Elucidating Reaction Kinetics with Time-Resolved
Frequency Comb Spectroscopy
byBryce J. Bjork
B.A., Gustavus Adolphus College, 2011

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulllmentof the requirements for the degree ofDoctor of Philosophy
Department of Physics
2017This thesis entitled:
Elucidating Reaction Kinetics with Time-Resolved Frequency Comb Spectroscopy
written by Bryce J. Bjork
has been approved for the Department of Physics

Jun YeCarl Lineberger

Date

The nal copy of this thesis has been examined by the signatories, and we nd that both thecontent and the form meet acceptable presentation standards of scholarly work in the above
mentioned discipline.

Bjork, Bryce J. (Ph.D., Physics)

Elucidating Reaction Kinetics with Time-Resolved Frequency Comb Spectroscopy

Thesis directed by Prof. Jun Ye

The kinetics of the hydroxyl radical (OH) + carbon monxide (CO) reaction, which is fundamental to both atmospheric and combustion chemistry, are complex because of the formation of thehydrocarboxyl radical (HOCO) intermediate. Despite extensive studies of this reaction, HOCO has
not been observed under thermal reaction conditions. In this thesis, we report the development of
a sensitive and multiplexed technique, time-resolved frequency comb spectroscopy (TRFCS) for theobservation of reactive chemical intermediates on the microsecond timescale. Using this technique,we observed deuteroxyl radical (OD) + CO reaction kinetics and detected all relevant reactants
and products. By simultaneously measuring the time-dependent concentrations of the OD,
DOCO,trans-

cis-DOCO and CO2 , we observed unambiguous low-pressure termolecular dependence ofthe reaction rate coecients for N2 and CO bath gases.
mation mechanism and quantify its yield.
isomerization and quantied its rate.

These results conrm the HOCO for-Additionally, we observed

cis-DOCO

trans-DOCO

Dedication

To my family, for their love and support

Acknowledgements

My interest in physics and mathematics began at a young age. My parents always encouraged me
to explore and understand the world. This only increased in the high school classroom of Dennis
Symalla.

His unique style of teaching conveyed his excitement and passion for physics, pushing

us to think critically about the world in which we live.

After his classes, the decision to pursue

an undergraduate degree in physics was easy. During my undergraduate experience at Gustavus
Adolphus College, I had the opportunity to work with a few excellent professors.

In particular,

I'd like to thank Thomas Huber and Steven Mellema for sharing their knowledge, enthusiasm,
and laboratory skills. My interest in optics began midway though college, but I really began myexperimental optics at Caltech, as part of the LIGO SURF program. During this experience, I had
the opportunity to work with Eric Black and Greg Ogin, who were excellent instructors.
During my time at JILA, I've had the opportunity to work with quite a few amazing people. Firstand foremost, I am truly grateful for the opportunity to work with Jun. He inspires a laboratory
atmosphere of collaboration and innovation, with a driving urgency to solve the problem at hand.
I am constantly astounded by his ability to simultaneously manage so many dierent projects yet
maintain a laser-like focus in all of them. Most importantly, however, it is clear that he truly cares
about his students and post-docs. I've learned a great deal from Jun about experimental physics,
experience that will prove invaluable wherever life takes me.
When I joined the lab, I had the opportunity to work with Alexandra Foltynowicz, Piotr
Maslowski, Adam Fleisher, Ben Spaun, and Oliver Heckl on the mid-infrared team, who helped
teach me the basics of frequency comb spectroscopy. On the extreme ultraviolet team, I overlappedwith Tom Allison, Arman Cingoz, Craig Benko, Francois Labaye, and Linqiang Hua. I am grate-vi

ful for discussions with all of them - their unique perspectives were very valuable. Additionally, I
had the pleasure of interacting with Jan Hall, who was always willing to share his knowledge andenthusiasm. I would like to thank Travis Nicholson, Ben Bloom, Ross Hutson, Toby Bothwell, Wei
Zhang, Matt Grau, Will Cairncross, Ed Marti, Shimon Kolkowitz, Dave Reens, Alejandra Collopy,
Matt Hummon, Mark Yao, Kevin Cossel, Dan Gresh, Yuval Shagam, and all of the other membersof the Ye group with whom I've overlapped.
I would like to thank the current members of the mid-infrared and extreme ultraviolet teams,
Thinh Bui, Bryan Changala, Kana Iwakuni, Gil Porat, Christoph Heyl, and Steven Schoun, forexcellent discussions. It is clear to me that the future of the group is in good hands. I would like togive a special thanks to Thinh Bui and Oliver Heckl, who have been great friends and colleagues.
Thinh has a very broad understanding of chemistry and a unique ability to nd problems that areboth interesting and technically accessible. Combined with his genial personality and strong work
ethic, he is a force to be reckoned with.

Oliver was a constant pleasure to have in the lab.

His

optics expertise and consistently positive outlook brightened the lab's atmosphere.
JILA would not be what it is today without its sta shops. I'd like to thank the sta of themachine and electronics shop, particularly Hans Green, Terry Brown, and Kim Hagen, for sharing
their technical expertise, enthusiasm, and positive outlook. I'd like to thank J.R. Raith from thecomputing department for helping to sort out strange computer issues.
There are a few people outside the lab who I'd like to thank for helping me maintain sanity
during the diculties of grad school. Adam Reed, Steven Moses, Karl Mayer, Adam Keith, Dan
Palken, Travis Autry, Felix Vietmeyer, and many others who I have not mentioned have been greatfriends and activity partners throughout my graduate career.
Finally, I'd like to thank my family for supporting me on this journey. I would not be where I
am without them.

Contents
1 Introduction

12 Frequency Combs and Molecular Spectroscopy

4

2.1

Molecular Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

2.2

Enhancement with an Optical Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.3

Mirror Dispersion Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.4

Detection Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

2.5

Demonstration: Detection of H2 O2 in the presence of H2 O . . . . . . . . . . . . . . .

18

3 Time-Resolved Frequency Comb Spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

3.1

Overview

3.2

Mid-Infrared Frequency Comb Source. . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.3

Frequency Comb Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

3.4

Optical Enhancement Cavity

29

3.5

Virtually Imaged Phased Array (VIPA). . . . . . . . . . . . . . . . . . . . . . . . .

31

3.6

Locking the Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

3.7

Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

3.8

Temporal Resolution and Sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . .

38

3.9

Demonstration of the time-resolved spectrometer: acrylic acid . . . . . . . . . . . . .

41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 The OH+CO Reaction: Introduction
4.1

Overview

2349. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

49

CONTENTS

viii

4.2

Atmospheric Importance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

4.3

Combustion Importance and Additional Applications . . . . . . . . . . . . . . . . . .

51

4.4

History of the OH+CO Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

4.5

Mechanics of the OH+CO Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

4.6

Experimental Approach: OD Generation . . . . . . . . . . . . . . . . . . . . . . . . .

57

4.7

Spectral Characteristics of Key Species . . . . . . . . . . . . . . . . . . . . . . . . . .

61



5 Direct Measurement of OD+CO trans -DOCO Kinetics

67

5.1

Main Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

5.2

Supplementary Materials and Methods:. . . . . . . . . . . . . . . . . . . . . . . . .

82

5.2.1

Experimental description and conditions . . . . . . . . . . . . . . . . . . . . .

82

5.2.2

Data extraction & analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

5.2.3

Sources of error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

5.2.4

Rate Equation Model

5.2.5

Table of Statistical and Systematic Errors . . . . . . . . . . . . . . . . . . . . 108. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 CO2 and cis -DOCO Channels

109

6.1

The OD + CO → D + CO2 Channel

6.2

The OD + CO → cis−DOCO Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 113. . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7 Conclusion and Outlook

132

A Selected Mathematical Derivations

134

A.1

The Frequency Comb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

A.2

OH+CO Lindemann Expressions

A.3

trans -DOCO

cis -DOCO Isomerization

A.4

trans -DOCO

cis -DOCO Isomerization with Formation and Loss . . . . . . . . . . 137

B Frequency comb locking notes
B.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135. . . . . . . . . . . . . . . . . . . . . . . . 136

139

Stabilization of the Repetition Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

CONTENTS

ix

B.2

Locking the Carrier Envelope Oset Frequency

B.3

The Fiber Bragg Grating

C MATLAB Code
C.1

. . . . . . . . . . . . . . . . . . . . . 140. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

144

VIPA Fringe Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

List of Figures
2.1

The optical frequency comb as an accumulation of stabilized pulses. . . . . . . . . . .

5

2.2

Time- and frequency-domain interpretation of rep and f0 . . . . . . . . . . . . . . . . .

6

2.3

Spectral ux of Globar vs. Mid-IR OPO Frequency Comb. . . . . . . . . . . . . . . .

8

2.4

The v=0

1 ro-vibrational spectrum of OD. . . . . . . . . . . . . . . . . . . . . . . .

9

2.5Reectivity and dispersion of a quarter-wave stack. . . . . . . . . . . . . . . . . . . .

15

2.6

Eect of dispersion on cavity absorption features. . . . . . . . . . . . . . . . . . . . .

15

2.7

Cavity transmission in the presence of dispersion. . . . . . . . . . . . . . . . . . . . .

16

2.8

Experimental methane spectra with dispersion.

. . . . . . . . . . . . . . . . . . . . .

16

2.9

Experimental setup for H2 O2 detection.

. . . . . . . . . . . . . . . . . . . . . . . . .

19



2.10 Experimental spectra of hydrogen peroxide and water.

. . . . . . . . . . . . . . . . .

21

3.1

Yb comb oscillator and amplier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

3.2

Spectrum of Yb:ber oscillator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

3.3

Photo of the Yb:ber amplier in operation. . . . . . . . . . . . . . . . . . . . . . . .

28

3.4

Diagram of the ow cell used in the TRFCS work . . . . . . . . . . . . . . . . . . . .

30

3.5

TRFCS ow cell

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

3.6

Three-point mount installed on the input and output of the reaction cell. . . . . . . .

32

3.7

Physical picture of VIPA etalon.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

3.8

Reection spectrum of the mid-IR VIPA etalon. . . . . . . . . . . . . . . . . . . . . .

33

3.9

VIPA spectrometer images.

35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.10 Comb mode resolved VIPA image.

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

38

LIST OF FIGURES

xi

3.11 Locking diagram for TRFCS experiment. . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.12 Timing diagram for TRFCS experiment. . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.13 Oscilloscope screenshot of sweep signals. . . . . . . . . . . . . . . . . . . . . . . . . .

40

3.14 Two isomers of AA-d1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

3.15 Bubbler used to introduce AA-d1 to the reaction cell. . . . . . . . . . . . . . . . . . .

43

3.16 Typical broadband absorption spectrum of AA-d1 .

. . . . . . . . . . . . . . . . . . .

43

3.17 Time-dependent AA-d1 depletion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

3.18 Transient absorption following the photolysis of AA-d1 . . . . . . . . . . . . . . . . . .

46

3.19 Absorption spectrum of C2 HD.

47. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.20 Measured time-dependent concentrations of HOD, D2 O, C2 HD, andtrans -DOCO.

.

48

4.1

Role of OH+CO in the O3 balance of the atmosphere.

. . . . . . . . . . . . . . . . .

51

4.2

Simple Arrhenius reaction surface and temperature dependence. . . . . . . . . . . . .

53

4.3

Early reaction surface and temperature dependence of OH+CO. . . . . . . . . . . . .

53

4.4

One dimensional potential energy surface for OH+CO. . . . . . . . . . . . . . . . . .

55

4.5

Pressure dependence of the OH+CO reaction rate within the Lindemann formalism.

56

4.6

UV Photolysis cross sections for O3 and N2 O. . . . . . . . . . . . . . . . . . . . . . .

59

4.7

Photo of ozone trap.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.8

UV LED spectrum (blue, left axis) and O3 absorption cross section (red, right axis).

61

4.9

Integrated time-dependent ozone concentration. . . . . . . . . . . . . . . . . . . . . .

62

4.10 Mid-IR Absorption Spectra of Key Species.

. . . . . . . . . . . . . . . . . . . . . . .

63

4.11 OH RKR potential energy and dipole moment functions. . . . . . . . . . . . . . . . .

65

4.12 OH and CO calculated vibrational wavefunctions. . . . . . . . . . . . . . . . . . . . .

65



5.1

Potential energy surface for OH + CO

H + CO. . . . . . . . . . . . . . . . . . . .

69

5.2

Schematic of important reactions in our system. . . . . . . . . . . . . . . . . . . . . .

69

5.3

Experimental time-dependent spectra oftrans -DOCO, OD, and D2 O. . . . . . . . . .

74

5.4

Fitted time-dependent concentrations of OD andtrans -DOCO. . . . . . . . . . . . .

75

LIST OF FIGURES

xii

5.5

Determination of the termoleculartrans -DOCO formation rate. . . . . . . . . . . . .

77

5.6

Rate equation model tting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

5.7

Schematic of mid-IR TrFCS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

5.8

Measurement of Ozone photolysis fraction. . . . . . . . . . . . . . . . . . . . . . . . .

83

5.9

Finesse from spectrally resolved cavity-ringdown measurements. . . . . . . . . . . . .

94

5.10 Knife edge scan of YAG beam.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.11 Kinetics cell half-life from D2 O loss.

. . . . . . . . . . . . . . . . . . . . . . . . . . .

5.12 The ratio of retrieved k1a values for 50 μs and 10 μs integration times.

94
96. . . . . . . .

98

5.13 Representative spectrum of OD(v=0) and OD(v=1) for measuring [OD(v>0)]. . . . .

98

5.14 First order decay rate of OD(v=1) as a function of [CO]. . . . . . . . . . . . . . . . . 100
5.15 OD(v=0) rise as a function of [CO].

. . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.16 Variation of k1a with D2 concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.17 Variation of k1a with O3 concentration.

. . . . . . . . . . . . . . . . . . . . . . . . . 102

5.18 Basic schematic of the rate equation model.
5.19 Results of tting the DOCO loss rate.

. . . . . . . . . . . . . . . . . . . . . . . 103. . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.1

Measured time-dependent spectra of OD and CO2 .

. . . . . . . . . . . . . . . . . . . 110

6.2

Time-dependent concentrations of CO and OD(v=0). . . . . . . . . . . . . . . . . . . 112

6.3

D+CO2 formation rate as a function of N2 , CO, and He bath gases.

6.4

Geometry of

6.5

Zoomed6.6

Full cis-DOCO spectrum.

6.7

Time-dependent concentrations of OD, cis-DOCO, trans-DOCO, and CO.

6.8trans -DOCO spectrum.

6.9

Ratio of [trans-DOCO] to [cis-DOCO] vs. time and [CO].

. . . . . . . . . 114

trans- and cis-HOCO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

cis-DOCO spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117. . . . . . 119. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120. . . . . . . . . . . . . . . 122

6.10 Variation of rloss with O3 concentration. . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.11 Variation of k1a,sum with D2 concentration.

. . . . . . . . . . . . . . . . . . . . . . . 124

6.12 Termolecular rate coecients for DOCOtot vs. CO and N2 .

. . . . . . . . . . . . . . 127

LIST OF FIGURES
6.13 Fitted isomerization rate coecients forxiii

cistrans and transcis.

6.14 Fitted eective bimolecular formation rate coecients for. . . . . . . . . . 128

trans -DOCO and cis -DOCO.129

6.15 Comparison of k1a,trans + k1a,cis + k1b with k1 . . . . . . . . . . . . . . . . . . . . . . 131

B.1

Supercontinuum Fiber Spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

B.2

In-loop error signal from p + i beat with pump supercontinuum. . . . . . . . . . . . . 142

B.3

Response of frep and f0 to ber bragg grating temperature.

. . . . . . . . . . . . . . 143

List of Tables
3.1

VIPA alignment parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

4.2

Atmospherically relevant oxidizing species. . . . . . . . . . . . . . . . . . . . . . . . .

50

4.3

Methods of OD production.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

4.5

Experimental and calculated dipole matrix elements for OH and OD (Debye). . . . .

64

4.7

Theoretical ν1 ro-vibrational band positions and intensities fortrans- and cis -DOCO.

66

5.1

Measurement conditions used for the determination of k1a . . . . . . . . . . . . . . . .

84

5.2

D2 O line positions and intensities.

89

5.3

Rates used for modelling the OD + CO reaction.

5.4

Summary of statistical and systematic errors.

6.1

cis -DO12 CO and cis -DO13 CO spectral features and assignments. . . . . . . . . . . . 116

6.2

Summary of spectral parameters for

6.3

Comparison of experimental isotope shifts with theoretical isotope shifts for

6.4

Summary of statistical and systematic errors for. . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . 104. . . . . . . . . . . . . . . . . . . . . . 108

cis -DO12 CO and cis -DO13 CO. . . . . . . . . . . 117

xiv

cis -DOCO.118

trans -DOCO values . . . . . . . . . 125

Chapter 1
Introduction
The characterization of chemical reactions has always been a dicult task, placing stringent requirements on instrumentation and techniques. Clean experimental data require low reactant concentrations to avoid secondary reactions, producing even lower concentrations of the reaction products.
These reactions reach completion on short timescales, in the μs range for bimolecular processes andapproaching the fs level for unimolecular processes.

As our understanding of chemical reactions

has grown, we have learned that many chemical processes that were previously thought to be bimolecular actually involve bound intermediate species whose signatures are manifested by complex
temperature and pressure dependencies[1, 2, 3, 4]. To fully understand these reactions requires thesimultaneous detection of many molecules, which is dicult using traditional kinetics techniques.
The carbonylation of hydroxyl radical, OH + CO → H + CO2 , is one such reaction which has
been known since the early 1970s to exhibit complex product branching. Interest in this reaction
due to the reaction's importance in atmsopheric and combustion processes has stimulated many
experimental and theoretical eorts.

One main experimental technique that has been commonly

employed in its study is uorescence spectroscopy; the time-dependent concentration of hydroxyl
radical is detected through its uorescence.

The OH+CO reaction rate is then determined byvarying the CO concentration and observing its change on the OH loss rate. The primary advantageof this technique is its sensitivity, with detection limits lower than 10

9 molecules cm-3 [5], with μs

time resolution.

First, it cannot be applied

However, this technique has two major drawbacks.

1

CHAPTER 1. INTRODUCTION

2

to every molecule - there are many chemical intermediate species that do not have convenientuorescent transitions.

In many cases, such as in the OH+CO reaction, this precludes access tocritical mechanistic detail, such as branching kinetics.

Second, absolute concentrations can beaccessed in this manner, but require cumbersome calibration.

Even so, this technique has beena workhorse for kinetics measurements for many years and the tabulated OH+CO termolecular
reaction rates are entirely determined in this manner[6].
It's not that supplementary techniques do not exist.

Step-scan Fourier Transform Infrared(FTIR) has also been used for the determination of reaction rates, which has demonstrated simultaneous access to many molecular species, at μs temporal resolution[7]. However, this technique tradeso spectral resolution for sensitivity, with one study achieving a CH2 OO molecular sensitivity of
13

10

-3

molecules cm-1

and 12.5 μs time resolution at the expense of 1 cm

spectral resolution[8]. On

the other hand, highly-sensitive techniques such as cw (continuous-wave) cavity ring-down spectroscopy are able to capture events on the μs timescale, but require scanning over a broad range tocapture all species relevant to the reaction[9].
In this thesis, we present a technique to bridge this gap, time-resolved frequency comb spectroscopy, which utilizes the broad bandwidth and spatiotemporal coherence of the optical frequency
comb to provide simultaneous access to reactants and products with high molecular sensitivity andμs time resolution[10]. The optical frequency comb, described in Chapter 2, has broad success infrequency metrology, chemical sensing, as well as rf generation. Moreover, many of the components
necessary for the study of chemical reactions have already been independently demonstrated in thenear-infrared. Broadband molecular spectroscopy of multiple trace gases and the ability to accurately determine their concentrations has been shown for FTIR[11], VIPA[12], and dual-comb[13, 14]detection techniques. The enhancement of molecular sensitivity using an optical enhancement cavity
has also been demonstrated[15].
However, molecular absorption cross-sections in the near-infrared are weak, as they mostly
consist of combination bands.

Therefore, it is necessary to move to the mid-infrared molecularngerprint region, above 3 μs, which brings larger absorption cross-sections at the cost of technicalCHAPTER 1. INTRODUCTION
complexity.

3

Laser sources, dielectric coatings, and detection techniques are all signicantly lessdeveloped and signicantly more expensive than their telecom (≤1.5 µm) brethren.

Commondevices which are readily available in the near-infrared such as electro-optic modulators (EOMs) andacousto-optic modulators (AOMs) are still in their infancy. Even alignment and characterizationof optical beams requires more time and care, since the invisible beams cannot be detected onuorescent cards or CCDs. Instead, thermal paper and microbolometer cameras are used, whichhave slow response times (seconds) and poor detection sensitivities.
Even so, mid-infrared time-resolved frequency comb spectroscopy is already very useful and its
utility will continue to grow with mid-infrared instrumentation. The specics of the technique aredescribed in Chapter 3. Briey, the technique consists of a 3-5 μm mid-infrared frequency comb
source, an optical absorption enhancement cavity, and a spatially-dispersive spectrometer based on
the virtually-imaged phased array (VIPA). This technique is rst applied to the study of acrylic acidphotodissociation, which produces thetrans-HOCO radical intermediate of the OH+CO reaction.

The atmospheric and combustion implications of OH+CO chemistry are introduced in Chapter
4, along with a brief account of its experimental history.
generation,

O3 photolysis, is also introduced.

The experimental approach for OH

The main results of this thesis are presented in

Chapters 5 and 6, in which the absolute concentrations of OD,

trans -DOCO, cis -DOCO, and CO2

are directly detected from the OD+CO reaction, allowing for the unambiguous determination ofreaction branching rates.

Additionally,cistrans isomerization is observed for the rst time,

illustrating the rich dynamics possible in this system. Finally, Chapter 7 concludes the work andpresents an outlook for future investigations.

Chapter 2
Frequency Combs and Molecular Spectroscopy
The development of the optical frequency comb in the 1990s and early 2000s by John Hall[16] andTheodore Hänsch[17] has permitted many new applications including metrology, laser ranging, andabsorption spectroscopy. Indeed, we are even now adding new applications to this list. Extensive
review articles[18, 19, 20], theses[21, 22, 23, 24] and books[25] exist describing the operation andapplication of the comb. To understand why the frequency comb has become such a useful tool,
it is illustrative to look at its properties in both the time and frequency domain. The frequency
comb can be understood in the time domain as a stabilized train of laser pulses. The characteristic
comb structure is then derived by taking the Fourier transform of this time sequence, as shown in
Figure 2.1 and given mathematically (see A.1) by

E(t) =nf
X

FT

A(t − nτ )ei(ωc t−nωc τ +n∆φce ) −−→ Ẽ(ω) = Ã(ω − ωc )

n=1

nf
X

e−inωτ +in∆φce .

(2.1)

n=1

The left side of this expression represents the time-domain electric eld, E(t), of a sequence of nf
pulses, each with a pulse shape A(t). ωc and τ are the center angular frequency of the spectrum andtime between subsequent pulses, respectively.

∆φce is the a pulse-to-pulse slip between the pulse

envelope, A(t), and the carrier frequency, ωc , indicated in Fig.

2.2.

Ẽ(ω) and Ã are the fouriertransforms of E(t) and A(t), respectively. From this expression, a few things are clear. First, thespectral envelope, Ã(ω), is given by the fourier transform of the pulse envelope, A(t). Therefore,

4CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

5One Pulse

Two Pulses

Many Pulses
Frequency

Time

Figure 2.1: The optical frequency comb as an accumulation of stabilized pulses for nf =1, 2, and 9
pulses.

a broad spectral bandwidth requires a short pulse duration. Second, even through the spectrumof a single pulse is broad, the coherent addition of many pulses creates a series of comb teeth
underneath the single-pulse envelope. These terms add constructively when 2πm = ωτ − ∆φce . Bythdening frep = 1/τ and f0 = ∆φce /(2πτ ), we arrive at a precise frequency relationship for the m
comb tooth, given by[26]fm = mfrep + f0 .
thwhere fm is the optical frequency of the m(2.2)

comb tooth, frep is the pulse repetition rate, and f0

is the carrier envelope oset frequency. This relationship is simple, yet extremely powerful, since

frep and f0 are in the rf (radio-frequency) domain. These ~ 100 MHz signals may be detected andstabilized, thus stabilizing the ~ 100 THz optical comb teeth (fm ).

2.1 Molecular Spectroscopy
Molecular spectroscopy, the study of the interaction between molecules and light, has been aroundsince at least the 1670s, when Sir Isaac Newton used a prism to disperse visible light. Since then, anumber of tools and techniques have been developed that allow for the characterization of molecules

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

6

Figure 2.2: Time- and frequency-domain interpretation of frep and f0 . Reproduced from Ref. [21].

through the spectral response of their interaction with light.

Linear absorption spectroscopy is

perhaps the oldest technique, but its utility cannot be understated since it allows for the quantitative
determination of molecular concentrations. It has been applied to such problems as the detection ofgases for manufacturing processes[27, 28, 29], detection of poisonous gasses and explosives[30, 31],human breath analysis for medical applications[32, 33, 34, 35], environmental monitoring[36, 37, 38,39], and optical

14

C dating[40]. Many of these applications require the ability to detect a numberof small-amplitude spectral features across a wide bandwidth, in a short amount of time.
Many spectroscopic techniques have been developed to help solve these issues.

