Measurements of CO, HCN, and C2H6 total columns in smoke ...
SHOCK TUBE MEASUREMENTS OF ELEMENTARY OXIDATION … · iv 306 nm, respectively. CH radicals were...
Transcript of 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
4.2 Experimental Set-up.......................................................................................60
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
5.2 Experimental Set-up.......................................................................................80
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
6.2 Experimental Set-up.......................................................................................96
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
x
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
coefficient for reaction i. ...........................................................................55
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
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. ...........................................................................71
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
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
xviii
sensitivity analysis, S = (dXOH/dki)(ki/XOH), where ki is the rate
coefficient for reaction i. ...........................................................................90
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.............91
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.............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
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.......197
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
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
xxvi
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]
34
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
T [K] P [atm] k6 [cm3mol-1s-1]
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)
58
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
T [K] P [atm] k2 [cm3mol-1s-1]
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
200 ppm TBHP (and water), 50 ppm (CH2O)3, balance Ar
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]
100 ppm TBHP (and water), 80 ppm (CH2O)3, balance Ar
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%)
Wavemeter reading (+/- 0.01 cm-1 in UV)
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%)
Wavemeter reading (+/- 0.01 cm-1 in UV)
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
6.53 ppm trioxane, 0.5% O2, balance Ar
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
6.67 ppm trioxane, 0.5% O2, balance Ar
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
T [K] P [atm] k4 [cm3mol-1s-1]
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
10 ppm C2H6, balance Ar
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
10 ppm C2H6, balance Ar
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
(J-rotor)Adiabatic Moments of Inertia /AMU A2 13.8
(K-rotor) Active External Rotor/AMU A2 3.60
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
(J-rotor)Adiabatic Moments of Inertia /AMU A2 12.89
(K-rotor) Active External Rotor/AMU A2 3.60
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
Experiment Model (k5a, best fit) Model (k5a x 0.5)
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
Experiment Model (k5a, best fit) Model (k5a x 0.5)
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
130
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),
131
(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
132
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
133
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
135
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%
136
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.
137
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
138
(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
140
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
141
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
143
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
10.04 ppm C2H6 , 10.1% N2, balance Ar
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
10.03 ppm C2H6 , 10.05% N2, balance Ar
2910 1.034 1.30 x 1011 3080 1.027 1.60 x 1011
10.34 ppm C2H6 , 10.08% N2, balance Ar
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
24.89 ppm acetic anhydride , 10.16% N2, balance Ar
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
25.46 ppm acetic anhydride , 15.04% N2, balance Ar
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
Rate Coeff. [cm3 mol-1 s1] Reaction A n E, kcal/mol
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
Rate Coeff. [cm3 mol-1 s1] Reaction A n E, kcal/mol
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
101.39 ppm C2H6 , balance N2
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
102.69 ppm C2H6 , balance N2
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
Rate Coeff. [cm3 mol-1 s1] Reaction A n E, kcal/mol
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
Experiment BR=1 BR=0
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
Experiment BR=1 BR=0
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
178
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).
180
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.
181
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
182
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.
183
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
184
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).
200
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]
210
211
References
1. Goodger, E.; Vere, R. Aviations Fuel Technology; MacMillan Publishers Ltd.:
London, 1985.
2. ASTM Special Technical Publication No. 225; American Society of Testing
Materials: Philadelphia, 1958.
3. Emdee, J.J.; Brezinsky, K.; Glassman, I. J. Phys. Chem. 1992, 96, 2151.
4. Davis, S.G.; Wang, H.; Brezinsky, K.; Law, C.K. Proc. Combust. Inst. 1996,
26, 1025.
5. Lindstedt, R.P.; Maurice, L.Q. Combust. Sci. and Tech. 1996, 120, 119.
6. Pitz, W.J.; Seiser, R.; Bozzelli, J.W.; Da Costa, I.; Fournet, R.; Billaud, F.;
Battin-Leclerc, F.; Seshadri, K.; Westbrook, C.K. Second Joint Meeting, US
Sections of the Combust. Inst., Paper 253, 2001.
