EXPERIMENTAL DETERMINATION OF RATE CONSTANTS
FOR REACTIONS OF THE HYDROXYL RADICAL WITH
ALKANES AND ALCOHOLS
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Genny Anne Pang
August 2012
http://creativecommons.org/licenses/by-nc/3.0/us/
This dissertation is online at: http://purl.stanford.edu/rh393tq1232
© 2012 by Genny Anne Pang. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.
ii
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Ronald Hanson, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Craig Bowman
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
David Golden
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.
iii
iv
Abstract
Over one quarter of the energy usage in the United States currently occurs in the
transportation sector. Improvements in energy conversion efficiency and sustainabil-
ity in transportation applications, therefore, can substantially contribute to improved
energy security in our future. The design of advanced high-efficiency energy conver-
sion devices for transportation applications can be facilitated with complex computer
models of combustion processes. The development of these models requires a large
experimental database to ensure accuracy of the computational predictions. This
thesis discusses how experimental studies are utilized to create a database of rate
constants for elementary reactions; these rate constants are integral components of
any computational model of combustion chemistry.
During a combustion process, the reaction of the hydroxyl (OH) radical, a highly
reactive chemical intermediate, with a combustible fuel molecule is a major fuel
consumption pathway under many combustion conditions. Thus, the rate con-
stants for these types of reactions must be accurately known to develop a com-
putational model that correctly describes the combustion chemistry. This thesis
presents an experimental method for measuring rate constants in the reaction family
of OH + Fuel −→ Products using a shock tube reactor, laser diagnostics, and tert-
butylhydroperoxide (TBHP) as an OH radical precursor. Important rate constant
parameters describing subsequent reactions of TBHP decomposition are also studied.
Current transportation fuels of interest in the combustion community include
molecules in the alkane and butanol classes. Alkane molecules are a major compo-
nent of many petroleum-derived fuels such as gasoline and jet fuel. Isomers of the
v
butanol molecule are gaining popularity as a potential renewable alternative to gaso-
line because of their high energy density and the many known methods of production
from biomass and agricultural byproducts. The rate constant measurement method
is applied to the reaction of OH with three alkane molecules (n-pentane, n-heptane,
and n-nonane) and four isomers of butanol (n-butanol, iso-butanol, sec-butanol, tert-
butanol), and the results are reported in this thesis. Comparison of the rate constant
results to estimation methods in the literature are presented, and, for several of the
isomers of butanol studied, the measured data are also used to validate and/or suggest
refinements to existing detailed kinetic mechanisms.
vi
Acknowledgment
The work presented in this thesis would not have been possible without the extensive
support provided by my primary advisor Prof. Ron Hanson. I thank him for hav-
ing confidence in me when I was initially exploring my graduate school options, for
without his encouragement I may not have spent my graduate studies working in his
world-class laboratory. And I am thankful that his support for me has never faded
throughout my time at Stanford. His constant push to strive for the best in quality
of work and presentation has no doubt led me to be a become a better researcher,
scholar, teacher, and mentor than I would have been without his guidance.
I would also like to thank Profs. Tom Bowman and Dave Golden for being my
reading committee members and weekly consultants for my work. Prof. Bowman’s
meticulous attention to detail has taught me what high-quality research is, and also
how to achieve it in my work. I thank Prof. Golden for teaching me to think like a
chemist. The direction of this thesis work would not have been the same without his
inspiration.
I owe thanks to Profs. Jen Wilcox for chairing my oral exam, and also for teaching
me about about topics that have increased my depth of understanding in this work. I
am very thankful to Prof. Mark Cappelli for serving on my oral exam committee on
short notice, and also being a supportive faculty member all throughout my graduate
studies, starting from my very first class at Stanford. I also want to acknowledge
support from Prof. Justin Du Bois. His patience and enthusiasm in teaching organic
chemistry helped me develop a foundation to base many parts of this work, and I
thank him for many interesting and insightful discussions in his office.
I am immensely grateful for Dr. Dave Davidson’s presence in the laboratory, and
vii
also in my life as a mentor, colleague, and friend. I am especially thankful for his
willingness to always make time for students, whether by getting up from his desk
to examine a laboratory problem with me, or just to provide wisdom, laughter, and
chocolate during both good and difficult times. I also thank Dr. Jay Jeffries for his
assistance in managing the laboratory and for helping me with occasional tasks.
I feel fortunate to have worked with the extraordinary group of students in the
Hanson Group. I particularly want to acknowledge the experimental assistance from
Venky Vasudevan and Rob Cook. I thank them for their patience in teaching me to
use the laser equipment and helping troubleshoot problems; the experimental work
presented in this thesis would have been much more difficult without their help. I am
grateful for the rest of my friends and colleagues from the Hanson Group, past and
present, as my memories of group lunches, coffee breaks, ski trips, and other activities
with the group will always be highlights of my time at Stanford.
Perhaps most importantly, I am indebted to my friends, family, and loved ones
outside of the laboratory who have made my experience in graduate school special.
Their company and support has enriched my life in ways that I never would have
imagined; and for that, I will be forever grateful.
Financial support for the specific research presented in this thesis was pro-
vided by the U.S. Department of Energy, Office of Basic Energy Sciences, with Dr.
Wade Sisk as Program Manager. The National Defense Science and Engineering
Graduate Fellowship, awarded by the Department of Defense, also provided tuition
and stipend support for the early years of my graduate studies. Countless faculty,
students, and affiliates of the Combustion Energy Frontier Research Center, funded
by the U.S. Department of Energy, are also acknowledged for their support.
viii
Contents
Abstract v
Acknowledgment vii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Development of Kinetic Mechanisms for Combustion . . . . . 2
1.2.2 Alkane Combustion Kinetics . . . . . . . . . . . . . . . . . . . 6
1.2.3 Butanol Combustion Kinetics . . . . . . . . . . . . . . . . . . 8
1.3 Scope and Organization of Thesis . . . . . . . . . . . . . . . . . . . . 10
2 Experimental Setup 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Kinetics Shock Tube Facility . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Shock Tube Overview . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Gas-mixing Facility Overview . . . . . . . . . . . . . . . . . . 17
2.3 Laser Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 OH Mole-fraction Diagnostic . . . . . . . . . . . . . . . . . . . 20
2.3.2 Organic Fuel Mole Fraction Diagnostic . . . . . . . . . . . . . 24
2.4 Test Mixture Chemicals . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 Decomposition of tert-Butylhydroperoxide 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
ix
3.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 Objectives of the Current Chapter . . . . . . . . . . . . . . . 29
3.2 TBHP Kinetic Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Mechanism Generation . . . . . . . . . . . . . . . . . . . . . . 30
3.2.2 OH Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . 31
3.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 OH Mole Fraction Measurements . . . . . . . . . . . . . . . . . . . . 34
3.4.1 OH Time-history . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.2 OH Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Rate Constant Determinations . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 Determination of k3.1 . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.2 Determination of k3.3 . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4 Reactions of OH with n-Alkanes 47
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.2 Objectives of the Current Chapter . . . . . . . . . . . . . . . 48
4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3.1 Pseudo-first-order . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3.2 Kinetic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4.1 Rate Constant Measurements . . . . . . . . . . . . . . . . . . 54
4.4.2 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 Comparisons with Literature . . . . . . . . . . . . . . . . . . . . . . . 60
4.5.1 Previous Experimental Works . . . . . . . . . . . . . . . . . . 60
4.5.2 Validation of Estimation Methods . . . . . . . . . . . . . . . . 62
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5 Reaction of OH with n-Butanol 69
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
x
5.1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . 69
5.1.2 Objectives of the Current Chapter . . . . . . . . . . . . . . . 71
5.2 Analysis of n-Butanol Kinetic Mechanisms . . . . . . . . . . . . . . . 72
5.2.1 Influence of TBHP Kinetics . . . . . . . . . . . . . . . . . . . 72
5.2.2 Sensitivity of k5.1 Determination to Mechanism . . . . . . . . 75
5.2.3 Mechanism Generation for Current Work . . . . . . . . . . . . 78
5.3 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.5 Influence of Secondary Reactions . . . . . . . . . . . . . . . . . . . . 83
5.5.1 OH Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . 83
5.5.2 Reaction Pathway Analysis . . . . . . . . . . . . . . . . . . . 85
5.6 Uncertainty Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.7 Comparison with Literature . . . . . . . . . . . . . . . . . . . . . . . 89
5.7.1 Previous Experiments at High Temperatures . . . . . . . . . . 89
5.7.2 Ab initio Calculations . . . . . . . . . . . . . . . . . . . . . . 93
5.7.3 Atmospheric-relevant Temperature Rate Constants . . . . . . 94
5.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6 Reaction of OH with iso-Butanol 97
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . 97
6.1.2 Objectives of the Current Chapter . . . . . . . . . . . . . . . 99
6.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3 Kinetic Modeling and Analysis . . . . . . . . . . . . . . . . . . . . . . 100
6.3.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3.2 OH Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . 103
6.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.4.1 Rate Constant Measurements for the non-β Pathways . . . . . 104
6.4.2 Comparison to Rate Constant Recommendations . . . . . . . 107
6.5 Overall Rate Constant Recommendation . . . . . . . . . . . . . . . . 109
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
xi
7 Reaction of OH with sec-Butanol 113
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . 113
7.1.2 Objectives of the Current Chapter . . . . . . . . . . . . . . . 115
7.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.3 Secondary Reaction Pathway Modeling . . . . . . . . . . . . . . . . . 116
7.4 OH Time-histories and Rate Constant Determination . . . . . . . . . 120
7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.5.1 Mechanism Performances . . . . . . . . . . . . . . . . . . . . . 123
7.5.2 Low-temperature Rate Constants . . . . . . . . . . . . . . . . 124
7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
8 Reaction of OH with tert-Butanol 129
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
8.1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . 129
8.1.2 Objectives of the Current Chapter . . . . . . . . . . . . . . . 132
8.1.3 Organization of this Chapter’s Results . . . . . . . . . . . . . 132
8.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.3 Net OH Removal Rates . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.4 Kinetic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.4.1 Net OH Removal Rate by Reaction with tert-Butanol . . . . . 139
8.5 Branching Ratio Determinations . . . . . . . . . . . . . . . . . . . . . 142
8.5.1 Evaluation of brOH . . . . . . . . . . . . . . . . . . . . . . . . 142
8.5.2 Evaluation of brβ . . . . . . . . . . . . . . . . . . . . . . . . . 142
8.6 Overall Rate Constant Determination . . . . . . . . . . . . . . . . . . 145
8.6.1 Comparisons to Mechanism Predictions . . . . . . . . . . . . . 146
8.6.2 Comparisons to Low-temperature Literature . . . . . . . . . . 148
8.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
9 Concluding Remarks 151
9.1 Summary of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
9.2 Implications for Addressing Global Challenges . . . . . . . . . . . . . 156
xii
9.3 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . 156
9.3.1 Alkane Combustion Kinetics . . . . . . . . . . . . . . . . . . . 156
9.3.2 Butanol Combustion Kinetics . . . . . . . . . . . . . . . . . . 157
A Shock Tube Cleaning Techniques 161
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
A.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
A.3 Impurity Characterization . . . . . . . . . . . . . . . . . . . . . . . . 163
A.4 Gas-mixing Facility Cleaning Methods . . . . . . . . . . . . . . . . . 170
A.5 Shock Tube Cleaning Methods . . . . . . . . . . . . . . . . . . . . . . 173
A.6 Additional Comments . . . . . . . . . . . . . . . . . . . . . . . . . . 177
B Microwave Discharge System 179
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
B.2 Equipment Setup and Procedure . . . . . . . . . . . . . . . . . . . . . 179
B.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
B.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
C Fuel Measurement using a Helium-neon Laser 185
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
C.2 Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
C.3 Mixing Time Determination . . . . . . . . . . . . . . . . . . . . . . . 186
C.4 Mole Fraction Measurements in a Multi-pass Cell . . . . . . . . . . . 187
D Rate Constant Estimation Methods 199
D.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
D.2 Empirical Estimation Methods . . . . . . . . . . . . . . . . . . . . . . 201
D.3 Transition State Theory . . . . . . . . . . . . . . . . . . . . . . . . . 207
D.4 Ab initio Prediction Methods . . . . . . . . . . . . . . . . . . . . . . 208
E Estimation of Rate Constants for Unimolecular Reactions 211
E.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
E.2 High-pressure Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
xiii
E.3 Fall-off Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Bibliography 217
xiv
List of Tables
2.1 Double-dilution mixture preparation procedure example to prepare a
mixture of 50 ppm TBHP/water and 150 ppm n-heptane in argon. . 21
3.1 Reactions added and rate constants modified in the JetSurf 1.0 mech-
anism to generate the alkane/TBHP mechanism used for this study. 31
3.2 Measured rate constant for Reaction (3.1) from 799 to 990 K. . . . . 39
4.1 Individual data points fit using the alkane/TBHP mechanism for the
rate constant for Reaction (4.1): C5H12 + OH −→ C5H11 + H2O. . . 58
4.2 Individual data points fit using the alkane/TBHP mechanism for the
rate constant for Reaction (4.2): C7H16 + OH −→ C7H15 + H2O. . . 58
4.3 Individual data points fit using the alkane/TBHP mechanism for the
rate constant for Reaction (4.3): C9H20 + OH −→ C9H19 + H2O. . . 59
5.1 List of reactions and rate constants of the n-butanol/TBHP mechanism
of the current work. . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2 Determinations of the rate constant for Reaction (5.1) from the exper-
imental OH time-history data. . . . . . . . . . . . . . . . . . . . . . 83
5.3 Individual and coupled uncertainties and influence of the uncertainties
on the determination of the rate constant for Reaction (5.1) at 1197 K
and 925 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4 Differences in the mechanisms in the current work and the work of
Vasu et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
xv
6.1 Rate constants for the reactions of significance in iso-butanol kinetics
that were added to the base mechanism. . . . . . . . . . . . . . . . . 102
6.2 Rate constants knon-β6.1 and koverall6.1 for each experimental data point, and
the resulting branching ratio for the β-channel. . . . . . . . . . . . . 107
7.1 Rate constant determination for Reaction (7.1) for each experimental
data point. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.1 Pseudo-first-order and second-order rate constants determined for each
experimental temperature. . . . . . . . . . . . . . . . . . . . . . . . 135
8.2 Rate constants determined for each experimental temperature. . . . 141
D.1 Group rate constants from Walker. . . . . . . . . . . . . . . . . . . . 203
D.2 Improved group scheme rate constant terms recommended by Sivara-
makrishnan and Michael. . . . . . . . . . . . . . . . . . . . . . . . . 207
E.1 Families of addition reactions with equivalent rate constants. . . . . 214
xvi
List of Figures
1.1 Reaction path diagram for the n-heptane autoignition process showing
many of the major reaction pathways. . . . . . . . . . . . . . . . . . 5
1.2 Average composition of commercial gasoline in the United States as
reported in Pitz et al. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 The four structural isomers of butanol . . . . . . . . . . . . . . . . . 10
2.1 Position-time (x-t) diagram of a standard pressure driven shock tube
operation and schematics of a shock tube at various times. . . . . . . 15
2.2 Schematic of the cross-sectional view of shock tube. . . . . . . . . . 16
2.3 Schematic of the gas-mixing facility showing the different elements con-
nected to the 14-port gas-mixing manifold. . . . . . . . . . . . . . . 18
2.4 Schematic of the laser diagnostic system. . . . . . . . . . . . . . . . 23
3.1 Two-step decomposition mechanism of tert-butylhydroperoxide. . . . 29
3.2 OH sensitivity for a mixture of 20.5 ppm TBHP in argon at 928 K and
1.22 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 OH sensitivity for a mixture of 20.0 ppm TBHP in argon at 1158 K
and 1.10 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 OH time-histories at 928 K, 1.22 atm for 20.5 ppm TBHP argon. . . 35
3.5 OH time-histories at 1158 K, 1.10 atm for 20.0 ppm TBHP argon. . 36
3.6 Measured OH yield as a function of the initial TBHP/water solution
mole fraction in a test mixture. . . . . . . . . . . . . . . . . . . . . . 38
3.7 Arrhenius plot of the rate constant for Reaction (3.1). . . . . . . . . 40
3.8 Arrhenius plot of rate constants for reactions of CH3 + OH. . . . . . 42
xvii
4.1 OH sensitivity for pseudo first-order experiments to measure the overall
rate of n-nonane+OH. . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 OH time-histories at 1167 K, 1.00 atm for 168 ppm n-nonane, 16.0 ppm
TBHP, argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3 OH time-history on a semi-logarithmic scale for conditions of 937 K,
1.20 atm for 214 ppm n-nonane, 16.5 ppm TBHP, argon. . . . . . . 56
4.4 Measured rate constants for Reactions (4.1), (4.2), and (4.3), reactions
of OH with n-pentane, n-heptane, and n-nonane, respectively. . . . . 57
4.5 Factors considered in the uncertainty analysis for the rate constant for
Reaction (4.3) at 1167 K, 1.00 atm. . . . . . . . . . . . . . . . . . . 60
4.6 Rate constants for Reactions (4.1), (4.2), and (4.3). . . . . . . . . . . 63
5.1 OH time-histories from Chapter 3 for experiments of dilute mixtures
of TBHP in argon. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Arrhenius plot of the rate constant for Reaction (5.1). . . . . . . . . 74
5.3 Reaction pathways important in the calculation of OH time-history
under the current experimental conditions. . . . . . . . . . . . . . . 77
5.4 OH time-histories for 1197 K and 0.96 atm for a mixture of 150 ppm
n-butanol and 13.3 ppm TBHP, and 925 K and 1.22 atm for a mixture
of 201 ppm n-butanol and 10.3 ppm TBHP. . . . . . . . . . . . . . . 82
5.5 OH sensitivity calculation for a mixture of 201 ppm n-butanol and
10.3 ppm TBHP at 925 K at 1.22 atm. . . . . . . . . . . . . . . . . 84
5.6 OH reaction path analysis at 1197 K and 0.96 atm for a mixture of
150 ppm n-butanol and 13.3 ppm TBHP. . . . . . . . . . . . . . . . 86
5.7 Measured OH time-histories at 1182 K, 2.04 atm, 150 ppm n-butanol,
13 ppm TBHP and at 1165 K, 2.25 atm, 147 ppm n-butanol, 11 ppm
TBHP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.8 Arrhenius plot of the rate constant for Reaction (5.1). . . . . . . . . 92
5.9 Arrhenius plot of the rate constant for Reaction (5.1) shown with pub-
lished data at atmospheric-relevant conditions. . . . . . . . . . . . . 95
6.1 Dominant reaction pathways of iso-butanol after reaction with OH. . 98
xviii
6.2 OH sensitivity calculation at 1079 K, 1.1 atm with 220 ppm iso-butanol
and 15 ppm TBHP. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.3 OH time-histories at temperatures of 1134 K, 1079 K, 1047 K, and
937 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.4 Rate constant measurements for knon-β6.1 . . . . . . . . . . . . . . . . . 106
6.5 Overall rate constant for the reaction of OH with iso-butanol. . . . . 110
7.1 Dominant reaction pathways of sec-butanol after reaction with OH. . 115
7.2 OH sensitivity analysis of the 214 ppm sec-butanol and 14 ppm TBHP
mixture at 969 K and 1.15 atm. . . . . . . . . . . . . . . . . . . . . 117
7.3 Branching ratios for Reactions (7.1a) through (7.1e). . . . . . . . . . 118
7.4 Branching ratios for the consumption of the CH2CH(OH)CH2CH3 and
CH3CH(OH)CHCH3 radicals. . . . . . . . . . . . . . . . . . . . . . . 119
7.5 OH time-history for an experiment at 969 K, 1.15 atm with 214 ppm
sec-butanol and 14 ppm TBHP. . . . . . . . . . . . . . . . . . . . . . 120
7.6 Arrhenius plot of the rate constant for Reaction (7.1). . . . . . . . . 121
7.7 Arrhenius plot of the rate constant for Reaction (7.1). . . . . . . . . 125
8.1 Dominant reaction pathways of tert-butanol after reaction with OH. 131
8.2 OH time-history at 943 K on a semi-logarithmic plot. . . . . . . . . 134
8.3 Brute force sensitivity for the pseudo-first-order rate constant. . . . . 137
8.4 OH reaction path diagram. . . . . . . . . . . . . . . . . . . . . . . . 138
8.5 Arrhenius plot of the product of k8.1 · (1− brOH · brβ). . . . . . . . . 140
8.6 Arrhenius plot of the overall rate constant for Reaction (8.1). . . . . 141
8.7 The temperature-dependent branching ratio brβ. . . . . . . . . . . . 143
8.8 Arrhenius plot of experimental determinations for the overall rate con-
stant for the reaction of OH with tert-butanol and the best-fit 3-
parameter expression. . . . . . . . . . . . . . . . . . . . . . . . . . . 145
9.1 Arrhenius plot of the rate constant determinations for Reac-
tions (5.1), (6.1), (7.1), and (8.1) from the current work. . . . . . . . 154
xix
A.1 Schematic of the driven section of the Kinetics Shock Tube and gas-
mixing facility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
A.2 Impurity measurement history in the shock tube facilities. . . . . . . 165
A.3 OH time-history measurements in hot 2% O2/Ar shocks near 1655 K
for different fill locations in the shock tube. . . . . . . . . . . . . . . 166
A.4 Peak OH mole fraction formed in hot 2% O2/Ar shocks around 1655 K
as a function of fill location. . . . . . . . . . . . . . . . . . . . . . . . 167
A.5 Peak OH mole fraction formed in hot 2% O2/Ar shocks at various
temperatures and different fill locations. . . . . . . . . . . . . . . . . 168
A.6 OH time-histories measured in 2% O2/Ar shocks, filled into the shock
tube from the mixing facility. . . . . . . . . . . . . . . . . . . . . . . 172
B.1 Schematic of He/H2O microwave discharge cell and H2O saturator
setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
B.2 OH line shapes, calculated and measured. . . . . . . . . . . . . . . . 182
B.3 Measured OH line shape compared with the Doppler profile fit at a
temperature of 800 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 183
C.1 Measured n-heptane mole fractions of a n-heptane/argon mixture after
being filled into the shock tube after different mixing times. . . . . . 187
C.2 Alignment card setup for the multi-pass cell using the manufacturer
supplied cards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
C.3 Multi-pass cell setup with HeNe laser. . . . . . . . . . . . . . . . . . 189
C.4 Gas flow diagram of the multi-pass cell setup. . . . . . . . . . . . . . 192
C.5 Uncertainty in the measured mole fraction using an absorption diag-
nostic with a 3% uncertainty in laser intensity. . . . . . . . . . . . . 193
C.6 Absorption measurements at various pressures of the 50 ppm
TBHP/water in argon mixture. . . . . . . . . . . . . . . . . . . . . . 195
D.1 The carbons of the n-heptane and iso-butanol molecules described us-
ing the terminology used in this appendix. . . . . . . . . . . . . . . . 201
xx
E.1 Three beta-scission decomposition pathways for the 1-hydroxy-but-2-yl
radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
E.2 Isomerization reactions for C4H9O radicals. . . . . . . . . . . . . . . 212
E.3 Rate constants for addition reactions of alkene+CH3 and alkene+OH
from Manion et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
xxi
xxii
Chapter 1
Introduction
1.1 Motivation
Combustion has been a dominant process for energy conversion in automobiles since
the development of the internal combustion engine in the 1800’s. Recent energy con-
sumption statistics in 2011 from the United States Energy Information Agency point
out that 94% of the energy used in our nation’s transportation sector comes from
petroleum resources [1], indicating that combustion is still a dominant energy conver-
sion process of importance. The continued use of petroleum-fueled automobiles in the
present day introduces concerns revolving around future environmental impact, sus-
tainability, and political and economic issues. In response to these concerns, research
on the development of advanced transportation engine technologies capable of gener-
ating lower emissions, operating with increased efficiency, and/or converting energy
from renewable resources, is being carried out in laboratories all over the world. Opti-
mization of these advanced transportation engine technologies can be facilitated with
accurate predictive models describing the combustion phenomena that occur within
the engine. A predictive combustion model consists of mathematical descriptions of
the transport, fluid mechanics, and chemistry phenomena relevant to the combustion
process. The development of these models typically begins with the development and
validation of individual models for each phenomenon.
1
2 CHAPTER 1. INTRODUCTION
Chemical kinetics, the study of rates of chemical processes, is an important pro-
cess to include in a comprehensive combustion model. Kinetic models are of critical
importance in the design of certain types of advanced engine technologies. For exam-
ple, the ignition event in a homogeneous charge compression ignition (HCCI) engine
is controlled by the kinetics of combustion, as opposed to traditional spark-ignition
or diesel engines where ignition is controlled by spark or injection, respectively. Rate
constants for elementary reactions in the mechanism are a critical part of the model,
and certain chemical species and reactions play key roles in the combustion process.
Chemical species with unpaired electrons, called radicals, are important in every com-
bustion process, and reactions of radicals with the combusting fuel can constitute a
major fuel consumption pathway. Rate constants for these types of reactions must
be known well to develop accurate detailed kinetic models for combustion.
In this thesis, rate constants for important reactions in the combustion process
were studied in a pressure-driven shock tube using laser-based diagnostics, and the
results expand the experimental database of rate constants for use in the development
of detailed kinetic mechanisms. The key reactions studied fall in the family of reac-
tions of hydrogen-atom abstraction by the hydroxyl radical (OH) of a normal alkane
molecule or an isomer of the butanol molecule; normal alkanes and butanol represent
two families of organic molecules that are of current interest regarding transporta-
tion fuels. Narrow-linewidth laser absorption by OH was employed for quantitative
time-resolved measurement of OH mole fraction in experiments designed with high
sensitivity to the rate constants of interest. tert-Butylhydroperoxide (TBHP) was
used as a fast source of OH radicals, and improvements to the modeling of the de-
composition of TBHP as the OH precursor were also undertaken in this study.
1.2 Background
1.2.1 Development of Kinetic Mechanisms for Combustion
Accurate knowledge of the rate constants for the types of reactions studied in this
thesis are of critical importance in developing accurate predictive kinetic mechanisms
1.2. BACKGROUND 3
for combustion. Detailed kinetic models for the high-temperature oxidation (combus-
tion) of organic compounds contain three parts: 1) a list of each elementary reaction
expected to occur in the process, 2) a rate constant for each elementary reaction,
including a description of the rate constant dependence on temperature and pressure,
and 3) thermodynamic parameters describing the temperature-dependent enthalpy
and entropy for each chemical species present in the mechanism. A model with these
three components constitutes a detailed kinetic mechanism.
The number of elementary reactions needed to fully describe the combustion chem-
istry of a given fuel typically grows with the complexity of the fuel of interest. For
example, a current detailed kinetic mechanism describing hydrogen combustion is
comprised of 20 reactions with 10 chemical species [2]. A popular mechanism devel-
oped for methane combustion consists of 325 reactions and 53 chemical species [3],
and a mechanism for n-heptane combustion has 2450 reactions and 550 chemical
species [4]. Detailed kinetic mechanisms are often reduced to fewer reactions for com-
putational simplicity; these reduced mechanisms, however, typically are limited in
application and can be no more accurate than the detailed mechanism from which
they originate.
The rate constants for each of the elementary reactions in a mechanism are con-
ventionally expressed in a modified Arrhenius form given by Eq. 1.1, where ki is the
rate constant for Reaction (i) and its dependence on temperature, T , can be described
using the three parameters A, b, and E.
ki = A · T b · exp
(− E
T
)(Eq. 1.1)
The parameters A, b, and E for each elementary reaction can be determined via sev-
eral methods, including direct measurements, ab initio calculations, or estimations
based on analogous reactions or global experimental studies. Because the number of
reactions and rate constants needed in a detailed combustion kinetic model is large,
many rate constants in a kinetic mechanism are typically determined using estimation
techniques because of the time required for other methods of rate constant determi-
nation. However, several types of reactions are of high importance in predicting
4 CHAPTER 1. INTRODUCTION
experimental benchmarks, including the types of reactions in the current study, and
the rate constants for these reactions must be ascribed accurately in a mechanism to
correctly predict combustion behavior.
Detailed kinetic mechanisms for combustion are often validated against a large
number of experimental datasets. Shock tube ignition delay time experiments, mea-
suring the time required for autoignition, are a common type of validation target for
kinetic models. Similarly, multi-species time-history measurements in shock tubes
during high-temperature pyrolysis and oxidation of fuels have recently gained popu-
larity for validating kinetic models. Other experimental facilities such as flow reactors,
rapid compression machines, jet-stirred reactors, and flames are also used by the ex-
perimental combustion community to expand the experimental database of validation
targets for the development of detailed kinetic mechanisms. These types of experi-
ments can elucidate deficiencies of kinetic mechanisms in development and suggest
the need for refinement of the mechanism for increased accuracy. However, while
these types of experiments provide valuable global validation targets, the data are
typically sensitive to numerous rate constants in the mechanism, leading to difficul-
ties in determining which rate constant are in error if the mechanism fails to predict
the data. A reaction path diagram of a n-heptane autoignition process is shown in
Figure 1.1, illustrating the number of reactions involved during this chemical process.
Therefore, experiments designed specifically to be sensitive to important rate con-
stants are crucial for improving kinetic model performance, in addition to the global
validation targets.
Shock tube reactors offer several advantages for high-temperature rate constant
measurements, including a near-ideal constant volume test platform, well-determined
temperatures and pressures behind the reflected shock waves, and clear optical access
for laser diagnostics. Temperature, pressure, mixture composition, and measured
data type are typical variables that can be varied in a shock tube experiment, and
careful design of these variables can lead to experiments that isolate a reaction of
interest. One such method to isolate a reaction in a shock tube study is to study a
mixture of only the two reactants (typically in an inert diluent), and to monitor the
time-dependent decay of one or several reactant or product concentrations. In the
1.2. BACKGROUND 5
Figure 1.1: Reaction path diagram for the n-heptane autoignition process showing many of the majorreaction pathways. The percentages listed by the hydrogen-atom abstraction reactions represent thefraction of the reaction that occurs via abstraction with each specific molecule, calculated for astoichiometric n-heptane/air mixture at 1000 K and 1 atm at a time of 20 ms using the Curran etal. mechanism [4].
study of bimolecular reactions, a pseudo-first-order reaction approximation technique
is commonly employed, where one reactant is present in large excess (over ten times)
of the other reactant; this technique leads to an exponential decay of the concentration
of the lower concentration reactant, and the time constant is typically sensitive to
only the rate constant for the reaction and the initial concentration of the reactant
in excess. As seen in Figure 1.1, the bimolecular reaction of OH with n-heptane is
a major fuel consumption pathway under certain conditions, according to the kinetic
mechanism of Curran et al. [4]. Thus, the rate constant for this reaction, and similar
types of reactions, should be measured with high accuracy.
In the study of bimolecular reactions involving unstable radical species, such as
the reactions of interest in this study, stable radical precursors that rapidly decom-
pose via shock heating or laser photolysis can be used as a fast source for the radical
reactant. Several stable species have been used as precursors for OH radicals, in-
cluding hydrogen peroxide [5], tert-butylhydroperoxide [6–12], methanol [13], and
6 CHAPTER 1. INTRODUCTION
hydroxylamine [13], each having certain advantages and disadvantages. Challenges
to experimental determination of rate constants arise when secondary reactions in-
fluence the measured data. These secondary reactions can include reactions due to
secondary products of the decomposition of the stable radical precursor, or reactions
of the products of the bimolecular reaction of interest. In this work, both of these is-
sues appear, and the effects are accounted for through experimental study and kinetic
modeling.
1.2.2 Alkane Combustion Kinetics
Current commercial gasoline, diesel and jet fuels are composed of a mixture of organic
compounds. Figure 1.2 presents the average composition of commercial gasoline in the
United States as reported by Pitz et al. [14]. Alkane molecules, also known as paraf-
fins or saturated hydrocarbons or hydrocarbons with exclusively single bonds, are in
the majority, making up over 50% of the gasoline composition. Many of these alka-
nes are large straight-chain normal alkanes (referred to as n-alkanes). In addition to
their presence in current commercial fuels, n-alkanes are are also popular component
choices for surrogate fuels, which are mixtures of a few select hydrocarbon compounds
with combustion characteristics similar to those of commercial fuels. For example,
n-heptane is widely used as a surrogate for gasoline, n-hexadecane a surrogate for
diesel, and n-decane and n-dodecane as surrogates for jet fuel [14–16]. Furthermore,
n-heptane is a primary reference fuel used to determine the octane rating of com-
mercial gasoline. Because of the importance of large straight-chain n-alkanes in both
practical and surrogate fuels, development of accurate kinetic mechanisms describing
the combustion characteristics of n-alkanes is important.
Kinetic mechanisms for hydrocarbon fuels, including n-alkanes, have been rapidly
evolving over the past few decades. The ability to develop and run calculations with
kinetic mechanisms for large n-alkane fuels has only recently been made possible,
owing to the substantial improvements in computing systems, which are now capable
of performing calculations for the thousands of reactions in these mechanisms in a
reasonable time frame. Several long-term development projects for high-temperature
1.2. BACKGROUND 7
27.8%
9.6%
6.06%
56.6%
Alkanes Naphthenes Olefins Aromatics
Average Composition of Commercial U.S. Gasoline
Figure 1.2: Average composition of commercial gasoline in the United States as reported in Pitz etal. [14]. Representative structures of each type of molecules are shown in the chart.
kinetic mechanisms of large n-alkane exist. For example, n-heptane combustion chem-
istry can be found in the mechanisms suggested by Curran et al. [4], Ranzi et al. [17],
and Smith et al. [18], among others. The rapid progress in the development of larger
kinetic mechanisms for larger fuels calls for expansion of the experimental database
for validating these mechanisms at a similar rate. The current work contributes to
expanding the experimental database for the kinetics of large n-alkanes, specifically
rate constants for reactions of OH with n-pentane (C5H12), n-heptane (C7H16), and
n-nonane (C9H20). To date, only estimation methods have been developed [11, 19–26]
to predict the temperature dependence of the rate constant for the reaction of OH
with n-nonane at combustion-relevant temperatures, and thus, the current work seeks
to extend the experimental database of rate constants to validate these estimation
methods. Using the data presented in this thesis, the accuracy of estimation meth-
ods to obtain rate constants for reactions in the family of OH plus n-alkanes will be
examined to increase the confidence in predicting the rate constants for this family
of reactions involving even larger n-alkanes.
8 CHAPTER 1. INTRODUCTION
1.2.3 Butanol Combustion Kinetics
Factors such as unstable oil prices, a desire for increased sustainability and energy
security, and concerns about greenhouse gas emissions from fossil fuels have led to in-
creased efforts to introduce biofuels into the current transportation economy. Biofuels
are fuels derived from biological carbon fixation, thus the combustion of biofuels leads
to lower net carbon dioxide emissions as compared to gasoline (a common misconcep-
tion is that biofuel combustion always leads to “net zero” carbon emissions; however,
the processes used to produce and transport many biofuels typically lead to some
carbon dioxide emission). Because biofuels can be produced from renewable organic
material, with common feedstocks including animal fats, corn, and sugarcane, supply
can ideally be infinitely renewable, and production of biofuels is not limited to only
certain areas of the world. Furthermore, study of the combustion of oxygenated hy-
drocarbon fuels, such as bio-alcohol fuels, has shown that the presence of oxygenated
compounds in the fuel mixture can suppress soot formation in diesel engines [27].
The most widely used liquid biofuel in the transportation sector currently is bio-
derived ethanol, produced by fermentation of crops such as corn or sugarcane. In
the United States, ethanol fuel is largely introduced into traditional vehicles in low-
level blends with gasoline up to 10%. Commercially available flex-fuel vehicles have
recently become increasingly popular, which have modified internal combustion en-
gines that are capable of operating on a maximum blend of 85% ethanol with 15%
gasoline (called E85 fuel). While use of ethanol as a transportation fuel has attributed
to some success in increased energy security and reduced greenhouse gas emissions,
there are still shortcomings to using ethanol fuel, including low energy density, prop-
erties incompatible with several components of current internal combustion engines
(thus the need for modified flex-fuel engines for operation on E85 fuel), and difficul-
ties in transporting ethanol in the current gasoline infrastructure because ethanol is
miscible with water.
Biobutanol is a second-generation biofuel for transportation applications and has
many advantages over ethanol. Compared with ethanol, butanol has a higher energy
density, a lower propensity to attract water (thus it can be more easily transported
1.2. BACKGROUND 9
and stored in the current gasoline infrastructure), and properties suitable for oper-
ation in unmodified gasoline engines [28]. Biobutanol can be produced via similar
production methods as ethanol (via the acetone-butanol-ethanol process) using feed-
stocks such as corn and sugarcane. In addition, biobutanol can also be made from
lignocellulosic sources like crop waste and non-food plants such as switch grass. Pro-
duction of biobutanol from algae is also possible. The energy content of butanol still
falls short of the energy content of gasoline, however, combustion of 100% butanol
fuel will occur over a more uniform temperature and pressure compared to gasoline
(the many components of gasoline leads to ignition over a broad range of temperature
and pressure). Thus, engines optimized for operation on 100% butanol fuel can be
tuned to deliver a high fuel economy.
Butanol is a four-carbon alcohol and has four structural isomers: n-butanol, iso-
butanol, sec-butanol, and tert-butanol; these structural isomers of butanol are shown
in Figure 1.3. Methods for producing n-butanol, iso-butanol, and sec-butanol from
biological sources are currently known. While no methods have been established for
the production of tert-butanol from biological matter, this isomer of butanol is widely
used as a fuel additive. Thus, all four isomers of butanol are relevant as transportation
fuels and detailed kinetic mechanisms describing the high-temperature oxidation of
each of the butanol isomers are important.
Detailed chemical kinetic models for high-temperature combustion of the isomers
of butanol have become of recent research interest, lending support to the introduction
of biobutanol into the transportation sector. The efforts towards kinetic modeling
of n-butanol combustion is by far the most extensive. Dagaut and coworkers [29,
30] published one of the first kinetic mechanisms of n-butanol in 2008, using data
from a jet-stirred reactor as validation targets. In the same year, Moss et al. [31]
collected shock tube ignition delay time data for all four of the isomers of butanol and
developed a kinetic mechanism including high-temperature chemistry for each isomer.
Researchers from around the world quickly followed suit, adding to the literature
additional mechanisms and experimental validation targets for n-butanol and the
other isomers. Mechanisms for butanol combustion continue to be improved upon in
the current day, indicating that work in this area is far from complete and that a larger
10 CHAPTER 1. INTRODUCTION
H3C
H2C
CH2
H2C
OH H3CCH
CH2
OH
CH3
H3CCH
CH2
CH3
OH CH3
CH3C OH
CH3
n-butanol iso-butanol
sec-butanol tert-butanol
Figure 1.3: The four structural isomers of butanol
kinetic experimental database would be beneficial. Various experimental targets of
global butanol combustion phenomena have been collected in different types of reactor
systems, including jet-stirred reactor species profiles [29, 30, 32], rapid compression
machine and shock tube ignition delay times and speciation studies [31, 33–39], and
flame studies [32, 40–46]. However, relatively few experimental data exist describing
phenomena with high-sensitivity to key elementary reactions. The first measurements
for the high-temperature rate constant for the reaction of OH with n-butanol was
performed by Vasu et al. [47] in 2010. Besides the study of Vasu et al., however,
no other experimental studies published in the literature directly focus on the rate
constant for the reactions of OH with butanol at combustion-relevant temperatures.
The current work extends upon the work of Vasu et al., extending the temperature
range of their measurements and producing the first experimentally determined high-
temperature rate constants for the reaction of OH with the other butanol isomers.
1.3 Scope and Organization of Thesis
The objective of this thesis is to collect low-noise OH time-history measurements at
experimental conditions designed to have high sensitivity to the rate constants for
1.3. SCOPE AND ORGANIZATION OF THESIS 11
the reactions of the OH radical with n-alkane and butanol molecules at combustion-
relevant conditions. These data expand the experimental database for n-alkane and
butanol combustion kinetics and can be used for the validation and refinement of
kinetic mechanisms for the respective fuels. Three large n-alkanes (n-pentane, n-
heptane, and n-nonane) and the four isomers of butanol (n-butanol, iso-butanol,
sec-butanol, and tert-butanol) were studied. In the process of completing this work,
several other research areas were examined, including the development of a fuel mole-
fraction measurement method for ultra-low concentration experiments, experimental
study and modeling of tert-butylhydroperoxide as a stable precursor for OH radicals,
and detailed modeling studies of butanol after reaction with OH.
Chapter 2 of this thesis discusses the experimental facilities and methods used
for the data collection, including a discussion of the precautions taken to mini-
mize experimental error and a description of the method developed for validating
fuel concentration in ultra-low concentration mixtures. Chapter 3 introduces tert-
butylhydroperoxide (TBHP) as a stable source of OH radicals, and present the re-
sults of experiments designed to develop a model for high-temperature TBHP de-
composition. Chapter 4 presents the results of the experimental work on n-pentane,
n-heptane, and n-nonane, and also includes discussion of the comparison of the cur-
rent data with previous experimental, theoretical, and empirical modeling studies.
Chapters 5 through 8 present the experimental work for n-butanol, iso-butanol,
sec-butanol, and tert-butanol, and also include discussions on butanol combustion
modeling and comparison to previous works. Supporting work, including discussions
on preparing the experimental facilities and background on rate constant estimation
methods, are included in the Appendices.
At the time of publication, the contents of this thesis appear in several publica-
tions. The contents of Chapters 3 and 4 are adapted with permission from G. A. Pang,
R. K. Hanson, D. M. Golden, and C. T. Bowman, “High-temperature measurements of
the rate constants for reactions of OH with a series of large normal alkanes: n-pentane,
n-heptane, and n-nonane,” Zeitschrift fur Physikalische Chemie, Volume 225, 2011,
Pages 1157-1178; copyright c© 2011 Oldenbourg Wissenschaftsverlag GmbH. The
content in Chapter 5 is adapted with permission from G. A. Pang, R. K. Hanson,
12 CHAPTER 1. INTRODUCTION
D. M. Golden, and C. T. Bowman, “Rate Constant Measurements for the Overall Re-
action of OH + 1-Butanol → Products from 900 K to 1200 K,” Journal of Physical
Chemistry A, Volume 116, 2012, Pages 2475-2483; copyright c© 2012 American Chem-
ical Society. The content in Chapter 6 is adapted with permission from G. A. Pang,
R. K. Hanson, D. M. Golden, and C. T. Bowman, “High-temperature Rate Constant
Determination for the Reaction of OH with iso-Butanol,” Journal of Physical Chem-
istry A, Volume 116, 2012, Pages 4720-4725; copyright c© 2012 American Chemical
Society.
Chapter 2
Experimental Setup
2.1 Introduction
The first shock tube was constructed in France in 1899 [48], though this type of
device was not applied to the study of high-temperature chemical kinetics until the
1950’s [49]. The advantages of using a shock tube for the experimental study of high-
temperature kinetics include instantaneous heating by shock waves, well-determined
initial temperatures and pressures behind reflected shock waves, near-ideal constant
volume reaction reaction environment, and clear optical access for laser diagnostics.
The use of laser diagnostics to probe high-temperature reacting experiments enables
the collection of in situ, time-resolved, species-specific measurements. This chapter
details the shock tube facility and diagnostics utilized for the experiments performed
in this work, as well as the basic procedures that were followed.
2.2 Kinetics Shock Tube Facility
The experiments reported in this thesis were all performed behind reflected shock
waves in the Kinetics Shock Tube Facility located in the Mechanical Engineering
Research Laboratory (MERL) of Stanford University. This shock tube facility consists
of a pressure-driven shock tube and a high-purity gas mixing system.
13
14 CHAPTER 2. EXPERIMENTAL SETUP
2.2.1 Shock Tube Overview
The Stanford Kinetics Shock Tube is a pressure-driven stainless-steel shock tube
with a circular cross-section of 14.13 cm (inner-diameter) in both the 8.54-m long
driven section and the 3.35-m long driver section. The low-pressure driven section
is separated from the high-pressure driver section by a polycarbonate diaphragm of
0.127 to 0.254 mm in thickness (Polycarbonate film DE1-1 Gloss/Gloss supplied by
Professional Plastics). In a typical experiment, a premixed gas-phase test mixture is
first filled into the driven section. The driver section is then subsequently filled to
high-pressure with helium, or a mixture of helium and nitrogen, until the diaphragm is
ruptured by a set of cross-shaped cutting blades residing on the driven-section side of
the diaphragm. The rupture of the diaphragm allows the high-pressure driver gas to
expand, creating an incident shock wave that propagates towards the driven-section
endwall before subsequently reflecting back towards the driver section. Behind the
reflected shock wave near the driven-section endwall is a high-temperature reaction
environment closely representing a constant volume reactor. The shock tube process
can be best represented on a position-time (x-t) plot, which is shown in Figure 2.1
for the operation of a standard pressure driven shock tube.
The temperature and pressure behind the reflected shock wave are controlled by
changing the incident shock velocity. In the current work, this was achieved by chang-
ing the thickness of the diaphragm, changing the axial position of the cutting blades
responsible for the diaphragm rupture, and/or changing the composition of nitrogen in
the driver gas. Five axially-spaced piezoelectric pressure transducers (PCB model no.
113A26 with 483B08 amplifier) were positioned at 2.0 cm, 38.8 cm, 69.3 cm, 99.7 cm,
and 130.2 cm from the driven-section endwall for measurement of the incident-shock
velocity. The signals from these pressure transducers were sent to four time-interval
counters to determine the average incident shock velocity at four axial positions near
the driven-section endwall. The measured incident-shock attenuation, typically in
the range of 0.5-1.5%/m, was used to extrapolate the incident-shock velocity at the
driven-section endwall. The reflected-shock velocity was calculated from the endwall
incident-shock velocity, assuming a zero-axial-velocity boundary condition at the end-
wall.
2.2. KINETICS SHOCK TUBE FACILITY 15
t
cont
act s
urfa
ce
incide
nt sho
ck
expansion fan
part
icle
pat
h
x
reflec
ted
rarefa
ction
fan
Driven sectionDriver section t0, before diaphragm burst
t1 > t0, incident shock
t2 > t1, reflected shockpressure
transducers(shock velocity measurement)
driven section endwall
diaphragm
region representing constant volume reactor
Figure 2.1: Position-time (x-t) diagram of a standard pressure driven shock tube operation andschematics of a shock tube at various times. Also shown in one of the time schematics are axially-spaced pressure transducers that can be used to measure the shock velocity.
The pressure and temperature conditions behind the reflected shock waves were
determined using adiabatic one-dimensional shock relations and the known (mea-
sured) incident-shock velocities. These calculation were performed using an in-house
code that contained thermodynamic data for the gas mixture; the results are iden-
tical to calculations using thermodynamic data from Goos et al. [50] for the species
present in the gas mixture. Vibrational equilibrium was assumed in the gases behind
the incident and reflected shock waves. Uncertainty in the incident-shock velocity
determination at the driven-section endwall leads to uncertainties of less than 1% in
both the reflected-shock temperatures and pressures at the measurement location.
The reactive gas mixture behind the reflected shock wave was monitored at an ax-
ial location 2 cm from the driven-section endwall using a Kistler piezoelectric pressure
transducer (PZT, model no. 603B1 with 5010B amplifier) and the laser absorption
diagnostic discussed in Section 2.3.1. The PZT was mounted such that its surface was
recessed approximately 1 mm from the inner diameter surface and the surface was
coated with a layer of red silicon RTV approximately 1 mm thick to protect the sensor
16 CHAPTER 2. EXPERIMENTAL SETUP
from thermal shock and temperature-induced changes in sensitivity. The signal from
the PZT was used to confirm uniform pressure during the experiments. The laser
absorption diagnostic was used to monitor the test gas 2 cm from the driven-section
endwall through a pair 0.75” diameter sapphire windows of 0.125” thickness mounted
directly opposite of each other tangent and flush to the inner surface of the shock
tube. Figure 2.2 shows a schematic of the cross-sectional view of the shock tube at
the axial location 2 cm from the driven-section endwall with the diagnostics used in
this thesis.
0.75'' diameter sapphire windows, 0.125'' thickness
PCB 113A26
Kistler 603B1
UV laser
Cross-sectional view of the shock tube diagnostic area located 2 cm from the driven section endwall
Figure 2.2: Schematic of the cross-sectional view of shock tube at the axial location 2 cm fromthe driven-section endwall. The pressure transducers and the windows for the laser absorptiondiagnostics are shown, along with the alignment of the laser through the windows. The laser beamis angled to avoid interference from internal reflections.
The shock tube facility was thoroughly cleaned before the start of experiments,
and also between experiments as needed. Prior to each set of experiments, the impu-
rities in the shock tube were confirmed to contribute to less than 1 ppm of hydrogen
atoms using the laser diagnostics described in Section 2.3.1. Further details of the
shock tube cleaning procedures and impurity detection is described in Appendix A.
Before each individual experiment, the shock tube driven section was evacuated to a
pressure at or below 5×10−6 Torr using a combination of a roughing pump and a tur-
bomolecular pump. This vacuum corresponded to a shock tube leak-plus-outgassing
rate at or below 50 × 10−6 Torr/minute. An ion gage tube vacuum sensor was con-
nected to the vacuum sections to measure the ultimate pressure of the shock tube.
Experiments were performed with and without passivation of the shock tube walls
2.2. KINETICS SHOCK TUBE FACILITY 17
using the initial mixture, a technique that has previously been demonstrated to re-
duce losses of chemicals due to wall adsorption [51]. The results of the passivation
experiments concluded that passivation has no effect and is thus unnecessary. Mea-
surements of the fuel mole fraction in the prepared gas mixtures using the laser
absorption technique described in Appendix C further confirm that no liquid fuel loss
occurs.
2.2.2 Gas-mixing Facility Overview
The experimental test mixtures were all prepared in a gas-mixing facility consisting
of a 12-liter internally-stirred electro-polished stainless-steel mixing tank and a 14-
port gas-mixing manifold. The mixing tank contains a brass mixing vane coupled to
a magnetic stirrer, controlled by a Fischer Scientific Thermix Stirrer (Model 220T);
the stirrer controller was set to medium speed and never turned off. The mixing
manifold is constructed with a central welded stainless steel piece of cross pipe of 3/8”
diameter, and each port can be connected to various sources via Swagelok stainless
steel 8BK bellow valves. Figure 2.3 shows a schematic of the gas-mixing facility
and the ports used for the experiments described in this thesis. A 100 Torr and
a 10,000 Torr high-capacitance Baratron manometer (both Model 690A) were each
located at different mixing manifold ports. The gas-mixing facility is connected to
the shock tube driven section at a location 5.74 m from the driven-section endwall via
a port on the mixing manifold. The gas-mixing facility has a two-stage evacuation
procedure, with separate roughing and turbomolecular pumps than the shock tube.
The vacuum pumps were connected to the mixing facility through a mixing manifold
port when used for evacuation of the manifold, and were also connected to the mixing
tank through a larger diameter valve for evacuation of the mixing tank and entire
facility. An ion gage tube vacuum sensor was connected to the vacuum line to measure
the ultimate pressure of the mixing facility. The gas-mixing facility was thoroughly
cleaned using a brute-force disassembly method prior to the start of the experiments in
this thesis, and chemical cleaning methods were used between each set of experiments.
The laser diagnostic system described in Section 2.3.1 was used to periodically verify
18 CHAPTER 2. EXPERIMENTAL SETUP
that less than 1 ppm of hydrogen atom impurities were present in the mixing facility.
Appendix A describes the cleaning and impurity detection methods used in this work.
Mixing Tank12 L
to vacuum pumps
to shock tube (5.74 m from the driven section endwall)
vent to atmosphere
liqui
d ch
emic
al #
1 (T
BH
P)
liqui
d ch
emic
al #
2empt
yem
pty
empt
y
empt
y
empt
y Arg
on
1000
0 To
rrB
arat
ron
100 TorrBaratron
Figure 2.3: Schematic of the gas-mixing facility showing the different elements connected to the14-port gas-mixing manifold.
Three ports on the mixing manifold were used for the chemicals in the mixture
preparation for this thesis work (Section 2.4 details the specific chemicals used). A sin-
gle port was connected to a high-pressure argon gas cylinder through a CGA-590 reg-
ulator. Liquid chemicals for the experiments were placed in glass vessels (Chemglass
part no. AF-0092-01 with an AF-0070-0 adapter), interfaced with the stainless-steel
ports of valves of the mixing manifold via 3/8” Swagelok Ultra-Torr vacuum fittings.
