al. mechanism, for a series of four shocks spanning

the temperature range 1600 – 1800 K. Agreement is excellent at moderate-to-high

temperatures, while at low temperatures, the modeled OH concentrations lag the

measured time-histories.

Rate of production (ROP) analysis with the Pitz et al. model shows that OH

scavenging by benzaldehyde is primarily responsible for the formation of the first OH

plateau. A recently updated version of the Pitz et al. model [182], with new

decomposition channels for benzyl and benzaldehyde, fails to capture this feature (see

Figure A.5, labeled as Pitz (2003)). In this model, C6H5CHO is formed mainly by the

reaction of benzyl and O, and is removed by thermal decomposition to C6H5CO and

H. The removal appears to be occurring too fast for OH to be scavenged and this

prevents the early-time (75-275 μs) plateau from being formed. The Dagaut et al.

model, on the other hand, points to OH removal by reaction with cyclopentadienyl

(C5H5). Improved measurements of the following reactions at high temperatures would

help resolve this issue: C6H5CHO C6H5CO + H, C5H5 + OH Products and

C6H5CHO + OH C6H5CO + H2O.

Measured and modeled OH concentration profiles at a higher initial fuel

concentration (1000 ppm, φ=1) are presented in Figure A.7. All three models follow

the measured profile reasonably well, though quantitatively, there exist differences

between model and experiment. It is to be noted that at all the equivalence ratios

studied at high fuel concentrations, all the models under-predict the first OH plateau.

187

Incorporating the GRI-Mech rate for the H+O2 chain branching reaction in the Pitz et

al. model causes no significant change in the level of the first OH plateau. The

modeled OH trace, however, shifts to the right resulting in a much longer ignition

delay than that measured (see Figure A.7).

Sensitivity analysis using the modified Pitz et al. model indicates that at early

times, in addition to the H+O2 chain branching reaction, OH is sensitive to the

following reactions (in decreasing order of sensitivity),

(9) C6H5CH3 + H C6H5CH2 + H2

(1) C6H5CH3 + OH Products

(10a) C6H5CH3 C6H5CH2 + H

(10b) C6H5CH3 C6H5 + CH3

Modeling early-time OH and the subsequent rise could be improved by adjusting the

rates of these reactions within their uncertainty limits. The reaction between toluene

and OH (reaction 1) has almost exclusively been studied only at temperatures lower

than ~1050 K [11]. Investigations at higher temperatures are warranted, especially

because OH + RH reactions have been shown to exhibit non-Arrhenius behavior

[183]; high-temperature measurements of k1 are described in Chapter 3 of this thesis.

Reaction (10b) (in the above list), the smaller of the two toluene decomposition

channels, though not as sensitive to OH concentration levels as reactions (9), (1),

(10a), is nonetheless vital for accurately modeling the ignition delay. The longer

ignition delay predicted by the modified Pitz et al. mechanism could (see Figure A.7),

in part, be attributed to the uncertainty in the rate of this reaction, which is

approximately a factor of 5 [181]. We note that increasing the rate coefficient for this

reaction by a factor of three in the modified Pitz et al. model results in improved

agreement with the measured trace; recent measurements of reaction (10b) are

consistent with this observation [95a].

A.4 Early-Time OH Chemistry Figure A.8 presents a comparison between the early-time OH chemistry in n-

heptane (a linear n-alkane), iso-octane (a branched chain alkane), and toluene (an

188

aromatic). Iso-octane shows pronounced OH radical scavenging at early times [175].