7. Dagaut, P.; Pengloan, G.; Ristori, A. Phys. Chem. Chem. Phys. 2002, 4, 1846.
8. Miyama, H. J. Phys. Chem. 1971, 75, 1501.
9. Burcat, A.; Farmer, R.C.; Espinoza, R.L.; Matula, R.A. Combust. Flame 1979,
36, 313.
10. Burcat, A.; Snyder, C.; Brabbs, T. NASA TM-87312, 1986.
11. Baulch, D.L.; Bowman, C.T.; Cobos, C.J.; Cox, R.A.; Just, Th.; Kerr, J.A.;
Pilling, M.J.; Stocker, D.; Troe, J.; Tsang, W.; Walker, R.W.; Warnatz, J. J.
Phys. Chem. Ref. Data 2005, 34, 757.
12. Perry, R.A.; Atkinson, R.; Pitts Jr., J. N. J. Phys. Chem. 1977, 81, 296.
13. Tully, F.P.; Ravishankara, A.R.; Thompson, R.L.; Nicovich, J.M.; Shah, R.C.;
Kreutter, N.M.; Wine, P.H. J. Phys. Chem. 1981, 85, 2262.
14. Markert, F.; Pagsberg, P. Chem. Phys. Lett. 1993, 209, 445.
15. Knispel, R.; Koch, R.; Siese, M.; Zetzsch, C. Ber. Bunsenges. Phys. Chem.
1990, 94, 1375.
212
16. Friedrichs, G.; Davidson, D.F.; Hanson, R.K. Phys. Chem. Chem. Phys. 2002,
4, 5778.
17. Bott, J.F.; Cohen, N. Intl. J. Chem. Kinet. 1991, 23, 1075.
18. Peeters, J.; Mahnen, G. Proc. Combust. Inst. 1973, 16, 133.
19. Vandooren, J; de Guertechin, L.O.; Van Tiggelen, P.J. Combust. Flame 1986,
64, 127.
20. (a) D’Anna, B; Bakken, V.; Beukes, J.A.; Nielsen, C.J.; Brudnik, K.;
Jodkowski, J.T. Phys. Chem. Chem. Phys. 2003, 5, 1790.
(b) Xu, S.; Zhu, R.S.; Lin, M.C. Intl. J. Chem. Kinet. 2006, 38, 322.
21. Kumaran, S.S.; Carroll, J.J.; Michael, J.V. Proc. Combust. Inst. 1998, 27, 125.
22. Just, Th. in: Lifshitz, A. (Ed.), Shock Waves in Chemistry. Dekker, 1981, p.
279, as reported in Ref. [21]
23. Saito, K.; Kakumoto, T.; Nakanishi, Y.; Imamura, A. J. Phys. Chem. 1985, 89,
3109.
24. Dean, A.M.; Johnson, R.L.; Steiner, D.C. Combust. Flame 1980, 37, 41.
25. Irdam, E.A.; Kiefer, J.H.; Harding, L.B.; Wagner, A.F. Intl. J. Chem. Kinet.
1993, 25, 285.
26. Hidaka, Y.; Taniguchi, T.; Kamesawa, T.; Masaoka, H.; Inami, K.; Kawano,
H. Intl. J. Chem. Kinet. 1993, 25, 305.
27. Eiteneer, B.; Yu, C.-L.; Goldenberg, M.; Frenklach, M. J. Phys. Chem. 1998,
102, 5196.
28. Friedrichs, G.; Davidson, D.F.; Hanson, R.K. Intl. J. Chem. Kinet. 2002, 34,
374.
29. Troe, J. J. Phys. Chem. 2005, 109, 8320.
30. Hidaka, Y.; Taniguchi, T.; Tanaka, H.; Kamesawa, T.; Inami, K.; Kawano, H.;
Combust. Flame 1993, 92, 365.