All liquid chemicals were purified using a freeze-pump-thaw procedure; this procedure
involves freezing the liquid chemical using a thermos filled with liquid nitrogen, and
then pumping with a combination of the roughing and turbomolecular pumps desig-
nated for the mixing facility. Each time a new liquid chemical was connected to the
mixing facility, the freeze-pump-thaw procedure was employed to remove the initial
air in the vessel and any trapped gas impurities. The freeze-pump-thaw procedure
was repeated several times for each chemical to increase the chemical purity. In the
2.2. KINETICS SHOCK TUBE FACILITY 19
first freeze-pump-thaw cycle, the liquid was pumped to an ultimate pressure of less
than or equal to 1× 10−6 Torr; in subsequent freeze-pump-thaw cycles, a vacuum of
less than or equal to 1× 10−3 Torr was achieved. For pure chemicals, the second and
subsequent purification cycles typically omitted the freeze and thaw steps, employing
only direct pumping of the vapors above the liquid with a roughing pump (for liquid
mixtures such as the tert-butylhydroperoxide/water solution, the freeze and thaw
steps were never omitted to prevent distillation of the solution). After purification
of the liquid chemicals, the liquid vapors were introduced directly into the mixing
facility, driven into the mixing facility by the pressure difference between the mixing
facility and the liquid vapor pressure. In several cases where the vapor pressure of the
liquid was not high enough to cause the vapor to flow into the mixing facility at an
acceptable rate, a thermos filled of lukewarm water (approximately 35 ◦C) was used
to raise the temperature, and thus the vapor pressure, of the desired liquid chemical.
The test mixtures in this work contain parts-per-million (ppm) levels of tert-
butylhydroperoxide and a fuel component, diluted in argon (for the experiments in
Chapter 3, the fuel component was omitted). The mixtures were all prepared using
a double-dilution process to allow for accurate pressure measurements in the mano-
metric preparation of highly dilute mixtures. The chemicals were introduced into
the mixing tank through the manifold one at a time, with the vapors from the liquid
chemicals first, typically in the order of increasing vapor pressure. In the first dilution
stage, the 100 Torr manometer was used to measure the total pressure of the system
(from which the partial pressures of each component was determined) during the in-
troduction of the vapors from the liquid chemicals into the mixing tank. The 10,000
Torr manometer was used for measurement of total pressure after filling with the
argon diluent. The partial pressures for the initial dilution stage were chosen based
on the lowest vapor pressure of the chemicals in the mixture. After complete mixing
of the initial mixing step, the mixture was diluted by evacuating part of the initial
mixture, and diluting with additional argon. Each dilution stage was allowed to mix
in the internally-stirred mixing tank for 45 to 60 minutes to ensure homogeneity and
consistency. The mixing time was determined by utilizing the laser diagnostic system
described in Appendix C. Table 2.1 presents a sample procedure for a mixture of
20 CHAPTER 2. EXPERIMENTAL SETUP
50 ppm TBHP/water and 150 ppm n-heptane in argon, and includes the total pres-
sure after adding each chemical addition and dilution step. Each prepared mixture
yields 4 to 8 experiments, depending on the temperatures and pressures of study.
This limitation is set by the maximum pressure allowable in the mixing tank.
The mixing tank and manifold are both equipped with electrical heating elements.
For the experiments described in this thesis, both the mixing tank and manifold were
electrically heated to approximately 50 ◦C to prevent condensation of liquid chemicals
onto the stainless-steel surfaces. During the mixture preparation process, the pressure
of the liquid vapors introduced into the mixing tank was never raised above one half of
the room-temperature saturated vapor pressure of the liquid to avoid the possibility
of condensation on the mixing tank walls.
2.3 Laser Diagnostics
2.3.1 OH Mole-fraction Diagnostic
The main component of the laser diagnostic system for quantitative OH detection
is a Spectra-Physics 380 ring-dye laser cavity with a temperature-tuned intra-cavity
AD*A frequency-doubling crystal. This ring-dye cavity was pumped with a Rho-
damine 6G dye solution that was excited using a continuous-wave (CW) Coherent
Verdi 532 nm solid-state laser. A schematic of the laser system and all of the optical
components is shown in Figure 2.4. The Rhodamine 6G dye solution was prepared
with 0.33 g/L of Rhodamine 6G (from Exciton, also called Rhodamine 590) in an
ethylene glycol solvent (spectrophotometric grade ≥ 99% from Sigma Aldrich). This
concentration of dye was found to provide the maximum laser power by Herbon [52].
Each prepared dye solution was allowed to mix for over 24 hours before being circu-
lated through the dye-cavity. The dye solution in the laser system was periodically
replaced with a new solution when the output laser power decreased significantly.
This laser system produced a 25 to 30 mW visible laser beam around 613.4 nm,
and a 1 to 2 mW ultra-violet (UV) laser beam that was tuned to the center of the
R1(5) absorption line in the OH A–X (0,0) band near 306.7 nm. The majority of
2.3. LASER DIAGNOSTICS 21
Table 2.1: Double-dilution mixture preparation procedure example to prepare a mixture of 50 ppmTBHP/water and 150 ppm n-heptane in argon.
Step Action Mixing tanktotalpressure(Torr)
Mixing tank contents
1 Evacuate entire mixing facility < 5× 10−6
2 Add ∼5 Torr of the TBHP/watersolution to mixing tank
5.08 100% TBHP/water
3 Isolate mixing tank. Evacuatemanifold
4 Add ∼15 Torr of n-heptane 20.04 25% TBHP/water, 75%n-heptane
5 Isolate mixing tank. Evacuatemanifold
6 Add argon 1007 0.5% TBHP/water, 1.5%n-heptane, argon
7 Isolate mixing tank. Evacuatemanifold
8 Mix first dilution stage for 45 minutes
9 Evacuate mixing tank to ∼50 Torr 50.39 0.5% TBHP/water, 1.5%n-heptane, argon
10 Isolate mixing tank. Evacuatemanifold
11 Add argon to mixing tank limit 5005 50 ppm TBHP/water,150 ppm n-heptane,argon
12 Mix second dilution stage for 45minutes
13 Final mixture 50 ppm TBHP/water,150 ppm n-heptane,argon
22 CHAPTER 2. EXPERIMENTAL SETUP
the visible light was monitored by a Burleigh WA-1000 visible wavemeter. A portion
of the visible light was split off into a scanning interferometer system to monitor
the mode quality and ensure single-mode operation. The majority of the UV light
was directed into the diagnostic windows of the shock tube, located 2 cm from the
driven-section end wall. The beam path entering the shock tube was slightly angled
in the cross-sectional plane of the shock tube to minimize the possibility of internal
reflections exiting the shock tube (see Figure 2.2). Several focusing optics consisting
of CaF2 spherical lenses were placed in the beam path to prevent beam divergence
and to shape the resulting beam diameter entering and exiting the shock tube to
approximately 1.5 mm. A portion of the UV light was also split off upstream of the
shock tube using a UV-grade beam splitter so that common-mode rejection could
be employed to reduce the effects of noise caused by fluctuations in laser intensity.
Both the intensity of the UV light beam split off upstream of the shock tube, and
the intensity of the transmitted laser light exiting the shock tube were monitored
through Schott Glass UG11 filters with in-house-modified UV-enhanced Thorlabs
PDA36A photo-diode detectors, each with a bandwidth of 758 kHz. These detectors
collected data at a rate of 1000 kHz.
To monitor the wavelength of the laser light, the visible laser beam was directed
into a Burleigh WA-1000 visible wavemeter. The accuracy of the visible light wave-
length measurement is 0.016 cm−1 with proper alignment of the wavemeter, resulting
in knowledge of the UV light wavelength to within 0.032 cm−1. Because larger inac-
curacies in the wavemeter reading are possible due to poor alignment of the device,
the visible laser beam from the dye cavity was aligned to follow a co-linear path
with the emitted tracer laser of the wavemeter for over 1 m; improper alignment of
the wavemeter was found to lead to errors of 0.05 cm−1. Furthermore, a microwave
discharge lamp system, discussed in Appendix B, was employed to verify the correct
wavemeter reading at the peak of the R1(5) absorption line in the OH A–X (0,0)
band.
The current optical system allowed for time-resolved quantitative measurement of
the OH mole fraction (called OH time-histories) calculated using the Beer-Lambert
Law, given by Eq. 2.1, where T is the measured fractional UV transmission, I is the
2.3. LASER DIAGNOSTICS 23
intensity of the transmitted UV beam, I0 is the intensity of the upstream split-off UV
beam normalized by the initial fractional transmission, kν is the absorption coefficient
for OH, L is the path length equal to the shock tube diameter, P is the reflected-shock
pressure, and x is the measured mole fraction of OH.
T =I
I0= exp(−kν · P · x · L) (Eq. 2.1)
The absorption coefficient for OH was taken from work of Herbon [52] who provided
temperature- and pressure-dependent values accounting for broadening of the line-
shape.
Coherent Verdi pump laser
Spectra-Physics ring-dye cavity
Scanninginterferometer
Detector
Burleigh wavemeter
Shock tube
613.4 nm (visible)
306.7 nm (UV)
532
nm
Legend
Flat plate beam splitterUV-grade beam splitterMirrorUG11 filterCaF2 spherical lens
f = 100 cm
Modified PDA36A detector
f = 10 cm
f = 6 cm Iris
Figure 2.4: Schematic of the laser diagnostic system used in this work to generate ultra-violet laserlight near 306.7 nm for OH absorption in the A–X (0,0) band. Image adapted from Herbon [52].
The time zero in the measurement trace was defined as the instant of the reflected
shock passing at the measurement location. The time zero could be inferred from the
measured data trace at the appearance of a Schlieren effect, caused because the laser
beam is momentarily steered off the detector by the large density gradient at the shock
24 CHAPTER 2. EXPERIMENTAL SETUP
wave, and is visually manifested as a 3-µs-wide spike in the transmitted signal; the
time zero was defined as the peak of this spike. The noise in the measured fractional
UV transmission was less than 0.1% before time zero; however, beam steering occurs
after the passing of the shock waves at the measurement location, therefore, after
time zero the measured fractional UV-transmission noise was typically ±0.4% or less.
Under typical experimental conditions the minimum OH mole fraction detectivity is
approximately 1.5 ppm. The experiments in this work were designed such that the
signal-to-noise ratio at the peak OH mole fraction is greater than or equal to six.
All sets of experiments in this thesis were examined for two main types of diag-
nostic interference. Off-line absorption measurements with the UV laser wavelength
tuned off of the R1(5) absorption line were performed for all different test mixtures
used, and these measurements did not reveal any interference (background) absorp-
tion. Measurements of each different test mixture with the UV laser blocked were
also performed, and the results verified that the transmitted signals do not include
any molecular emission.
In addition to collecting time-resolved OH mole fraction time-histories during
experiments, this OH absorption diagnostic technique was also used to periodically
verify the cleanliness of the combined shock tube, mixing tank, and mixing manifold
system as described in Appendix A.
2.3.2 Organic Fuel Mole Fraction Diagnostic
An infra-red Jodon Helium-Neon laser (HeNe, Model HN-10GIR) of wavelength
3.39 µm was utilized to determine the mixing time required for the mixture prepa-
ration process, and also to verify the composition of the double-dilution-prepared
mixtures of n-heptane and n-butanol. Light absorption at a wavelength of 3.39 µm
occurs due to the C–H stretch mode, and thus, the mole fraction of any absorb-
ing species can be determined using Eq. 2.1 if the absorption cross-section for each
chemical of interest at 3.39 µm is known. An absorption cross-section for n-heptane
from Klingbeil et al. [53] was used in determining the n-heptane mole fraction, and
an absorption cross-section for n-butanol was taken from Sharpe et al. [54]. The
2.3. LASER DIAGNOSTICS 25
intensity of the HeNe laser light was measured using liquid-nitrogen-cooled indium
antimonide (InSb) detectors from IR Associates (model no. IS-2.0). The procedure
for determining the mixing time required for the mixture preparation process is de-
scribed in Appendix C along with the procedure for verifying the composition of the
double-dilution-prepared mixtures. A brief description of the latter procedure will be
provided here.
An experimental setup containing the 3.39 µm HeNe laser system and an external
multi-pass absorption cell (Toptica Photonics model no. CMP30) of total path length
30 m was designed to confirm the composition of the experimental test mixture.
This confirmation is necessary to eliminate concerns about the possibility of wall
adsorption occurring in the experimental facility, and the long-path-length external
multi-pass cell is needed for adequate absorption to occur due to the highly-dilute
mixtures of interest in this work. The composition of the double-dilution-prepared
mixture was verified for several n-heptane and n-butanol mixtures by sampling a
portion of the final mixture prepared, using the process described in Section 2.2.2,
into the external multi-pass absorption cell. The total pressure of the gas mixture in
the cell was chosen such that the absorption of the HeNe laser light passing through
the cell was between 10% and 90% (in all cases, several pressures were examined to
test the repeatability of the mole fraction measurements). Mixtures of n-heptane (or
n-butanol) in argon, TBHP in argon, and n-heptane (or n-butanol) and TBHP in
argon were examined. The mixtures of TBHP in argon were used to determined the
absorption cross section of the TBHP/water solution (see Section 2.4 for chemical
description) to ∼2 m2 per mole of TBHP/water solution (because the amount of
TBHP/water solution in the mixtures of interest is relatively small compared to the
amount of fuel, this absorption cross-section did not require measurement to high
accuracy). The mixtures with n-heptane or n-butanol were first introduced into the
cell initially through the mixing manifold, and it was confirmed that no fuel loss
occurred during the mixing process. The mixtures were also introduced into the
cell through a port at 2 cm from the driven-section endwall (so the mixture would
be filled into the shock tube from the mixing tank before entering the multi-pass
cell, simulating an actual experiment), and the mixture composition in the shock
26 CHAPTER 2. EXPERIMENTAL SETUP
tube was confirmed to be equivalent to what was expected from the manometric
preparation, with a measurement uncertainty of the fuel concentration of ±5%. The
other n-alkanes and isomers of butanol studied in this thesis have similar properties
to n-heptane and n-butanol, respectively, and therefore no fuel loss will be assumed
for all mixtures prepared in this thesis and this measurement uncertainty is taken to
be the overall uncertainty of the fuel concentration in all mixtures prepared. More
details of the multi-pass cell setup, alignment procedures, and measurement results
are discussed in Appendix C.
2.4 Test Mixture Chemicals
A commercially available solution of 70%, by weight, tert-butylhydroperoxide
(TBHP) in water, from Sigma Aldrich (Luperox TBH70X, product no. 458139), was
used in all experiments described in this thesis. The TBHP/water solution was stored
chilled at -8 ◦C until typically the day of its introduction into the mixing tank (in a
few instances, the solution had up to three days of residence at room temperature).
Argon gas (99.998% purity), supplied by Praxair, Inc., was used as the mixture dilu-
ent for all experiments in this work. Additional chemicals that were used particular
to specific chapters in this thesis will be described in their respective chapters.
Chapter 3
Decomposition of
tert-Butylhydroperoxide
3.1 Introduction
3.1.1 Background
In the high-temperature study of reaction kinetics involving one or more highly-
reactive radical species, stable chemical species are typically used as precursors to
generate the radical(s) of interest. For example, kinetic studies involving the hy-
droxyl (OH) radical have employed several different stable chemical precursors, in-
cluding hydrogen peroxide [5], tert-butylhydroperoxide [6, 8–12], methanol [13], and
hydroxylamine [13]. Methods applying laser photolysis techniques also allow for OH
radicals to be generated through photolysis and reaction of a combination of chemi-
cals, such as H2O with N2O [55] and N2O with NH3 [56]. Each of these methods of
generating OH radicals has certain advantages and disadvantages that vary depending
on the conditions of interest.
The use of tert-butylhydroperoxide (TBHP: (CH3)3COOH) as an OH precursor
was pioneered by Cohen and coworkers [6–9] in the 1980’s, when they used the stable
compound for the study of rate constants for reactions of OH with various organic
compounds in shock tubes at temperatures near 1100 K. One advantage of TBHP
27
28 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
as an OH precursor is its ease of handling as compared with hydrogen peroxide, the
latter of which is corrosive on stainless-steel reactor surfaces. A second advantage is
that TBHP undergoes rapid decomposition at temperatures as low as 1000 K (with
a characteristic decomposition time of ∼1 µs at 1000 K). Many recent efforts in
advanced engine technologies utilized intermediate- or low-temperature combustion
at temperatures around 1000 K or lower, and thus kinetic experiments are needed
near these temperatures for model validation. Thus, other stable chemical species
that are commonly used as OH precursors, such as methanol and hydroxylamine
(each with characteristic decomposition times >100 µs at 1500 K), are limited in use
for experiments in this temperature range.
A current drawback to using TBHP as an OH precursor is the secondary reaction
chemistry due to the additional chemical species formed during TBHP decomposition.
TBHP generates OH radicals and other products during its two-step decomposition
mechanism described by Reactions (3.1) and (3.2).
(CH3)3COOH −→ (CH3)3CO + OH (3.1)
(CH3)3CO −→ CH3 + CH3COCH3 (3.2)
Figure 3.1 illustrates this two-step decomposition mechanism. In addition to OH
radicals, methyl radicals and acetone molecules are also formed, and these molecules
can be involved in secondary elementary reactions during the experiment that affect
the OH radical pool, such as Reactions (3.3) and (3.4).
CH3 + OH −→ CH2(s) + H2O (3.3)
CH3COCH3 + OH −→ CH2COCH3 + H2O (3.4)
In Reaction (3.3), CH2(s) represents the excited singlet state of CH2. Using a detailed
mechanism to accurately account for relevant secondary reactions that occur during
TBHP decomposition can address the changes in the OH radical pool due to TBHP-
related secondary chemistry.
Another drawback of TBHP as an OH precursor for combustion-relevant
3.1. INTRODUCTION 29
CH3
H3C O
CH3
OHCH3
CH3C O
CH3
OH+
H3CC
H3CO CH3+
Figure 3.1: Two-step decomposition mechanism of tert-butylhydroperoxide into final products ofOH, methyl, and acetone via Reactions (3.1) and (3.2). Red arrows illustrate movement of electronsthat occur during the reactions.
intermediate-temperature experiments is that TBHP has limited use as a simple OH
precursor at temperatures lower than 1000 K. Because most combustion reactions
occur on time scales on the order of tens to hundreds of µs, at temperatures lower
than 1000 K where the OH formation from TBHP decomposition takes several µs to
occur, the rate of decomposition, governed by the rate constant for Reaction (3.1),
influences the observations of the reactions of interest. While measurements of the
rate constant for Reaction (3.1) have been presented in the literature by several
sources [57–62], large scatter in these data exist and improvements to the accuracy
of those measurements can contribute to improved understanding of low-temperature
experiments employing TBHP as an OH precursor.
3.1.2 Objectives of the Current Chapter
In this chapter, the results of experiments designed to be sensitive to the rate con-
stants for elementary reactions important in TBHP decomposition are presented. OH
time-histories were measured in experiments of TBHP, dilute in argon, in the tem-
perature range from 799 to 1316 K, and a detailed kinetic mechanism was created
to accurately describe the background chemistry occurring during and after TBHP
30 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
decomposition.
3.2 TBHP Kinetic Mechanism
3.2.1 Mechanism Generation
A chemical kinetic mechanism detailing TBHP chemistry, and also including alkane
chemistry for use the subsequent chapter, was generated to model the effect of TBHP
kinetics on measured OH time-histories. The base of this mechanism is the JetSurF
1.0 mechanism [18], with Reactions (3.1), (3.2), (3.5a) and (3.5b) added for TBHP
chemistry.
(CH3)3COOH + OH −→ (CH3)3C + H2O + O2 (3.5a)
−→ (CH3)2C−−CH2 + H2O + HO2 (3.5b)
All reactions were considered to be reversible.1 Thermodynamic parameters for
TBHP and tert-butoxyl were obtained from the thermodynamic database from Goos
et al. [50], and the thermodynamic parameters for OH were updated from Herbon et
al. [52].
The rate constant for Reaction (3.1) was set to the rate measured by Vasudevan
et al. [61] for initial analysis, however, this rate constant was updated to that which
was measured in Section 3.5 of this work for the final analyses of this chapter, and
subsequent chapters of this thesis. The rate constant for Reaction (3.2) was taken
from Choo and Benson [63], the rate constant for Reaction (3.5a) was estimated to
be half the rate constant for the reaction OH + H2O2 −→ HO2 + H2O as measured by
Hong et al. [64], and the rate constant for Reaction (3.5b) was estimated to be half the
rate constant for the reaction OH + tetramethylbutane −→ Products as measured by
Sivaramakrishnan and Michael [11]. The rate constant for Reaction (3.3) was modified
to fit the TBHP chemistry as determined in Section 3.5. Updated rate constants
were used for Reaction (3.4) for acetone chemistry from Vasudevan et al. [12] and for
1The reversibility of reactions is considered for all reactions written in this thesis, even thoughan arrow in only the forward direction is always used
3.2. TBHP KINETIC MECHANISM 31
Reactions (3.6) and (3.7) for hydrogen/oxygen chemistry from Hong et al. [2].
H + O2 −→ OH + O (3.6)
OH + OH −→ H2O + O (3.7)
The reactions added to the JetSurF 1.0 mechanism and the updated rate constants
are listed in Table 3.1. From this point forward, the detailed mechanism compiled
as described above will be referred to as the alkane/TBHP mechanism. Some repre-
sentation of this alkane/TBHP mechanism will be used for the analysis of all of the
experiments described in the subsequent chapters of this thesis.
Table 3.1: Reactions added and rate constants modified in the JetSurf 1.0 mechanism to generate thealkane/TBHP mechanism used for this study. Units for A are [cm3molecule−1s−1] for bimolecularreactions and [s−1] for unimolecular reactions, units for E are [cal mol−1K−1].
No. Reaction k = A · T b exp(−E/RT ) Reference
A b E
(3.1) (CH3)3COOH −−→ (CH3)3CO+OH 3.57× 10+13 0.0 +3.57× 104 This work
(3.2) (CH3)3CO −−→ CH3 +CH3COCH3 1.26× 10+14 0.0 +1.53× 104 [63]
(3.3) CH3 +OH −−→ CH2(s) + H2O 2.74× 10−11 0.0 0.00 This work
(3.4) CH3COCH3 +OH −−→ CH2COCH3 +H2O 4.90× 10−11 0.0 +4.59× 103 [12]
(3.5a) (CH3)3COOH+OH −−→ (CH3)3C+H2O+O2 3.82× 10−11 0.0 +5.22× 103 [64]
(3.5b) (CH3)3COOH+OH −−→ (CH3)2C−−CH2 +H2O+HO2
4.13× 10−11 0.0 +2.66× 103 [11]
(3.6) H + O2 −−→ OH+O 1.73× 10−10 0.0 +1.53× 104 [2]
(3.7) OH +OH −−→ H2O+O 5.93× 10−20 2.4 −2.11× 103 [2]
The CHEMKIN-PRO R© suite of programs by Reaction Design was used to per-
form analyses with this alkane/TBHP mechanism in this chapter and all subsequent
chapters of this thesis. Constant volume and constant internal energy constraints
were placed on all simulations.
3.2.2 OH Sensitivity Analysis
Figures 3.2 and 3.3 show the top four reactions appearing in the results of OH sensi-
tivity analyses at 928 K and 1158 K, respectively, using the alkane/TBHP mechanism
for mixtures of approximately 20 ppm TBHP dilute in argon. The OH sensitivity is
32 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
defined by Eq. 3.1 where SOH,i is the time-dependent OH sensitivity to the rate con-
stant for Reaction (i), xOH is the local time OH mole fraction, and ki is the rate
constant for Reaction (i).
SOH,i =∂xOH
∂ki· kixOH
(Eq. 3.1)
The OH sensitivity describes the influence of a perturbation on ki on the simulated
OH time-history.
The results of the OH sensitivity analyses indicate that Reaction (3.3) (the re-
action of OH with methyl radicals) is important in defining the simulated OH time-
history under both temperatures examined. Other reactions involving methyl radi-
cals, acetone, and OH radicals, all final products of the TBHP decomposition, are
also important to varying degrees, depending on the simulation conditions. The rate
constant for Reaction (3.1) appears as a dominant reaction in the OH sensitivity
analysis for temperatures below 1000 K.
The rate constant for Reaction (3.7) was updated with the recommendation from
Hong et al. [2], whose review of this reaction reveals that measurements from various
studies converge to an agreed-upon rate constant. The rate constant for Reaction (3.4)
has been measured by Vasudevan et al. [12] with a 25% uncertainty, and is the rate
constant used in this analysis. Therefore, the rate constants for these two reactions
are considered adequately accurate for the analyses in this thesis work. Accurate
knowledge of the rate constants for Reactions (3.1) and (3.3) is not as readily available
in the literature, and thus the current chapter discusses the results of experiments
designed to determine these rate constants as necessary for future experiments using
TBHP as an OH precursor in shock tube experiments.
3.3 Experimental
The experiments in this chapter were conducted with the experimental setup and
chemicals described in Chapter 2. OH time-histories were measured after the shock-
heating of dilute mixtures of the TBHP solution in argon. While the actual mixture
3.3. EXPERIMENTAL 33
0 10 20 30 40 50 60-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
(3.1)
(3.3)928 K, 1.22 atm20.5 ppm TBHP, argon
OH
Sen
sitiv
ity
Time [s]
(3.1) (CH3)3COOH -> (CH3)3CO + OH (3.3) CH3 + OH -> CH2(s) + H2O CH3+OH(+M) -> CH3OH(+M) CH3+CH3(+M) -> C2H6(+M)
Figure 3.2: OH sensitivity for a mixture of 20.5 ppm TBHP in argon at 928 K and 1.22 atmillustrating the importance of the rate constant for Reaction (3.1) in the early-time (<30 µs inthis case) simulated OH time-history under these conditions. The simulated OH time-history ismost sensitive to the rate constant for the reaction shown with a solid line, Reaction (3.1), and therate constant for this reaction can be determined from a measured OH time-history under theseconditions.
0 20 40 60 80 100-0.3
-0.2
-0.1
0.0
0.1
(3.7)(3.4)
(3.3)
1158 K, 1.10 atm20 ppm TBHP, argon
OH
Sen
sitiv
ity
Time [s]
(3.1) (CH3)3COOH -> (CH3)3CO + OH (3.3) CH3 + OH -> CH2(s) + H2O (3.4) CH3COCH3 + OH -> CH2COCH3 + H2O (3.7) OH + OH -> H2O + O
(3.1)
Figure 3.3: OH sensitivity for a mixture of 20.0 ppm TBHP in argon at 1158 K and 1.10 atmillustrating the importance of the rate constant for Reaction (3.3) in the simulated OH time-historyunder these conditions. The simulated OH time-history is most sensitive to the rate constant forthe reaction shown with a solid line, Reaction (3.3), and and the rate constant for this reaction canbe determined from a measured OH time-history under these conditions.
34 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
has a small fraction of water, the presence of water is not expected to have an effect on
the measurement; thus, the mixtures will be referred to as TBHP only in this chapter,
and the subsequent chapters. Several test mixtures were prepared for the experiments
discussed in this chapter; the composition of the mixtures ranged from 20 to 30 ppm
of TBHP diluted in argon. The reflected-shock conditions were controlled to generate
temperatures in the range of 799 to 1316 K under pressures of 1 to 3 atm. For the
dilute mixtures and short test times in the current experiments, the measured reaction
pressure (and thus temperature) remains constant. The measured OH time-histories
were analyzed with the kinetic mechanism described in Section 3.2 with constant
volume and constant internal energy constraints.
3.4 OH Mole Fraction Measurements
3.4.1 OH Time-history
Sample measured OH time-histories for mixtures of approximately 20 ppm TBHP in
argon are shown in Figures 3.4 and 3.5 for reflected-shock conditions of 928 K and
1.22 atm, and 1158 K and 1.10 atm, respectively. Simulated OH time-histories are
also shown, and these are discussed in Section 3.5. As evident from the measured
OH time-histories shown in Figures 3.4 and 3.5, the decomposition of TBHP upon
heating in a shock tube does not lead to a step-function source of OH radicals (which
is the ideal case for a radical precursor). Thus, a model describing the OH time-
history behavior due to TBHP decomposition is needed to accurately analyze any
experiments monitoring the OH mole fraction in mixtures containing TBHP, and this
can be done by using accurate rate constants for key reactions in the alkane/TBHP
mechanism described in Section 3.2.
Note that a main difference between the two measured traces in Figures 3.4 and 3.5
is the finite time (greater than 1 µs) required for the formation of OH at 928 K versus
the near instantaneous formation of OH from the decomposition of TBHP to OH at
1158 K. All measured OH time-histories at temperatures below 1000 K demonstrate
slow decomposition trends similar to as shown in Figure 3.4; the rate of OH formation
3.4. OH MOLE FRACTION MEASUREMENTS 35
at these temperatures is used to determined the rate constant for Reaction (3.1), and
the results are presented in Section 3.5. Similarly, all measured OH time-histories
at temperatures above 1000 K show near-instantaneous OH formation like in Fig-
ure 3.5, with a subsequent OH decay following the peak OH mole fraction. The rate
of the measured subsequent OH decay is used to determine the rate constant for
Reaction (3.3), and the results are also presented in Section 3.5.
0 10 20 30 40 50 600
4
8
12
16
20
Data 1.0 x k3.1
0.7 x k3.1
1.3 x k3.1
Reaction (3.1): (CH3)3COOH -> (CH3)3CO + OH
OH
mol
e fra
ctio
n [p
pm]
Time [μs]
928 K, 1.22 atm20.5 ppm TBHP, argon
Figure 3.4: Measured OH time-histories at 928 K, 1.22 atm for 20.5 ppm TBHP argon. Also shownare simulated OH time-histories with the best-fit rate constant for Reaction (3.1) and perturbationsof ±30% on the best-fit rate constant.
3.4.2 OH Yield
The commercial TBHP/water solution described in Chapter 3 that the test mixtures
were prepared from is 70% by weight TBHP, which equates to about 30% by mole
liquid concentration of TBHP in water. However, because this is a non-ideal solution,
the concentration of TBHP in the vapor phase is not simple to calculate. At temper-
atures above 1000 K, all of the initial TBHP decomposes almost instantaneously into
OH radicals and other products, as shown in Figure 3.5, thereby allowing inference
of the initial TBHP concentration (assumed to be equal to the peak concentration
36 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
0 20 40 60 80 1000
4
8
12
16
20
OH
mol
e fra
ctio
n [p
pm]
Time [μs]
Data 1.0 x k3.3
0.7 x k3.3
1.3 x k3.3
Reaction (3.3): CH3 + OH -> CH2(s) + H2O
1158 K, 1.10 atm20 ppm TBHP, argon
Figure 3.5: Measured OH time-histories at 1158 K, 1.10 atm for 20.0 ppm TBHP argon. Also shownare simulated OH time-histories with the best-fit rate constant for Reaction (3.3) and perturbationsof ±30% on the best-fit rate constant.
of OH formed) directly from each high-temperature (>1000 K) measured OH time-
history. For each given mixture, the measured value of initial TBHP composition
was typically consistent within 10% from shock to shock. In a few mixtures, if the
mixing tank was heated to higher than 50 ◦C (e.g. if the controller to the electrical
heating element was not setting the temperature correctly), the initial TBHP com-
position would noticeably drop from shock to shock, possibly indicating that some
initial decomposition of TBHP was occurring inside the shock tube; these effects were
examined and found to negligibly influence the rate constant determinations in the
subsequent chapters.
The OH yield can be determined in experiments at temperatures above 1000 K,
and is defined as the measured peak OH mole fraction divided by the initial mole
fraction of the TBHP/water solution
Figure 3.6 presents the measured peak OH mole fraction for a representative set
of experiments at temperatures above 1000 K as a function of the initial mole fraction
of the TBHP/water solution. The initial mole fraction of the TBHP/water solution
3.4. OH MOLE FRACTION MEASUREMENTS 37
is determined from manometric preparation, which is described in Chapter 2. At
temperatures above 1000 K, all of the measured OH can be assumed to be instanta-
neously formed from TBHP in a one-to-one ratio; therefore, in these experiments, the
TBHP yield from the TBHP/water solution can be defined as the measured peak OH
mole fraction divided by the initial mole fraction of the TBHP/water solution. The
total amount of TBHP yield from the TBHP/water solution was found to be between
20 and 32% across all the mixtures prepared (in the experiments in this chapter and
the subsequent chapters). The measured TBHP yields are similar to the TBHP yields
found by other researchers who performed similar experiments [47, 62, 65, 66], with
the exception of Vasudevan [67] who consistently found a lower TBHP yield, which
could possibly be attributed to adsorption or decomposition in the mixing tank or
premature TBHP decomposition prior to introduction in the mixing facility.
The TBHP yields discovered in the current work indicate that the solution va-
por composition is similar to the liquid solution composition. The deviations of
TBHP yield from mixture to mixture could be due to different residence times of the
TBHP/water solution outside of the chilled storage, where the TBHP may slowly
decompose at room temperature, the result of a different pattern of pumping cycles
during purification where the solution may consequently become partially distilled, or
premature decomposition in the mixing tank due to excessive heating by the electric
heaters. Adsorption of TBHP onto the stainless steel surfaces of the facility are also
possible, as noted in other works [12, 62]. Uncertainties in the initial TBHP con-
centration, including effects of TBHP adsorption and premature decomposition, are
addressed in the uncertainty analysis of the rate constant determinations in the sub-
sequent chapters, and do not have a significant effect on the measured rate constants
described in this thesis.
In the simulated OH time-histories in this chapter (and subsequent chapters),
the initial TBHP composition was inferred directly from the measured OH time-
history as described above. For experiments at temperatures less than 1000 K, the
initial TBHP composition could not be inferred directly due to the finite time re-
quire for the TBHP decomposition. Therefore, for low-temperature (<1000 K) ex-
periments, an initial TBHP composition value in agreement with an inferred initial
38 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
0 50 100 150 2000
10
20
30
40
50
32%
OH Y
ield
Mea
sure
d pe
ak O
H y
ield
[ppm
]
Initial TBHP/water solution vapor [ppm]
Current work Masten Vasudevan Vasu et al. Cook et al.
OH yield from TBHP/water solution
20% OH Yield
Figure 3.6: Measured OH yield as a function of the initial TBHP/water solution mole fraction in atest mixture. Shown for the representative experimental work for this thesis, and also compared toother experiments in the literature [47, 62, 65–67]. Both data from mixtures of TBHP in argon (thischapter) and mixtures of TBHP and an organic compound (from subsequent chapters) in argon areincluded.
high-temperature-experiment TBHP composition from the same mixture was used
in the kinetic simulations. In all kinetic simulations, an initial water concentration
was prescribed in the mixture as the difference between the initial amount of TBHP
measured and the amount of TBHP/water solution vapor originally placed in the
mixture (known from the manometric preparation procedure); however, calculations
have shown that the presence of water has a negligible effect on the results, thus the
prescription of water in the simulated mixture could be omitted if desired.
3.5 Rate Constant Determinations
3.5.1 Determination of k3.1
For the current experimental mixtures studied at temperatures below 1000 K, the
simulated OH time-histories using the alkane/TBHP mechanism are highly sensitive
to the rate constant for Reaction (3.1) at early times, as can be seen from the OH
3.5. RATE CONSTANT DETERMINATIONS 39
sensitivity analysis in Figure 3.2. The results of the measured OH time-histories from
the experiments conducted at temperatures from 799 to 990 K and pressures from 1
to 3 atm were used to determine the rate constant for Reaction (3.1). The early-time
simulated OH time-history was matched to the measured trace by changing only the
rate constant for Reaction (3.1). Figure 3.4 shows a sample measured OH time-history
and the early-time effect of the rate constant for Reaction (3.1) on the simulated OH
time-history.
The rate constant for Reaction (3.1) as a function of temperature was determined
from all of the experimental data traces at temperatures from 799 to 990 K, and the
results are shown in Figure 3.7. The individual data points are also presented in Ta-
ble 3.2. The data were taken at pressures from 1 to 3 atm, and no significant pressure
dependence was observed from the experimental data. Therefore, the measurements
of the rate constant for Reaction (3.1) can be expressed in Arrhenius form by Eq. 3.2.
k3.1 = 3.57× 10+13 exp
(− 18000
T [K]
)s−1 (Eq. 3.2)
Eq. 3.2 is valid for temperatures from 799 to 990 K and pressures from 1 to 3 atm.
Table 3.2: Measured rate constant for Reaction (3.1) from 799 to 990 K, determined from fittingmeasured OH time-histories of TBHP dilute in argon with the alkane/TBHP mechanism, using therate constant for Reaction (3.1) as the free parameter.
T [K] P [atm] k3.1 [s−1]
990 2.15 3.53 ×105
928 1.22 1.30 ×105
920 2.38 1.32 ×105
881 1.29 5.20 ×104
871 2.40 5.10 ×104
856 1.35 2.80 ×104
820 1.36 9.50 ×103
812 2.41 8.00 ×103
799 2.52 5.00 ×103
40 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
1.0 1.2 1.4 1.6 1.8 2.0 2.210-7
10-5
10-3
10-1
101
103
105
107
Current data: 1 to 3 atm Arrhenius fit to current data Vasu et al. (2010): 0.5 to 3 atm Vasudevan et al. (2005): 2 to 3 atm Vasudevan et al. fit (2005) Sahetchian et al. (1992): 1 atm Mulder and Louw (1984): 1 atm Benson and Spokes (1968): high-pressure limit Kirk and Knox (1960): 10-20 Torr
k 3.
1 [s-1]
1000/T [K-1]
1000 K 714 K 556 K 455 K
Reaction (3.1): (CH3)3COOH -> (CH3)3CO + OH
1.0 1.1 1.2 1.3103
104
105
106
1000 K 909 K 833 K 769 K
Figure 3.7: Arrhenius plot of the rate constant for Reaction (3.1) from the literature [57–62] andcompared with the rate found in the current work.
The measured rate constant for Reaction (3.1) is compared to other works [57–
62] in Figure 3.7. While the rate constant for Reaction (3.1) has been measured by
Vasudevan et al. [61] and Vasu et al. [62] using similar methods in approximately
the same temperature range of interest, only one experimental data point in both
of those studies was obtained in the absence of another organic compound in the
experimental mixture. The current measurements focus on the kinetics of TBHP only,
and therefore, uncertainties in the rate constants for reactions of other other organic
compounds with the TBHP decomposition products are not of concern in the current
analysis. An uncertainty analysis on this rate constant determination reveals that the
major uncertainty contribution is the initial concentration of TBHP, which leads to an
estimated ±30% uncertainty in this rate constant. The current determination for the
rate constant for Reaction (3.1) agrees with most other measurements in the literature
within combined uncertainty estimates. A discrepancy just outside of the combined
uncertainty estimates exists near 1000 K with the rate constant determination from
3.5. RATE CONSTANT DETERMINATIONS 41
Vasudevan et al. [61]; though at temperatures near 1000 K where the discrepancy
in this rate constant exists, the rate constant for Reaction (3.1) has minimal effects
on the overall rate constant determinations presented in the subsequent chapters
of this thesis. Therefore, uncertainties in the rate constant for Reaction (3.1) at
the temperature where this discrepancy exists will not influence the rate constant
determinations in the subsequent chapters of this thesis. The rate constant given in
Eq. 3.2 will be used in analysis of all data discussed in this thesis.
3.5.2 Determination of k3.3
Methyl radicals (CH3) are a byproduct of the decomposition of TBHP, and there-
fore, the rate constant for the reaction of OH with CH3 is important to consider
in the analysis of OH time-history measurements in shock tube experiments using
TBHP. At temperatures above 800 K, the rate constant for the overall reaction of
CH3 + OH −→ Products has been studied experimentally by Bott and Cohen [8],
Krasnoperov and Michael [68], Srinivasan et al. [69], and Vasudevan et al. [51]. A
theoretical study of the rate constant for reaction of CH3 + OH has also been per-
formed by Jasper et al. [70] and Ree et al. [71]. Figure 3.8 shows that a factor of
six discrepancy exists among the rate constants for the reaction CH3 + OH in the
literature. To address the large discrepancy in the rate constant for Reaction (3.3)
in the literature, the results of measured OH time-histories in the high-temperature
decomposition of TBHP for temperatures from 799 to 1316 K were used for accurate
determination of the rate constant.
The reaction channel of CH3 +OH yielding the specific products in Reaction (3.3)
was claimed to be the major product channel at high temperatures [68, 69]; however,
a recent study by Ree et al. presents calculations that show the reaction channel
leading to the product CH3OH may also be significant, though the rate constant for
Reaction (3.3) is still the fastest. Therefore, even if accounting for other reactions
channels for the reaction of CH3 + OH, a large discrepancy still exists in the rate
constant for Reaction (3.3).
The simulated OH time-history using the alkane/TBHP mechanism shows high
42 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
0.7 0.8 0.9 1.0 1.1 1.2 1.3
1
10
α Azomethane precursorμ Methyl iodide precursor
Reaction (3.3): 1
CH3 + OH -> CH2(s) + H2O Srinivasan et al. (2007) JetSurF 1.0 Mechanism (2009)1
Ree et al. (2011)1
Current work (799-1316 K)1
CH3 + OH -> Products Bott and Cohen (1991) Krasnoperov and Michael (2004)1 Jasper et al. (2007): 760 Torr1
Vasudevan et al. (2008) α
Vasudevan et al. (2008) μ
Ree et al. (2011)1
k CH
3 +
OH [
10-1
1 cm
3 mol
ecul
e-1 s
-1]
1000/T [K-1]
1428 K 1111 K 909 K 769 K
(k3.3)
Figure 3.8: Arrhenius plot of rate constants for reactions of CH3 + OH from the literature [8, 18,51, 68–71] and compared with the rate constant for Reaction (3.3) from the current work.
sensitivity to the rate constant for Reaction (3.3) at all temperatures in mixtures of
dilute TBHP in argon, as illustrated in Figures 3.2 and 3.3. Therefore, the rate con-
stant for Reaction (3.3) can be determined by fitting simulated OH time-histories to
the measured traces by adjusting only the rate constant for Reaction (3.3), within the
limits of the rate constants provided in literature, in the alkane/TBHP mechanism.
Using the rate constant described by Eq. 3.3 in the alkane/TBHP mechanism was
found to generate simulated OH time-histories that best fit the experimental data
over the entire temperature range studied (799 to 1316 K).
k3.3 = 2.74× 10−11cm3molecule−1s−1 (Eq. 3.3)
The best-fit simulated OH time-history using the alkane/TBHP mechanism with this
rate constant for Reaction (Eq. 3.3) is shown in Figure 3.5, along with the simulated
OH time-histories with the rate constant perturbed by ±30%. The uncertainty in
this rate constant determination for Reaction (3.3) is primarily due to fitting the
3.5. RATE CONSTANT DETERMINATIONS 43
data trace, thus the expected the overall uncertainty of this rate constant is approxi-
mately ±30%. The uncertainty of the rate constants for secondary reactions can also
contribute to the uncertainty in the rate constant determination for Reaction (3.3);
however, because uncertainties in these secondary rate constants are not well known,
it is difficult to determine the effects on the current rate constant determination.
The work here proposes a rate constant for Reaction (3.3) that correctly predicts
OH time-histories in experiments with TBHP, given the current secondary chemistry
used; further comments on this uncertainty is discussed at the end of this section.
Comparison of the current rate constant determination for Reaction (3.3) is shown
in Figure 3.8. The current rate constant determination is 34% slower than the orig-
inal rate constant from the JetSurf 1.0 mechanism. The experiments in the work
of Vasudevan et al. [51] utilized two different stable precursors for methyl radicals
(azomethane and methyl iodide), each paired with TBHP as the OH precursor. Their
experiments show high sensitivity to the rate constant for Reaction (3.3) and span
the temperature range 1081 to 1426 K. The current rate constant determination sug-
gested by Eq. 3.3 agrees well with the measurements from Vasudevan et al., and
therefore the current determination rate constant for Reaction (3.3) is assumed to
be accurate up to temperatures of 1426 K. The current rate constant determination
shows reasonable agreement with the experimental results of Bott and Cohen [8] and
Krasnoperov and Michael [68], and also with the theoretical calculations of Jasper
et al. [70] and Ree et al. [71]. Discrepancies exist between the current rate constant
determination and the rate constant from Srinivasan et al. [69]; however, the results
in the work of Srinivasan et al. were determined from experiments of dilute methanol
decomposition, and their rate constant determination was found to be sensitive to
other secondary rate constants and also show discrepancies with an earlier study
from the same authors [69].
The recent study by Ree et al. [71] on the rate constants associated with all
reaction channels of CH3 + OH claims that the pressure-dependent reaction channel
leading to the products CH3OH should be considered. Figure 3.8 shows the rate
constant for the overall reaction of CH3 + OH −→ Products predicted by Ree et al.
is approximately twice the rate constant for Reaction (3.3). In the alkane/TBHP
44 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
mechanism, the rate constant for the reaction CH3 + OH −→ CH3OH is from the
JetSurF 1.0 mechanism [18], and this rate constant does become significant relative
to the rate constant for Reaction (3.3) at temperatures less than 1000 K, agreeing with
the branching ratio predictions of Ree et al. [71]. According to the rate constants in
the alkane/TBHP mechanism, the branching ratio of the overall reaction of CH3+OH
that proceeds via Reaction (3.3) is 55% at 800 K, though at temperatures above
1000 K, this branching ratio is greater than 70%. Thus, the rate constant for the
reaction CH3 + OH −→ CH3OH becomes important at low temperatures, as shown
by the OH sensitivity analysis in Figure 3.2. While there may be uncertainty in the
current determination of the rate constant for Reaction (3.3) due to uncertainty in
the branching ratio, using the currently suggested rate constant in the alkane/TBHP
mechanism yields a detailed kinetic mechanism that is expected to correctly simulate
the OH time-history in shock tube experiments with TBHP for temperatures from
799 to 1426 K. Thus, any rate constant errors cancel out, and this mechanism can
be used for accurate analysis in any shock tube experiments of mixtures containing
TBHP in this temperature range.
3.6 Summary
The rate constant measurements obtained in this section for TBHP chemistry are used
in the alkane/TBHP mechanism compiled in Section 3.2, and the resulting mechanism
correctly predicts the OH decay rate resulting from TBHP chemistry from approxi-
mately 800 to 1400 K. Table 3.1 lists all of the reactions and rate constants which were
added and modified in the JetSurf 1.0 [18] base mechanism to create the alkane/TBHP
mechanism in this work.
The majority of the subsequent work presented in this thesis uses this
alkane/TBHP mechanism either as the sole mechanism for analysis or as the base
for which further reactions are added to include kinetic descriptions for additional
species (i.e. butanol). The exception is in Chapter 7 where an alternate approach
was used, involving the creation of a mechanism capable of accurately describing the
3.6. SUMMARY 45
TBHP-related OH time-histories by using the reactions and rate constants in Ta-
ble 3.1 in other published mechanisms, instead of using the JetSurf 1.0 mechanism
as a starting point. This alternate approach is also discussed in some detail in Chap-
ter 5, and is expected to be successful in converting the majority of published kinetic
mechanisms to accurately simulate TBHP-related kinetics. Simple calculations to
verify that converted mechanisms simulate OH time-histories that match the mea-
sured traces in Figures 3.4 and 3.5 should always be done to confirm the accuracy
of any mechanism created with reactions and rate constants in Table 3.1 for TBHP
chemistry.
46 CHAPTER 3. DECOMPOSITION OF TERT-BUTYLHYDROPEROXIDE
Chapter 4
Reactions of OH with n-Alkanes
4.1 Introduction
4.1.1 Background
As mentioned in Chapter 1, the rate constants for reactions of OH with n-alkanes
are important in the kinetic mechanisms describing the combustion of many current
practical and surrogate fuels. Many experiments have been performed to measure
the rate constants for n-alkane+OH at low-temperatures (250 to 440 K) [72–82], and
recent studies have extended the experimental database with high-temperature (800
to 1300 K) data for several n-alkanes [6, 7, 9–11]. Attempts to measure the rate
constants for reactions of OH with large n-alkanes become increasingly difficult with
increasing molecular weight of the alkane because the alkane vapor pressure typically
decreases with increasing molecular weight. This results in difficulties introducing
high concentrations of the alkane into the experimental apparatus in the gas phase
(preparation of gas-phase mixtures is typically preferred for kinetic experiments be-
cause of the ease of creating a homogeneous mixture). Therefore, diagnostics capable
of measuring highly dilute mole fractions of OH, such as the diagnostics described in
Chapter 2, are necessary for experiments with large n-alkanes.
Most detailed kinetic mechanisms involving large alkanes use estimated rate con-
stants [18, 83, 84], usually obtained through an additivity scheme, with parameters
47
48 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
based on experimental data of measured rate constants for smaller alkanes. For exam-
ple, a simple estimation method could assume a fixed rate constant for OH reacting
with hydrogen atoms at each primary carbon site, and a different rate constant at
each secondary carbon site. Greiner [19] was the first to develop an estimation method
which resembles this approach for reactions of OH with n-alkanes. Recent literature
has reported new rate constant estimation methods developed for reactions of OH with
n-alkanes yielding improved agreement with experimental data [11, 20, 22, 25, 82].
Confidence in the accuracy of all of the estimation methods used for generat-
ing rate constants for reactions reactions of OH with n-alkanes is limited by the
experimental database. For reactions of OH with n-alkanes, the availability of ex-
perimental data for rate constants above 800 K decreases with increasing length of
the n-alkane chain. For example, the largest n-alkane studied in the works of Cohen
and coworkers [6, 7, 9] was n-decane with a single-temperature-point measurement
around 1100 K, while Michael and coworkers [10, 11] made measurements of the tem-
perature dependence of the reactions of n-alkane+OH for temperatures from 800 to
1300 K for a series of alkanes, where n-heptane was the largest n-alkane studied.
Therefore, there is a need to extend the experimental database of rate constants for
reactions of OH with n-alkanes to larger normal alkanes, and to improve knowledge
of the temperature dependence of these rate constants.
4.1.2 Objectives of the Current Chapter
The work in this chapter determines the rate constants for the overall reactions of
OH with three large normal alkanes: n-pentane (C5), n-heptane (C7) and n-nonane
(C9).
C5H12 + OH −→ C5H11 + H2O (4.1)
C7H14 + OH −→ C7H13 + H2O (4.2)
C9H20 + OH −→ C9H19 + H2O (4.3)
High-temperature shock tube experiments employing laser absorption by OH at
4.2. EXPERIMENTAL 49
306.7 nm were used to measure the OH time-history behind reflected shock waves
under experimental conditions that are kinetically pseudo-first-order in OH. The
OH radicals were generated by the near-instantaneous decomposition of tert-
butylhydroperoxide (TBHP), which generates an OH radical and a tert-butoxyl rad-
ical that subsequently decomposes into a methyl radical and acetone. Measurements
of the rate constants for Reaction (4.1), (4.2), and (4.3) are compared with several
estimation methods in the literature that predict the rate constant for reactions in
the family of hydrogen-atom abstraction by OH of n-alkanes.
4.2 Experimental
The shock tube and laser diagnostics described in Chapter 2 of this thesis were used
for the experimental work described in this chapter. In addition to the chemicals de-
scribed in Chapter 2 (TBHP/water solution 70%, by weight TBHP, and argon gas),
spectrophotometric grade n-pentane and n-heptane (each ≥ 99%), and anhydrous
n-nonane (≥ 99%), all from Sigma Aldrich, were used in the mixture preparation.
Mixtures of tert-butylhydroperoxide (TBHP) with an n-alkane in excess and diluted
in argon were prepared; the mixture compositions of the experiments in this chap-
ter are listed in Tables 4.1, 4.2 and 4.3. Reflected-shock pressures between 0.74 and
2.1 atm were used, and all mixture compositions had an initial n-alkane-to-TBHP
concentration ratio greater than or equal to ten to yield near-pseudo-first-order ki-
netics in OH. Measurements of OH time-histories at various temperature and pressure
conditions represent the data collected.
4.3 Data Analysis
The measured OH time-histories presented in this chapter were analyzed using a
pseudo-first-order technique and also using a detailed kinetic model to infer the rate
constants for Reaction (4.1), (4.2), and (4.3). Each technique is discussed in the
subsequent subsections, and the advantages and disadvantages of each method are
also described. A comparison of the final rate constant results using the two analysis
50 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
methods is discussed in Section 4.4.
4.3.1 Pseudo-first-order
A first-order reaction is a chemical reaction where the rate of reaction is proportional
to the concentration of only one reactant. For a bimolecular reaction, the rate of the
reaction typically depends on the concentration of both reactants. If, however, one
reactant in a bimolecular reaction is present in large excess of the other reactant, a
pseudo-first-order reaction is observed, as the concentration of the reactant in excess
remains relatively constant. Thus, the rate law can be written as a function of the
concentration of only one reactant, and resembles a first-order reaction rate law. For
example, for Reaction (4.3), the rate law for the disappearance of OH can be written
as Eq. 4.1, where the brackets around a chemical species refer to the time-dependent
concentration of that species in the mixture.
d[OH]
dt= −k4.3[OH][C9H20] (Eq. 4.1)
For the mixtures used in the experiments in this chapter, with n-nonane in excess of
OH, the rate law can be expressed in the pseudo-first-order form of Eq. 4.2, where k′4.3
is defined by Eq. 4.3 and can be assumed constant, and the subscript t = 0 denotes
the initial concentration.
d[OH]
dt= −k′4.3[OH] (Eq. 4.2)
k′4.3 = k4.3 · [C9H20]t=0 (Eq. 4.3)
The integrated form of the rate law in Eq. 4.2 results in Eq. 4.4, which expresses the
concentration of OH as a function of k′4.3 and time only.