Absorption

spectroscopy based on continuous-wave (cw) techniques can oer high sensitivity, especially whencoupled to an optical enhancement cavity for path length increases.

However, it is necessary toscan these lasers across the wavelength range of interest in order to acquire a spectrum, with scantime proportional to the desired wavelength range. Still, modulation techniques[41], [42] and opticalcavities[43] can provide exceptional sensitivity. NICE-OHMS[44, 45] combines these two techniques.
This allows for high signal-to-noise[46] and the ability to measure very small absorption signals[47].

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

7

Thermal sources, such as a light bulb or even the sun, have traditionally been simple and robust
sources of optical radiation, especially due to their low cost. Their most appealing feature is theirbroad spectrum, which can easily exceed 100s of THz in bandwidth. However, the lack of spatial
and temporal coherence comes with a large cost. The spectral resolution of an instrument using athermal source will be dened by the spectral resolution of the detector, which can be 10s of GHz
in the case of a reection grating.

Additionally, their spatial incoherence decreases the available

power and precludes the coupling of these sources to optical cavities with high eciency to improvetheir molecular sensitivity. Therefore, these sources typically require much longer averaging times toapproach sensitivities comparable to those oered by cw-laser based systems. Globar is a common
source of low-cost high-power thermal radiation between 4 and 15 μm[48]. These sources have ahigh spectral ux (W/Hz), as indicated in Fig.

2.3.

However, the focusability of these sources

is very poor since the light originates from a macroscopic object radiating in all directions.

For

example, the Globar source used in Fig. 2.3 is a cylinder 104 mm in length and 6 mm in diameter.
Using the concept of etendue (optical phase space volume), this source can at best be focused to a
5 cm diameter spot. This means that fairly standard photodetector with 4 mm

2 active area would

only capture 0.2% of this light! A laser source, which can be focused to dimensions approaching its
wavelength, does not have this restriction, allowing all of its power to be used. The solid blue curve
2

in Fig. 2.3 reects the 0.02% useable power of the Globar source, in the case of a 4 mm

detector

active area.
The frequency comb is in its own category, combining the advantages of the thermal and cw
techniques. The broad bandwidth of the comb is given by its spectral envelope, while its resolution
is given by the narrow spectral width of the comb teeth beneath the envelope.
frequency comb is a

~ 100,000× multiplexed version of the cw-laser.

Essentially, theAlthough the total power

available from frequency comb sources may be less than broadband thermal sources, all of thisspatially coherent light can be used for measurements (see Fig. 2.3). Finally, we will see in the next
section that the frequency comb also permits ecient coupling to an optical enhancement cavity.
The interaction of light with a sample in linear spectroscopy is described by the Beer-LambertCHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

8

Figure 2.3: Spectral ux of Globar (blue) compared with Mid-Infrared OPO Frequency Comb (red).
The y-axis represents power per comb mode (µW) for the the frequency comb and the power per
frep = 136 MHz bandwidth for the Globar source. The solid red curve represents the power at asingle center OPO wavelength, while the dashed red curve represents the tuning range of the OPO.
The dotted blue curve is the total spectral ux from the globar source, while the solid blue curve isthe maximum possible concentrated ux (0.2%) on a typical 4 mm

2 detector area.

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY
P

(a)

2400

2450

2500

Q

2550

2600

9

R

2650

2700

2750

2800

2850

Wavenumber (cm -1)

(b)

v=1

J=2
J=1
J=0

v=0

J=2
J=1
J=0

Figure 2.4: (a) The v=0→1 ro-vibrational spectrum of OD, simulated with PGopher[49] using tted
ro-vibrational parameters from Abrams

et al. (b) Simple ro-vibrational energy level diagram. v andJ are the vibrational and rotational quantum numbers, respectively.
correspond to the allowed ro-vibrational transitions ∆J

The P, Q, and R branches= −1, 0, 1, respectively from the v=0 tov=1 vibrational levels.

law[50],It (ν)/I0 (ν) = e−α(ν)l ,where α(ν) is the absorption coecient in cm

-1

(2.3)

, l is the interaction length in cm, and It (ν) andI0 (ν) are the transmitted and incident light intensities, respectively. Many molecular transitions
contribute to α(ν): electronic (visible), vibrational (mid-infrared), and rotational (radio frequency),
and are typically very spectrally distinct. The mid-infrared spectral region, 2-20 μm, is especially
useful for molecular spectroscopy since in this region each molecule has a unique spectral ngerprint, allowing for identication. A simulated ro-vibrational in this spectral region of the deuteroxyl
radical (·OD) is shown in Fig.

2.4a, where the P(∆J= −1), Q(∆J = 0), and R(∆J = +1)

branches can be clearly seen. These three sets of transitions arise from the ro-vibrational selection
rule ∆J= 0, ±1, where J is the angular momentum quantum number[51]. These transitions areindicated in Fig. 2.4b for a few ro-vibrational levels. The narrow Doppler linewidths of these tran-

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY-1sitions (~ 300 MHz) and the breadth of the full spectrum (~ 300 cm

10) show why the multiplexedcapabilities of the frequency comb are very useful. Excellent resources exist[51, 52] summarizing
the details of ro-vibrational spectroscopy.

2.2 Enhancement with an Optical Cavity
From Beer's law, it is clear that the strength of the signal (and the minimum detectable concentration) is determined by the interaction length of the light with the sample. For this reason, it
is important to make the interaction length as long as possible.

One method of increasing thisabsorption interaction length is simply to use a longer sample. This technique is commonly usedin atmospheric sensing, where light from the sun passes through the atmosphere and is detected at
the surface of the Earth[53]. Another method of performing this type of sensing is to transmit alaser source through the atmosphere to a mountain-mounted retro-reector[54] or a mobile drone.
However, there are many situations where space is limited and the amount of available sample issmall.

In these situations, the extra optical path length may be obtained through the use of aWhite[55] or Harriet[56] cell, in which light reects many times between two mirrors, before it iseventually ejected for analysis.
Another method for optical enhancement exists, which relies on the coherent properties of light.
This device is the optical cavity, which at its simplest, consists of two highly-reective mirrors. The
transmitted electric eld of such a device is given by the innite sum of all possible paths throughthe two mirrors. Due to the high reectivity of the mirrors, an average photon will spend a longtime inside the cavity, increasing its interaction with the molecular sample. The eective absorption
interaction length, lef f , of such a device is given by lef f= βF lcav /π where F = π/(1 − R) is thenesse of a cavity formed with mirrors of reectivity R, lcav is the physical length of the cavity,and 1 ≤ β ≤ 2 is a parameter dependent on the method used to lock the laser frequency to thecavity[57, 58]. Since nesse values of F > 3000 (R > 99.9%) can be easily reached across a broad
1

range of wavelengths, lef f can easily reach values 1000× the physical length of the cavity .

1

Ref. [59, ch. 3] is an excellent resource for the traditional derivation of cw optical cavity reection and transmission

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

11

In order to maintain this large length enhancement, a laser beam must experience constructive
interference within the optical cavity. In the time domain, this criterion ensures that the optical eldmust repeat itself upon one round trip within the cavity. Each laser pulse, upon entering the cavity,
must overlap with the pulse already inside the cavity. In the frequency domain, each comb toothmust be uniquely matched to an optical cavity resonance so that it is transmitted by the cavity.
A number of methods have been demonstrated for maintaining a resonant frequency relationshipbetween lasers and optical resonators. In most cases, these techniques were initially demonstratedusing cw-laser systems and modied later for the frequency comb. The general principle of all oftheses techniques is the same; an error signal, representing the deviation from ideal laser-cavity
coupling is generated and this is used to gently nudge the laser's or cavity's frequency towards amore ideal value. Two key requirements exist for this error signal: it must be zero when the laser
frequency is matched with a cavity mode and it must be monotonic in detuning near this ideal
2

value .
The Pound-Drever-Hall (PDH) technique[61, 62] is a very common method for maintaining atight lock between an laser source and optical cavity. The error signal for this technique is generated
by introducing phase-modulation sidebands to the laser. When these sidebands are at a frequency
much larger than the cavity linewidth, they are completely reected o of the input mirror of thecavity and serve as a phase reference for the lock. The carrier (unmodulated) frequency interacts
with the cavity and picks up a phase shift upon reection from the cavity.

Demodulating thereected intensity at the modulation frequency yields a signal proportional to the laser frequency's
3

deviation from the optical cavity mode .
An alternative approach is the sweep lock, where the laser frequency is swept across the cavity
mode, with the cavity mode stabilized to the center of the sweep. The total transmitted intensity
through the optical cavity is then detected as the integral over the sweep period. This techniquesignicantly reduces frequency-to-amplitude noise conversion on the transmission of the cavity, sinceproperties.

2

These techniques fall within the domain of control theory, which describes the behavior of a dynamical system

under feedback[60].

3

Excellent tutorials for the PDH technique are found in Refs. [62, 59, 4.7].

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

12a small change in the length of the cavity will cause the transmitted cavity pulse to shift within
its integration window without changing its total integrated intensity.

However, this improved

amplitude noise comes with the drawback of reduced intensity, since light is only transmitted throughthe cavity at the middle of the laser sweep.
As described, these techniques apply to cw-laser systems; modications must be made to stabilize
both parameters, frep and f0 , of a frequency comb to a cavity. In the PDH technique, this can bedone by generating two PDH error signals at the low- and high- wavelength portions of the spectrum
and feeding these signals to the appropriate frep and f0 actuators in the frequency comb. In thesweep lock, a single error signal is generally used to stabilize frep , with f0 stabilized to an rf source.
If high-resolution is not required,e.g. at high pressures and/or temperatures, f0 may even be left tofreely drift, as it only minimally aects the sweep lock. Other techniques for locking lasers to cavities
exist, but were not explored in this thesis work. For example, the Hänsch-Couillaud technique[63]uses an intracavity Brewster plate to generate a frequency-dependent elliptical polarization in thereected light, thus avoiding frequency modulation of the incident laser beam.

2.3 Mirror Dispersion Characteristics
In Section 2.2, it was suggested that it might be possible to perfectly couple an optical frequency
comb to an optical enhancement cavity such that each comb tooth is perfectly resonant with every
cavity mode. In general, this is impossible due to the tendency of an optical cavity to change its free
spectral range (FSR) with wavelength. To see why this is the case, we look briey at the reective
and dispersive properties of a standard quarter-wave-stack.

The reectivity and dispersion of aquarter-wave stack is plotted in Fig. 2.5. The changing group delay of the mirrors, τ =∂φ∂ω , gives

rise to a changing FSR through the formula

F SR(ω) =c∂φ
2lcav + c ∂ω

,

(2.4)

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

13

where lcav is the physical length of the optical cavity and φ is the wavelength-dependent spectralphase of the reected light o of the HR mirror[64]. The wavelength-dependent FSR is also plottedin Fig.

2.5.

Due to the changing FSR with wavelength, the comb modes are no longer able tosimultaneously maintain resonance with the optical cavity.

This causes two problems:(1) thecavity transmission is decreased where the comb-cavity frequency dierence is greatest and (2) the
molecular dispersion is coupled to the output of the optical cavity. For molecular spectroscopy, (1)can be mitigated by acquiring a reference spectrum prior to the absorption spectrum. However, thetransmitted spectrum through the cavity will still be narrowed through the eects of dispersion.
This can be seen in the bottom panel of Fig. 2.7, where the two-point lock trace is obtained bystabilizing frep and f0 using spectrally ltered PDH signals at low wavelength (red trace) and highwavelength (black trace). A schematic for this scheme is shown in Fig. 2.9a, where the two PDH
signals are generated at photodiodes PD1 and PD2. The dashed curves of Fig. 2.7 are obtained byengaging only one lock (pump lock) and detuning the other lock (opo lock), producing a spectrumof narrow bandwith but high intensity. As the lock point is tuned, the peak of the narrow one-lockspectrum traces out the maximum transmission available at a given wavelength. The two-lock value
may be compared with this value to determine the wavelength-dependent comb tooth detuning fromthe cavity mode, assuming a Lorentzian cavity mode lineshape. This detuning is given byr∆ν = ΓL

P1 − P2
,
P2

(2.5)

where P1 and P2 are the transmitted power for the one-point and two-point locks, respectively, andΓL = F SR/(2F ) is the cavity mode's half-width at half max. This wavelength-dependent detuningis plotted in the top panel of Fig. 2.7.
However, (2) remains an issue. The exact formula for the transmission of an enhancement cavityof length L in the presence of an analyte is given by[65, 11]

It (ν)
I0 (ν)

2−2δ(ν)Lt (ν)e= 1−r2 (ν)e−4δ(ν)L −2r(ν)e−2δ(ν)L cos[2φ(ν)L+ϕ(ν)]
2 (ν)e−α(ν)L= 1−r2 (ν)e−2α(ν)L −2r(ν)et −α(ν)Lcos[4πνL(n+nanalyte (ν))/c]

,

(2.6)

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

14

where It (ν) and I0 (ν) are transmission spectra from the cavity with (Sample) and without (Reference) an absorber in the cell.

δ(ν) and φ(ν) are the attenuation and phase shift of the electriceld due to the analyte per unit length, given in terms of the analyte's absorption coecient, α(ν),
and index of refraction, nanalyte (ν) by δ(ν) = α(ν) and φ(ν) = 2πνnanalyte (ν)/c. t(ν) and r(ν) are
the the frequency-dependent intensity transmission and reection coecients of the cavity mirrors,
respectively.

ϕ(ν) is the round-trip phase shift in the cavity without the analyte. For a buer gasof refractive index n, this is given by ϕ(ν) = 4πνnL/c, where c is the speed of light.
At this point, it is common to series expand Eq. 2.6 for small α(ν), yielding the expression

It (ν) − I0 (ν)
2F (ν)≈
α(ν)L,
I0 (ν)
π
where F (ν) is the cavity nesse, dened as πpr(ν)/ [1 − r(ν)][65, 11].

(2.7)

This expression may becompared with the equivalent expansion of the Beer-Lambert law, [It (ν) − I0 (ν)] /I0 (ν) ≈ α(ν)L,to see the 2F (ν)/π path length increase due to the optical cavity.
Additionally, Eq. 2.6 describes the distortion of a molecular lineshape after transmitting througha cavity with non-negligible dispersion properties, where some comb teeth are not perfectly matchedwith their corresponding cavity modes. In this case, the round-trip intracavity phase shift is given byϕ(ν) = 2π∆ν/F SR(ν)+2qπ , where ∆ν is the frequency detuning of the comb tooth from the centerof its corresponding cavity mode and q is an integer.

Figure 2.6a shows the complex absorption

prole of an example molecular feature and Figure 2.6b depicts this feature, as transmitted throughan optical cavity with F = 5000 and a comb-cavity mismatch of ∆ν = 20 kHz.
The top panel of Fig.

2.8 shows an experimental spectrum of methane, in which dispersion

clearly aects the line shape of the experimental data (black) at low wavelength. This can clearly
be seen in the t residual when the eects of dispersion are not included (∆ν = 0, middle panel).
The red trace and bottom panel show the improvement in the t and its residual due to the inclusionof dispersion eects using eq. 2.6.

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

15

(a)

(b)

Figure 2.5: Reectivity and dispersion of a quarter-wave stack. (a) Reectivity and phase delay.
(b) Finesse and wavelength-dependent change in FSR, calculated from (a).

(a)

(b)

Figure 2.6: Eect of dispersion on cavity absorption features.

(a) Real and complex absorptioncoecient. (b) The same absorption feature, enhanced by an optical cavity, with laser-cavity detunings of 0, 25 kHz, and 50 kHz. The cavity-enhanced plot is given by − log(It (ν)/I0 (ν))π/(2F l),with It (ν)/I0 (ν) given by eq. 2.6.

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

16

Figure 2.7: Cavity transmission in the presence of dispersion.

Figure 2.8: Experimental spectra of 10 ppm CH4 in 760 torr N2 at room temperature (black curve).
The red curve, inverted and oset for clarity, shows model spectra calculated using data from the
HITRAN database. With ∆ν = 0 xed, the model breaks down at the edge of the mirror bandwidth.

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

17

2.4 Detection Methods
Due to the broadband nature of the frequency comb, the transmitted light from the optical cavity must be spectrally resolved in order to obtain information about the molecular sample being
probed. Many detection methods have been explored[66], but only two of these have proved useful for the work in this thesis: the Fourier Transform Spectrometer (FTS) and Virtually Imaged
Phased Array (VIPA). The FTS has existed for many decades and is widely used across many areasof physics, chemistry, and biology[67]. The general principle of the FTS is to convert optical frequencies to radio frequencies so that they may be detected. This is done using a variable-path-delay
Michelson interferometer, shown in Fig. 2.9b. The fourier transform of the light intensity at theinterferometer's output yields the intensity spectrum of the light.
An alternative detection technique is the Virtually Imaged Phased Array (VIPA), in which lightis spatially dispersed in 2D and detected using a camera. The VIPA technique is discussed in 3.5.
Like the FTS, the VIPA can be operated in the hard lock conguration, where the frequency
comb teeth are always near the center of their respective cavity modes. However, the VIPA permits
another sweep-lock conguration in which the repetition rate (or oset frequency) is swept acrossthe cavity modes such that the comb is only resonant with the cavity for a short period of time
during each sweep. This has the distinct advantage of being fairly immune to mirror dispersion,
since each comb tooth will come into resonance with its respective cavity mode during each sweep
period. This type of dispersion immunity has not yet been demonstrated in the FTS.
It is worth pointing out that many other detection methods exist, which are not utilized inthis thesis. Dual-comb spectroscopy has received great interest due to its ability to acquire spectra
quickly and with no moving parts[68]. Additionally, frequency-comb-based streak spectroscopy has
been demonstrated, which uses a moving mirror to map time to space, allowing for the acquisitionof a broad spectrum with microsecond time resolution[66]. Of course, there is no perfect detection
technique; each of the techniques listed here has advantages and disadvantages in time resolution,
spectral resolution, complexity, and cost.

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

18

2.5 Demonstration: Detection of H2O2 in the presence of H2O
As a demonstration of this technique's ability to simultaneously detect trace concentrations of multiple molecular species, we applied the system to the detection of hydrogen peroxide (H2 O2 ) in thepresence of a large concentration of water. The increased presence of H2 O2 in human breath could
be used for early diagnostics and monitoring of such diseases as asthma[69, 70, 71], chronic obstructive pulmonary disease[72], or acute respiratory distress syndrome[73, 74], a severe inammatory
condition with up to 50% mortality[75]. The detection of H2 O2 in human breath is most commonly
performed with the creation of a breath condensate and the use of absorption of uorescence spectroscopic methods, achieving detection limits in the range of a few ppb to a few hundred ppb[76].
Commercial biosensors are available and oer detection limits in the range of a few tens of ppb,
but require everyday calibration[77]. Additionally, the need for breath condensation and the useof chemical reactions for analysis precludes the use of these techniques for real-time applications.
High-resolution laser spectroscopy has been recognized as a tool for quantitative breath analysis
in the gas phase, eliminating the need for sample condensation and pre-ltering[34, 35]. Despite
the molecule's importance as a potential marker for numerous diseases, no laser-spectroscopy-based
system for its optical detection in human breath has been reported.
One of the main challenges underlying the detection of H2 O2 in the breath is the large concentration of water, which can approach saturation. Exhaled breath at 35°°

C can thus approach awater concentration of 5%. As the breath cools to 21 C, some of the water will condense, bringing
the water concentration to less than 3%. For many techniques, this causes signicant contaminationand can completely obsure the H2 O2 signal. To simulate this high-water environment, a solution
was prepared with ∼ 27% H2 O2 in water. This liquid was placed in the removable tray of a speciallydesigned optical cavity, as shown in Fig. 2.9a, and its vapor was allowed to ll the cell. Heaters
on the bottom of the cell allowed the temperature of the cell to be tuned from room temperature(23°C) to a more biologically-relevant temperature of 39°

C. Two ow ports on the top of the cellallowed for a small ow of pure N2 to reduce the amount of water vapor in the sample, maintain-

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

19

(a)

(b)

Figure 2.9: Schematic diagrams of the (a) experimental setup and (b) fourier transform spectrometer.

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY20

ing the pressure of the cell at an atmospheric pressure of 630 torr. The mirrors were attached to
the glass spacer using Torr Seal, after ensuring that the cavity FSR was correctly matched to thefrequency comb (27.4 cm, matched to F SR = 4 × 136.6 MHz). A piezo was installed on the output
coupler of the cavity, allowing for ne length adjustment.

°

Observed H2 O2 spectra are shown in Fig. 2.10a and b, for liquid temperatures of 23°

C and 39

C, respectively. A sum of model spectra of H2 O2 and H2 O are tted to the data, shown in red andblue, respectively. Spectral data for the water lines (H2 O and HOD) are taken from the HITRAN
database[78], where the isotopic abundances of 0.99731 and 0.00031 are used, respectively. Highresolution data for the ν2 +ν6 combination band of H2 O2 in this spectral region does not exist, so weused absorbance values from the Pacic Northwest National Laboratory (PNNL) database of quantitative IR data[79]. The PNNL data are intended for open-path monitoring and the experimental
spectral are obtained using a conventional FTS with the sample back-pressurized to 760 Torr using
dry nitrogen and with absorbance values normalized to a mixing ratio of 1 ppm at a temperatureof 296 K and a path length of 1 m[80].

The PNNL absorbance were recalculated by scaling forthe path length and the lower atmospheric pressure, 630 torr, in our laboratory. Since the H2 O2spectrum is a series ofR

Q0 sub-branches[81], accounting for the pressure-broadening coecients issomewhat complicated. Thus, a scaling factor of 0.828 was introduced to partially account for the
lower pressure. This pressure discrepency is likely the source of the structure in the t residual,
seen in the bottom panel of Fig. 2.10a, which causes a systematic error in the H2 O2 concentration
retrieved by the t, which is estimated to be 20%. At the peak absorption at the strongest H2 O2−7 cm−1 for 1 ppm at 630 torr.

line at 3761 nm, we estimate the absorption to be 7 × 10

This

indicates that the noise equivalent concentration detection limit of H2 O2 in the absence of water is
8 ppb at 1s averaging time.
In order to determine the concentration detection limit of H2 O2 in the presence of water ata biologically-relevant (percentage) levels, we measured spectra under the same temperature andpressure conditions as were used for Fig. 2.10 and lled the container with deionized (DI) water
only. A sum of H2 O2 and H2 O was tted to 100 consecutive water spectra in the wavelength range

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

21

(a)

(b)

Figure 2.10: Experimental spectra of hydrogen peroxide and water, shown in black, inverted and°oset for clarity. Fitted model spectra of H2 O2 (red) and H2 O (blue) are shown upright. The tem-°

peratures and tted molecular concentrations are (a) room temperature (23[H2 O]−645ppm and (b) T = 39 C, [H2 O2 ]−5ppm, [H2 O]−1.2 %.

C), [H2 O2 ]−3.6ppm,

CHAPTER 2. FREQUENCY COMBS AND MOLECULAR SPECTROSCOPY

22

with the highest SNR, i.e. between 3720 and 3790 nm. The mean water concentration returned bythe ts was 2.83(6)%, while the mean H2 O2 concentration was 75 ppb with standard deviation of
130 ppb. Thus, the detection limit of H2 O2 in the presence of almost 3% of water is 130 ppb. Thisis worse than the limit determined from the background noise level due to the structure in the tresidual after the model water spectrum is subtracted o. The detection limit could therefore be
improved by rening the line-shape model, using more precise spectral data for the water lines, andby reducing the baseline drift in the experiment, but the achieved detection limit of H2 O2 is alreadysucient for medical applications where a typical concentration is > 10 ppm.

Chapter 3
Time-Resolved Frequency Comb Spectroscopy

3.1 Overview
Over the past 50 years, spectroscopy has proved a very valuable tool for the study of chemicallyinteresting species in the gas phase. The slow evolution of molecules such as methane and carbon
dioxide in the atmosphere are constantly observed by cavity-ringdown techniques[82], dierential
optical absorption spectroscopy (DOAS) methods[53], and dual-comb spectroscopic techniques[54].
Due to the stability and long lifetime of these molecules, their spectral features can be very narrow, allowing for a simple recovery of the atmospheric molecular concentration. In addition, thelong lifetimes of these molecules allow for long averaging and spectral scanning times to collect23

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

24

broad-bandwidth spectra with high spectral resolution. On the other hand, femtosecond transientabsorption spectroscopy allows for the study of unimolecular ps-timescale reactions[83].

In thiscase, spectral resolution requirements are minimal since the molecular spectral response is lifetimebroadened to some THz.
In this work, we are concerned with the middle ground: the observation and characterizationof stable, but highly reactive, molecules which form, re-arrange, and decay on the μs timescale.
Lifetime broadening of these molecules should be limited to ~ 1 MHz, preserving the rich structureof the molecules' spectral response, and thus information about the molecular geometery and its
vibrational, rotational, and thermal temperatures.