31. Baldwin, R.R.; Fuller, A.R.; Longhorn, D.; Walker, R.W. J. Chem. Soc.
Faraday. Trans. 1974, 70, 1257.
32. Michael, J.V.; Kumaran, S.S.; Su, M.-C. J. Phys. Chem. A 1999, 103, 5942.
213
33. Srinivasan, N.K.; Su, M.-C.; Sutherland, J.W.; Michael, J.V. J. Phys. Chem. A
2005, 109, 7902.
34. Michael, J.V.; Su, M.-C.; Sutherland, J.W.; Fang, D.-C.; Harding, L.B.;
Wagner, A.F.; Maity, D.K.; Lin, D.; Tirtowidjojo, M.; Truong, T.N. J. Phys.
Chem. A, in preparation.
35. Dean, A.J.; Hanson, R.K. Intl. J. Chem. Kinet. 1992, 24, 517.
36. Röhrig, M.; Petersen, E.L.; Davidson, D.F.; Hanson, R.K.; Bowman, C.T. Intl.
J. Chem. Kinet. 1997, 29, 781.
37. Markus, M.W.; Woiki, D.; Roth, P. Proc. Combust. Inst. 1992, 24, 581.
38. Markus, M.W.; Roth, P. Proc. Symp. Shock Waves 1995, 19, 95.
39. Markus, M.W.; Roth, P.; Just, Th. Intl. J. Chem. Kinet. 1996, 28, 171.
40. Bhaskaran, K.A.; Frank, P.; Just, Th. Proc. Symp. Shock Waves 1980, 12, 503.
41. Roth, P.; Barner, U.; Loehr, R. Ber. Bunsenges Phy. Chem. 1979, 83, 929.
42. Lim, K.P.; Michael, J.V. Proc. Combust. Inst. 1994, 25, 713.
43. Eng, R.A.; Gebert, A.; Goos, E.; Hippler, H.; Kachiani, C. Phys. Chem. Chem.
Phys. 2001, 3, 2258.
44. Fulle, D.; Hippler, H. J. Chem. Phys. 1997, 106, 8691.
45. Brooks, B.R.; Schaefer, H.F. J. Chem. Phys. 1977, 76, 5146.
46. Miller, J.A.; Bowman, C.T. Prog. Energy Combust. Sci. 1989, 15, 287.
47. Fenimore, C.P. Proc. Combust. Inst. 1971, 13, 373.
48. Dean, A.J.; Hanson, R.K.; Bowman, C.T. Proc. Combust. Inst. 1990, 23, 259.
49. Lindackers, D.; Burmeister, M.; Roth, P. Proc. Combust. Inst. 1990, 23, 251.
50. Blauwens, J.; Smets, B.; Peeters, J. Proc. Combust. Inst. 1977, 16, 1055.
51. Matsui, Y.; Yuuki, A. Jpn. J. Appl. Phys. 1985, 24, 598.
52. Wada, A.; Takayanagi, T. J. Chem. Phys. 2002, 116, 7065.
53. Cui, Q.; Morokuma, K.; Bowman, J.M.; Klippenstein, S.J. J. Chem. Phys.
1999, 110, 9469.
54. Miller, J.A.; Walch, S.P. Int. J. Chem. Kinet. 1997, 29, 253.
55. Rodgers, A.S.; Smith, G.P. Chem. Phys. Lett. 1996, 253, 313.
56. Moskaleva, L.V.; Lin, M.C. Proc. Combust. Inst. 2000, 28, 2393.
214
57. Driscoll, J.J.; Sick, V.; Farrow, R.L.; Schrader, P.E. Proc. Combust. Inst. 2002,
29, 2719.
