EXPERIMENTAL DETERMINATION OF RATE CONSTANTS FOR REACTIONS...

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



http://purl.stanford.edu/rh393tq1232

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


Craig Bowman


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

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


4.2 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


5.2 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


5.5.2 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



6.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.3 Kinetic Modeling and Analysis . . . . . . . . . . . . . . . . . . . . . . 100

6.3.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . 100


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



7.2 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



8.1.3 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





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


5.3 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


5.9 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



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

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


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


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.


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


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,


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


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


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


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


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


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


6 Add argon 1007 0.5% TBHP/water, 1.5%n-heptane, argon


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


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


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


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


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


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


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


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


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.


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


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


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


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


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


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


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


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


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.

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.


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


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


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)


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).


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).


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]


k4.3 = 3.17× 10−10 exp

(− 1801

T [K]


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.


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



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



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


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


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


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.


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


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


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.

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.


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.


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.


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]


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


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%.


5.2.2 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


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)


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.


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.


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.


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


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


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.


0 10 20 30 40 50 60 70 801

10

925 K, 1.22 atm201 ppm n-butanol, 10.3 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]


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.


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


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


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)


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


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


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


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


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


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


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.


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.


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)


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]


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


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


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.



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


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



(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.


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.


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


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.


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]




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]



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


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]


The current work represents the first experimentally-determined rate constant for

Reaction (6.1) at combustion-relevant temperatures.


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]


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


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


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)


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).


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.


7.2 Experimental



(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


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


6%83%

11%

82%

9%

9%

Grana et al.

Van Geem et al.

OH

+

+

OH

C2H5HO


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.


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


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]


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


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]


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.


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.

Chapter 8

Reaction of OH with tert-Butanol

8.1 Introduction


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


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


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.


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


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


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


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


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


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)


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%.


8.4.1 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]


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


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].


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


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


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]


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].


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


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]


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.

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)



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]


k4.2 = 2.43× 10−10 exp

(− 1804

T [K]


k4.3 = 3.17× 10−10 exp

(− 1801

T [K]


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]


k6.1 = 1.85× 10−10 exp

(− 2155

T [K]


k7.1 = 6.97× 10−11 exp

(− 1550

T [K]


k8.1 = 1.91× 10−11 exp

(− 725

T [K]


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


(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]


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]


k6.1 = 1.65× 10−21T 3.18 exp

(+

1304

T [K]


k7.1 = 4.95× 10−20T 2.66 exp

(+

1123

T [K]


k8.1 = 8.93× 10−20T 2.60 exp

(+

450

T [K]


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.


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


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.

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.


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


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


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


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.


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.


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


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


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.


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


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.

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


(“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.


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


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.


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.


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.


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


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


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


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


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.


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


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


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)


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.


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


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]


kt = 1.89× 10−18T 2 exp

(− 696

T [K]


koh = 2.10× 10−18T 2 exp

(− 85

T [K]


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


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.


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


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.

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.


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


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.

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