Furthermore, the determination of absolutetime-dependent molecular concentrations, especially in the presence of other absorbing species, isconsiderably simpler. The study of this type of reaction has three main requirements:

1. High temporal resolution

2. Broad spectral bandwidth and high spectral resolution

3. High molecular sensitivity

Traditional broadband absorption techniques such as FTIR have allowed for the detection of sometransient species[7], but do not have the molecular sensitivity to observe and characterize trace
concentrations. Highly sensitive techniques such as cw cavity ringdown spectroscopy allow for thedetection of very small concentrations at short timescales[9, 84] with high spectral resolution, but
are unable to scan over a suently broad bandwidth to capture a global portrait of the chemical
reaction surface. Cavity-enhanced direct frequency comb spectroscopy (CE-DFCS) simultaneously
solves all of these problems. The broad bandwidth of the pulsed source allows for many molecules tobe observed simultaneously, while the absorption length enhancement of the optical cavity increases

Ö

the signal amplitude by ~ 1000

. The transmitted light from the cavity is then spatially dispersed

and imaged on a camera to simultaneously detect the broad bandwidth of the frequency comb witha time resolution limited by the ringdown time of the optical cavity (a few μs). Additionally, thespectral resolution of this technique is limited only by the linewidth of the comb teeth, which can be

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

25<1 MHz. At room temperature, this allows the rotational features of small molecules to be resolved
so that the molecules may be uniquely identied and characterized. At low temperatures, this highspectral resolution can be utilized to access the narrow features of larger species which have a small
rotational spacing[85].
In this chapter, I will rst describe the frequency comb source, the optical enhancement cavity,
and the dispersive detection system.

I will also describe the method used to ensure the proper

timing in the experiment and to ensure proper coupling between the cavity and comb. Finally, I
will describe the use of this system to measure the photolysis and subsequent reactions of deuterated
acrylic acid.

3.2 Mid-Infrared Frequency Comb Source
The mid-IR frequency comb source consists of three parts: oscillator, power amplier, and opticalparametric oscillator (OPO). The oscillator and amplier are described in Refs.

[86, 87], while

the OPO is described in Ref. [88]. The oscillator itself is a linear cavity design, with a ber bragg
grating (FBG) output coupler, as shown in Fig. 3.1. Pump light at 976 nm enters the oscillator gainber through a wavelength division multiplexer (WDM). The gain ber is ~ 15 cm of double-clad1

ber from OFS . Directly following the gain ber is a free-space section, where the free-space light
is focused onto a semiconductor saturable absorber mirror (SESAM), which provides the nonlinearreectivity required to start the mode-locking process. Also in the free-space section is a polarizing
beam splitter on a rotation mount for mode-locking through nonlinear polarization rotation. Whilemode-locked, nonlinear polarization rotation is the main saturable absorber mechanism - the SESAM
only serves to make the oscillator self-starting. A spectrum of the oscillator is given in Fig. 3.2,
which has the characteristic parabolic shape associated with a similariton pulse[89].
Following the oscillator, the ~ 90 fs pulse is broadened to ~ 70 ps using a 30 m long stretcher berbefore injection into the amplier. The amplier is based on a 2 m DC-200-40-PZ-Yb ber and is1

Approximately 5 cm of this ber has been replaced with SMF-28 after a burn of the gain ber tip. The splice

was done using a Fujikura FSM-40 PM fusion splicer in the cladding-alignment mode.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

26

Figure 3.1: Yb comb oscillator and amplier. Reproduced from Ref. [87].

0Amplitude (dBc)

-5
-10
-15
-20
-25
-30
1000

1020

1040

1060

1080

1100

Wavelength (nm)Figure 3.2: Spectrum of Yb:ber oscillator.

1120

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

27

2reverse-pumped by 60 W of 976 nm light . This ber is very common in high-power systems due
to its ability to handle high power and its large numerical aperture in the cladding mode (0.6) forthe pump. A photo of the amplier in operation is shown in Fig. 3.3. The input power into theamplier is 30 mW, while the total output power is 15 W. The output of the amplier is then sent
into a pulse compressor, which compresses the pulses to 110 fs with a power eciency of 66%.
To generate useful mid-IR light, the compressor output is coupled into an optical parametricoscillator, which features a fan-out PPLN crystal for converting the light to 3-5 μm. The output of
the OPO has three key features:

Broad Bandwidth: The spectrum is approximately 200 nm broad.

Broad Tunability: The center wavelength of the source may be tuned between 2.8 and 4.8 μm
by vertically translating a PPLN crystal.

High Power: A maximum power of 1.5 W is reached at a center wavelength 3.5 μm

3.3 Frequency Comb Stabilization
In order to use the frequency comb for high-resolution spectroscopy, it is necessary to x frep and

f0 , ensuring the absolute stability of each comb tooth.

Despite eorts to decouple acoustic andthermal processes from the Yb-comb and OPO, some residual noise remains. This residual noise isremoved by measuring the frep and f0 and applying feedback to the appropriate actuator. In ourcase, there is a slight twist, since the OPO allows an additional freedom in f0 :f0,p = f0,s + f0,i ,(3.1)

where f0,p , f0,s , and f0,i are the oset frequencies for the pump, signal, and idler, respectively. The
repetition rates of the pump, signal, and idler combs are identical. To stabize frep and f0 of theidler comb for spectroscopy, there are a few options. For example, it may seem easiest to simply

2Part number K976AA5RN-60.0WN0N-10522B10ENA0 from BWT. The amplier previously consisted of 8 m of

DC-200-40-PZ-Yb ber, pumped at 915 nm. The ber and the pump diode were both replaced following catastrophic
failure of the ber's output facet.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

28

Figure 3.3: Photo of the Yb:ber amplier in operation. The NKT ber is the green glowing beron the aluminum ring.

measure frep and f0,i , which in our case are <200 MHz, and stabilize them to radio frequency(rf ) sources. This approach does have the advantage of simplicity. Specically, it allows f0,p and

f0,s to drift, unstabilized; only two feedback loops are necessary. However, this simplicity comeswith a cost: any noise written to frep though its feedback loop will be multiplied into the opticaldomain, limiting the achievable linewidth. For example, typical RF crystal oscillators have a relative−10 , which will already broaden a 4 μm comb to 7.5 kHz before any in-loop

frequency instability of 10

errors are considered. For molecular spectroscopy, where spectral features are typically hundredsof MHz broad, even a linewidth of 1 MHz is sucient.

On the other hand, if a narrower comb

tooth linewidth is desired, it is necessary to stabilize frep with an optical source to remove the noise
multiplication process. In practice, there are 6 distinct actuators available in the mid-IR frequency
comb:

1. Oscillator pump current (fast)

2. Oscillator ber stretcher (slow)

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

29

3. Oscillator SESAM piezo (fast)

4. Oscillator ber bragg grating temperature (very slow)

5. OPO bullet mount piezo (fast)

6. OPO translation stage piezo (slow)

With the exception of (5) and (6), which only change the oset frequencies of the signal and idler,these actuators are non-orthogonal in frep and f0,p .

Additionally, each of these actuators has adierent spectral response.
The oscillator pump current changes
the self-phase modulation.

frep and f0,p by shifting the wavelength and changing

However, the frep shift can be minimized by operating the oscillator

cavity near zero second-order dispersion[90]. The ber stretcher and fast piezo should ideally change
mostly frep , but bending in the ber also causes coupling to f0 . The ber bragg grating temperatureprovides the largest actuator for f0 , but is extremely slow. Changing the temperature of the gratingchanges its eective periodicity through thermal expansion and its thermo-optic coecient[91]. The
group delay of the grating is modied, since the center of the optical spectrum is now reected oof a dierent portion of the grating.

However, the chirped nature of the grating gives rise toanother eect: shorter periods expand less than longer periods, causing dispersion to increase withtemperature. Chirped gratings are commonly used for optical dispersion management[92] and theirtemperature properties are well-described[93].

3.4 Optical Enhancement Cavity
Light from this OPO is sent through two spatial mode-matching lenses into an optical cavity madeÖffrom 6 m radius of curvature mirrors, separated by 54.88 cm (FSR = 2

rep ) such that half of the

comb modes are resonant with the cavity. The waist and rayleigh length of the TEM00 cavity modeare 1.3 mm and 1.25 m, respectively, using the symmetric cavity equations[59]. The geometry of
the absorption-enhancement cell is shown in Fig. 3.4 and a physical picture of the cell is shown in
Figure 3.5.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

Figure 3.4: Diagram of the ow cell used in the TRFCS work

Figure 3.5: TRFCS ow cell30

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

31

Since the pressure of the cell must be varied over a large range (0-500 torr) for kinetics measurements, it is constantly necessary to re-align the cavity to maintain resonance with the frequency
comb. If just the refractive index of N2 is considered, the eective cavity length will change by 20

μm per 100 torr increase in N2 , which is more than the range of the long-throw piezo on the output
coupling mirror. In practice, the length of the cell actually changes much more than this due topressure-induced mechanical deformations. To allow for easier alignment, two three-point mounts
were installed on the input and output of the cavity, shown in Fig. 3.6.

3.5 Virtually Imaged Phased Array (VIPA)
The output of the optical cavity is then spectrally resolved using a mid-infrared Virtually Imaged
Phased Array (VIPA)[94], which spatially disperses the light and allows for time-resolved measurements. VIPA etalons were rst demonstrated in the near-infrared and optical spectral regions andare currently manufactured in the near-infrared spectral region by several companies.

However,these parts are commonly produced with fused silica substrates, which begins to absorb near 2800
nm. This absorption would eectively degrade the quality factor of the VIPA etalon, worsening its
transmission and spectral resolution. An alternative material is silicon, which is very transmissivein the mid-infrared.
The VIPA etalon itself consists of a transparent material with a highly-reective (HR) coatingon the input surface (~ 99.99%) and a partially transmissive (PR) coating on the output surface(~ 98%), as shown in Fig.

3.8.

There is a small anti-reective (AR) coated entrance window on

the input surface, which allows for light to be coupled into the VIPA. The mid-infrared beam iscoupled into the VIPA by focusing vertically so that it is transmitted through a small gap in the
HR coating on the input surface, as shown in Figure 3.7. The beam size must be constrained suchthat the beam reected o of the PR surface does not clip on the input edge.
The light from the mid-IR VIPA etalon is reected o of a reection grating, which disperses
light along a direction that is transverse to the VIPA dispersion, and then imaged onto an InSb focal
plane array. The intensity pattern on the camera then consists of a series of stripes, as shown inCHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

Figure 3.6: Three-point mount installed on the input and output of the reaction cell.

32CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

33

Figure 3.7: Physical picture of VIPA etalon. Mid-IR light is incident from the right. The VIPA
etalon is held with a rubber clamp in the center of the image. The large size of the etalon is due toa thick (5 mm) fused silica optical at for mechanical stability.

Figure 3.8: Reection spectrum of the mid-IR VIPA etalon for the input (HR) and output (PR)faces.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

34

Figure 3.9b. Without the grating, these stripes would all overlap, as shown in Figure 3.9a, where thecamera response is shown with the grating set to zero-order. Finally, Figure 3.9c shows the camera
response with N2 O in the beam path.

The black spots in the image indicate strong absorption

by N2 O. An alignment strategy for the VIPA spectrometer is described in an earlier thesis of ourlab[21].
The intensity pattern at the detector is given[21] by the product of the response functions of
the VIPA (y-direction) and grating (x-direction),2

2fc2 y 2f 2 w2−2(x−αω)12ω0Idet (x, y, ω) ∝ Iin ee(1 − Rr)2 + 4Rr sin2 (k∆/2)tan(θv ) cos(θiv )y t cos(θv )y 2−.
∆ = 2tnr cos(θv ) − 2t
f
nf 2

−

(3.2)

(3.3)

In these expressions, w is the incident beam radius, k = 2π/λ is the wavenumber of the beam, andthe other parameters are described in Table 3.1. The instrument lineshape functions in the x and y2directions are thus Gaussian and Lorentzian, with FWHM of 2/ω0 andc(1−Rr)√ , respectively.
2πtn cos(θv ) Rr

The frequency dispersion in the y dimension is given by



∆λ
2t
cos(θv )y=−tan(θv ) cos(θtv ) +
.
∆y
mf
nf

(3.4)

Parameter

Value

λ
w0
n
θiv
θv
t
f
fc
R
r

3.8 μmWavelength of light

4 mm

Incident beam collimated size

3.3

Index of refraction (silicon)

15

VIPA etalon incident angle

°
°

4.5

0.8 mmDescription−1

VIPA internal angle, given by sin

1n sin (θiv )Etalon thickness

308 mm

Focal length of imaging lens

254 mm

Focal length of cylindrical lens

99.8%

HR surface reectivity98%

PR surface reectivity

Table 3.1: VIPA alignment parameters

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

(a)

35

(b)

(c)

Figure 3.9: Camera image with the grating set to (a) zero and (b) rst order. Introduction of N2 O
into the beam path results in image (c), where the black bands indicate absorption.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY36

To obtain a 1D spectrum (absorbance vs. wavelength), three steps are followed:

1. Identify (x,y) position of VIPA fringes.

2. Integrate over the horizontal extent of each fringe and construct a matrix consisting of vertical
pixel vs. fringe number

3. Identify absorption features and t to known line positions to determine the wavelength calibration.

4. Flatten these objects to obtain arrays A and ν̃ .

Step (1) is achieved by beginning in the vertical center of the image and walking up and down thefringes, recording their horizontal position. MATLAB code for this procedure is given in Appendix
C. Step (2) is simply a discrete convolution operation, which is achieved easily in MATLAB. Step(3) is a bit more complicated. We now have a 2D array of integrated intensities, which we need toassociate with corresponding wavelengths. From Eq. 4.1, we note that the VIPA vertical dispersion
is approximately given by a second order polynomial in vertical (y ) camera position. The horizontal
dispersion is given by the FSR of the VIPA. Therefore, the wavelength calibration function, ν̃(n, y)2

is given by ν̃(n, y) = ν̃0 + a1 (n − n0 ) + a2 (y − y0 ) + a3 (y − y0 ) , where n0 and y0 are taken to be
the center of the fringe image so that ν̃(0, 0) is the optical frequency at the center of the images.
By observing many molecular features, ν̃0 , a1 , a2 , and a3 may be tted to obtain the calibration.
Since the resolution bandwidth of the VIPA is larger than the repetition rate of our frequency
comb, comb teeth cannot be resolved. Without resolving individual comb teeth, the spectral resolution of the system is limited to the VIPA resolution. However, better resolution can be achievedat the expense of total power by ltering the comb. There are generally two methods for doing this.
The rst option is to build a short cavity with its FSR set to a large multiple of frep, for example
FSR = 20frep . In this case, every 20th comb tooth will be transmitted through the cavity, withall other teeth rejected. The repetition rate of the transmitted comb is thus 20frep ∼= 2.7 GHz. A
similar option is to match FSR of the lter cavity to a Vernier multiple of the repetition rate, sayCHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY37

FSR =(8/5)frep . In this case, the repetition rate at the output of the cavity will be 8frep (8 being
the numerator of the irreducible fraction 8/5). This approach was used in Spaunet al. [85].

To determine the spectral resolution of the VIPA, the rst approach was used: a lter cavity wasconstructed with an FSR of 2 GHz, enough to resolve individual comb teeth. A comb-mode-resolved
camera image is shown in Fig. 3.10. Since the comb teeth are very narrow relative to the VIPA
response function, the vertical and horizontal widths of the spots yield the response functions for
the VIPA and grating, respectively.

3.6 Locking the Cavity
As mentioned earlier, there are two main methods of ensuring ecient coupling between comb teeth
and cavity modes, the tight lock and the sweep lock. Early on, the tight lock was utilized in the
kinetics experiments due to its high on-resonance transmission. However, this can cause problems inphotolysis experiments where there is a sudden jump in gas pressure and hence the eective optical
path length within the cavity. The sweep lock is signicantly less sensitive to this pressure jump
and also helps to reduce other frequency-to-amplitude noise conversion processes.
The cavity sweep lock is performed in our case by sweeping the repetition rate, frep , of themid-IR frequency comb source with a 50 kHz sine wave. As the frequency comb teeth come into
resonance with the cavity modes, the cavity transmits a pulse of light.

This transmission signal

is mixed with a phase-shifted version of the repetition rate modulation signal, low-passed, and fed
back to the cavity piezo. The sweep signals and cavity transmission are shown in Fig. 3.13.

3.7 Timing
Since this is a chemical kinetics experiment, it is necessary to properly synchronize each of theelements of the experiment. A simplied timing diagram is indicated in Fig. 3.11. The repetition
rate of the Yb oscillator is swept with a 50 kHz sine or triangle wave (DS345 function generator)
using its fast PZT. The 50 kHz synchronization signal from the function generator is used to trigger

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

38

Figure 3.10: Comb mode resolved VIPA image obtained by ltering the 136 MHz comb through a
2 GHz lter cavity.

an Arduino, which generates the YAG, optical shutter, and FLIR camera trigger.

3.8 Temporal Resolution and Sensitivity
There are two key parameters that characterize TRFCS, the temporal resolution and the absorption
sensitivity. The temporal resolution is given by the ringdown time of the cavity of length lcav andnesse F ,τ=F lcav.
πc(3.5)

The absorption sensitivity, however, is determined by the incident power on the camera, I relative
to any noise processes, δI , scaled by the eective cavity interaction length, lef f = βF lcav (see 2.2).
This yields αmin =δI
1
I βF lcav . A few noise sources in this experiment include:

1. Intensity noise, (δIint = Aint I ). This originates from either intensity uctuations of the OPO
comb or frequency-to-amplitude noise conversion in the cavity.

2. Shot noise, (δIshot = Ashot

√

I ).

3. Camera dark noise, (δIdark = Adark ). There are two main processes here: camera readout (orCHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

Phase
Delay
50 kHz sine
DS345
Fn. Gen39

Loop
FilterMixertransmission

Cavityfast frep PZT

cavity lengthsync
197 us Delay

ArduinoDDG

FLIR
Cameralamp
Q sw
OpcalShuerFigure 3.11: Locking diagram for TRFCS experiment.

ShuerLamp
Q-SwitchtQ
Camera

B

R

4 ms

S1

S2

t

Figure 3.12: Timing diagram for TRFCS experiment.

SN

YAG

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

40

Figure 3.13: Oscilloscope screenshot of sweep signals. The green and yellow signals correspond tothe cavity sweep and camera integration window, respectively.

digitization) noise and dark current noise.

In these expressions, Aint , Ashot , and Adark are the intensity-independent scaling for each process.
These noise processes scale with the intensity and camera integration time as√(δI)2 = (Aint I)2 + (Ashot I)2 + (Adark )2 .
The minimum detectable absorption is then αmin =this setup, the δIdark term was dominant, so αmintotal incident intensity on the camera.

1
βF l

(3.6)

p
(Aint )2 + (Ashot )2 /I + (Adark )2 /I 2 . In

∝ Adark /(F I) was heavily dependent on the

Practically, there are two elements that mainly limit the

total intensity of light on the camera: the optical cavity and the VIPA etalon. Our optical cavity
has an on-resonance transmission of approximately 36%, while the VIPA etalon has a transmissionof approximately 20%.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

41

3.9 Demonstration of the time-resolved spectrometer: acrylic acid
To demonstrate TRFCS for use in the analysis of chemical reactions, it was applied to the photolysisof acrylic acid. This photolysis pathway has been studied previously and it is a well-known method
for generating HOCO/DOCO species[95, 96]. At 193 nm, there are four primary photodissociation
pathways[97]:

H2 C = CHCOOH + hν

H C = CH + HOCO
H C = CHCO + OH
H C = CH + CO
H C = COH + CO
2

(3.7)

2

(3.8)

2

2

2

2

Of particular concern is eq. 3.7, the ππ∗ C-C transition, which is known to generate(3.9)(3.10)

trans -HOCO.

Additionally, partially deuterated acrylic acid, acrylic acid-d1 (AA-d1 ) is used and the OD stretch is-1monitored to avoid contamination by water lines at 3600 cm
as shown in Fig.

3.14.
-1

about 2.5 kJ mol

Theoretical calculations suggest that the-1[98]. At room temperature (∼ 2.5 kJ mol

molecules will be in the. AA-d1 exists as one of two isomers,s-cis isomer is more stable by), this means that about 37% of thes-cis state.

AA-d1 is a liquid at room temperature, so it is necessary to use a carrier gas (N2 ) to introduce
it to the reaction cell. This was done using a custom-designed bubbler, shown in Fig. 3.15. The
total pressure and temperature of the cell were maintained at approximately 12 torr and 21◦ C,

cis -AA-d1 (left) s-trans -AA-d1 (right) [99].

Figure 3.14: AA-d1 exists in two stable planar forms, s-CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

42

respectively.
Once in the cell, the concentration of AA-d1 is readily determined by absorption spectroscopy of
its fundamental ν1 band (OD stretch). An example of such a spectrum is given in Fig. 3.16. Since
there are no known spectral information available for AA-d1 , the concentration was determined byshifting and scaling the absorption spectrum from undeuterated acrylic acid. The ne structure thatappears in the blue trace is due to periodic baseline oscillations. From this analysis, we determinedthat the AA-d1 concentration is approximately 4

Ö

14

-3

10

molecules cm

over the cell's 12 cm chemicalinteraction region.
A 10 ns, 193 nm ArF laser (Optex Pro) was used to photolyze the AA-d1 at a repetition rate of
0.2 Hz, with an energy of 4.8 mJ and a spot size of 1 cm×3 cm. By monitoring the time-dependent
concentration of AA-d1 , the fractional photolysis and cell residence time may be estimated, as shownin Fig. 3.17. From the exponential t, we determine a maximum depletion of 1.61% ± 0.04% and apump-out rate of kpump = 3.0 ± 0.1 (1σv statistical uncertainty from the t). The expression for thephotodepletion of AA-d1 in terms of its 193 nm absorption cross-section, σAA , is[AA]
= 1 − exp(−σAA ΦH),
[AA]0

(3.11)-2

where Φ is the photodissociation quantum yield and H is the 193 photon uence in photons cm

15 photons cm-2 yields σ

Assuming Φ = 1 and a photon uence of H ≈ 1.6 × 10.

−17 cm-2 ,AA = 1 × 10

−18 cm-2 ) reported in Ref. [100].

which is close to the value (7.5 × 10

In addition to the depletion of AA-d1 , the formation ofobserved, as shown in Fig.

3.18.

trans -DOCO, HOD, and D2 O were

The P, Q, and R branches of the-1

spectrum can clearly be seen within the 40 cm

trans -DOCO rovibrational

bandwidth, but the HOD and D2 O bands are too

broad to be seen in their entirety. The formation of
but the prompt formation of HOD is unexpected.

trans -DOCO from Eq. 3.7 is not surprising,A t of thetrans -DOCO spectrum from Fig.

12 cm−3 . Moving to another spectral region, we are

3.18A yields a concentration of (3.1 ± 0.5) × 10

able to observe the ν3 P-branch of deuterated acetylene, C2 HD, directly following photolysis, shownin Fig.

3.19.

This spectrum was assigned using a line list measured by Baldacci

et al [101]. A

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

43

Figure 3.15: Bubbler used to introduce AA-d1 to the reaction cell.

Experimental spectrum
Fit simulation

Figure 3.16: Typical broadband absorption spectrum of AA-d1 in blue. A shifted spectrum (red)of undeuterated acrylic acid is used to t the concentration.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

44

Figure 3.17: Percent depletion of the integrated AA-d1 band intensity as a function of time (50μs integration time) after the 193 nm photolysis pulse. An exponential decay t (blue) reveals a-1
pump-out rate of kpump = 3.0 ± 0.1 s .

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY-1

calculated fundamental band intensity of 20.6 km mol45

was obtained by calculating the optimized

geometry and fundamental vibrational frequencies and intensities at the CCSD(T)/aug-pVDZ level
using CFOUR[102].
By tting the time-dependent spectra of all of these species, we are able to see their formationand decay characteristics, as shown in Fig. 3.20. Three species are promptly formed:
HOD, and C2 HD.

trans -DOCO,

trans -DOCO decays with a lifetime kDOCO = (9.6 ± 0.9) × 10−3 s−1 , which issimilar to the HOCO loss rates observed by Petty

et al [103], which they attribute to fast bimolecular

reactions with other radicals such as the vinyl radical or DOCO. At longer times (> 200 µs), D2 O
grows as HOD decays, likely due to the isotope exchange reactions HOD+HOD and HOD+AA-d1 .
The observation of prompt HOD and C2 HD is surprising. Bulk phase experiments have foundevidence for CO (carbonylation), CO2 (carboxylation), and HOCO products[104].
beam experiments, photodissociation leads only to two prompt channels, Eqs.

In molecular

3.7 and 3.8 [97].

Such high yields of HOD and C2 HD suggest that AA-d1 undergoes isomerization reactions leading
to intramolecular H-atom abstraction, as well as H/D exchange or D-atom insertion. This would
yield a full dehydrocarbonylation reaction of the form

H2 C = CHCOOD + hν→ C2 HD + H2 O + CO.
→ C2 H2 + HOD + CO
The observation of prompt C2 H2 and H2 O may help elucidate this mechanism.

(3.12)

Clusters areanother possible pathway for the formation of C2 HD and HOD; acrylic acid is well known to form
dimers and larger clusters at room temperature. However, based on the dimerization equilibrium
constant of

Kp = 2.6 torr (measured by Osborne et al, Ref.

[104]), and the spectroscopicallymeasured partial pressure of AA-d1 , the fraction of dimers is estimated to be < 1%. Therefore, it
is unlikely that clusters are responsible for the formation of C2 HD and HOD.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

46

Figure 3.18: Transient absorption following the photolysis of AA-d1 . Experimental data is shown inblack and molecular simulations are inverted and shown in magenta, dark blue, and light blue fortrans -DOCO, HOD, and D2 O, respectively. The camera integration time was set to 50 μs, beginning(A) with the photolysis pulse, (B) 4 ms after photolysis, and (C) 80 ms after photolysis. The fourQ-branch transitions intrans -DOCO are known to be perturbed by a Coriolis or Fermi interaction[95] and are not included in the ts.