58. Berman, M.R.; Lin, M.C. J. Phys. Chem. 1983, 87, 3933.
59. Becker, K.H.; Geiger, H.; Wiesen, P. Int. J. Chem. Kinet. 1996, 28, 115.
60. Smith, G.P. Chem. Phys. Lett. 2003, 367, 541.
61. Sutton, J.A.; Williams, B.A.; Fleming, J.W. 5th Joint US Combustion Meeting
2007; also submitted to Combust. Flame, 07/07.
62. Najm, H.N.; Paul, P.H.; Mueller, C.J.; Wyckoff, P.S. Combust. Flame 1998,
113, 312.
63. de Guertechin, L.O.; Vandooren, J.; Van Tiggelen, P.J. Bull. Soc. Chim. Belg.
1983, 92, 663.
64. Dean, A.M.; Johnson, R.L.; Steiner, D.C. Combust. Flame 1980, 37, 41.
65. Westenberg, A.A.; Fristom, R.M. Proc. Combust. Inst. 1965, 10, 473.
66. Tsang, W.; Hampson, R.F. J. Phys. Chem. Ref. Data 1986, 15, 1087.
67. Kiefer, J.H..; Kumaran, S. S. J. Phys. Chem. 1993, 97, 414.
68. Herbon, J.T. Mechanical Engineering Dept. report TSD-153, Stanford
University, USA, 2004.
69. Herbon, J.T.; Hanson, R.K.; Golden, D.M.; Bowman, C.T. Proc. Combust.
Inst. 2002, 29, 1201.
70. Dean, A.J.; Hanson, R.K. J. Quant. Spectrosc. Radiat. Transfer 1991, 95, 183.
71. Herbon, J.T.; Hanson, R.K.; Bowman, C.T.; Golden, D.M. Proc. Combust.
Inst. 2005, 30, 955.
72. Huber, K.P.; Herzberg, G. “Molecular Spectra and Molecular Structure: IV.
Constants of Diatomic Molecules”, Van Nostrand Reinhold Company, 1979.
73. Smith, G.P., Teleconference on 11/14/2006.
74. Zachwieja, M. J. Mol. Spect. 1995, 170, 285.
75. Luque, J.; Crosley, D.R. “LIFBASE: Database and Spectral Simulation
Program (Version 1.5)”, SRI International Report No. MP 99-0099, 1999.
76. Luque, J.; Crosley, D.R. J. Chem. Phys. 1996, 104, 2146.
77. Brazier, C.R.; Brown, J.M. Can. J. Phy. 1984, 62, 1563.
215
78. Chang, A.Y.; Hanson, R.K. J. Quant. Spectrosc. Radiat. Transfer 1989, 42,
207.
79. (a) Dean, A.J.; Hanson, R.K.; Bowman, C.T. Proc. Combust. Inst. 1990, 23,
955.
(b) Dean, A.J.; Hanson, R.K.; Bowman, C.T. J. Phys. Chem. 1991, 95, 3180.
80. Takubo, Y.; Yano, H.; Matsuoka, H.; Shimazu, M. J. Quant. Spectrosc.
Radiat. Transfer 1983, 30, 207.
81. Rank, D.H.; Saksena, D.; Wiggins, T.A. J. Opt. Soc. Am. 1958, 48, 521.
82. Harned, B.W.; Ginsburg, N. J. Opt. Soc. Am. 1958, 48, 178.
83. Luque, J.; Klein-Douwel, R.J.H.; Jeffries, J.B.; Smith, P.; Crosley, D.R. Appl.
Phys. B 2002, 75, 779.
84. Peterson, K.A.; Oh, D.B. Optics Letters 1999, 24, 667.
85. Rea, E.C.; Chang, A.Y.; Hanson, R.K. J. Quant. Spectrosc. Radiat. Transfer
1987, 37, 117.