[OH] = [OH]t=0 exp(−k′4.3 · t) (Eq. 4.4)
Thus k′4.3 can be determined from the measurement of the exponential decay rate of
the OH concentration, which can be determined from the measured OH time-history
4.3. DATA ANALYSIS 51
because the OH mole fraction is proportional to the concentration. The rate constant
for Reaction (4.3) can be determined if the initial concentration of n-nonane is known,
assuming that the approximations required for a pseudo-first-order analysis are valid.
An advantage of designing experiments where the concentration of the measured
species follows a pseudo-first-order (exponential) decay is that the rate constant de-
termination is insensitive to the initial concentration of the chemical species measured
(i.e. [OH]t=0) and to the absolute value of the absorption coefficient for this species.
For the experiments of the current chapter, this can be advantageous because small
fluctuations in the initial concentration of OH occur, due to reasons specified in Sec-
tion 3.4.2. Another advantage of the pseudo-first-order method is that the analysis
is relatively simple and thus can be performed quickly.
A major assumption required in applying the pseudo-first-order method to the
work in this chapter is that secondary reactions have negligible influence on the mea-
sured OH time-histories. Systematic errors in the rate constant determination may
arise if this assumption does not hold true.
4.3.2 Kinetic Modeling
Complete kinetic modeling of the experiments can account for any secondary reactions
that might influence the simulated OH time-history. In addition to the pseudo-first-
order method, the detailed alkane/TBHP mechanism developed in Chapter 3 was
also used to determine the rate constants for Reaction (4.1), (4.2), and (4.3) from
measured OH time-histories. The alkane/TBHP mechanism contains the JetSurF 1.0
mechanism [18], and therefore it already contains reactions relevant to n-alkane chem-
istry, and the modifications to the mechanism discussed in Chapter 3 account for the
secondary chemistry from using TBHP as the OH precursor.
The results of an OH sensitivity analysis performed with the alkane/TBHP mech-
anism under conditions of pseudo-first-order kinetics in OH are shown in Figure 4.1
for representative experiments with n-nonane at 1167 and 937 K. OH sensitivity is
defined by Eq. 3.1, and the sensitivity to the overall rate constant for Reaction (4.3)
52 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
is defined as the sum of the OH sensitivity from all possible product channels. Fig-
ure 4.1 illustrates that under these conditions at both temperatures, the simulated
OH time-history is highly sensitive to the overall rate constant for Reaction (4.3).
Reaction (3.3) also appears in the OH sensitivity results because this reaction also
contributes to OH removal at both temperatures. Methyl radicals are generated from
the decomposition of TBHP, and thus will be present at similar levels as OH. While
increasing the alkane concentration could minimize the relative contribution of OH re-
moval through this channel, this would also decrease the time scale of the experiment,
which would also be undesirable. Therefore, if Reaction (3.3) contributes significantly
to OH removal relative to Reaction (4.3), a detailed mechanism that correctly cap-
tures the OH removal by Reaction (3.3), such as the alkane/TBHP mechanism from
Chapter 3, is necessary in determining the rate constants for Reaction (4.3) and the
other n-alkane+OH reactions. Another important reaction that must be accounted
for when using TBHP as an OH precursor is Reaction (3.1), which is only signifi-
cant in the OH sensitivity analysis shown in Figure 4.1 at 937 K (and also for any
temperature below 1000 K). The rate constant for Reaction (3.1) was measured in
Chapter 3.
Because the rate constants of the significant secondary reactions appearing in
the OH sensitivity analysis are well known, for a given experimental temperature,
the rate constant for Reaction (4.3) can be determined by matching the simulated
OH time-history with the measured data trace, using only the overall rate constant
for Reaction (4.3) as a free parameter. While Reaction (4.3) can proceed via five
different product channels, the identity of the products of Reaction (4.3) are assumed
to have negligible influence on the rate constant determination, and this assumption
was confirmed in a detailed uncertainty analysis that is presented Section 4.4.
The results of OH sensitivity analyses for experiments with n-pentane and n-
heptane are similar to those shown in Figure 4.1. Therefore, a method identical to the
rate constant determination method for Reaction (4.3) is used to determine the rate
constants for Reactions (4.1) and (4.2) from measured OH time-histories. A major
advantage of using a detailed kinetic mechanism for the rate constant determination
is that influences of secondary reactions are accounted for in the analysis. Because the
4.3. DATA ANALYSIS 53
alkane/TBHP mechanism developed in Chapter 3 was validated against experiments
with neat TBHP dilute in argon, the mechanism is assumed to correctly describe the
TBHP-related secondary chemistry, including Reactions (3.1) and (3.3). Therefore, if
the rate constant results from the kinetic modeling method differ from that which was
determined using the pseudo-first-order method, the rate constant determined using
the kinetic modeling method is considered to be more representative of the actual rate
constant. Because using a kinetic mechanism for the rate constant determination is
more complex than the pseudo-first-order method, in certain cases the additional
complexity and time required for the kinetic simulations may be unnecessary for
experiments with negligible secondary chemistry; however, Section 4.4 shows that
this was not found to be the case in the current experiments.
0 20 40 60 80-6
-4
-2
0
21167 K, 1.00 atm, 168 ppm C9H20, 16 ppm TBHP, argon937 K, 1.20 atm, 214 ppm C9H20, 16.5 ppm TBHP, argon
OH
Sen
sitiv
ity
Time [s]
/ (3.1) (CH3)3COOH -> (CH3)3CO + OH/ (3.3) CH3 + OH -> CH2(s) + H2O/ (4.3) C9H20 + OH -> C9H19 + H2O
Figure 4.1: OH sensitivity for pseudo first-order experiments to measure the overall rate of n-nonane+OH, Reaction (4.3). Calculations with conditions for a representative high-temperatureexperiment (1167 K, 1.00 atm for 168 ppm n-nonane, 16.0 ppm TBHP, argon) are shown in blackand has minimal secondary chemistry from Reaction (3.3). Calculations with conditions for a rep-resentative low-temperature experiment (937 K, 1.20 atm for 214 ppm n-nonane, 16.5 ppm TBHP,argon) are shown in red and illustrate larger OH sensitivity to TBHP decomposition, Reaction (3.1),at early times in addition to secondary chemistry from from Reaction (3.3). At both conditions, thesimulated OH time-history is predominately sensitive to the rate constant for Reaction (4.3).
54 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
4.4 Results
4.4.1 Rate Constant Measurements
Figures 4.2 and 4.3 show sample measured OH time-histories for experiments with n-
nonane at 1167 and 937 K, respectively. The OH time-histories follow an exponential
decay, as expected from a pseudo-first-order experiment; the exponential decay can
be seen more clearly on a plot of lnxOH versus time, as shown in Figure 4.2, or an
semi-logarithmic plot of the OH time-history, as shown in the inset of Figure 4.3,
where a linear decay is visible.
0 20 40 60 80-2
-1
0
1
2
3
Current data1
Linear fit
Time [μs]
1167 K, 1.00 atm2168 ppm C9H20, 16.0 ppm TBHP, argon
ln (x
OH [p
pm]) Slope = -7.16x10-2 μs-1
0 20 40 60 80
0
5
10
15
20
Reaction (4.3): C9H20 + OH -> Products
Simulations: k4.3 = 6.48 x 10-11
cm3molecule-1s-11
k4.3 -30%1
k4.3 +30%
Time [μs]
OH
mol
e fra
ctio
n [p
pm]
Figure 4.2: Measured OH time-histories at 1167 K, 1.00 atm for 168 ppm n-nonane, 16.0 ppm TBHP,argon. OH mole fraction trace is shown versus time (main plot), and the natural logarithm of theOH mole fraction is shown versus time (upper right). Also shown is a linear fit to lnxOH versustime and the simulated OH time-histories using the alkane/TBHP mechanism with the best-fit rateconstant for Reaction (4.3) and perturbations of ±30% on the best-fit rate constant.
The time-constant of exponential decay (determined from the slope of ln xOH
versus time) is the pseudo-first-order rate constant, defined by Eq. 4.3. For the ex-
periment at the 1167 K shown in Figure 4.2, the pseudo-first-order rate constant
is k′4.3 = 7.16 × 104 s−1; the concentration of n-nonane for the conditions in the
4.4. RESULTS 55
experiment is [C9H20] = 1.06 × 1015 molecule/cm3, leading to a rate constant for
Reaction (4.3) of k4.3 = 6.77 × 10−11 cm3molecule−1s−1 at 1167 K. The best-fit sim-
ulated OH time-history for the experimental conditions of Figure 4.2 is obtained
using a rate constant for Reaction (4.3) of 6.48 × 10−11 cm3molecule−1s−1 in the
alkane/TBHP mechanism. This simulated OH time-history is shown in Figure 4.2,
along with perturbations of ±30% to k4.3. The pseudo-first-order method leads to
rate constant determinations which are approximately 4% too fast at the current
experimental conditions, primarily due to Reaction (3.3) (the reaction of OH with
methyl radicals). In experiments with temperatures higher than 1000 K, the dis-
crepancy between the rate constant determined from the pseudo-first-order method
and the kinetic modeling method varies with the initial n-alkane-to-TBHP ratio and
the identity of the n-alkane, reaching a discrepancy as high as 10% for experiments
with initial n-pentane-to-TBHP ratios of ten. The rate constants determined us-
ing the kinetic modeling method are independent from the initial n-alkane-to-TBHP,
supporting the assumption that the TBHP-related secondary chemistry is accounted
for correctly. The discrepancy between the rate constant determined from the two
analysis methods becomes larger than 10% at temperatures less than 1000 K for all
n-alkanes studied, because the rate constant for Reaction (3.1) (the decomposition
of TBHP) also influences the rate of OH decay. For these reasons, the kinetic mod-
eling method is concluded to be a better method for inferring the most accurate rate
constant from the current data for reactions of OH with n-alkanes.
While the time-constant describing the exponential decay of OH cannot be used
directly to infer the rate constant for Reaction (4.3) without a systematic error due
to neglecting the importance of Reaction (3.3), the exponential decay relationship is
especially helpful in determining the rate constant that best fits the OH time-history
at temperatures below 1000 K, where the peak OH mole-fraction depends on the
best-fit rate constant for Reaction (4.3). For example, Figure 4.3 presents the OH
time-history on a semi-logarithmic plot where the sensitivity of the peak OH mole-
fraction to the rate constant for Reaction (4.3) is less prominent, and only the rate
of OH decay is clearly seen to be sensitive to perturbations in the rate constant for
Reaction (4.3).
56 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
0 20 40 60 800.1
1
10
Reaction (4.3): C9H20 + OH -> Products
Current data1
k4.3 = 4.65 x 10-11
cm3molecule-1s-11
k4.3 -30%1
k4.3 +30%
937 K, 1.20 atm, 214 ppm C9H20, 16.5 ppm TBHP, argon
OH
mol
e fra
ctio
n [p
pm]
Time [μs]
Figure 4.3: Measured OH time-history on a semi-logarithmic scale for conditions of 937 K, 1.20 atmfor 214 ppm n-nonane, 16.5 ppm TBHP, argon. Also shown are simulated OH time-histories usingthe alkane/TBHP mechanism with the best-fit rate constant for Reaction (4.3) and perturbationsof ±30% on the best-fit rate constant.
The measured OH time-histories for the experiments in this chapter are all similar
to the traces shown in Figures 4.2 and 4.3. Therefore, the kinetic modeling method
can be applied to all OH time-history measurements of this chapter. The current
determinations for the rate constants for the Reactions (4.1), (4.2), and (4.3) can be
expressed in Arrhenius form by Eq. 4.5, Eq. 4.6, and Eq. 4.7, respectively.
k4.1 = 2.10× 10−10 exp
(− 2038
T [K]
)cm3molecule−1s−1 (Eq. 4.5)
k4.2 = 2.43× 10−10 exp
(− 1804
T [K]
)cm3molecule−1s−1 (Eq. 4.6)
k4.3 = 3.17× 10−10 exp
(− 1801
T [K]
)cm3molecule−1s−1 (Eq. 4.7)
Eq. 4.5, Eq. 4.6, and Eq. 4.7 are valid for approximately the temperature range 880 to
1360 K. The individual data points are listed in Tables 4.1, 4.2, and 4.3 for n-pentane,
n-heptane, and n-nonane, respectively. These data are shown in Figure 4.4.
4.4. RESULTS 57
0.7 0.8 0.9 1.0 1.1 1.21
2
3
4
56789
10
(4.1) C5H12+ OH -> C5H11+ H2O(4.2) C7H16+ OH -> C7H15+ H2O(4.3) C9H20+ OH -> C9H19+ H2O
n-pentane+OH
n-heptane+OH
n-nonane+OH
k n-al
kane
+OH [1
0 -1
1 cm
3 mol
ecul
e-1s-1
]
1000/T [1/K]
1250 K 1000 K 833 K
Figure 4.4: Measured rate constants for Reactions (4.1), (4.2), and (4.3), reactions of OH with n-pentane, n-heptane, and n-nonane, respectively, inferred from the measured OH time-histories usingthe kinetic modeling method. Solid lines are the Arrhenius fits to the data. The error bars representthe results of a detailed uncertainty analysis.
The magnitudes of the rate constants follow the same order the n-alkane size, with
Reaction (4.1) the slowest and n-pentane having the fewest carbon atoms (C5), and
Reaction (4.3) the fastest and n-nonane having the most carbon atoms (C9). This is
expected since the larger n-alkane has more hydrogen-atom abstraction sites for the
reaction to occur. n-Heptane has four more hydrogen atoms than n-pentane, and
these hydrogen atoms are bonded to secondary carbon atoms, and n-nonane has four
more hydrogen atoms than n-nonane, also on secondary carbon atoms; therefore, the
difference between the measured rate constants for Reactions (4.1), (4.2), and (4.3)
can yield information about the rate of reaction at secondary carbon abstraction
sites, provided that the differences in neighboring atom effects is negligible. This
type of strategy is how empirical additivity methods can be developed to estimate
rate constants for reactions in the family of n-alkane+OH. Further discussion on
additivity methods is presented in Section 4.5.2, where an existing additivity model
is shown to predict the current data well. Additional discussion on additivity models
is also presented in Appendix D.
58 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
Table 4.1: Individual data points fit using the alkane/TBHP mechanism for the rate constant forReaction (4.1): C5H12 + OH −−→ C5H11 + H2O.
Mixture T [K] P [atm] k4.1 [cm3molecule−1s−1]
303 ppm C5H12, 1364 0.84 4.90×10−11
12 ppm TBHP, 1253 0.93 4.07×10−11
Argon 1196 1.20 3.82×10−11
1077 1.35 3.07×10−11
874 1.24 2.16×10−11
211 ppm C5H12, 1320 0.85 4.57×10−11
14 ppm TBHP, 1182 0.96 3.74×10−11
Argon 1091 1.02 3.16×10−11
1025 1.08 2.82×10−11
960 1.18 2.57×10−11
200 ppm C5H12, 1291 0.74 4.40×10−11
20 ppm TBHP, 1282 0.87 4.23×10−11
Argon 1190 0.82 3.82×10−11
1186 0.94 3.74×10−11
1058 0.94 2.82×10−11
1002 1.12 2.90×10−11
869 1.27 1.99×10−11
197 ppm C5H12, 1225 0.94 4.15×10−11
13 ppm TBHP, 1221 0.96 3.99×10−11
Argon 1164 0.99 3.65×10−11
917 1.24 2.24×10−11
892 1.28 2.16×10−11
Table 4.2: Individual data points fit using the alkane/TBHP mechanism for the rate constant forReaction (4.2): C7H16 + OH −−→ C7H15 + H2O.
Mixture T [K] P [atm] k4.2 [cm3molecule−1s−1]
206 ppm C7H16, 1364 0.842 6.73×10−11
12 ppm TBHP, 1112 1.020 4.65×10−11
Argon 1101 1.014 4.48×10−11
1083 1.047 4.57×10−11
939 1.155 3.49×10−11
198 ppm C7H16, 1187 0.966 5.40×10−11
15 ppm TBHP, 1099 1.047 4.65×10−11
Argon 970 1.157 3.90×10−11
892 1.233 3.32×10−11
869 1.254 2.99×10−11
150 ppm C7H16, 1216 0.927 5.48×10−11
15 ppm TBHP, 1165 0.993 5.06×10−11
Argon 1159 1.928 5.06×10−11
1077 2.060 4.57×10−11
1055 1.054 4.48×10−11
992 1.128 3.99×10−11
4.4. RESULTS 59
Table 4.3: Individual data points fit using the alkane/TBHP mechanism for the rate constant forReaction (4.3): C9H20 + OH −−→ C9H19 + H2O.
Mixture T [K] P [atm] k4.3 [cm3molecule−1s−1]
214 ppm C9H20, 1352 0.874 8.64×10−11
16 ppm TBHP, 1330 0.855 8.30×10−11
Argon 1124 0.990 5.98×10−11
1103 1.071 6.48×10−11
975 1.170 4.81×10−11
937 1.201 4.65×10−11
884 1.263 4.31×10−11
168 ppm C9H20, 1246 0.939 7.31×10−11
16 ppm TBHP, 1167 1.003 6.48×10−11
Argon 1154 1.010 7.06×10−11
1021 1.126 5.31×10−11
4.4.2 Uncertainty Analysis
A detailed uncertainty analysis, accounting for uncertainty in temperature, pressure,
initial TBHP concentration, initial n-alkane concentration, laser intensity, data fit-
ting, impurities, reaction products, and the rate constants of the four most important
secondary reactions, was performed for an experiment with n-nonane at 1167 K. The
influence of uncertainties in each of these parameters on the uncertainty of the rate
constant for Reaction (4.3) was obtained by perturbing each uncertainty source to
its 2σ error bounds and redetermining the best-fit rate constant for Reaction (4.3).
Figure 4.5 shows the contribution from each source of uncertainty considered to the
overall uncertainty of the rate constant for the Reaction (4.3) determined using the
kinetic modeling method in this work. The primary contributions to the overall uncer-
tainty include the fitting of the model to the experimental data trace, and the initial
transmitted laser intensity. Secondary contributions to the uncertainty are the initial
fuel concentration and the rate constant for Reaction (3.3), which were minimized
through laser absorption measurements at 3.39 µm and measurement of OH decay
in neat TBHP experiments, respectively. The uncertainties presented in Figure 4.5
were assumed to be uncorrelated, and these uncertainties were combined in a root-
sum-squared method to yield a total uncertainty in the rate constant measurement.
At 1167 K, the estimated overall uncertainty in the rate constant for Reaction (4.3)
is ±11%, and this uncertainty estimate is approximately valid for each of the rate
60 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
constants for Reaction (4.1), (4.2), and (4.3) in the temperature range from 1000 to
1364 K. For temperatures below 1000 K, the influence of the uncertainty of the rate
constant for Reaction (3.1) in the final rate constant determinations increases with
decreasing temperatures, leading to a maximum uncertainty of ±23% at 869 K for
each of the rate constants for Reaction (4.1), (4.2), and (4.3).
-10 -5 0 5 10 15 20
CH3+CH3(+M) -> C2H6(+M) (uncertainty factor 2)
CH3+OH(+M) -> CH3OH(+M) (uncertainty factor 2)
(3.3) CH3 + OH -> CH2(s)+H2O (+/- 30%)
TBHP adsorption or decomposition in mixing tank (max 10%)
Laser intensity (+/- 0.15%)
(3.1) (CH3)3COOH -> (CH3)3CO + OH (+/- 30%)
Branching ratio of n-alkane+OH
Impurities (+1 ppm H)
Fitting (+/- 7%)
n-Alkane concentration (+/- 5%)
Wavelength (+/- 0.032 cm-1 in UV)
OH absorption coefficient (+/- 3%)
Pressure (+/- 1%)
Time zero (+/- 1.5 μs)
Contribution to uncertainty in k4.3 [%]
Temperature (+/- 1%)
1167 K, 1.00 atm168 ppm C9H20, 16.0 ppm TBHP
Overall RSS uncertainty:1 +/- 11%1Reaction (4.3): C9H20 + OH -> C9H19 + H2O
Uncertainty source (+/- 2σ uncertainty)
Figure 4.5: Factors considered in the uncertainty analysis for the rate constant for Reaction (4.3) at1167 K, 1.00 atm. Each error source is listed with its 2σ uncertainty bound which was propagatedinto the final rate constant determination. The overall uncertainty of ±11% for the rate constantfor Reaction (4.3) at 1167 K is determined using a root-sum-squares combination of the individualuncertainty contributions.
4.5 Comparisons with Literature
4.5.1 Previous Experimental Works
Cohen and coworkers [6, 7, 9] pioneered the use of TBHP as an OH precursor to study
the rate constants for reactions in the family of n-alkane+OH at temperatures near
4.5. COMPARISONS WITH LITERATURE 61
1100 K in the 1980’s. Koffend and Cohen [9] used OH absorption near 310 nm gen-
erated from a microwave discharge, and monitored the OH mole fraction exponential
decay time-constant for multiple single-temperature experiments with varying initial
OH mole fractions to determine an overall n-alkane+OH rate constant for n-heptane
and n-nonane. The single-temperature rate constant measurements of Koffend and
Cohen for n-heptane+OH and n-nonane+OH are 28% and 26% slower, respectively,
than the current data. Though Koffend and Cohen only claimed to measure the rate
constant value at a single temperature, their reported rate constant is an average over
many experiments which span a temperature range of approximately 100 K surround-
ing the average temperature reported for the measured rate constant, and their data
for the repeated experiments exhibit high scatter. Both of these factors are likely to
contribute to the discrepancy of their results with the current measurements. While
the rate constants of Koffend and Cohen are fit from high-scatter data, their work
was the first to show the relationship between the high-temperature rate constants of
the reactions of OH with n-heptane and n-nonane, which show that the rate constant
involving n-nonane is faster by approximately 30%. The current measurements also
illustrate this relationship to hold true.
High-temperature measurements for n-alkane+OH reaction rate constants have
also been recently performed by Sivaramakrishnan and Michael [11] to yield rate con-
stant measurements as a function of temperature for a set of large alkanes, including
n-pentane and n-heptane. Their work employed a technique similar to the current
work with TBHP and shock tubes. In the work of Sivaramakrishnan and Michael, very
dilute mixtures of an alkane and TBHP in argon (on the order of tens of ppm) were
used with an initial alkane-to-TBHP concentration ratios averaging ten for experi-
ments with n-pentane, but only averaging six for experiments with n-heptane. The
OH time-histories of Sivaramakrishnan and Michael were monitored using multi-pass
absorption of light from an OH resonance lamp, and all rate constant determinations
were performed with a pseudo-first-order analysis, claiming negligible effects of TBHP
chemistry, and obtaining overall n-alkane+OH rate constants directly from the time-
constant of OH decay. The current measurements for n-pentane and n-heptane are
approximatley 20% faster than the data from Sivaramakrishnan and Michael. The
62 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
source of this discrepancy is still unclear. Although Sivaramakrishnan and Michael
performed analysis with a detailed kinetic mechanism to conclude that secondary ki-
netics from Reactions (3.3) and (3.4) did not effect the OH concentrations under their
experimental conditions, the rate constant they used for Reaction (3.3) was ∼50%
slower than the rate constant determined in Chapter 3 of this thesis. Hence, the
TBHP kinetic effects on the OH concentration likely were non-negligible. However,
an analysis using the current kinetic mechanism to account for secondary chemistry
on the OH time-histories from Sivaramakrishnan and Michael’s experiments would
only serve to widen the discrepancy between their rate constant measurements and
the current work. Other parameters which can commonly cause this sort of system-
atic error seen between the data sets include the presence of impurities, or alkane loss
due to adsorption or condensation onto the facility surfaces. The absence of impuri-
ties and the initial composition of the test mixtures used in the current experiments
were each verified using different laser absorption techniques, as described in Chap-
ter 2, and any uncertainties were accounted in the detailed error analysis described
in Section 4.4. If an analysis of systematic errors for the work of Sivaramakrishnan
and Michael were to be conducted, it is likely that their rate constant measurements
would have overlapping uncertainty limits with the present work.
The current data obtained for the overall rate constants for Reactions (4.1), (4.2),
and (4.3) in this study are shown in Figure 4.6 in comparison with the data of Koffend
and Cohen [9] and Sivaramakrishnan and Michael [11]. Also shown are a few estimated
rate constants which are discussed in Section 4.5.2. To the author’s knowledge, the
data taken for the rate constant for Reaction (4.3) are the first measurements showing
the temperature-dependence of the rate of OH reaction with n-nonane at combustion-
relevant temperatures.
4.5.2 Validation of Estimation Methods
The current rate constant measurements describe the overall rate constant for each
n-alkane+OH reaction, though several different abstraction sites are possible for each
4.5. COMPARISONS WITH LITERATURE 63
0.7 0.8 0.9 1.0 1.1 1.2 1.31
2
3
4
56789
10
2.5 3.0 3.5 4.00.2
0.6
1
1.4
1.8
n-pentane
n-heptane
n-nonane
Estimation MethodsIGS - Srinivasan and Michael (2009)
C5H12 C7H16 C9H20
SAR - Kwok and Atkinson (1995) C5H12 C7H16 C9H20
k n-al
kane
+OH
[10-1
1 cm
3 mol
ecul
e-1 s
-1]
1000/T [K-1]High-Temperature Data
Current Work Sivaramakrishnan
and Michael (2009) Koffend and Cohen (1996)
1250 K 1000 K 833 K
Red: (4.1) C5H12 + OH -> C5H11 + H2OGreen: (4.2) C7H16 + OH -> C7H15 + H2OBlue: (4.3) C9H20 + OH -> C9H19 + H2O
k OH
+n-a
lkan
e [1
0-11 c
m3 m
olec
ule-1
s-1]
1000/T [K-1]
Low-Temperature Data Darnall et al.
(1978)Nolting et al. (1988)
Abbatt et al. (1990) Talukdar et al.
(1994) Ferrari et al. (1996)
Donahue et al. (1998) Coeur et al. (1998)
DeMore and Bayes (1999) Colomb et al. (2004) Li et al. (2006) Wilson et al. (2006)
400 K 333 K 285 K
Figure 4.6: Measured rate constants for Reactions (4.1), (4.2), and (4.3), reactions of OH with n-pentane, n-heptane, and n-nonane, respectively, from the current work compared with data [72–82]and estimation methods [11, 22] from the literature for (main plot/top) high temperatures 800 to1300 K, and (bottom right) low temperatures 250 to 440 K.
64 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
reaction, leading to different isomers of the radical product. While the current ex-
perimental results do not yield information about the relative rate constants of the
different abstraction channels (the rate constant determination is independent of the
branching ratios between the different abstraction sites), several different types of es-
timation methods lead to determination the rate constants of n-alkane+OH for each
abstraction site, and the accuracy of these methods can be determined by comparing
the measured results with the estimated overall rate constant for the n-alkane+OH
reaction, obtained by summing over all the product channels.
Estimation methods capable of site-specific rate constant predictions have existed
since Greiner [19] developed the first additivity model in 1970. Since then, others
have developed similar models [23], improved additivity models which include carbon
neighbor interactions [11, 20–22, 82], and other estimation methods employ transition-
state theory [24, 25] and incorporate reaction-class factors obtained through linear
energy-relationships [26]. These estimation methods can be used to determine the
relative branching ratios leading to different product channels, information which is
useful in developing detailed kinetic mechanisms. Further information on determining
site-specific rate constants using these estimation methods is described in Appendix D,
and comparisons to two of the most recent of them will be discussed here.
The improved group scheme (IGS) by Sivaramakrishnan and Michael [11] ap-
plies additivity principles for predicting n-alkane+OH reaction rate constants, and
uses a large experimental database for n-alkanes for molecules as large as n-heptane.
Sivaramakrishnan and Michael’s empirical IGS ascribes a different rate constant for
hydrogen-atom abstraction by OH at each different carbon center dependent on car-
bon interactions from neighbors up to the next-next-nearest neighbor. While Sivara-
makrishnan and Michael developed the IGS to fit their experimental data for n-
alkanes as large as n-heptane, only a single temperature data point for n-nonane+OH
was available from Koffend and Cohen [9] for validation of the scheme for larger n-
alkanes. The IGS comes close to predicting the rate constant for the n-nonane+OH
reaction around 900 K; however, the rate constant measurements for n-nonane+OH
for temperatures of 884 to 1352 K in the current study show a steeper temperature
4.5. COMPARISONS WITH LITERATURE 65
dependence than predicted by the IGS, as can be seen in Figure 4.6. The use of Kof-
fend and Cohen’s [9] n-heptane+OH rate constant measurement in determining the
parameters for the IGS is at least partially responsible for the discrepancy between
the rate constant predictions by the IGS and the current measurements. As discussed
in Section 4.5.1 and evident in Figure 4.6, the Koffend and Cohen rate constant for
n-heptane+OH is slower than both the current measurements and measurements of
Sivaramakrishnan and Michael for the same reaction. Furthermore, the abstract of the
Koffend and Cohen paper incorrectly reports the temperature of their n-heptane+OH
rate constant measurement as 1186 K, and Sivaramakrishnan and Michael appear to
have used this temperature for this data point in their modeling (Table III in the
Koffend and Cohen text clearly reports 30 individual data points at temperatures
which average to 1086 K for their n-heptane experiments). Therefore, the attempt
of Sivaramakrishnan and Michael to include the Koffend and Cohen n-heptane+OH
rate constant measurement in the development of an estimation method for the rate
constants for n-alkane+OH reactions would result in rate constant estimations which
would be too slow near 1186 K.
The additivity estimation methods by Atkinson and coworkers [20–22] are termed
structure-activity relationships (SAR) which ascribe a rate constant for hydrogen-
atom abstraction by OH for each primary, secondary, and tertiary carbon site. The
SAR estimation accounts for neighboring atom effects by lowering the activation en-
ergy of the H-atom abstraction at each carbon site, depending on the identity of
the neighboring atom, and the degree of the activation energy change is determined
through examining literature databases for data from 250 to 1000 K. While the most
recent SAR values updated by Kwok and Atkinson [22] were developed for temper-
atures from 250 to 1000 K, this updated SAR estimation precisely predicts the rate
constants for the n-alkane+OH reactions measured in this study up to 1364 K for all
three of the alkanes (n-pentane, n-heptane, and n-nonane) and fits the temperature
dependence well.
While both the improved group scheme of Sivaramakrishnan and Michael [11] and
the updated structure-activity relationship from Kwok and Atkinson [22] are adequate
at predicting the overall n-alkane+OH rate constants for n-pentane, n-heptane, and
66 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
n-nonane at temperatures from 250 to 440 K [72–82], as shown in Figure 4.6, only the
SAR estimation of Kwok and Atkinson correctly predicts the temperature dependence
for the overall rate constant for n-alkane+OH from the data in the current work at
temperatures greater than 800 K.
4.6 Conclusions
The overall rate constants for Reactions (4.1), (4.2) and (4.3), describing reactions of
OH with n-pentane, n-heptane, and n-nonane, respectively, were studied behind re-
flected shock waves by using tert-butylhydroperoxide (TBHP) to generate OH radicals
in mixtures with each n-alkane dilute in argon to yield pseudo-first-order kinetics in
OH. OH time-histories were monitored using narrow-linewidth laser absorption near
306.7 nm, and the results were examined using both a pseudo-first-order analysis and
with a detailed kinetic mechanism that was developed to account for both TBHP and
n-alkane kinetics. The current rate constant measurements show agreement within
20% with those measured by Sivaramakrishnan and Michael [11] for n-pentane and
n-heptane, and provide the first known temperature-dependent rate constant mea-
surements for n-nonane+OH above 800 K. Systematic errors due to impurities and
uncertainty in mixture composition were minimized with laser absorption measure-
ments verifying the absence of impurities and confirming accurate knowledge of the
initial n-alkane composition, leading to an overall uncertainty in the rate constant
measurements of ±11% for temperatures from 1000 to 1364 K. The overall uncer-
tainty in the rate constant determination increases with decreasing temperature below
1000 K, up to ±23% at 869 K.
The current rate constant measurements for Reactions (4.1), (4.2) and (4.3) were
compared to two recent estimation methods from the literature for predicting rate
constants of reactions in the family of n-alkane+OH. The most recent improved group
scheme model of Sivaramakrishnan and Michael [11], developed from data using nor-
mal alkanes of C7 and smaller, fails to predict the temperature dependence of the
current n-nonane+OH reaction rate constant measurements at temperatures above
800 K. The structure-activity relationship model developed by Atkinson [20, 21],
4.6. CONCLUSIONS 67
updated with parameters by Kwok and Atkinson [22], was developed using data in
the temperature range 250 to 1000 K, and is shown to well-predict the current n-
alkane+OH rate constant data taken for n-pentane, n-heptane, and n-nonane, even
up to 1364 K.
68 CHAPTER 4. REACTIONS OF OH WITH N-ALKANES
Chapter 5
Reaction of OH with n-Butanol
5.1 Introduction
5.1.1 Background and Motivation
In 2006, DuPont and BP announced a partnership to begin production of n-butanol
(1-butanol: CH3CH2CH2CHOH) from biomass, also referred to as biobutanol, be-
cause of the advantages of biobutanol over ethanol for use as a fuel additive or alter-
native fuel [28]. In the years following, efforts towards developing detailed chemical
kinetic models for high-temperature combustion of n-butanol have expanded rapidly
to support the introduction of biobutanol into the transportation sector.
According to Moss et al. [31], the reaction of OH with n-butanol is a major fuel
consumption pathway during combustion of n-butanol. Therefore, the rate constant
for this reaction must be known well to develop an accurate detailed kinetic mecha-
nism for n-butanol combustion. The abstraction of a hydrogen atom from n-butanol
by OH can proceed through five different reaction channels which result in different
product species, as described by Reactions (5.1a) through (5.1e). The products of
Reactions (5.1a) through (5.1d) consist of a water molecule and a 1-hydroxy-butyl
radical, the latter of which can exist in four isomers; this thesis will use a naming con-
vention which denotes different isomers of the 1-hydroxybutyl radicals by their radical
position relative to the hydroxyl group. For example, Reaction (5.1a) produces an
69
70 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
the α-radical (1-hydroxy-but-1-yl: CH3CH2CH2CHOH), Reaction (5.1b) produces an
the β-radical (1-hydroxy-but-2-yl: CH3CH2CHCH2OH), and so on.1 The products of
Reaction (5.1e) consist of a water molecule and a 1-butoxyl radical.
CH3CH2CH2CH2OH + OH −→ CH3CH2CH2CHOH + H2O (5.1a)
−→ CH3CH2CHCH2OH + H2O (5.1b)
−→ CH3CHCH2CH2OH + H2O (5.1c)
−→ CH2CH2CH2CH2OH + H2O (5.1d)
−→ CH3CH2CH2CH2O + H2O (5.1e)
Early detailed kinetic mechanisms of n-butanol combustion included site-specific rate
constants for Reactions (5.1a) through (5.1e) that were estimated from analogous
reactions with alkanes or ethanol [29–32]. The mechanism of Black et al. [85] used
additional knowledge from theoretical calculation of the individual bond energies in
the n-butanol molecule to estimate the site-specific rate constants for Reactions (5.1a)
through (5.1e). The mechanism of Grana et al. [40] used estimations for the rate
constants for Reactions (5.1a) through (5.1e) made with the basis of a systematic
approach for similar reactions of hydrocarbon species [86], while also considering
quantum calculations of Galano et al. [87] for reactions of OH with alcohols.
Recently, studies focusing directly on the high-temperature rate constant for the
reaction of OH with n-butanol have been undertaken, including high-temperature ex-
perimental measurements [47] and ab initio studies with high-level electronic structure
calculations [88]. Vasu et al. [47] conducted the first high-temperature measurements
of the overall rate constant2 for Reaction (5.1) using tert-butylhydroperoxide (TBHP)
as a fast OH precursor in shock tube experiments in the temperature range 1017 to
1The terms α-radical, β-radical, and γ-radical will be used in the subsequent chapters in thisthesis to refer to different radicals. In all cases, the Greek letter distinguishes the position of theradical with respect to the hydroxyl group on the butanol radical isomer of the respective chapter.
2Reactions with the same reactants but different products will be labeled with same reactionnumber, appended with different letters of the alphabet. The term “overall reaction” will be usedto refer to the overall reaction of the reactants, including all product channels. Reference to thereaction number without any letters always refers to the overall reaction. The rate constant for theoverall reaction is always defined as the sum of the site-specific rate constants, similar to in Eq. 5.1.
5.1. INTRODUCTION 71
1269 K. Their measurements yielded only the overall rate constant, which is related
to the site-specific rate constants by Eq. 5.1.
k5.1 = k5.1a + k5.1b + k5.1c + k5.1d + k5.1e (Eq. 5.1)
Studies focusing on the site-specific rate constants for Reactions (5.1a) through (5.1e)
include ab initio calculations, such as those published by Zhou et al. [88]; confidence in
ab initio rate constant calculations is typically gained by comparison of the calculated
overall rate constant, determined by Eq. 5.1, with experimental data. Experimental
measurements are necessary to investigate the validity of ab initio calculations, though
the reported rate constants of Vasu et al. [47] can be sensitive to kinetic modeling.
As numerous advances in the kinetic modeling of n-butanol have occurred since the
work of Vasu et al., the influences of kinetic modeling on the determination of the
rate constant for Reaction (5.1) need to be examined.
5.1.2 Objectives of the Current Chapter
The sensitivity of the experimental rate constant reported by Vasu et al. [47], together
with recent improvements in the kinetic modeling of the OH precursor (from Chap-
ter 3) and n-butanol [36, 40, 85, 89], draws attention to deficiencies in the analysis of
Vasu et al., causing concerns about the accuracy of their experimental data and the
reported rate constant. Furthermore, the temperature range studied by Vasu et al.
(1017 to 1269 K) provides limited confidence in the temperature dependence of the
rate constants obtained by ab initio calculations for combustion-relevant conditions.
These two concerns motivate the work presented in this chapter.
This chapter examines effects of discrepancies in kinetic modeling for both TBHP
decomposition and n-butanol chemistry on the determination of the rate constant
for Reaction (5.1) from the experimental data of Vasu et al. [47]. In addition, new
experiments were also conducted to extend the experimental database of rate con-
stant measurements for Reaction (5.1) to lower combustion-relevant temperatures (to
900 K), to enable validation of rate constants for this reaction calculated using ab
initio methods over a wider temperature range.
72 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
The results presented in this chapter include rate constant measurements in shock
tube experiments at temperatures from 900 to 1200 K where laser absorption by OH
was carried out behind reflected shock waves in mixtures of tert-butylhydroperoxide
(TBHP) and n-butanol dilute in argon. A detailed kinetic mechanism was constructed
to include updated rate constants of all reactions of TBHP and n-butanol which influ-
ence the near-first-order OH concentration decay under the experimental conditions;
this mechanism was used as the final analysis tool for the determination of the overall
rate constant for Reaction (5.1) in this chapter. The measured overall rate constant
for Reaction (5.1) is compared to previously published experimental data [47], ab
initio calculations [88], and a structure-activity relationship [20–22, 90].
5.2 Analysis of n-Butanol Kinetic Mechanisms
Chapter 4 revealed that kinetic modeling was necessary in the analysis of experiments
using TBHP as an OH precursor to determine the rate constant for reactions of OH
with an organic compound. The kinetic mechanism used for analysis must include
reactions and rate constants describing TBHP decomposition, and also a base mech-
anism describing other secondary reactions that would be expected to occur following
the reaction of interest. In the work of Vasu et al. [47], they used a kinetic mechanism
based on n-butanol kinetics from the work of Sarathy et al. [32] to determine the rate
constant for Reaction (5.1) from measured OH time-histories under experimental con-
ditions for near-pseudo-first-order kinetics. In this section, the influence of changes
in kinetic modeling on the analysis of the Vasu et al. data will be examined, and the
kinetic mechanism used for the analysis in this chapter will be presented.
5.2.1 Influence of TBHP Kinetics
For the analysis in their work, Vasu et al. [47] used the n-butanol mechanism from
Sarathy et al. [32] with Reactions (3.1) and (3.2) added, reactions describing the de-
composition of TBHP and the tert-butoxyl radical, respectively. The rate constants
5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 73
Vasu et al. used for Reactions (3.1) and (3.2) are similar to those discussed in Chap-
ter 3. As shown in Figure 5.1, the mechanism used by Vasu et al. does not correctly
predict the OH time-histories of TBHP decomposition that were measured in Chap-
ter 3. Therefore, their mechanism does not correctly account for secondary reactions
associated with TBHP decomposition, and these errors were likely propagated into
their determination of the rate constant for Reaction (5.1).
0 20 40 60
0
4
8
12
16
20
0 20 40 60 80 100
0
4
8
12
16
20
Time [s]
928 K, 1.22 atm20.5 ppm TBHP, argon
OH
mol
e fra
ctio
n [p
pm]
1158 K, 1.10 atm20 ppm TBHP, argon
Data (from Chapter 3) Vasu et al. (2010) Modified Vasu et al. (see text)
Figure 5.1: Measured OH time-histories from Chapter 3 for experiments of dilute mixtures of TBHPin argon. Also shown are simulated OH time-histories using the mechanism used for analysis by Vasuet al. [47] and a modified version of the Vasu et al. mechanism with the rate constants presentedin Table 3.1. Conditions are (left) 1158 K, 1.10 atm for 20.0 ppm TBHP, argon and (right) 928 K,1.22 atm for 20.5 ppm TBHP, argon.
The rate constant for the reaction of OH with methyl radicals, Reaction (3.3),
in the mechanism of Vasu et al. [47] (from the Sarathy et al. [91] mechanism) is
over an order of magnitude slower than the rate constant determined in Chapter 3
of this work for the same reaction. This discrepancy is the leading cause of the
inability of the mechanism used by Vasu et al. to correctly predict the measured OH
time-histories during TBHP decomposition. If the rate constants of the reactions in
Table 3.1 were used in the mechanism of Vasu et al., their mechanism would correctly
predict the measured OH time-histories during neat TBHP decomposition, as shown
in Figure 5.1. The resulting mechanism obtained by updating the rate constants in
74 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
the mechanism of Vasu et al. with the rate constants presented in Table 3.1 will be
referred to as the modified Vasu et al. mechanism in this chapter.
The modified Vasu et al. mechanism was used to determine the rate constant
for Reaction (5.1) from the measured OH time-histories of Vasu et al. [47] at their
highest and lowest temperature data points. Similar to the analysis used by Vasu
et al., in the current analysis with the modified mechanism, the rate constant for
Reaction (5.1b) was preserved and only the sum of the rate constants for Reac-
tions (5.1a), (5.1c), (5.1d), and (5.1e) was varied to determine the overall rate con-
stant for Reaction (5.1). The results are shown in Figure 5.2 in comparison to the
published rate constants presented by Vasu et al., illustrating that the inadequate
modeling of the OH time-history during TBHP decomposition using the Vasu et al.
mechanism leads to a discrepancy of approximately 10%.
0.75 0.80 0.85 0.90 0.95 1.001
2
3
4
5
k 5.1
[10-1
1 cm
3 mol
ecul
e-1s-1
]
1000/T [K-1]
Kinetic mechanism used for analysis: Vasu et al. (2010) Modified Vasu et al. (2010) Modified Grana et al. (2010) Modified Sarathy et al. (2012)
1250 K 1111 K 1000 K
Reaction (5.1): CH3CH2CH2CH2OH + OH -> Products
Figure 5.2: Arrhenius plot of the rate constant for Reaction (5.1) determined from the measured OHtime-histories in the work of Vasu et al. [47]. The rate constant for Reaction (5.1) was determinedby fitting simulated OH time-histories using the different mechanisms [40, 47, 91] noted the legendto the measured traces. Each mechanism label “Modified” contains the reactions and rate constantspresented in Table 3.1 (see text in Section 5.2.2). The error bars shown on the reported data ofVasu et al. represent their reported uncertainty of ±14%.
5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 75
5.2.2 Sensitivity of k5.1 Determination to Mechanism
Numerous detailed kinetic mechanisms for n-butanol combustion can be found in
the literature today. The first models appeared in the literature in 2008 when Da-
gaut and coworkers [29, 30] and Moss et al. [31] each published separate mechanisms,
using data from a jet-stirred reactor and shock tube ignition delay times, respec-
tively, as validation targets. Researchers from around the world quickly followed
suit, adding to the literature additional and revised n-butanol mechanisms developed
from new experimental validation targets [32, 34, 36, 40, 85, 89, 91]. Each of these
n-butanol mechanisms can be modified to include TBHP chemistry by adding the
Reactions (3.1) and (3.2) with the respective rate constants in Table 3.1. Further-
more, updating the rate constants for Reactions (3.3) and (3.4) in each mechanism
with the values listed in Table 3.1 typically leads the mechanism to correctly simulate
the measured OH time-histories in the neat TBHP experiments from Chapter 3.
The n-butanol mechanisms from the works of Grana et al. [40] and Sarathy et
al. [91] (different from the mechanism of Sarathy et al. [32] that was used in the
Vasu et al. [47] analysis) were modified to include TBHP chemistry in the manner
described above, and used to analyze the measured OH time-histories of Vasu et
al. at their highest and lowest temperature data point. The rate constant deter-
mination can be sensitive to the branching ratios of Reaction (5.1), therefore, the
branching ratios for the overall reaction excluding the Reaction (5.1b) channel (i.e.
k5.1a/(k5.1a + k5.1c + k5.1d + k5.1e), etc.) specified in each mechanism were preserved
in the analysis, and the sum of k5.1a + k5.1c + k5.1d + k5.1e was varied to adjust the
simulated OH time-history fit while the rate constant for Reaction (5.1b) from each
respective mechanism was preserved. The resulting overall rate constant for Reac-
tion (5.1) determined from these different mechanisms is shown in Figure 5.2. A
peak-to-peak discrepancy of ∼30% is found for the rate constant determined for Re-
action (5.1), depending on which base mechanism for n-butanol kinetics was used.
This discrepancy is due entirely to differences in the kinetic mechanisms because the
same OH time-histories from the work of Vasu et al. were used as the starting point of
the analysis. The discrepancy is larger than the overall uncertainty limit of ±14% de-
termined by Vasu et al., suggesting that their uncertainty analysis did not adequately
76 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
account for uncertainties in the secondary kinetics.
Many reactions and rate constants in the mechanisms used for the analysis of
the Vasu et al. [47] data differ, and a few key rate constants that contribute to this
discrepancy can be elucidated by examining the reaction pathways of n-butanol after
reaction with OH, as shown in Figure 5.3. These include the following types of
reactions:
1. Reactions of n-butanol, including bimolecular reactions with OH and H radicals,
such as Reactions (5.1) and (5.2).
CH3CH2CH2CH2OH + H −→ CH3CH2CH2CHOH + H2 (5.2a)
−→ CH3CH2CHCH2OH + H2 (5.2b)
−→ CH3CHCH2CH2OH + H2 (5.2c)
−→ CH2CH2CH2CH2OH + H2 (5.2d)
−→ CH3CH2CH2CH2O + H2 (5.2e)
2. Reactions of 1-butoxyl and hydroxybutyl radicals, including unimolecular beta-
scission decomposition reactions and unimolecular isomerization reactions, such
as Reactions (5.3) through (5.7).
CH3CH2CH2CHOH −→ C2H5 + CH2−−CHOH (5.3a)
−→ CH2CH2CH2CH2OH (5.3b)
CH3CH2CHCH2OH −→ 1−C4H8 + OH (5.4a)
−→ CH3 + CH2−−CHCH2OH (5.4b)
CH3CH2CHCH2OH −→ CH2OH + C3H6 (5.5a)
−→ CH3CH2CH2CH2O (5.5b)
CH2CH2CH2CH2OH −→ CH2CH2OH + C2H4 (5.6a)
−→ CH3CH2CH2CH2O (5.6b)
CH3CH2CH2CH2O −→ CH2CH2CH3 + CH2O (5.7)
5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 77
3. Reactions of smaller n-butanol radical fragments, including bimolecular reac-
tions with OH radicals and unimolecular beta-scission decomposition reactions,
such as Reactions (5.8) through (5.13).
C2H5 + OH −→ C2H4 + H2O (5.8a)
−→ CH3 + CH2O + H (5.8b)
−→ C2H5OH (5.8c)
CH2OH + OH −→ CH2O + H2O (5.9)
CH2CH2OH + OH −→ C2H4O + H2O (5.10)
C2H5 −→ C2H4 + H (5.11)
CH2OH −→ CH2O + H (5.12)
CH2CH2OH −→ C2H4 + OH (5.13)
+OH
OH
+OH
C2H4+H2OCH3+CH2O+HC2H5OH
(5.1a)
C2H4+H
OH
OH
OH CH3
+OH (5.1b)
+OH
OH
OH
+OH
CH2O+H2OCH2O+H
(5.1c)
OH
OH
+OH
(5.1d)
C2H4+OH
O
+OH
(5.1e)
C2H4+CH3
+OH
C3H6+H2O
33%
8% 23%34%
2%
(5.3a)
(5.4a) (5.4b) (5.5a)
(5.12) (5.9)(5.13)
(5.6a)
(5.7)
(5.8)(5.11)
(5.3b)(5.6b)
(5.5b)
+CH2O
+C2H4
+C3H6
+1-C4H8 +C3H5OH
+CH2CHOH
+H2O
H2O+ +H2O
+H2O+H2O
OH-consuming reaction
OH-producing secondary reaction
Other secondary reaction
α-radical
β-radical γ-radicalδ-radical
1-butoxyl
Figure 5.3: Reaction pathways important in the calculation of OH time-history under the currentexperimental conditions. Reactions involved in OH consumption are red and reactions involvedin OH production are green. The relative magnitudes of the rate constants to different productchannels of Reaction (5.1) at 1197 K are illustrated by the thickness of the reaction arrow. Thebranching ratios for Reaction (5.1) from Zhou et al. [88] are listed next to the arrows.
78 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
Differences in the rate constants for Reactions (5.2) through (5.13) in the various
mechanisms examined [32, 40, 47, 91] lead to the large discrepancies seen in the de-
termination of the rate constant for Reaction (5.1) from the same raw data (as shown
in Figure 5.2). Therefore, a mechanism with accurate rate constants for important
reactions must be carefully chosen, or constructed, for the analysis of the measured
OH time-histories for the determination of the rate constant for Reaction (5.1). Fur-
ther discussion on the important secondary reactions that influence the simulated OH
time-history is presented in Section 5.5.
5.2.3 Mechanism Generation for Current Work
A detailed kinetic mechanism was constructed to include secondary reactions of im-
portance involving both TBHP and n-butanol kinetics, using the current best-known
rate constants for key reactions. The alkane/TBHP mechanism presented in Chap-
ter 3 was used as the starting point; this base mechanism includes alkane kinetics
from the JetSurF 1.0 mechanism [18] and added reactions shown to accurately de-
scribe measured OH time-histories during TBHP decomposition.
Reactions (5.2) through (5.13) were added to the alkane/TBHP mechanism; many
of these added reactions are shown in Figure 5.3. Thermodynamic data for all new
chemical species added to the base mechanism were taken from Sarathy et al. [91]
who used the THERM program [92] to calculate temperature-dependent enthalpy
and entropy values. Rate constants for Reactions (5.2) through (5.13) were taken
from recent literature experiments and calculations [91, 93–99], and the rate constant
values are listed in Table 5.1. A method based on the work of Curran [100] was
used to estimate rate constants for radical decomposition reactions where appropriate
published rate constants could not be found, and a description of this procedure is
provided Appendix E. For unimolecular reactions where only the high-pressure-limit
rate constant could be found, the variation of the rate constant with pressure was
estimated using the Kassel Integral method [99] with S = Smax/2. This method for
estimating pressure dependence is also detailed in Appendix E.
5.2. ANALYSIS OF N-BUTANOL KINETIC MECHANISMS 79
Table 5.1: Partial list of reactions and rate constants of the n-butanol/TBHP mechanism of thecurrent work. Units for A are [cm3molecule−1s−1] for bimolecular reactions and [s−1] for unimolec-ular reactions, units for E are [cal mol−1K−1]. All unimolecular reaction rate constants calculatedat 1 atm, and the 3-parameter fits are valid for 800 to 1300 K. f Denotes pressure dependence wasestimated from the high-pressure rate constant using the Kassel Integral method [99]. R Denotesrate constant calculated from the reverse rate constant using the mechanism thermodynamic data.