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

47

Figure 3.19: Absorption spectrum of C2 HD. Experimental data is shown in black and the t isshown in red. The full spectrum is shown in panel (a) and a zoomed-in version is shown in panel(b), along with its t residual in panel (c).

CHAPTER 3. TIME-RESOLVED FREQUENCY COMB SPECTROSCOPY

48

Figure 3.20: Measured absolute concentrations of HOD (dark blue squares), D2 O (light blue diamonds), C2 HD (orange triangles), andtrans -DOCO (red circles) as a function of time. The CH2 D

plot uses the right concentration axis, all other plots use the left axis.
progressively zoomed-in versions of the same data set.

Panels A, B, and C areChapter 4
The OH+CO Reaction: Introduction
4.1 Overview
1b
OH + CO1a

The OH+COHOCO*
M

H + CO2

HOCO

H+CO2 reaction has long been studied due to its relevance in atmospheric andcombustion chemistry.

When OH and CO collide, they form the energetically excited species*

HOCO , which may then be collisionally stabilized to ground state HOCO or react to form H+ CO2 .

In the rst few sections of this chapter, I will discuss the importance of this reaction

in atmospheric and combustion chemistry. Later, I'll briey introduce the history of experimental
studies on this reaction.

4.2 Atmospheric Importance
The OH radical participates in many ways to the complex chemistry of the atmosphere. OH radicals
1

are formed in the atmosphere through the photolysis of O3 to O( D) and its subsequent reaction
with H2 O. Once formed, OH acts as the primary daytime oxidant in the atmosphere[105, 106],
breaking down large organic compounds and removing them from the atmosphere. For this reason,

49

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

50

OH has been referred to as an atmospheric vacuum cleaner [107]. Additionally, OH reacts with O3
and HO2 to form H2 O2 . The three molecules OH, O3 , and H2 O2 largely determine the oxidizing
capacity of the atmosphere[108] and rough average concentrations are given in Table 4.2 along withan example reaction rate with isoprene. It is interesting to note that the atmospheric concentrationsof O3 and H2 O2 tend to be orders of magnitude larger than OH, but the fast reaction rates of OH
more than compensate for the low concentration.
A second eect of OH radicals in the atmosphere is to modulate the concentration of O3 throughtheir reaction with CO[111]. This modulation occurs in the troposphere through a somewhat complex series of reactions, as shown in Figure 4.1, in which OH acts as a catalyst for the net reaction
CO+2 O2 → CO2 +O3 . Interestingly enough, this eect is reversed in the stratosphere, where OH
catalyzes the destruction of O3 .
These eects make clear that any attempt to understand atmospheric chemistry must include a
detailed understanding of OH+CO and other OH reactions. However, these reactions are not fully
understood; current atmosperic models tend to overpredict the formation of OH and underpredict its
loss[112, 113]. Additionally, the OH+CO reaction has many branching channels which may further
react to re-form OH. Therefore, it is important to understand the partitioning of this reaction into
its many products.

Species

Concentration (molecules cm

O3

1.8 × 1012
2.8 × 1010
5 × 105
2 × 107
1 × 105

H 2 O2
OH
NO3
Cl

-3

)

k(X+isoprene) (molecules cm

-3

s

-1

)

Rate (s-1)

9.6 × 10−18 [109]1.7 × 10−5



1 × 10−10 [109]7.2 × 10−13 [110]4.3 × 10−10 [110]5 × 10−5
1 × 10−5
4 × 10−5

Table 4.2: Approximate concentrations and reaction rates of a few oxidating species in the atmosphere. k(X+isoprene) is the bimolecular loss rate of the species with isoprene.

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION
O2

HO2

H

CO2

CO

OH

51

O3

NO

h +O2
O2

NO2

Figure 4.1: Role of OH+CO in the O3 balance of the atmosphere.

4.3 Combustion Importance and Additional Applications
The OH+CO reaction is also of fundamental importance to combustion chemistry due to the roleit plays in CO/CO2 conversion.

This reaction is of particular importance in the combustion ofsyngas, H2 +CO, where large concentrations of OH are formed during the reaction. The role of the
OH+CO→HOCO channel in combustion processes is not yet clear, although preliminary investigations suggest that the channel may not signicantly impact the combustion of syngas[114].
HOCO may also play a role in extra-terrestrial atmospheric chemistry. Boxeet al. have indicatedthat HOCO molecules generated on the surface of Mars may have an extrordinarily long lifetime of
30 µs at the Martian surface to 1.2 days at 240 km away from the surface due to the low oxygen
content of the Martian atmosphere[115].

Finally, the OH+CO reaction is an important testbed

reaction for computational chemistry techniques.

Due to the small (3N-6=6) number of degrees

of freedom, this reaction can still be tractable with current classical computer systems. Even the
addition of a single atom would result in 3 additional degrees of freedom and would exponentially
increase the required Hilbert space in the simulation. Quantum computers may help in this regard
by allowing for polynomial scaling with system size[116], but no such device is yet powerful enough.

4.4 History of the OH+CO Reaction
The study of the OH+CO reaction has a long history, due primarily to its signicance in atmosphericand combustion processes.

Until the early 1970s, however, it was believed this reaction followedCHAPTER 4. THE OH+CO REACTION: INTRODUCTIONa very simple Arrhenius mechanism, shown in Fig.

52

4.2a, in which there is only a single barrier

between the reactants, OH+CO, and products, H+CO2 . In this simple case, the reaction rate may
be expressed in the form k(T ) = Ae

−Ea /(RT ) , where A and E are the pre-exponential factor anda

the activation energy of the reaction, respectively. In a very simple sense, e−Ea /(RT ) is proportional

to the fraction of reactants above the reaction barrier and A is a steric factor dependent on the
shape of the potential energy surface. The constants A and Ea are typically determined through alinear t of an Arrhenius plot, Fig. 4.2b, where ln(k) is plotted vs 1/T.
By 1972, the OH+CO reaction rate had been determined at a variety of temperatures andpressures, but the analysis was proving problematic within the Arrhenius framework:

clearly a

new approach was needed. This is perhaps most clearly illustrated by a 1972 review of hydroxyl
reaction rates which states, the hydroxyl radical has been a problem species in chemical kinetics.
The accepted value for the room temperature rate constant of [OH+CO] has varied by a factorof 1000 over the last 10 years. [117].

The article primarily attributes this inconsistency to therelative diculty in preparing the reactive OH species in the absence of other competing reactive
species. This may have been part of the problem, but a much better explanation soon came from analternative source: the reaction mechanism itself. In 1973, Smith and Zellner were able to explain
the strange behavior of this reaction in terms of a reactive complex, HOCO[118].

The HOCO

complex was proposed to be a short-lived, loosely bound, state between the OH+CO reactants andthe products, H+CO2 . By adding this complex to the OH+CO reaction surface, as indicated in
Fig 4.3a, they were able to explain the anomalous (non-Arrhenius) temperature dependence in Fig.
4.3b.
Work on this reaction accelerated and, through time-dependent studies of OH uorescence[119,120], more comprehensive models were developed for OH+CO reaction rate temperature and pressure dependence[119, 120, 121, 122, 123].

Additionally, microwave[124] and infrared studies[96]determined that Smith and Zellner's HOCO complex is actually a highly reactive, but tightly
bound, molecule consisting of
HOCO+O2 andtrans -HOCO and cis -HOCO isomers. A few reaction rates, trans -trans -HOCO+NO, were determined[103], showing this very fast reactivity. Progress

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

(b)

53

oset: ln(A)slope:-Ea/R

ln(k)

(a)
OH+CO

H+CO2

1/T

Figure 4.2: (a) Simple Arrhenius reaction surface and (b) expected temperature dependence of sucha reaction.

Figure 4.3:(a) Reaction surface and (b) temperature dependence of the OH+CO reaction, as[118]. The straight lines correspond to the Arrhenius

determined by Smith and Zellner in 1973

temperature dependence, which do not t the experimental data points. These plots are reproduced
from Smithet al.[118].

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

54

on the deuterated reaction, OD+CO, proceeded largely in tandem, with many of the same results.
The microwave and infrared spectra oftrans -DOCO were obtained, showing its stability in its

ground vibrational state[95, 125].
Despite these advances, a few key components of this reaction have remained unexplored. Since
the majority of the OH+CO and OD+CO reaction rate studies only observed the loss of OH/OD in
the presence of CO, they were unable to directly study the transformation of OD into its respective
product channels. In fact, by 2016 there was still no direct observation of HOCO or DOCO formationfrom the OH+CO or OD+CO reactions. Additionally, infrared vibrational spectra ofcis -HOCO andcis -DOCO had not been observed. The direct observation of trans -DOCO, cis -DOCO, and D+CO2
from OD+CO would allow for the characterization of all relevant reaction rates and branching ratios
for this reaction, allowing for unprecedented access to the OD+CO potential surface.

4.5 Mechanics of the OH+CO Reaction
The OH+CO reaction and its deuterated analogue proceed on the potential surface indicated in Fig.
*

4.4, where OH and CO rst associate to form the rotationally and vibrationally excited HOCO

molecule. When isolated, this molecule has a lifetime on the order of ps[126], and dissociates to form*

H+CO2 . In the presence of large concentrations of a bath gas, however, HOCO
quenched to its ground vibrational state.

is vibrationallyThis complex reaction pathway can be simplied into

an equivalent model, with two pathways, reactions 1a and 1b. The bimolecular reaction 1a, with
rate k1a (P,T) describes the formation of ground statetrans - or cis -HOCO, while the bimolecular

reaction 1b, with rate k1b (P,T) describes the formation of H+CO2 .

The Lindemann mechanism

yields a good rst-order approximation to these parameters. As applied to the OH+CO reaction
and derived in A.2, this mechanism simply enforces the steady-state approximation for the HOCO
species (*dd∗dt [HOCO ] = 0) as well as CO ( dt [CO] = 0). With these constraints, eective pressure-dependent rates k1a and k1b for the formation of HOCO and H+CO2 are

k1 = k1a + k1b(4.1)

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION
TS3

Energy (kJ/mol)

40
0

55

OH+CO

TS2

TS1

OH…CO
H-CO2

-40

TS5

TS4
-80
trans-HOCO-120

cis-HOCO

H+CO2

Reaction Progress
Figure 4.4: One dimensional potential energy surface for OH+CO using values from Nguyen

et al.

[123].

k1a =[M ]k1a,0
1 + [M ]k1a,0 /k1a,∞

(4.2)

k1b =

k1b,0
,
1 + [M ]k1a,0 /k1a,∞(4.3)

where the subscripts  0 and  ∞ refer to zero pressure and very large pressure, respectively. At
low pressures, [M] k1a,∞ /k1a,0 , the HOCO formation pathway, k1a ≈ k1a,0 [M ], is proportional topressure and the CO2 formation pathway, k1b ≈ k1b,0 , is constant with pressure. Figure 4.5 shows

k1 , k1a , and k1b vs. [He] using experimentally-determined parameters from Fulle et al. [120]. In−33 , k−12 , and k−13 .
1a,∞ = 1.1 × 10
1b,0 = 1.3 × 10

this case, k1a,0 = 3.9 × 10

While the Lindemann formalism generally gives the correct behavior of the reaction rate withpressure, it fails to provide a correct quantum treatment of the excited HOCO vibrational androtational states.

An extension to the unimolecular Lindemann theory is the Troe formalism, inwhich unimolecular Lindemann-type reaction rates are multiplied by broadening factors[4, 127] thataect the pressure dependence in the intermediate pressure range. The bimolecular case of OH+CO
is more complicated[120], but the limiting functional form at low and high pressures remain the same

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

56

Rate constant (cm 3 molecule -1 s-1)

10-11

10-12

10-13

10-14

k1=k1a+k1b

10-15

k1a
k1b

10-16
1017

1018

1019

1020

1021

1022

[He] (molecules cm -3)
Figure 4.5: Pressure dependence of the OH+CO reaction rate within the Lindemann formalism(solid curves). Fitted reaction rates are taken from Fulle

et al. [120]. The dashed curves include

emperical broadening factors needed to t the data in Ref. [120].

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

57

as in the Lindemann case.

4.6 Experimental Approach: OD Generation
Many methods exist for the generation of OD (and OH) radicals, a few of which are listed inTable 4.3. However, there are benets and drawbacks associated with each method. For example,
the discharge of D2 O can generate a very large concentration of OD radicals, but will inevitably
generate[128] other species such as O, DO2 , and D2 O2 . Due to the diculties in characterizing thespecies produced in this manner, this approach is not viable. In general, photolysis is the cleanest
method of generating these radicals, since a specic molecular bond is broken by the photolysis laser.
Of the photolysis-based techniques, we settled on photolysis of O3 at 266 nm, and its subsequent
1

reaction of O( D) with D2 as the ideal production pathway for OD. This decision allowed us to
avoid D2 O2 and D2 O spectral contamination in the precursor and also provided for signicantly
higher OD yields when compared with the photolysis of N2 O. The photolysis cross sections for O3 ,N2 O, and H2 O2 are shown in Fig. 4.6, where it is easily seen that the O3 cross-section dominates
by several orders of magnitude. Additionally, high-energy pulses at 266 nm from quadrupled pulsed
YAG lasers are readily available.
Ozone itself is fairly reactive and will not live long at room temperatures. The walls of a steel
vessel will catalyze its conversion to O2 within about 1 day.

For this reason, the ozone used in

our kinetics experiments was generated on-demand using a commercial ozone generator and was
puried with a silica-gel ozone trap at low temperature. A trap was originally constructed using
the description in Ref. [130], but was modied many times and now looks considerably dissimilar.
The nal iteration of the trap consists of a U-shaped stainless-steel tube lled with 6-12 mesh silica
gel. Due to the implosive hazards of glass dewars, we housed the ozone trap in a durable Nalgene
dewar.
The general operating procedure for the ozone trap was:

1. Cool the ozone trap using a LN2 +isopropanol slurry. The slurry will become very viscous,

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

PathwayO3 +hν

1

1



O( D)+O2

D2 +O( D)OD+D(O3 Photolysis)

N2 O+hν11

O( D)+N2

D2 +O( D)OD+D(N2 O Photolysis)

D2 O2 +hν

2 OD

(D2 O2 Photolysis)-

D2 O+e

products(D2 O Discharge)

Notes














Very large O3 photolysis cross-section at 266 nm
Messy D, OD, O3 regeneration chemistry1

D2 +O( D) generates OD in high (v=9) vibration
Pure O3 is dicult to generate and stabilize

N2 O is stable and can be easily purchased
1

D2 +O( D) generates OD in high (v=9) vibration
Photolysis of N2 O is inecient, even at low wavelengths

Pure D2 O2 is dicult/impossible to obtain, since D2 O2degrades to D2 O
Severe spectral contamination by D2 O2 and D2 O

D2 O is readily available and D2 O discharge is wellestablished
Generates many reactive species
Severe spectral contamination by D2 O

Table 4.3: Methods of OD production.

58

Absorption Cross Section (cm2)

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

59

10-16

10-18

10-20

10-22

10-24
150

200

250

300

350

Wavelength (nm)Figure 4.6: UV Photolysis cross sections for O3 (blue) and N2 O (red). Data for O3 and N2 O areobtained from HITRAN2012[129] and Burkholder

et al.[6], respectively.

Figure 4.7: Photo of ozone trap.

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION60

but should not solidify.

2. Begin owing ~ 2 slm O3 +O2 over the trap. In our case, the mixture was 8% O3 in O2 . Wait
about 1 hour for the trap to ll. A large concentration of ozone behind the trap is a good
indication that the silica gel is close to saturation.

3. Close the O3 source and ow N2 over the silica-gel, slowly releasing the ozone into the kinetics
cell.

The concentration of ozone in our reaction cell was directly measured by absorption spectroscopy
at 270 nm with a UV LED. The spectrum of the LED is shown in Fig. 4.8 along with the ozone
cross section across the range. The large variation of ozone cross section with wavelength permits
two methods for determining the concentration:

1. A two-beam measurement, in which the LED output is split into reference and signal
beams that are sent around and through the chemistry cell, respectively. The ozone concentration in the cell is then simply given by

nO3 = −

1
σO3 l


ln

IS
IR


.

2. A single-beam measurement in which the LED output is sent directly through the chemistrycell onto a spectrometer (Ocean Optics USB2000+). The ozone ow is turned o and a single
reference spectrum, IR (λ), is taken. The transmitted LED spectrum with ozone ow, IS (λ),
is monitored and the ozone concentration is calculated using a two parameter (nO3 ,δ) linear
t to − ln (IS (λ)/IR (λ)) = nO3 σO3 l − δ , where δ accounts for small uctuations in the diodetransmission due to varying current or slow drifts in alignment. At concentrations of 1 × 10
-3molecules cm

15, δ is much smaller than nO3 σO3 l.

The total concentration of trapped ozone was determined by observing the time-dependent
concentration of ozone at the exit of the trap. Ozone is trapped using the above protocol and isallowed to warm up at t=0. The measured ozone is integrated vs time to provide a total ozone ow,

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

61

Figure 4.8: UV LED spectrum (blue, left axis) and O3 absorption cross section (red, right axis).

shown in Fig. 4.9. By 100 mins, the ozone trap is depleted, yielding a total integrated concentrationof ~ 160 torr min. With the measured pumping speed of 193 ml/s, the trapped ozone is determined

22 molecules.

to be 6.1 × 10

Additionally, extreme care must be taken during the purication process, since ozone is highly
explosive[131]. Generally, this risk can be appropriately mitigated by (1) constructing the ozone
trap from stainless steel to contain the potential blast and (2) ensuring that the LN2 +isopropanolslurry does not freeze, maintaining O3 above its condensation temperature of 161 K. Finally, theozone must be destroyed prior to being pumped out of the system to avoid damage to the pump.
In order to achieve this, a copper cylinder was lled with copper mesh and heated to ~ 140 degrees
C. This was installed directly prior to the roughing pump.

4.7 Spectral Characteristics of Key Species
The absorption spectra of a few key species are shown in Figure 4.10. Since our OPO frequency comb
is tunable between 2.8 μm to 4.8 μm, we can detect each of these species by tuning our spectrum
appropriately. The OD ro-vibrational spectrum is also very broad, allowing for the simultaneoustrans -DOCO, OD+cis -DOCO, or OD+CO2 in the same spectral window. Thisdetection of OD+

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

62

180

integrated pressure (torr min)

160
140
120
100
80
60
40
20
0
0

50

100

150

200

250

300

time (min)Figure 4.9: Integrated time-dependent ozone concentration.

important feature allows for the removal of the path length (given by the Finesse and photolysis
length) from the analysis, since Atrans−DOCO /AOD
similarly for= ntrans−DOCO σtrans−DOCO / (nOD σOD ) andcis -DOCO and CO2 . However, the relative cross sections, σv, remain important.

Line positions for OD(v=0,1) were readily available from Abrams et al [132]. Line strengths for
OD(v=0,1), however, have not been measured and are necessary to calculate the OD cross section,

σOD . Since the OH(v=0) cross section has been measured by Nesbitt et al [133, 134], it was possible
to determine the OD(v=0) cross section through mass scaling.
The dipole matrix element, µν 0 ,ν 00 , is given byZµν 0 ,ν 00 =ψν∗0 (r)µ(r)ψν 00 (r) dr ,(4.4)

where ψν and µ(r) are the wave function and dipole moment, respectively. Since deuteration does
not change the charge of the H or O atoms, the dipole moment function remains the same for OH
and OD. However, the wavefunctions are modied under deuteration. A Hamiltonian appropriate

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

63

Wavelength ( m)
4.3

4.2

4.0

3.8

3.7

3.6

3.4

3.3
CO2
D2O
trans-DOCO
cis-DOCO
OD

2300

2400

2500

2600

2700

2800

2900

3000

Wavenumber (cm -1)
Figure 4.10: Mid-IR Absorption Spectra of Key Species.

for OH is[134]H = Tr + V (r) + A(r)L · S + B(r)R2 ,(4.5)

where Tr is the kinetic energy operator, V (r) is the OH internuclear potential, A(r) is the spinorbit coupling constant, B(r) is the rotational constant, and L, S , and R are the electronic orbital,
electronic spin, and nuclear end-over-end angular moment, respectively. Since the A(r) and B(r)terms are small, we will neglect them for this calculation. In the continuous position basis, H is

~2 d2
δ(r − r0 ) + V (r)δ(r − r0 ) ,2m dr2(4.6)

where m is the reduced mass. The position variables are discretized, r, r

0 → r , r , and we use thei jH(r, r0 ) = −nite dierence method to approximate the derivative,

d2
dr2

1
→ (∆r)2 (δi.j+1 − 2δi,j + δi,j−1 ). This

yieldsHi,j = −~2(δi.j+1 − 2δi,j + δi,j−1 ) + V (ri )δi,j ,2m(∆r)2(4.7)

where ∆r is the grid spacing in ri . Since V (r) remains unchanged under deuteration, we use themeasured OH RKR potential (shown in Fig. 4.11a) and scale the kinetic operator for the OD case.

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION64

The OH and OD vibrational wavefunctions obtained using this method are shown in Fig. 4.12 alongwith the OH internuclear potential.
With these wave functions determined, it is possible to calculate the dipole matrix element using
the measured OH dipole moment function from Nesbitt et al [134], shown in Fig. 4.11b. Eq. 4.4
was used to calculate the dipole matrix elements for OH(v=0-3) and OD(v=0-3). These values areshown in Table 4.5 along with available experimental values.
Spectral parameters for the ν1 ro-vibrational band of trans-DOCO have previously been determined by Petty and Moore[95]. Using PGopher, it is possible to obtain the relative line strengths
within the ro-vibrational band, but a dipole moment is needed for absolute line strengths.

The

absolute determination of line strengths for transient reactive species is notoriously dicult, so
we turned to theory.

Table 4.7 includes theoretical band positions and intensities fortrans - andcis -DOCO.
Finally, CO2 required no spectral treatment, since comprehensive line positions and strengths
already exist in the HITRAN database[129]. D2 O was also observed; line positions and strengths
were obtained through private communication with Keeyoon Sung of JPL (see Table 5.2).

Mode

Empirical Dipole[135, 136]

This calculation

OH(01)

0.03420.0343

OH(12)

0.041

0.0408OH(23)

0.040

0.039

OD(01)



0.0303

OD(12)



0.0386

Table 4.5: Experimental and calculated dipole matrix elements for OH and OD (Debye).

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION(a)

Figure 4.11:(b)Functions used in this calculation.

(a) OH RKR potential energy from Nesbitt

al.[135, 136] along with t. (b) Dipole moment function from Nesbitt et al.[135, 136].

(a)

65

et

(b)

Figure 4.12: Calculated vibrational wavefunctions for (a) OH and (b) OD. Wavefunctions are in
red, oset by their vibrational energy. The tted potential energy surface is in black.

CHAPTER 4. THE OH+CO REACTION: INTRODUCTION

t -DOCOPosition-1(cm
Johnsonet al (2011))

t -DOCOc -DOCO

Intensity(km mol-1

66

Position
)

-1

(cm

)

c -DOCO
Intensity(km mol

2688



2555



2691



2558



2685.147.97

2551.6

14.75

2685



2544





65



14.4

-1

)

[137]
Mladenovi¢

et al (2013)[138]
Huang et al (2013)
[139]
Wang

et al (2014) [140]

Stanton, private
communication

Table 4.7: Theoretical ν1 ro-vibrational band positions and intensities fortrans- and cis -DOCO.

Chapter 5
Direct Measurement of OD+COtrans -DOCO Kinetics
This chapter is published as

B. J. Bjork, T. Q. Bui, O. H. Heckl, P. B. Changala, B. Spaun, P. Heu, D. Follman, C. Deutsch,G. D. Cole, M. Aspelmeyer, M. Okumura, and J. Ye, Direct Frequency Comb Measurement of
OD + CO

Abstract:



DOCO Kinetics, Science 354, 6311 (2016), pp. 444-448. [141]The kinetics of the hydroxyl radical (OH) + carbon monxide (CO)reaction, which is fundamental to both atmospheric and combustion chemistry,
are complex because of the formation of the hydrocarboxyl radical (HOCO)
intermediate.

Despite extensive studies of this reaction, HOCO has not been

observed under thermal reaction conditions.

Exploiting the sensitive, broad-band, and high-resolution capabilities of time-resolved cavity-enhanced direct
frequency comb spectroscopy, we observed deuteroxyl radical (OD) + CO reaction kinetics and detected stabilized

trans -DOCO, the deuterated analog oftrans -HOCO. By simultaneously measuring the time-dependent concentrationsof thetrans -DOCO and OD species, we observed unambiguous low-pressure

termolecular dependence of the reaction rate coecients for N2 and CO bathgases. These results conrm the HOCO formation mechanism and quantify its
yield.

67

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

68

5.1 Main Text
The apparent simplicity of gas phase bimolecular reaction kinetics of free radicals often belies thecomplexity of the underlying dynamics. Reactions occur on multidimensional potential energy surfaces that can host multiple pre-reactive complexes and bound intermediate complexes as well as
multiple transition states. As a result, eective bimolecular rate coecients often exhibit complex
temperature and pressure dependence. The importance of free radical reactions in processes such as
combustion and air pollution chemistry has motivated eorts to determine these rate constants bothexperimentally and theoretically. Quantitative

ab initio modeling of kinetics remains a major con-temporary challenge[142], requiring accurate quantum chemical calculations of energies, frequencies
and anharmonicities, master equation modeling, energy transfer dynamics, and, when necessary,calculation of tunneling and non-statistical behavior.