86. Herzberg, G.; Travis, D.N. Canadian J. Phys. 1964, 42, 1658.
87. Smith, G.P.; Copeland, R.A.; Crosley, D.R. J. Chem. Phys. 1989, 91, 1987.
88. Beaton, S.A.; Ito, Y.; Brown, J.M. J. Molec. Spectrosc. 1996, 178, 99.
89. Brezinsky, K. Prog. Energy. Combust. Sci. 1986, 12, 1.
90. Bounaceur, R.; Da Costa, I.; Fournet, R.; Billaud, F.; Battin-Leclerc, F. Intl. J.
Chem. Kinet. 2005, 37, 25.
91. Vasudevan, V.; Davidson, D.F.; Hanson, R.K. Proc. Combust. Inst. 2005, 30,
1155.
92. Yu, C.L.; Frenklach, M.; Masten, D.A.; Hanson, R.K.; Bowman, C.T. J. Phys.
Chem. 1994, 98, 4470.
93. Eng, R.A.; Gebert, A.; Goos, E.; Hippler, H.; Kachiani, C. Phys. Chem. Chem.
Phys. 2002, 4, 3989.
94. Luther, K.; Troe, J.; Weitzel, K.–M. J. Phys. Chem. 1990, 94, 6316.
95. (a) Oehlschlaeger, M.A.; Davidson, D.F.; Hanson, R.K. Proc. Combust. Inst.
2007, 31, 211.
216
(b) Oehlschlaeger, M.A.; Davidson, D.F.; Hanson, R.K. J. Phys. Chem. A
2006, 110, 9867.
96. Bott, J.F.; Cohen, N. Intl. J. Chem. Kinet. 1991, 23, 1017.
97. Vasudevan, V.; Davidson, D.F.; Hanson, R.K. Intl. J. Chem. Kinet. 2005, 37,
98.
98. Kee, R. J.; Rupley, F.M.; Miller, J.A. The Chemkin Thermodynamic Database
Report No. SAND87-8215B; Sandia National Laboratories: Livermore, CA,
1987.
99. Jaynes, D.N.; Beam, B.H. Appl. Optics 1969, 8, 1741.
100. Curran, H.J.; Gaffuri, P.; Pitz, W.J.; Westbrook, C.K. Combust. Flame 1998,
114, 149.
101. Zhong, X.; Bozzelli, J.W. Intl. J. Chem. Kinet. 1997, 29, 893.
102. Zhong, X. Ph.D thesis, New Jersey Institute of Technology: Newark, NJ, 1998.
103. Zhong, X.; Bozzelli, J.W. J. Phys. Chem. 1998, 102, 3537.
104. Ernst, J.; Wagner, H.; Zellner, R. Ber. Bunsenges Phy. Chem. 1977, 81, 1270-
1275.
105. Wooldridge, M.S.; Hanson, R.K.; Bowman, C.T. Proc. Combust. Inst. 1994,
25, 741.
106. Bott, J.F.; Cohen, N. Intl. J. Chem. Kinet. 1984, 16, 1557.
107. Koffend, B.J.; Cohen, N. Intl. J. Chem. Kinet. 1996, 28, 79.
108. Benson, S.W.; O’Neal, H.E. Kinetic Data on Gas Phase Unimolecular
Reactions NSRDS-NBS 21; 1970.
109. Choo, K.Y.; Benson, S.W. Intl. J Chem Kinet. 1981, 13, 833.
110. Pitz, W.J. Personal communication, 2004.
111. Smith, G.P.; Golden, D.M.; Frenklach, M.; Moriarty, N.W.; Eiteneer, B.;
Goldenberg, M.; Bowman, C.T.; Hanson, R.K.; Song, S.; Gardiner Jr., W.C.;
Lissianski, V.V.; Qin, Z. http://www.me.berkeley.edu/gri_mech/.
112. Baldwin, R.R.; Scott, M.; Walker, R. W. Proc. Combust. Inst. 1986, 21, 991.
113. Yamada, T.; Taylor, P.H.; Goumri, A.; Marshall, P. J. Chem. Phys. 2003, 119,
10600.
217
114. Gierczak, T.; Gilles, M.K.; Bauerle, S.; Ravishankara, A.R. J. Phys. Chem. A
2003, 107, 5014.