This is attributed to the rapid removal of OH by iso-butene, which is formed via iso-

octane oxidation. For n-heptane, the OH trace shows an initial steep rise up to about

10 μs, followed by an intermediate region where the OH concentration grows more

slowly [174]. OH scavenging similar to that seen with iso-octane is not apparent, and

this results in generally shorter ignition times for n-heptane than iso-octane. In the

case of toluene, some OH is formed at early times, but to a lesser degree, and also

forms a plateau under certain conditions; longer ignition times, than either n-heptane

or iso-octane, are a result. Similar OH measurements were recently performed during

the oxidation of xylene, gasoline and surrogate-fuel mixtures and are described

elsewhere [188]. These measurements of OH concentration profiles in different fuels

clearly provide critical kinetic validation targets for the important pool of small

radicals, and these targets are significantly different for each fuel. Refinement of

kinetic models based on these measurements, as well as direct studies of targeted

secondary reactions, should lead to improved ignition time predictions that are linked

to the actual small radical pool populations and chemistry, rather than simply to

parametric fits of ignition times.

A.5 Recommendations & Suggestions for Future

Work The major recommendations of the current toluene oxidation study are

summarized below,

1) The optimized GRI rate [111] for H+O2 OH + O and the recently measured

)298( KHOHfΔ [69] should be used in kinetic models for toluene oxidation – this

leads to much better agreement between the modeled and measured OH traces for

dilute mixtures.

2) Agreement between model and experiment is greatly improved if the rate used for

C6H5CH3 C6H5 + CH3 in the Pitz et al. mechanism is increased by a factor of

three (see Figure A.7). A kinetic study of toluene decomposition, via laser

189

absorption at 266 nm, was recently performed in our laboratory by Oehlschlaeger

et al. [95a]; the new rate measurements are consistent with the conclusions of the

present study.

3) The reaction C6H5CH3 + OH Products is vital to accurately modeling early-time

OH plateau levels during toluene ignition. To our knowledge, there have been no

direct measurements of the rate of this reaction at elevated temperatures (> 1050

K); high-temperature studies of this critical reaction are needed. Kinetic

measurements of the rate coefficient of the reaction between toluene and OH are

described in Chapter 3.

4) There is some difference between the Pitz et al. and Dagaut et al. models over the

reactions responsible for OH removal at early times. Further studies of important

cyclopentadiene (CPD) and benzaldehyde reactions like C5H5 + OH Products,

C6H5CHO Products and C6H5CHO + OH Products should help resolve this

issue and enable models to accurately capture the early-time OH plateau observed

in experiment.

The ignition time data and OH time-histories collected in this work have helped

identify key reactions that need to be studied further. Monitoring the time-histories of

other important species would provide additional kinetic targets to further refine the

model. To this end, experiments with cw laser absorption diagnostics for CH3 and

C6H5CH2, in addition to OH, are presently planned.

A.6 Conclusions An ignition time and OH concentration time-histories database for toluene

ignition has been generated. These new data were correlated with earlier work by

Burcat et al. [10], and a global correlation for ignition delay time applicable over a

wide experimental range has been proposed. The ability of three toluene oxidation

mechanisms to predict ignition times and OH concentration time-histories was

analyzed. In general, the mechanisms successfully predicted ignition delay to within a

factor of two of the experiment, though some trends, such as the roll-off behavior at

high fuel concentrations, were not properly captured. Characteristic features of the

190

OH concentration profiles were reproduced well by the models, especially for very

dilute mixtures. But, the mechanisms were unable to capture the early-time OH

plateau at higher fuel concentrations. Suggestions to improve model performance

have been made and key reactions that need to be studied further have been identified.

The data presented in this study provides critical kinetic targets to evaluate model

performance, and should prove useful for researchers engaged in kinetic model

development of hydrocarbon oxidation.

191

Table A.1: Summary of toluene OH absorption data T (K)

P (atm)

k (atm-1 cm-1)

t (first plateau) (μs)

XOH (1st plateau) (ppm)

tign (μs)

XOH (peak) (ppm)

0.025% C6H5CH3 , 0.225% O2, balance Ar 1607 2.03 142 121 12 949 87 1648 2.03 136 104 15 608 96 1700 1.89 132 64 23 369 109 1783 1.84 117 24 36 136 118

0.1% C6H5CH3 , 0.9% O2, balance Ar 1564 1.95 145 127 31 1068 324 1586 1.90 150 97 32 702 377 1614 1.80 146 64 40 389 388 1689 1.79 130 43 56 209 460 1527 4.54 110 a 32 798 306 1541 4.43 110 a 36 651 318 1697 4.26 95 37 53 150 421