Experimentally, detection of the transientintermediates, which is the key to unraveling the dynamics, is often quite challenging.
The reaction of hydroxyl radical with CO (eq. 5.1),

OH + CO → H + CO2 , ∆r E0 = −103.29 kJ mol−1(5.1)(∆r E0 , standard energy of the reaction at 0 K) has been extensively studied over the last four
decades because of its central role in atmospheric and combustion chemistry[123]; it has cometo serve as a benchmark for state-of-the-art studies of chemical kinetics of complex bimolecular
reactions[143, 144]. In Earth's atmosphere, OH is critical as the primary daytime oxidant[105, 106].
CO, a byproduct of fossil fuel burning and hydrocarbon oxidation, acts through eq.

5.1 as animportant global sink for OH radicals; this reaction is the dominant OH loss process in the freetroposphere. In fossil fuel combustion, OH + CO is the nal step that oxidizes CO to CO2 and is
responsible for a large amount of heat released.
The rate of the reaction in eq. 5.1 is pressure dependent and exhibits an anomalous temperaturedependence, which led Smith and Zellner[118] to propose that the reaction proceeds through a highly
energized, strongly bound intermediate, HOCO, the hydrocarboxyl radical (Fig.

5.1A, inset).

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.1: Potential energy surface for the OH + COfrom Nguyen et al. [123]. OH + CO

69

H + CO2 reaction, with energies taken

H + CO2 proceeds through vibrationally excited HOCO*,

which is either deactivated by bath gas M or reacts to form H + CO2 . The inset shows the simplied
OH + CO reaction mechanism. TS, transition state.

Figure 5.2: Schematic showing the most important reactions in our system. Time-dependent concentrations of trans-DOCO, OD(v = 0), OD(v = 1), and D2 O (red) are measured by cavity-enhanced
absorption spectroscopy; the concentrations of the precursors (purple) are set by ow controllers or
meters. O3 is measured by UV absorption.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

70

Formation of H + CO2 products is an example of a chemically activated reaction. The course of thereaction is governed by the dynamics on the potential energy surface, shown schematically in Fig.
5.1. The OH and CO pass through a pre-reactive weakly bound OH-CO complex to form a highly
energized HOCO*

in one of two isomers, trans-HOCO or the less stable*

low pressure limit at room temperature, HOCO

cis -HOCO[123]. In the

primarily back-reacts to OH + CO, but there is a-1

small probability of overcoming the low barrier (8.16 kJ mol) and reacting to form H + CO2 . In

the presence of buer gas, energy transfer by collisions with third-bodies M (termolecular process)*can deactivate or further activate the HOCO . Deactivation can lead to the formation of stable,
thermalized HOCO products (reaction 1a), which diminishes the formation of H + CO2 (reaction
1b).

Approaching the high pressure limit, HOCO formation becomes the dominant channel andH + CO2 product formation decreases. The overall reaction rate is characterized by an eective
bimolecular rate constant k1 ([M], T ) = k1a ([M], T ) + k1b ([M], T ), where T is temperature [119, 3,
120, 145, 121].
There have been numerous experimental studies of the temperature and pressure dependence ofthe overall rate coecient; these all measure OH loss in the presence of CO[119, 120, 121, 146, 147,
148, 149, 150]. In principle, master equation calculations with accurate potential energy surfaces
within a statistical rate theory can compute k1 ([M ], T ), buta priori kinetics are rarely possible

because the energy transfer dynamics are generally not known. A number of studies have thus t
the theoretical models to the observed overall rate constants, using a small number of parameters
to describe collisional energy relaxation and activation [119, 120, 148, 149, 151, 152].

Althoughthese previous studies have had success in describing k1 ([M ], T ), they do not capture the dynamics
that would be revealed from the pressure-dependent branching between stabilization of HOCO andbarrier crossing to form H + CO2 products. Detection of the stabilized HOCO intermediate andmeasurement of its pressure-dependent yield would conrm the reaction mechanism and quantitatively test theoretical models. The spectroscopy of HOCO is well established, and recently HOCO
has been observed from the OH + CO reaction generated in a discharge[125, 153, 124]; however,measurements under thermal conditions are necessary to derive rate constants.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS71

sTo directly and simultaneously measure the time-dependent concentrations of reactive radical
intermediates such as HOCO and OH, we applied the recently developed technique of time-resolved
direct frequency comb spectroscopy (TRFCS)[10]. The massively parallel nature of frequency-comb
spectroscopy allows time-resolved, simultaneous detection of a number of key species, includingintermediates and primary products, with high spectral and temporal resolution. The light source
is a mid-IR (≈3-5 μm) frequency comb, generated from an optical parametric oscillator (OPO)
synchronously pumped with a high repetition rate (frep = 136 MHz) mode-locked femtosecondber laser [88].

The OPO spectrum is composed of spectrally narrow comb teeth evenly spaced

by frep and shifted by an oset frequency, f0 .

By matching and locking the free spectral range(FSR) of the enhancement cavity to 2 × frep , we keep the full comb spectrum resonant with thecavity during the data acquisition. The broadband transmitted light (~65 cm-1

bandwidth, ~7100

comb teeth) is spatially dispersed in 2D by a virtually-imaged phased array (VIPA) etalon anda grating combination, which is then imaged on an InSb camera (Fig.

5.7).

Absorption spectra

are constructed from these images as a function of time (with a resolution of 10 μs determinedby the camera integration time), which are compared with known molecular line intensities toobtain absolute concentrations. The absorption detection sensitivity is greatly enhanced with ourhigh nesse (F≈4100) optical cavity that employs mid-IR mirrors with low-loss crystalline coatings.
These mirrors, with a center wavelength of 3.72 μm and a spectral bandwidth of about 100 nm, havesignicantly lower optical losses and hence yield enhanced cavity contrast compared with traditional
amorphous coatings as covered in detail in Ref. [154], enabling an improved sensitivity by a factorof 10 for the direct detection oftrans -DOCO.

In this experiment, we studied the deuterium analogue of eq.

5.1, OD + CO→D + CO2 ,exploiting the sensitivity and resolution of TRFCS to detect the reactant OD (in both v=0 and v=1
states) and the product trans-DOCO by absorption spectroscopy in a pulsed-laser-photolysis owcell experiment. We sought to measure the pressure-dependent eective bimolecular rate coecientsand the yield of trans-DOCO at 27 to 75 Torr (3.3 to 10 kPa) total pressure. Such measurements
would be especially sensitive to the competition between termolecular DOCO stabilization andCHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
reaction to form D+CO2 .

72

Detection of the deuterated species allowed us to avoid atmosphericwater interference in our spectra. We further anticipated that the yield of stable DOCO would behigher, as deuteration substantially reduces the rate of tunneling to form D + CO2 products while
increasing the lifetime of DOCO*

due to the higher density of states.

The OD + CO reaction was initiated in a slow-ow cell by photolyzing O3 in a mixture of D2 ,CO, and N2 gases with 266 nm (32 mJ, 10 Hz) pulses from a frequency-quadrupled Nd:YAG laser,
expanded to a prole of 44 mm

Ö7 mm and entering the cell perpendicular to the cavity axis. [O3 ]0Öwas xed at a starting concentration of 1

15

10

-3

molecules cm

and veried by direct UV absorption

spectroscopy. The initial concentrations of CO, N2 , and D2 were varied over the range 1 to 47 TorrÖ

(0.13 to 6.3 kPa) while the O3 concentration was restricted to 3 to 300 mTorr (4

-4

10

to 4

Ö

-2

10

kPa) to minimize secondary reactions. A complete description and tabulation of the experimental
conditions is included in (5.2.1).
1Each photolysis pulse dissociated 15% of the ozone (5.2.1) to form O2 + O( D) at nearly unity
1

quantum yield [155]. The resulting O( D) either reacts with D2 to form OD + D or is quenched by
3

1

background gases to O( P) within 1 s. O( D) + D2 is known to be highly exothermic and produces
vibrationally excited OD(v = 0 - 4) with an inverted population peaking at v = 2 and v = 3[156].
Vibrationally excited OD was rapidly quenched or formed D atoms by collisions with CO[157, 158].
Formation of vibrational Feshbach resonances of DOCO*

from collisions of OD(v>0) with CO

may be possible, but the lifetimes are on the order of picoseconds, as previously observed for the*

HOCO

case[83, 159, 160, 161].

Therefore, only vibrationally/rotationally thermalized OD(v=0)

are expected to form DOCO by the mechanism described in Fig. 5.1A inset. OD and DOCO reacha steady-state after 100 μs through cycling reactions depicted in Fig. 5.1B: D atoms produced fromOD + CO D + CO2 reacted with O3 to regenerate the depleted OD.
-1Absorption spectra covering a ~65 cm

bandwidth were recorded at a sequence of delays fromthe t = 0 photolysis pulse, using a camera integration time of either 10 or 50 μs depending on oursensitivity toand ~150

trans -DOCO signals. The broad bandwidth of the comb covers 6 OD, ~200 D2 O,

trans -DOCO transitions. These spectra were normalized to a spectrum acquired directly

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

73

preceding the photolysis pulse and were tted to determine time-dependent concentrations. With
this approach, we captured the time-dependent kinetics of trans-DOCO, OD, and D2 O from OD-1+ CO within a spectral window of 2660 to 2710 cm
delay times are shown in Fig. 5.3.

The OD and. Representative snapshots at three dierent

trans -DOCO data were compared to simulated

spectra, generated with PGopher [49] using measured molecular constants[95, 132, 162] and known
or computed intensities. The simulated spectra are tted to these experimental data at each timedelay to map out the full time trace of the three observed species, as shown in Fig. 5.4A-B, witherror bars derived directly from the t residual. See (SM, 5.2.2) for details of data analysis.
We determined the eective bimolecular rate coecient for the trans-DOCO channel, k1a ([M ], T )from simultaneous measurements of both time-dependenttrans -DOCO and OD. In the low pressure

regime studied here, the DOCO formation rate obeys a termolecular rate law, while the eective
bimolecular coecient for the D + CO2 channel remains close to the zero pressure value, k1a ([M ] =0). We measured the dependence of the eective bimolecular rate constant on the concentrationsof all of the major species (N2 , CO, D2 , and O3 ) present in the experiment.
We analyzed the early-time (t <200 μs) rise oftrans -DOCO in order to decouple the measurementof k1a from secondary loss channels at longer times. The expected time dependence of the DOCO
concentration is given by eq. 5.2.

d[DOCO]= k1a [CO][OD](t) − kloss [X][DOCO](t) .
dt

(5.2)

kloss describes a general DOCO decay through a reaction with species X, and [OD](t) refers to
the time-dependent concentration of OD in the ground vibrational state. The solution to eq. 5.2
is a convolution of the DOCO loss term with [OD](t), given by the integral in eq. 5.3. [CO] is inlarge excess and remains constant throughout the reaction.

Z t[DOCO](t) = k1a [CO]e−(kloss [x])(t−u) [OD](u)du .

(5.3)

0
The eective bimolecular rate coecient k1a can be reduced into two terms dependent on N2 andCHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.3:

Experimental spectra (black) were recorded with an integration time of 50

74

μs andosets of 50 (before photolysis), 100, and 4000 μs from the photolysis pulse. These spectra weretrans -DOCO (orange) to
determine their temporal concentration proles. The P, Q, and R branches of trans -DOCO arethen tted to the known line positions of OD (blue), D2 O (green), andindicated above the 100-μs experimental trace.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

75

Figure 5.4: (a) An analytical functional form for [OD](t) was obtained by tting the data (black
circles) to a sum of boxcar-averaged exponential functions (red line). At each time, the data point
represents ~300 averaged spectra, and the error bars are from statistical uncertainties in the spectral
t. (b) The bimoleculartrans -DOCO rise rate was obtained by tting the data (black circles) to

Ö

Ö

Ö

Eq. 5.3 (red line). The data in (a) and (b) were obtained at a 10-μs camera integration time andÖ

precursor concentrations of [CO] = 5.9
15

10

=3 .
molecules cm

1710, [N2 ] = 8.9

1710, [D2 ] = 7.4

16

10, and [O3 ] = 1

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

76

CO concentrations(CO)

k1a = k1a(CO)where k1a(N 2)

and k1a(N 2)[CO] + k1a [N2 ] ,(5.4)

are the termolecular rate coecient dependence on CO and N2 , respectively.

By simultaneously tting [DOCO](t) and [OD](t) as a function of [CO] and [N2 ], we uniquelydetermined all of the k1a termolecular coecients.

Figure 5.3B shows an early-time segment ofour data at 10 μs camera integration for both [trans-DOCO](t) and [OD](t). To t the nonlinear
time-dependence of [OD](t), we used derived analytical functions composed of the sum of boxcaraveraged exponential rise and fall functions (SM, 5.2.3). Equation 5.3 gives the functional form

trans -DOCO](t), which includes the integrated [OD](t) over the tted time window offor tting [-25 to 160 μs. The tted parameters are k1a and atrans -DOCO loss rate, rloss,exp (≡ kloss [X]).

For our rst set of data, we varied the CO concentration. At each set of conditions, we acquired
data at both 10 and 50 μs camera integration time. By plotting k1a versus [CO] for both 10 μs and50 μs, we did not observe any systematic dependence on camera integration time. Moreover, weobserved a clear linear dependence (with reduced chi-squared, ), indicating a strong termolecular(CO)dependence of k1a on CO, or k1a(Fig.

termolecular dependence of k1a , or k1a(N2)5.5A). The oset in the linear t comes from the N2. We then varied N2 concentration and observed a similarlinear dependence of k1a from eq. 5.4. A 50 μs camera integration time was used for this second
data set due to lower

trans -DOCO signals at higher N2 concentrations. The results are shown in

Fig. 5.5B. Because both the oset terms from the linear t to the CO data and the linear t to
the N2 plot correspond to k1a (N2 ), we performed a multidimensional linear regression to eq. 5.4 todetermine k1a (CO), k1a (N2 ), and rloss simultaneously. Because rloss,exp describes

trans -DOCO loss,

it is expected to be invariant to [CO] and [N2 ]. Therefore, rloss,exp serves as a shared, tted constantin the global t across the CO and N2 data sets. From the ts shown in red in Fig. 5.5A-B, we(N 2)obtained k1a

± Ö

(4.0
5.4.

0.4)

4

10

=
s

-1

Ö

-33

10

cm

6

molecules

-2

s

-1

(CO)

, k1a

=

Ö

-32

10

cm

6

molecules

-2

s

-1

and rloss,exp =. The statistical and systematic errors in these parameters are collected in Table

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.5: Determination of the termolecular77

trans -DOCO formation rate. The bimolecular trans -DOCO formation rate coecient, k1a , is plotted as a function of [CO] and [N2 ] to determine thetermolecular rate coecients Embedded Image and Embedded Image. Each point represents oneof 26 experimental conditions tabulated in table 5.1.

ÖÖ
ÖIn both panels, the error bars represent

uncertainties from ts to Eqs. 5.2 to 5.4 and the measured densities of the gases. (A) k1a is plotted
as a function of [CO] while [N2 ] = 8.9

as a function of [N2 ] while [CO] = 5.6
and O3 concentrations are xed at 7.4

17

10

17

=3 is held constant. (B) k1a is plottedmolecules cm

Ö

-3

10

molecules cm

16

15

10

and 1

10

is held constant. In both plots, D2-3molecules cm, respectively. Blue and red

data points indicate 50- and 10-μs camera integration times, respectively. The data in (A) and (B)are simultaneously tted to Eq. 5.4. The black lines in (A) and (B) are obtained from weighted
linear ts. The y osets in the data arise from the nonzero concentrations of N2 and CO in (A) and(B), respectively.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS78

To verify the reaction kinetics, we constructed a rate equation model of the OD + CO chemistry,
which included the decay channels from secondary chemistry, in order to t the trans-DOCO andOD time traces up to 1 ms (5.2.4).

We t one overall scaling factor for both OD and trans-

DOCO, which accounts for uncertainties in (i) the optical path length and (ii) photolysis yield and*subsequent OD

quenching reactions that establish the initial steady-state concentration of OD. We

also t an additionaltrans -DOCO loss, rloss,model , in order to correctly capture the trans -DOCO

concentration at t >100 μs.
TheÖtrans -DOCO + O3 OD + CO2 + O2 rate coecient (9) (kO3 +DOCO ≈ 4 10-11 cm3-1moleculess-1) and the OD + CO termolecular rate coecients from our experimentally mea-

sured values were xed in the model.

Representative ts for two dierent conditions using thesame rate equation model are shown in Fig.

2

5.6A-B. We found good ts (χred≈ 0.71) with asingle, consistent set of parameters over a wide range of CO, N2 , and O3 concentrations, giving± Ö

rloss,model = (4.7

0.7)

3

10

-1

s

for all conditions (Fig. 5.19A). The sum of loss contributions fromÖ

kO3 +DOCO[O3 ] and an additional loss from rloss,model gives a total loss of ~4.5

4

10

-1

s

, consistent

with our measured rloss,exp. One possibility for rloss,model is a second product branching channeloftrans -DOCO + O3 to produce DO2 + CO2 + O. The slight discrepancy of the trans-DOCO

data with the rate equation model in Fig. 5.6B is possibly due to the inadequately constrained loss
processes at long delay times.
Sources of systematic uncertainty have been carefully evaluated. First, we considered the impactof vibrationally hot OD at early times. We constrained the population of vibrationally excited OD
in our system by directly observing several hot band transitions from OD(v=1) (Fig. 5.13). We
observed that CO is an ecient quencher of OD vibration, with a measured OD(v=1) lifetime(Fig. 5.14) consistent with the OD(v=1) + CO quenching rate reported by Brunning et al. [150]and Kohno et al. [158]. These measurements reveal that the lifetime is well below the minimum
integration time of 10 μs and the total population of [OD(v=1)] is less than 10% of [OD(v=0)] in
this time window. As OD(v=1) is expected to produce stabilized

trans -DOCO less eciently thanOD(v=0), the systematic eect caused by the vibrationally hot OD is estimated to be < 10%, which

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

79

has been included in our total error budget (Table 5.4).
Another systematic uncertainty arises from the nite camera integration time, which is large(50 μs) or comparable (10 μs) to the early trans-DOCO rise time. The recovered k1a values fromthe two integration times are consistent with each other to within 21%, which we have included asa systematic uncertainty in our measurement (Fig. 5.12).
A third source of systematic uncertainty comes from any factors that would cause deviations
from eq.

5.2; specically, we investigated the dependence of k1a on D2 and O3 concentrations.

Additional experiments were conducted in the same manner as the CO and N2 experiments butÖvarying [O3 ] (1

14

10

Ö

 4

15

10

-3

molecules cm

Ö) and [D2 ] (7

16

10

Ö

 1

18

10

-3

molecules cm).

At

our experimental conditions and using a 50 μs camera integration window, we observed a weak
dependence of k1a on [O3 ] (Fig. 5.17) and no statistically signicant variation with [D2 ] (Fig. 5.16).

Ö

The O3 dependence was measured at a CO concentration of 1.5of the early-time

17

10

molecules cm-3. From analysis

trans -DOCO rise as a function of [O3 ] and [D2 ], we determined that O3 and D2

contribute additional 11% and 8% statistical uncertainty, respectively, to our total budget (Table
5.4).
We nd that CO is approximately 100% more eective as a collision partner than N2 in promoting
the termolecular association of trans-DOCO. This result was missed in previous studies, which
minimized the CO concentration (<4

Ö

16

10

-3

molecules cm) to avoid biasing a pseudo-rst orderkinetics measurement[121]. One might naively expect CO to be similar to N2 as a third body; thesignicant dierence observed here could be due to (i) near-resonant energy transfer between CO*

and the CO mode in DOCO, (ii) a stronger interaction potential between CO and DOCO , or (iii)
the inuence of more ecient CO on OD(v) quenching which we have not correctly accounted for.
In the low pressure regime, our measurements of the association rate, k1a , can be comparedto the pressure dependence of k1 , the overall rate of OD+CO, measured in previous experiments
in N2 . Most of the pressure dependence of k1 comes from k1a , because k1b is expected to change
only slightly in this range. From earlier studies by Paraskevopoulos et al. [147] and Golden et al.
[119], the termolecular (linear) component of their reported k1 values fall within 1σv of our measured

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
(N 2)

k1a

, which may suggest a k1a contribution to the previously reported k1 .

80

Apparent curvaturein the pressure dependence seen elsewhere suggests that k1a may already be in the fall-o regime.
In order to estimate thetrans -DOCO branching yield (% yield ≈ k1a /(k1a + k1 (p = 0)), we took

the average value of k1 from Paraskevopoulos et al. [147], Golden et al. [119], and Westernberg etal. [163]. Even at low total pressures (75 Torr of N2 ), our results show that OD+CO produces a±trans -DOCO yield of nearly (28 11)%.
Optical frequency comb spectroscopy provides broadband, time-resolved absorption detection ofradicals with exceptional sensitivity and high spectral resolution. These results clearly demonstrate
the capabilities of time-resolved cavity-enhanced frequency comb spectroscopy to elucidate chemicalmechanisms through the quantitative detection of intermediates and primary products in real time.
Our quantication of the termolecular dependence reveals additional factors that impact the productbranching of the OH + CO reaction, which must be included in future atmospheric and combustion
model predictions. For example, sensitivity analyses by Boxe et al. [115] have shown that dependingon the branching ratio, HOCO can contribute 25 to 70% of the total CO2 concentration in theMartian atmosphere.

The current experiment can be readily extended to detect other primary

products (DO2 , CO2 ) as well as to study the OH/HOCO system.

Furthermore, dynamics andnonthermal processes such as chemical activation, energy transfer and rovibrational state-specickinetics can be studied. With the bandwidth of optical frequency comb sources spanning an octave
or more, the potential of this approach has not yet been fully realized. The technologies of frequency
comb sources, detection methods and mirror coatings are developing rapidly and will allow for more
expansive applications of this multiplexed technique to many other classes of important chemistry
problems.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.6: Rate equation model tting. The OD (blue) and81

trans -DOCO (red) traces are weighted

ts to the model (solid and dashed lines for OD and trans-DOCO, respectively) described in the
Supplementary Material. The integration time was 50 μs. The error bars are from uncertainties inthe spectral t in the same manner as for Fig. 5.3B. The input k1a values for both CO and N2 werefrom the early-timetrans -DOCO rise analysis and were xed in the t. The oated parameterstrans -DOCO intensities and an extra DOCO lossÖ

included a single scaling factor for the OD andÖÖchannel.

(A) [CO] = 5.9

17

16

8.9

10

, [D2 ] = 7.4

10

17

10

Ö

-3

molecules cm, and [O3 ] = 1

15

10

Ö

; (B) [CO] = 1.2-3

molecules cm

18

10

molecules cm-3.

[N2 ] =

were xed for both data sets.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

82

5.2 Supplementary Materials and Methods:

5.2.1 Experimental description and conditions
Scientic Apparatus

A schematic of the instrument is depicted in Fig. 5.5 and discussed ex-tensively in the main text.

Generation of OD

The ozone used to generate OD in this reaction was generated in a ow-discharge of pure O2 gas. This mixture contains approximately 8% of O3 in a buer of O2 . This
mixture was own across a silica gel trap immersed in an isopropanol/LN2 bath at -90°

C. Theozone trap was allowed to pump out for about 20 minutes after stopping the O3 /O2 ow to remove
residual O2 .

The steady state concentration of O3 in the reaction cell was measured using thedirect absorption of the collimated 270 nm light from a UV LED (UVTOP-270).

By comparing

this absorption measurement to a static total pressure measurement in the cell, it is estimated that
O3 comprises >70% of the mixture owing.
mmÖFrequency quadrupled 266 nm light (beam size: 44

7 mm, power = 32mJ/pulse) from a Spectra Physics INDI-HG-105 Nd:YAG propagating

orthogonal to the mid-IR probe beam was the photolysis beam. In this method, 15% of the O3 in1

3

the cavity was photolyzed into O( D), O( P), and O2 to start the reaction. OD was then promptly
1

formed from the O( D) + D2

1

OD + D reaction. O3 photolysis to O( D): In order to accurately

simulate the kinetics of the OD + CO chemical system, we measured the fraction of O3 photolyzed
at 266 nm. This was done by measuring the transmission of a 270 nm LED through the photolysis
region of the chemical cell before and after the photolysis of O3 in a buer of N2 . We measured aphotolysis fraction of fphot = 0.15 ± 0.02.

Experimental conditions

Table S1 shows the measurement conditions used for determining k1a .

The initial concentrations of D2 , CO, N2 , and O3 were determined by calibrated ow controllers
and a capacitance manometer asCHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.7:

83

A mid-IR frequency comb is coupled into an enhancement cavity, consisting of two

high reectivity crystalline (HRc) mirrors, where a 266 nm laser pulse photolyzes O3 to initiate
the chemistry.

The transmission from the cavity is spatially dispersed by a VIPA etalon and adiraction grating and imaged on an InSb camera. Simulated cavity absorbance images are shownfor OD (red),trans -DOCO (green), and D2 O (magenta) to illustrate the camera pixel to wavelength

mapping.

Figure 5.8: Measurement of Ozone photolysis fraction.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS[N2 ]0 = P

QN 2
QD2 + QCO + QN 2 + QO3

84


(5.5)

where P is the total pressure of the reaction cell and the QX are the ows of each gas into thereaction cell. By swapping ow controllers and pressure meters, the concentration uncertainty inthis method is estimated to be 7%.