115. Wollenhaupt, M.; Carl, S.A.; Horowitz, A.; Crowley, J.N. J. Phys. Chem. A
2000, 104, 2695.
116. Tranter, R.S.; Walker, R.W. Phys. Chem. Chem. Phys. 2001, 3, 1262.
117. Wallington, T.J.; Kurylo, M.J. J. Phys. Chem. A 1987, 91, 5050.
118. Le Calve, S.; Hitier, D.; Le Bras, G.; Mellouki, A. J. Phys. Chem. A 1998, 102,
4579.
119. Friedrichs, G.; Davidson, D.F.; Hanson, R.K. Phys. Chem. Chem. Phys. 2002,
4, 5778.
120. Friedrichs, G.; Davidson, D.F.; Hanson, R.K. Intl. J. Chem. Kinet. 2002, 34,
374.
121. Friedrichs, G.; Davidson, D.F ; Hanson, R.K. Intl. J. Chem. Kinet. 2004, 36,
157.
122. Vasudevan, V.; Davidson, D.F.; Hanson, R.K. J. Phys. Chem. A 2005, 109,
3352.
123. Pitz, W.J. Private communication (2003). Available from LLNL combustion
chemistry at: http://www.cms.llnl.gov/combustion/combustion2.html
124. Irdam, E.A.; Kiefer, J.H. Chem. Phys. Letters 1990, 166, 491.
125. Mulder, P.; Louw, R. Recl. Trav. Chim. Pays-Bas 1984, 103, 148.
126. Sahetchian, K.A.; Rigny, R.; Tardieu de Maleissye, J.; Batt, L.; Anwar Khan,
M.; Mathews, S. Proc. Combust. Inst. 1992, 24, 637.
127. Kirk, A.D.; Knox, J.H. Trans. Faraday Soc. 1960, 56, 1296.
128. Benson, S.W.; Spokes, G.N. J. Phys. Chem. 1968, 72, 1182.
129. IUPAC 1998, Supplement VII, as reported in Ref. [11].
130. Stief, L.J.; Nava, D.F.; Payne,W.A. ; Michael, J.V. J. Chem. Phys. 1980, 73,
2254.
131. Sivakumaran, V.; Holscher, D; Dillon, T.J.; Crowley, J.N. Phys. Chem. Chem.
Phys. 2003, 5, 4821.
132. Atkinson, R.; Pitts, J.N., Jr. J. Chem. Phys. 1978, 68, 3581.
218
133. Niki, H.; Maker, P.D.; Savage, C.M.; Breitenbach, L.P. J. Phys. Chem. 1984,
88, 5342.