0.1% C6H5CH3 , 1.8% O2, balance Ar 1458 1.99 172 a 23 1123 424 1504 1.98 161 230 26 725 448 1540 1.96 148 110 31 501 455 1550 1.94 156 54 31 386 501 1666 1.92 135 28 65 153 591

0.1% C6H5CH3 , 0.6% O2, balance Ar 1616 1.82 140 100 35 1090 162 1627 1.92 136 47 36 922 201 1714 1.77 127 26 55 384 259 1847 1.75 110 12 83 143 298

0.5% C6H5CH3 , 4.5% O2, balance Ar 1434 2.03 174 a 75 1070 sat.b

1454 1.66 180 a 87 750 sat. 1618 1.88 138 a 177 130 sat. 1635 1.83 137 a 182 107 sat.

a plateau not well defined. b sat. – saturated signal; transmission ~ 0

192

-100 0 100 200 300 400 500 600

0

100

200

300

400

500O

H M

ole

Frac

tion

[ppm

]

Time [μs]

Reflected shockarrival

XOH (peak)=460 ppm

XOH (50% Peak)=230 ppm

tign=209 μs

1

2

3

XOH(1st plateau)=56 ppm

Figure A.1 Example OH concentration time-history; Reflected shock conditions: φ=1, 0.1% C6H5CH3, 0.9% O2, balance Ar at 1689 K, 1.796 atm; Ignition delay time defined as the time to 50% peak OH concentration with zero time defined as arrival of reflected shock; tign = 209 μs.

193

0.54 0.57 0.60 0.63 0.6610

100

1000

10000

1538 K

Igni

tion

Del

ay T

ime

[μs]

1000/T

1818 K

Figure A.2 Variation of ignition delay time with temperature; Reflected shock conditions: φ=1, 0.1% C6H5CH3, 0.9% O2, balance Ar at P=1 atm; solid squares, current experimental results; Simulations are: dotted line, Dagaut et al. [7]; dashed line, Pitz et al. [6]; dash-dot line, Lindstedt et al. [5].

194

1E-4 1E-3 0.0110

100

1000

10000

Igni

tion

Del

ay T

ime

[μs]

Fuel Mole Fraction

Figure A.3 Variation of ignition delay time with fuel mole fraction; Reflected shock conditions: φ=1, 1600K, P=1 atm; solid squares and solid line, current experimental results; crossed squares, Burcat et al. [10] experiments; Simulations are: dotted line, Dagaut et al. [7]; dashed line, Pitz et al. [6]; dash-dot line, Lindstedt et al. [5].

195

0.50 0.55 0.60 0.65 0.70 0.75 0.801

10

100

1000

10000

1250 K

Igni

tion

Del

ay T

ime

[μs]

1000/T

1818 K

Figure A.4 Normalized ignition times: various shock tube studies; all data normalized to φ=1, 1% C6H5CH3, 9% O2, 1 atm using equation 2; solid circles, current study; crossed circles, Burcat et al. [10]; open squares, Pitz et al. [6]; open circles, Burcat et al. [9].

196

0 200 400 600 800 1000

0

25

50

75

100

125

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Pitz (2003)

Pitz et al. (2001)

Lindstedt et al. (1996)

modified Pitz et al.

Dagaut et al. (2002)

Figure A.5 OH concentration profiles; Reflected shock conditions: φ=1, 0.025% C6H5CH3, 0.225% O2, balance Ar at 1648 K, 2.03 atm; solid line, current study; dashed line, Pitz et al. [6]; dotted line, Dagaut et al. [7]; dash-dot line, Lindstedt et al. [5]; dash-dot-dot line, modified Pitz et al; short dot line, Pitz [182].