1

The initial concentrations of O3 , O( D), and O2 just after

photolysis by the YAG beam are given by[O3 ]0 = (1 − fphot )[O3 ]LED[O(1 D)]0 = qO(1D) fphot [O3 ]LED

(5.6)

[O(3 P )]0 = qO(3D) fphot [O3 ]LED
where qO(1D) = 0.90 and qO(3P ) = 0.10 are the quantum yields [167] of the photolysis of O3 into1

3

O( D) and O( P), respectively, fphot = 0.15±

0.02 the O3 photolysis fraction, and [O3 ]LED is thesteady-state concentration of O3 recorded by the absorption of the 270 nm UV LED.

Table 5.1: Measurement conditions used for the determination of k1a .
-3[D2 ], and [O3 ] are molecules cm.

[CO]
CO Scan

7.41
1.48
2.96
2.96
5.92
5.92
5.92
7.41
7.41

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

The units for [CO], [N2 ],

[N2 ]
16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

8.89
8.89
8.89
8.89
8.89
8.89
8.89
8.89
8.89

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

[D2 ]
16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

2.96
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

[O3 ]
16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

Int. Time (μs)

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

50
50
10
50
10
50
50
10
50

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
[CO]
8.89
9.63
9.63
1.18
1.18
1.18
1.48
N2 Scan

5.92
5.92
5.92
5.92
5.92
5.92
5.92
5.92
5.92
5.92

O3 Scan

1.48
1.48
1.48
1.48
2.96
2.96
2.96
2.96

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

[N2 ]
16

10

16

10

16

10

18

10

18

10

18

10

18

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

8.89
8.89
8.89
8.89
8.89
8.89
8.89
1.48
2.96
5.92
7.41
9.92
1.18
1.33
1.33
1.48
1.48
8.89
8.89
8.89
8.89
8.89
8.89
8.89
8.89

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

[D2 ]
16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

18

10

18

10

18

10

18

10

18

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
7.41
9.57
8.74
7.41
7.41

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

[O3 ]
16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
5.00
1.00
2.50
5.00
1.00
5.00
1.00
2.00

Int. Time (μs)

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

15

10

14

10

15

10

15

10

15

10

14

10

14

10

15

10

15

10

10
10
50
10
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50

85

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
[CO]
2.96
D2 Scan

2.96
2.96
2.96
2.96
2.96

OD(v=1) lifetime

Ö
Ö
Ö
Ö
Ö
Ö

[N2 ]
16

10

16

10

16

10

16

10

16

10

16

10

0

8.89
8.89
8.89
8.89
8.89
8.89
9.98

2.06
4.08
5.64
8.19
9.79

Ö
Ö
Ö
Ö
Ö

16

10

16

10

16

10

16

10

16

10

9.91
9.79
9.67
9.83
9.80

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

[D2 ]
16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

16

10

8.16
1.48
2.96
5.92
8.89
1.18
8.32
8.26
8.16
8.06
8.19
8.16

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

[O3 ]
16

10

16

10

16

10

16

10

16

10

18

10

16

10

16

10

16

10

16

10

16

10

16

10

5.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00

86

Int. Time (μs)

Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö
Ö

15

10

15

10

15

10

15

10

15

10

15

10

16

10

16

10

16

10

16

10

16

10

16

10

50
50
50
50
50
50
50
50
50
50
50
50

5.2.2 Data extraction & analysis
Spectral acquisition

The transmitted mid-IR light was spatially dispersed using a Virtually

Imaged Phased Array (VIPA) and detected using a FLIR SC6000 InSb camera, in the same manneras Fleisher et al.[10]. The camera integration (50 μs or 10 μs integration time) was synchronized
to the Nd:YAG photolysis pulse.

A digital delay generator sets the variable delay times fromthe photolysis pulse. Since we are not resolving individual frequency comb modes, we calibrated
our frequency axis each day to known D2 O line positions from Ref.[162].

The experiment was

conducted at a 10 Hz repetition rate, set by the maximum repetition rate of the pulsed Nd:YAG
laser. A reference image was collected directly prior to each Nd:YAG pulse and signal images
were collected at various delay times following the Nd:YAG pulse.

Since the InSb camera has adark current oset that drifts with ambient temperature, a background image was also collected
at the same repetition rate by briey blocking the camera with an optical shutter. After collecting
each set of images, the absorbance was constructed in the following manner ,CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
A = − log

S−B
R−B

87


,

(5.7)

where S, R, and B are the signal, reference, and background images, respectively. Due to slowlyvarying baseline uctuations in the transmission through the cavity, a sliding average was subtracted
from the measured absorbance as a function of wavenumber, forming a high-passed signal Ã =A − H[A], where H is the sliding average function. Following the high-pass lter operation, theerror at each point in the spectrum is estimated by taking the standard deviation of the surrounding
points.

In this manner, each collected spectrum is assigned a value and error corresponding toÃ ± δ Ã. Averaging many of these values yields an average value Ãmean ± δ Ãmean . Since this sliding
standard deviation operation includes some of the absorption peaks in the spectrum, it is a slightoverestimate of the error in the spectrum.

Spectral tting

In direct absorption spectroscopy, the concentration of a species is related tothe transmission of a probe beam through the relation

IS (ν̃)= e−nσ(ν̃)l ,IR (ν̃)(5.8)

where and are the light intensities with and without the sample, n is the molecular concentration in-3

molecules cm

2,σ(ν̃) is the molecular absorption cross section in cm , l is the path length through-1

the sample in cm, and ν̃ is wavenumber in cm. For this experiment, is recorded 4 ms before thephotolysis pulse and is recorded after the photolysis pulse by the InSb camera. If multiple species
are present, the transmission versus time is now given by

1
− log
l



IS (ν̃)IR (ν̃)= nA (t)σA (ν̃) + nB (t)σB (ν̃) + · · · ,(5.9)

where A and B are two sample molecules. If σA (ν̃), σB (ν̃) are linearly independent as a functionof wavelength, then nA (t), nB (t) are determined uniquely through linear regression. σ(ν̃) is related
to the molecular line strength S through σ(ν̃) = Sg(ν̃ − ν̃0 ) where g(ν̃ − ν̃0 ) is the area normalizedCHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

88

lineshape function. In our case, g(ν̃ − ν̃0 ) is a Gaussian function with FWHM = 900 MHz. This issignicantly larger than the molecular Doppler width, so convolution with the molecular lineshapeis neglected.
Since we high-pass the measured absorbance, A(ν̃), to reduce the eects of cavity uctuations,
it is also necessary to perform the same operation on the calculated molecular cross sections. This
will not aect the tted concentration values, since the sliding average operation H[A] is a linear
function and thus−1log (A − H[A]) = nA (t)(σA (ν̃) − H[σA (ν̃)]) + nB (t)(σB (ν̃) − H[σB (ν̃)]) + · · · ,lwhere A is the absorbance, given by A = − log

Spectral line intensities(5.10)IS (ν̃,t)IR (ν̃) .

Experimental details for obtaining line positions and line intensities

for D2 O are found in Ref. [162] and Ref. [164], respectively. Unpublished line intensities (Table 5.2)
measured by Dr. Robert A. Toth using a Fourier transform spectrometer[162] are generously provided through private communication with Dr. Keeyoon Sung of JPL. Line positions for OD(v=0,1)
were obtained from Ref. [132]. PGopher [49] was used along with t parameters from Ref. [132]to obtain relative line strengths for each line in the spectrum. The OD v=0 and v=1 transition

01

12

dipole moments |µOD | = 0.0303 and |µOD | = 0.0386 D were obtained from mass-scaling the OH

01

12transition dipole moments. The |µOH | = 0.0343 and |µOH | = 0.0408 D transition dipole moments
were calculated using the RKR potential and dipole moment functions reported by Nesbitt andcoworkers[134, 133]. The error in the transition dipole moments is estimated to be <10% for OD.

trans -DOCO ν1 ro-vibrational parameters were obtained from Ref. [95] and used to simulate thero-vibrational spectrum in PGopher. As there are no known measurements of theintensity, we assume a trans-DOCO ν1 band strength of Strans−DOCO = 65±trans -DOCO band

5 km/mol, estimatedfrom a series of anharmonic VPT2 vibrational calculations performed at the CCSD(T)/ANOn (n= 0,1,2) and CCSD(T)/cc-pCVXZ (X = D,T,Q) levels of theory (personal communication with J.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS89

F. Stanton).

-1

Table 5.2: D2 O line positions (cm) and intensities (cm molecule-1) from Toth et al.[162]. Notethat only the line positions are published, whereas the line intensities are provided through private
communication with Dr. Keeyoon Sung of JPL.

Position

Intensity

Position

Intensity

2640.2345

2.64 ×10

2640.4272

5.23 ×10

2641.2913

7.85 ×10

2641.53603

7.85 ×10

2642.3123

2.93 ×10

2642.6734

1.23 ×10

2643.143

1.38 ×10

2643.5818

3.23 ×10

2643.59308

1.27 ×10

2643.9221

1.73 ×10

2643.99044

2.82 ×10

2644.2378

8.58 ×10

2644.4066

4.29 ×10

2644.566

6.46 ×10

2644.6401

3.64 ×10

2644.7931

8.58 ×10

2645.1625

2.66 ×10

2645.335

7.64 ×10

2645.7443

4.41 ×10

2646.18699

1.9 ×10−222649.42945

4.41 ×10−222649.5656

6.13 ×10−242649.6475

2.37 ×10−242649.86673

4.86 ×10−212650.0932

1.2 ×10−212650.24288

6.78 ×10−222650.52625

3.82 ×10−222650.61934

2.61 ×10−232651.0157

1.19 ×10−212652.1988

1.18 ×10−212652.7398

2.55 ×10−242652.8054

7.44 ×10−242652.8692

3.71 ×10−232654.5461

2.49 ×10−222654.5589

2.66 ×10−242655.2742

1.56 ×10−242655.299

1.01 ×10−222655.7285

1.25 ×10−222655.8308

7.93 ×10

2655.928

4.41 ×10−21

Position

Intensity−21

2658.5228

3.42 ×10−232659.1482

1.12 ×10−232659.9311

1.12 ×10−212660.1669

1.86 ×10

2660.57108

4.45 ×10−212660.7399

3.8 ×10−232661.1383

1.88 ×10−212661.1527

3.81 ×10−232661.3546

3.61 ×10−212661.55001

4.41 ×10−232661.7319

1.36 ×10−222663.6125

2.79 ×10−222663.6323

5.43 ×10−212663.91535

3.88 ×10−212664.1152

1.13 ×10−222664.25555

3.61 ×10−222664.4722

1.83 ×10−212664.9705

4.49 ×10−232664.98852

9.44 ×10−232665.9744

5.8 ×10

−21

−22
−20
−23
−23
−23

−21
−23
−23
−23
−21
−22
−21
−21
−21
−21
−21
−23
−22
−22

−23

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Position

Intensity

Position

Intensity

2646.68677

2.39 ×10−212657.027

1.13 ×10

2646.723

3.85 ×10−212657.1548

5.48 ×10

2647.0682

2.12 ×10−212657.4666

3.44 ×10

2647.205

1.57 ×10−212657.52565

8.09 ×10

2647.34975

4.17 ×10−212657.7129

3.81 ×10

2647.3844

1.63 ×10−232657.848

4.37 ×10

2648.28

6.95 ×10−212658.12175

3.91 ×10

2649.043

1.01 ×10−222658.20235

3.58 ×10

2649.061

7.03 ×10−242658.2584

1.99 ×10

2649.0898

1.5 ×102658.3467

2.37 ×10

2670.8972

7.68 ×10−232682.7988

3.24 ×10

2670.9733

1.57 ×10−222683.0851

6.7 ×102671.5212

5.43 ×10−232684.0578

1.64 ×10

2671.5883

4.07 ×10−222684.16277

9.19 ×10

2671.6725

2.78 ×10−232684.4509

3.24 ×10

2671.7708

2.28 ×10−232684.5865

4.29 ×10

2671.91013

1.38 ×10−232685.00147

2.82 ×10

2672.1342

1.73 ×10−232685.2205

1.56 ×10

2672.3234

1.27 ×10−202685.4227

3.61 ×10

2672.4246

1.25 ×10−222685.7946

7.56 ×10

2672.57006

2.55 ×10−232686.09833

5.31 ×10

2672.71

1.18 ×10−222686.79348

1.35 ×10

2672.7446

1.92 ×10−222686.986

7.48 ×10

2672.771

7.36 ×10−232688.01359

7.97 ×10

2672.81345

3.01 ×10−232688.5288

3.08 ×10−23

90

Position

Intensity−23

2666.5308

1.35 ×10−24

2666.99383

7.97 ×10−232667.1147

7.27 ×10−212667.2057

2.58 ×10−212668.64249

6.78 ×10−232668.91278

1.14 ×10−222669.2846

1.28 ×10−212669.5047

4.45 ×10−222670.13472

5.56 ×10−232670.54029

5.11 ×10−212693.6488

1.25 ×10

2694.1202

2.49 ×10−222694.23385

4.01 ×10−212695.3701

1.53 ×10−212695.516

1.57 ×10−232695.9146

2.17 ×10−232696.25256

2.14 ×10−232696.4641

7.48 ×10−232696.8033

1.57 ×10−232697.27755

1.75 ×10−232697.3128

1.54 ×10−212697.6058

1.5 ×10−232697.7648

1.12 ×10−232697.81728

2.3 ×10−212698.6272

3.69 ×10

−23

−22
−21
−23
−21
−21
−20
−23
−22
−21
−23
−21
−22
−23
−21
−22
−21
−20
−23
−24
−21
−22

−22
−23

−23
−22

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Position

Intensity

Position

Intensity

2674.1562

3 ×102688.55586

5.97 ×10

2674.2478

8.74 ×10−232688.7263

2.68 ×10

2675.0847

8.99 ×10−232688.82239

7.64 ×10

2675.359

1.17 ×10−222689.0089

1.49 ×10

2676.21568

5.27 ×10−212689.3199

2.47 ×10

2676.3165

2.67 ×10−212689.4355

2.21 ×10

2676.47655

4.7 ×102689.90787

2.63 ×10

2676.6666

1.25 ×10−212690.1185

4.82 ×10

2676.999

1.44 ×10−222690.4366

1.1 ×102677.5985

1.75 ×10−202690.8628

1.52 ×10

2678.22986

1.03 ×10−202691.1606

1.36 ×10

2679.5902

5.07 ×10−212691.46408

8.74 ×10

2679.8475

6.5 ×102691.6066

1.98 ×10

2679.9658

1.81 ×10−222691.69857

6.46 ×102680.3429

2.01 ×10−202691.7401

1.21 ×102680.55718

9.19 ×10−212691.91439

1.09 ×102680.60718

1.88 ×10−202691.993

2.27 ×102680.83526

1.75 ×10−202692.10628

1.37 ×102680.8799

3.58 ×10−232692.26094

1.29 ×10

2681.1146

1.48 ×10−232692.49856

1.79 ×10

2681.8938

1.32 ×10−212692.7442

4.25 ×10

2682.04028

7.23 ×10−232692.7624

1.53 ×10

2682.44429

3.66 ×10−232693.22996

2.42 ×10

2704.8754

7.52 ×10−222717.55131

1.06 ×10

2705.52613

4.99 ×10−212718.0281

8.09 ×10

−24

−23

−23

91

Position

Intensity−21

2699.0851

1.26 ×10−232699.09974

9.4 ×10−212699.39049

4.29 ×10−212700.0094

2.73 ×10−222700.0249

2.38 ×10−242700.1138

8.54 ×10−202700.1409

6.95 ×10−222700.4127

1.79 ×10

2700.4855.8 ×10−242700.62468

7.97 ×10−202700.8671

7.44 ×10−232701.0039

1.29 ×10−212701.1606

5.6 ×10−23−212701.24658

3.5 ×10−20−202701.4495

8.54 ×10−202702.01668

1.88 ×10−222702.447

1.51 ×10−242702.635

2.64 ×10−202702.6618

5.48 ×10−202702.76315

1.14 ×10−232702.79603

3.43 ×10−202703.0353

1.25 ×10−242703.1091

5.48 ×10

−22

−20
−24

−21

−22
−23
−23
−22
−22
−22
−20

−22
−21
−22
−21

−23
−20
−22
−22
−23
−22
−20
−21
−23

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Position

Intensity

Position

Intensity

2705.86502

3.45 ×10

2706.17996

2.62 ×10

2706.86418

6.13 ×10−202718.3284

3.37 ×10−202719.52848

2.19 ×10

2707.1581

4.66 ×10

2708.56546

1.31 ×10

2708.6163

8.05 ×10

2709.2377

3.24 ×10

2709.312

3.72 ×10

2710.24857

6.5 ×102710.57106

3.32 ×10

2710.7739

9.85 ×10

2711.0795

5.43 ×10

2711.21661

4.29 ×10

2712.35984

2.37 ×10

2712.45137

4.41 ×10

2712.5763

8.99 ×10

2713.3275

3.79 ×10

2713.37758

8.17 ×10

2713.48368

1.27 ×10

2713.6902

1.89 ×10

2713.7529

3.19 ×102714.0415

1.99 ×102714.63906

1.12 ×102715.016

9.52 ×102715.6114

5.23 ×10

−22
−22
−20
−22
−21
−22

−22
−21
−22
−22
−20
−20
−20
−22
−23
−23
−22
−23
−22
−20
−22
−22
−22

Position−22−20

Intensity92CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Position

Intensity

Position

2715.8032

5.19 ×102715.835

2.41 ×102715.9995

1.03 ×102716.4458

4.33 ×102716.8877

1.73 ×10

2717.26396

4.29 ×10

Intensity

Position

93

Intensity

−22
−22
−21
−22
−21
−23

Photolysis Path Length and Finesse

In cavity-enhanced spectroscopy, the path length l isgiven by the physical path length multiplied by a factor of F , where F is the nesse of the opticalcavity and 1 ≤ β ≤ 2 is a parameter that arises when a sweep-lock is used[66]. In addition, the path
length is reduced to the width of the photolysis beam, lphot. Thus, the eective optical absorption
path length is given by

lef f =

βF lphot.
π(5.11)

The cavity nesse F as a function of wavelength was measured using cavity ringdown (Fig. 5.9).
The photolysis path length, lphot , was determined in two ways: (1) The width (46±5 mm) of theburn spot on a photographic lm from YAG beam, and (2) a razor blade scan across the beam andtting the OD concentration at each point of the scan (Fig. 5.10). The razor blade method gave abeam width of 42±

4 mm, which is in agreement with the photographic lm method. The weighted

average of these two methods is 44±

3 mm. The error in the eective path length is given assδlef f = lef f±which yields lef f = 58

δβ
β

2


+

δF
F

2


+

4 m at the nesse peak of 3725 nm.

δlphotlphot

2,(5.12)

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.9: Finesse from spectrally resolved cavity-ringdown measurements.

Figure 5.10: Knife edge scan of YAG beam.

94

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Flow cell gas residence time95

To ensure that fresh gas is introduced into the kinetics cell prior

to each photolysis pulse, we measured the residence time by monitoring the D2 O stable productat our ow conditions. Fig. 5.11A shows the D2 O temporal prole at a few CO concentrations,along with a semi-empirical t for estimating the gas half-life in our ow cell.

[D2 O](t) was t−b1 t − (1 − α)e−b2 t )e−bf all t2 , where the rise of D O is expected to be bi-

to [D2 O](t) = A(1 − αe2exponential and the fall is expected to be determined by the spatial prole of the YAG beam aswell as diusion dynamics. We determine the half-life of the cell by setting the fall function to 50%,
which yields τ1/2 =

q

ln(2)
bf all . This parameter is plotted as a function of [CO] in Fig. 5.11B. Since we

do not see a systematic variation of the pump out time with [CO], we use the mean, 20.1±

0.5 ms,as an estimate of the gas half-life for all conditions. Inserting this back into the pump out function,
we estimate that <1% of residual gas remains between photolysis pulses, separated by 100 ms.

5.2.3 Sources of error
Spectral interference from D2 O

In performing a linear spectral t to OD, D2 O, andDOCO, it is possible that absorption from one species may interfere with another.

trans -

This cross-contamination eect can be exacerbated if the lineshape of the t does not exactly match theexperiment.

The largest cross-contamination eect in our experiment is between OD and D2 O,

since half of the OD lines in our spectral window are contaminated by strong D2 O transitions.
However, this is nearly negligible in the rst 100 μs, where D2 O concentrations are low. Based on
a comparison of contaminated and uncontaminated OD absorption features, we estimate that thesystematic error due to cross-contamination is <1%.

Initial Rate Method

At early times, we expect DOCO to behave according to the rst-orderdierential equation[DOCO](t) = k1a [CO][OD](t) − kloss [X](5.13)

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

96

Figure 5.11: (A) Experimental [D2 O](t) (grey dots) for a few CO concentrations, along with temporal ts (red lines), which yield its half-life in the kinetics cell (blue circles). (B) D2 O half-life isplotted as a function of [CO] (blue circles). The mean of these values is indicated by a red dashedline.

where [X] is the primary loss partner for DOCO and [OD](t) refers to the time-dependent concentration of OD in the ground vibrational state, OD(v=0). With the initial condition that [DOCO(t=0)]= 0, we can solve this equation directly for [DOCO](t) in terms of [OD](t), which yields

Z t[DOCO](t) = k1a [CO]e−(kloss [X])(t−u) [OD](u)du .

(5.14)

0
To obtain an analytic form for [OD](t), we t a sum of exponentials to our experimental data,
constrained by [OD](t=0) = 0.

[OD](t) = a1 e−b1 t + a2 e−b2 t − (a1 + a2 )e−b3 t(5.15)

Here, b1 and b2 are bi-exponential decay terms while b3 is a rise term. The b3 rise term for OD(v=0)
is directly related to the decay of OD(v=1) where it originates. OD(v=1) decay will be discussed
in more detail in the following sections. Using this expression for OD(t), DOCO(t) is given by
e−b1 t − e−rloss te−b2 t − e−rloss te−b3 t − e−rloss t[DOCO](t) = k1a [CO] a1+ a2− (a1 + a2 )(5.16)
b1 − rlossb2 − rlossb3 − rloss

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
DOCO(t) contains two free parameters in this expression, k1a , and rloss ( ≡ kloss [X]).
rloss,exp = (4.0

± Ö
0.4)

4

10

s

-1

97

We t ato all data with constant [O3 ], while our t value of k1a varies with

N2 and CO. From our t values of the bimolecular rate constant k1a, we determine the termolecular(CO)

rates k1a(N 2)

and k1afrom a multidimensional linear regression to the expression(CO)

k1a = k1a

(CO)

The statistical error in our values of k1a(N 2)[CO] + k1a [N2 ] .
(N 2)

and k1a(5.17)

are established from the variation in thet residuals. Uncertainty in the Initial Rate Method: To investigate the variation in our tted k1avalues with integration time, we divided our values for k1a (see main text) for 50 and 10 μs andplotted these values as a function of CO concentration. We display this value, r =k1a,10µs
k1a,50µs , with CO

in Fig. 5.12.
In order to estimate a general systematic error in a given data set, we calculate the weighted
mean and standard deviation of this data, which are and , respectively. We interpret as a systematic
shift due to our 50 μs integration time and as an estimate of the statistical variation of k1a withrespect to integration time and [CO].

Eect of OD Vibrational Excitation

Since vibrationally hot OD(v>0) was generated under

our experimental conditions, we investigated the eect of vibrational quenching of hot OD under1

conditions relevant for tting the OD + CO DOCO rate. First, O( D) + D2 OD + D promptly
produces excited OD up to the 4th vibrational state[165]. The second reaction, D + O3 →OD +O2 , continually generates hot OD up to the 9th vibrational state[166]. Due to the broad bandwidthand high sensitivity of our kinetics apparatus, we were simultaneously able to detect OD(v=0) andOD(v=1) in a time-resolved manner during each experimental run.

Fig.

5.13 show an acquired

spectrum containing both strong OD(v=0) (blue) and OD(v=1) (red) transitions.
To constrain the extent to which OD(v>0) introduces error into our overall determination of

k1a , we conducted experiments to measure both the density and lifetime of OD(v=1) over a rangeof CO densities. Experiments were conducted with [O3 ] = 1

Ö

16

10

molecules cm-3, which provided

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.12: The ratio of retrieved k1a values for 50 μs and 10 μs integration times.

Figure 5.13: Representative spectrum of OD(v=0) and OD(v=1) for measuring [OD(v>0)].

98

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICSan upper limit for the vibrationally excited OD population. [CO] ranged from 0-9
-3

cm

Ö

16

10

99

molecules, which is well below the lowest [CO] used in our k1a measurement. We observed high signal-

to-noise ratio OD(v=1) transitions, but not any OD(v>1), indicating that either 1) the densities
are too low and/or 2) the lifetimes are too short for higher exited states.