134. Morris, E.D., Jr.; Niki, H. J. Chem. Phys. 1971, 55, 1991.
135. Temps, F.; Wagner, H.G. Ber. Bunsenges Phys. Chem. 1984, 88, 415.
136. Ravishankara, A. Personal communication (2004).
137. IUPAC Subcommittee on Gas Kinetic Data Evaluation – Data Sheet Hox-
VOC11, 2002 , http://www.iupac-netic.ch.cam.ac.uk/datasheets/gas
138. Vandooren, J.; Van Tiggelen, P.J. Proc. Combust. Inst. 1977, 16, 1133.
139. Zabarnick, S.; Fleming, J.W.; Lin, M.C. Intl. J. Chem. Kinet. 1988, 20, 117.
140. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.;
Cheeseman, J.R.; Zakrzewski, V.G.; Montgomery, J.A.; Stratmann, R.E.;
Burant, J.C.; Dapprich, S; Millam, J.M.; Daniels, A.D.; Kudin, K.N.; Strain,
M.C.; Farkas, O; Tomasi, J; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.;
Pomelli, C.; Adamo, C. ; Clifford, S.; Ochterski, J. ; Petersson, G.A.; Ayala,
P.Y.; Cui, Q.; Morokuma, K.; Malick, D.K.; Rabuck, A.D.; Raghavachari, K.;
Foresman, J.B.; Cioslowski, J; Ortiz, J.V. ; Baboul, A.G.; Stefanov, B.B.; Liu,
G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R.L.;
Fox, D.J.; Keith, T.; Al-Laham, M.A.; Peng, C.Y.; Nanayakkara, A.;
Gonzalez, C.; Challacombe, M.; Gill, P.M.W.; Johnson, B.; Chen, W.; Wong,
M.W.; Andres, J.L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E.S.; Pople,
J.A. Gaussian, Inc., Pittsburgh PA (1998).
141. Zhang, S.; Troung, T.N. Kinetics (CSEO Version 1.0), University of Utah
(2003).
142. Li, J.; Zhao, Z.; Kazakov, A.; Dryer, F.L. Intl. J. Chem. Kinet. 2004, 36, 566.
143. Millikan, R.C.; White, D.R. J. Chem. Phys. 1963, 39, 3209.
144. Golden, D.M. in: Bartok, W. and Sarofim, A.F. (Eds.), Fossil Fuel
Combustion: A Sourse Book. John Wiley, 1991, p. 49.
145. Vasudevan, V.; Davidson, D.F.; Hanson, R.K.; Bowman, C.T.; Golden, D.M.
Proc. Combust. Inst. 2007, 31, 175.
146. Markus, M.W.; Roth, P.; Tereza, A.M. Proc. Combust. Inst. 1994, 25, 705.
219
147. Hippler, H.; Kachiani, C.; Olzmann, M. Proceedings of the European
Combustion Meeting 2003.
148. Barker, J. R. Intl. J. Chem. Kinet. 2001, 33, 232.
149. Barker, J. R. MultiWell-2.01 Software, APR 2006, designed and maintained
by Barker, J.R. with contributions from Ortiz, N.F.; Preses, J.M.; Lohr, L.L;
Maranzana, A.; Stimac, P.J.; University of Michigan, Ann Arbor, MI;
http://aoss.engin.umich.edu/multiwell/. 2006.
150. Golden, D. M. Intl. J. Chem. Kinet. 2005, 37, 625.
151. Mayneris, J.; Saracibar, A.; Goldfield, E. M.; Gonzalez, M.; Garcia, E.; Gray,
S. K. J. Phys. Chem. A 2006, 110, 5542.
152. Harding, L.B. 28th Annual Combustion Research Conference 2007.
153. Glarborg, P.; Alzueta, M.U.; Dam-Johansen, K.; Miller, J.A. Combust. Flame
1998, 115, 1.
154. White, D.R. J. Chem. Phys. 1968, 48, 525.
155. Bise, R.T.; Choi, H.; Neumark, D.M. J. Chem. Phys. 1999, 11, 4923.
156. Vasudevan, V.; Hanson, R.K.; Golden, D.M.; Bowman, C.T.; Davidson, D.F.
J. Phys. Chem. A 2007, 111, 4062.
157. Akao, M.; Saito, K.; Okada, K.; Takahashi, O.; Tabayashi, K. Ber. Bunsenges.
Phys. Chem. 1996, 7, 1237.
158. Szwark, M.; Murawski, J. Trans. Faraday. Soc. 1951, 47, 269.
159. Blake, P.G.; Speis, A. J. Chem. Soc.(B) 1971, 1877.
160. Friedrichs, G.; Wagner, H.Gg. Z. Phys. Chem. 2001, 215, 1601.
161. Wagner, H. Gg.; Zabel, F. Ber. Bunsenges. Phys. Chem. 1971, 75, 114.
162. Frank, P.; Bhaskaran, K.A.; Just, T. J. Phys. Chem. 1986, 90, 2226.
163. Mackie, J.C.; Doolan, J.C. Int. J. Chem. Kinet. 1984, 16, 525.
164. Saito, Ko.; Sasaki, T.; Yoshinobu, I.; Imamura, A. Chem. Phys. Lett. 1990,
170, 385.