No. Reaction k = A · T b exp(−E/RT ) Reference
A b E
(5.1a) CH3CH2CH2CH2OH+OH −−→ CH3CH2CH2CHOH+H2O
4.85×1013 0.00 3.910×103 This work
(5.1b) CH3CH2CH2CH2OH+OH −−→ CH3CH2CHCH2OH+H2O
1.41×1013 0.00 5.383×103 This work
(5.1c) CH3CH2CH2CH2OH+OH −−→ CH3CHCH2CH2OH+H2O
3.92×1013 0.00 4.319×103 This work
(5.1d) CH3CH2CH2CH2OH+OH −−→ CH2CH2CH2CH2OH+H2O
1.67×1014 0.00 7.700×103 This work
(5.1e) CH3CH2CH2CH2OH+OH −−→ CH3CH2CH2CH2O+H2O
6.77×1012 0.00 7.030×103 This work
(5.2a) CH3CH2CH2CH2OH+H −−→ CH3CH2CH2CHOH+H2
8.79×104 2.68 2.915×103 [91]
(5.2b) CH3CH2CH2CH2OH+H −−→ CH3CH2CHCH2OH+H2
1.08×105 2.69 4.440×103 [91]
(5.2c) CH3CH2CH2CH2OH+H −−→ CH3CHCH2CH2OH+H2
1.30×106 2.40 4.471×103 [91]
(5.2d) CH3CH2CH2CH2OH+H −−→ CH2CH2CH2CH2OH+H2
6.66×105 2.54 6.756×103 [91]
(5.2e) CH3CH2CH2CH2OH+H −−→ CH3CH2CH2CH2O+H2
9.45×102 3.14 8.701×103 [91]
(5.3a) CH3CH2CH2CHOH −−→ C2H5 +CH2−−CHOH 7.44×1041 -8.59 4.049×104 Appendix E f
(5.3b) CH3CH2CH2CHOH −−→ CH2CH2CH2CH2OH 1.14×1014 -1.08 2.900×104 [94] f
(5.4a) CH3CH2CHCH2OH −−→ 1-C4H8 +OH 6.95×1027 -4.49 3.488×104 Appendix E f
(5.4b) CH3CH2CHCH2OH −−→ CH3+CH2−−CHCH2OH 5.52×1034 -6.33 4.268×104 Appendix E f
(5.5a) CH3CH2CHCH2OH −−→ CH2OH+C3H6 1.37×1039 -7.72 3.943×104 Appendix E f
(5.5b) CH3CH2CHCH2OH −−→ CH3CH2CH2CH2O 1.40×1023 -4.56 3.009×104 [94] f
(5.6a) CH2CH2CH2CH2OH −−→ CH2CH2OH+C2H4 3.82×1033 -6.22 3.354×104 Appendix E f
(5.6b) CH2CH2CH2CH2OH −−→ CH3CH2CH2CH2O 2.92×1019 -2.92 1.756×104 [95] f
(5.7) CH3CH2CH2CH2O −−→ CH2CH2CH3 +CH2O 2.63×1026 -4.74 1.295×104 [91](5.8a) C2H5 +OH −−→ C2H4 +H2O 1.31×1021 -2.44 3.795×103 [96](5.8b) C2H5 +OH −−→ CH3 +CH2O+H 4.91×1021 -2.30 6.477×103 [96](5.8c) C2H5 +OH −−→ C2H5OH 1.82×1057 -13.4 8.795×103 [101] R
(5.9) CH2OH+OH −−→ CH2O+H2O 1.20×1014 0.00 0.00 [96](5.10) CH2CH2OH+OH −−→ C2H4O+H2O 9.00×1013 0.00 0.00 [96](5.11) C2H5 −−→ C2H4 +H 1.30×1039 -7.93 2.482×104 [98] R
(5.12) CH2OH −−→ CH2O+H 2.98×1029 -5.57 2.080×104 [96](5.13) CH2CH2OH −−→ C2H4 +OH 8.22×1041 -9.22 1.862×104 [97] R
80 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
The mechanism described in this section will be referred to as the n-
butanol/TBHP mechanism from hereon in this thesis. While this is not a compre-
hensive mechanism for describing pyrolysis or oxidation of n-butanol, it does contain
all of the reactions that would be expected to influence the OH time-history under
the current experimental conditions with the best-known rate constants at present
for these reactions.
To determine the overall rate constant for Reaction (5.1), the value of the rate
constant for Reaction (5.1) in the n-butanol/TBHP mechanism was varied until the
simulated OH time-history best fit the measured OH time-history for each tempera-
ture data point, similar to the analysis described in Chapter 4. In the analysis of data
for n-butanol, the branching ratios for the different abstraction sites of Reaction (5.1)
can influence the rate constant determination because certain channel of the reaction
can lead to subsequent OH production; branching ratios were not important in the
rate constant determination for the reactions of OH with n-alkanes in Chapter 4
because no OH-producing reactions were possible. In the current analysis for the
n-butanol data, the site-specific rate constants for Reactions (5.1a) through (5.1e)
used in the n-butanol/TBHP mechanism during the analysis were calculated with
the temperature-dependent branching ratios from the Zhou et al. [88] work with the
G3 potential energy surface. Figure 5.3 illustrates these branching ratios at 1197 K.
In this study, the branching ratios were assumed to be constant within the variations
of the rate constant for Reaction (5.1).
5.3 Experimental
The shock tube and laser diagnostics described in Chapter 2 of this thesis were used
for the work in this chapter. In addition to the chemicals described in Chapter 2
(TBHP/water solution 70%, by weight TBHP, and argon gas), anhydrous n-butanol
(99.8% purity) from Sigma Aldrich, was also used in the mixture preparation for the
experiments in this chapter. The current experimental procedure closely follows the
procedure used by Vasu et al. [47], with added improvements in that the n-butanol
composition of the test mixtures was verified to within ±5% by laser absorption at
5.4. RESULTS 81
3.39 µm in an external multi-pass absorption cell, and the impurities in the shock
tube were experimentally confirmed to contribute less than 1 ppm OH using the laser
absorption method described in Chapter 2.
Measurements of OH time-histories were carried out in shock tube experiments
performed with dilute mixture of tert-butylhydroperoxide (TBHP) and n-butanol,
with initial n-butanol-to-TBHP concentration ratios of 12 and 20 (150 ppm n-butanol
with 13 ppm TBHP, and 201 ppm n-butanol with 10 ppm TBHP, both dilute in
argon). Temperatures in the range of 896 to 1197 K were studied; the upper limit of
the temperature range was constrained by decomposition of n-butanol and the lower
temperature limit was set by slow decomposition of TBHP. Pressures of nominally
1 atm were used, with the exception of a single measurement at 2 atm to compare
the results with Vasu et al. [47] under identical experimental conditions.
5.4 Results
The measured OH time-histories typically follow a near-exponential decay after the
peak OH concentration is reached. Sample measurement traces of the OH time-history
are shown in Figure 5.4 at 1197 K and at 925 K. The simulated OH time-histories
with the best-fit rate constant for Reaction (5.1) in the n-butanol/TBHP mechanism
are also shown in comparison to the measured traces in Figure 5.4. The effects
of perturbations of ±30% on the rate constant for Reaction (5.1) are also shown,
illustrating the sensitivity of the simulated OH rate of decay to the rate constant for
Reaction (5.1).
At temperatures below 1000 K, the decomposition of TBHP occurs over a finite
time-scale, as shown in the example measured OH time-history in Figure 5.4 at 925 K
where the peak OH mole fraction is not reached until approximately 13 µs. At these
temperatures, the OH time-history is accurately modeled by the n-butanol/TBHP
mechanism at early times, and only the post-peak-OH behavior shows sensitivity to
the rate constant for Reaction (5.1). Therefore, the rate constant for Reaction (5.1)
can be determined from measured OH time-histories even at temperatures at which
TBHP does not decompose instantaneously.
82 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
0 10 20 30 40 50 60 70 801
10
925 K, 1.22 atm201 ppm n-butanol, 10.3 ppm TBHP
1197 K, 0.96 atm150 ppm n-butanol, 13.3 ppm TBHP
OH
mol
e fra
ctio
n [p
pm]
Time [s]
Current data1
k5.1 (best fit) k5.1 + 30% k5.1 - 30%
Reaction (5.1):CH3CH2CH2CH2OH + OH -> Products
Figure 5.4: Measured OH time-histories for 1197 K and 0.96 atm for a mixture of 150 ppm n-butanol and 13.3 ppm TBHP, and 925 K and 1.22 atm for a mixture of 201 ppm n-butanol and10.3 ppm TBHP, shown with simulations with the n-butanol/TBHP mechanism using the best-fitrate constant for Reaction (5.1) and perturbations of ±30%.
The overall rate constant for Reaction (5.1) was determined with the n-
butanol/TBHP mechanism for each measured OH time-history. Table 5.1 presents
the site-specific rate constants for Reactions (5.1a) to (5.1e) (calculated using the
temperature-dependent branching ratios from the Zhou et al. [88] calculations us-
ing the G3 potential energy surface) that were used in the analysis. The measured
rate constant was found to be independent of both pressure and initial mixture com-
position, and the results can be summarized in Arrhenius form by Eq. 5.2 in the
temperature range 896 to 1197 K.
k5.1 = 3.24× 10−10 exp
(− 2505
T [K]
)cm3molecule−1s−1 (Eq. 5.2)
A list of all experimental conditions for the work in this chapter and the final rate
constant determined for each individual data point is provided in Table 5.2. The
individual data points will be shown on an Arrhenius plot in comparison to other
5.5. INFLUENCE OF SECONDARY REACTIONS 83
works in Section 5.7.
Table 5.2: Determinations of the rate constant for Reaction (5.1) from the experimental OH time-history data.
Mixture T [K] P [atm] k5.1 [cm3molecule−1s−1]
150 ppm n-butanol, 1028 1.14 2.82× 10−11
∼13 ppm TBHP 1095 1.05 3.32× 10−11
1182 2.04 3.99× 10−11
1197 0.96 3.99× 10−11
201 ppm n-butanol, 896 1.24 1.99× 10−11
∼10 ppm TBHP 925 1.22 2.16× 10−11
963 1.17 2.41× 10−11
993 1.16 2.57× 10−11
1137 1.00 3.49× 10−11
1196 0.94 3.99× 10−11
5.5 Influence of Secondary Reactions
5.5.1 OH Sensitivity Analysis
Under the experimental conditions studied, Reaction (5.1) dominates the OH sensi-
tivity, defined by Eq. 3.1. Figure 5.5 shows the top six reactions appearing in the
OH sensitivity calculated using the n-butanol/TBHP mechanism for representative
experimental conditions at 925 K. The OH sensitivity to the individual channels of
Reaction (5.1) is shown, along with the overall OH sensitivity to Reaction (5.1), which
is computed as the sum of OH sensitivity to the individual channels.
The top four reactions contributing to secondary OH sensitivity interference are
Reactions (3.1), (3.3), (5.6a), and (5.6b). The OH sensitivity to Reaction (3.1),
the unimolecular decomposition of TBHP, is high only at early times, and the rate
constant for Reaction (3.1) has been measured in Chapter 3 resulting in accurate
simulation of the early-time OH time-history as seen in Figure 5.4. The rate constant
for Reaction (3.3) was also measured in Chapter 3, and is assumed to accurately
84 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
describe the secondary reaction of OH with methyl radicals (a final decomposition
product of TBHP) because the measured values of the rate constant for Reaction (5.1)
are independent of initial n-butanol-to-TBHP concentration ratio. Reactions (5.6a)
and (5.6b), which also appear in the OH sensitivity analysis, are competing reactions
pathways for consumption of the δ-radical; the OH time-history is sensitive only to
the branching ratio k5.6a/k5.6, where k5.6 = k5.6a + k5.6b, because the products of
Reaction (5.6a) lead to an OH-producing pathway through Reaction (5.13), while
the Reaction (5.6b) is a non-OH-producing reaction channel (Reaction (5.3b) also
contributes to consumption and production of the δ-radical, however, its influence on
the δ-radical concentration is negligible in comparison to Reactions (5.6a) and (5.6b)).
0 10 20 30 40 50 60 70 80-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
(5.6a)(5.6b)
(3.3)
(5.1c)
(5.1a)
(5.1)
OH
Sen
sitiv
ity
Time [s]
(5.1) CH3CH2CH2CH2OH + OH -> Products (5.1a) CH3CH2CH2CH2OH + OH -> CH3CH2CH2CHOH + H2O (5.1c) CH3CH2CH2CH2OH + OH -> CH3CHCH2CH2OH + H2O (3.1) (CH3)3COOH -> (CH3)3CO + OH (5.6a) CH2CH2CH2CH2OH -> CH2CH2OH + C2H4
(5.6b) CH2CH2CH2CH2OH -> CH3CH2CH2CH2O (3.3) CH3 + OH -> CH2(s) + H2O
(3.1)
925 K, 1.22 atm201 ppm n-butanol, 10.3 ppm TBHP
Figure 5.5: OH sensitivity calculation with the n-butanol/TBHP mechanism for a mixture of201 ppm n-butanol and 10.3 ppm TBHP at 925 K at 1.22 atm. The overall rate constant forReaction (5.1) dominates the OH sensitivity. The four secondary reactions with the highest OHsensitivity are Reactions (3.1), (3.3), (5.6a), and (5.6b).
Minor secondary OH sensitivity interference is also present from Reac-
tions (5.2b), (5.2d), (5.4a), and (5.4b), however at a lesser amount than the reactions
shown in Figure 5.5. The top reactions appearing in the OH sensitivity analysis are
5.5. INFLUENCE OF SECONDARY REACTIONS 85
similar for all temperatures studied in the current work, with an exception at tem-
peratures greater than 1000 K where the OH sensitivity to Reaction (3.1) becomes
negligible.
The magnitudes of the OH sensitivity to the site-specific channels of Reaction (5.1)
follow the order |SOH,5.1a| > |SOH,5.1c| while |SOH,5.1b| ≈ |SOH,5.1d| ≈ |SOH,5.1e| ≈ 0.
The branching ratio k5.1a/k5.1 is greater than k5.1c/k5.1, thus influencing the ordering of
the two reactions most significant in the OH sensitivity. The branching ratios k5.1b/k5.1
and k5.1e/k5.1 are assumed to be 6% and 1%, respectively, at 925 K, and therefore
these reactions do not contribute significantly to the OH sensitivity. Furthermore,
the net OH consumption through Reaction (5.1b) is expected to be near zero because
the β-radical product is expected to undergo a rapid beta-scission decomposition to
reproduce OH via Reaction (5.4a), and this reaction pathway also contributes to
the low OH sensitivity to Reaction (5.1b). The explanation for the near-zero OH
sensitivity to Reaction (5.1d) is more complicated, and can be elucidated with the
rate of production analysis discussed in the following section.
5.5.2 Reaction Pathway Analysis
Figure 5.6 presents a detailed reaction pathway analysis of the OH radical at 1197 K,
and illustrates how secondary reactions can contribute to consumption and produc-
tion of OH radicals. The net OH rate of production, defined as d[OH]/dt, is also shown
compared with the OH rate of production due to Reaction (5.1) and secondary re-
actions. The secondary reactions that produce OH radicals are Reactions (5.4a)
and (5.13), which subsequently occur after formation of the β-radical and δ-radical,
respectively. In these reactions, cleavage of the C—OH bond in the radical fragment
of n-butanol occurs to produce an OH radical indistinguishable from the OH pro-
duced from TBHP, thus retarding the net rate of OH decay. As mentioned in the
previous section, the decomposition of the β-radical via Reaction (5.4a) contributes
to the near-zero OH sensitivity to Reaction (5.1b). Because Reaction (5.4b) is a
non-OH-producing competing pathway for consumption of the β-radical, minor OH
sensitivity is present from Reactions (5.4a) and (5.4b). The amount of OH produced
86 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
via Reaction (5.13) is controlled by the branching ratio of k5.6a/k5.6, and therefore
only Reactions (5.6a) and (5.6b) appear in the OH sensitivity while the OH sensitivity
to Reaction (5.13) is near zero.
Figure 5.6: OH reaction path analysis at 1197 K and 0.96 atm for a mixture of 150 ppm n-butanoland 13.3 ppm TBHP. The net rate of OH consumption (i.e. the observed pseudo-first-order rate)is 20% slower than the rate of OH consumption by Reaction (5.1) at these conditions. All valuesrepresent calculations at 10 µs.
Using the best-known rate constants listed in Table 5.1 to describe the important
n-butanol secondary reactions in the n-butanol/TBHP mechanism, the branching
ratio of k5.6a/k5.6 is predicted to be 92% at 1197 K; thus the subsequent reactions
to follow Reaction (5.1d) are predicted to mostly lead to OH radical production,
causing a near-zero net consumption of OH via Reaction (5.1d), and a negligible OH
sensitivity to Reaction (5.1d). Reactions (5.2b) and (5.2d) also lead to production of
β-radicals and δ-radicals, and therefore these reactions have a minor contribution to
the OH sensitivity.
Secondary consumption of OH radicals can also occur, where the dominant sec-
ondary reaction for OH consumption is Reaction (3.3), the bimolecular reaction of
an OH radical with a methyl radical; this reaction contributes to consumption of OH
in any experiment using TBHP as the OH precursor because methyl radicals will be
produced at similar levels as OH during TBHP decomposition. The TBHP kinetic
5.5. INFLUENCE OF SECONDARY REACTIONS 87
sub-mechanism was studied in Chapter 3 and accurate rate constants are used in the
n-butanol/TBHP mechanism. Therefore, confidence in this mechanism to accurately
describe the rate of secondary OH consumption by Reaction (3.3) is high.
The rate of production analysis also illustrates that the net OH rate of production
(i.e. the pseudo-first-order decay rate) does not quite equal the OH rate of production
through Reaction (5.1). For example, the net OH production at 1197 K is 20% slower
than the OH rate of production by Reaction (5.1). Thus, directly inferring a rate
constant for Reaction (5.1) from the observed pseudo-first-order decay rate can lead
to significant errors.
Recent results of ab initio calculations presented by Zhang et al. [102] indicate that
the rate constant pressure dependence for beta-scission decomposition reactions, such
as Reaction (5.3), is stronger than predicted using the Kassel Integral method [99],
as is done in the current work. The fall-off factor calculated by Zhang et al. for
Reaction (5.3) is approximately an order of magnitude larger than used in the current
work, and if similar levels of fall-off exist for similar decomposition processes, such
as Reaction (5.6a), this discrepancy can lead to large uncertainties in the predicted
branching ratio of k5.6a/k5.6. For example, with the current mechanism this branching
ratio is predicted to be 92% at 1197 K; using a rate constant pressure dependence for
Reaction (5.6a) that results in a 1-atm rate constant an order of magnitude slower
would yield a branching ratio k5.6a/k5.6 that predicts that the Reaction (5.6a) pathway
is no longer favored in the consumption of the δ-radical, if all other rate constants
remain unchanged. However, Zhang [103] has found that the pressure dependence
for the unimolecular isomerization reactions is also expected to be stronger than
currently predicted. Therefore, minimal effect of pressure dependence is expected on
the branching ratio k5.6a/k5.6 from the difference in estimation methods for pressure
dependence, provided that the high-pressure limit rate constants are correct.
As previously mentioned, the branching ratio k5.6a/k5.6 controls the amount of
OH reproduction that occurs via Reaction (5.13) and can affect the OH sensitivity
to Reaction (5.1d). The detailed uncertainty analysis carried out in the following
section shows that the effect of the uncertainty of the branching ratio of k5.6a/k5.6 on
the rate constant determination of Reaction (5.1) is the largest contribution to the
88 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
overall uncertainty near 1200 K. An uncertainty factor of 2 has been assumed for the
rate constants for the unimolecular reactions in the fall-off region. Because of the
possibility of significant uncertainty in the branching ratio k5.6a/k5.6, further exper-
imental investigations of the pressure-dependent rate constants for Reactions (5.6a)
and (5.6b) are recommended.
5.6 Uncertainty Estimation
A detailed uncertainty analysis, accounting for both experimental and rate constant
uncertainties was carried out. The major experimental uncertainties are the initial
n-butanol concentration in the reactant mixture and the fitting of the data trace,
and the major kinetic rate constant uncertainties include the rate constants for Re-
actions (3.1), (3.3), (5.2b), (5.2d), (5.4a), (5.4b), (5.6a), and (5.6b). A conservative
uncertainty of ±30% each is assumed for the rate constant for Reaction (3.1) and
(3.3) (see Chapter 3), and a factor of 2 uncertainty is assumed for each of the rate
constants for Reactions (5.2b), (5.2d), (5.4a), (5.4b), (5.6a), and (5.6b). The branch-
ing ratios k5.1b/k5.1 and k5.1d/k5.1 also contribute to the uncertainty in the current
rate constant determination, and the uncertainty limits for these branching ratios are
estimated to be ±30%.
To assess individual uncertainties, each independent source of uncertainty was
perturbed to its uncertainty limit, and the experimental data trace was refit with a
new rate constant for Reaction (5.1). Because not all of the uncertainty factors are
independent, the individual uncertainties cannot simply be combined using a root-
sum-squares method to obtain an overall uncertainty. For example, the uncertainty
in the rate constants for Reactions (5.6a) and (5.6b) are coupled together, as well as
with the uncertainty of the branching ratio k5.1d/k5.1. To determine the uncertainty
influence of a group of coupled uncertainty factors, each uncertainty source in the
group was perturbed to its uncertainty limit (with the directions chosen such that the
effects would not cancel out), and the data trace was refit to obtain the uncertainty-
influenced determination of the rate constant for Reaction (5.1). A total uncertainty
in the rate constant for Reaction (5.1) was determined by combining the effects of
5.7. COMPARISON WITH LITERATURE 89
the coupled uncertainties with the independent individual uncertainties in a root-
sum-squares summation. The total estimated uncertainty for the rate constant for
Reaction (5.1) is ±20% at 1197 K, where the majority of this uncertainty is due to
uncertainties in k5.1d/k5.1, and the rate constants for Reactions (5.6a) and (5.6b). At
925 K, this group of coupled uncertainty factors contributes a smaller amount to the
overall uncertainty, however the rate constant for Reaction (3.1) has an important
role in the OH sensitivity calculations at these temperatures, leading to an overall
uncertainty in the rate constant for Reaction (5.1) at 925 K of approximately ±23%.
At this temperature, the largest contribution to the uncertainty becomes the rate
constant for Reaction (3.1). Table 5.3 provides details of the effect of the uncertainties
on the final rate constant determinations at 1197 K and 925 K.
Table 5.3: Individual and coupled uncertainties and influence of the uncertainties on the determi-nation of the rate constant for Reaction (5.1) at 1197 K and 925 K.
Uncertainty Sources (Uncertainty ascribed to source) Uncertainty in Uncertainty ink5.1 at 1197 K k5.1 at 925 K
Experimental Uncertainties
Initial n-butanol concentration (±5%) ±5% ±5%Fitting (±10%) ±10% ±10%
Modeling Uncertainties
k3.3 (±30%) ±3% ±2%k5.1b/k5.1 (±30%) & k5.4a (factor 2) & k5.4b (factor 2) ±6% ±4%k5.1d/k5.1 (±30%) & k5.6a (factor 2) & k5.6b (factor 2) ±14% ±12%k5.2b (factor 2) ±3% ±2%k5.2d (factor 2) ±4% ±2%k3.1 (±30%) ±0% ±15%
Overall RSS Uncertainty ±20% ±23%
5.7 Comparison with Literature
5.7.1 Previous Experiments at High Temperatures
Vasu et al. [47] published the first high-temperature measurements of the rate con-
stant for Reaction (5.1) from 1017 to 1269 K. Their experiments employed similar
90 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
techniques as the current work, using narrow-linewidth laser absorption by OH in
a shock tube and TBHP as the OH precursor. The current set of experiments in-
cludes one measurement at similar temperature, pressure, and mixture composition
(1182 K, 2.04 atm, 150 ppm n-butanol, 13 ppm TBHP) as used in the Vasu et al.
work (1165 K, ∼2.25 atm, 147 ppm n-butanol, 11 ppm TBHP). This measured OH
time-history of the current work is shown in Figure 5.7 in comparison to the closely
equivalent trace of Vasu et al. The measured OH time-history of the current work
displays a first-order decay rate which is closely equal to that which was measured
by Vasu et al., indicating that the current measured OH time-history data are in
excellent agreement with their work.
0 10 20 30 40 50 601
10
OH
mol
e fra
ctio
n [p
pm]
Time [s]
Dashed lines show the same rates of first-order decay in the first 30 s
Current work1182 K, 2.04 atm150 ppm n-butanol,13.5 ppm TBHP
Vasu et al.1165 K, 2.08 atm147 ppm n-butanol,10.8 ppm TBHP
Figure 5.7: Measured OH time-histories from the current work with conditions 1182 K, 2.04 atm,150 ppm n-butanol, 13 ppm TBHP and from Vasu et al. [47] with conditions 1165 K, 2.25 atm,147 ppm n-butanol, 11 ppm TBHP. The data traces show similar measured first-order decay rates.
Vasu et al. [47] determined an overall rate constant for Reaction (5.1) using a
detailed mechanism which they constructed using an early n-butanol mechanism of
Sarathy et al. [32], modified with TBHP chemistry from literature sources [67, 104].
While Vasu et al. pioneered the high-temperature experimental work on the reaction
of OH with n-butanol, recent improved understanding of high-temperature n-butanol
5.7. COMPARISON WITH LITERATURE 91
oxidation kinetics allows for more accurate selection of rate constants for secondary
reaction pathways in the current work, as discussed in Section 5.2.
Three major differences exist between the mechanism used in the current analy-
sis and the mechanism constructed by Vasu et al. [47] from the Sarathy et al. [32]
mechanism.
1. The mechanism of Sarathy et al. uses a rate constant for Reaction (3.3) that
is an order of magnitude slower than the rate constant measured in Chapter 3
of this thesis for the same reaction. The mechanism constructed by Vasu et
al., therefore, does not correctly predict secondary OH consumption and under-
predicts the rate of OH decay due to TBHP kinetics; this introduces a 7% error
in their determination of the rate constant for Reaction (5.1). The uncertainty
in the rate constant for Reaction (3.3) was not included in the uncertainty
analysis of Vasu et al.
2. The analysis of Vasu et al. assumes the rate constant for Reaction (5.1b) is
equal to that in the Sarathy et al. mechanism. This estimation of the rate
constant for Reaction (5.1b) is approximately three times faster than the rate
constant inferred in the current analysis. The uncertainty in the rate constant
for Reaction (5.1b) was accounted for in the uncertainty analysis of Vasu et al.
3. In the analysis by Vasu et al., nearly all (>98% at 1017 K) of the δ-radicals
formed were predicted to be consumed through isomerization reactions, in-
stead of unimolecular decomposition which leads to OH production via Re-
action (5.13). The rate constants used for Reactions (5.6a) and (5.6b) in the
current work suggest that the unimolecular decomposition pathway is favored.
Uncertainties for the rate constants Reactions (5.6a) and (5.6b) were not in-
cluded in the uncertainty analysis of Vasu et al.
The major differences between the current mechanism and the mechanism used in the
Vasu et al. analysis are presented in Table 5.4, along with the influence of each of the
mechanism differences on the rate constant for Reaction (5.1). The overall influence
of all of the mechanism differences is also presented in Table 5.4.
92 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
Table 5.4: Differences in the mechanisms used for analysis of measured OH time-histories in thecurrent work and the work of Vasu et al. [47], and the influence on the Vasu et al. determination ofthe rate constant for Reaction (5.1) at 1165 K.
Rate constant(s) changed Justification Influence on Influence onin current mechanism k5.1 at 1269 K k5.1 at 1017 K
k3.3 (×20) Chapter 3 -7% -7%k5.1b (×0.33) [88] -15% -16%k5.6a & k5.6b (see text) [93, 94, 99] +33% +17%
Overall influence of current mechanism changes +10% -6%
0.7 0.8 0.9 1.0 1.1 1.21
2
3
4
5
1428 K 1250 K 1111 K 1000 K 909 K 833 K
k 5.1 [1
0-11 c
m3 m
olec
ule-1
s-1]
1000/T [K-1]
Current work Vasu et al. data as published Vasu et al. data with current analysis Zhou et al. calculation CCSD(T) PES Zhou et al. calculation G3 PES
Reaction (5.1): CH3CH2CH2CH2OH -> Products
Figure 5.8: Arrhenius plot of the rate constant for Reaction (5.1) determined in the current work(filled squares) compared with rate constant determination as reported in Vasu et al. [47] (opendiamonds) and their data reinterpreted with the mechanism from the current work (open squares).Also shown are rate constant calculations from Zhou et al. [88]. The solid line is an Arrhenius fit tothe current experimental data, and the dashed line is a fit to the reinterpreted data of Vasu et al.using the current mechanism. The error bars on the current data represent the results of a detaileduncertainty analysis, see Table 5.3.
5.7. COMPARISON WITH LITERATURE 93
Figure 5.8 compares the overall rate constant for Reaction (5.1) determined in
the current work with the values determined by Vasu et al. [47] using their reported
mechanism. Also shown are the results of a rate constant determination analysis for
two raw data traces from the work of Vasu et al. (their highest and lowest temper-
ature data points) using the n-butanol/TBHP mechanism developed for the current
work. The figure illustrates that the rate constant as reported in the work of Vasu
et al. is within 10% of the current work, with the discrepancy almost entirely due
to mechanistic differences in the analysis. This is expected considering, as initially
mentioned, that the raw data of OH decay in the current work was found to be in
excellent agreement with their work.
The current experiments extend the temperature range of the Vasu et al. [47]
work, providing the first rate constant measurements for reaction of OH with n-
butanol from 900 to 1000 K. The current determination of the rate constant for
Reaction (5.1) shows a slightly stronger temperature dependence than was found by
Vasu et al., and this temperature dependence is verified over a wider temperature
range.
5.7.2 Ab initio Calculations
Zhou et al. [88] performed detailed ab initio calculations for the rate constants for
Reaction (5.1a), (5.1b), (5.1c), (5.1d), and (5.1e) using a two-transition-state model.
They produced two different potential energy surfaces, using CCSD(T) and G3 meth-
ods, yielding two sets of rate constant calculations. Their site-specific rate constant
calculations can be summed to obtain the overall rate constant for Reaction (5.1),
and these calculated values are compared to the current experimental measurements
in Figure 5.8. Their overall rate constant for Reaction (5.1) calculated with the two
different methods differ by up to 50% in the temperature range of interest, and the
current measurements of the rate constant for Reaction (5.1) fall between the two rate
constant calculations. Their calculation using the G3 potential energy surface falls
within the uncertainty estimate of the measured value at 1197 K. At 925 K, however,
both the G3- and CCSD(T)-calculated value of the rate constant for Reaction (5.1)
94 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
from Zhou et al. fall just outside of the uncertainty limits of the measured rate con-
stant. The temperature dependence of the CCSD(T)-calculated overall rate constant
is more representative of the measured rate constant than the G3-calculated value.
5.7.3 Atmospheric-relevant Temperature Rate Constants
Several experimental studies of the rate constant for Reaction (5.1) have been carried
out at atmospheric-relevant temperatures from 292 to 372 K. [105–111] A 3-parameter
modified Arrhenius expression can be empirically fit to these data and the current
determination of the rate constant for Reaction (5.1) at combustion-relevant temper-
atures for interpolation of the rate constant at intermediate temperatures; Eq. 5.3
presents an expression for the rate constant for Reaction (5.1) that fits experimental
data from 372 to 1197 K.
1.78× 10−21T 3.22 exp
(+
1160
T [K]
)cm3molecule−1s−1 (Eq. 5.3)
Figure 5.9 presents the current recommendation for the rate constant for Reac-
tion (5.1) in comparison to the measured rate constants at atmospheric-relevant con-
ditions.
The empirical structure-activity relationship (SAR) of Atkinson and cowork-
ers [20–22] introduced in Chapter 4 (and also described in detail in Appendix D)
can also be applied to reactions of OH with alcohols, and updated substituent factors
for reactions involving alcohols are presented by Bethel et al. [90]. The SAR was devel-
oped from rate constant data at atmospheric-relevant temperatures, and adequately
represents all data for the rate constant for Reaction (5.1) at both atmospheric- and
combustion-relevant temperatures. However, the results of ab initio calculations by
Zhou et al. [88] suggest formation of a hydrogen-bonded complex in several of the
channels of Reaction (5.1), and therefore the rate constant estimated using the SAR
method may not correctly represent the relative rate constants of the overall reaction.
The rate constant estimated using the SAR method of Atkinson and coworkers is also
shown in Figure 5.9 (labeled Bethel et al. [90]) in comparison to experimental data.
5.8. CONCLUSIONS 95
1.0 1.5 2.0 2.5 3.0 3.5 4.0
1
2
3
45
Reaction (5.1): CH3CH2CH2CH2OH -> Products
Rate Constant Recommendations
Current work Bethel et al. (2001)
Experimental Data Current work Campbell et al. (1976) Wallington and Kurylo (1987) Nelson et al. (1990) Yujing and Mellouki (2001) Cavalli et al. (2002) Hurley et al. (2009)
k 5.1 [
10-1
1 cm
3 mol
ecul
e-1s-1
]
1000/T [K-1]
1000 K 500 K 333 K 250 K
Figure 5.9: Arrhenius plot of the rate constant for Reaction (5.1) determined in the current workshown with published data at atmospheric-relevant conditions. [105–111] Also shown is the 3-parameter fit to the data given by Eq. 5.3 and the overall rate constant estimate from the structure-activity relationship in Bethel et al. [90].
5.8 Conclusions
The rate constant for Reaction (5.1), the overall reaction of OH with n-butanol,
was determined from OH time-histories measured behind reflected shock waves, and
the results extend the range of experimentally determined high-temperature rate con-
stants to 900 to 1200 K; there were no previous high-temperature measurements below
1017 K. A detailed uncertainty analysis was conducted yielding an overall uncertainty
of ±20% at 1197 K and ±23% at 925 K. The largest contributions to the overall un-
certainty at 1197 K is the relative rate constant for the channel of Reaction (5.1) that
produces a δ-radical, and the rate constants for the reactions leading to consumption
of the δ-radical. For decreasing temperatures, the influence of the uncertainty in the
rate constant for the OH precursor decomposition reaction also becomes significant.
Further experimental investigations on the rate constants important in describing the
reproduction pathways of OH from n-butanol are recommended.
The measured OH time-histories of the current work are in excellent agreement
96 CHAPTER 5. REACTION OF OH WITH N-BUTANOL
with the similar experiments of Vasu et al. [47]. However, the current determination
of the rate constant for Reaction (5.1) disagrees with the Vasu et al. determination
for the same reaction by up to 10%, where the discrepancy is almost entirely due to
differences in the kinetic mechanisms used for the analysis. Ab initio rate constant
calculations by Zhou et al. [88] using a G3 potential energy surface yield an overall
rate constant that shows agreement with the current experimental work at 1197 K,
while their rate constant obtained using a CCSD(T) potential energy surface does not.
At 925 K, however, both of rate constant calculations by Zhou et al. fall just outside
of the uncertainty limits of the measured rate constant. The CCSD(T)-computed
overall rate constant of Zhou et al. best matches the temperature dependence of the
current data. The empirically developed structure-activity relationship of Atkinson
and coworkers [20–22, 90] also agrees within the uncertainty limits of the current rate
constant determination.
Chapter 6
Reaction of OH with iso-Butanol
6.1 Introduction
6.1.1 Background and Motivation
While the traditional structure of butanol present in biobutanol is the n-butanol
isomer, recent technologies have been developed to economically synthesize the iso-
butanol isomer (2-methyl-1-propanol) from biomass sources. For example, the strat-
egy developed by Atsumi et al. [112] demonstrates high-yield, high-specificity pro-
duction of iso-butanol from glucose using native organisms. Because iso-butanol is
becoming an important butanol isomer present in economically-produced biobutanol,
developing accurate detailed kinetic mechanisms describing the high-temperature ox-
idation of iso-butanol is of importance for optimizing the design of practical trans-
portation engines powered by combustion of biobutanol.
The hydrogen-atom abstraction by a hydroxyl radical (OH) from iso-butanol is
an important elementary reaction in a high-temperature iso-butanol oxidation mech-
anism because this reaction describes a dominant fuel consumption pathway during
the combustion process under many conditions. This reaction can occur via four
channels, as described by Reactions (6.1a) through (6.1d), to produce water and a
radical with the chemical formula C4H9O in one of the following radical structures:
iso-butoxyl or one of four isomers of a hydroxyalkyl radical (α, β, γ, distinguished
97
98 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
by the radical position with respect to the oxygen atom).1
(CH3)2CHCH2OH + OH −→ (CH3)2CHCHOH + H2O (6.1a)
−→ (CH3)2CCH2OH + H2O (6.1b)
−→ CH3(CH2)CHCH2OH + H2O (6.1c)
−→ (CH3)2CHCH2O + H2O (6.1d)
The radical products are expected to react through rapid isomerization and beta-
scission decomposition. Figure 6.1 illustrates the four reaction pathways of Reac-
tion (6.1) and the major subsequent reaction pathways. To date, no studies have
been found that present experimental data on the rate constant for Reaction (6.1) at
combustion-relevant conditions.
OH
iso-Butanol
OH
OH
CH3 +
(α-radical) OH
CH3
OH
OH
CH2O + H
+
(γ-radical)
+
OH
OH+
(β-radical)
+OH
OH-consuming reactionOH-producing secondary reactionOther secondary reaction
net zero OH consumption pathway
(6.1a)
O
H + C3H6
+CH2OH
(iso-butoxyl)
+OH +OH
+OH
(6.1b) (6.1c)
(6.1d)
(5.12)
(6.2)
Figure 6.1: Dominant reaction pathways of iso-butanol after reaction with OH. OH-consumingreactions are shown with red arrows, and OH-producing reactions are shown with green arrows.
1Note that the terms α-radical, β-radical, and γ-radical are also used in Chapter 5 of this thesisto refer to different radicals. In this chapter, the Greek letter distinguishes the position of theradical with respect to the hydroxyl group on the radical produced by hydrogen-abstraction fromiso-butanol.
6.1. INTRODUCTION 99
6.1.2 Objectives of the Current Chapter
The experimental techniques used in Chapter 4 of this thesis have become a method
that is commonly used for measuring OH time-histories to determine rate constants
for reactions of OH with combustion-relevant organic compounds. However, the work
presented in Chapter 5 elucidated the importance of accounting for subsequent OH-
producing reactions in the study of reactions in the family of butanol + OH. For the
reaction of OH with iso-butanol, the only critical secondary OH-producing reaction is
Reaction (6.2), the beta-scission decomposition of the β-radical (1-hydroxy-2-methyl-
prop-2-yl: (CH3)2CCH2OH).
(CH3)2CCH2OH −→ (CH3)2C−−CH2 + OH (6.2)
Reaction (6.2) has no significant competing secondary reaction pathways because
there is only one C–C bond two bonds away from the radical (hence only one dom-
inant beta-scission pathway) and no isomerization reactions of the radical can occur
through 5- or 6-ring transition-state structures (isomerization reactions with larger
ring transition states are more likely to occur). Thus, Reaction (6.1b) has a net-zero
contribution to the OH consumption, and cannot be measured using the technique
described in Chapter 4. The measured data, however, are sensitive to the over-
all rate constant of all other channels of Reaction (6.1). The site-specific rate con-
stants for Reaction (6.1) can be categorized into three different rate constants, defined
by Eq. 6.1, Eq. 6.2, and Eq. 6.3, each of which will be examined in this chapter.
kβ6.1 = k6.1b (Eq. 6.1)
knon-β6.1 = k6.1a + k6.1c + k6.1d (Eq. 6.2)
koverall6.1 = k6.1a + k6.1b + k6.1c + k6.1d (Eq. 6.3)
This chapter presents the results of OH mole-fraction time-history measurements
in reflected shock experiments of TBHP with iso-butanol in excess and uses the data
to examine knon-β6.1 and koverall6.1 . The overall rate constant for Reaction (6.1) minus
the rate constant for the β-radical-producing channel, knon-β6.1 , is determined under
100 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
combustion-relevant conditions from the measured OH mole-fraction time-histories.
An overall rate constant for Reaction (6.1), koverall6.1 , is suggested based on the rate con-
stant for the β-radical-producing reaction channel, kβ6.1, of Merchant and Green [113].
Comparisons to rate constants for Reaction (6.1) presented in the literature are made.
6.2 Experimental
The shock tube and laser diagnostics described in Chapter 2 of this thesis were used
for the work in this chapter. In addition to the chemicals described in Chapter 2
(TBHP/water solution 70%, by weight TBHP, and argon gas), anhydrous 99.5% 2-
methyl-1-propanol (iso-butanol) from Sigma Aldrich, was used in the mixture prepa-
ration for the experiments in this chapter. OH time-histories were measured in
reflected-shock experiments of mixtures of TBHP with iso-butanol in excess, diluted
in argon. Two test mixtures were prepared, 150 ppm iso-butanol with 15 ppm TBHP,
and 220 ppm iso-butanol with 15 ppm TBHP, leading to initial iso-butanol-to-TBHP
concentration ratios of 10 and 15, respectively. The reflected shock conditions were
nominally 1 atm, with temperatures ranging from 907 to 1147 K.
6.3 Kinetic Modeling and Analysis
6.3.1 Model Description
A kinetic mechanism was constructed to describe the time evolution of the reaction
process with the current test mixtures of dilute TBHP and iso-butanol in excess.
In addition to Reactions (6.1a) through (6.1d), this mechanism consists of a base
mechanism that includes secondary reactions due to the presence of TBHP as the OH
precursor, as well as reactions important in iso-butanol kinetics. The base mechanism
used is the n-butanol/TBHP mechanism described in Chapter 5, which contains
alkane reactions from the JetSurF 1.0 mechanism [18], reactions and rate constants
for the TBHP-related reactions from Chapter 3, and updated rate constants for small
alkyl and hydroxyalkyl radical reactions relevant to butanol chemistry.
6.3. KINETIC MODELING AND ANALYSIS 101
The reactions important in iso-butanol kinetics include the subsequent reactions
that are expected to occur following Reaction (6.1), as illustrated in Figure 6.1, and
Reactions (6.3a) through (6.3d) which describes reactions of hydrogen radicals with
iso-butanol, of which can lead to the production of β-radicals.
(CH3)2CHCH2OH + H −→ (CH3)2CHCHOH + H2 (6.3a)
−→ (CH3)2CCH2OH + H2 (6.3b)
−→ CH3(CH2)CHCH2OH + H2 (6.3c)
−→ (CH3)2CHCH2O + H2 (6.3d)
The rate constants describing important secondary reactions of iso-butanol are taken
from Merchant and Green [113] and Sarathy et al. [91], and are listed in Table 6.1.
The isomerization and beta-scission reactions shown in 6.1 involving the iso-butoxyl
and iso-C4H8OH radicals were considered in the current analysis; the following section
will demonstrate that the OH time-history is insensitive to rate constants for these
reactions, as long as a reasonable estimate was used (k ≥ 105 s−1).
In addition to the beta-scission reactions cleaving at the C–C or C–O bonds, beta-
scission reactions eliminating a hydrogen radical are also possible; however, these
reactions are expected to occur at a much slower rate than the beta-scission reac-
tions that break a C–C or C–O bond, due to bond energy arguments. The relative
rate constants for the hydrogen-eliminating beta-scission reactions in the Sarathy et
al. mechanism [91] further confirm that the beta-scission reactions breaking a C–H
bond are negligible. Therefore, hydrogen-eliminating beta-scission reactions are not
included in the current mechanism; however, the influence of up to 10% of the β-
radical reacting through such a channel (instead of regenerating OH) is considered in
the uncertainty analysis of the rate constant determination in Section 6.4.
Reactions describing the unimolecular decomposition of iso-butanol also were not
included in the current mechanism because these reactions are not expected to be
important at temperatures less than 1200 K. The addition of the unimolecular de-
composition reactions of iso-butanol and the corresponding rate constants (and per-
turbations of those rate constants by up to a factor of 2) from the Sarathy et al.
102 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
mechanism [91] to the current mechanism was examined, and these changes intro-
duced negligible change (less than a 2% change in the rate of OH decay) in the
simulated OH time-histories at 1200 K. Furthermore, the absence of iso-butanol de-
composition was verified experimentally by using the OH absorption diagnostic in
shock-heated mixtures of dilute iso-butanol in argon (without TBHP); no OH for-
mation was observed in these experiments, further supporting the assumption on the
absence of iso-butanol decomposition in the current experimental temperature range.
The current kinetic mechanism thus contains all the reactions expected to occur
under the experimental conditions of the current work; however, this mechanism will
not fully describe experiments outside of the current temperature range or iso-butanol
oxidation.
Table 6.1: Rate constants for the reactions of significance in iso-butanol kinetics that were addedto the base mechanism from Merchant and Green [113] and Sarathy et al. [91]. The units of Aare [cm3molecule−1s−1], and the units of E are [cal mol−1K−1]. The sum of the three absent rateconstants is determined in the current work.
No. Reaction k = A · T b exp(−E/RT ) Reference
A b E
Reactions with OH
(6.1a) (CH3)2CHCH2OH+OH −−→(CH3)2CHCHOH+H2O
- - - This Work
(6.1b) (CH3)2CHCH2OH+OH −−→(CH3)2CCH2OH+H2O
2.56× 10−24 3.70 −4.94× 103 Merchant and Green [113]
(6.1c) (CH3)2CHCH2OH+OH −−→CH3(CH2)CHCH2OH+H2O
- - - This Work
(6.1d) (CH3)2CHCH2OH+OH −−→(CH3)2CHCH2O+H2O
- - - This Work
Reactions with H
(6.3a) (CH3)2CHCH2OH+H −−→(CH3)2CHCHOH+H2
1.46× 10−19 2.68 +2.92× 103 Sarathy et al. [91]
(6.3b) (CH3)2CHCH2OH+H −−→(CH3)2CCH2OH+H2
1.08× 10−18 2.40 +4.47× 103 Sarathy et al. [91]
(6.3c) (CH3)2CHCH2OH+H −−→CH3(CH2)CHCH2OH+H2
2.21× 10−18 2.54 +6.76× 103 Sarathy et al. [91]
(6.3d) (CH3)2CHCH2OH+H −−→(CH3)2CHCH2O+H2
1.57× 10−21 3.14 +8.70× 103 Sarathy et al. [91]
6.3. KINETIC MODELING AND ANALYSIS 103
6.3.2 OH Sensitivity Analysis
The results of an OH sensitivity analysis at 1079 K and 1.1 atm with a representative
test mixture are shown in Figure 6.2. The OH sensitivity is defined by Eq. 3.1. The
OH sensitivity to knon-β6.1 is dominant, and the magnitudes of the OH sensitivity to the
individual channels will follow the order of the branching ratio of the channels, which
have not been previously studied in this temperature range. The early-time (first ∼ 40
µs) total OH sensitivity to knon-β6.1 does not depend on the non-β branching ratios (i.e.
k6.1a/knon-β6.1 , k6.1c/k
non-β6.1 , k6.1d/k
non-β6.1 ), therefore, no assumptions will be made about
these branching ratios in this work. While the OH sensitivity to knon-β6.1 is dominant,
the OH sensitivity to kβ6.1 is zero, regardless of the branching ratio of this channel. This
is expected because the β-radical will rapidly decompose to produce an OH radical via
Reaction (6.2) and there are no competing non-OH-producing consumption reaction
pathways for the consumption of the β-radical. Hence, Reaction (6.1b) results in a
net-zero rate of OH concentration change. Therefore, simulated OH time-histories
are insensitive to kβ6.1, and the simulated rate of OH decay is sensitive to only knon-β6.1 .
0 20 40 60 80-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
(3.3)
(6.3b)(3.1)
(6.1a,c,d)
OH
Sen
sitiv
ity
Time [s]
1079 K, 1.1 atm220 ppm iso-butanol,15 ppm TBHP
(3.1) . . .(CH3)3COOH -> (CH3)3CO + OH (3.3) . . .CH3 + OH -> CH2(s) + H2O (6.1a,c,d) (CH3)2CHCH2OH + OH -> non- radicals + H2O (6.1b). . .(CH3)2CHCH2OH + OH -> -radical + H2O (6.3b) .. .(CH3)2CHCH2OH + H -> -radical + H2
(6.1b)
Figure 6.2: OH sensitivity calculation using the current kinetic mechanism at 1079 K, 1.1 atm with220 ppm iso-butanol and 15 ppm TBHP.
104 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
Minor OH sensitivity to secondary reactions is present from a reaction of iso-
butanol with a hydrogen atom, and reactions related to the TBHP as the OH precur-
sor. Reaction (6.3b) will lead to subsequent OH production via decomposition of the
β-radical product. While the rate constant for this reaction is not well known, the
OH concentration is only sensitive to this reaction at later times (after the hydrogen
radical pool has had time to build up), and thus the early-time OH time-history can
be assumed to be relatively insensitive to the rate constant for this reaction. Rate
constants for the reactions important in the OH sensitivity analysis that are related
to TBHP as the OH precursor, such as Reactions (3.1) and (3.3), have been stud-
ied in Chapter 3 of this thesis, with uncertainties of ±30%. The rate constants for
the isomerization and beta-scission decomposition of the iso-butanol radicals are not
significant in the OH sensitivity analysis, and therefore these rate constants have
negligible influence on the OH time-history and estimates for the rate constants for
these reactions are sufficient.
6.4 Results and Discussion
6.4.1 Rate Constant Measurements for the non-β Pathways
Four sample measured OH time-histories are shown in Figure 6.3 at representative
temperatures over the experimental range. The OH time-histories are shown on
a semi-logarithmic plot, illustrating a near-exponential decay at all temperatures
after the initial TBHP decomposition to OH, which occurs over a finite time at
temperatures under 1000 K. The decomposition rate can be captured by the kinetic
mechanism described in Section 6.3. The OH time-histories for the two different
mixtures can be compared in Figure 6.3, illustrating that for similar temperatures, a
faster OH decay rate will be observed in the mixture with a larger initial iso-butanol-
to-TBHP concentration ratio; these measurements confirm the expected behavior.
For each experimental temperature, knon-β6.1 was determined by matching a sim-
ulated OH time-history from the kinetic mechanism with each measured OH time-
history, using knon-β6.1 as the free parameter. The OH simulations from the kinetic
6.4. RESULTS AND DISCUSSION 105
0 20 40 60 80
1
10
0 20 40 60 80
1
10
0 20 40 60 80
1
10
0 20 40 60 80
1
10
1047 K, 1.1 atm150 ppm iso-butanol15 ppm TBHP
OH
mol
e fra
ctio
n [p
pm]
Measured OH Current data
Simulated OH knon- (best-fit) knon- -30% knon- +30%
Time [s]
937 K, 1.2 atm220 ppm iso-butanol15 ppm TBHP
1079 K, 1.1 atm220 ppm iso-butanol15 ppm TBHP
1134 K, 1.0 atm150 ppm iso-butanol15 ppm TBHP
Figure 6.3: Sample OH time-history measurements at temperatures of 1134 K, 1079 K, 1047 K, and937 K. Left figures are mixture of 150 ppm iso-butanol and 15 ppm TBHP, right figures are 220 ppmiso-butanol and 15 ppm TBHP. Also shown are simulated OH time-histories using the current kineticmechanism with the best-fit rate constant for knon-β6.1 and with the best-fit rate perturbed by ±30%.
mechanism with the best-fit to the data are shown in Figure 6.3, along with the OH
simulations with the best-fit value of knon-β6.1 perturbed by ±30% to illustrate the sen-
sitivity of the OH decay rate to knon-β6.1 . Table 6.2 lists the values for knon-β6.1 determined
from the current measured OH time-histories for each of the experimental tempera-
tures, and Figure 6.4 presents an Arrhenius plot of knon-β6.1 . The data can be described
in Arrhenius form by the expression in Eq. 6.4.
knon-β6.1 = 1.84× 10−10 exp
(− 2, 350
T [K]
)cm3molecule−1s−1 (Eq. 6.4)
106 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
Eq. 6.4 is valid over the temperature range 907 to 1147 K. These are the first ex-
perimental rate constants determined that are associated with Reaction (6.1) in this
temperature range.
0.8 0.9 1.0 1.1 1.21
2
3
4Current work
Data 2-parameter fit
k non-
β [1
0-11 cm
3 mol
ecul
e-1 s
-1]
1000/T [K-1]
Oxidation Mechanisms Merchant and Green (2012) Sarathy et al. (2021) Grana et al. (2010)
Structure-Activity Relationship Atkinson and coworkers
1250 K 1111 K 1000 K 909 K 833 K
Figure 6.4: Rate constant measurements for knon-β6.1 . The error bars represent the results of a detaileduncertainty analysis. Also shown are comparisons to the corresponding rate constants used inrecently developed iso-butanol oxidation mechanisms [40, 91, 113] and using the structure-activityrelationship of Atkinson and coworkers [20–22, 90].
A detailed uncertainty analysis was performed to examine the total uncertainty
in the determination of knon-β6.1 based on uncertainties in temperature, pressure, initial
TBHP and iso-butanol concentrations, laser intensity and wavelength, OH absorp-
tion coefficient, data fitting, impurities, branching ratios of the non-β reactions, the
rate constants of the three most important secondary reactions in the mechanism,
and the possible influence of unimolecular iso-butanol decomposition reactions and
hydrogen-producing beta-scission reactions of the β-radical that were omitted from
the mechanism. The influence of these uncertainties on the total uncertainty on
knon-β6.1 is estimated to be ±12% at temperatures above 1000 K, with the laser noise
and the initial iso-butanol concentration as the dominant factors contributing to the
6.4. RESULTS AND DISCUSSION 107
Table 6.2: Rate constants knon-β6.1 and koverall6.1 for each experimental data point, and the resultingbranching ratio for the β-channel. All rate constants are in units of cm3molecule−1s−1.