The results from thisexperiment are shown in Fig 5.14. At our operating conditions for determining k1a , the lifetime of
OD(v=1) is <5 μs. The measured densities for OD(v=1) are also <10% of OD(v=0). Therefore,
even if OD(v>0) forms ground statetrans -DOCO at the same rate as OD(v=0), this would only

introduce a <10% uncertainty in our measurement, which has been included in our systematic error
budget (Table 5.4).
OD(v=1) loss is due, at least in part, to quenching to ground state OD(v=0). The equation for[OD(v=0)](t), given by eq. 5.15, is used to t [OD](t) as a function of [CO]. In eq. 5.15, the tted
parameter b3 , which describes the rise rate of OD, is plotted as a function of [CO] in Fig. 5.15. The
tted slope yields a rise rate constant for OD(v=0) of (3.8

± Ö
±
0.5)

is slightly larger than our measured OD(v=1)+CO loss rate, (3.3This is expected since OD(v=2)

Eect of D2
-3

3

cm

Ö

0.2)

-1

molecule

-13

10

3

cm

OD(v=1) quenching competes with OD(v=1)



-1

s

, which-1

molecule-1s.

OD(v=0) loss.

In order to determine the systematic eects of large [D2 ], we varied [D2 ] under con-Ö

stant [N2 ]=8.9
cm



-13

10

17

10

-3

molecules cm, [CO] =3.0

Ö

17

10

-3

molecules cm

Ö, and [O3 ]=1.01510molecules. The results, shown in Fig. 5.16, show no statistically signicant variation with [D2 ]. While

there are no literature estimates of the DOCO

*



+ D2

DOCO + D2 quenching eciency, we might

expect this rate to be slower than the N2 rate by about a factor of 2, given similar comparisons intoluene[167]. In this case, we would expect the termolecular rate k1a to change by about 0.5
3

cm

-1

moleculess-1with a 1

Ö

18

10

tainty in Fig. 5.16 is about 0.6

Ö-3molecules cm
31014 cmÖ

14

10

variation in [D2 ]. The magnitude of the uncer-1

molecules-1s, and hence a termolecular D2 eect, if itexists, is masked by the noise. Ideally, k1a is determined in the limit of [D2 ]

0. To determine theshift associated with nonzero D2 , we performed a linear t to this data, resulting in a slope of (1.3

±

0.8)

Ö

10-33 cm6 molecules-2 s-1 and an oset of (1.44

±

0.06)

Ö

-14

10

3

cm

-1

molecules

s

-1

. At

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

± Ö

100

Figure 5.14: First order decay rate of OD(v=1) as a function of [CO]. The tted rate constant for
OD(v=1) loss is (3.3± ÖFigure 5.15:
(3.8

0.5)

0.2)

-13

3

10

cm

molecules

-1

-1

s

.

OD(v=0) rise as a function of [CO]. The tted rate constant for OD(v=0) rise is
-13

10

3

cm

-1

molecule-1s.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICSÖ

our typical operating concentration of [D2 ] = 7.4
shift of (0.7

±

16

10

molecules cm

-3

101

, this results in a systematic0.4)%. However, this analysis assumes that k1a is linear with D2 . As a much moreconservative estimate of our systematic error, we use the mean-normalized standard deviation, , ofthe data in Fig. 5.16 as the fractional statistical error due to nonzero [D2 ].

Eect of O3(N 2)

and k1a
-3

cm

(CO)

In order to determine the systematic eects of [O3 ] in our measurement of k1aÖ, we varied [O3 ] under constant [N2 ]=8.9, and [D2 ]= 7.4

Ö

16

10

molecules cm

-3

.

17

10

-3

molecules cmÖ± ÖWith xed [O3 ]=1

experimental data is consistent with a constant rloss,exp = (4.015Ö, [CO]=1.510molecules cm

0.4)

10

4

-1

s

17

10

-3

molecules, we nd our, independent of [N2 ],[D2 ], and [CO]. In the case of varying [O3 ], however, we nd that a constant rloss,exp term resultsin poor ts and also an observed systematic variation of k1a with [O3 ].
assumption that rloss,exp scales with [O3 ], i.e.
-1molecules-1s

We therefore make therloss,exp = kO3 [O3 ], where kO3 = 4.0

Ö

-11

10

3

cm

is xed by the results of the constant [O3 ] data. The retrieved values of k1a vs [O3 ],shown in Fig. 5.17, display a weak dependence of k1a on [O3 ]. The weighted mean and standard
deviation of this data are and , respectively. Ideally, k1a is determined in the limit of [O3 ]

0.

Since we do not see a systematic variation of our retrieved k1a value with [O3 ], we interpret as a
maximum statistical error due to nonzero [O3 ].

5.2.4 Rate Equation Model
A full rate equation model that includes all of the most relevant rates for the reaction of OD + CO
is given in Table 5.3. The system of sti dierential equations was integrated using the SimBiology
software package from MathWorks and also by the Kintecus software package[168], both of whichwere in strong agreement.

As the experimental data were integrated over 50 or 10 μs, we also

boxcar-averaged the results from the rate equation model to t to experimental data.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.16: Variation of k1a with D2 concentration.

Figure 5.17: Variation of k1a with O3 concentration.

102

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

Figure 5.18:

Basic schematic of the rate equation model used in the present studies.

103

Absolutetrans -DOCO, OD(v=0), OD(v=1), and D2 O)

time-dependent concentrations of the red molecules (are measured through cavity-enhanced absorption spectroscopy, while the concentrations of the
precursors (purple) are xed by controlling the ows of N2 , CO, and D2 and measuring the UV
absorption of O3 , respectively.
green.

The two relevant OD + CO branching reactions are indicated in

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

104

6

Table 5.3: Rates used for modelling the OD + CO reaction. Units for termolecular rates are cm-2-1

moleculess3and cm-1

molecules

Reaction-1s

300 and k 300 , respectively.
∞

for k0

Rate
3

(cm
1

O( D) + N2








-1

-1

molecule

± Ö
± Ö
± Ö
± Ö
± Ö
± Ö
± Ö
± Ö
± Ö
± Ö
± Ö
± Ö

s

(3.1

0.3)

10

O + CO

(5.8

1.2)

10

O + O2(3.95

O2 + O2

(1.2

0.2)

10

O2 + O + O

(1.2

0.2)

10

OD + D

(1.1

0.1)

10

DO2 + O2

(7.3

1.1)

10

D2 O + D

(1.65

0.13)

10

OD + OD

D2 O + O

(4.34

0.63)

10

OD + DO2

D2 O + O2(3.8

OD + D2 O2

D2 O + DO2

(5.91

1

O( D) + CO
1

O( D) + O2
1

O( D) + O3
1

O( D) + O3
1

O( D) + D2
OD + O3
OD + D2

OD + CO








D + CO2(5.6

SDOCO Ref(s)

(%)

(%)

DM

63

58

[6, 169]

DM

12

11

[170]

DM

0

0

[6, 171]

DM

0

0

[6]

DM

0

0

[6]

DM

75

69

[172]

DMH

1

1

[6, 173]

DM

1

1

[174]

DM

0

0

[175]

DM

0

0

[176]

DM

0

0

[177]

-11

0.4)

10-11

-10
-10
-10
-14

0.9)

-15
-13

-11

10

0.42)

0.2)

DM

28

31

[149,

)

-11

O + N2

-13

10

-14

10

1

SOD

Source147, 163,
178]
OD + CO + N2
N2

DOCO +

± Ö

(9.1

3.6)

-33

10

(this
work)

OD + CO + CO



DOCO

± Ö

(2.0

0.8)

-32

10

(this

+ CO
OD + OD

work)

D 2 O2

Termolecular:

Ö
= Ö

-31

k0300 =6.9

10

k0300

10

2.6

-11

DMH

0

0

[6]

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Reaction

Rate
3

(cm








-1

molecule

±
±
±
±
±

Ö
Ö
Ö
Ö
Ö

-1

s

SDOCO Ref(s)

(%)

(%)

DMH

7

8

[6]

DMH

33

45

[6]

DMH

0

0

[6]

DMH

0

0

[6]

)

-11

O + OD

O2 + D

(3.3

0.5)

10

D + O3

OD + O2

(2.9

0.3)

10

-11
-11

1

SOD

SourceD + DO2

OD + OD

(7.2

1.4)

10

D + DO2

O + D2 O

(1.6

0.8)

10

D + DO2

D2 + O2

(6.9

2.8)

10

DMH

0

0

[6]

Termolecular:

DMH

0

0

[6]

TH

0

2

[179]

FIT

2

45

(this

D + O2

DO2

300
0

7.5

D2 O + CO

1.39

10

OD + CO2(4




DOCO + O3

-32

10

-11

10

-11

0.4)

-11

10

DOCO + D

D2 + CO2

DOCO + OD
DOCO + O

DOCO + O2






work)

Ö
Ö
Ö
± Ö
-11

9.31

10

1.03

10

OD + CO2

1.44

10

CO2 + DO2

(1.9

0.2)

D2 O + CO2

DOCO LOSS

-11
-11

-12

10

TH

1

14

[179]

TH

0

3

[180]

TH

0

8

[181]

DMH

0

3

[103]

DM

0

0

[6]

DMH

1

0

[6]

DMH

0

0

[6]

DMH

0

0

[6]

(tted for each trace)

O2 + O2

±
±
±
±

Ö
Ö
Ö
Ö

-15

(8.0

0.8)

10

-11

O + DO2

OD + O2

(5.9

0.3)

10

O + D 2 O2

OD + DO2

(1.7

0.3)

10

DO2 + O3

OD + O2 +

(1.9

0.3)

10

O2

(overall

t)

+ O2

O + O3

-12

Ö
k
= Ö
Ö
± Ö

k0300 =4.4

DOCO + D

-12

-15
-15

105

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Reaction

Rate
3

(cm
1

Source-1molecule

-1

s

1

)

106

SOD

SDOCO Ref(s)

(%)

(%)

The source of the value used in the model is indicated: (TH) indicates a theoretical value,(DMH) indicates a direct experimental measurement of the Hydrogen-substituted reaction, and(DM) indicates a direct experimental measurement. (FIT) indicates a globally tted reaction rate,± Ö

specically DOCO + O3 , which provided the best t at (4.0

0.4)

-11

10

cm

3

-1

molecule-1sfor allscans.

Notes on Specic Reaction Rates

OD + CO

D + CO2 This reaction rate was determinedfrom the weighted average of three measurements from Paraskevopoulos et al.
al. [178], and Westenberg et al. [163]. These values are k1 = (5.2

± Ö
± Ö

and (5.48

0.2)

(5.6

10

0.2)

-14

-14

10

3

cm

3

cm

-1

molecules-1

molecules

s

-1

-1

s

± Ö
0.5)

-14

10

[147], Golden et, (6.6

± Ö
0.4)

-14

10

,

, respectively. The result of the weighted average is k1 =. Sensitivity Analysis: In order to determine the sensitivity ofthe model on each of these parameters, a sensitivity analysis was done, measuring the variation of
the DOCO and OD peak concentrations with each of the rate constants. The sensitivity, SDOCO ,is dened for a given rate constant k as

SDOCO =k∂[DOCO]max,[DOCO]max∂k(5.18)

where [DOCO]max is the maximum concentration of DOCO. SOD is dened in a similar manner.
These values essentially represent the fractional uctuation of [DOCO] or [OD] with a fractionalchange in k. Values of these parameters are given in Table S3 for the conditions

Ö
Ö
Ö
Ö

15

[O3 ] = 1

10

[D2 ] = 1

10[CO] = 1

10[N2 ] = 1

10

17
17

18

-3

molecules cm-3molecules cm-3molecules cm-3molecules cm.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS
Results of rate equation model ts

107

To compare the rate equation model to the experimental

data, two parameters were tted for each [OD](t), [DOCO](t) trace: an overall scaling factor for both
OD and DOCO and a DOCO loss rate. Additionally, we found it necessary to x the DOCO+O3
rate as a constant and shared parameter for all traces, which yields a rate constant of 4
3

cm

-1

molecule

-1

s

Ö

-11

10

. The scaling factor accounts for uncertainties in both the eective optical path

length and the OD*

chemistry involved that establishes the initial OD concentration measured atsteady-state. The results of these ts as a function of CO are shown in Fig. 5.19A-B. The averaged
values for the overall scaling factor and the DOCO loss rate are 0.14±

0.05 and (4.7

± Ö
0.7)

3

10

s

-1

,

respectively. We observe a 65% correlation between the tted overall scaling factor and DOCO loss
rate.

CHAPTER 5. DIRECT MEASUREMENT OF OD+COTRANS-DOCO KINETICS

108

Figure 5.19: Results of tting the DOCO loss rate (A) and overall scaling factor (B) in the modelto the data.

5.2.5 Table of Statistical and Systematic Errors
Table 5.4: Summary of statistical and systematic errors.
Error Source
Statistical Errors(statistical, from t residual)

Experimental Control

Flow & Pressure

(CO)

(N 2)

k1a

k1a

6%

10%
7%(stat)Measurement
Molecular Parameters

Secondary Reactions

Data Analysis

OD Cross Section

10%(stat)

DOCO Cross Section

10%(stat)Eect of D2

8%(stat)Eect of O3

11%(stat)

Cross-contamination of OD-1%(sys)and D2 O
Eect of Integration Time+9%(sys),21%(stat)

OD Vibrational Excitation-10%(sys)

Total Systematic Error(-11%,+9%)

BudgetTotal Statistical Error

28%

29%

(-39%,+37%)(-40%,+38%)

BudgetTotal Error BudgetChapter 6
CO2 and cis -DOCO Channels
In the last chapter, we demonstrated the ability of TRFCS to observe the OD+COtrans

-DOCO

reaction on the microsecond timescale, where it can extract quantitative formation and decay rates
for the reactants and products. However, this reaction is still far from being solved; there are still
two main product channels, D+CO2 andcis -DOCO, that have not been observed. In this chapter,

we will report that the frequency comb is also able to provide quantitative information regarding
the branching to these channels.

6.1 The OD + CO → D + CO2 Channeltrans -DOCO, we approach the ν3 asymmetric stretch band of

Tuning to lower wavenumber from

-1

CO2 , with a band center of 2349 cm. Due to the large ambient concentration of CO2 (≈ 400 ppm),

it is necessary to strike a balance between sensitivity to CO2 generated in the kinetics cell andabsorption in the lase beam line due to ambient CO2 .

In practice, we found the best balance−1 , as shown in Fig.

at a spectrum between 2390 − 2450 cm

6.1.

As an additional benet, weare able to observe OD(v=0) lines within this spectral region, allowing us to determine CO2 andOD(v=0) concentrations simultaneously.
-1

R(76) transition at 2390.552 cm

The strongest CO2 line observed in this window is its−22 cm molecule−1 . The

with a line intensity of S = 4.140 × 10

strongest OD(v=0) line is its P1e (9.5) transition near 2433.6 cm−1 with a line intensity of S =1.64 × 10−21 cm molecule−1 . The OD line positions and strengths were obtained using the method109

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

Figure 6.1: Measured spectra (black) at 25 and 1000 μs delay from the photolysis pulse.

110

These

spectra are tted to reference OD(v=0) (magenta) and CO2 (blue) spectra to acquire the temporalprole. The decay of OD(v=0) and the rise of CO2 are apparent between 25 and 1000 μs delay.

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS
described in 4.7.

111

The CO2 line positions and strengths were obtained from the HITRAN2012

database[129].
By tting the integrated areas for both species, we obtained the time-dependent curves in Fig.
6.2. The error bars on the CO2 and OD(v=0) concentrations are determined from the t errors combined with a 7% statistical error due to our ow uncertainty. An emperical sum of box-car-convolved(100 μs integration time) exponential functions, Eq. 5.15, was t to [OD(v=0)](t), providing a functional form for the data.

The OD(v=0) decay is observed to be bi-exponential, with the initial

decay (time window ≈ 100 to 300 μs) coming from reactions with CO. The second exponential decay occurs approximately after 300 μs and OD(v=0) approaches steady-state at longer times (t>1ms). OD(v=0) regeneration reactions D+O3



OD+O2 and DOCO+O3

OD+CO2 +O2 dominate

at longer times. Only the earliest time behavior (<300 μs) captures the initial OD+CO



D+CO2

branching reaction and is used for the analysis of k1b . The time-dependent concentration for [CO2 ](t)in excess [CO] was modeled as a pseudo-unimolecular rise,d[CO2 ]
= k1b [CO][OD(v−0) ](t),
dt

(6.1)



where k1b is the eective bimolecular rate for OD+CO

D+CO2 . Contrary to DOCO, CO2 does nothave a large loss channel with O3 at early (< 1 ms) timescales. The solution to this with constant[CO] is the integral of [OD(v=0)](t),Z t[CO2 ](t) = k1b [CO][OD](u) du .

(6.2)

0
This expression was t to our experimental data for [CO2 ](t), shown in the top panel of Fig. 6.2.
These measurements were performed for CO, N2 , and He bath gases at a variety of pressures.

17 to 1.0 ×

For CO, the concentration range was limited to 3.5 × 10

18-3molecules cm . At low CO
10densities, complications arose due to incomplete vibrational quenching of OD(v>0). At high CO1

densities, the concentration of OD(v=0) was reduced due to the ecient O( D)+CO

3

O( P)+CO

quenching reaction. In this intermediate range, OD(v>0) accounts for no more than 10% of theCHAPTER 6. CO2 AND CIS-DOCO CHANNELS

112

Figure 6.2: Time-dependent concentrations of CO2 and OD(v=0), obtained by tting their timedependent spectra. (bottom) An analytical functional form for [OD](t) is obtained by tting thedata (black circles) to a sum of box-car averaged exponential rise and fall functions (red line).
(top) The rise rate of CO2 is obtained from tting the data (black squares) to Eq. 6.2 (red line).
The error bars include contributions from uncertainties in the spectral ts as well as concentration
measurements. The camera integration time was xed at 100 μs.

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS
total OD. For N2 and He, the upper limit densities of ≈ 3.5 × 10

113

18 molecules cm−3 were dictated bytechnical considerations: high molecular densities result in large mechanical vibrations which aect
cavity locking stability. The ts across these three bath gases are shown in Fig. 6.3, which showsthat k1b is roughly constant over the measured pressure ranges within its experimental uncertainty.

−14 , 6.6(8) × 10−14 , and 6.1(7) × 10−14 cm3 molecules-1

The averaged values for k1b are 5.6(7) × 10
-1s

for CO, N2 , and He, respectively.
Another possible source of systematic error could arise from the DOCO+O3



CO2 +OD+O2

reaction, which would contribute an additional source of CO2 . To provide a quantitative esitmate

15 molecules cm-3 ),for this channel, we measured k1b as a function of O3 density (2 to 4.5 × 10

2 ≈ 0.3) within theand observed no dependence (t of a at line to the data yielded a reduced χstatistical uncertainty. This is consistent with the fact that [DOCO] is much smaller than [CO2 ] bymore than an order of magnitude, so DOCO+O3 could contribute at most a 10% error. Nonetheless,
10% systematic error is accounted for in our uncertainty budget.
These results can be analyzed using unimolecular rate theory and the associated Lindemannmechanism expressions given in 4.5. In the low pressure limit, eq. 4.3, k1b ([M ] → 0) is expected to
be independent of pressure (See eq. 4.3). Any apparent curvature in the pressure dependence would
suggest deviations from the Lindemann mechanism or departure from the low-pressure limit andtransition into the fall-o region, which cannot be ruled out given the measurement uncertainties
in Fig. 6.3.

6.2 The OD + CO → cis−DOCO Channel
The nal unquantied channel of the OD+CO reaction is that ofabout

cis -DOCO. Not a lot is known

cis -DOCO or cis -HOCO, as they have not been observed in the infrared, let alone as partof the OD+CO or OH+CO reactions. However, the structures ofmeasured by McCarthycis - and trans-HOCO have been

et al. and are shown in Fig. 6.4 . Armed with theoretical band centers(see sec. 4.7), we set out to observe this key species as part of the OD+CO reaction. Since theband center was expected to be well outside of the mirrors we used for thetrans -DOCO work,

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

114

Figure 6.3: The formation rate (k1b ) of the activated products, D+CO2 , as a function of bath gases([M]=N2 (red diamond), CO (black squares), and He (blue circles)) and pressure. The error bars
include contributions from the t uncertainties as well as concentration measurements.

Figure

6.4:

Geometryoftrans- (left) and cis-HOCO (right), determined with microwave

spectroscopy[125]. The a (red) and b (green) rotational axes are indicated.

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

115

we used the same mirrors for the enhancement cavity as in the CO2 work.
spectrometer around the expected

Centering the VIPA

cis -DOCO band center of 2550 cm-1 , we observed new spectralfeatures that were present with the addition of CO and absent without. To conrm that these newspectral features belonged tocis -DOCO, 12 CO was substituted for the 13 CO isotopically substituted

version, resulting in shifted spectra, as shown in Figs. 6.5 and 6.6.
The simple shift in the spectrum only conrms that the unknown molecule contains carbon,
which is a start. The compiled observed transitions and their approximate transition frequencies
Due to Doppler broadening (∼ 300 MHz) andfor both isotopomers are compiled in Table 5.1.

instrument broadening (∼ 900 MHz), we were unable to resolve the individual rotational featuresof each Q-branch. A Watson A-reduced asymmetric top Hamiltonian was t to these transitions in
PGopher, allowing us to determine the vibrational band origin and A rotational constants for both
species. Due to the unresolved Q-branches, it was necessary to x a few parameters in the t, theground state A rotational constant of the12

C species and the B and C rotational constants for both

species, to literature values with theoretical isotopic shifts.
The isotopic shifts in these constants can then be compared to theoretical values, shown in Table
6.3. In this table, the vibrational shift is given by A12 (v = 1) − A12 (v = 0) for
for

13

12

C and similar

C. The isotopic shift is given by A13 (v = 0) − A12 (v = 0) for v=0 and similar for v=1. The

shifts in these constants can seem very esoteric, but there is a simple way of understanding them
if the molecular geometry can be assumed to remain approximately constant under the isotopic
substitution, which should be an appropriate approximation in our case, sinceheavier than

12

13

C is only slightly

C. In this case, the moment of inertia along the a axis of the molecule is given byXh1
× = IA =mi ||r¯i × nˆa ||2 ,2
2π c A

(6.3)

i

th

where mi and r¯i are the mass and position of the iatom in the molecule relative to the center ofmass and nˆa is the unit normal in the direction of the molecule's a-axis such that ||r¯i × nˆa || is theperpendicular distance from the ithatom to the a-axis. Under isotopic substitution, the dierence

between the two moments of inertia is given by

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

Figure 6.5: Zoomed

Table 6.1: Experimental spectral features for

116

cis-DOCO spectrum.

cis -DO12 CO and cis -DO13 CO and their ro-vibrational

assignments. The quantity in parenthesis denotes an estimate of the uncertainty in the line position-1(in cm) due to the FWHM linewidth of the unresolved Q-branch feature.
0

00

12

-1

13

-1

ka

ka

7

8

2489.220(0.147)*

2491.106(0.147)*

6

72496.040(0.08)

2497.718(0.08)

562502.931(0.05)

2504.295(0.05)

452509.764(0.05)



3

4

2516.524(0.05)

2517.282(0.05)

2

3





1

2





2

1

2548.102(N/A)*

2547.572(N/A)*

3

2





4

3

2562.550(0.13)

2561.517(0.13)

542568.954(0.11)

2567.638(0.11)

652575.191(0.10)

2573.687(0.10)

762581.414(0.10)

2579.658(0.10)

8

7





C Position (cm)

C Position (cm)

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

Figure 6.6:

The fullcis -DOCO spectrum.

117

The data and simulation are given by positive andcis -DO12 CO (blue), cis -DO13 CO (red), OD
12 CO and cis-DO 13 CO are shown(green), and D2 O (gray). For clarity, only the simulated cis-DO
negative absorbance, respectively. The color codes are:for comparison with experimental results in the zoomed-in bottom panels where the two strongest
Q branches are located.

Table 6.2: Summary of spectral parameters foris 0.014 cm

-1

.

12
-1

Origin (cm)

A (MHz)B (MHz)C (MHz)a

McCarthyb12c12

et al., 2016 [125]C(v=0)
0cis -DO12 CO and cis -DO13 CO. The average t error

12

13

C(v=1)

2539.909(3)0110105.52

109313(4)106124(5)

a

b

c

a

11423.441a10331.423

11422.882b10324.228c10291.999

C(v=0) value + VPT2 vibrational shifts
C(v=0) value + VPT2 isotopic shift & vibrational shift

13

C(v=1)

2539.725(4)11420.075

C(v=0) value + VPT2 isotopic shiftd12

C(v=0)

105423(5)d11419.559

d10284.951

CHAPTER 6. CO2 AND CIS-DOCO CHANNELSh×2π 2 c

1
1−
A13 A12



118= I13,A − I12,A = (m13C − m12C )||r¯i × nˆa ||2 ,where (m13C − m12C ) is the isotopic shift in mass of the carbon atom,≈ 1 amu.

(6.4)

This showsthat the dierence in the inverse A constants simply yields the squared distance of the isotopically
substituted atom from the molecular a-axis.

In our case, this is 0.42 Å for the v=0 vibrational

level. Equation 6.3 can also be used along with the measured molecular geometry of McCarthy

etal [125] to calculate an isotopic shift in A, again assuming that the geometry does not change with
deuteration.

This yields a shift of A13 (v = 0) − A12 (v = 0) = 4029 MHz, which is close to ourmeasured value.
Now that the identity of the unknown molecule has been established as cis−DOCO, the fullreaction kinetics may be studied, including all products. Fig. 6.7 shows the time-dependent concentrations of all four relevant species,

trans -DOCO, cis -DOCO, and CO2 . trans -DOCO was re-measured for this study due to new enhancement mirrors and dierent YAG focusing conditions,with an example spectrum shown in Fig. 6.8 . This data was originally analyzed using the same
method astrans -DOCO (using Eq. 5.3), but the analysis was changed when it was realized thattrans cis isomerization plays a large role in the kinetics. This was determined by looking at theratio oftrans -DOCO to cis -DOCO as a function of time on short timescales, as shown in Fig. 6.9.