165. Duan, X.; Page, M. J. Am. Chem. Soc. 1995, 117, 5114.
166. Blake, P.G.; Jackson, G.E. J. Chem. Soc.(B) 1969, 94.
220
167. Wooldridge, M.S.; Hanson, R.K.; Bowman, C.T. Proc. Combust. Inst. 1994,
25, 741.
168. Zhu, R.S.; Lin, M.C. Intl. J Chem Kinet. 2005, 37, 593.
169. Zhu, R.S.; Lin, M.C. J. Phys. Chem. A 2007 (in press)
170. Chen, H.-T.; Ho, J.-J J. Phys. Chem. A 2005, 109, 2564.
171. Huang, C.-L.; Tseng, S.Y.; Wang, T.Y.; Wang, N.S.; Xu, Z.F.; Lin, M.C. J.
Chem. Phys. 2005, 122, 184321.
172. Westbrook, C.K.; Pitz, W.J.; Curran, H.J. J. Phys. Chem. A 2006, 110, 6912.
173. Horning, D.C. Mechanical Engineering Dept. report TSD-135, Stanford
University, USA, 2001.
174. Horning, D.C.; Davidson, D.F. Hanson, R.K. J. Propul. Power 2002, 18, 363.
175. Davidson, D.F.; Oehlschlaeger, M.A.; Herbon, J.T.; Hanson, R.K. Proc.
Combust. Inst. 2002, 29, 1295.
176. Petersen, E.L.; Davidson, D.F.; Hanson, R.K. J. Propul. Power 1999, 15, 82.
177. Davidson, D.F.; Horning, D.C.; Herbon, J.T.; Hanson, R.K. Proc. Combust.
Inst. 2000, 28, 1687.
178. Baulch, D.L.; Cobos, C.J.; Cox, R.A.; Esser, C.; Frank, P.; Hayman, G.; Just,
Th.; Kerr, J.A.; Pilling, M.J.; Troe, J.; Walker, R.W.; Warnatz, J. J. Phy.
Chem. Ref. Data 1992, 21, 411-429.
179. Garrett, B.C.; Miller, J.A. Intl. J. Chem. Kinet. 1997, 29, 275.
180. Drallmeier, J.A. Appl. Optics 2003, 42, 979.
181. Baulch, D.L.; Cobos, C.J.; Cox, R.A.; Frank, P.; Hayman, G.; Just, Th.; Kerr,
J.A.; Murrells, T.; Pilling, M.J.; Troe, J.; Walker, R.W.; Warnatz, J. J. Phy.
Chem. Ref. Data 1994, 23.
182. W.J. Pitz, Private communication (2003) [email protected].
183. Cohen, N. Intl. J. Chem. Kinet. 1982, 14, 1339.
184. Kang, J.K.; Musgrave, C.B. J. Chem. Phys. 2001, 115, 11040.
185. NIST Standard Reference Database 101, Release 10, August 2004:
http://srdata.nist.gov/cccbdb/
221
186. Lide, D.R. CRC Hand Book of Chemistry and Physics, 80th ed; CRC Press:
Boca Raton, FL, 1999-2000.
187. Mertens, J.D.; Dean, A.J.; Hanson, R.K.; Bowman, C.T. Proc. Combust. Inst.
1992, 24, 701.
188. Davidson, D.F.; Vasudevan, V; Hanson, R.K. Proc. Combust. Inst. (in
preparation).
189. Srinivasan, N.K.; Su, M.-C.; Michael, J.V. Phys. Chem. Chem. Phys. 2007
(advance article, available online); also presented at the 5th Joint US
Combustion Meeting 2007.
190. El bakali, A.; Pillier, L.; Desgroux, P.; Lefort, B.; Gasnot, L.; Pauwels, J.F.; da
Costa, I. Fuel 2006, 85, 896.