Mixture T [K] P [atm] knon-β6.1 from data kβ6.1 from [113] koverall6.1kβ6.1
koverall6.1
[%]
150 ppm iso-butanol, 1147 1.0 2.37× 10−11 4.68× 10−12 2.84× 10−11 1615 ppm TBHP 1134 1.0 2.31× 10−11 4.60× 10−12 2.77× 10−11 17
1047 1.1 1.96× 10−11 4.11× 10−12 2.37× 10−11 171011 1.1 1.74× 10−11 3.93× 10−12 2.14× 10−11 18
220 ppm iso-butanol, 1079 1.1 2.13× 10−11 4.28× 10−12 2.55× 10−11 1715 ppm TBHP 974 1.2 1.62× 10−11 3.76× 10−12 1.99× 10−11 19
937 1.2 1.49× 10−11 3.60× 10−12 1.85× 10−11 19925 1.2 1.49× 10−11 3.55× 10−12 1.85× 10−11 19907 1.2 1.37× 10−11 3.48× 10−12 1.72× 10−11 20
total uncertainty. Uncertainty in the rate constants for the three most important sec-
ondary reactions have only a small (<4%) contribution to the uncertainty in knon-β6.1
at temperatures over 1000 K. This was determined using an uncertainty of ±30% for
the rate constants for Reactions (3.1) and (3.3), and an uncertainty factor of 2 for
the Reaction (6.3b). While the large uncertainty of the rate constant for the latter
reaction can have a significant effect on the late-time OH mole fraction (at times >40
µs), there is only minimal effect on the early-time OH decay rate; only the early-time
OH decay rate was used for the rate constant determination. For temperatures below
1000 K, the uncertainty of the rate constant for Reaction (3.1) (the TBHP decompo-
sition reaction) becomes a more significant factor in the overall uncertainty of knon-β6.1
as the temperature decreases, and the largest overall uncertainty for knon-β6.1 is ±21%
at 907 K. These uncertainty limits are illustrated in Figure 6.4.
6.4.2 Comparison to Rate Constant Recommendations
Several detailed kinetic mechanisms for iso-butanol oxidation have been developed
in recent years [31, 37, 40, 91, 113]. Each of these mechanisms includes four site-
specific rate constants for Reactions (6.1a), (6.1b), (6.1c), and (6.1d), estimated by
examination of the rate constants for analogous reactions. Comparison of the current
determination of knon-β6.1 with the corresponding rate constant sum from three most
recent mechanisms [40, 91, 113] is shown in Figure 6.4. The rate constant sum from
the Merchant and Green mechanism [113] shows the best agreement with the current
108 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
work. Over the current experimental temperature range, the rate constant sum from
the Sarathy et al. mechanism [91] is 15 to 25% slower than the current measurements,
and the rate constant sum from the Grana et al. mechanism [40] is 25 to 40% slower
than the current measurements. The rate constant sum from the Sarathy et al. and
Grana et al. mechanisms show agreement within the uncertainty limits of the current
work only at the lowest temperatures studied.
Atkinson and coworkers [20–22, 90] developed an empirical structure-activity re-
lationship (SAR) to estimate the rate constants for reactions of OH with organic
compounds, including alcohols, at temperatures from 250 to 1000 K. The parameters
in their SAR include a rate constant term for each hydrogen-atom abstraction site
(primary, secondary, and tertiary carbons and hydroxyl group) in the organic com-
pound, and substituent factors that influence the rate constant term at each reaction
site based on the identity of the neighboring substituent groups. Further description
of using the SAR method of Atkinson and coworkers to estimate rate constant pa-
rameters is presented in Appendix D. An estimation of knon-β6.1 using the updated SAR
method can be computed by omitting the rate constant term and substituent factors
associated with reaction at the tertiary carbon site of iso-butanol (the reaction site
leading to a β-radical product); this computed rate constant is shown in comparison
to the current work in Figure 6.4. The estimated knon-β6.1 determined with the SAR
method is in very good agreement with the current work.
The current results are useful in validating high-level ab initio rate constant cal-
culations for the site-specific channels of Reaction (6.1), such as those by Zheng et
al. [114]. Their calculated knon-β6.1 , obtained by the sum of the respective site-specific
rate constants calculated using a potential energy surface based on CCSD(T)/CBS,
is approximately a factor of 1.5 lower than the current measurements at 1000 K.
In the absence of the current experiments, one might believe CCSD(T)/CBS to be
more reliable than density functional theory. However, the calculated rate constant
using a potential energy surface based on M08-SO/MGS, also done by Zheng et al., is
found to have better agreement with the current work than the CCSD(T)/CBS-based
rate constant calculations. This observation demonstrates the utility of the current
experimental results as a guide for theoretical work.
6.5. OVERALL RATE CONSTANT RECOMMENDATION 109
6.5 Overall Rate Constant Recommendation
The total overall rate constant for Reaction (6.1) can be determined from the current
measurements if an estimate of kβ6.1 is made. The temperature-dependent expression
for kβ6.1 found in the Merchant and Green mechanism [113] was chosen to best represent
the actual value, for the reasons that their total knon-β6.1 shows excellent agreement with
the current data. The expression for kβ6.1 in the Merchant and Green mechanism is
approximated by using the rate constant for the hydrogen-atom abstraction by OH
from the β-carbon site of n-butanol, from the high-level ab initio calculations of Zhou
et al. [88], with an adjustment in the activation energy to account for the difference
in the C–H bond energy between a tertiary and secondary carbon; this rate constant
is listed in Table 6.1.
The total overall rate constant is the sum of kβ6.1 from the Merchant and Green
mechanism [113] and the measured knon-β6.1 from the current work, as defined by the
expression in Eq. 6.5.
koverall6.1 = [knon-β6.1 ]meas. + [kβ6.1]Merchant and Green (Eq. 6.5)
Values for kβ6.1 and koverall6.1 at each experimental temperature are listed in Table 6.2.
The branching ratio for the β reaction channel, defined as kβ6.1/koverall6.1 , is also listed,
and over the temperature range studied, 17 to 20% of the overall reaction of OH with
iso-butanol is expected to produce a β-radical product under the assumptions used
in the current analysis.
Figure 6.5 presents koverall6.1 at each experimental temperature on an Arrhenius
plot. In the current experimental temperature range of 907 to 1147 K, koverall6.1 can be
expressed in Arrhenius form by Eq. 6.6.
koverall6.1 = 1.85× 10−10 exp
(− 2155
T [K]
)cm3molecule−1s−1 (Eq. 6.6)
The current work represents the first experimentally-determined rate constant for
Reaction (6.1) at combustion-relevant temperatures.
110 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
1.0 1.5 2.0 2.5 3.0 3.5 4.0
1
2
3
45
Oxidation Mechanisms Merchant and Green (2012) Sarathy et al. (2012) Grana et al. (2010)
Structure-activity Relationship Atkinson and coworkers
k over
all [
10-1
1 cm
3 mol
ecul
e-1 s
-1]
1000/T [K -1]
Experimental Data Current work Anderson et al (2010) Mellouki et al (2004) Wu et al. (2003)
Current Recommendation 3-parameter fit
0.5
1000 K 500 K 333 K 250 K
Figure 6.5: Overall rate constant for the reaction of OH with iso-butanol from the current work andmeasurements from the literature [111, 115, 116] at near-atmospheric temperatures and pressures.
The error bars represent only the influence of the kβ6.1 discrepancies on the uncertainty of koverall6.1 .Also shown are corresponding rate constants used in published iso-butanol oxidation mechanisms [40,91, 113], a recommendation from the structure-activity relationship of Atkinson and coworkers [20–22, 90], and the current recommendation.
The overall rate constant for Reaction (6.1) has previously been studied at at
near-atmospheric temperatures and pressures using relative-rate methods by Wu et
al. [111], Mellouki et al. [115], and Anderson et al. [116]. Mellouki et al. also used a
pulsed laser photolysis-laser-induced fluorescence method for absolute rate measure-
ments. These data are also shown on Figure 6.5. By combining the current rate
constant recommendation at high-temperatures with the atmospheric-temperature
data from the literature, koverall6.1 can be described with a 3-parameter expression in
modified Arrhenius form by Eq. 6.7, valid from 296 to 1147 K.
koverall = 1.65× 10−21T 3.18 exp
(+
1304
T [K]
)cm3molecule−1s−1 (Eq. 6.7)
The recommended expressions for koverall6.1 given by Eq. 6.6 and Eq. 6.7 are purely
6.5. OVERALL RATE CONSTANT RECOMMENDATION 111
empirical relations. The uncertainties of the data used in generating the expression
for koverall6.1 should be taken into account when using these expressions for koverall6.1 .
The low-temperature data exhibit a negative temperature dependence, which can be
indicative of initial formation of a hydrogen-bonded complex and, therefore, the rate
constant at low temperatures may be pressure and bath gas dependent; thus, caution
must be taken when applying the current expression for koverall6.1 at low temperatures
(less than 400 K) and pressures (less than 100 Torr).
The current recommendation for koverall6.1 is compared with the corresponding
recommendations from the structure-activity relationship (SAR) of Atkinson and
coworkers [20–22, 90] and the three mechanisms [40, 91, 113] in Figure 6.5. Ap-
pendix D described the process of using the SAR to determine the rate constant.
The prediction of koverall6.1 with the SAR method extrapolated to the current temper-
ature range provides a reasonable fit to both the current high-temperature data and
the low-temperature measurements [111, 115, 116], and is shown in Figure 6.5. None
of the mechanism recommendations for koverall6.1 agree with both the current overall
rate constant determinations at high temperatures and the low-temperature data.
While kβ6.1 was taken from the Merchant and Green mechanism [113] to determine
koverall6.1 , the values for kβ6.1 suggested by the Sarathy et al. [91] and Grana et al. [40]
mechanisms can also be reasonable estimates for kβ6.1, as they are slower than kβ6.1
from the Merchant and Green recommendation by less than a factor of two. Further-
more, the rate constant term and substituent factors associated with reaction at the
tertiary carbon site of iso-butanol from the structure-activity relationship of Atkin-
son and coworkers [20–22, 90] (see Appendix D) yields a rate constant representing
kβ6.1 approximately 1.5 faster than the Merchant and Green recommendation. These
discrepancies in kβ6.1 contribute an uncertainty of less than ±10% in the total overall
rate constant for Reaction (6.1), as shown in 6.5. The choice of kβ6.1, given the current
literature sources, does not have a significant impact on the current determination of
koverall6.1 relative to the large discrepancies in the value of koverall6.1 from each mechanism
and the SAR method. The different expressions for kβ6.1 from the current literature
sources will lead to different branching ratio estimations for kβ6.1/koverall6.1 , ranging from
9% at the lowest using kβ6.1 from the Sarathy et al. mechanism to 27% at the highest
112 CHAPTER 6. REACTION OF OH WITH ISO-BUTANOL
using kβ6.1 from the SAR method.
6.6 Conclusions
A rate constant for the non-β-radical producing channels of the reaction of OH with
iso-butanol (knon-β6.1 ) was determined from OH time-history measurements in reflected-
shock experiments of tert-butylhydroperoxide with iso-butanol in excess. To the best
of the author’s knowledge, these are the first experimentally determined rate con-
stants related to the reaction of OH with iso-butanol to be published at combustion-
relevant conditions. The site-specific rate constants for the overall reaction of OH
with iso-butanol in the most recent Merchant and Green mechanism [113] sum to
a knon-β6.1 that matches the current measurements well. The knon-β6.1 predicted from
extrapolation of the structure-activity relationship of Atkinson and coworkers [20–
22, 90] to high-temperatures also shows good agreement with the current data. An
overall rate constant recommendation (koverall6.1 ) is provided at high-temperature con-
ditions from 907 to 1147 K by using the rate constant from the Merchant and Green
mechanism [113] for the β-radical-forming reaction channel, and a three-parameter
expression for the overall rate constant is suggested that matches both the current
high-temperature rate constant recommendation and low-temperature measurements
from the literature [111, 115, 116].
Chapter 7
Reaction of OH with sec-Butanol
7.1 Introduction
7.1.1 Background and Motivation
The sec-butanol isomer of butanol (2-butanol) can be produced from glucose through
a process involving fermentation and other chemical processes [117]. Thus, the com-
bustion chemistry of sec-butanol is of interest in kinetic mechanisms describing the
combustion of biobutanol. The reaction of OH with sec-butanol can occur through
five different reaction channels, described by Reactions (7.1a) through (7.1e).
CH3CH(OH)CH2CH3 + OH −→ CH2CH(OH)CH2CH3 + H2O (7.1a)
−→ CH3C(OH)CH2CH3 + H2O (7.1b)
−→ CH3CH(OH)CHCH3 + H2O (7.1c)
−→ CH3CH(OH)CH2CH2 + H2O (7.1d)
−→ CH3CH(O)CH2CH3 + H2O (7.1e)
Similar to the reactions pathways possible for n-butanol and iso-butanol, as discussed
in Chapters 5 and 6, respectively, the C4H9O radicals produced from the hydrogen-
atom abstraction reactions will react via beta-scission reactions and isomerization
113
114 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
reactions. Cleavage at C–C and C–O bonds are the dominant channels for the beta-
scission reactions (cleavage at C–H bonds will occur to a lesser extent), and the
dominant isomerization reactions are the ones proceeding through a 5-membered-ring
transition state. Figure 7.1 illustrates the dominant reactions occurring subsequent
to Reaction (7.1).
Reactions (7.2a) and (7.3a) are secondary OH-generating reactions that will occur,
and thus the determination of the rate constant for Reaction (7.1) from a measured
pseudo-first-order OH decay will be complicated by these reactions and any non-OH-
producing competing reaction channels, such as Reactions (7.2b), (7.2c), and (7.3b).
CH2CH(OH)CH2CH3 −→ 1−C4H8 + OH (7.2a)
−→ CH2CHOH + C2H5 (7.2b)
−→ CH3(OH)CHCH2CH2 (7.2c)
CH3CH(OH)CHCH3 −→ 2−C4H8 + OH (7.3a)
−→ CH3CH−−CHOH + CH3 (7.3b)
Formation of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals that
can lead to secondary OH-producing reactions can also occur through hydrogen-
abstraction from sec-butanol by hydrogen radicals that are eventually produced from
subsequent decomposition of the C4H9O radicals. The hydrogen-abstraction from sec-
butanol by hydrogen radicals can occur through five different pathways as described
by Reactions (7.4a) through (7.4e).
CH3CH(OH)CH2CH3 + H −→ CH2CH(OH)CH2CH3 + H2 (7.4a)
−→ CH3C(OH)CH2CH3 + H2 (7.4b)
−→ CH3CH(OH)CHCH3 + H2 (7.4c)
−→ CH3CH(OH)CH2CH2 + H2 (7.4d)
−→ CH3CH(O)CH2CH3 + H2 (7.4e)
7.1. INTRODUCTION 115
OH
OOH OH OH
OHOH OH OH
sec-butanol
CH3
OH
++
++
+
O
C2H5
OH+
C2H5
C2H4+HC2H4+H C2H4OH+H
OH+
CH3
+H
OH-consuming reaction
OH-producing secondary reaction
Other secondary reaction(7.1a)
(7.1b) (7.1c)(7.1d)
(7.1e)
(7.4a)
+OH
(7.4b) (7.4c) (7.4d)
(7.4e)+OH+H +H +H
+H+OH
+OH
+OH
CH2CH(OH)CH2CH3 CH3CH(OH)CHCH3
(7.2a) (7.2b) (7.3a) (7.3b)
(7.2c)
Figure 7.1: Dominant reaction pathways of sec-butanol after reaction with OH. OH-consumingreactions are shown with red arrows, and OH-producing reactions are shown with green arrows.
Few studies have been found that focus specifically on the rate constants for Reac-
tions (7.2), (7.3), or other secondary reactions occurring subsequent to Reaction (7.1).
However, detailed kinetic mechanisms describing global oxidation of sec-butanol have
been published by Moss et al. [31], Grana et al. [40], Van Geem et al. [37], and Sarathy
et al. [91]. These mechanisms contain rate constants for secondary reactions occurring
subsequent to Reaction (7.1) and can be used in the analysis of data sensitive to the
overall rate constant for Reaction (7.1).
7.1.2 Objectives of the Current Chapter
This chapter presents the results of OH time-history measurements in shock tube
experiments of mixtures of tert-butylhydroperoxide (TBHP), as a fast source of OH,
with sec-butanol in excess. Three kinetic mechanisms from the literature are used
to analyze the OH time-history measurements and an overall rate constant for Reac-
tion (7.1) is presented. The sensitivity of the rate constant determination to secondary
chemistry is also discussed.
116 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
7.2 Experimental
The shock tube and laser diagnostics described in Chapter 2 of this thesis were used
for the work in this chapter. In addition to the chemicals described in Chapter 2
(TBHP/water solution 70%, by weight TBHP, and argon gas), anhydrous 99.5% sec-
butanol (2-butanol) from Sigma Aldrich, was used in the mixture preparation for
the experiments in this chapter. OH time-histories were measured in reflected-shock
experiments of mixtures of TBHP with sec-butanol in excess, diluted in argon. Two
test mixtures were prepared, containing 151 ppm sec-butanol with nominally 14 ppm
TBHP, and 214 ppm sec-butanol with nominally 14 ppm TBHP. Temperatures of
888 to 1178 K were studied at pressures around 1 atm.
7.3 Secondary Reaction Pathway Modeling
As shown by Figure 7.1, Reactions (7.2a) and (7.3a) are secondary OH-generating
reactions that will occur subsequent to Reactions (7.1a) and (7.1c), respectively.
Therefore, simulated OH time-histories using a sec-butanol detailed kinetic mech-
anism are expected to be sensitive to the relative amount of Reaction (7.1) that
proceeds via Reactions (7.1a) and (7.1c); this can be described by the branch-
ing ratios k7.1a/k7.1 and k7.1c/k7.1. Furthermore, Reactions (7.2b) and (7.2c) are
non-OH-producing reactions competing with Reaction (7.2a) as a decomposition
pathway for the CH2CH(OH)CH2CH3 radical, and Reaction (7.3b) is a non-OH-
producing reaction competing with Reaction (7.3a) as a decomposition pathway for
the CH3CH(OH)CHCH3 radical. Thus, simulated OH time-histories are also expected
to be sensitive to the branching ratios k7.2a/k7.2 and k7.3a/k7.3. Knowledge of these
branching ratios are necessary to determine the rate constant for Reaction (7.1) from
the experimental data collected for this chapter.
Detailed kinetic mechanisms describing sec-butanol combustion, such as those by
Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91], can be used to account
for secondary reaction pathways. Each of these mechanisms can be modified with
the reactions and rate constants presented in Table 3.1 to correctly account for the
7.3. SECONDARY REACTION PATHWAY MODELING 117
OH time-history behavior associated with TBHP; in this text, the use of the term
“modified” to describe one of these sec-butanol mechanisms refers to the addition
and/or modification of the reactions and rate constants in Table 3.1.
Figure 7.2 presents the results of an OH sensitivity analysis of the modified Sarathy
et al. mechanism under typical experimental conditions. OH sensitivity is defined
by Eq. 3.1. The rate constant for Reaction (7.1) dominates the OH sensitivity; how-
ever, Reactions (3.3), (7.3b), and (7.3a), (7.4c), among others, are shown to influ-
ence the simulated OH time-history, as would be expected from examination of the
reaction pathways in Figure 7.1. The secondary reactions appearing in the OH sensi-
tivity analysis support conclusions suggesting the importance of the branching ratios
k7.1a/k7.1, k7.1c/k7.1, k7.2a/k7.2 and k7.3a/k7.3 in the simulated OH time-history. Similar
OH sensitivity analysis results are generated with the modified Grana et al. and Van
Geem et al. mechanisms.
0 20 40 60 80 100-1.5
-1.0
-0.5
0.0
0.5
1.0
(7.4c)(7.3b)
(7.3a)
(3.1)
(3.3)
OH
Sen
sitiv
ity
Time [s]
(3.1) (CH3)3COOH -> (CH3)3CO + OH (3.3) CH3 + OH -> CH2(s) + H2O (7.1) CH3CH(OH)CH2CH3 + OH -> Products (7.3a) CH3CH(OH)CHCH3 -> 2-C4H8 + OH (7.3b) CH3CH(OH)CHCH3 -> CH3CH2=CH2OH + CH3
(7.4c) CH3CH(OH)CH2CH3 + OH -> CH3CH(OH)CHCH3 + H2
969 K, 1.15 atm214 ppm secbutanol, 14 ppm TBHP (7.1)
Figure 7.2: OH sensitivity analysis of the 214 ppm sec-butanol and 14 ppm TBHP mixture at 969 Kand 1.15 atm using the Sarathy et al. [91] mechanism.
To the author’s knowledge, no studies have focused directly on any of the branch-
ing ratios important in simulating the OH time-history under the current experimental
conditions; however, each detailed mechanism contains estimated rate constants for
the reactions needed in calculating the branching ratios. Figure 7.3 illustrates the
118 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
branching ratios k7.1a/k7.1 and k7.1c/k7.1 at 969 K as described by the mechanisms of
Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91]. These three mecha-
nisms show reasonable agreement on the branching ratios for k7.1a/k7.1 and k7.1c/k7.1.
The branching ratios k7.2a/k7.2 and k7.3a/k7.3 calculated at 969 K from the three mech-
anisms are shown in Figure 7.4. The relative amounts of OH regeneration subsequent
to the formation of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals do
not reach agreed-upon values when comparing the predicted branching ratios from
the three mechanisms.
OH
OOH OH OHOH
+OH+OH
+OH+OH
+OH
OH
OOH OH OHOH
+OH
+OH
+OH+OH
+OH
Grana et al.
Van Geem et al.
17% 33% 28% 17% 5%
14% 49% 24% 7% 6%
Relative branching in the OH + sec-butanol reaction at 969 K
OH
OOH OH OHOH
+OH+OH
+OH+OH
+OH
Sarathy et al.
17% 44% 17% 18% 4%
(7.1a) (7.1b)(7.1c)
(7.1d) (7.1e)
Figure 7.3: Branching ratios for Reactions (7.1a) through (7.1e) as suggested by the detailed mech-anisms of Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91] The thickness of the arrowsillustrate the relative rates of each reaction channel.
Modified versions of the Grana et al. [40], Van Geem et al. [37], and Sarathy
7.3. SECONDARY REACTION PATHWAY MODELING 119
et al. [91] mechanisms are used for the analysis of the measured OH time-histories
reported in this chapter. These three mechanisms will each be used to determine
the rate constant for Reaction (7.1) from the experimental data and to explore the
sensitivity of the determination of the rate constant for Reaction (7.1) to secondary
chemistry. The rate constant for Reaction (7.1) is inferred for each measured data
trace using a kinetic mechanism by adjusting the rate constant for Reaction (7.1) in
the mechanism to generate a simulated OH time-history that fits the experimental
data. In the analyses, the relative branching between Reactions (7.1a) through (7.1e)
(i.e. k7.1a/k7.1, etc.) suggested by each mechanism are preserved, as well as the rate
constants for all secondary reactions.
OH
+OH
OH
+
+
OH
C2H5HO
other (H + enols, gamma-radical, etc.)
OH
+
+
OH
C2H5HO
other (H + enols, gamma-radical, etc.)
6%83%
11%
82%
9%
9%
Grana et al.
Van Geem et al.
OH
+
+
OH
C2H5HO
other (H + enols, gamma-radical, etc.)
15%85%
0%
Sarathy et al.
(7.2a)
(7.2b)
(7.2c), etc.
(7.2a)
(7.2b)
(7.2c), etc.
(7.2c), etc.
(7.2b)
(7.2a)
Grana et al.
Van Geem et al.
OH
+
+
OH
CH3HO
other (H + enols)
15%75%
10%
OH
+
+
OH
CH3HO
other (H + enols)
77%
23%
0%
OH
+
+
OH
CH3HO
other (H + enols)
53%
43%
4%
Sarathy et al.
(7.3a)
(7.3b)
(7.3b)
(7.3a)
(7.3a)
(7.3b)
+OH(7.1a) (7.1c)
CH2CH(OH)CH3CH3 CH3CH(OH)CHCH3
Reaction pathways of Reaction pathways of
Figure 7.4: Branching ratios for the consumption of the CH2CH(OH)CH2CH3 andCH3CH(OH)CHCH3 radicals as suggested by the detailed mechanisms of Grana et al. [40], VanGeem et al. [37], and Sarathy et al. [91]. The thickness of the arrows illustrate the relative rates ofeach reaction channel.
120 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
7.4 OH Time-histories and Rate Constant Deter-
mination
A representative measured OH time-history at 969 K is shown in Figure 7.5 with the
simulated OH time-history from the modified mechanism of Sarathy et al. [91] with the
value of the rate constant for Reaction (7.1) (1.25×10−11 cm3molecule−1s−1) that leads
the best fit to the measured trace. Also shown are simulations using perturbations of
the best-fit rate constant for Reaction (7.1) by ±30%, illustrating the sensitivity of the
simulated OH decay rate to the rate constant. While a rate constant for Reaction (7.1)
of 1.25×10−11 cm3molecule−1s−1 in the modified Sarathy et al. mechanism leads to a
simulated OH time-history that shows an excellent fit to the data at at 969 K, a value
of 1.88×10−11 cm3molecule−1s−1 for the rate constant for Reaction (7.1) is needed in
the modified Van Geem et al. mechanism to generated a simulated OH time-history
that matches the experimental data. Thus, the determination of the rate constant
for Reaction (7.1) from the experimental data is mechanism dependent, indicating
differences in the modeling of secondary reactions.
0 20 40 60 80 1001
10
Data1
Simulation, best fit 1
Simulation, k7.1 + 30% Simulation, k7.1 - 30%
OH
mol
e fra
ctio
n [p
pm]
Time [s]
969 K, 1.15 atm214 ppm sec-butanol,14 ppm TBHP
Figure 7.5: Measured OH time-history for an experiment at 969 K, 1.15 atm with 214 ppm sec-butanol and 14 ppm TBHP. Also shown are simulated OH time-histories using the modified mech-anism of Sarathy et al. [91] with the best-fit value of the rate constant for Reaction (7.1) andperturbations of ±30% on the best-fit value of the rate constant for Reaction (7.1).
7.4. OH TIME-HISTORIES AND RATE CONSTANT DETERMINATION 121
Figure 7.6 presents an Arrhenius plot of the mechanism-dependent rate constant
for Reaction (7.1) determined from the experimental data, and also illustrates the
sensitivity of the inferred value of the rate constant for Reaction (7.1) to the kinetic
mechanism used for analysis. Table 7.1 presents a list of the inferred rate constants
for each experimental data point from all three mechanisms. The peak-to-peak dis-
crepancy of the inferred value of the rate constant for Reaction (7.1) from the different
mechanisms is approximately a factor of 0.5, with the rate constant inferred using the
modified Grana et al. mechanism the slowest, and the rate constant inferred using
the modified Van Geem et al. mechanism the fastest. The analysis using the modi-
fied Sarathy et al. mechanism results in rate constant determinations similar to those
determined using the modified Grana et al. mechanism.
0.8 0.9 1.0 1.1 1.2
1
2
3
4
Reaction (7.1): CH3CH(OH)CH2CH3 + OH -> Products
k 7.1
[10-1
1 cm
3 mol
ecul
e-1 s
-1]
1000/T [K-1]
Mechanism: Grana et al. (2010) Van Geem et al. (2010) Sarathy et al. (2012)
1250 K 1111 K 1000 K 909 K 833 K
0.6
Solid line - Rate constant determination from measured data with different secondary chemistryDotted line - Rate constant in mechanism
Figure 7.6: Arrhenius plot of the rate constant for Reaction (7.1) determined using three differentmodified kinetic mechanisms for sec-butanol from the literature [37, 40, 91]. Points are shown forthe rate constant determination for each individual data point using the modified Sarathy et al.mechanism [91], along with a fit to the data points (solid line). For clarity, only the fits to the rateconstant determinations using the modified Grana et al. [40] and Van Geem et al. [37] mechanismsare shown. Also shown (dashed lines) are the rate constants in the Grana et al. and Sarathy et al.mechanisms (the rate constant from the Van Geem et al. mechanism does not fit on a reasonablescale on the figure).
The rate constant determination dependence on mechanism is not surpris-
ing given that the mechanisms predict different branching pathways for the
122 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals, as illustrated by Figure 7.4.
The mechanisms of Grana et al. and Sarathy et al. both ascribe rate constants
for the channels of Reactions (7.2) and (7.3) that predict the non-OH-forming
decomposition/isomerization reaction channels of the CH2CH(OH)CH2CH3 and
CH3CH(OH)CHCH3 radicals to be dominant. Therefore, the majority of the de-
cay in simulated OH time-histories using the modified mechanisms of Grana et al.
and Sarathy et al. is caused by Reaction (7.1). In the Van Geem et al. mechanism,
however, the rate constants for Reactions (7.2) and (7.3) describe reaction pathways
indicating that the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3 radicals will react
dominantly through OH-producing channels. This leads to simulated OH regener-
ation, and thus a faster value for the rate constant for Reaction (7.1) is needed to
simulate the same experimental OH time-history.
Reactions (7.2a), (7.2b), (7.2c), (7.3a), and (7.3b) are obviously important sec-
ondary reactions in the analysis of the current data. However, to the author’s knowl-
edge, no studies have focused directly on the rate constants for these reactions or the
branching ratios of interest. Therefore, the secondary chemistry described by these
reactions from the different mechanisms will be assumed to represent the approximate
bounds of uncertainty in the rate constant determination.
The overall rate constant for Reaction (7.1) can be described by the expression
in Eq. 7.1 with uncertainty limits of ±30%, valid from 888 to 1178 K.
kav.7.1 = 6.97× 10−11 exp
(− 1550
T [K]
)cm3molecule−1s−1 (Eq. 7.1)
Eq. 7.1 was determined using a linear least-squares fit to ln(kav.7.1) versus 1/T , where
ln(kav.7.1) at each temperature was taken to be the average of the three ln(k7.1) values
determined from each mechanism for each data point. The uncertainty limit of ±30%
accounts for the uncertainty in the secondary chemistry within the analysis; this un-
certainty is larger than the experimental errors, and thus approximately represents
the overall uncertainty of the rate constant for Reaction (7.1), including all experi-
mental and modeling errors. This averaged overall rate constant for Reaction (7.1) is
listed in Table 7.1 for each data point and shown in Figure 7.7.
7.5. DISCUSSION 123
Table 7.1: Rate constant determination for Reaction (7.1) for each experimental data point us-ing the modified mechanisms of Grana et al. [40], Van Geem et al. [37], and Sarathy et al. [91].Also listed is kav.7.1 where ln kav.7.1 was taken to be the average of the three ln k7.1 values determinedfrom each mechanism determination at each temperature point. All rate constants are in units ofcm3molecule−1s−1.
Mixture T [K] P [atm] k7.1 k7.1 k7.1 kav.7.1Grana et al. Van Geem et al. Sarathy et al.
151 ppm sec-butanol, 1112 1.03 1.41× 10−11 2.24× 10−11 1.58× 10−11 1.71× 10−11
15 ppm TBHP 1032 1.09 1.33× 10−11 1.99× 10−11 1.33× 10−11 1.52× 10−11
977 1.10 1.28× 10−11 1.91× 10−11 1.28× 10−11 1.46× 10−11
214 ppm sec-butanol, 1178 0.95 1.58× 10−11 2.50× 10−11 1.74× 10−11 1.90× 10−11
14 ppm TBHP 1144 0.99 1.54× 10−11 2.41× 10−11 1.66× 10−11 1.83× 10−11
1118 1.00 1.41× 10−11 2.24× 10−11 1.58× 10−11 1.71× 10−11
969 1.15 1.25× 10−11 1.88× 10−11 1.25× 10−11 1.43× 10−11
939 1.15 1.13× 10−11 1.74× 10−11 1.16× 10−11 1.32× 10−11
888 1.24 1.08× 10−11 1.58× 10−11 1.08× 10−11 1.22× 10−11
7.5 Discussion
7.5.1 Mechanism Performances
The performance of a mechanism can be evaluated by how well the experimentally-
determined rate constant for Reaction (7.1) from a given mechanism matches the
original rate constant used in that mechanism. Figure 7.6 shows the overall rate con-
stants for Reaction (7.1) from the Grana et al. [40] and Sarathy et al. [91] mechanisms.
The original rate constant for Reaction (7.1) from the Van Geem et al. [37] mechanism
is not shown because it is over an order of magnitude slower than the data shown in
Figure 7.6. The rate constant for Reaction (7.1) determined from the experimental
data using the secondary chemistry of the Sarathy et al. mechanism is within 10%
of their original rate constant value; therefore, the Sarathy et al. mechanism best
simulates the current measured OH time-histories. The Grana et al. mechanism also
appears to be capable of simulating OH time-histories in reasonable agreement with
the current data, as their original rate constant for Reaction (7.1) is within 25% of the
experimentally-determined rate constant using the Grana et al. secondary chemistry.
The Van Geem et al. [37] mechanism uses a rate constant for Reaction (7.1) an
order of magnitude slower than all of the experimentally-determined values of the rate
constant for Reaction (7.1). Therefore, OH time-histories simulated using the Van
124 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
Geem et al. mechanism will provide poor agreement with the current data and the
simulated OH time-history using their mechanisms will predict an OH decay much
slower than the measured values. While the value of the rate constant for Reac-
tion (7.1) in the Van Geem et al. mechanism appears to be incorrect, there is no
compelling evidence to suspect that the rate constants for important secondary re-
actions in their mechanism are subject to the same degree of inaccuracy. Therefore,
the value for the rate constant for Reaction (7.1) determined from the current data
using the secondary chemistry in the Van Geem et al. mechanism may be a reason-
ably accurate evaluation of the actual rate constant, and using this rate constant
determination in the Van Geem et al. mechanism would significantly improve their
kinetic mechanism.
While comparison of the original rate constant for Reaction (7.1) used in a mech-
anism with the experimentally-determined rate constant using the same mechanism
can illustrate the performance of a mechanism, no insight can be gained on the ac-
curacy of any specific rate constants. This is because of the number of important
secondary reactions involved in the simulation of the OH time-history, as illustrated
by the OH sensitivity analysis shown in Figure 7.2. Excellent performance of a mech-
anism could indicate the use of accurate rate constants; however, this could also be
due to errors in rate constants fortuitously canceling out. Therefore, further studies
into the important branching ratios discussed in this chapter are necessary to develop
sec-butanol kinetic mechanisms that are accurate over a wide range of conditions and
experimental validation targets.
7.5.2 Low-temperature Rate Constants
The current determination of the rate constant for Reaction (7.1) can be com-
pared with data presented in the literature [118–120] regarding the rate constant
at atmospheric-relevant conditions (near 298 K). Figure 7.7 presents an Arrhenius
plot of the current data (the current data represents the average of the rate constant
for Reaction (7.1) determined using the three mechanisms, where ln(kav.7.1) was taken
7.5. DISCUSSION 125
to be the average of the three ln(k7.1) values determined from each mechanism deter-
mination at each temperature point) compared with recommendations for the overall
rate constant from the literature from atmospheric-relevant studies. Eq. 7.2 presents
an empirical 3-parameter fit to the data for the rate constant for Reaction (7.1).
k7.1 = 4.95× 10−20T 2.66 exp
(+
1123
T [K]
)cm3molecule−1s−1 (Eq. 7.2)
Eq. 7.2 is valid for the temperature range 263 to 1178 K. The low-temperature data
exhibit a negative temperature dependence, also seen in the iso-butanol data exam-
ined in Chapter 6. Therefore, the rate constant at low temperatures may be pressure
and bath gas dependent and caution must be taken when applying the current ex-
pression for the rate constant for Reaction (7.1) at pressures outside of the range of
the data presented in the literature [118–120] for temperatures under ∼400 K.
1.0 1.5 2.0 2.5 3.0 3.5 4.00.5
1
1.5
2
2.5
3
Current work (3-parameter fit) Atkinson (Structure-activity Relationship)
k 7.
1 [10
-11 c
m3 m
olec
ule-1
s-1]
1000/T [K-1]
Experimental Data Current work (average) Jiminez et al. (2005) Baxley and Wells (1998) Chew and Atkinson (1996)
1000 K 500 K 333 K 250 K
Reaction (7.1): CH3CH(OH)CH2CH3 + OH -> Products
Figure 7.7: Arrhenius plot of the rate constant for Reaction (7.1). The data from the current workis the average of the rate constants determined using the three mechanisms discussed in this work,and the uncertainty limits of ±30% encompass the mechanism dependence of the rate constantdetermination. Also shown are data at atmospheric-relevant temperatures [118–120] and the rateconstant estimated using the structure-activity relationship (SAR) of Atkinson and coworkers [20–22, 90] extrapolated to high temperatures.
126 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
The rate constant estimated using the structure-activity relationship (SAR) of
Atkinson and coworkers [20–22, 90] that was empirically developed for rate constants
for similar reactions at atmospheric-relevant temperatures is also shown on Figure 7.7
for comparison with the data. The rate constant predicted using the SAR method is
∼20% higher than the low-temperature data, and also fails to predict the current de-
termination of the high-temperature rate constant within the ∼30% uncertainty limit.
Discrepancies of this sort between experimentally-measured and SAR-estimated rate
constants have been previously discovered in the literature for reactions of OH with
alcohols [90, 115], with the most likely explanation that long-range effects with re-
spect to hydrogen atom abstraction at sites remote from the substituent group due
to the formation of a hydrogen-bonded complex; the SAR rate constant estimation
method considers only effects of the alcohol group on the alpha and beta carbon sites.
Therefore, the 3-parameter expression in Eq. 7.2 is recommended for a more accurate
description of for the rate constant for Reaction (7.1).
7.6 Conclusions
OH time-histories were measured in shock-heated mixtures of tert-butylhydroperoxide
(TBHP) with sec-butanol in excess, diluted in argon. Rate constants were determined
for the overall reaction of OH with sec-butanol by fitting simulated OH time-histories
from modified detailed mechanisms of sec-butanol combustion from the literature to
the measured data, using the overall rate constant of interest as the free parameter.
The rate constant determination from the measured OH time-histories was found to
be mechanism dependent, and analysis of the differences in the mechanisms indicate
that the reaction pathways of the CH2CH(OH)CH2CH3 and CH3CH(OH)CHCH3
radicals need to be better understood. An Arrhenius expression for the rate constant
for the overall reaction of OH with sec-butanol is suggested and a ±30% uncertainty is
ascribed to account for the mechanism dependence of the rate constant determination.
The measured OH time-histories are best simulated using the Sarathy et al. [91]
mechanism. While this agreement could indicate the use of accurate rate constants
in this mechanism, the agreement could also be attributed to errors in rate constants
7.6. CONCLUSIONS 127
canceling out in the simulation, therefore, further studies on the rate constants of im-
portant secondary reactions in sec-butanol kinetics are necessary to develop accurate
sec-butanol kinetic mechanisms. The structure-activity relationship (SAR) of Atkin-
son and coworkers [20–22, 90] overpredicts both previously reported low-temperature
(near 298 K) measured rate constants for the reaction of OH with sec-butanol, and
also the current high-temperature determination. A 3-parameter modified Arrhenius
expression is developed to correctly predict both the current high-temperature rate
constant data and the low-temperature data from the literature.
128 CHAPTER 7. REACTION OF OH WITH SEC-BUTANOL
Chapter 8
Reaction of OH with tert-Butanol
8.1 Introduction
8.1.1 Background and Motivation
Gasoline-grade tert-butanol, (CH3)3COH, is a common fuel additive used as an oc-
tane booster to prevent knock in spark-ignition engines. The addition of tert-butanol
to traditional hydrocarbon-based automotive fuels also serves to reduce air pollu-
tant emissions such as CO, NOx, and soot. Previous experimental studies on the
combustion kinetics of tert-butanol include shock tube ignition delay [31, 35], shock
tube pyrolysis [121], premixed [43] and diffusion [122] flames, and speciation measure-
ments during oxidation [122, 123] and pyrolysis [124] in flow reactors. Several detailed
kinetic mechanisms have been developed [31, 37, 40, 91] for the high-temperature ox-
idation of tert-butanol using these experimental studies as validation targets. While
the existing detailed mechanisms perform well in predicting some of these global ki-
netic targets, many of the rate constants in the tert-butanol oxidation mechanisms
are poorly known and vary by orders of magnitude between mechanisms. To the
author’s knowledge, no high-temperature experimental studies have yet been carried
out that are specifically designed with high sensitivity to rate constants for important
combustion-relevant tert-butanol reactions.
An important reaction in detailed high-temperature oxidation mechanisms for
129
130 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
any fuel is the reaction of the fuel with the hydroxyl (OH) radical. For tert-butanol,
this reaction proceeds via the two reaction channels described by Reactions (8.1a)
and (8.1b).
(CH3)3COH + OH −→ (CH3)2(CH2)COH + H2O (8.1a)
−→ (CH3)3CO + H2O (8.1b)
The overall rate constant for Reaction (8.1) has been measured using relative-rate
methods by Cox and Goldston [125], and Wu et al. [111], and absolute measurement
methods by Wallington et al. [126], Teton et al. [127], and Saunders et al. [128] at
atmospheric-relevant conditions. These rate constant measurements span the limited
temperature range 240 to 440 K, making it difficult to accurately extrapolate the rate
constant for Reaction (8.1) to combustion-relevant temperatures.
Overall rate constant measurements for Reaction (8.1) at elevated temperatures
are complicated by the catalytic conversion of alcohols to alkenes, a phenomena first
discussed by Hess and Tully [129], during which hydrogen-atom abstraction by OH
from beta-sites in alcohols produce an hydroxyalkyl intermediate that rapidly disso-
ciates to OH + alkene at elevated temperatures (for ethanol, this occurs at T > 500
K). Reaction (8.1a) is the beta-site abstraction for tert-butanol, and this reaction
channel is expected to dominate the overall reaction, thus complicating measure-
ment of the overall reaction rate constant because of the possibility of the subsequent
beta-scission decomposition by Reaction (8.2a) that can rapidly reproduce an OH
radical at elevated temperatures. To make matters more complex, Reaction (8.2b) is
a non-OH-forming reaction that competes with Reaction (8.2a).
(CH3)2(CH2)COH −→ (CH3)2C−−CH2 + OH (8.2a)
−→ (CH3)(CH2)COH + CH3 (8.2b)
Figure 8.1 shows the reaction pathways of tert-butanol after reaction with OH.
The tert-butoxyl radical product of Reaction (8.1b) will rapidly decompose via Re-
action (3.2) to final products of a methyl radical and acetone molecule; these final
8.1. INTRODUCTION 131
products do not include OH radicals and thus do not interfere with rate constant
measurement. Because of the subsequent OH-producing nature of Reaction (8.1a),
measuring the overall rate constant for the reaction of OH with tert-butanol becomes
more challenging at elevated temperatures.
OH
OH
CH3
O CH3
(8.2a)
(8.2b)
(3.2)
+OH
+OH
+
+
+
brOH = k8.1a/(k8.1a+k8.1b)
brβ = k8.2a/(k8.2a+k8.2b)
OH
OH
O
+H2O
+H2O
OH-consuming reactionOH-producing reactionOther secondary reaction
(8.1a)
(8.1b)
Figure 8.1: Dominant reaction pathways of tert-butanol after reaction with OH. OH-consumingreactions are shown with red arrows, and OH-producing reactions are shown with green arrows.Important branching ratios that describe competition between OH-producing and non-OH-producingpathways are also defined.
Overall rate constant measurements for the reaction of OH with alcohols above
500 K have been done using isotopic substitution for the OH precursor (H218O)
in heated reactor experiments by Hess and Tully [129] for ethanol (up to 599 K)
and Dunlop and Tully [130] for 2-propanol (up to 745 K). Shock tube experiments
using tert-butylhydroperoxide (TBHP) as an OH precursor have become a common
technique for rate constant measurements in the temperature range 800 to 1300 K,
as illustrated in the previous chapters of this thesis. In the case of the shock tube
experiments employing TBHP for determining the overall rate constant for reaction
of OH with alcohols, 18O-substituted precursors or alcohols are difficult to obtain, and
deuterium-substituted alcohols can undergo ROD→ROH exchange, which introduces
difficulties in knowing the actual fraction of deuterium-substituted alcohol in the
132 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
experiments. Therefore, experimental determinations of the overall rate constant for
reaction of OH with alcohols in shock tubes at temperatures above 800 K have relied
on kinetic modeling to account for secondary reactions, as was done in the previous
chapters of this thesis.
8.1.2 Objectives of the Current Chapter
This chapter extends the work in the previous chapters on reactions of OH with
butanol and presents the results of OH time-history measurements in shock tube
experiments sensitive to the rate constant for the reaction of OH with tert-butanol.
Dilute mixtures of TBHP, as a fast source of OH, with tert-butanol in excess were
heated behind reflected shock waves, and narrow-linewidth laser absorption by OH
was employed for quantitative time-resolved measurements of the pseudo-first-order
OH time-history decay. The pseudo-first-order rate constant was determined, and
the net OH rate of decay due to reaction with tert-butanol is presented and used
to validate and refine the performance of three recent kinetic mechanisms of tert-
butanol. Additionally, rate constants for secondary reactions were estimated based
on the information available in the literature and an overall rate constant for the
reaction of OH with tert-butanol is suggested.
8.1.3 Organization of this Chapter’s Results
The presentation of the results and discussion regarding the experimental work carried
out for this chapter follow a unique order because of the complexity of the problem.
Section 8.2 presents the details of the experiments performed for this chapter. Sec-
tion 8.3 presents the experimental results as pseudo-first-order OH decay rates and
reports the observed net rate of OH removal during the experiments. Section 8.4
introduces a kinetic model developed to account for secondary reactions in the tert-
butanol and TBHP kinetic system. Using this mechanism, a net rate of OH removal
due to reaction with tert-butanol (without influence of TBHP as the OH precursor) is
derived. Section 8.5 presents a discussion on the estimation of several key branching
ratios from the information available in the literature; and finally, in Section 8.6, the
8.2. EXPERIMENTAL 133
overall rate constant for the reaction of OH with tert-butanol is inferred from the
data and the results are compared to the literature.
8.2 Experimental
The shock tube and laser diagnostics described in Chapter 2 of this thesis were used
for the experimental work described in this chapter. In addition to the chemicals
described in Chapter 2 (TBHP/water solution 70%, by weight TBHP, and argon
gas), anhydrous tert-butanol from Sigma Aldrich, ≥99.5% purity, was used in the
mixture preparation for the experiments in this chapter. Because the melting point
of tert-butanol is 23-26◦C, the laboratory room temperature was raised to greater
than 26◦C during the experiments of this chapter to facilitate the production of tert-
butanol vapors and to ensure that the tert-butanol vapor remained in the vapor phase
throughout the experiments and prevent the condensation or solidification onto the
facility surfaces.
OH time-histories were measured from 902 to 1197 K for two mixture composi-
tions: 445 ppm tert-butanol with 17 ppm TBHP, and 300 ppm tert-butanol with
14 ppm TBHP, both mixtures dilute in argon. The temperature range of the current
experiments was constrained by slow TBHP decomposition at temperatures less than
900 K and tert-butanol decomposition at temperatures above 1200 K. All experiments
were taken at reflected-shock pressures near 1 atm.
8.3 Net OH Removal Rates
A sample OH time-history measurement trace at 943 K is shown in Figure 8.2. Subse-
quent to the initial OH formation, the OH time-history follows an exponential decay,
and low-noise measurements of the OH time-history are observed for times up to
about 200 µs. At temperatures under 1000 K, the OH formation occurs over a finite
time interval (up to 30 µs at 907 K); at higher temperatures the OH formation time
is shorter.
Using a pseudo-first-order analysis, similar to the one described in Section 4.3.1, a
134 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
0 40 80 120 160 2001
10
OH
mol
e fra
ctio
n [p
pm]
Time [μs]
943 K, 1.20 atm445 ppm (CH3)3COH, 17 ppm TBHP
Current data k8.1(1 - brOH*brβ ) = 1.87x10-12
cm3 molecule-1s-1
k8.1(1 - brOH*brβ ) +30% 1
k8.1(1 - brOH*brβ ) -30%
Reaction (8.1): (CH3)3COH + OH -> Products brOH = k8.1a / (k8.1a + k8.1b) brβ = k8.2a / (k8.2a + k8.2b)
Figure 8.2: Measured OH time-history at 943 K on a semi-logarithmic plot; an exponential decay isseen after the initial formation of OH (∼30 µs). Also shown is the best-fit simulated OH time-historywith the current mechanism, and simulated OH time-histories with k8.1 · (1− brOH · brβ) perturbedby ± 30%. The simulated OH time-history with the perturbed k8.1 · (1− brOH · brβ) is independentof whether k8.1 or brβ is perturbed for an overall perturbation of 30%.
pseudo-first-order rate constant for the net OH removal can be defined by by Eq. 8.1,
where k′ is the pseudo-first-order rate constant, xOH is the OH mole fraction, and t is
time. Measurements of k′ were determined from each data trace by taking the slope
of a linear least-squares fit of ln xOH vs. t using the data from the time after the
complete decomposition of TBHP to 200 µs. A second-order rate constant can also
be defined by Eq. 8.2, where k′′ is a second-order rate constant for the net removal
rate of OH, and [(CH3)3COH] is the concentration of tert-butanol.
k′ = −d(lnxOH)
dt(Eq. 8.1)
k′′ =−1
[(CH3)3COH]· d(lnxOH)
dt(Eq. 8.2)
The pseudo-first-order rate constant and second-order rate constant for the net re-
moval rates of OH are listed in Table 8.1 for each experimental temperature. These
rate constants describe the net OH removal in the current experiments, including the
8.4. KINETIC MODELING 135
reaction of OH with tert-butanol and several secondary reactions involving OH radi-
cals. Further analysis using kinetic modeling is needed to determine the rate constant
for the reaction of OH with tert-butanol because the net removal rate of OH is not
the same as the rate constant for Reaction (8.1). This is due to the influence of Reac-
tion (8.2a) as an OH-producing secondary reaction and to other secondary reactions
associated with the use of TBHP as the OH precursor such as Reactions (3.5), (3.3),
and (3.4).
Table 8.1: Pseudo-first-order and second-order rate constants determined for each experimental tem-perature. The pseudo-first-order and second-order rate constants are defined by Eq. 8.1 and Eq. 8.2,respectively, and describe the measured OH decay rate, including the influence of the final TBHPdecomposition products.
Mixture T [K] P [atm] k′ [s−1] k′′ [cm3molecule−1s−1]
307 ppm tert-butanol 1197 0.93 1.04 ×104 5.93 ×10−12
15 ppm TBHP 1166 0.98 0.97 ×104 5.11 ×10−12
1162 0.97 1.00 ×104 5.31 ×10−12
1113 0.99 1.07 ×104 5.29 ×10−12
1079 1.03 0.89 ×104 4.17 ×10−12
1020 1.05 0.92 ×104 3.97 ×10−12
974 1.15 1.09 ×104 4.10 ×10−12
445 ppm tert-butanol 1058 1.06 1.49 ×104 6.64 ×10−12
17 ppm TBHP 1004 1.13 1.40 ×104 5.53 ×10−12
962 1.16 1.44 ×104 5.30 ×10−12
943 1.20 1.42 ×104 4.98 ×10−12
902 1.21 1.46 ×104 4.83 ×10−12
8.4 Kinetic Modeling
A detailed mechanism describing the kinetics of the reaction of OH with tert-butanol
and subsequent secondary reactions was compiled using the alkane/TBHP mechanism
from Chapter 4 as a base mechanism that accurately describes the secondary reactions
due to the presence of TBHP as the OH precursor. Reactions (8.1a), (8.1b), (8.2a),
and (8.2b) were added to the alkane/TBHP mechanism to account for the tert-
butanol-related reactions. Rate constants for these reactions were initially taken from
the published mechanisms on tert-butanol [37, 40, 91] for initial examination of OH
136 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
sensitivity; subsequently, these rate constants were updated to values as discussed in
the Section 8.5. This kinetic mechanism contains all the reactions expected to occur
under the experimental conditions of the current work; however, this mechanism may
not fully describe experiments outside of the current experimental conditions.
Brute force sensitivity of the pseudo-first-order rate constant k′ was computed
using the final current mechanism for the experimental conditions in Figure 8.2, and
the results are shown in Figure 8.3 for the top nine reactions that influence the
sensitivity. The brute force sensitivity is defined by Eq. 8.3.
∆k′
∆ki· kik′
(Eq. 8.3)
The simulated pseudo-first-order rate constant is predominately sensitive to the rate
constants of Reactions (3.3), (3.4), (8.1a), (8.1b), (8.2a), and (8.2b), and minor contri-
bution is also present from reactions of CH3+OH −→ CH3OH, CH3+CH3 −→ C2H6,
and iC4H8 + OH −→ Products. Reactions (3.3), (3.4), CH3 + OH −→ CH3OH, and
CH3 + CH3 −→ C2H6 are all important in the TBHP sub-mechanism, which was
validated in Chapter 3. The only tert-butanol-related reactions that contribute sig-
nificantly to the sensitivity are Reactions (8.1a), (8.1b), (8.2a), and (8.2b). Because
of the high sensitivity of the simulated pseudo-first-order rate constant to the rate
constants for Reactions (8.2a), and (8.2b), the rate constant for Reaction (8.1) cannot
be determined from the measured OH time-histories without accurate rate constants
for Reactions (8.2a) and (8.2b), or at least accurate knowledge of the relative rate
constants between these reactions.