197

0 250 500 750 1000 1250 15000

50

100

150

200 1783 K, 1.84 atm 1700 K, 1.89 atm1648 K, 2.03 atm1607 K, 2.03 atm

OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

Figure A.6 OH concentration profiles; Reflected shock conditions: φ=1, 0.025% C6H5CH3, 0.225% O2, balance Ar; solid line, current study; dashed line, modified Pitz et al.; upper trace, 1783 K; lower trace, 1607 K.

198

0 200 400 600 800 1000

0

100

200

300

400

modified Pitz et al.

modified Pitz et al.with 3xk10b

Pitz et al. (2001)O

H M

ole

Frac

tion

[ppm

]

Time [μs]

Lindstedt et al. (1996)

Dagaut et al. (2002)

Figure A.7 OH concentration profiles; Reflected shock conditions: φ=1, 0.1% C6H5CH3, 0.9% O2, 1586 K, balance Ar at 1.9 atm; solid line, current study; dashed line, Pitz et al. [6]; dash-dot-dot line, modified Pitz et al. ; dotted line, Dagaut et al. [7]; dash-dot line, Lindstedt et al. [5]; short dash line, modified Pitz et al. with 3 x k10b.

199

0 200 400 600 800 1000 12000

100

200

300

400

500

600

700

0 20 40 60

0

20

40

60φ=11 - 500ppm iso-octane, 1611K, 1.5atm2 - 300ppm n-heptane, 1640K, 2atm3 - 250ppm toluene, 1648K , 2atm

3OH

Mol

e Fr

actio

n [p

pm]

Time [μs]

1

2

2

3

1

early times

Figure A.8 Early-time OH chemistry: a qualitative comparison between n-alkanes (n-heptane, 2), branched chain alkanes (iso-octane, 1), and aromatics (toluene, 3).

201

Appendix B: Ab Initio Study of CH2O + O2 Products

B.1 Introduction In this appendix, results of theoretical calculations of reaction (4) are

described.

(4) CH2O + O2 HCO + HO2

Calculations have been carried out at different levels of theory and basis set. Geometry

optimization and energy calculations have been carried out using the following

method-basis set combinations,

(a) B3LYP/6-31++g** (b) B3LYP/cc-pVDZ

(c) BHandHLYP/6-31++g** (d) BHandHLYP/cc-pVDZ

(e) KMLYP/6-31++g** (f) KMLYP/cc-pVDZ

(g) CCSD(T)/cc-pVDZ//B3LYP/6-31++g**

(h) CCSD(T)/cc-pVTZ//B3LYP/6-31++g**

Cases (a) and (b), and Cases (c) and (d) allow for comparison between two relatively

large basis sets, cc-pVDZ and 6-31++g**, while Cases (g) and (h) make possible a

comparison between the cc-pVDZ and cc-pVTZ basis sets with respect to their ability

to predict reaction energetics. Cases (a) & (c) and (b) & (d) facilitate comparison

between the B3LYP and BHandHLYP methods, while cases (e) and (f) allow us to

ascertain the efficacy of the recently developed KMLYP method [184] to predict

reaction energetics and activation barriers. The ab initio frequencies and energies have

been used to calculate rate coefficients for reaction (4) over a wide temperature range,

and the results have been compared with experiment.

202

B.2 Ab Initio Calculations Table B.1 presents vibrational frequencies for the reactants, saddlepoint and

products, while experimental frequencies for the stable species are given in Table B.2.

Calculated frequencies are given for all the method-basis set combinations used in this

study. It is clear from Tables B.1 and B.2 that the calculated frequencies are greater

than experiment for both reactants and products – this is expected since these methods

are known to overpredict vibrational frequencies. We find that amongst the methods

used, the B3LYP method tends to yield frequencies that are in best agreement with

experiment, while the BHandHLYP and KMLYP methods overpredict the

experimental frequencies to a greater extent. Also, the frequencies predicted by the

BHandHLYP and KMLYP methods are very similar to one another.

In general, the vibrational frequencies predicted by a method (B3LYP,

BHandHLYP and KMLYP) with the cc-pVDZ and 6-31++g** basis sets are similar.