A rate of production (ROP) analysis for the current experimental conditions
at 943 K indicates that 80% of the gross OH consumption (considering only OH-
consuming reactions and not OH-producing reactions) is due to Reaction (8.1);
the results of the ROP analysis also indicate that a steady-state approxima-
tion is appropriate for the concentration of the (CH3)2(CH2)COH radical (i.e.
d[(CH3)2(CH2)COH]/dt = 0). The ROP results are summarized in the reaction path
diagram for OH shown in Figure 8.4. Based on this analysis, the kinetic rate law can
8.4. KINETIC MODELING 137
kOH+iC4H8
kCH3+CH3
kCH3+OH+M
k3.4
k3.3
k8.2b
k8.2a
k8.1b
k8.1a
-50 -25 0 25 50 75
Brute Force Pseudo-first-order Rate Constant Sensitivity:
(Δ k' / Δki ) * (ki / k' ) x 100%
primary tert-butanol-related kinetics
TBHP-related kinetics
secondary tert-butanol kinetics
943 K, 1.20 atm1
445 ppm (CH3)3COH, 17 ppm TBHP
Figure 8.3: Brute force sensitivity for the pseudo-first-order rate constant using the current kineticmechanism for the experimental conditions in Figure 8.2.
be written as Eq. 8.4 for the rate of change of OH concentration in time.
−d[OH]
dt= k8.1
(1− k8.1a
k8.1a + k8.1b
k8.2ak8.2a + k8.2b
)[(CH3)3COH][OH] +
n∑i=5
ki[Xi][OH]
(Eq. 8.4)
In Eq. 8.4, Xi represents secondary species that can react with OH, such as TBHP,
CH3, and acetone. Eq. 8.4 indicates that the pseudo-first-order rate constant deter-
mined in Section 8.3 (k′ listed in Table 8.1) can be expressed by Eq. 8.5, where the
branching ratios brOH and brβ are defined by Eq. 8.6 and Eq. 8.7, respectively, and
illustrated in Figure 8.1.
k′ = k8.1 · (1− brOH · brβ)[(CH3)3COH] +n∑i=5
ki[Xi] (Eq. 8.5)
brOH = k8.1a/(k8.1a + k8.1b) (Eq. 8.6)
brβ = k8.2a/(k8.2a + k8.2b) (Eq. 8.7)
138 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
Both branching ratios brOH and brβ each represent competition between OH-
producing and non-OH-producing reaction pathways. Values for the branching ra-
tios brOH and brβ will be discussed in Section 8.5.
The last term in Eq. 8.5 contributes only 20% of all positive OH consumption
at 943 K according to the kinetic mechanism; at the same temperature, however,
this term contributes 53% of k′ because of the OH regeneration by Reaction (8.2a).
While further experiments could be conducted with a higher initial tert-butanol-to-
TBHP concentration ratio to minimize the contribution of secondary OH-consuming
reactions, the validation of the base mechanism in Chapter 3 provides confidence in
the calculated contribution ofn∑i=5
ki[Xi].
OH(8.1a)
(8.1b)
OH
O
+other
+t-butanol
(8.2a)
(8.2b)non-OH products53%
82%
18%
11%
36%
4%76%
+t-butanol
20%
% of gross OH consumption
(3.2)
% of net OH consumption
(3.3),(3.4),(3.5), etc.
OH-consuming reactionOH-producing reactionOther secondary reaction
CH3 + acetone
Figure 8.4: OH reaction path diagram for the experimental conditions in Figure 8.2 from OH rateof production calculations at 45 µs, with brOH = 0.95 and brβ = 0.82. Reactions (8.1a) and (8.1b)contribute to a total of 80% of the gross OH consumption rate (considering only reactions thatconsume OH). Notice that Reaction (8.2a) is an OH-producing reaction that decreases the net OHdecay rate that occurs subsequent to Reaction (8.1a). The overall contribution of Reactions (8.1a)and (8.1b) to the net (observed) OH consumption rate, therefore, is only 47%.
8.4. KINETIC MODELING 139
8.4.1 Net OH Removal Rate by Reaction with tert-Butanol
The net OH removal rate constant due to reaction with tert-butanol can be described
by the product k8.1 ·(1−brOH ·brβ). This term is independent of any influence of TBHP
as the OH precursor, thus it differs from the second-order rate constant k′′. The value
of k8.1 · (1 − brOH · brβ) is determined using the detailed mechanism to simulate OH
time-histories to fit the experimental data, where the parameters k8.1, brOH, and brβ
are adjusted as free parameters. Obviously, the value of k8.1 required to simulate an
OH time-history that fits the experimental data is dependent on the values of brOH,
and brβ in the mechanism. With the current kinetic mechanism, however, it was
found that for any value of brOH from 0.5 to 1.0 and brβ from 0.2 to 0.8, the value
of k8.1 required to simulate an OH time-history that matches the measured OH time-
history leads to a constant product of k8.1 · (1 − brOH · brβ) (assuming that the rate
constants for k8.2a and k8.2b are of reasonable orders of magnitude ≥ 105 s−1).
Figure 8.2 shows the simulated OH time-history from the kinetic mechanism that
best matches the measured data, and the simulated OH time-history with the product
of k8.1 · (1 − brOH · brβ) perturbed by ±30%. The simulated OH time-history with
k8.1 · (1 − brOH · brβ) perturbed by ±30% is independent of which parameter in the
product is perturbed to introduce an overall perturbation of ±30%. The values for
the product of k8.1 · (1− brOH · brβ) from the measured OH time-histories are listed in
Table 8.2 and differ from the values of k′′ listed in Table 8.1 due to secondary reactions
of OH, most of which occur due to the decomposition products of TBHP as the OH
precursor. The measured values of k8.1 · (1− brOH · brβ) are shown in Figure 8.5, and
can be described by the Arrhenius expression in Eq. 8.8, valid for the temperature
range 902 to 1197 K.
k8.1 · (1− brOH · brβ) = 2.62× 10−11 exp
(− 2435
T [K]
)cm3molecule−1s−1 (Eq. 8.8)
The overall rate constant for the reaction of OH with tert-butanol can be deter-
mined if the branching ratios brOH and brβ are known. Figure 8.6 presents values for
140 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
k8.1 for different values of brOH and brβ, illustrating the sensitivity of the determina-
tion of k8.1 from the current data to the branching ratios. The closer the branching
ratio brβ approaches the value 1.0, the more influence the branching ratio brOH has on
the determination of the rate constant for Reaction (8.1). To the author’s knowledge,
no studies, experimental or otherwise, have focused on the rate constants for the re-
actions involved in brOH and brβ or the branching ratios themselves. In the following
section, values for the branching ratios are estimated given the information currently
available in the literature.
0.8 0.9 1.0 1.1 1.2
1
10
k8.
1 * (1
- br
OH*b
r β )
[10-1
2 cm
3 mol
ecul
e-1 s
-1]
1000/T [K-1]
Current data (solid line: fit)Calculated from Mechanisms
Sarathy et al. (2012) Grana et al. (2010) Van Geem et al. (2010)
1250 K 1111 K 1000 K 909 K 833 K
Figure 8.5: Arrhenius plot of the product of k8.1 · (1− brOH · brβ) determined at each experimentaltemperature from the measured OH time-histories, and an Arrhenius fit to the data. The productk8.1 · (1− brOH · brβ) describes the net rate of OH decay due to the reaction OH + tert-butanol. Alsoshown is the product k8.1 · (1 − brOH · brβ) computed using the rate constants from three detailedmechanisms for high-temperature tert-butanol oxidation [37, 40, 91].
8.4. KINETIC MODELING 141
0.8 0.9 1.0 1.1 1.21
10
brOH = 0.95, brβ = -4.37x10-4T + 1.23
brβ=0.2brβ=0.4
brβ=0.6
brOH = 1.00 brOH = 0.95 brOH = 0.90
1250 K 1111 K 1000 K 909 K 833 K
k 8.1 [
10-1
2 cm
3 mol
ecul
e-1 s
-1]
1000/T [K-1]
brβ=0.8
Reaction (8.1): (CH3)3COH + OH -> Products
Figure 8.6: Arrhenius plot of the overall rate constant for Reaction (8.1) with various values for brOH
and brβ illustrating the sensitivity of the rate constant for Reaction (8.1) to these branching ratios.Also shown is the rate constant for Reaction (8.1) determined from the experiments assuming thebranching ratios evaluated in Section 8.5.
Table 8.2: Rate constants determined for each experimental temperature. The product k8.1 · (1 −brOH · brβ) describes the rate of OH decay due to reaction with tert-butanol, independent of the OHprecursor. The branching ratio brβ and overall rate constant for Reaction (8.1) determined usingthe analysis discussed in Sections 8.5 and 8.6 are also given. ‡Units of second order rate constantsis [cm3molecule−1s−1].
Mixture T [K] P [atm] k8.1 · (1− brOH · brβ) ‡ brβ k8.1‡
307 ppm tert-butanol 1197 0.93 3.48 ×10−12 0.71 1.06 ×10−11
15 ppm TBHP 1166 0.98 3.22 ×10−12 0.72 1.02 ×10−11
1162 0.97 3.24 ×10−12 0.72 1.03 ×10−11
1113 0.99 2.87 ×10−12 0.74 0.98 ×10−11
1079 1.03 2.64 ×10−12 0.76 0.94 ×10−11
1020 1.05 2.44 ×10−12 0.78 0.96 ×10−11
974 1.15 2.29 ×10−12 0.80 0.97 ×10−11
445 ppm tert-butanol 1058 1.06 2.79 ×10−12 0.77 1.03 ×10−11
16 ppm TBHP 1004 1.13 2.17 ×10−12 0.79 0.87 ×10−11
962 1.16 2.07 ×10−12 0.81 0.90 ×10−11
943 1.20 1.87 ×10−12 0.82 0.84 ×10−11
902 1.21 1.81 ×10−12 0.84 0.88 ×10−11
142 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
8.5 Branching Ratio Determinations
8.5.1 Evaluation of brOH
The branching ratio brOH represents the fraction of the reaction of OH with tert-
butanol that proceeds via Reaction (8.1a), the product channel that leads to sub-
sequent OH production. Reaction (8.1a) is the result of hydrogen-atom abstraction
from the tert-butyl group, where nine hydrogen atoms exists, each with a approx-
imately equal probability of abstraction. The other channel of the reaction of OH
with tert-butanol, Reaction (8.1b), results from hydrogen-atom abstraction from the
alcohol group where there is only one hydrogen atom available for abstraction. The
rate of abstraction of the hydrogen atom on the alcohol group via Reaction (8.1b)
is expected to be slower than the abstraction of a single hydrogen on the tert-butyl
group based on bond energy arguments. Therefore, the value of the branching ratio
brOH is expected to be no less than 9/(9 + 1), or, in other words, between 0.9 and
1.0. This is consistent with the branching ratio calculated from the rate constants
for Reactions (8.1a) and (8.1b) used in the Grana et al. [40] and Sarathy et al. [91]
butanol oxidation mechanisms. A branching ratio brOH = 0.95 will be assumed in the
current work with a conservative uncertainty of ±5%.
8.5.2 Evaluation of brβ
The branching ratio brβ represents the fraction of the (CH3)2(CH2)COH radicals
that decomposes via Reaction (8.2a) to regenerate an OH radical. Figure 8.7 shows
the temperature dependence of brβ calculated with the rate constants for Reac-
tions (8.2a) and (8.2b) from the tert-butanol oxidation mechanisms of Van Geem
et al. [37] and Sarathy et al. [91]. The detailed mechanism of Grana et al. [40] does
not include Reaction (8.2b), however, a non-OH-producing decomposition channel
of (CH3)2(CH2)COH −→ CH3COCH3 + CH3 is included in the mechanism, and the
products of this reaction are not expected to significantly affect the simulated OH
time-history differently than the products of Reaction (8.2b). Thus, a branching ratio
8.5. BRANCHING RATIO DETERMINATIONS 143
brβ can still be calculated from the Grana et al. mechanism representing the frac-
tion of the (CH3)2(CH2)COH radical that decomposes to form an OH radical versus
other non-OH products; this calculated value from the Grana et al. mechanism is also
shown in Figure 8.7. The three mechanisms predict values for the branching ratio brβ
that vary by up to a factor of seven over the current experimental temperature range,
motivating a detailed estimation for the branching ratio brβ based on the literature.
0.8 0.9 1.0 1.1 1.20.0
0.2
0.4
0.6
0.8
1.01250 K 1111 K 1000 K 909 K 833 K
brβ =
k8.
2a /
( k8.
2a+
k 8.2b
)
1000/T [K-1]
Current recommendation Sarathy et al. (2012) Grana et al. (2010) Van Geem et al. (2010)
Figure 8.7: The temperature-dependent branching ratio brβ computed using the rate constants inthree detailed mechanisms from the literature, and the current recommendation of brβ = −4.37 ×10−4T + 1.23 based on rate constants from Bozzelli and coworkers [131, 132].
Bozzelli and coworkers [131, 132] have several works that suggest rate constants
relevant to estimating brβ. Chen and Bozzelli [131] analyzed the mechanism of tertiary
butyl oxidation and suggest a high-pressure limit rate constant for Reaction (8.2b)
based on thermodynamic properties from THERM group additivity and the addition
rate constant for OH with iso-butene from Mallard et al. [133]. QRRK analysis was
used to determine the rate constant for Reaction (8.2b) at 1 atm; their 1-atm rate
constant for Reaction (8.2b) is given in Eq. 8.9. Sun and Bozzelli [132] use canonical
transition-state theory to calculate the high-pressure-limit unimolecular rate constant
for the decomposition of the neo-pentyl radical to iso-butene plus a methyl radical.
Using the rate constant and thermodynamic data in their publication, the rate con-
stant for the addition reaction of methyl to iso-butene can be computed. In the
144 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
current work, the assumption is made that the rate constant of the addition reaction
of a methyl radical plus iso-butene is equivalent to the rate constant for the addition
reaction of a methyl radical plus propen-2-ol, the reverse of Reaction (8.2b), therefore,
a calculation of the reverse rate constant yields the high-pressure-limit rate constant
for Reaction (8.2b). To compute the reverse rate constant, the thermodynamic data
for propen-2-ol were estimated from the group additivity values of Khan et al. [134]
and the thermodynamic data for the (CH3)2(CH2)COH and the methyl radicals were
taken for from Chen and Bozzelli [131]. To estimate the pressure dependence of the
rate constant for Reaction (8.2b), the Kassel integral was applied to the high-pressure
limit rate constant (see Appendix E) using S = 14 (chosen as the parameter that pre-
dicts the pressure-dependence for the rate constant for Reaction (8.2a) calculated by
Chen and Bozzelli using a QRRK method). The 1-atm rate constant inferred for
Reaction (8.2b) is given by Eq. 8.10.
Using rate constants based on the work of Bozzelli and coworkers [131, 132], the
temperature-dependent branching ratio brβ is estimated to be bound between 0.70
and 0.85 in the current experimental temperature range, and the current estimated
value is shown in Figure 8.7. The current recommendation for the branching ratio
brβ can be expressed by Eq. 8.11.
k8.2a = 2.33× 1045 · T−9.88 · exp
(− 20612
T [K]
)s−1 (Eq. 8.9)
k8.2b = 2.27× 1041 · T−8.53 · exp
(− 22035
T [K]
)s−1 (Eq. 8.10)
brβ = −4.37× 10−4T + 1.23 (Eq. 8.11)
The current evaluation of brβ shows excellent agreement with the corresponding
branching ratio calculated using the rate constants in the Sarathy et al. [91] mech-
anism. However, the performance of the Sarathy et al. [91] mechanism, or any of
the mechanisms examined, also depends on the mechanism’s rate constant of Reac-
tion (8.1a) and (8.1b), which are typically determined independently of the branching
ratio brβ. The performance of each of the mechanisms examined is discussed in the
Section 8.6.1.
8.6. OVERALL RATE CONSTANT DETERMINATION 145
8.6 Overall Rate Constant Determination
With knowledge of the branching ratios brOH and brβ, the overall rate constant for Re-
action (8.1) can be determined from the measurements of the net rate of OH removal
from reaction with tert-butanol that were presented in Section 8.4.1. The overall rate
constant for each of the experimental temperatures is shown in Figures 8.6 and 8.8,
and can be summarized in Arrhenius form by Eq. 8.12, valid for the temperature
range 902 to 1197 K.
k8.1 = 1.91× 10−11 · exp
(− 725
T [K]
)cm3molecule−1s−1 (Eq. 8.12)
The rate constants determined for each experimental temperature are also presented
in Table 8.2.
1 2 3 40.1
1
10
k 8.1 [1
0-12 c
m3 m
olec
ule-1
s-1]
1000/T [K-1]
Current work 3-parameter fit
Literature Data Wu et al. (2003) Saunders et al. (2002) Teton et al. (1996) Wallington et al. (1988) Cox and Goldstone
(1982)Mechanisms
Sarathy et al. (2012) Grana et al. (2010) Van Geem et al. (2010)
SAR Bethel et al. (2001)
1000 K 500 K 333 K 250 K
Reaction (8.1): (CH3)3COH + OH -> Products
Figure 8.8: Arrhenius plot of experimental determinations for the overall rate constant for thereaction of OH with tert-butanol and the best-fit 3-parameter expression of k8.1 = 8.93 × 10−20
·T 2.60 exp(450/T [K]) cm3molecule−1s−1. Also shown is comparison with the corresponding rateconstant used in three detailed mechanisms [37, 40, 91] and the structure-activity relationship ofAtkinson and coworkers [20–22] with the most up-to-date parameters from Bethel et al. [90].
146 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
An uncertainty analysis for the current measurements of the net rate of OH re-
moval from reaction with tert-butanol was conducted, and an overall ±14% uncer-
tainty was found for the product k8.1 · (1 − brOH · brβ), accounting for uncertainty
in temperature, pressure, initial TBHP and tert-butanol concentration, laser noise,
impurities, unimolecular reaction of tert-butanol, and rate constants for secondary
reactions in the TBHP mechanism. The uncertainty in the determination of the rate
constant for Reaction (8.1), however, is larger due to the uncertainties in the branch-
ing ratios brOH and brβ. If the uncertainty of each of the rate constants from the
work of Bozzelli and coworkers [131, 132] is taken to be a factor of two, the total
uncertainty in the rate constant for Reaction (8.1) is approximately a factor of two.
The largest uncertainty factor in the rate constant determination is the uncertainty
in the branching ratio brβ; thus, further studies on this branching ratio or the rate
constants for Reactions (8.2a) and (8.2b) are recommended.
8.6.1 Comparisons to Mechanism Predictions
The accuracy of three detailed mechanisms containing tert-butanol oxidation kinetics
was examined in regards to their ability to predict the net rate of OH removal due to
reaction with tert-butanol, and the overall rate constant used for Reaction (8.1) in
each mechanism was also assessed. Figure 8.5 shows the product of k8.1 ·(1−brOH ·brβ)
determined from the rate constants in the Van Geem et al. [37], Grana et al. [40],
and Sarathy et al. [91] mechanisms in comparison with the currents measurements.
Agreement of the product of k8.1 · (1 − brOH · brβ) in a mechanism with the current
determination of the product is the indicator of whether the OH time-histories would
be correctly simulated under the current conditions. The Van Geem et al. mechanism
has rate constants for Reactions (8.1a), (8.1b), (8.2a), and (8.2b) that lead to a value
of k8.1 · (1− brOH · brβ) that best matches the current measured value, and thus this
mechanism is capable of predicting within 20% the measured net rate of OH removal
from the pseudo-first-order reaction of OH with tert-butanol. The Sarathy et al.
mechanism also will show good agreement in the prediction of the OH time-history
near 1200 K; however, the mechanism predicts a net pseudo-first-order rate constant
8.6. OVERALL RATE CONSTANT DETERMINATION 147
that is a factor of two too slow near 900 K. The Grana et al. mechanism predicts a
pseudo-first-order rate constant that is a factor of four faster than the current data.
Because a mechanism may correctly predict the OH time-histories of the current
measurements with only the correct product of k8.1 · (1 − brOH · brβ), there is a pos-
sibility for large errors to be present in the individual rate constants that cancel out.
Because the rate constant for Reaction (8.1) in a mechanism is typically determined
independently from the rate constants included in the branching ratio brβ, both the
rate constant for Reaction (8.1) and the branching ratio brβ must be examined, and
reasonable values for these parameters should be used to improve the mechanism’s
performance over a wide range of conditions. As was previously shown in Figure 8.7,
the Sarathy et al. [91] mechanism uses a value for brβ in best agreement with the cur-
rent determination, while the Van Geem et al. [37] and Grana et al. [40] mechanisms
used rate constants yielding brβ values much lower than the current determination.
Figure 8.8 presents a comparison of the current determination of the rate constant
for Reaction (8.1) in comparison to the value used in the three mechanisms from
literature. Analysis of Figures 8.5, 8.7 and 8.8 together can elucidate the accuracy of
the rate constants used in each mechanism.
The Grana et al. [40] mechanism uses an overall rate constant for Reaction (8.1)
that is in good agreement with the current determination, considering the overall un-
certainty (Figure 8.8); however, their value of the branching ratio brβ is much lower
than the current determination (Figure 8.7). This suggests that updating the rate
constant to Reaction (8.2a) and/or including Reaction (8.2b) as a non-OH-producing
decomposition pathway of the (CH3)2(CH2)COH radical in the Grana et al. mech-
anism would improve the mechanism’s ability to predict the current measured OH
time-histories.
The overall rate constant for Reaction (8.1) used in the Sarathy et al. [91] mech-
anism also shows good agreement with the current determination near 1200 K (Fig-
ure 8.8), and the current determination of the branching ratio brβ is excellent agree-
ment with their rate constants over the entire temperature range (Figure 8.7). How-
ever, as the temperature decreases, the product of k8.1 · (1 − brOH · brβ) from the
148 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
Sarathy et al. mechanism begins to deviate from the current data (Figure 8.5). In-
creasing the overall rate constant for Reaction (8.1) in the Sarathy et al. mechanism
at temperatures below 1200 K would improve the agreement between their model
simulations and the current measured OH time-histories over the temperature range
900 to 1200 K.
While the Van Geem et al. [37] mechanism predicts the measured net OH decay
rate best (Figure 8.5), their mechanism uses an overall rate constant for Reaction (8.1)
that is a factor of 3 slower than the current determination (Figure 8.8). Their branch-
ing ratio brOH is also over a factor of two smaller than the current recommendation
of 0.95 that was presented in Section 8.5 based on counting hydrogen atoms and
energy arguments. Changes to the relative rate constants between Reactions (8.1a)
and (8.1b) that also increase the overall value of the rate constant for Reaction (8.1)
are recommended for the Van Geem et al. mechanism to improve the accuracy of the
rate constants used in their mechanism.
8.6.2 Comparisons to Low-temperature Literature
Measurements for the overall rate constant for the reaction of OH with tert-butanol
have also been performed by Cox and Goldston [125], Wu et al. [111], Wallington et
al. [126], Teton et al. [127], and Saunders et al. [128] in the temperature range 240 to
440 K, and these data are shown with the current determination of the rate constant
for Reaction (8.1) in Figure 8.8. The three-parameter modified Arrhenius expression
given in Eq. 8.13 fits all the measured data for the temperature range 240 to 1197 K.
k8.1 = 8.93× 10−20T 2.60 exp
(+
450
T [K]
)cm3molecule−1s−1 (Eq. 8.13)
The structure-activity relationship (SAR) of Atkinson and coworkers [20–22, 90]
can be used to estimate the overall rate constant for the reaction of OH with tert-
butanol (see Appendix D for details of the structure-activity relationship). Bethel
et al. [90] shows that this method can predict the rate constant for Reaction (8.1)
well at 298 K using their revised substituent factor that accounts for effects of the
8.7. CONCLUSIONS 149
alcohol group as far as the β position, and comparison of the measured data with the
SAR-calculated rate constant is shown in Figure 8.8. However, the SAR method is
extrapolated to higher temperatures using the temperature-dependence suggested by
Atkinson, the SAR-calculated rate constant overpredicts the rate constant for Reac-
tion (8.1) at all temperatures above 298 K, including all temperatures in the current
experimental conditions. This discrepancy is larger than the factor of two uncertainty
in the current rate constant determination. Bethel et al. reports significant disagree-
ments of calculated rate constants with measurements for several hydroxy-containing
compounds using the general approach of Atkinson, and therefore the disagreement
of the SAR-calculated rate constant with the current high-temperature data is not
unexpected.
8.7 Conclusions
OH time-histories were measured during the pseudo-first-order reaction of OH with
tert-butanol, where the initial tert-butanol-to-OH concentration ratio was in excess
of 30:1 and tert-butylhydroperoxide (TBHP) was used as the OH precursor. From
these measurements, the following rates were determined: the net rate of pseudo-first-
order OH decay, the net rate of OH decay due to reaction with tert-butanol (without
influence of TBHP as the OH precursor), and the overall rate constant for the reaction
of OH + tert-butanol → Products. To facilitate these rate constant determinations,
a kinetic mechanism with TBHP and tert-butanol kinetics was developed, which in-
cluded evaluation of important branching ratios in the kinetic system. Comparison
of the current results to three tert-butanol combustion mechanisms [37, 40, 91] pub-
lished in the literature reveal that improvements to each of these mechanism must be
made to correctly simulate the measured OH time-histories. Recommendations are
made on which key rate constant parameters in the mechanisms can be adjusted to
best improve the agreement of the simulated OH time-history with the experimental
data. To the author’s knowledge, this is the first experimental study on the high-
temperature oxidation kinetics of tert-butanol designed with high-sensitivity to key
rate constant parameters.
150 CHAPTER 8. REACTION OF OH WITH TERT-BUTANOL
Chapter 9
Concluding Remarks
9.1 Summary of Work
The objective of the research presented in this thesis was to expand the experimental
database of rate constants for reactions of the hydroxyl radical (OH) with different
types of organic compounds that are of current interest as transportation fuels. The
organic compounds of interest fell in the category of either a normal alkane molecule or
an isomer of the butanol molecule. Using a narrow-linewidth laser absorption diagnos-
tic to quantitatively measure OH mole-fraction time-histories behind reflected shock
waves, experiments were designed with high sensitivity to the rate constants of inter-
est, including overall rate constants for Reactions (4.1), (4.2), (4.3), (5.1), (6.1), (7.1),
and (8.1).
C5H12 + OH −→ Products (4.1)
C7H16 + OH −→ Products (4.2)
C9H20 + OH −→ Products (4.3)
CH3CH2CH2CH2OH + OH −→ Products (5.1)
(CH3)2CHCH2OH + OH −→ Products (6.1)
CH3CH(OH)CH2CH3 + OH −→ Products (7.1)
(CH3)3COH + OH −→ Products (8.1)
151
152 CHAPTER 9. CONCLUDING REMARKS
For all these experiments, tert-butylhydroperoxide (TBHP) was used as a fast
source of OH radicals. To support the current research objectives, the rate constants
for Reactions (3.1) and (3.3), which are important in simulating the OH time-history
during decomposition of TBHP, were also measured.
(CH3)3COOH −→ (CH3)3CO + OH (3.1)
CH3 + OH −→ CH2(s) + H2O (3.3)
The rate constants for Reactions (3.1) and (3.3) can be described by Eq. 3.2
and Eq. 3.3, respectively.
k3.1 = 3.57× 10+13 exp
(− 18000
T [K]
)s−1 (Eq. 3.2)
k3.3 = 2.74× 10−11 cm3molecule−1s−1 (Eq. 3.3)
The rate constants for Reactions (3.1) and (3.3) are valid over the experimental tem-
perature ranges of this study (approximately 900 to 1400 K) and have an estimated
uncertainty of ±30%.
The measured rate constants for the reactions involving the n-alkanes can be
summarized in Arrhenius form by Eq. 4.5, Eq. 4.6, and Eq. 4.7 for a temperature
range of approximately 860 to 1360 K.
k4.1 = 2.10× 10−10 exp
(− 2038
T [K]
)cm3molecule−1s−1 (Eq. 4.5)
k4.2 = 2.43× 10−10 exp
(− 1804
T [K]
)cm3molecule−1s−1 (Eq. 4.6)
k4.3 = 3.17× 10−10 exp
(− 1801
T [K]
)cm3molecule−1s−1 (Eq. 4.7)
These rate constant determinations improve upon similar previous works because
of improved accounting for the kinetics of TBHP as an OH precursor. Furthermore,
9.1. SUMMARY OF WORK 153
systematic errors due to impurities and uncertainty in mixture composition were min-
imized using laser absorption techniques. The overall uncertainty in the rate constant
measurements for Reactions (4.1), (4.2), and (4.3) are ±11% for temperatures from
1000 to 1364 K; the overall uncertainty increases with decreasing temperature below
1000 K, up to approximately ±23% at 869 K. The current results demonstrate that
the structure-activity relationship (SAR) developed by Atkinson [20], updated with
parameters by Kwok and Atkinson [22], can be extrapolated to temperatures up to
1364 K to accurately predict the overall rate constants for Reactions (4.1), (4.2),
and (4.3). This SAR method is recommended for predicting the overall rate constant
for reactions in the family of OH plus n-alkanes.
Rate constants for the reactions of OH with the isomers of butanol were deter-
mined from measured OH time-histories in shock-heated mixtures of OH (generated
from fast decomposition of TBHP) with butanol in excess. To facilitate the rate con-
stant determination and account for secondary chemistry, kinetic mechanisms that
accurately simulate the OH time-history during TBHP decomposition were modi-
fied by the addition of important OH-forming and OH-consuming reactions related
to butanol molecules. The results suggest the overall rate constants described by
Eq. 5.2, Eq. 6.6, Eq. 7.1 and Eq. 8.12, valid over a temperature range of approxi-
mately 900 to 1200 K.
k5.1 = 3.24× 10−10 exp
(− 2505
T [K]
)cm3molecule−1s−1 (Eq. 5.2)
k6.1 = 1.85× 10−10 exp
(− 2155
T [K]
)cm3molecule−1s−1 (Eq. 6.6)
k7.1 = 6.97× 10−11 exp
(− 1550
T [K]
)cm3molecule−1s−1 (Eq. 7.1)
k8.1 = 1.91× 10−11 exp
(− 725
T [K]
)cm3molecule−1s−1 (Eq. 8.12)
Figure 9.1 presents the rate constants for the reactions of OH with each isomer of
butanol in a single Arrhenius plot. The rate constants follow the order of n-butanol
154 CHAPTER 9. CONCLUDING REMARKS
(fastest), iso-butanol, sec-butanol, and tert-butanol (slowest). This is the same or-
der that the ignition delay times for the isomers of butanol follow (with n-butanol
having the shortest ignition delay time and tert-butanol having the longest ignition
delay time) as found in shock tube experiments by Stranic et al. [35], supporting the
notion that in a combustion reaction the reaction of OH with the oxidizing fuel is an
important reaction pathway to ignition.
0.8 0.9 1.0 1.1 1.20.1
1
10
(5.1) OH + n-Butanol(6.1) OH + iso-Butanol(7.1) OH + sec-Butanol(8.1) OH + tert-Butanol
k OH
+ B
utan
ol ->
Pro
duct
s
[10-1
1 cm
3 mol
ecul
es-1 s
-1]
1000/T [K-1]
1250 K 1111 K 1000 K 909 K 833 K
Figure 9.1: Arrhenius plot of the rate constant determinations for Reactions (5.1), (6.1), (7.1),and (8.1) from the current work. The error bars represent the estimated uncertainty due to experi-mental and modeling uncertainties.
The rate constant determinations for Reactions (5.1), (6.1), (7.1), and (8.1)
are sensitive to rate constants for secondary reactions related to decomposi-
tion of the respective butanol isomers. Thus, each rate constant provided by
Eq. 5.2, Eq. 6.6, Eq. 7.1 and Eq. 8.12 has a different level of uncertainty, as illus-
trated in Figure 9.1. In the current analysis, the best-known rate constants were
ascribed to the important secondary OH-forming and OH-consuming reactions in the
system to minimize the uncertainty in the overall rate constant. For the experiments
investigating reactions with iso-butanol and tert-butanol, the kinetic parameters de-
scribed by Eq. 6.4 and Eq. 8.8 were also determined, respectively, in addition to the
9.1. SUMMARY OF WORK 155
overall rate constant.
knon-β6.1 = 1.84× 10−10 exp
(− 2, 350
T [K]
)cm3molecule−1s−1 (Eq. 6.4)
k8.1 · (1− brOH · brβ) = 2.62× 10−11 exp
(− 2435
T [K]
)cm3molecule−1s−1
(Eq. 8.8)
These kinetic parameters approximately represent the rate of OH decay due to the
reaction of OH with the respective butanol isomer, and the determined expressions
were found to have reduced sensitivity to secondary rate constant parameters. The
kinetic expressions given by Eq. 6.4 and Eq. 8.8 can be useful for validating high-level
ab initio rate constant calculations, and also to validate and refine detailed kinetic
mechanisms describing the combustion of iso-butanol and tert-butanol, respectively.
The current high-temperature rate constant measurements can be combined with
the data available in the literature reporting measurements of rate constant measure-
ments at atmospheric-relevant conditions to generate empirical 3-parameter fits for
the rate constants for Reactions (5.1), (6.1), (7.1), and (8.1) at intermediate temper-
atures. These three-parameter fits, expressed in a modified Arrhenius form, are given
by Eq. 5.3, Eq. 6.7, Eq. 7.2, and Eq. 8.13.
k5.1 = 1.78× 10−21T 3.22 exp
(+
1160
T [K]
)cm3molecule−1s−1 (Eq. 5.3)
k6.1 = 1.65× 10−21T 3.18 exp
(+
1304
T [K]
)cm3molecule−1s−1 (Eq. 6.7)
k7.1 = 4.95× 10−20T 2.66 exp
(+
1123
T [K]
)cm3molecule−1s−1 (Eq. 7.2)
k8.1 = 8.93× 10−20T 2.60 exp
(+
450
T [K]
)cm3molecule−1s−1 (Eq. 8.13)
Eq. 5.3, Eq. 6.7, Eq. 7.2, and Eq. 8.13 are purely empirical relations that can be useful
for interpolating rate constants at intermediate temperatures.
156 CHAPTER 9. CONCLUDING REMARKS
9.2 Implications for Addressing Global Challenges
The rate constants presented in this thesis for reactions of OH with n-alkanes and iso-
mers of butanol succeed in extending the experimental database of high-temperature
kinetic measurements for molecules relevant to transportation fuels. The results of
this thesis can be applied to the improvement of detailed kinetic mechanisms describ-
ing the combustion of current practical and surrogate fuels (e.g. commercial gasoline,
gasoline surrogates) and the next-generation biofuel (biobutanol). With the capability
to create accurate detailed kinetic combustion mechanisms for transportation fuels,
multi-scale combustion modeling capabilities can be improved and utilized to opti-
mize the design and operation of advanced transportation engines burning evolving
fuels, addressing our nation’s and world’s energy needs.
9.3 Recommendations for Future Work
9.3.1 Alkane Combustion Kinetics
The experimental techniques described in this thesis can be extended to the study
of high-temperature rate constants for reactions of OH with larger n-alkanes (≥C10)
and branched alkanes to expand the experimental kinetic database for other alkane
molecules important in the understanding of transportation fuels. n-Decane and n-
dodecane are popular surrogates for diesel and jet fuels, respectively, and iso-octane is
a primary reference fuel. Very few experimental studies have been reported in the lit-
erature regarding the rate constants for reactions of OH with these alkane molecules.
The larger n-alkanes will have lower vapor pressures than the n-alkanes studied in
this thesis, and therefore techniques for working with with low-vapor pressure fuels
may need to be utilized, such as heating of the shock tube and gas-mixing facilities
or use of an aerosol shock tube. These techniques should be compatible with the
rate constant measurement methods developed in this thesis, though in experiments
with low vapor pressure fuels, it is especially recommended that the laser absorption
techniques described in this thesis, or other methods, be employed to verify initial
9.3. RECOMMENDATIONS FOR FUTURE WORK 157
fuel concentration. Furthermore, in experimental work with low vapor pressure com-
pounds, there is a higher tendency for impurities to build up on the surfaces of the
experimental facilities, and therefore the techniques for facility cleaning and impu-
rity detection described in this thesis should be utilized. Experimental measurements
of rate constants for larger n-alkanes and branched alkanes can be used to validate
the extrapolation of structure-activity relationship methods to more types of alkanes,
and these rate constant measurements can also lead to more accurate combustion
mechanisms for various transportation fuels.
9.3.2 Butanol Combustion Kinetics
The studies carried out in this thesis on the reactions of OH with butanol have
elucidated many areas relating to the high-temperature kinetics of the isomers of
butanol. Future work including both experimental and theoretical studies on certain
key reactions are recommended.
In the current work, assumptions on the branching ratios of the reactions of OH
with butanol were made in order to determine the overall rate constant. Improve-
ments in the understanding of these branching ratios would be of great importance in
advancing the understanding of biobutanol combustion. These branching ratios can
be studied via theoretical or experimental means. For example, the works of Zhou et
al. [88] and Zheng et al. [114] demonstrate the ability of ab initio methods to predict
branching ratios for the OH plus butanol reactions for the n-butanol and iso-butanol
isomers, respectively. These branching ratios can also be studied experimentally with
the use of isotopic substitution. Deuterium substitution has been previously used
by Carr et al. [135] and Tully and coworkers [129, 130] to determine branching ra-
tios in reactions of OH with alcohols; however, deuterium-substituted alcohols can
undergo ROD→ROH exchange, especially on stainless-steel surfaces, which intro-
duces difficulties in knowing the actual fraction of deuterium-substituted alcohol in
the experiments. Thus research efforts into methods for preventing this exchange
or quantifying it would support efforts to measure the branching ratios of the OH
158 CHAPTER 9. CONCLUDING REMARKS
plus butanol reactions. Tully and coworkers also performed experiments with an 18O-
labeled OH precursor; their experiments, however, were limited in temperature range
and their highest temperature studied was near 750 K. Further research on using an18O-labeled OH precursor for kinetic experiments near 1000 K is needed. Research
using 18O-labeled alcohols for kinetic studies is also another avenue of isotopic labeling
studies recommended for future work.
The reactions of the isomers of hydroxybutyl radicals are also important reaction
pathways in the high-temperature kinetics of the isomers of butanol. Certain hydrox-
ybutyl radicals have competing reaction pathways between an OH-producing channel
and a non-OH-producing channel. These competing reactions can be beta-scission
decomposition reactions or isomerization reactions. Because the formation and con-
sumption of OH radicals is an important process in any combustion reaction, the
competition between these decomposition channels of hydroxybutyl radicals is impor-
tant. The works of Zador and Miller [93] and Zhang et al. [102] have demonstrated
methods for calculating rate constants for beta-scission reactions of hydroxypropyl
and 1-hydroxybutyl radicals, respectively, and can be extended to studies of all iso-
mers of hydroxybutyl radicals. The experimental studies with isotopic labeling may
also provide some insight on the relative rate constants for reactions of the isomers
of hydroxybutyl radicals. With better understanding of the rate constants for reac-
tions of hydroxybutyl radicals, important branching ratios of hydroxybutyl radical
reactions can be determined.
The reaction of OH with tert-butanol is an especially good candidate to study
using isotopic substitution. Only two reaction channels are present in this reaction,
and the channel describing abstraction from the tert-butyl group is expected to lead to
some OH regeneration. While the radical product after H-atom abstraction from the
tert-butyl group, the hydroxybutyl radical (CH3)2(CH2)COH, is likely to decompose
to form an OH radical, a non-OH-producing channel is also present. The branching
ratios between these channels complicate the rate constant measurements carried
out in this thesis. However, if either the oxygen or hydrogen atom in the alcohol
group was labeled (with a 18O or D atom, respectively), then the OH regenerated
9.3. RECOMMENDATIONS FOR FUTURE WORK 159
after abstraction from the tert-butyl group does not interfere with the OH time-
history measurement, and thus an overall rate constant can be directly measured
with fewer interfering secondary reactions present. If the results are compared with
the experiments presented in the current work (using the non-isotope-labeled tert-
butanol), information about the important branching ratios can be determined.
An example suggested future experiment is to repeat the experiments in Chapter 8
using 18O-labeled tert-butanol, and assume negligible kinetic isotope effects. The OH
sensitivity analysis will show sensitivity of OH only the overall rate constant for
Reaction (8.1), and sensitivity to any branching ratios will be negligible. Therefore,
the overall rate constant for Reaction (8.1) can be determined from the measured
data. Because the product of k8.1 · (1− brOH · brβ) has been determined in the current
work and the branching ratio brOH can be estimated to a reasonable accuracy (see
Section 8.5), the branching ratio brβ can be determined by combining the results of
the current work and new measurements using 18O-labeled tert-butanol. The type
of measurement could yield the first experimental study on the branching ratio brβ.
The largest obstacle to completing this example experiment is financial because 18O-
labeled compounds must be custom synthesized from H182 O, and H18
2 O is an expensive
starting product.
160 CHAPTER 9. CONCLUDING REMARKS
Appendix A
Shock Tube Cleaning Techniques
A.1 Introduction
This appendix outlines a method for characterizing the cleanliness of a shock tube,
what to consider about impurities when running shock tube experiments, and various
procedures for eliminating impurities. Sample case studies of shock tube cleaning
anecdotes are presented, with all of the work being done on the Stanford Kinetics
Shock Tube (KST) in the Mechanical Engineering Research Laboratory (MERL room
112) at Stanford University. These methods should be applicable on other shock tubes
if the same assumptions and conclusions for appropriate cleaning methods for the KST
also apply. Suggestions on improvements in shock tube design to minimize the effect
of impurities on experiments are also made.
A.2 Background
Shock tube experiments for studying chemical kinetics can be highly sensitive to
impurities. For example, in ignition delay time studies of hydrogen combustion,
hydrogen atom impurities initially in the shock tube can cause the chain branching
reactions (i.e. H + O2 −→ OH + O) to occur sooner than when starting with pure
H2/O2 reactants. Additionally, kinetic rate constant measurements in shock tubes are
typically performed with low levels of reactants on the order of tens to hundreds of
161
162 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
ppm, such as the work described in this thesis, therefore, small ppm levels of impurities
can compose a substantial fraction of the starting material in an experiment. Before
designing a shock tube experiment, and during the analysis of data, it is important
to understand the level of impurities in the shock tube and how the data may be
affected.
Impurities
Understanding the type(s) and origin of impurities that will have an effect on ex-
periments will help one determine when one should be concerned about impurities
in shock tube experiments. In the combustion process, the role of radicals is impor-
tant, therefore, any artificial addition to the radical pool can have significant effect
on kinetic experiments. Because shock tube experiments generally involve organic
compounds (molecules containing carbon, and typically hydrogen), these molecules
can condense and/or adsorb onto the shock tube facility surfaces, and remain even
after long-term pumping of the facility using vacuum pumps. Compounds that are
liquid at room temperature with low room temperature vapor pressures (on the order
of tens of Torr or less) are more likely to “stick” to surfaces than compounds which
are gas-phase at room temperature. Upon shock heating, hydrogen atoms, methyl
radicals, and other alkyl fragments can separate from any molecules residing on the
shock tube walls and react with the high-temperature gases.
Kinetics Shock Tube
The Stanford Kinetics Shock Tube is a stainless steel shock tube of 14.13 cm inner-
diameter in both the 8.54-m long driven section and the 3.35-m long driver section.
This facility is described in detail in Chapter 2 of this thesis. Typical experiments
in this facility include ignition delay time measurements of gaseous and heavy hy-
drocarbon fuels (using on the order of a percent of fuel) and kinetic rate constant
measurements (using on the order of tens to hundreds of ppm of fuel). Between ex-
periments, the driven section is evacuated in two stages, first with a roughing pump
and then a turbo pump, and the driver section is evacuated with its own roughing
A.3. IMPURITY CHARACTERIZATION 163
pump. Experimental measurements in the Kinetics Shock Tube are typically per-
formed behind reflected shock waves at measurement ports located 2 cm from the
endwall.
The experimental mixtures are typically prepared in an internally-stirred 12-L
stainless steel mixing tank through a mixing manifold with 14-port mixing manifold
with 3/8” diameter stainless steel pipes before being introduced into the shock tube
driven section through the mixing manifold at a location 5.74 m from the shock tube
endwall. The mixing facility also has a two-stage evacuation procedure, with separate
roughing and turbo pumps than the shock tube. A schematic of the mixing facility
and the shock tube are shown in Figure A.1.
Mixing Tank
Total driver section length = 8.54 m
Diaphragm
Measurement location 2 cm from endwall
Mixture fill port 5.74 m
from endwall
Not to scale
Figure A.1: Schematic of the driven section of the Kinetics Shock Tube and gas-mixing facility.
A.3 Impurity Characterization
The purpose of cleaning the shock tube is to remove impurities, however, cleanliness
is always relative. It means nothing to say a shock tube is clean if no proper baseline
is set, and to set a baseline we must have a method to gage how clean a shock
tube actually is. This section will outline a method to quantitatively determine the
cleanliness of a shock tube, provide a case study of examining the cleanliness of the
Kinetics Shock Tube, and then discuss how one might go about deciding what clean
enough is.
164 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
Previous Work
The thesis of J.T. Herbon [52] (on p. 77) notes that the identity and character of
the shock tube impurities encountered are unknown, but were characterizable with
OH absorption. Herbon found in the Kinetics Shock Tube that “in 10% O2/Ar shock
tube experiment after large hydrocarbon experiments and cleaning and vacuuming,
still∼10 ppm OH formed at 1800 K equivalent to 8 ppm CH3. Flowing O2 directly into
the shock tube reduced this to 1 ppm at 1700 K.” Herbon’s observations also included
that impurities would accrue in the mixing tank as the residence time of the mixture
increased. To reduce impurities in the mixing tank, a separate turbomolecular pump
was installed for the mixing tank and mixing manifold and Herbon found that “using
a new cleaner mixing assembly 100% O2 shocks at 1750 K give 2 ppm OH. At 10%
O2 yielded 0.8 ppm at 1850 K and 2 ppm at 2150 K.”
Previous users of the shock tube facilities in the High-Temperature Gasdynamics
Laboratory at Stanford University have used the same OH absorption technique to
characterize the impurities in different shock tubes. Their (unpublished) results are
shown in Figure A.2. Impurities are present at higher levels at higher temperatures,
likely due to increased reactivity of radicals with O2 or faster decomposition of the
organic compounds “stuck” to the shock tube walls.
Procedure
OH absorption can be performed using a Spectra Physics 380 ring-dye cavity pumped
with Rhodamine 6G dye and frequency doubled using an AD*A intra-cavity crystal
(the same as the OH laser absorption system described in Chapter 2) to produce UV
laser light around 306.7 nm, where OH absorbs strongly from the A-X (0,0) band.
OH absorption measurements are typically performed at the experimental diagnostic
ports 2 cm from the shock tube endwall, and it is assumed that all experiments shown
in Figure A.2 are conducted there. A typical experiment involves filling the shock
tube with a mixture of O2/Ar, tuning the laser to an absorption feature (i.e. R1(5)
at 32606.54 cm−1), and measuring the absorption. Using absorption coefficients from
Herbon [52], the mole fraction of OH formed can be calculated, leading to an inference
A.3. IMPURITY CHARACTERIZATION 165
of the amount of hydrogen atom impurities in the shock tube required to generate
that amount of OH.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.01
0.1
1
101250K
After FuelExperiments
Equ
ival
ent H
-Ato
m Im
purit
ies
[ppm
]
1000/T [1/K]
HPST Petersen Kinetics Vasudevan Kinetics Herbon NASA Masten NASA Li
Incident Shock
2500K
Figure A.2: Impurity measurement history in the shock tube facilities of the High-TemperatureGasdynamics Laboratory at Stanford University (unpublished). Data are shown for three differentshock tube facilities.
Case Study of a Contaminated Shock Tube
The cleanliness of the Kinetics Shock Tube facility was examined in the process
of completing this thesis work. This work began after the shock tube was used for
experimentation to study the ignition delay times of heavy organic fuels. It is believed
that after the experiments, the shock tube driven section was cleaned with acetone-
soaked cotton rags. While the source of the impurities cannot be uncovered, the
locations where impurities are most deposited can be determined.
A commercial mixture of 2% O2/Ar, prepared by Praxair, was used to fill the
shock tube from several different fill locations:
• Through the mixing manifold through an unused port and into the mixing tank
where it was allowed to mix for at least 30 minutes (filled to ∼1 atm) before
166 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
being introduced into the shock tube, again through the mixing manifold.
• Through the mixing manifold through an unused port and directly into the
shock tube, bypassing the mixing tank.
• Directly to ports along the shock tube, completely bypassing the mixing mani-
fold and mixing tank. Ports exist at 2 cm, 70 cm, 130 cm, 250 cm, 574 cm, and
814 cm from the driven section endwall.
Depending on where the O2/Ar mixture was introduced into the shock tube, dif-
ferent amount of OH were formed in experiments at similar temperatures. These
experiments were repeated several times, indicating that these hot oxygen shocks
did nothing to remove any impurities. Figure A.3 shows sample OH time-history
measurements. OH is formed immediately after the reflected shock passing, and ex-
periments which allowed the oxygen mixture to reside in the mixing tank produced
the largest amount of OH, while filling from the mixing assembly also generated a
significant amount of impurities.
0 1 2 3 4 5 6
1
10
100
OH
mol
e fra
ctio
n [p
pm]
Time [ms]
Endwall 1640 K Diaphragm 1668 K Mixing Manifold 1654 K Mixing Tank 1668 K
OH time-histories in hot 2% O2/Argon shocks around 1655 K for different fill locations in the shock tube
Figure A.3: OH time-history measurements in hot 2% O2/Ar shocks near 1655 K for different filllocations in the shock tube. “Endwall” is a port 2 cm from the driven section endwall, “diaphragm”is a port 814 cm from the endwall, “mixing assembly” is through the manifold bypassing the mixingtank, and mixing tank is from the mixing tank after a 30 minute residence.
From these results, it can be concluded that the mixing tank and mixing assembly
are a major source of impurities. The shock tube, however, is also a major contributor
A.3. IMPURITY CHARACTERIZATION 167
to impurities, which can be seen in the experiments where the oxygen mixture is filled
directly into the shock tube at ports along the driven section. Figure A.4 shows the
peak OH mole fractions formed as a function of the fill location. The largest impurities
were observed to form when the oxygen mixture was filled furthest from the endwall,
and no impurities were visible when the oxygen mixture was filled at the diagnostic
location at the endwall. This indicates that a gaseous mixture introduced into the
shock tube will entrain any impurities as it propagates to the endwall. Therefore,
when cleaning the shock tube, the entire section between the filling location and
the measurement location must be cleaned, and it is not enough to just clean the
measurement location.
0 1 2 3 4 5 6 7 81
10
100
Filled directly into shock tube Fill through the mixing assembly Fill through the mixing tank
Equ
ival
ent H
-Ato
m Im
purit
ies
[ppm
]
Distance from the endwall [meters]
Endwall Diaphragm
Figure A.4: Peak OH mole fraction formed in hot 2% O2/Ar shocks around 1655 K as a function offill location.
These experiments were done at several temperatures and shown in Figure A.5
compared with the previous measurements in the kinetics shock tube, and it is obvious
that the shock tube is very dirty at this point. Figure A.5 also shows measurements
done after attempted cleaning of the shock tube by “baking” the shock tube at 60 ◦C
and using a turbomolecular pump to remove impurities. This method is shown to be
ineffective since the level of measured impurities after the “baking” does not change.
168 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.01
0.1
1
10
100
1000
Equ
ival
ent H
-Ato
m Im
purit
ies
[ppm
]
1000/T [1/K]
2500K 1667 K 1250 K 1000 K
Vasudevan/Herbon
Endwall
Diaphragm
Mixing manifold
Mixing tank
Amount of OH observed in hot shocks of 2% O2 in Argon
Mix manifold location
Previous Measurements(Assumed filled from endwall)
Vasudevan Herbon
Current Measurements(Before heated pumping)
Fill from diaphragm Fill through mixing tank Fill through mixing manifold Fill from endwall
Current measurements(After 5 days of pumping a heated shock tube)
Fill from diaphragm Fill from mixing manifold Fill from 2.5 m from endwall Fill form 70 cm from endwall Fill from 130 cm from endwall Fill from endwall
Figure A.5: Peak OH mole fraction formed in hot 2% O2/Ar shocks at various temperatures anddifferent fill locations and compared to previously taken data (unpublished).
This case study illustrates several important principles. First, the shock tube
facilities can get very dirty after months of ignition delay time experiments, even
after some cleaning is done. Even if the shock tube driven section is thought to
have been cleaned by “washing” with acetone-soaked rags, impurities can still exist.
Second, for high-temperature experiments in excess of 1500 K, up to 100 ppm of
equivalent H atoms originating from the facility surfaces can be present, which can
have a large impact on kinetic rate constant measurements. Impurities do have a
smaller impact at lower temperatures, however, so even at temperatures less than
1000 K, one should expect no more than ∼10 ppm of equivalent H atoms regardless
of the shock tube cleanliness state (at least if the assumption is made that the state
for this case study was “as dirty as a shock tube will get”). Third, because gas
mixtures can entrain impurities from contaminated surfaces, shock tube experiments
with mixtures introduced at the measurement location (in this case the endwall)
would eliminate the need to clean the entirety of the driven section.
A.3. IMPURITY CHARACTERIZATION 169
Modeling Impurities
In the previous section, it was found that up to 100 ppm of equivalent H-atoms in
the shock tube can be present, though as low as a few ppm have been previously
detected. The next question one might ask after finding out the level of impurities
in the shock tube is what to do about the impurities. If 100 ppm of impurities
has no noticeable effect on the experiments that are to be conducted, then spending
time cleaning the facility is just an exercise in compulsivity.1 To determine whether
the amount of impurities found in the shock tube have significant effect, detailed
kinetic mechanisms can be used. Many kinetic experiments performed are compared
with kinetic mechanisms, so it is likely a mechanism is already available describing
the kinetic system of interest. If not, a kinetic mechanism for a similar fuel can be
used. Because the source of the impurities is unknown, modeling them is not entirely
straightforward. Two simple options exist: 1. model the impurities as H atoms, and
run kinetic calculations with the planned experimental conditions, but with a starting
concentration of H atoms equal to the equivalent H-atom impurities measured, or 2.
because the impurities may also come from hydrocarbon fragments which can fall
apart during shock heating, modeling the impurities as methyl radicals may also
be appropriate. In this case, run kinetic calculation with the planned experimental
conditions, but with a starting concentration of CH3 equal to the equivalent H-atom
impurities measured divided by three. Larger hydrocarbon fragments can also be
considered in a similar manner.
If both simulations yield negligible effects on the desired result quantity of interest
(as compared to the simulations without any impurities in the initial composition),
then cleaning the shock tube may be unnecessary. If the calculations of the data you
are studying are sensitive to either form of impurities, cleaning the shock tube is a
good option. It should be noted, though, that kinetic mechanisms may not always
be accurate, and impurities can have a larger effect if the radical chemistry in the
1That said, however, this is only true if you uncover the impurities during your experimentalrun. Proper lab equipment sharing etiquette would require you to clean up the facility after yourselffor the next user, regardless of what their experiments are, or whose experiments deposited theimpurities on the facility to begin with
170 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
kinetic mechanism is in error. Therefore, always use proper judgment of the analysis
tool when making experimental decisions.
Notes on Characterizing Impurities
Using the OH laser to characterize the amount of impurities in the shock tube facility,
and examining where the majority of the impurities are, can be a very useful tool in
determine whether to and where to clean your shock tube. After cleaning the shock
tube, one should always re-characterize the impurity level to verify that the cleaning
was successful. If modeling indicated that less than 1 ppm of equivalent H-atom
impurities is needed for eliminating experimental sensitivity to impurities, then a
more sensitive diagnostic than the Spectra Physics cavity used for OH measurements
is necessary.
While characterizing the impurities is useful, it may not always be practical, for
example if the diagnostic is not set up, or if the researcher is not familiar with the
operation of the OH laser. In this case, all parts of the shock tube facility should
be cleaned frequently during experiments, and level of impurities can be estimated
based on past work.
A.4 Gas-mixing Facility Cleaning Methods
Because the mixing tank and mixing manifold can be a large source of impurities,
learning methods to clean them is essential. This section will discuss two different
methods of cleaning these. All examples discussed refer to data taken on the Kinetics
Shock Tube Facility.
Brute Force Disassembly for Cleaning
As described in Chapter 2, the mixing manifold is constructed with a central welded
piece of cross pipe of 3/8” diameter, and connected to various sources via Swagelok
stainless steel 8BK bellow valves which use PCTFE (Polychlorotrifluoroethylene)
A.4. GAS-MIXING FACILITY CLEANING METHODS 171
stem tips. Ultra-Torr fittings were used in connecting the values with the liquid
chemical components.
Brute force cleaning of the mixing assembly can be completed by removing all the
valves, thereby freeing the center piece of cross pipe to be cleaned as well. Each valve
can be disassembled into the valve body and the bellow section, so that the stem tips
and gaskets can be replaced. Each valve body can be cleaned using acetone-soaked
cotton swabs until no color residue comes off onto the swabs when used to abrasively
rub the valve surface. For components that are excessively dirty, they can be sent to
be professionally cleaned, or replacement parts can be purchased. The miscellaneous
parts, such as the Ultra-Torr fittings, and minor piping to other components, can also
be cleaned with acetone-soaked cotton swabs. New stem tips can be installed after
cleaning of the valve components.
The mixing tank can be disconnected from the manifold and disassembled. The
stainless steel body and brass mixing vanes can be cleaned by using a solvent such
as acetone, and scrubbing with cotton or cheesecloth rags. The mixing vanes can be
disassembled and the joints cleaned. If the interior of the mixing tank looks espe-
cially dirty, a professionally done electro-polish may be necessary. Prior to the work
presented in this thesis, the mixing tank body and mixing vanes were professionally
electro-polished.
The above procedure described the cleaning done on the mixing facility immedi-
ately before the start of the experiments presented in this thesis.
Chemical Cleaning
The brute force cleaning of the mixing assembly is very thorough, and allows all the
cracks and crevices in the assembly to be cleaned. However, that method requires
disassembly of the entire mixing assembly, which is not always practical, especially
when chemicals frequently remain on the facility surfaces after only a few experiments.
After brute force disassembly and professional cleaning in the brute force method, all
impurities were eliminated from the mixing tank and manifold, however, after making
one mixture 1% n-nonane and argon, over 100 ppm of equivalent H-atom impurities
172 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
were found in the mixing tank, as illustrated by the measured OH time-histories
in Figure A.6. A simpler method of cleaning the mixing facility involves flushing
with peroxide chemicals, and does not require any disassembly of the mixing facility.
Before describing the procedure, Figure A.6 shows evidence for this working.
-1 0 1 2 3 4
0
50
100
150
200
250
300
-1 0 1 2 3 4
0
50
100
150
200
250
300
-1 0 1 2 3 4
0
50
100
150
200
250
300
Measurement after "flushing" with TBHP method (1382 K)
2% O2/Ar shocks, filled from mixing tank after residence for ~ 1 hour
Time [100 s]
Measurement after making one mixture in the "clean" mixing facility (1368 K)
OH
mol
e fra
ctio
n [p
pm]
Measurement after professional cleaning of mixing facility components in the brute force disassembly method (1350 K)
Figure A.6: OH time-histories measured in 2% O2/Ar shocks, filled into the shock tube from themixing facility after residence in the mixing tank for∼1 hour, illustrating that preparing mixtures canquickly contaminate the mixing assembly, and “flushing” with TBHP can improve the cleanliness.
tert-Butylhydroperoxide (TBHP) is used as the peroxide for cleaning, largely be-
cause it is also the OH precursor used for the kinetic experiments in this thesis and is
easily available and easy to handle. TBHP decomposes into OH, methyl, and acetone
(see Figure 3.1), and decomposition rates have been studied in Chapter 3. Upon
decomposition, the radicals can react with any organic molecules adhering to the fa-
cility walls, and either water or methane gas will form that can be evacuated from
the facility, removing hydrogen-containing impurities.
The procedure for “flushing” with the TBHP solution2 in the Kinetics Shock Tube
which was found to remove impurities is as follows:
2In this case, reference to the TBHP solution will refer to the commercially available solution of70%, by weight, TBHP in water from Sigma Aldrich, the same chemical described in Chapter 2 ofthis thesis.
A.5. SHOCK TUBE CLEANING METHODS 173
1. Heat the mixing tank and mixing manifold to 50 ◦C and isolate them from the
shock tube.
2. Place some amount of the TBHP solution in a glass storage vessel and attach to
the shock tube and attach it to a liquid fuel connector on the mixing manifold.
3. Use the mixing facility roughing pump to pump out the air in the glass vessel.
(not all of the air must be removed, just the majority of the vapor should be
from the TBHP solution).
4. Introduce approximately 7 to 14 Torr of the TBHP solution vapor into the
mixing tank and manifold.
5. Let sit and react overnight.
6. Pump out the TBHP solution vapor and any reacted products using the two-
step roughing and turbo pump procedure for the mixing facility. Overnight
pumping is recommended.
This procedure was the one followed to eliminate the impurities shown in Figure A.6.
While this cleaning procedure is simpler than disassembling the mixing assembly, it
is still a two-day process. The necessity of allowing the TBHP solution vapors to sit
and react overnight has not been scientifically proven, however, two hours of reacting
has been shown to be ineffective. Since water is likely formed in reactions during
“flushing,” a long pump out time is recommended.
A.5 Shock Tube Cleaning Methods
Because the shock tube was also shown to be a possible large contributor to hosting
impurities, methods for cleaning the shock tube itself must be examined. Several
methods for cleaning the shock tube exist, some being highly effective, some are
myths, and some have not yet been tested.
174 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
Cleaning Myths
Myth 1: Shock Tube Baking
Several research publications, including Herbon [52], have suggested baking the shock
tube and pumping on it overnight would drive any impurity residue off of the walls.
In Section A.3, experiments were performed that illustrate this to not be effective.
Myth 2: Cotton Rags
Researchers in the High Temperature Gasdynamics Laboratory at Stanford University
have, in the past, used the procedure of passing acetone-soaked cotton t-shirt rags
through the shock tube, using a plunger-like device with a slightly larger diameter
than the shock tube as the main cleaning method of the shock tubes. This was
done after ignition delay time experiments with heavy hydrocarbon fuels, and the
impurities remaining in the shock tube were characterized in Section A.3. This was
found to be largely ineffective, likely because the cotton rags are not very absorbent;
therefore, not a lot of solvent will be present on them during this type of cleaning, and
larger scrubbing forces would be required to remove any residue stuck to the surfaces.
After using a plunger device to pass acetone-soaked cotton rags through the Kinetics
Shock Tube, the cleanliness of the shock tube was tested by scrubbing the interior of
the shock tube with more acetone-soaked cotton rags by hand using larger scrubbing
forces (at the endwall and at the shock tube interior done by taking apart the shock
tube segments) and it was found that residue still came off of the walls. Therefore,
this cleaning technique will only work if larger scrubbing forces can be applied (i.e.
larger diameter plunger) or more solvent can be placed on the rags. A similar yet
superior cleaning technique is presented in the following subsection.
Solvent Cleaning with Cheesecloth Rags
Cheesecloth rags are many times more absorbent than cotton t-shirt rags. A test
of comparing the effectiveness of cleaning using an acetone-soaked cheesecloth rag
with an acetone-soaked t-shirt rag was performed by trying to clean old permanent
A.5. SHOCK TUBE CLEANING METHODS 175
marker writings from the optical tables. Using the acetone-soaked cotton rag, large
amounts of force were required to scrub the permanent marker clean, however, using
the cheesecloth rag soaked with acetone, only a feather-light wiping action was needed
because of the much larger amount of acetone released onto the surface upon contact.
Therefore, the acetone-soaked-cheesecloth-on-a-plunger technique for cleaning the
shock tube interior should be a superior technique to the cotton t-shirt rags.
Brute Force Disassembly for Cleaning
For a more thorough cleaning of the shock tube, all the divisions can be disassembled,
and the crevices cleaned. In this process, the o-ring and o-ring grooves can also be
replaced or cleaned. This process is recommended to be done periodically, and for
the Kinetics Shock Tube, takes approximately one to two weeks to complete. The
next paragraph of this subsection will report the brute force cleaning procedure used
prior to the start of the experiments conducted in this thesis.
The shock tube driver section is composed of two sections. The end cap of the
driver section was removed, and the section cleaned with acetone-soaked-cheesecloth-
on-a-plunger technique until the rags came out clean. The shock tube driven section
is composed of six pieces of large steel tube, of where each piece, except the two
nearest the endwall, is supported by two rollers and can traverse axially and rest
independently without being attached to another piece. The piece second closest to
the endwall is bolted to a concrete slab attached to the ground, and the endwall
section is removable entirely. The endwall section was unbolted first. The section
is heavy, requiring two average people to lift it. All the plugs were removed and
cleaned. Because the entire end section was fully removable and mobile, it was sent
to be professionally electro-polished. The unbolting of the rest of the driven section
had to begin at the diaphragm end because of where the shock tube was affixed to
the ground. The first section was unbolted. To create a larger space to separate
the sections to clean between, the diaphragm end section was raised such that the
side plug would not contact the end support. The tee-section was removed before
proceeding to the next section. The mechanical pumps were detached from the tee
176 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
section, as was the cooling fan of the turbo pump, and all other components that
were attached via a Kwik-flange fitting. The tee section was supported on a rolling
cart before being unbolted. This allowed for easy movement of the tee section after
unbolting. The rod seat was used to pull out the valve seat. All accessible areas of
the tee section were cleaned, and all the o-rings of the tee section replaced. The last
section of the shock tube was unbolted, cleaned, placed with a new o-ring, and then
bolted back together. All the shock tube sections and tee section were then bolted
back together. After unbolting and cleaning all the shock tube sections, all the plugs
were removed and cleaned, and the o-rings replaced. The unbolting and cleaning of
the entire shock tube took a fully dedicated six days (approximately 40 hours), with
more than two people working only on three of these days.
Untested Methods
Untested Method 1: Chemical Cleaning
The “flushing” method with the TBHP solution in theory should also work for the
shock tube, however, has not been tested to the author’s knowledge. However, when
extending the flushing method to the shock tube, one must take into consideration
that most shock tubes are not heated, and the reactions that contribute to the cleaning
of impurities during “flushing” are temperature dependent (and recall in the TBHP
“flushing” procedure the mixing assembly was heated to 50 ◦C). If the shock tube is
at room temperature, expect the cleaning process to occur more slowly because the
decomposition rate of TBHP is four orders of magnitude slower at room temperature
than at 50 ◦C (recall this rate constant was measured in Chapter 3, see Figure 3.7
for the results). If attempting to use TBHP “flushing” to clean the shock tube, it
is recommended that the shock tube walls are heated or the time intervals in the
procedure be extended.
A.6. ADDITIONAL COMMENTS 177
Untested Method 2: Non-hydrogen Containing Solvent
If cleaning using a solvent, one might be concerned with using a hydrogen-based
solvent because it might introduce more hydrogen into the shock tube. Trichlorotri-
fluoroethane is a non-hydrogen containing solvent, which has been shown to be stable
on stainless steel surfaces [136], and is an alternative for solvent cleaning.
A.6 Additional Comments
This appendix only covers shock tube cleaning to remove impurities. Proper mainte-
nance of the shock tube facilities include frequent cleaning and leak checks. The leak
checks should be performed after any brute force disassembly for cleaning. Mainte-
nance suggested by the manufacturer’s manuals for the pumps and other equipment
is also recommended.
Because impurities have been shown to build up in the shock tube facilities over
time, experimentalists should periodically check to ensure that their facilities are
clean. To keep track of what might be the causes of impurities, keeping an exper-
imental and maintenance log record is recommended, including information on the
date of experiments, chemical used, number of shocks, diaphragm thickness, cleaning
history, pump maintenance record, etc.
178 APPENDIX A. SHOCK TUBE CLEANING TECHNIQUES
Appendix B
Microwave Discharge System
B.1 Introduction
Improper alignment of the Burleigh WA-1000 visible wavemeter was found to lead
to errors of up to 0.05 cm−1 in the visible laser wavelength measurement. This was
discovered by using a Bristol 621 wavemeter to simultaneously measure the laser wave-
length. To check the accuracy of the wavelength measurements from these wavemeters
and further reduce concerns about errors in the wavelength measurement, a microwave
discharge of He/H2O was used to generate OH radicals; the absorption line center
position is known for OH, thereby allowing confirmation of the measured wavelength.
B.2 Equipment Setup and Procedure
An Opthos MPG-4 microwave generator was used with an Evenson cavity for this
experimental setup. An H2O saturator was created with an Erlenmeyer flask and
a 2-hole rubber stopper with 1/4” stainless-steel piping entering and exiting, and
Swagelok ball valves were also used. Figure B.1 shows a schematic of the microwave
discharge cell setup with an H2O saturator used for generating a pool of OH radicals.
The UV laser beam was split off from the laser setup described in Chapter 2 (see
Figure 2.4) using a UV-grade beam splitter and passed through the discharge cavity.
In-house modified PDA36A detectors were used to monitor both the incident and
179
180 APPENDIX B. MICROWAVE DISCHARGE SYSTEM
transmitted light intensities as the laser was tuned over the OH lineshape while the
visible laser wavelength was monitored with the Burleigh WA-1000 visible wavemeter.
The following procedure was used for in the operation of the microwave discharge
cell and H2O saturator:
1. Turn on the pump.
2. Turn the power control all the way counter clockwise on the Opthos MPG-4
microwave generator and turn on the power.
3. Open the valve (1) to the cooling air coming from the building compressed air
lines.
4. Check to make sure the valves (3,4) connecting the H2O saturator are closed,
and the through line valve (2) for helium is open.
5. Open the helium regulator and valves (5) such that you begin flowing pure
helium through the cell so that the Baratron reads 6 Torr.
6. After at least 3 minutes past turning on the microwave generator, turn on the
High Voltage switch on the generator.
7. Increase the power control until approximately 50 W appears on the forward
power.
8. Use a Tesla coil to start the discharge.
9. Once the discharge has started, adjust the threaded tuning stub projecting into
the Evenson cavity (a) and the three part tuning handle that slides along the
center conductor (b) until the reverse power is minimized.
10. Slowly open the valve (4) to the H2O saturator and valve (5) allowing helium
to flow into the saturator without allowing the pressure to increase too much.
This may involve closing the valve (2) for the helium through line.
To shut off:
1. Turn off the microwave power generator.
2. Close the valve (1) for the cooling air.
3. Close the valve (5) and the regulator for the helium.
B.3. RESULTS 181
Figure modified from John Herbon’s thesis
Microwave Power Supply
Helium gas
Cooling air
H2O saturator
1000 Torr Baratron
UV beam
Microwave discharge cavity
(4)
(2)
(3)
(1)
Building Compressed Air
(5)
(a)
(b)
Pump
Figure B.1: Schematic of He/H2O microwave discharge cell and H2O saturator setup. Figure adaptedfrom Herbon [52].
B.3 Results
The microwave discharge cell was run at a pressure of ∼1 Torr and with a net power
of 30 Watts to the cavity. The wavelength of the UV laser was tuned using the
in-cavity etalon over the R1(4) and R1(5) lines in the A–X (0,0) band of the OH
absorption spectrum, and the transmission of the UV laser through the discharge cell
recorded with an uncertainty of 4%. The expected line shapes are calculated using
the work of Herbon [52], and compared with the measured UV transmission data in
Figure B.2. The peaks of the experimental transmission matched the line centers
within 0.003 cm−1, which is well within the resolution and uncertainty limits of the
wavemeter. This agreement in wavelength of the line center was only found when
the wavemeter was aligned properly according to the manufacturer’s specifications
182 APPENDIX B. MICROWAVE DISCHARGE SYSTEM
(“the tracer beam and input laser beam must be precisely collinear over a one meter
path from the Wavemeter input aperture within 1.5 mm”). A fiber-coupled input
to the Burleigh WA-1000 was also tested, and this setup also yielded results that
indicated correct wavelength measurements. The fiber-coupled input was also easier
to ensure proper alignment, because any improper alignment through the fiber would
not produce a measurement reading on the wavemeter.
16296.4 16296.5 16296.6 16296.7
0.0
0.2
0.4
0.6
0.8
1.0
Abs
orpt
ion
Cro
effic
ient
[Arb
itrar
y un
its] /
Tra
nsm
issi
on Measured transmission through OH in the He/H2O cell OH lineshape at 298 K, 1 Torr
Wavenumbers (vis) [cm-1]
line center 16296.555 cm-1
R1(4) line
16303.1 16303.2 16303.3 16303.4
0.0
0.2
0.4
0.6
0.8
1.0
R1(5) line
line center 16303.275 cm-1
Figure B.2: OH line shapes, calculated and measured.
At 298 K, the full width at half maximum (FWHM) of the line shape is 0.1
cm−1. In the pre-frequency doubled visible beam which is being monitored by the
wavemeter, that line center becomes 16303.22775 cm−1, and the FWHM becomes
0.05 cm−1. The FWHM of the line shape is consistent with what would be found
assuming only Doppler broadening exists at this low pressure (at 298 K). Because
the discharge cell was operated at low pressures, minimal pressure broadening can
be assumed and a Doppler line shape can be fit to the data. Figure B.3 shows this,
using Eq. B.1 to fit the measured line shape.
∆νDoppler = 2(ln 2)1/2ν0
(2kT
mc2
)1/2
= 0.098cm−1 (Eq. B.1)
B.4. CONCLUSIONS 183
From these results, we can deduce a temperature of approximately 800 K, which
is reasonable considering much of the 100 W of forward power coming from the
microwave power supply must go towards increasing the translational temperature of
the gas.
16303.2 16303.3 16303.40
5
10
15
20
OH
Abs
orpt
ion
Coe
ffici
ent
[Arb
itrar
y un
its]
R1(5) line
Wavenumber (visible) [cm-1]
OH absorption data in the He/H2O cell Doppler profilie fit using experimental line width (T=800 K)
-100
0
100
Res
idua
l[%
]
Figure B.3: Measured OH line shape compared with the Doppler profile fit at a temperature of800 K.
B.4 Conclusions
In this process of examining how the wavelength is measured using the Burleigh WA-
1000 visible wavemeter, it was learned that the wavemeter reading can be sensitive to
alignment, especially when not following the specifications required for alignment as
stated in the manual. Using the fiber-coupled input provides a more robust alignment,
and should be preferred, but is not necessary if the proper alignment procedure is
followed for freespace alignment. By using a microwave discharge source to generate
OH atoms in a He/H2O mixture, it was concluded that the wavemeter measurement
using the freespace alignment is accurate when aligned properly.
184 APPENDIX B. MICROWAVE DISCHARGE SYSTEM
The proper use of the Burleigh WA-1000 wavemeter should always involve the
following procedures:
• Aligning the tracer beam from the Wavemeter free-space aperture to the incom-
ing laser beam over a path length of > 1 m to be separated by no more than
1.5 mm.
• Because the incoming laser beam and the tracer beam have finite diameters,
placing an iris both at the dye laser cavity exit and near the Wavemeter entrance
can help facilitate ensuring the laser beams are aligned. Because the Wavemeter
entrance is in itself an aperture, and iris at this location is not as critical.
• The alignment must be checked every time the optics in the laser dye cavity are
adjusted.
Appendix C
Fuel Measurement using a
Helium-neon Laser
C.1 Introduction
Light absorption at a wavelength of 3.39 µm occurs due to excitation of the C–H
stretch vibrational mode, and thus the mole fraction of any hydrocarbon species can
be determined using the Beer-Lambert law, given by Eq. 2.1, if the absorption cross-
section for the chemical of interest at 3.39 µm is known. This appendix describes the
utilization of laser absorption at 3.39 µm to determine the mixing time required for
the mixture preparation process and to verify the composition of the double-dilution-
prepared mixtures.
C.2 Equipment
An infra-red Jodon Helium-Neon laser (HeNe, Model HN-10GIR) of wavelength
3.39 µm was utilized to generate laser light at 3.39 µm. The intensity of the HeNe
laser light was measured using liquid-nitrogen-cooled indium antimonide (InSb) de-
tectors from IR Associates (model no. IS-2.0). Miscellaneous optics were used in the
alignment of the laser light, all compatible with transmitting, reflecting, filtering, and
splitting of laser light at 3.39 µm. This laser light was passed into a cell containing
185
186 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER
the absorbing gas; both the shock tube described in Chapter 2 of this thesis and a
Toptica Photonics model no. CMP30 multi-pass cell of total path length 30 m were
utilized as absorption cells.
C.3 Mixing Time Determination
Several mixtures of approximately 0.3% n-heptane in argon were prepared in the gas-
mixing facility described in Chapter 2, each in one single-dilution step, to determine
the mixing time required in the mixture preparation process to ensure homogeneity
and consistency. Each mixture was allowed to mix for different initial amounts of time
before being filled into the shock tube to a pressure of 100 Torr. The HeNe laser was
passed through the shock tube at the windows 2 cm from the driven section endwall to
measure the composition of n-heptane in the mixture. The optical setup was similar
to the setup for the OH diagnostic system shown in Figure 2.4, except with the
HeNe laser, InSb detectors, IR beam splitter, and 3.39 µm bandpass filters in place
of the OH laser system, modified PDA36A detectors, UG-grade beam splitter, and
UG11 filters, respectively. Common-mode rejection was employed, and the measured
transmission was averaged over several seconds. An absorption cross-section for n-
heptane from Klingbeil et al. [53] was used in determining n-heptane mole fraction
from the Beer-Lambert law given by Eq. 2.1.
From these experiments, it was determined that the mole fraction of n-heptane
in the gas mixture reached a homogeneous mixture of the expected composition after
approximately 30 minutes. A plot of the measured n-heptane mole fraction versus
mixing time is shown in Figure C.1. The experiments described in this thesis used
a mixing time of greater than or equal to 45 minutes for each mixing step of all
mixtures. It should be noted that even after 45 minutes in the mixing tank, a small
portion of the gas mixture near the exit valve remains unmixed (between the mixing
tank and the closest valve to the mixing tank; see Figure 2.3), and this portion of the
gas mixture must be vented out through the manifold prior to use of the mixture.
C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 187
0 10 20 30 40 50 600.0
0.1
0.2
0.3
0.4
n-h
epta
ne c
once
ntra
tion
[%]
Mixing time [minutes]
Figure C.1: Measured n-heptane mole fractions of a n-heptane/argon mixture after being filled intothe shock tube after different mixing times.
C.4 Mole Fraction Measurements in a Multi-pass
Cell
The test mixtures prepared for the experimental work presented in this thesis are
composed of highly dilute (ppm levels) of organic compounds. Uncertainties in the
rate constant determinations are almost 1:1 proportional to the uncertainty in the
known initial fuel composition in the test mixtures. Because the fuels of interest
in this thesis are all liquid at room temperature, concerns about fuel condensation
and/or adsorption onto the facility wall surfaces are present, and these effects can lead
to lower initial fuel compositions than would be predicted according to the manomet-
rically prepared predictions. Therefore, efforts were placed into developing a method
for experimental confirmation of the composition of the prepared mixture.
Because of the ultra-low concentrations of absorbing species in the mixtures, typ-
ical laser absorption techniques for quantitative mole fraction measurements can be
difficult because of low absorption fractions. To address this problem, a 74-pass, 30 m
multi-pass absorption cell was set up to perform fuel mole fraction measurements at
188 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER
3.39 µm; the details of the cell are as follows:
• Toptica Photonics CMP30 Multi-pass absorption cell
• Total path length = 29.87 m (74 passes)
• Total transmission (excluding window) ≥26%
• Mirrors are BK7, windows are CaF2, all work with 3.39 microns
Alignment Procedure
The cell alignment is straight forward. According to the manufacturer’s instructions,
two alignment cards come with the cell, and are to be placed along the holes on the
optical table that the cell is to be bolted into. The alignment cards each have a
target, and the cell is aligned by aligning the laser through the target holes on the
alignment cards, and then removing the cards and bolting the cell in at the location
of the cards. This is easily done with a visible helium-neon laser. See Figure C.2 for
a photo of the alignment card set up. The alignment can be checked by counting 36
reflections on the inner mirror of the cell.
Alignment of an infra-red (IR) helium-neon laser into the multi-pass cell is more
difficult because of the inability to see the IR laser beam and check its alignment
through the cards. The following procedure was developed to align the IR laser beam
through the multi-pass cell by making use of a visible helium-neon laser; Figure C.3
shows a schematic of the optical setup.
1. Direct the IR HeNe laser beam to reflect off of M1 and arrive on M2.
Temperature-sensitive paper cards can facilitate this.
2. Place irises at two locations in the beam path between M1 and M2, such that
the IR beam passes through both.
3. Raise the flipper mirror for the visible HeNe, and align that mirror and the
visible HeNe such that the visible beam passes through both irises.
4. Use the visible beam to place M3 and M4 in approximate locations such that
the visible beam is directed through the multi-pass cell.
5. Place a suitable long focal length spherical lens between M2 and M3 such that
the laser light is focused at the center of the multi-pass cell.
C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 189
Manufacturer supplied alignment cards Alignment cards with large window holes for IR laser alignment
Det
ecto
rAlignmentmirror Mx
Figure C.2: Alignment card setup for the multi-pass cell using the manufacturer supplied cards(left). Also shown are the alignment cards duplicated with large window holes for alignment of theIR laser beam (right).
Jodon IR HeNe Laser
Multi-pass Cell
InSbDetector
InSbDetector
Visible HeNe
InSbDetector
M2M3
M4
M1
Mx
flippermirror
Iris 1Iris 1
Lens
Figure C.3: Multi-pass cell setup with HeNe laser.
190 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER
6. Adjust M3 and M4 as necessary to follow the alignment procedures detailed in
the multi-pass cell instruction manual using the provided alignment cards.
7. Place the multi-pass cell in place, and observe the laser light coming out of
the cell (Note that you will see two beams exiting from the cell window: one
is the reflected beam from the window, and the other is the transmitted light.
Examination of the reflection geometry will tell you which is which).
8. Place a short focal length lens or focusing mirror in the transmitted beam path,
and a suitable IR detector (e.g. a liquid-nitrogen-cooled InSb detector) at the
focal point of the lens/mirror.
9. Un-flip the flipper mirror for the visible HeNe to allow the IR laser light to pass,
and remove the irises to ensure that none of the laser beam is cut off.
10. If you now see a voltage on the IR detector, the alignment is complete and the
subsequent steps can be skipped.
If no IR beam is detected, this means that the visible and IR laser beams were not
perfectly aligned to be co-linear using the irises. This is not a problem. The following
additional steps were developed to fine tune the alignment of the IR laser into the
multi-pass cell.
11. Remove the multi-pass cell from the table and put the alignment cards back in
place, but with large window holes centered at the points where the laser beam
should pass through (see Figure C.2). Duplicates of the alignment cards are
suggested to be made as to not cut holes in the original manufacturer supplied
alignment cards.
12. Place a focusing mirror or lens where the laser beam would exit the alignment
cards (Mx). This can be facilitated by raising the flipper mirror for the visible
HeNe and aligning Mx with the visible laser light.
13. Place another IR detector at the focal point of the focusing optic (see Fig-
ure C.2), and align the detector such that it detects the IR laser beam, and
that the laser beam hits the center of the detector’s active area. Note that
the IR laser beam may hit the detector at a slightly different location than the
visible laser beam because the two may not be exactly co-linear.
C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 191
14. If desired, use this opportunity to check that the IR laser beam is not clipped on
any of the optics by using a knife edge (or business cards) to locate the position
of the IR laser beam at all important locations. The measured laser intensity of
the newly set up detector should fall once the knife edge has clipped one edge
of the laser beam.
15. Use a knife edge to locate the position of the IR laser beam at the location
of the alignment cards, and adjust M3 and M4 until the IR beam is aligned
properly, through the center of the holes in the alignment cards.
16. Once alignment is verified, put the multi-pass cell back in place. If the previous
step was done carefully, the IR detector should now detect the transmitted
beam. If it still does not, repeat the above steps carefully until alignment is
achieved.
17. As an alternate solution to the above steps, if temperature-sensitive paper cards
are able to detect the position of the IR laser beam at the position of the multi-
pass cell, these can be used to check whether the IR beam is aligned correctly
through the alignment tools provided by the multi-pass cell manufacturer. The
above steps are only necessary if the IR laser intensity has attenuated enough
that the temperature-sensitive paper cards available can not detect the laser
beam location (as was the case for the Jodon HeNe laser).
If common-mode rejection is desired, follow the following steps.
18. Raise the flipper mirror for the visible HeNe such that the visible laser is aligned
into the multi-pass cell.
19. Locate the reflected beam from the window of the cell, and align the reflected
light into a focusing optic and a suitable IR detector.
20. Lower the flipper mirror. The IR detector should detect the reflected IR laser
light from the cell window and this signal can be used for common-mode rejec-
tion.
It should be noted that the above procedure only explains how to provide a successful
alignment of the cell. Additional steps were performed to check the beam diameter at
the cell window entrance, cell center, and rear cell mirror using an InSb detector and
192 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER
a vertical slit; to determine the beam diameter at a particular position, the vertical
slit was used to determine when the slit width spanned exactly the laser diameter.
The multi-pass cell setup was connected to the mixing manifold of the shock tube
to make absorption measurements for low-concentration prepared mixtures. One end
of the multi-pass cell is connected to the mixing manifold to allow the mixture to
flow in, and the other end of the cell is connected to the vacuum pumps of the mixing
facility, a 1000 Torr Baratron, and a vent; see Figure C.4 for a schematic. Absorption
can be monitored in a flowing or static system. The entire setup is mounted onto a
2’ x 4’ optical breadboard, so that it is self-contained and can be easily moved to the
shock tube end wall, or another experimental facility (i.e. another shock tube), with
the only things required to reconnect are the tubes to the vacuum pumps, the inlet
of the gas mixture, and the coaxial cables to the data-acquisition system.
Multi-Pass Cell
Baratron
Gas flow in from mixing assembly
or shock tube
To pump
Vent
Figure C.4: Gas flow diagram of the multi-pass cell setup.
The alignment procedure described in this section typically took the author one to
two hours to complete from scratch if none of the optics were in place. Realignment
typically took less than 30 minutes if the optics were setup but had become misaligned
(e.g. if the table got bumped, the laser was borrowed, etc.).
Laser Noise
A measurement of the laser intensity, over a span of 5 minutes, yields a drift of 3% in
laser intensity fluctuation in five minutes, even using common-mode rejection (from
an incident power measured off the reflection of the cell window) because the frac-
tion of light reflected off the cell window is not constant. This amount of noise still
C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 193
leads to species mole fraction measurements with an uncertainty of 4% if the condi-
tions are chosen as such to yield 50% absorption. Figure C.5 shows the dependence
of the uncertainty in the measured mole fraction as a function of the percent ab-
sorption, illustrating that higher uncertainties are present at lower absorption levels.
The uncertainty in the measured mole fraction is determined by propagating a 3%
uncertainty in incident laser intensity into the Beer-Lambert law, Eq. 2.1. Because
the laser noise contributes a random error, the overall uncertainty can be reduced by
repeated measurements of the same parameter.
0 10 20 30 40 50 60 70 80 90 1000.01
0.1
1
10
100
Per
cent
err
or in
mea
sure
men
t of m
ole-
fract
ion
due
to a
3%
unc
erta
inty
in I 0
% Absorption
Figure C.5: Uncertainty in the measured mole fraction using an absorption diagnostic with a 3%uncertainty in laser intensity. The uncertainty is shown a function of the percent absorption, illus-trating that higher uncertainties are present at lower absorption levels.
Cell Length Calibration using Propane Mixture
The length of the multi-pass cell was checked with a 0.1% propane in argon mixture,
prepared manometrically in the mixing tank. Because propane is naturally in the
gas phase at room temperature, there is no concern of it adsorbing on the walls, and
the manometrically predicted mole fraction is likely accurate. The 0.1% propane in
argon mixture was introduced into the cell at pressures yielding 30 to 60% absorption,
both in static and flowing conditions. An absorption cross-section for propane from
194 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER
Klingbeil et al. [53] was used in determining the absorbing path length using the
Beer-Lamber law, Eq. 2.1, assuming a known propane concentration. The cell length
was measured to match the manufacturers specified length of 29.87 m within ±3%
(measurements from 28.9 to 31.0 m were found). This fluctuation in cell length
measurement is likely due to the fluctuations in the laser intensity. Because the
scatter of all the measurements center on the manufacturers specified length, that
length will be used in future measurements.
Measurements of n-Heptane Composition
A mixture of 200 ppm n-heptane in argon was prepared with the same double-dilution
mixing procedure as used for the n-heptane experiments as described in Chapter 2,
with the exception of no added TBHP. The mixture was introduced into the multi-pass
cell from the mixing tank at pressures to field 30 to 80% absorption. An absorption
cross-section for n-heptane from Klingbeil et al. [53] was used in determining the
n-heptane mole fraction. The measurements of heptane mole fraction scatter from
196 ppm to 207 ppm. This measurement confirms the manometric preparation of n-
heptane in an n-heptane/argon mixture within the±3% of scatter, which is attributed
to the laser noise. Other major independent uncertainties in the measurement include
absorption cross-section (3% uncertainty), and path length (3% uncertainty), and if
each of these major uncertainties are combined using a root-sum-squares method, the
total uncertainty of n-heptane mole fraction is ±5%.
Measurements of TBHP Absorption Cross-section
A 50 ppm TBHP/water solution vapor in argon mixture was prepared (using the
TBHP/water solution described in Chapter 2), and absorption at 3.39 µm was mea-
sured for 10-25% absorption. The amount of absorption was limited because the
cell was filled to 1 atm at ∼25% absorption, therefore no higher absorption could be
generated. This low concentration of TBHP/water in argon was chosen because it is
the concentration used in the mixtures prepared for the work of this thesis. To mini-
mize uncertainty in the measurement of absorption cross-section at 3.39 µm, multiple
C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 195
absorption measurements at various pressures were performed.
A plot of ln(I/I0)/(x · L), normalized for units, versus pressure gives an absorp-
tion cross-section slope of approximately 2 m. This plot is shown in Figure C.6.
If the TBHP yields are assumed to be the same as in measured in Chapter 3 (of
approximately 12 ppm TBHP per 50 ppm TBHP/water solution), the measured ab-
sorption cross-section corresponds to a TBHP absorption cross-section at 3.39 µm of
8.3 m2/mole. This is ∼30% lower than the absorption cross-section of tert-butanol at
3.39 µm from Sharpe et al. [54], which has a similar molecular structure with TBHP
(same number and type of C-H bonds). The uncertainty in the TBHP absorption
cross-section measurement is approximately ±15%, however, because the amount of
TBHP in each mixture is small compared to the amount of n-alkane or butanol in
the mixtures prepared for pseudo-first-order kinetics (by a factor of 10 to 20), this
large uncertainty in absorption cross-section for TBHP only propagates into a ∼1%
uncertainty in the fuel mole fraction measurements.
0.0 0.2 0.4 0.6 0.8 1.0 1.20.0
0.5
1.0
1.5
2.0
2.5
-ln (I
/I 0) / (x
L)
[see
cap
tion
for u
nits
]
Pressure [atm]
y = 1.95 x
Figure C.6: Absorption measurements at various pressures of the 50 ppm TBHP/water in argonmixture. Units are normalized such that the slope gives absorption cross-section in units of m2/mole.
196 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER
Measurements of n-Heptane Composition in Mixture of n-
Heptane/TBHP
A mixture of 50 ppm TBHP/water, 201 ppm heptane, and argon was prepared, and
the heptane mole-fraction was measured by absorption at 3.39 µm in the multi-pass
cell by assuming that the TBHP mole fraction and absorption cross-section were
known (using the measured absorption cross-section value from the previous section).
Ten measurements were done at total absorbances of 20 to 80%, and the average mole-
fraction value measured was 201.6 ppm, with a deviation of ±3%. This deviation is an
indication of the uncertainty due to baseline fluctuations, and the only other major
source of error is the n-heptane absorption cross-section, taken to be 3%, and if
these major uncertainties are combined using a root-sum-squares method, the total
uncertainty in the n-heptane mole fraction in a mixture in the presence of TBHP is
±5%.
Since for similar mixtures of n-pentane and n-nonane, the same mixing procedure
was used and the partial pressure of the n-alkane never exceeded more than 50%
of its saturated vapor pressure (as was the case for the n-heptane mixtures), and
the main difference in these molecules is only molecular weight and vapor pressure,
similar uncertainties in fuel mole fraction can be assumed for those mixtures as well.
Absorption measurements for those mixtures could be performed; however, because
the cross-sections for those n-alkanes are less well known, the uncertainties in the
measurements would be greater.
Measurements of mixture composition in the shock tube was not done because
passivation experiments have shown that no loss is found in the shock tube. Addi-
tionally, the measurements of n-butanol in the following subsection show that no loss
is expected in the shock tube.
Measurements of n-Butanol Composition
Because alcohols may have different interactions with walls and/or TBHP because of
the presence of a dipole (compared to no dipoles in n-alkanes), measurements of the
n-butanol mole fraction in mixtures prepared according to the double-dilution mixing
C.4. MOLE FRACTION MEASUREMENTS IN A MULTI-PASS CELL 197
procedure from Chapter 2 were conducted. Even though passivation experiments have
eliminated most of the worry about any fuel condensing or adsorbing to the shock
tube wall surfaces, recent ignition delay time experiments of n-butanol by Stranic
et al. [35] in the same facility and similar shock tube facilities found evidence of n-
butanol loss to wall surfaces. Therefore, the possibility of n-butanol loss to the shock
tube walls was examined as well by filling the cell both directly through the mixing
facility, and also by filling the cell by first filling the mixture into the shock tube, and
then filling the cell through a port 2 cm from the shock tube endwall.
A mixture of 190 ppm n-butanol in argon was prepared, and absorption of 3.39 µm
was measured in the multi-pass cell. The absorption cross-section for n-butanol was
taken from Sharpe et al. [54]. The results yield an n-butanol mole fraction measure-
ment of 180 ppm when filling both from the mixing tank, and 181 from the shock
tube endwall (with fluctuations of ±3%). This seems to indicate that the mixture
in the shock tube is the same as that coming out of the mixing tank, but also that
the measured mole fraction in both cases is low by 5%. However, recent unpub-
lished measurements by Stranic [137] of the n-butanol absorption cross-section yield
a cross-section that is approximately 4% lower than the value from Sharpe et al. If the
measured absorption cross-section from Stranic is used, the measured n-butanol mole
fraction in the mixture is 188 ppm, which is only 1% lower than the manometrically-
prepared predicted amount. Because the absorption cross-section of n-butanol likely
does not have an accuracy to better than 1%, the uncertainty of the n-butanol mole
fraction is equal to that of the absorption cross-section combined with the measure-
ment fluctuations (±3%), leading to an overall uncertainty in n-butanol mole fraction
of ±5%, the same as for the n-alkanes.
A mixture of 203 ppm n-butanol, 50 ppm TBHP/water and argon was also pre-
pared and absorption was measured at 3.39 µm was measured in the multi-pass cell,
filling from the mixing tank. The TBHP mole fraction and absorption cross-section
were taken to be known, and the measured n-butanol mole-fraction using the n-
butanol absorption cross-section from Stranic [137] was 207 ppm, with a measure-
ment scatter of ±3%. Because the uncertainty of this measurement also includes
the uncertainty of the TBHP absorption cross-section, the n-butanol mole fraction
198 APPENDIX C. FUEL MEASUREMENT USING A HELIUM-NEON LASER
can be assumed to be verified within 3% in the presence of TBHP. Because the
measured value for this mixture is higher than the manometric prediction, and the
measured mole fraction in the previous n-butanol and argon mixture was lower than
the manometrically predicted, this does not point to any sort of systematic error in
the absorption cross-section of n-butanol at 3.39 µm, and the deviation of the mea-
surements from the manometrically prepared predicted values are likely due to scatter
in the measurements.
For the same reasons as why absorption measurements in mixtures of n-pentane
and n-nonane were not performed, absorption measurements in mixtures of the other
butanol isomers were not performed, and similar uncertainties will be assumed. Be-
cause both the n-heptane and n-butanol measurements provided similar uncertainties
for fuel mole fraction, it seems reasonable that the other fuels would behave similarly.
Appendix D
Rate Constant Estimation
Methods
D.1 Introduction
In the past few decades, Sidney Benson’s additivity rules [138] have been important
for estimating molecular heats of formation for large molecules using the principle that
individual groups of atoms behave similarly in different molecules. In addition to es-
timating thermochemical properties, the additivity principle also has applications in
estimation of kinetics rate constants. For the class of reactions of the hydrogen-atom-
abstraction-by-OH type, predictive models for the rate constants using the additivity
principle based on structure-activity relationships have been investigated and im-
proved in the past few decades. Several different types of rate constant estimation
methods will be discussed in this appendix, including details on how to apply them
to estimate the rate constants for the reactions investigated in this thesis.
Definitions
A few common terms will be used to succinctly describe the estimation methods
discussed in this appendix. The terms primary, secondary, and tertiary are used to
distinguish different types of carbons in an organic molecule.
199
200 APPENDIX D. RATE CONSTANT ESTIMATION METHODS
• Primary carbon: a carbon atom bonded to only one other non-hydrogen atom.
A primary carbon is bonded to three hydrogen atoms.
• Secondary carbon: a carbon atom bonded to two other non-hydrogen atoms. A
secondary carbon is bonded to two hydrogen atoms.
• Tertiary carbon: a carbon atom bonded to three other non-hydrogen atoms. A
tertiary carbon is bonded to only one hydrogen atom.
In this thesis, the non-hydrogen atoms are typically carbon, except in the case
of butanol, where the an oxygen atom may take the place of a non-hydrogen atom.
For butanol molecules, the carbon atoms can also be distinguished by their position
relative to the oxygen atom.
• α-Carbon: the carbon atom adjacent to the oxygen atom.
• β-Carbon: the second carbon atom from the oxygen atom.
• γ-Carbon: the third carbon atom from the oxygen atom.
• δ-Carbon: the fourth carbon atom from the oxygen atom.
Primary, secondary, or tertiary carbons can also be differentiated by the neighbor-
ing groups. For example, in n-heptane, three secondary carbons exist. However, the
central secondary carbon is bonded to two other secondary carbons, and the other
secondary carbons are bonded to one primary carbon and one secondary carbon.
In this appendix, a notation will be used similar to the notation used in Benson’s
additivity rules [138].
• (CH3)–(CH2): a primary carbon bonded to a secondary carbon.
• (CH2)–(CH3)(CH2): a secondary carbon bonded to a primary carbon and a
secondary carbon.
• (CH2)–(CH2)(CH2): a secondary carbon bonded to two secondary carbons.
• (CH2)–(CH2)(OH): a secondary carbon bonded to a secondary carbon and an
OH group.
• (CH)–(CH2)(CH2)(CH2): a tertiary carbon bonded to three secondary carbons.
• and so on...
The neighboring groups on the right-hand side of the long hyphen will also be referred
to as substituent groups.
D.2. EMPIRICAL ESTIMATION METHODS 201
Figure D.1 shows the n-heptane and iso-butanol molecules and uses the above
terminology to describe each carbon atom.
H3C
H2C
CH2
H2C
CH2
Secondary carbon(CH2) - (CH2)(CH2)
Secondary carbon(CH2) - (CH3)(CH2)
Primary carbon(CH3) - (CH2) H3C
CH
CH2
OH
CH3 Tertiary carbon β-carbon(CH) - (CH3)(CH3)(CH2)
Secondary carbon α-carbon(CH2) - (CH)(OH)
Primary carbon γ-carbon (CH3) - (CH)
Hydroxyl group (OH) - (CH2)
H2C
CH3
Figure D.1: The carbons of the n-heptane (left) and iso-butanol (right) molecules described usingthe terminology used in this appendix.
D.2 Empirical Estimation Methods
Early Models Not Discussed in this Thesis
Greiner [19] (1970) presented data for hydrogen-atom abstraction by OH of ten dif-
ferent model alkanes, and used this data to generate a simple additivity model for
the kinetic rate constants, analogous to Benson’s model [138] for thermodynamic
quantities. All of Greiner’s experiments were for temperatures from 295 to 500 K.
The overall rate constant predicted for any alkane+OH reaction is a function of the
number of primary, secondary, and tertiary carbons present in the alkane, and given
by Eq. D.1, where NP , NS, NT are the number of primary, secondary, and tertiary
carbons in the alkane, respectively.
ktot/[cm3molecule−1s−1] =1.02× 10−12 ·NP · exp
(− 818
T [K]
)
+ 2.34× 10−12 ·NS · exp
(− 403
T [K]
)
+ 2.09× 10−12 ·NT · exp
(+
95
T [K]
)(Eq. D.1)
202 APPENDIX D. RATE CONSTANT ESTIMATION METHODS
Greiner found that his model worked well with his data for neo-pentane,
2,2,3,3-trimethhylbutane, pentane, n-butane, cyclohexane, n-octane, iso-butane,
2,3-dimethylbutane, 2,2,3-trimethylbutane, and 2,2,4-trimethylpentane. However,
Greiner found the abstraction rate with methane and ethane did not agree well with
his model.
Baldwin and Walker [23] (1979) proposed an additivity method for the rate con-
stants for reactions of alkanes+OH, depending on the number of primary, secondary,
and tertiary carbons, similar to Greiner [19]. The model of Baldwin and Walker
is based on their data taken at 500 ◦C combined with independent data at lower
temperatures. The overall rate constant is given relative to the rate constant of
OH + H2 −→ H2O + H as Eq. D.2.
ktot/kref = 0.214 ·NP · exp
(1070
T [K]
)+ 0.173 ·NS · exp
(1820
T [K]
)
+ 0.273 ·NT · exp
(− 2060
T [K]
)(Eq. D.2)
In Eq. D.2, kref is the rate constant for the reaction of OH+H2 −→ H2O+H. Baldwin
and Walker also proposed a relative rate constant expression to determine the overall
rate constants for reactions of alkanes+H.
In a subsequent paper, Walker [139] (1985) used reliable experimental data at room
temperature and 753 K to develop an additivity model for the rate of alkanes+OH,
presenting specific rate constant contributions for each abstraction site dependent on
the next-nearest neighbor (NNN) of the C–H bond. The experimental rate constant
evidence supports a pre-exponential rate constant temperature dependence based
on T 1. Walker’s recommended rate constant contributions are given in Table D.1.
Using Walker’s additivity method, rate constant agreement with the limited amount
of experimental data available at the time was found to be very good, though the
paper cautions that steric effects may limit this approach and the approach of similar
additivity methods on highly branched alkanes.
D.2. EMPIRICAL ESTIMATION METHODS 203
Table D.1: Group rate constants recommended by Walker [139]. Units for k are [cm3molecule−1s−1].
Carbon type at abstraction site Rate constant contribution per H atom
(CH3) (neopentane) k = 5.81× 10−15T exp(−605/T [K])(CH3) (tetramethylbutane) k = 2.32× 10−15T exp(−404/T [K])(CH2)–(CH3)(CH3) k = 4.82× 10−15T exp(−130/T [K])(CH2)–(CH3)(CH2) k = 4.82× 10−15T exp(−60.1/T [K])(CH2)–(CH2)(CH2) k = 4.82× 10−15T exp(+10.8/T [K])(CH2)–(CH2)(CH) k = 4.82× 10−15T exp(+10.8/T [K])(CH)–(CH3)(CH3)(CH3) k = 4.48× 10−15T exp(+75/T [K])(CH)–(CH3)(CH3)(CH2) k = 4.23× 10−15T exp(+160/T [K])(CH)–(CH3)(CH3)(CH) k = 3.99× 10−15T exp(+245/T [K])(CH)–(CH3)(CH3)(C) k = 3.65× 10−15T exp(+330/T [K])(CH)–(CH3)(CH2)(CH2) k = 3.99× 10−15T exp(+245/T [K])
Structure-activity Relationship of Atkinson and Coworkers
Atkinson [20] (1986) makes high-temperature rate constant estimations (250 to
1000 K) for reactions of OH with alkanes, haloalkanes, oxygenates, nitriles and ni-
trates. Atkinson’s model distinguished carbon sites with different neighboring groups,
rather than assuming all primary, secondary, and tertiary reaction sites were equiv-
alent between molecules. For alkanes, Atkinson’s defines a rate constant for the
hydrogen-atom abstraction via OH based on a structure-activity relationship, and
the estimated rate constant can be calculated with rates for each of the primary,
secondary, and tertiary carbons with F (X) factors for each substituent group. The
overall rate constant can be defined by Eq. D.3, where Fi(X) is a factor dependent on
the neighboring group(s) X, Y , and Z of the primary, secondary, and tertiary carbons
for each carbon i, and kp, ks, and kt are terms for the rate constant contributions at
primary, secondary, and tertiary carbon sites, respectively.
ktot =
NP∑i=1
kpFi(X) +
NS∑i=1
ksFi(X)Fi(Y ) +
NT∑i=1
kpFi(X)Fi(Y )Fi(Z) (Eq. D.3)
Each substituent factor term can be written in the temperature-dependent form of
Eq. D.4, effectively lowering the activation energy of each associated rate constant
204 APPENDIX D. RATE CONSTANT ESTIMATION METHODS
term.
F (X) = exp
(ExT
)(Eq. D.4)
Atkinson used data to recommend the F (X) factors for alkanes. Atkinson also
recommended F (X) factors for molecules containing oxygen, nitrogen and halogen
molecules. For example, the hydrogen-atom abstraction rates via OH of alcohols can
be estimated with the F (OH) factor.