As for the frequencies of the transition state (TS), it is interesting to note that while the

B3LYP method predicts a “broad” TS (imaginary frequency lower than 300 cm-1), the

BHandHLYP and KMLYP methods predict transition states that are sharply peaked

(evident from the large imaginary frequencies). Also, while the B3LYP method is

unable to find a saddle point with the cc-pVDZ basis set, it is able to locate a TS with

the larger 6-31++g** basis set. IRC scans were carried out to confirm that the

structures located are in fact saddle points on the potential energy surface.

Table B.3a presents electronic energies and zero point corrections for all

species. Table B.3b shows results from single point energy calculations at high levels

of theory and basis set, CCSD(T)/cc-pVDZ and CCSD(T)/cc-pVTZ, carried out on

geometries optimized at B3LYP/6-31++g**. Note that the energies presented in Table

B.3b are without any zero point correction. These energies are used to evaluate the

activation barrier and the heat of reaction for reaction (4) – these data are summarized

in Table B.4. We find, from Table B.4, that there is some discrepancy in the barriers

predicted by the different method-basis set combinations. The BHandHLYP method

predicts the highest barrier, while the B3LYP method predicts a barrier that is lower

than the former by ~4-5 kcal/mol. KMLYP yields a barrier that is in between B3LYP

O H

203

and BHandHLYP. Also, basis set dependence, for both BHandHLYP and KMLYP, is

found to be relatively small.

It is also evident that the high level single point calculation, CCSD(T)/cc-

pVTZ, on the optimized B3LYP/6-31++g** geometries, yields the ΔE that is in

closest agreement with experiment. The potential energy surface corresponding to this

calculation is shown in Figure B.1. Also shown is the structure of the transition state

for a KMLYP/cc-pVDZ calculation. ΔEexpt was evaluated using experimental heat of

formation data at 0K available on the NIST website [185]. Most of the calculations

yield ΔE that lie within the error limits of ΔEexpt. It is pertinent to note that for the two

single point calculations carried out using the CCSD(T) method, there is pronounced

basis-set dependence for ΔE, with ΔE increasing by ~3 kcal/mol when the cc-pVTZ

basis set is used instead of cc-pVDZ.

B.3 Transition State Theory The energies and frequencies tabulated in Tables B.1-B.4 were used to

calculate rate coefficients for reaction (4). The CSEO chemical kinetics software [141]

was used to compute rate data via transition state theory (TST). The following is the

rate expression that was obtained by carrying out TST calculations at CCSD(T)/cc-

pVTZ//B3LYP/6-31++g**,

k4,TST=1.08x10-20 T3.03 exp(-18527/T), [cm3 mol-1 s-1]

The results of this calculation are compared with experiment in Figure B.2. As is

evident, agreement is remarkably good. Similar TST theory calculations were carried

out for all the method-basis set combinations listed in Table B.4.

204

Table B.1: Ab initio vibrational frequencies

ν [cm-1] Species B3LYP/

6-31++g**

B3LYP/

cc-PVDZ

BHandHLYP/

6-31++g**

BHandHLYP/

cc-pVDZ

KMLYP/

6-31++g**

KMLYP/

cc-pVDZ

CH2O 1197, 1262,

1538, 1819,

2914, 2979

1186, 1253,

1515, 1832,

2865, 2917

1258, 1311,

1593, 1912,

3042, 3119

1247, 1302,

1570, 1924,

3001, 3070

1270, 1313,

1585, 1956,

3026, 3102

1256,

1307,

1571,

1969,

3028,

3104

O2 1641 1648 1806 1818 1889 1899

TS 279i, 63, 72,

273, 340,

893, 1060,

1160, 1555,

1718, 1952,

2753

No TS

found

2172i, 92, 72,

297, 428, 616,

1115, 1194,

1400, 1661,

2029, 2910

2037i, 107,

123, 319, 428,

613, 1108,

1157, 1406,

1673, 2045,

2832

2023i, 101,

131, 328,

441, 635,

1140, 1175,

1483, 1716,

2091, 2875

1838i,

130, 165,

349, 447,

638, 1128,

1142,

1493,

1724,

2104,

2838

HO2 1166, 1423,

3594

1162, 1418,

3535

1257, 1504,

3826

1250, 1502,

3783

1334, 1523,

3866

1330,

1521,

3839

HCO 1109, 1934,

2688

1095, 1936,

2603

1154, 2040,

2821

1140, 2043,

2747

1147, 2091,

2831

1144,

2094,

2809

205

Table B.2: Experimental vibrational frequencies [186]