Atkinson’s [20] approach was later revisited by Atkinson and co-workers [21, 22, 90]
(1987,1995,2001), generating an improved database of rate constants, and suggested
factors for new substituent groups, and updating the factors for the same previous
groups. The most recent relevant rate constants are from Kwok and Atkinson [22]
(1995), and are described by Eq. D.5, Eq. D.6, and Eq. D.7; these terms can be
substituted into Eq. D.3. For alcohols, Eq. D.8 adds an additional term to Eq. D.3
that can be affected by substituent factors.
kp = 4.49× 10−18T 2 exp
(− 320
T [K]
)cm3molecule−1s−1 (Eq. D.5)
ks = 4.50× 10−18T 2 exp
(+
253
T [K]
)cm3molecule−1s−1 (Eq. D.6)
kt = 1.89× 10−18T 2 exp
(− 696
T [K]
)cm3molecule−1s−1 (Eq. D.7)
koh = 2.10× 10−18T 2 exp
(− 85
T [K]
)cm3molecule−1s−1 (Eq. D.8)
The most recent F (X) factors for alkanes are also from Kwok and Atkinson, and
Bethel et al. [90] (2001) studied the rate constants for reactions of selected diols with
OH to determined updated substituent factors for alcohol-related substituent groups.
Eq. D.9, Eq. D.10, and Eq. D.11 extrapolate the new substituent factors proposed at
D.2. EMPIRICAL ESTIMATION METHODS 205
298 K by using Eq. D.4.
F (CH2) = F (CH) = F (C) = exp
(61.69
T [K]
)(Eq. D.9)
F (OH) = exp
(317.3
T [K]
)(Eq. D.10)
F (CH2OH) = F (CHOH) = F (COH) = exp
(284.7
T [K]
)(Eq. D.11)
Bethel et al. found that for hydroxyl-containing compounds, the substituent group
effect of the OH group needed to be considered at both the α-carbon and the β-
carbon, as suggested by Eq. D.11. The substituent group for a neighboring primary
carbon is one, F (CH3) = 1.
The structure-activity relationship (SAR) from Atkinson and coworkers [20–22, 90]
can be used to estimate the overall rate constants for the reactions of interest in
this thesis. For example, the rate constant for the reaction of OH with n-heptane,
Reaction (4.2) can be computed using Eq. D.12, and the rate constant for the reaction
of OH with iso-butanol, Reaction (6.1), can be computed using Eq. D.13.
kSAR4.2 = 2kpF (CH2) + 2ksF (CH2) + 3ksF (CH2)F (CH2) (Eq. D.12)
kSAR6.1 = 2kpF (CH) + ktF (CH2OH) + ksF (CH)F (OH) + kohF (CH2) (Eq. D.13)
Furthermore, site-specific rate constants can be estimated by examining the rate
constant term and substituent factor associated with each individual carbon site.
For example, abstraction at the β-carbon of iso-butanol, Reaction (6.1b), can be
described by the rate constant term associated with the tertiary carbon site, given
by Eq. D.14
kSAR6.1b = ktF (CH2OH) (Eq. D.14)
See Figure D.1 for the molecular structures and types of carbon abstraction sites for
n-heptane and iso-butanol.
206 APPENDIX D. RATE CONSTANT ESTIMATION METHODS
Improved Group Scheme of Sivaramakrishnan and Michael
The most recent development for an additive group scheme for the reaction rate of OH
with alkanes is from Sivaramakrishnan and Michael [11] (2009). Sivaramakrishnan
and Michael measured the rate constants for reactions of OH with alkanes up to
C7, and used the resulting experimental data to deduce the rates of abstraction from
primary, secondary, and tertiary carbon sites differentiated similarly to Walker’s next-
nearest neighbor (NNN) distinctions [139].
Motivated by high-level energetics calculations for bond energies, Sivaramakrish-
nan and Michael [11] also used their rate constant measurement results for their
largest normal alkane (n-heptane) to differentiate the abstraction rate constant at
secondary carbon sites even more, and accounted for effectively the next-next-nearest
neighbor. For example, in the n-heptane molecule shown in Figure D.1, the central
secondary carbon (CH2)–(CH2)(CH2) is bonded to two secondary carbons that are
both bonded to secondary carbons (they call this carbon S11’); however, the outer
secondary carbons (CH2)–(CH2)(CH2) are bonded to one secondary carbon that is
bonded to a secondary carbon and one secondary carbon bonded to a primary carbon
(they call this carbon S’11).
Using their experimental data, Sivaramakrishnan and Michael [11] came up with
empirical rate constant parameters for each type of carbon site, and their improved
group scheme successfully predicts the n-octane+OH rate constant measured by Kof-
fend and Cohen [9] near 1100 K. All rate constant fits were determined for experi-
mental data in the temperature range 298 to 1300 K. The rate constants terms for
Sivaramakrishnan and Michael’s improved group scheme additivity method are given
in Table D.2.
The improved group scheme by Sivaramakrishnan and Michael [11] can be used
to estimate the rate constants for the reactions of OH with n-pentane, n-heptane,
and n-nonane, Reaction (4.1), (4.2), and 4.3, respectively, that were studied in this
thesis. Eq. D.15, Eq. D.16, and Eq. D.17 use the improved group scheme to estimate
D.3. TRANSITION STATE THEORY 207
the rate constants of interest in this thesis.
kIGS4.1 = 2k(CH3)−(CH2)
+ 2k(CH2)−(CH3)(CH2)+ k(CH2)−(CH2)(CH2)(S11)
(Eq. D.15)
kIGS4.2 = 2k(CH3)−(CH2)
+ 2k(CH2)−(CH3)(CH2)+ 2k(CH2)−(CH2)(CH2)(S11)
+ k(CH2)−(CH2)(CH2)(S11’)(Eq. D.16)
kIGS4.3 = 2k(CH3)−(CH2)
+ 2k(CH2)−(CH3)(CH2)+ 2k(CH2)−(CH2)(CH2)(S11)
+ 3k(CH2)−(CH2)(CH2)(S11’)(Eq. D.17)
Table D.2: Improved group scheme rate constant terms recommended by Sivaramakrishnan andMichael [11]. Units for k are [cm3molecule−1s−1].
Carbon type at abstraction site Rate constant contribution per H atom
(CH3)–(CH2) k = 7.560× 10−18T 1.813 exp(−437/T [K])(CH3)–(CH) k = 9.267× 10−18T 2.078 exp(−189/T [K])(CH3)–(C) k = 9.087× 10−18T 1.763 exp(−374/T [K])(CH2)–(CH3)(CH3) k = 1.640× 10−17T 1.751 exp(+32/T [K])(CH2)–(CH3)(CH2) k = 5.856× 10−15T 0.935 exp(−254/T [K])(CH2)–(CH2)(CH2) (S11) k = 4.750× 10−18T 1.811 exp(+511/T [K])(CH2)–(CH2)(CH2) (S11’) k = 4.665× 10−13T 0.320 exp(−426/T [K])(CH)–(CH3)(CH3)(CH3) k = 8.044× 10−18T 1.840 exp(+503/T [K])(CH)–(CH3)(CH3)(CH) k = 7.841× 10−14T 0.320 exp(+35/T [K])
D.3 Transition State Theory
Cohen [24, 25] (1982,1991) developed a method for extrapolating existing experimen-
tal data on the rate constants for reactions of OH radicals with alkanes to higher
temperatures using conventional transition-state theory (TST). In Cohen’s earlier
work [24], all primary, secondary, and tertiary carbon abstraction sites were treated
the same in different alkanes. However, in a later development [25], Cohen revised the
transition-state theory model to include differences in contributions from each pri-
mary, secondary, and tertiary carbon abstraction site due to the next-nearest neighbor
(NNN). The NNN contribute to bond dissociation energy differences which effects the
208 APPENDIX D. RATE CONSTANT ESTIMATION METHODS
enthalpy of the transition state. In the revision of Cohen’s theory, Cohen also exam-
ined the affect in extrapolating the rate constant estimation method to large alkanes
due to increased mass. Cohen’s conclusion was that mass differences may possibly
affect the transition state entropy by up to 40%, which can introduce a factor of
2 error in rate constant. However, because the current experimental database for rate
constants for reactions of OH with large-alkanes is too small and the experimental
uncertainties too large, Cohen was unable to unambiguously distinguish the affect of
mass in the model.
D.4 Ab initio Prediction Methods
Alternative to empirical additivity methods are ab initio prediction methods that
utilize some form of ab initio calculation but do not require full electronic-structure
calculations for high-level rate constant calculations. Rate constants using these
methods are not discussed in comparison to the results of this thesis.
Huynh et al. [26] (2006) applies reaction class transition state theory (RC-TST)
to predict thermal rate constants for the hydrogen-atom abstraction reactions of the
type alkane+OH. Using the RC-TST coupled with linear energy relationships (LER),
Huynh et al. were able to predict relative rates in the alkane+OH reaction class
(relative to ethane+OH) with knowledge only of the reaction barrier height for the
general alkane reaction, which can be obtained using electronic structure calculations.
The RC-TST/LER rate theory by Huynh et al. is shown to have reasonable agreement
with literature rate values for a large number of reactions in this reaction class.
Sumathi and co-workers [140] (2001,2003) claim that while estimation methods
based on linear free energy relationships have been known for a long time, the draw-
backs of the LER theories can include thermodynamic inconsistency, missing infor-
mation about Arrhenius factors or lack of universality. Instead, the approach on
group additivity by Sumathi et al. [140] is to calculate thermodynamic properties of
transition states based on ab initio calculations to extract group additivity values for
“transition-state specific” moities. However, this work is done only for hydrogen-atom
D.4. AB INITIO PREDICTION METHODS 209
abstraction from alkanes by H and CH3 radicals, and no work is reported regarding ab-
straction by OH. Other hydrogen-atom abstraction rates from oxygenates, oxyalkyls
and alkoxycarbonyls were studied by Sumathi and Green [141], however, this work
also only covers abstraction by H and CH3 radicals.
210 APPENDIX D. RATE CONSTANT ESTIMATION METHODS
Appendix E
Estimation of Rate Constants for
Unimolecular Reactions
E.1 Introduction
Two main types of unimolecular reactions are discussed in this thesis as important
subsequent reactions that occur after the reaction of OH with the isomers of butanol.
beta-Scission reactions are an important class of reactions that lead to decompo-
sition of free radicals. This type of reaction describes the decomposition of a free
radical breaking at the bond β to the radical, meaning two bonds away from the
radical. The β-bond is the bond most likely to break because breaking of this bond
allows for the formation of a double bond. Typically, beta-scission through breaking
of a C–C bond or a C–O bond will occur more rapidly than cleavage of a C–H or
O–H bond because the latter pair of bonds are stronger. See Figure E.1 for an arrow
pushing diagram of a beta-scission reaction.
Radical isomerization can occur through unimolecular reactions. This type of
reaction typically occurs through a transition state structure where a hydrogen atom is
exchanged from one carbon (or oxygen) site to a radical site. The fastest isomerization
reactions to consider for butanol are ones that occur via a 5- or 6-membered ring
transition state structure (see Figure E.2). Smaller ring transition state structures
are not likely to occur, therefore, isomerization reactions that pass through these
211
212 APPENDIX E. RATE CONSTANTS FOR UNIMOLECULAR REACTIONS
types of structures are not likely to occur on combustion time scales.
CC
C
C
OH
HH
H
H
H
HHH
CC
C
C
OH
HH
H
H
H
HHH
CC
C
C
OH
HH
H
H
H
HHH
slow
H3C
H2C
CH
CH2
OH
CH3
H2C
CH
H2C
OH
H3C
HC
CH
H2C
OH
H
Three beta-scission decomposition pathways of the 1-hydroxy-but-2-yl radical
Figure E.1: Three beta-scission decomposition pathways for the 1-hydroxy-but-2-yl radical. Redarrows show the movement of electrons. Also shown in red is the free radical and the bond in theβ-position relative to the free radical involved in each reaction.
H2C
H2C
CH2
H2C
OH H3C
H2C
CH2
H2C
OH2C
H2CHC
H
CH2
O
1-hydroxy-but-4-yl 1-butoxyl
6-member-ring TS
H3C
HC
CH2
H2C
OH H3C
H2C
CH2
H2C
O
5-member-ring TS
HC
HC
CH2
O
H
H3C
1-butoxyl1-hydroxy-but-3-yl
Figure E.2: Isomerization reactions for C4H9O radicals. Example reactions proceeding through 6-and 5-member ring transition states are shown.
At high pressures, the rate constants for unimolecular reactions are only depen-
dent on temperature. All unimolecular reactions, however, necessarily proceed via
collision with a third body, and therefore, at lower pressures, the rate constant for a
given unimolecular reaction is dependent on the concentration of third body collision
partners. Thus, rate constants for unimolecular reactions can be pressure dependent
in addition to temperature dependent. Several methods are available for predicting
the pressure dependence of a unimolecular reaction; methods can be as complex as
E.2. HIGH-PRESSURE LIMIT 213
requiring high-level electronic structure calculations to determine the vibrational fre-
quencies of the reactants and transition states, or as simple as assuming the reaction
proceeds via a two-step Lindemann mechanism [99]. The work in this thesis takes an
approach with a complexity between these limits.
In this appendix, a method for determining the high-pressure limit rate constant
for beta-scission unimolecular reactions will be presented based on the examination of
analogous reactions. Furthermore, the methods of estimating the pressure dependence
of unimolecular reactions using the Kassel Integral [99] will be described.
E.2 High-pressure Limit
In Chapter 5, the high-pressure limit of the rate constants for reactions describing
beta-scission decomposition of the C4H9O radicals were estimated based on the re-
verse addition reaction, a method described in Curran [100] for similar decomposition
reactions of alkyl and alkoxyl radicals. The rate constants for the addition reactions
can be estimated by assuming that addition reactions with similar molecular inter-
actions have equivalent reaction rate constants. This assumption was made on the
basis of Figure E.3 which shows measured rate constants for addition reactions of
alkene+CH3 and alkene+OH from Manion et al. [142]. For example, the reverse
of Reaction (5.4a): CH3CH2CHCH2OH −→ 1- C4H8 + OH is the addition of an OH
radical with a 1-butene molecule, and the rate constant for such a reaction can be
estimated to be equivalent to the addition reaction of an OH radical with a propene
molecule to form a hydroxypropyl radical product. The rate constants for the latter
reaction and other classes of addition reactions, can be determined from applying the
law of mass action to the work of Zador and Miller [93], who performed ab initio
calculations on the unimolecular pathways for the decomposition of hydroxypropyl
radicals. In the current work, the assumption was made that calculated rate constants
at 100 bar are representative of the high-pressure limit rate constant. Thermodynamic
properties were taken from Sarathy et al. [91] in calculating the reverse rate constants.
Table E.1 presents the families of addition reactions and the rate constants assumed
for each using this method.
214 APPENDIX E. RATE CONSTANTS FOR UNIMOLECULAR REACTIONS
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.010-20
10-19
10-18
10-17
10-16
10-15
10-14
10-13
10-12
10-11
10-10
10-9
CH3 + alkenes
Rec
ombi
natio
n ra
te c
onst
ant
[cm
3mol
ecul
e-1s-1
]
1000/T [1/K]
Alkene type:1 C2
C3
iso-C4
n-C4
C2
C3
OH + alkenes
Figure E.3: Rate constants for addition reactions of alkene+CH3 and alkene+OH from Manion etal. [142].
Table E.1: Families of addition reactions with equivalent rate constants. High-pressure limit rateconstants are determined from the work of Zador and Miller [93] using thermodynamic propertiesfrom Sarathy et al. [91]. Units for A are [cm3mol−1s−1] , units for E are [cal mol−1K−1].
Addition Reaction k∞ = A · T b exp(−E/RT )
A b E
C2H5 + CH2O −−→ CH3CH2CH2O 1.81×101 2.55 -3.533×103
C3H7 + CH2O −−→ CH3CH2CH2CH2O 1.81×101 2.55 -3.533×103
CH3 + CH2−−CHOH −−→ CH3CH2CHOH 3.04×106 1.68 6.619×103
CH3 + CH2−−CHCH2OH −−→ CH3CH2CHCH2OH 3.04×106 1.68 6.619×103
C2H5 + CH2−−CHOH −−→ CH3CH2CH2CHOH 3.04×106 1.68 6.619×103
CH2OH + C3H6 −−→ CH3CHCH2CH2OH 3.04×106 1.68 6.619×103
OH + C3H6 −−→ CH3CHCH2OH 7.54×107 1.20 -1.705×103
OH + 1- C4H8 −−→ CH3CH2CHCH2OH 7.54×107 1.20 -1.705×103
CH2OH + C2H4 −−→ CH2CH2CH2OH 1.28×106 1.60 2.7767×103
2- C2H4OH + C2H4 −−→ CH2CH2CH2CH2OH 1.28×106 1.60 2.7767×103
E.3. FALL-OFF LIMIT 215
A similar method for estimating the high-pressure limit rate constant for beta-
scission decomposition reactions relevant to tert-butanol radicals was done in Chap-
ter 8. In that chapter, the assumption was made that the rate constant of the addition
reaction of a methyl radical plus iso-butene is equivalent to the rate constant for the
addition reaction of a methyl radical plus propen-2-ol, and the rate constant for the
former reaction was taken from the work of Sun and Bozzelli [132].
E.3 Fall-off Limit
Because all of the experiments and simulations in this thesis were at pressures of
1 to 2 atm, the rate constants for the unimolecular reactions, including both the
beta-scission and isomerization reactions of the C4H9O radicals, are likely not at the
high-pressure limit. To determine the amount of rate constant fall off from the high-
pressure limit rate constant, the Kassel Integral [99] is used, which is given by Eq. E.1,
where k∞ is the high-pressure limit rate constant, S represents the effective number
of oscillators, and B and D are defined by Eq. E.2 and Eq. E.3, respectively.
k
k∞= I(S,B,D) =
1
Γ(S)
∫ ∞0
xS−1e−x
1 + 10D[x/(B + x)]S−1dx (Eq. E.1)
B =E∗
kT(Eq. E.2)
D =ν
k−1[M](Eq. E.3)
In Eq. E.2 and Eq. E.3, E∗ is the activation energy of the high-pressure limit rate
constant, ν is the A-factor of the high-pressure limit rate constant, k−1 is the molecular
collision frequency dependent on temperature and pressure, and [M] is the molecular
gas concentration. The gamma function is Γ(S) = (S − 1)!. Estimation for the
number of effective oscillators can be made by assuming S = Smax/2, where Smax is
the maximum number of vibrational modes, or a value of S can be chosen that leads
the Kassel Integral to predict a relative pressure dependence determined using high-
level electronic structure calculations. In the current work, the integral in Eq. E.1
was evaluated using a Riemann sum method that was designed to converge to the
216 APPENDIX E. RATE CONSTANTS FOR UNIMOLECULAR REACTIONS
correct value.
For the beta-scission reactions, the Kassel Integral in Eq. E.1 is applied to the high-
pressure limit rate constant in the endothermic (dissociation) direction. However, for
the isomerization reactions, re-deriving the Kassel Integral using the same method as
in Benson [99] yields the integral in Eq. E.4.
k
k∞= I(S,B,D) =
1
Γ(S)
∫ ∞0
xS−1e−x
1 + 10D[x/(B + x)]S−1 + 10D′ [x/(B′ + x)]S−1dx
(Eq. E.4)
In Eq. E.4, D and B are calculated by Eq. E.2 and Eq. E.3, respectively, in any
chosen forward direction of the isomerization reaction, and D′ and B′ are calculated
by Eq. E.2 and Eq. E.3, respectively, in the corresponding reverse direction of the
isomerization reaction. It was found for the isomerization reactions of interest in this
thesis, Eq. E.4 is equivalent to Eq. E.1 applied to the isomerization reaction in the
exothermic direction.
Bibliography
[1] U.S. Energy Information Administration. Annual energy outlook, April 2011.
DOE/EIA-0383.
[2] Z. Hong, D. F. Davidson, and R. K. Hanson. An improved H2/O2 mechanism
based on recent shock tube/laser absorption measurements. Combust. Flame,
158:633–644, 2011.
[3] G. P. Smith, D. M. Golden, M. Frenklach, N. W. Moriarty, B. Eite-
neer, M. Goldenberg, C. T. Bowman, R. K. Hanson, S. Song, W. C. Gar-
diner Jr., V. V. Lissianski, and Z. Qin. GRI-Mech 3.0, April 2012.
http://www.me.berkeley.edu/gri mech/.
[4] H. J. Curran, P. Gaffuri, W. J. Pitz, and C. K. Westbrook. A comprehensive
modeling study of n-heptane oxidation. Combust. Flame, 114:149–177, 1998.
[5] J. N. Bradley, W. D. Capey, R. W. Fair, and D. K. Pritchard. A shock-tube
study of the kinetics of reaction of hydroxyl radicals with H2, CO, CH4, CF3H,
C2H4, and C2H6. Int. J. Chem. Kinet., 8:549–561, 1976.
[6] J. F. Bott and N. Cohen. A shock tube study of the reaction of the hydroxyl
radical with propane. Int. J. Chem. Kinet., 16:1557–1566, 1984.
[7] J. F. Bott and N. Cohen. A shock tube study of the reactions of the hydroxyl
radical with several combustion species. Int. J. Chem. Kinet., 23:1075–1094,
1991.
217
218 BIBLIOGRAPHY
[8] J. F. Bott and N. Cohen. A shock tube study of the reaction of methyl radicals
with hydroxyl radicals. Int. J. Chem. Kinet., 23:1017–1033, 1991.
[9] J. B. Koffend and N. Cohen. Shock tube study of oh reactions with linear
hydrocarbons near 1100 K. Int. J. Chem. Kinet., 28:79–87, 1996.
[10] R. Sivaramakrishnan, N. K. Srinivasan, M.-C. Su, and J. V. Michael. High
temperature rate constants for OH + alkanes. Proc. Combust. Inst., 32:107–
114, 2009.
[11] R. Sivaramakrishnan and J. V. Michael. Rate constants for OH with selected
large alkanes: Shock-tube measurements and an improved group scheme. J.
Phys. Chem. A, 113:5047–5060, 2009.
[12] V. Vasudevan, D. F. Davidson, and R. K. Hanson. High-temperature measure-
ments of the reactions of OH with toluene and acetone. J. Phys. Chem. A,
109:3352–3359, 2005.
[13] N. K. Srinivasan, M.-C. Su, and J. V. Michael. Reflected shock tube studies of
high-temperature rate constants for OH + C2H2 and OH + C2H4. Phys. Chem.
Chem. Phys., 9:4155–4163, 2007.
[14] W. J. Pitz, N. P. Cernansky, F. L. Dryer, F. N. Egolfopoulos, J. T. Farrell,
D. G. Friend, and H. Pitsch. Development of an experimental database and
chemical kinetic models for surrogate gasoline fuels. SAE Paper 2007-01-0175,
2007.
[15] J. T. Farrell, N. P. Cernansky, F. L. Dryer, D. G. Friend, C. A. Hergart, C. K.
Law, R. M. McDavid, C. J. Mueller, A. K. Patel, and H. Pitsch. Development
of an experimental database and kinetic models for surrogate diesel fuels. SAE
Paper 2007-01-0201, 2007.
[16] M. Colket, T. Edwards, S. Williams, N. P. Cernansky, D. L. Miller, F. Egol-
fopoulos, P. Lindstedt, K. Seshadri, F. L. Dryer, C. K. Law, D. Friend, D. B.
Lenhert, H. Pitsch, A. Sarofim, M. Smooke, and W. Tsang. Development of an
BIBLIOGRAPHY 219
experimental database and kinetic models for surrogate jet fuels. 45th AIAA
Aerospace Sciences Meeting and Exhibit, Reno, Nevada, paper no. AIAA-2007-
0770, 1991.
[17] E. Ranzi, A. Frassoldati, S. Granata, and T. Faravelli. Wide-range kinetic
modeling study of the pyrolysis, partial oxidation, and combustion of heavy
n-alkanes. Ind. Eng. Chem. Res., 44:5170–5183, 2005.
[18] G. P. Smith, D. M. Golden, M. Frenklach, N. W. Moriarty, B. Eite-
neer, M. Goldenberg, C. T. Bowman, R. K. Hanson, S. Song, W. C. Gar-
diner Jr., V. V. Lissianski, and Z. Qin. A high-temperature chemical ki-
netic model of n-alkane oxidation, JetSurF version 1.0, September 15, 2009.
http://melchior.usc.edu/JetSurF/Version1 0/Index.html.
[19] N. R. Greiner. Hydroxyl radical kinetics by kinetic spectroscopy. VI. Reactions
with alkanes in the range 300-500 K. J. Chem. Phys., 55:1070–1076, 1970.
[20] R. Atkinson. Estimations of OH radical rate constants from H-atom abstraction
from C-H and O-H bonds over the temperature range 250-1000 K. Int. J. Chem.
Kinet., 18:555–568, 1986.
[21] R. Atkinson. A structure-activity relationship for the estimation of rate con-
stants for the gas-phase reactions of OH radicals with organic compounds. Int.
J. Chem. Kinet., 19:799–828, 1987.
[22] E. S. C. Kwok and R. Atkinson. Estimation of hydroxyl radical reaction rate
constants for gas-phase organic compounds using a structure-reactivity rela-
tionship: An update. Atmos. Environ., 29:1685–1695, 1995.
[23] R. R. Baldwin and R. W. Walker. Rate constants for hydrogen+oxygen system,
and for H atoms and OH radicals+alkanes. J. Chem. Soc., Faraday Trans.,
75:140–154, 1979.
[24] N. Cohen. The use of transition-state theory to extrapolate rate coefficients for
reactions of OH with alkanes. Int. J. Chem. Kinet., 14:1339–1362, 1982.
220 BIBLIOGRAPHY
[25] N. Cohen. Are reaction rate coefficients additive? Revised transition state
theory calculations for OH + Alkane reactions. Int. J. Chem. Kinet., 23:397–
417, 1991.
[26] L. K. Huynh, A. Ratkiewicz, and T. N. Truong. Kinetics of the hydrogen
abstraction OH + Alkane→ H2O + Alkyl reaction class: An application of the
reaction class transition state theory. J. Chem. Phys. A, 110:473–484, 2006.
[27] C. K. Westbrook, W. J. Pitz, and H. J. Curran. Chemical kinetic modeling
study of the effects of oxygenated hydrocarbons on soot emissions from diesel
engines. J. Phys. Chem. A, 110:6912–6922, 2006.
[28] G. Hess. BP and DuPont plan ‘Biobutanol’. Chem. Eng. News, 84:9, June
2006.
[29] P. Dagaut and C. Togbe. Oxidation kinetics of butanolgasoline surrogate mix-
tures in a jet-stirred reactor: Experimental and modeling study. Fuel, 87:3313–
3321, 2008.
[30] P. Dagaut, S. M. Sarathy, and M. J. Thomson. A chemical kinetic study of n-
butanol oxidation at elevated pressure in a jet stirred reactor. Proc. Combust.
Inst., 32:229–237, 2009.
[31] J. T. Moss, A. M. Berkowitz, M. A. Oehlschlaeger, J. Biet, V. Warth, P.-A.
Glaude, and F. Battin-Leclerc. An experimental and kinetic modeling study
of the oxidation of the four isomers of butanol. J. Phys. Chem. A, 112:10843–
10855, 2008.
[32] S. M. Sarathy, M. J. Thomson, C. Togbe, P. Dagaut, F. Halter, and
C. Mounaim-Russelle. An experimental and kinetic modeling study of n-butanol
combustion. Combust. Flame, 156:852–864, 2009.
[33] K. E. Noorani, B. Akih-Kumgeh, and J. M. Bergthorson. Comparative high
temperature shock tube ignition of C1-C4 primary alcohols. Energy Fuels,
24:5834–5843, 2010.
BIBLIOGRAPHY 221
[34] S. Vranckx, K. A. Heufer, C. Lee, H. Olivier, L. Schill, W. A. Kopp, K. Leon-
hard, C. A. Taatjes, and R. X. Fernandes. Role of peroxy chemistry in the
high-pressure ignition of n-butanol experiments and detailed kinetic modelling.
Combust. Flame, 158:1444–1455, 2011.
[35] I. Stranic, D. P. Chase, J. T. Harmon, S. Yang, D. F. Davidson, and R. K.
Hanson. Shock tube measurements of ignition delay times for the butanol
isomers. Combust. Flame, 159:516–527, 2012.
[36] R. D. Cook, D. F. Davidson, and R. K. Hanson. Multi-species laser measure-
ments of n-butanol pyrolysis behind reflected shock waves. Int. J. Chem. Kinet.,
44:303–311, 2012.
[37] K. M. Van Geem, S. P. Pyl, G. B. Marin, M. R. Harper, and W. H. Green. Accu-
rate high-temperature reaction networks for alternative fuels: Butanol isomers.
Ind. Eng. Chem. Res., 49:10399–10420, 2010.
[38] B. W. Webber, K. Kumar, Y. Zhang, and C.-J. Sung. Autoignition of n-butanol
at elevated pressure and low-to-intermediate temperature. Combust. Flame,
158:809–819, 2011.
[39] D. M. A. Karwat, S. W. Wagnon, P. D. Teini, and M. S. Wooldridge. On the
chemical kinetics of n-butanol: Ignition and speciation studies. J. Phys. Chem.
A, 115:4909–4921, 2011.
[40] R. Grana, A. Frassoldati, T. Faravelli, U. Niemann, E. Ranzi, R. Seiser, R. Cat-
tolica, and K. Seshadri. An experimental and kinetic modeling study of com-
bustion of isomers of butanol. Combust. Flame, 157:2137–2154, 2010.
[41] P. Oßwald, H. Guldenberg, K. Kohse-Hoinghaus, B. Yang, T. Yuan, and F. Qi.
Combustion of butanol isomers a detailed molecular beam mass spectrometry
investigation of their flame chemistry. Combust. Flame, 158:2–15, 2011.
[42] X. Gu, Z. Huang, Q. Li, and C. Tang. Measurements of laminar burning ve-
locities and markstein lengths of n-butanol-air premixed mixtures at elevated
temperatures and pressures. Energy Fuels, 23:4900–4907, 2009.
222 BIBLIOGRAPHY
[43] X. Gu, Z. Huang, S. Wu, and Q. Li. Laminar burning velocities and flame
instabilities of butanol isomersair mixtures. Combust. Flame, 157:2318–2325,
2010.
[44] P. S. Veloo and F. N. Egolfopoulos. Flame propagation of butanol isomers/air
mixtures. Proc. Combust. Inst., 33:987–993, 2011.
[45] P. S. Veloo, Yang. L. Wang, F. N. Egolfopoulos, and C. K. Westbrook. A
comparative experimental and computational study of methanol, ethanol, and
n-butanol flames. Combust. Flame, 157:1989–2004, 2010.
[46] W. Liu, A. P. Kelley, and C. K. Law. Non-premixed ignition, laminar flame
propagation, and mechanism reduction of n-butanol, iso-butanol, and methyl
butanoate. Proc. Combust. Inst., 33:995–1002, 2011.
[47] S. S. Vasu, D. F. Davidson, R. K. Hanson, and D. M. Golden. Measurements
of the reaction of OH with n-butanol at high-temperatures. Chem. Phys. Lett.,
497:26–29, 2010.
[48] B.H. Henshall. On Some Aspects of the Use of Shock Tubes in Aerodynamic
Research. McGraw-Hill Book Company, Inc., 1957.
[49] H. S. Glick, W. Squire, and A. Hertzberg. A new shock tube technique for the
study of high temperature gas phase reactions. Proc. Combust. Inst., 5:393–402,
1955.
[50] E. Goos, A. Burcat, and B. Ruscic. Ideal Gas Thermochemical
Database with updates from Active Thermochemical Tables, August 2009.
ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics.
[51] V. Vasudevan, R. D. Cook, R. K. Hanson, C. T. Bowman, and D. M. Golden.
High-temperature shock tube study of the reactions CH3 + OH → Products
and CH3OH + Ar → Products. Int. J. Chem. Kinet., 40:488–495, 2008.
BIBLIOGRAPHY 223
[52] J. T. Herbon. Shock tube measurements of CH3+O2 kinetics and the heat of
formation of the OH radical. PhD thesis, Stanford University Mechanical En-
gineering Department, 2004.
[53] A. E. Klingbeil, J. B. Jeffries, and R. K. Hanson. Temperature- and pressure-
dependent absorption cross sections of gaseous hydrocarbons at 3.39 µm. Meas.
Sci. Technol., 17:1950–1957, 2006.
[54] S. W. Sharpe, T. J. Johnson, R. L. Sams, P. A. Chu, G. C. Rhoderick, and
P. A. Johnson. Gas-phase databases for quantitative infrared spectroscopy.
Appl. Spectrosc., 58:1452–1461, 2004.
[55] F. P. Tully, M. L. Kozszykowski, and J. S. Binkley. Hydrogen-atom abstrac-
tion from alkanes by OH. I. Neopentane and neooctane. Proc. Combust. Inst.,
20:715–721, 1984.
[56] J.D. Mertens, M.S. Wooldridge, and R.K. Hanson. A laser photolysis shock
tube study of the reaction of OH with NH3. Shock Waves, 19:37–42, 1995.
[57] A. D. Kirk and J. H. Knox. The pyrolysis of alkyl hydroperoxides in the gas
phase. Trans. Faraday Soc., 56:1296–1303, 1960.
[58] S. W. Benson and G. N. Spokes. Very low pressure pyrolysis. III. t-Butyl hy-
droperoxide in fused silica and stainless steel reactors. J. Phys. Chem., 72:1182–
1186, 1968.
[59] P. Mulder and R. Louw. Gas-phase thermolysis of tert-butyl hydroperoxide in a
nitrogen atmosphere. the effect of added toluene. Recl. Trav. Chim. Pays-Bas,
103:148 – 152, 1984.
[60] K. A. Sahetchian, R. Rigny, J. Tardieu de Maleissye, L. Batt, M. Anwar Khan,
and S. Matthews. The pyrolysis of organic hydroperoxides (ROOH). Proc.
Combust. Inst., 42:637–643, 1992.
224 BIBLIOGRAPHY
[61] V. Vasudevan, D. F. Davidson, and R. K. Hanson. Direct measurements of the
reaction OH+CH2O→ HCO+H2O at high temperatures. Int. J. Chem. Kinet.,
37:98–109, 2005.
[62] S. S. Vasu, Z. Hong, D. F. Davidson, R. K. Hanson, and D. M. Golden. Shock
tube/laser absorption measurements of the reaction rates of OH with ethylene
and propene. J. Phys. Chem A, 114:11529–11537, 2010.
[63] K. Y. Choo and S. W. Benson. Arrhenius parameters for the alkoxy radical
decomposition reactions. Int. J. Chem. Kinet., 13:833–844, 1981.
[64] Z. Hong, R. D. Cook, D. F. Davidson, and R. K. Hanson. A shock tube study of
OH + H2O2 → H2O + HO2 and H2O2 + M→ 2OH + M using laser absorption
of H2O and OH. J. Phys. Chem. A, 114:5718–5727, 2010.
[65] D. A. Masten. A shock tube study of reactions in the H2/O2 mechanism. PhD
thesis, Stanford University Mechanical Engineering Department, 1991.
[66] R. D. Cook, D. F. Davidson, and R. K. Hanson. High-temperature shock tube
measurements of dimethyl ether decomposition and the reaction of dimethyl
ether with OH. J. Phys. Chem. A, 113:9974–9980, 2009.
[67] V. Vasudevan. Shock tube measurements of elementary oxidation and decom-
position reactions important in combustion using OH, CH and NCN laser ab-
sorption. PhD thesis, Stanford University Mechanical Engineering Department,
2007.
[68] L. N. Krasnoperov and J. V. Michael. High-temperature shock tube studies
using multipass absorption: Rate constant results for OH + CH3, OH + CH2,
and the dissociation of CH3OH. J. Phys. Chem. A, 108:8317–8323, 2004.
[69] N. K. Srinivasan, M.-C. Su, and J. V. Michael. High-temperature rate constants
for CH3OH + Kr → Products, OH + CH3OH → Products, OH + (CH3)2CO
→ CH2COCH3 + H2O, and OH + CH3 → CH2 + H2O. J. Phys. Chem. A,
111:3951–3958, 2007.
BIBLIOGRAPHY 225
[70] A. W. Jasper, S. J. Klippenstein, L. B. Harding, and B. Ruscic. Kinetics of the
reaction of methyl radical with hydroxyl radical and methanol decomposition.
J. Phys. Chem. A, 111:3932–3950, 2007.
[71] J. Ree, Y. H. Kim, and H. K. Shin. Dynamics of the CH3 + OH reaction. Int.
J. Chem. Kinet., 43:455–466, 2011.
[72] K. R. Darnall, R. Atkinson, and J. N. Pitts Jr. Rate constants for the reaction
of the OH radical with selected alkanes at 300 K. J. Phys. Chem., 82:1581–1584,
1978.
[73] F. Nolting, W. Behnke, and C. Zetzsch. A smog chamber for studies of the
reactions of terpenes and alkanes with ozone and OH. J. Atmos. Chem., 6:47–
59, 1988.
[74] J. P. D. Abbatt, K. L. Demerjian, and J. G. Anderson. A new approach to
free-radical kinetics: Radially and axially resolved high-pressure discharge flow
with results for OH + (C2H6, C3H8, n-C4H10, n-C5H12) → products at 297 k.
J. Phys. Chem., 94:4566–4575, 1990.
[75] R. K. Talukdar, A. Mellouki, T. Gierczak, S. Barone, S.-Y. Chiang, and A. R.
Ravishankara. Kinetics of the reactions of OH with alkanes. Int. J. Chem.
Kinet., 26:973–990, 1994.
[76] C. Ferrari, A. Roche, V. Jacob, P. Foster, and P. Baussand. Kinetics of the
reaction of OH radicals with a series of esters under simulated conditions at
295 K. Int. J. Chem. Kinet., 28:609–614, 1996.
[77] N. M. Donahue, J. G. Anderson, and K. L. Derjian. New rate constants for ten
OH alkane reactions from 300 to 400 K: An assessment of accuracy. J. Phys.
Chem. A, 102:3121–3126, 1998.
[78] C. Coeur, V. Jacob, P. Foster, and P. Baussand. Rate constant for the gas-phase
reaction of hydroxyl radical with the natural hydrocarbon bornyl acetate. Int.
J. Chem. Kinet., 30:497–502, 1998.
226 BIBLIOGRAPHY
[79] W. B. DeMore and K. D. Bayes. Rate constants for the reactions of hydroxyl
radical with several alkanes, cycloalkanes, and dimethyl ether. J. Phys. Chem.
A, 103:2649–2654, 1999.
[80] A. Colomb, V. Jacob, P. Kaluzny, and P. Baussand. Kinetic investigation of
gas-phase reactions between the OH-radical and o-, m-, n-ethyltoluene and
n-nonane in air. Int. J. Chem. Kinet., 36:367–378, 2004.
[81] Z. Li, S. Singh, W. Woodward, and L. Dang. Kinetics study of OH radi-
cal reactions with n-octane, n-nonane, and n-decane at 240-340 K using the
relative rate/discharge flow/mass spectrometry technique. J. Phys. Chem. A,
110:12150–12157, 2006.
[82] E. W. Wilson Jr., W. A. Hillary, H. R. Kennington, B. Evans III, N. W. Scott,
and W. B. DeMore. Measurement and estimation of rate constants for the
reactions of hydroxyl radical with several alkanes and cycloalkanes. J. Phys.
Chem. A, 110:3593–3604, 2006.
[83] E. Ranzi, A. Frassoldati, S. Granata, and T. Faravelli. Wide-range kinetic
modeling study of the pyrolysis, partial oxidation, and combustion of heavy
n-alkanes. Ind. Eng. Chem. Res., 44:5170–5183, 2005.
[84] C. K. Westbrook, W. J. Pitz, O. Herbinet, H. J. Curran, and E. J Silke. A
detailed chemical kinetic reaction mechanism for n-alkane hydrocarbons from
n-octane to n-hexadecane. Combust. Flame, 156:181–199, 2009.
[85] G. Black, H. J. Curran, J. M. Simmie, and V. Zhukov. Bio-butanol: Combustion
properties and detailed chemical kinetic model. Combust. Flame, 157:363–373,
2010.
[86] E. Ranzi, M. Dente, T. Faravelli, and G. Pennati. Prediction of kinetic param-
eters for hydrogen abstraction reactions. Comb. Sci. Tech., 95:1–50, 1994.
[87] A. Galano, J. R. Alvarez-Idaboy, G. Bravo-Perez, and M. E. Ruiz-Santoyo. Gas
phase reactions of C1C4 alcohols with the OH radical: A quantum mechanical
approach. Phys. Chem. Chem. Phys., 4:4648–4662, 2002.
BIBLIOGRAPHY 227
[88] C.-W. Zhou, J. M. Simmie, and H. J. Curran. Rate constants for hydrogen-
abstraction by OH from n-butanol. Combust. Flame, 158:726–731, 2011.
[89] M. R. Harper, K. M. Van Geem, S. P. Pyl, G. B. Marin, and W. H. Green.
Comprehensive reaction mechanism for n-butanol pyrolysis and combustion.
Combust. Flame, 158:16–41, 2011.
[90] H. L. Bethel, R. Atksinson, and J. Arey. Kinetics and products of the reactions
of selected diols with the OH radical. Int. J. Chem. Kinet., 33:310–316, 2001.
[91] S. M. Sarathy, S. Vranckx, K. Yasunaga, M. Mehl, P. Oßwald, C. K. West-
brook, W. J. Pitz, K. Kohse-Hoinghaus, R. X. Fernandes, and H. J. Curran. A
comprehensive chemical kinetic combustion model for the four butanol isomers.
Combust. Flame, 159:2028–2055, 2012.
[92] E. R. Ritter and J. W. Bozzelli. THERM: Thermodynamics property estimation
for gas phase radicals and molecules. Int. J. Chem. Kinet., 23(9):767–778, 1991.
[93] J. Zador and J. A Miller. Hydrogen abstraction from n-, i-propanol and n-
butanol: A systematic theoretical approach. Paper 2B06 at the 7th US National
Technical Meeting of the Combustion Institute, March 2011.
[94] J. Zheng and D. G. Truhlar. Kinetics of hydrogen-transfer isomerizations of
butoxyl radicals. Phys. Chem. Chem. Phys., 12:7782–7793, 2010.
[95] X. Xu, E. Papajak, and D. G. Truhlar. Multi-structural variational transition
state theory: Kinetics of the 1,5-hydrogen shift isomerization of 1-butoxyl rad-
ical including all structures and torsional anharmonicity. Phys. Chem. Chem.
Phys., 14:4204–4216, 2012.
[96] S. J. Klippenstein. Chemistry Division, Argonne National Laboratory, 2011.
Personal Communication.
[97] J. P. Senosian, S. J. Klippenstein, and J. A. Miller. Reaction of ethylene with
hydroxyl radicals: A theoretical study. J. Phys. Chem. A, 110:6960–6970, 2006.
228 BIBLIOGRAPHY
[98] J. A. Miller and S. J. Klippenstein. The H+C2H2+M↔C2H3+M and
H+C2H2+M↔C2H5+M reactions: Electronic structure, variational transition-
state theory,and solutions to a two-dimensional master equation. Phys. Chem.
Chem. Phys., 6:1192–1202, 2004.
[99] S. W. Benson. The Foundations of Chemical Kinetics. McGraw-Hill Book
Company, Inc., 1960.
[100] H. J. Curran. Rate constant estimation for C1 to C4 alkyl and alkoxyl radial
decomposition. Int. J. Chem. Kinet., 38:250–275, 2006.
[101] R. Sivaramakrishnan, M.-C. Su, J. V. Michael, S. J. Klippenstein, L. B. Hard-
ing, and B. Ruscic. Rate constants for the thermal decomposition of ethanol and
its bimolecular reactions with OH and D: Reflected shock tube and theoretical
studies. J. Phys. Chem. A, 114:9425–9439, 2010.
[102] P. Zhang, S. J. Klippenstein, and C. K. Law. Ab initio kinetics of the decom-
position of α-hydroxybutyl radicals of n-butanol. Fall Technical Metting of the
Eastern States Section of the Combustion Institute, October 2011.
[103] P. Zhang. Department of Mechanical and Aerospace Engineering, Princeton
University, 2011. Personal Communication.
[104] S. W. Benson and H. E. O’Neal. Kinetic data on gas phase unimolecular reac-
tions. NSRDS-NBS, 21:438, 1970.
[105] I. M. Campbell, D. F. McLaughlin, and B. J. Handy. Rate constants for reac-
tions of hydroxyl radicals with alcohol vapours at 292 K. Chem. Phys. Lett.,
38:362–364, 1976.
[106] M. Yujing and A. Mellouiki. Temperature dependence for the rate constants of
the reaction of OH radicals with selected alcohols. Chem. Phys. Lett., 333:63–68,
2001.
BIBLIOGRAPHY 229
[107] F. Cavalli, H. Geiger, I. Barnes, and K. H. Becker. FTIR kinetic, product, and
modeling study of the OH-initiated oxidation of 1-butanol in air. Environ. Sci.
Technol., 36:1263–1270, 2002.
[108] L. Nelson, O. Rattigan, R. Neavyn, H. Sidebottom, J. Treacy, and O. J. Nielsen.
Absolute and relative rate constants for the reactions of hydroxyl radicals and
chlorine atoms with a series of aliphatic alcohols and ethers at 298 K. Int. J.
Chem. Kinet., 22:1111–1126, 1990.
[109] T. J. Wallington and M. J. Kurylo. The gas phase reactions of hydroxyl radicals
with a series of alphatic alcohols over the temperature range 240-440 K. Int. J.
Chem. Kinet., 19:1015–1023, 1987.
[110] M. D. Hurley, T. J. Wallington, L. Laursen, M. S. Javadi, O. J. Nielson, T. Y.
Yamanaka, and M. Kawasaki. Atmospheric chemistry of n-butanol: Kinetics,
mechanisms, and products of Cl atom and OH radical initiated oxidation in the
presence and absence of NOx. J. Phys. Chem. A, 113:7011–7020, 2009.
[111] H. Wu, Y. Mu, X. Zhang, and G. Jiang. Relative rate constants for the reactions
of hydroxyl radicals and chlorine atoms with a series of aliphatic alcohols. Int.
J. Chem Kinet., 35:81–87, 2003.
[112] S. Atsumi, T. Hanai, and J. C. Liao. Non-fermentative pathways for synthesis
of branched-chain higher alcohols and biofuels. Nature, 451:86–89, 2008.
[113] S. S. Merchant and W. H. Green. Department of Chemical Engineering, Mas-
sachusetts Institute of Technology, 2012. Personal Communication.
[114] J. Zheng, R. Meana-Paneda, and D. G. Truhlar. Department of Chemistry,
University of Minnesota, 2012. Personal Communication.
[115] A. Mellouki, F. Oussar, X. Lun, and A. Chakir. Kinetics of the reactions of OH
with 2-methyl-1-propanol, 3-methyl-1-butanol and 3-methyl-2-butanol between
241 and 373 K. Phys. Chem. Chem. Phys., 6:2951–2955, 2004.
230 BIBLIOGRAPHY
[116] V. F. Anderson, T. J. Wallington, and O. J. Nielson. Atmospheric chemistry
of i-butanol. J. Phys. Chem. A, 114:12462–12469, 2010.
[117] P. S. Nigam and A. Singh. Production of liquid biofuels from renewable re-
sources. Prog. Energy Combust. Sci., 37:52–68, 2011.
[118] A. A. Chew and R. Atkinson. OH radical formation yields from the gas-phase
reactions of O3 with alkenes and monoterpenes. J. Geophys. Res., 101:28649–
28653, 1996.
[119] J. S. Baxley and J. R. Wells. The hydroxyl radical reaction rate constant
and atmospheric transformation products of 2-butanol and 2-pentanol. Int. J.
Chem. Kinet., 30:745–752, 1998.
[120] E. Jimenez, B. Lanza, A. Garzon, B. Ballesteros, and J. Albaladejo. At-
mospheric degradation of 2-butanol, 2-methyl-2-butanol, and 2,3-dimethyl-2-
butanol: OH kinetics and UV absorption cross sections. J. Phys. Chem. A,
109:10903–10909, 2005.
[121] T. K. Choudhury, M. C. Lin, C.-Y. Lin, and W. A. Sanders. Thermal decompo-
sition of t-butyl alcohol in shock waves. Combust. Sci. and Tech., 71:219–232,
1990.
[122] J. K. Lefkowitz, J. S. Heyne, S. H. Won, S. Dooley, H. H. Kim, F. M. Haas,
S. Jahangirian, F. L. Dryer, and Y. Ju. A chemical kinetic study of teriary-
butanol in a flow reactor and counterflow diffusion flame. Combust. Flame,
159:968–978, 2012.
[123] T. S. Norton and F. L. Dryer. The flow reactor oxidation of C1-C4 alcohols and
MTBE. Proc. Combust. Inst., 23:179–185, 1991.
[124] J. Cai, L. Zhang, J. Yang, Y. Li, L. Zhoa, and F. Qi. Experimental and kinetic
modeling study of tert-butanol combustion at low pressure. Energy, 43:94–102,
2012.
BIBLIOGRAPHY 231
[125] R. A. Cox and A. Goldstone. Atmospheric reactivity of oxygenated motor fuel
additives. Phys. Chem. Behav. Atmos. Pollut. Proc. Eur. Symp., 2:112–119,
1982.
[126] T. J. Wallington, P. Dagaut, R. Liu, and M. J. Kurylo. Gas-phase reactions
of hydroxyl radicals with the fuel additives methyl tert-butyl ether and tert-
butyl alcohol over the temperature range 240-440 K. Environ. Sci. Technol.,
22:842–844, 1988.
[127] S. Teton, A. Mellouki, and G. Le Bras. Rate constants for reactions of OH
radicals with a series of asymmetric ethers and tert-butyl alcohol. Int. J. Chem.
Kinet., 28:291–297, 1996.
[128] S. M. Saunders, D. L. Baulch, K. M. Cooke, M. J. Pilling, and P. I. Smurth-
waite. Kinetics and mechanisms of the reactions of OH with some oxygenated
compounds of importance in tropospheric chemistry. Int. J. Chem. Kinet.,
35:81–87, 2002.
[129] W. P. Hess and F. P. Tully. Catalytic conversion of alcohols to alkenes by OH.
Chem. Phys. Lett., 152:183–189, 1988.
[130] J. R. Dunlop and F. P. Tully. Catalytic dehydration of alcohols by OH: An
intermediate case. J. Phys. Chem., 97:6457–6464, 1993.
[131] C.-J. Chen and J. W. Bozzelli. Analysis of tertiary butyl radical + O2, isobutene
+ HO2, and isobutene-OH adducts + O2: A detailed tertiary butyl oxidation
mechanism. J. Phys. Chem. A, 103:9731–9736, 1999.
[132] H. Sun and J. W. Bozzelli. Thermochemical and kinetic analysis on the reactions
of neopentyl and hydroperoxy-neopentyl radicals with oxygen: Part I. OH and
initial stable HC product formation. J. Phys. Chem. A, 108:1694–1711, 2004.
[133] W. G. Mallard, F. Westley, J. T. Herron, and R. F. Hampson. NIST Chemical
Kinetics Database. Version 6.0. NIST Standard Reference Data, Gaithersburg,
MD, 1994.
232 BIBLIOGRAPHY
[134] S. S. Khan, X. Yu, J. R. Wade, R. D. Malmgren, and L. J. Broadbelt. Thermo-
chemistry of radicals and molecules relevant to atmospheric chemistry: Deter-
mination of group additivity values using G3//B3LYP theroy. J. Phys. Chem.
A, 113:5176–5194, 2009.
[135] S. A. Carr, M. A. Blitz, and P. W. Seakins. Site-specific rate coefficients for the
reaction of OH with ethanol from 298 to 900 K. J. Phys. Chem. A, 115:3335–
3345, 2011.
[136] R. A. Gorski. Stability of trichlorotrifluoroethane-stainless steel systems. Amer-
ican Society for Testing and Materials, 538:65–76, 1973.
[137] I. Stranic. Department of Mechanical Engineering, Stanford University, 2011.
Personal Communication.
[138] S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O’Neal,
A. S. Rodgers, R. Shaw, and R. Walsh. Additivity rules for the estimation of
thermochemical properties. Chem. Rev., 69:279–324, 1969.
[139] R. W. Walker. Temperature coefficients for reactions of OH radicals with alkanes
between 300 and 1000 K. Int. J. Chem. Kinet., 17:573–582, 1985.
[140] R. Sumathi, H.-H. Carstensen, and W. H. Green. Reaction rate prediction via
group additivity part 1: H abstraction from alkanes by H and CH3. J. Phys.
Chem. A, 105:6910–6925, 2001.
[141] R. Sumathi and W. H. Green. Oxygenate, oxyalkyl, and alkoxycarbonyl ther-
mochemistry and rates fro hydrogen abstraction from oxygenates. Phys. Chem.
Chem. Phys, 5:3402–3417, 2003.
[142] J. A. Manion, R. E. Huie, R. D. Levin, D. R. Burgess Jr., V. L. Orkin, W. Tsang,
W. S. McGivern, J. W. Hudgens, V. D. Knyazev, D. B. Atkinson, E. Chai, A. M.
Tereza, C.-Y. Lin, T. C. Allison, W. G. Mallard, F. Westley, J. T. Herron,
R. F. Hampson, and D. H. Frizzell. NIST Chemical Kinetics Database, NIST
BIBLIOGRAPHY 233
Standard Reference Database 17, Version 7.0 (Web Version), Release 1.4.3,
Data version 2008.12, August 2011. http://kinetics.nist.gov/.