Species Experimental frequencies

CH2O 1167, 1249, 1500, 1746, 2783, 2843

O2 1580

HO2 1098, 1392, 3426

HCO 1081, 1868, 2485

206

Table B.3a: Electronic energies

Electronic Energiesa [Hartree] Species B3LYP/

6-31++g**

B3LYP/

cc-PVDZ

BHandHLYP/

6-31++g**

BHandHLYP/

cc-pVDZ

KMLYP/

6-31++g**

KMLYP/

cc-pVDZ

CH2O -114.4849

(0.026676)

-114.4812

(0.026361)

-114.4165

(0.027873)

-114.4154

(0.027599)

-114.2755

(0.027913)

-114.2464

(0.027875)

O2 -150.3238

(0.003739)

-150.3303

(0.00375)

-150.24725

(0.004116)

-150.2561

(0.004142)

-150.0457

(0.004303)

-150.0133

(0.004326)

TS -264.7567

(0.026974)

No TS -264.6025

(0.029363)

-264.61181

(0.026909)

-264.2629

(0.027603)

-264.2042

(0.027701)

HO2 -150.9015

(0.014088)

-150.9009

(0.013931)

-150.8211

(0.015008)

-150.8241

(0.014889)

-150.6291

(0.015317)

-150.5928

(0.01524)

HCO -113.8474

(0.013056)

-113.8478

(0.012836)

-113.7825

(0.013704)

-113.7852

(0.01351)

-113.6292

(0.013825)

-113.6028

(0.01378)

a total electronic energy with zero point correction (z.p.e), z.p.e in brackets

207

Table B.3b: Electronic energiesb

Electronic Energies [Hartree]

Species CCSD(T)/cc-pVDZ//

B3LYP/ 6-31++g**

CCSD(T)/cc-pVTZ//

B3LYP/ 6-31++g**

CH2O -114.2188 -114.3338

O2 -149.9858 -150.1290

TS -264.1377 -264.3989

HO2 -150.5586 -150.7126

HCO -113.5762 -113.6841

b all energies without zero point correction

208

Table B.4: Energy barrier and heat of reaction

ΔE [kcal/mol] Ea [kcal/mol]

Experiment 38.06 ± 1.4

B3LYP/6-31++g** 37.61 32.67

BHandHLYP/6-31++g** 37.72 38.44

BHandHLYP/cc-pVDZ 39.00 37.43

KMLYP/6-31++g** 39.37 36.54

KMLYP/cc-pVDZ 40.27 34.84

CCSD(T)/cc-pVDZ//

B3LYP/6-31++g**

41.11 39.81

CCSD(T)/cc-pVTZ//

B3LYP/6-31++g**

37.99 39.48

209

Reaction Coordinate

Pote

ntia

l Ene

rgy

CH2O+O2

HCO+HO2 TS

39.48 kcal/mol

1.49 kcal/mol

C

H O

O H

O

Figure B.1 Potential energy surface for the reaction between CH2O and O2; not to scale; energies shown are from a CCSD(T)/cc-pVTZ// B3LYP/6-31++g** calculation.

Figure B.2 Comparison of theory with experiment: solid squares, this work experiment (~±35% error bars); solid black line, this work least-squares fit; dashed gray line, this work transition state theory.

0.4 0.5 0.6 0.7107

108

109

1010

1011

1000/T [K-1]

k CH

2O+O

2 [cm

3 m

ol-1

s-1]

211

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