The main feature to note in this plot is the exponential approach to a steady-state or equilibrium
value. This is very characteristic of a simple

trans cis isomerization model, as seen in A.3. In

Table 6.3: Comparison of experimental isotope shifts with theoretical isotope shifts forExperiment

TheoryC-793(4)-877.296C-701(7)-797.649v=0-3982(5)-3976.926v=1-3890(6)-3897.279-0.184-0.207Vibrational shift in A (MHz)1213Isotopic shift in A (MHz)Isotopic shift in band origin (cm
e
f

VPT2

variational calculation

-1

)

e

cis -DOCO.

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

Figure 6.7: The time dependence of reactant OD(v=0) (green circles), intermediates(blue squares), and119

cis -DO12 COtrans -DOCO (brown diamonds), and product CO2 (purple triangles) obtained

from tting full experimental spectra for a sequence of time windows after the initiation of thereaction.

The quantity in parenthesis is the multiplicative scaling factor for the density.

camera integration time is 20 μs for OD(v=0),

cis - and trans -DOCO, and 50 μs for CO2 .

TheCHAPTER 6. CO2 AND CIS-DOCO CHANNELS

Figure 6.8: The

120trans -DOCO spectrum (black). Simulated trans -DOCO (brown), OD (green), andD2 O (gray) are shown as inverted absorbance.

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

121

trans - and cis-DOCO are formed with concentrations [trans ]0 and [cis ]0 , such

this simplest model,that the initial ratio is given by [trans](t−0)/ [cis](t−0) −[trans]0 /[cis]0 .
tions, thecis trans

At these initial condi-trans cis and cis trans rates are unbalanced; there is a net ow of population fromtrans cis or

until the rates equilibrate, resulting in the plateau shown in Fig.

Unfortunately, this model is inadequate, since the true model must include

6.9 .

trans - and cis -DOCO

formation, isomerization, and loss rates, given by the coupled equations

ddt [trans]= k1a,trans [CO][OD](t) − (rloss,trans + rtc )[trans](t) + rct [cis](t)ddt [cis]= k1a,cis [CO][OD](t) − (rloss,cis + rct )[cis](t) + rtc [trans](t)where k1a,trans and k1a,cis are the eective bimolecular formation rates for

,

(6.5)

trans - and cis -DOCO,

rloss,trans and rloss,cis are the eective unimolecular loss rates for trans - and cis -DOCO (e.g.
rloss,trans = kO3 [O3 ] for the trans -DOCO+O3 loss process), and rtc and rct are the eective unimolecular isomerization rates for thetrans cis and cis trans processes, respectively. The formation

rates and unimolecular isomerization rates are expected to be pressure dependent while the loss
rates are expected to depend only on the concentration of the loss partner, generally O3 in our
experiments. These expressions are fairly complicated and do not permit a straightforward method
for analyzing the kinetics data, especially considering the time window convolution that must be
taken into account. To isolate formation from isomerization, the sum of the DOCO isomers may
be analyzed, [DOCOsum ] ≡ [trans−DOCO] + [cis−DOCO]. This considerably simplies the model
if we also make the assumption that the loss rates for both species are approximately equivalent,rloss ≡ rloss,trans ≈ rloss,cis . Then, the model simplies tod[DOCOsum ] = k1a,sum [CO][OD](t) − rloss [DOCOsum ](t) ,
dt

(6.6)

where k1a,sum ≡ k1a,trans + k1a,cis . The solution to this equation is a convolution of the DOCOsum
loss term with [OD](t), given by

Z ∞[DOCOsum ](t) = k1a,sum [CO]0e−rloss (t−u) [OD](u) du .

(6.7)

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

122

(a)

(b)

Figure 6.9: The ratio of [trans -DOCO] to [cis -DOCO] as a function of time for dierent CO con-

17 molecules cm-3 for blue

centrations. The CO concentrations are 5.6, 6.0, 6.4, 6.7, and 7.1 × 10

squares, red circles, black diamonds, cyan hexagons, and green triangles, respectively.

Arbitraryy-osets of -5, -2.5, 0, +2.5, and +5, respectively, are added to plot (b) for ease of viewing (plot (a)has no osets). The dashed lines are ts of the rate equation model to the data.

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

123

The eective bimolecular rate constant, k1a,sum , can then be decomposed into three terms dependent on the concentrations of the three most abundant gases in our experiment: N2 , CO, andD2 . This yields

(CO)

(N 2)

(D2)

(0)

k1a,sum = k1a,sum [CO] + k1a,sum [N2 ] + k1a,sum [D2 ] + k1a,sum ,
(CO)

(N 2)

(6.8)

(D2)

where k1a,sum , k1a,sum , and k1a,sum are the termolecular rate coecient dependence on CO, N2 , and(0)D2 , respectively. k1a,sum is an oset term that accounts for additional background species.
The k1a termolecular coecients were obtained from simultaneously tting [DOCOsum ](t) and[OD](t) as a function of [CO], [N2 ] and [D2 ]. [OD](t) were t using a derived analytical sum of
exponential components in the same manner as thetrans -DOCO analysis (see Eq. 5.15). The

functional form for [DOCOsum ](t) was also the same as in the[DOCOsum ](t) =k1a,sum [CO] a1 etrans analysis, given by−b1 t −e−rloss t

b1 −rloss

+
! ,

(6.9)

−b t −e−rloss te−b3 t −e−rloss t
a2 e b22 −r
−
(a
+
a
)
1
2
b3 −rloss
loss

where

a1 , a2 , b1 , b2 , and b3 are determined by the [OD](t) t.

mined by the t to [DOCOsum ](t) are k1a,sum and rloss .

The only parameters deter-

These ts were performed over a tem-poral range of -25 μs (which accounts for the nite response time of the camera) to 200 μs.

Si-multaneous tting of [DOCOsum (t) and [OD](t) as a function of [CO], [N2 ] and [D2 ] yields the

k1a termolecular coecients. rloss,sum was determined independently by measuring the time dependence of

cis -DOCO and trans -DOCO while varying the density of O3 , and the results areshown in Fig.

6.10.

Here, we obtained a bimolecular rate coecient for loss to O3 ,2.5(3) × 10−11 cm3 molecules−1 s−1 .

By constraining

kO3 ≈rloss,sum to the total loss rate, the tted

termolecular rate coecients of DOCOsum with respect to CO, N2 , and D2 gases are displayedin Figs.

(N 2)

6.12 and 6.11.

(D2)

We performed a multidimensional t to Eq.

(CO)

6.8 to determine k1a,sum ,(0)

k1a,sum , k1a,sum , k1a,sum , and rloss simultaneously. As rloss describes DOCO loss to O3 , it is invariant to [CO], [N2 ], and [D2 ].

Therefore, rloss serves as a shared, tted constant in the global

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

Figure 6.10: Variation of rloss with O3 concentration.

Figure 6.11: Variation of k1a,sum with D2 concentration.

124

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

125

t across the CO, N2 , and D2 data sets. The results obtained from the multidimensional t are

(CO)

(N 2)

+0.3
−33 cm6 molecules−2 s−1 , k−32 cm6 molecules−2 s−1 andk1a,sum = 8.5+4.3−5.2 × 10
1a,sum = 1.3−0.4 × 10
(D2)

−33 cm6 molecules−2 s−1 . We observed an additional oset in the eective
k1a,sum = 9.6+23−24 × 10(0)+0.7

−14 cm3 molecules−1 s−1 . 80% of the oset term,bimolecular rate constant, k1a,sum = 1.5−0.8 × 10

(0)

(D2)

k1a,sum , can be accounted for by a combination of the upper limit of k1a,sum and t errors fromcorrelations with kO3 . Discussion of all statistical and systematic error sources for k1a is found in
Table 6.4 .
The analysis up to this point has excluded the DOCO isomerization reactions. We now turnto further analyze the quantitative details of the DOCO formation mechanism in OD+CO. To
resolve the dynamical coupling of the isomer-specic formation and isomerization, we measured
the time dependence of the trans/cis ratio.
time in Fig.

trans -DOCO]/[cis -DOCO] as a function of

Plots of [6.9 reveal clear experimental evidence for a transition between two distinct time-dependent processes: the early-time DOCO formation (k1a ) and subsequent
The decay/rise behavior of thefollows. The nascenttrans /cis isomerization.

trans /cis ratio at early times can be qualitatively understood astrans /cis ratio from extrapolating back to t ≈ 0 µs (prior to any isomerization

processes) is determined only by the ratio of the formation rate coecients (k1a,trans /k1a,cis ). At

0 < t < 50 µs, the transition between the DOCO formation and isomerization is exemplied by
the exponential decay/rise of thetrans /cis ratio as a function of time. The rate of the exponential

rise/decay increases with sum of kiso,tc and kiso,ct and is an indication of how fast theTable 6.4: Summary of statistical and systematic errors fortrans to cistrans -DOCO values
(N 2)

(CO)

Error Source

k1a,trans

k1a,trans

Statistical Errors(statistical, from t residual)

15%

47%

Experimental Control

Flow & Pressure Measurement

7% (stat)

Molecular Parameters

OD Cross Section

10% (stat)

Data Analysis

trans -DOCO Cross Section
cis -DOCO Cross Section

10% (stat)
10% (stat)

Cross-contamination of OD(v=0) and D2 O

-1% (sys)

Total Systematica Error Budget(-11%,+0%)

Total Statistical Error Budget

21%

49%

Total Error Budget(-32%,+21%)(-60%,+49%)

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

126

populations approach this steady-state.

At t > 50 µs, the isomerization reaction dominates andestablishes steady-state populations oftrans and cis isomers that persists at long times. In theabsence of loss processes for DOCO, thetrans /cis ratio is equivalent to kiso,ct /kiso,tc , which is theequilibrium constant for isomerization. From this qualitative picture, the relative magnitudes of theratios of the formation rate (k1a,trans /k1a,cis ) and isomerization rate (kiso,ct /kiso,tc ) dictate whether
decay or rise behavior is observed.
To provide a more quantitative understanding of the formation and isomerization mechanism,
the time-dependenttrans /cis ratio were measured as a function of CO density.

ratios at ve representative partial pressures of CO are plotted in Fig.

6.9.

The

trans /cis

The evolution fromdecay to rise towards the steady-state value at increasing pressure is indicative of the competition
between formation and isomerization. To quantify the isomerization and formation rate coecients,
an extended rate equation model of Eq. 6.5, which includes OD formation and decay, is used tot the time-dependenttrans /cis ratios across nine dierent CO pressures used in the experiment.

The dashed lines ( ≈ 1 to 2) are results obtained from tting k1a,sum , kiso,tc , and kiso,ct to all 9
experimental data sets simultaneously. Here, k1a,sum is taken from the measured value in Fig. 6.12.

rloss is independent of CO pressure and is xed to the tted value from Eq. 6.6. The tted isomer
specic kiso and k1a are given in Figs. 6.13 and 6.14 , respectively.
The observed trend in Fig.

6.9 can now be explained by comparing the

k1a,trans /k1a,cis ratios given in the insets of Figs.

6.13 and 6.14, respectively.

kiso,ct /kiso,tc and
The transition in

17 molecules cm−1 of CO, which isbehavior from decay to rise occurs at approximately 6.5 × 10

the crossing point of the decreasing kiso,ct /kiso,tc and increasing k1a,trans /k1a,cis . However, at thelowest CO pressures, loss processes (kloss ), which are xed in the t, are not negligible relative
to k1a and kiso and may introduce additional errors to this analysis. Additional evidence for thiscomplication can be found in the observed ratio of kiso,ct /kiso,tc from the inset of Fig. 6.13. Even
though kiso,ct /kiso,tc represents the equilibrium constant at all pressures, we observed a weak dependence at low pressures within our experimental uncertainty. Because k1a , kiso , and kloss are similar
in magnitude at the lowest CO pressures, their coupling may interfere with our tted results. At

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

127

(a)

(b)

Figure 6.12: The termolecular rate coecients for DOCOtot are plotted as a function of (a) COand (b) N2 . The red dashed lines show the ts obtained from a multidimensional linear regression
procedure. Data obtained in these plots were taken at 50 μs integration time.

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

128

The tted isomerization rate coecients for cis →trans (kiso,ct , blue squares) andtrans →cis (kiso,tc , red circles). The ratio of kiso,ct /kiso,tc as a function of [CO] is given in the inset.
Figure 6.13:

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS

Figure 6.14:

129

The tted eective bimolecular formation rate coecients (k1a ) for(k1a,trans , black diamonds) andcis -DOCO (k1a,cis , green squares).

rate coecients k1a,trans /k1a,cis is given in the inset.

trans -DOCO

The ratio of the formation

CHAPTER 6. CO2 AND CIS-DOCO CHANNELS
17 molecules cm−3 ), khigher pressures ([CO] > 6.5 × 10

130

iso dominates and kiso,ct /kiso,tc converges toa constant value. We can compare this fundamental quantity to that predicted by state-of-the-art
chemical kinetics theory. Using a theoretical method that combines semi-classical transition state
theory with 2-dimensional master equations [123, 151], we predict an equilibrium ratio of ≈ 14:1, incomparison with the experimentally observed ratio of ~ 5:1. A change of ≈ 2 kJ/mol in the relative
energies ofcis - and trans -DOCO would account for this dierence in the measured and predictedequilibrium constants.
New experimental insights into the energy transfer processes are obtained from the formation ratedependence on collision partner and total pressure for bothcis - and trans -DOCO isomers. While

the pressure-dependent competition between DOCO and CO2 is well established [120, 145], DOCO
may also exhibit isomer-specic formation rate, which is now resolved for the rst time. Fitted linear(CO)

slopes to the data in Fig. 6.14 gives termolecular formation rate coecients of k1a,trans = 1.4(4) ×(CO)

10−32 cm6 molecules−2 s−1 and k1a,cis = 6(2) × 10−33 cm6 molecules−2 s−1 . CO is twice as eective
in collisionally stabilizing

trans -DOCO* compared to cis -DOCO* . The unusually large enhancementby the CO collision partner for theof complex formation between

trans -DOCO isomer relative to cis -DOCO may be a consequencetrans -DOCO* and CO from a stronger interaction potential, which

would facilitate energy transfer. This mechanism is further supported by spectroscopic observationof thetrans -HOCO(CO) complex in the molecular beam environment by Oyama et al. (30).

Finally, the identication and quantication ofcis -DOCO, trans -DOCO, and D+CO2 amount to

all the possible branching pathways for OD+CO. It is now experimentally possible to deconstruct

k1 as a sum of reaction elementary steps, i.e. k1 ([M], T ) = k1a,trans ([M], T ) + k1a,cis ([M], T ) +k1b ([M], T ), where k1b ([M], T ) is the bimolecular rate coecient for the D+CO2 channel [182]. Thisapproximation is valid in the low pressure-limit, provided that k1 is only strongly dependent on k1awhile k1b remains constant with respect to the total pressure and collision partner [120, 145, 182].
Previously, k1 was determined with only contributions fromdictates thattrans -DOCO and CO2 . Mass balancecis -DOCO also contributes to the total k1 , which has been plotted in Fig. 6.15. The

observed agreement in k1 with previous studies by Golden et al. [119] and Paraskevopoulos andCHAPTER 6. CO2 AND CIS-DOCO CHANNELS

131

Figure 6.15: The measured k1 as a function of N2 are given by the shaded green region (within 1σv
uncertainties). Red diamonds and blue circles are the measured k1 values from Golden

et al. [119]and Paraskevopoulos & Irwin [147], respectively.

Irwin [147] provides additional conrmation that k1 can be treated as a sum of the rate coecientsof independent channels, k1a and k1b , in the low-pressure regime.

Chapter 7
Conclusion and Outlook
In this thesis, we have described the a new technique for the analysis of complex chemical reactions
on the μs timescale and we have demonstrated its capabilities. Applied to deuterated acrylic acid,the technique allowed for the simultaneous tracking of acrylic acid-d1 ,trans -DOCO, C2 HD, HOD,

and D2 O concentrations. HOD and C2 HD were observed immediately after photolysis, which was
unexpected considering previous knowledge of AA-d1 photolysis kinetics.

This may indicate an

unknown reaction pathway and warrants further investigation.



Next, we applied the technique to the OD+CO

D+CO2 reaction, the isotopically-substituted

version of the OH+CO reaction. Many experimental eorts have attempted to unravel the complex
mechanism of this reaction but have ultimately been unable to directly observe thetrans- and cis-

DOCO intermediate species, which are key branching pathways. Using the broad bandwidth, highresolution, and cavity-enhanced sensitivity of time-resolved frequency comb spectroscopy, we havedirectly quantied the concentrations of all relevant reactants and products in this reaction, namely
OD,

trans -DOCO, cis-DOCO, and CO2 . This allowed us to determine termolecular branching rates

for all three product channels. Additionally, we were able to observe

cis trans isomerization andquantify the forward and reverse unimolecular rate constants. Moreover, a class of similar reactions
exists where time-resolved frequency comb spectroscopy might be applied. Ozonolysis reactions, forexample, produce a so-called criegee intermediate as part of their reaction mechanism. One suchintermediate, CH2 OO, has been shown to live for 10s of μs[183].

132

CHAPTER 7. CONCLUSION AND OUTLOOK

133

Even with these successes, a much broader range of experiments would be made accessible, or atleast simpler, with improved sensitivity. One exciting direction for studies of the OH+CO reaction
is cold chemistry in a buer gas cell[85] at 10K or even ultracold stark-decelerated molecules[184].
These environments would allow access to the OH+CO potential energy surface with unprecedented
energy resolution to tunneling, isomerization, and complex formation dynamics. However, there istypically a trade-o between molecular temperature and density, with peak reported densities of

5 × 1012 and 5 × 1010 molecules cm-3 for the buer gas and ultracold environments, respectively.
Additionally, only a fraction of the molecules in the cell will react, yielding a much lower density of
products so the detection of cold chemistry could be rather challenging.
The multifaceted nature of time-resolved frequency comb spectroscopy makes it dicult to
optimize for one particular application. An increase in the cavity nesse will increase the eective
path length while degrading the time resultion from the longer ringdown time of the cavity. Similarly,
the sensitivity might be increased by reducing the spectral bandwidth of the laser source, but
at the cost of molecular accessibility.

However, there are a few ways to improve all parameterssimultaneously. For example, the total light ux at the camera could be increased by improving thetransmission of the optical cavity or VIPA etalon or increasing the power of the laser source. Since
the noise in our experiments was dominated by the dark counts of our InSb camera, this would
increase sensitivity. The InSb camera is another place for improvement. By improving the coolingof the detector array beyond its current 77K temperature or using a dierent detection technology,
an improvement might be made to the camera's dark noise, increasing sensitivity. Finally, longer
wavelengths provide larger band strengths and access to dierent molecular species. Moving beyond
5 μm would increase the sensitivity and allow for more experimental exibility[185].

Appendix A
Selected Mathematical Derivations
A.1 The Frequency Comb
We start with a sequence of pulses at a carrier frequency ωc , each with pulse envelope A(t). Thus,
the complex electric eld for a pulse train of nf pulses is given byE(t) =nf
X

A(t − nτ )ei(ωc [t−nτ ]+n∆φce ) ,

(A.1)

n=1
where a pulse-to-pulse phase slip,∆φce , has also been included.

The Fourier transform of thisexpression yields

Ẽ(ω) =

Pnf r ∞

n=1 −∞ A(t − nτ )ei(ωc [t−nτ ]+n∆φce ) e−iωt dtr−iωnτ ∞ A(t0 )ei(ωc t0 +n∆φce ) e−iωt0 dt0
n=1 e
−∞

=

Pnf

=

Pnf

r
−iωnτ +n∆φce ∞ A(t0 )e−i(ω−ωc )t0 dt0
n=1 e−∞
Pnf −iωnτ +in∆φceÃ(ω − ωc ) n=1 e

=

,

(A.2)

0 + nτ is used in the second line and f˜(ω) is the Fourier transformwhere a variable change of t → tof f (t).

In the case of many pulses, i.e.

nf → ∞, we look for constructive interference in theth comb tooth, f , is thenmexponential for all pulses, 2πm = ωτ − ∆φce . The frequency of the mgiven by134

APPENDIX A. SELECTED MATHEMATICAL DERIVATIONS
fm = mfrep +∆φcefrep ,
2π

135

(A.3)

where we have used frep = 1/τ .

A.2 OH+CO Lindemann Expressions
The system of equations for this system is given below, where brackets are used to indicate thetime-dependent concetration of a molecule (i.e.
-3molecules cm[X] is the time-dependent concentration of X in).

d[CO] = 0dtd[OH] = ka− [HOCO∗ ](t) − ka+ [OH][CO]dtd[HOCO∗ ] = 0 = ka+ [OH](t)[CO] − (ka− + kb− [M ] + kc− )[HOCO∗ ](t)dtd[HOCO] = kb− [M ][HOCO∗ ] − kb+ [M ][HOCO∗ ](t)dtd[H] = kc− [HOCO∗ ]dt
d[CO2 ] = kc− [HOCO∗ ]
dt

(A.4)

Making this approximation allows us to solve for the steady-state concentration of HOCO*, HOCO∗ =ka+ [OH][CO]ka− +kb− [M ]+kc− . This simplies the system of equations toka− ka+d[OH] =[OH][CO] − ka+ [OH][CO]dtka− + kb− [M ] + kc−
dka+ (kb− − kb+ )[M ][HOCO] =[OH][CO]dt
ka− + kb− [M ] + kc−.
dka+ kc−[H] =[OH][CO]dt
ka− + kb− [M ] + kc−
dka+ kc−[CO2 ] =[OH][CO]dt
ka− + kb− [M ] + kc−(A.5)

From these equations, we can determine bimolecular formation and loss rates for OH, HOCO, andCO2 as k1 , k1a , and k1b , respectively. These are given as

APPENDIX A. SELECTED MATHEMATICAL DERIVATIONS

136

k1 = k1a + k1b(A.6)

ka+ (kb− − kb+ )[M ]ka− + kb− [M ] + kc−
ka+ kc−k1b =ka− + kb− [M ] + kc−

k1a =A.3 trans -DOCO

(A.7)

(A.8)

cis -DOCO Isomerization

In isolation, the cis/trans isomerization may be modelled as a simple A

B approach to equilibrium.

The system of equations describing this system isd[A] = −rAB [A] + rBA [B]dtd[B] = rAB [A] − rBA [B]
dt

(A.9)

(A.10)

these equations permit the following solutions[A](t) = ([A]0 − Aeq )e−(rAB +rBA )t + Aeq(A.11)[B](t) = ([B]0 − Beq )e−(rAB +rBA )t + Beq(A.12)

Aeq = ([A]0 rBA + [B]0 rAB )/(rAB + rBA )(A.13)

Beq = ([A]0 rAB + [B]0 rBA )(rAB + rBA ),(A.14)

where Aeq and Beq are the equilibrium values of A[t] and B[t] at long times. It is also useful todene the behavior of the dimensionless quantity (A[t] − B[t])/(A[t] + B[t]),[A](t) − [B](t)=[A](t) + [B](t)[A]0 − [B]0 KA/B − 1−[A]0 + [B]0 KA/B + 1e−(rAB +rBA )t +KA/B − 1
KA/B + 1(A.15)

where it is clear that the equilibrium constant, KA/B = rBA /rAB , may be recovered from its longtimescale value.

APPENDIX A. SELECTED MATHEMATICAL DERIVATIONS

A.4 trans -DOCO137

cis -DOCO Isomerization with Formation andLoss
In reality, thetrans -DOCO and cis -DOCO species are continually being formed from the reaction

OD+CO, isomerize on some timescale, and are lost due to reactions. A simple version of this model
may be writtend[trans] = r+t [OD] − (r−t + rtc )[trans] + rct [cis]dtd[cis] = r+c [OD] − (r−c + rct )[cis] + rtc [trans].
dt(A.16)(A.17)At this point, we take the laplace transform of each equation. We now havesL[trans](s) = r+t L[OD](s) − (r−t + rtc )L[trans](s) + rct L[cis](s)(A.18)

sL[cis](s) = r+c L[OD](s) − (r−c + rct )L[cis](s) + rtc L[trans](s).

(A.19)

Solving for L[trans](s) and L[cis](s), we ndr+c rct + r+t (rct − rlc + s)
× L[OD](s)(rct − rlc + s)(−rlt + rtc + s) − rct rtc
r+t rtc + r+c (rtc − rlt + s)
L[cis](s) =× L[OD](s),(rct − rlc + s)(−rlt + rtc + s) − rct rtc

L[trans](s) =(A.20)(A.21)

which in the time domain is1aA −(rt +rs )/2taA −(rt −rs )/2t
[trans](t) =[rA +]e+ [rA −]e
∗ [OD](t)
2
rs
rs


1
aB −(rt +rs )/2taB −(rt −rs )/2t
[cis](t) =[rB +]e+ [rB −]e
∗ [OD](t).
2
rsrs(A.22)(A.23)

We now nd ourselves interested in the long-timescale dynamics of the above equations. Specically,
we would like to compare with the simple transcis isomerization case. Since the longest timescale

APPENDIX A. SELECTED MATHEMATICAL DERIVATIONS

138

components will occur for s → 0, we can solve for ([trans](t) − [cis](t))/([trans](t) + [cis](t)) whent→∞[trans](t) − [cis](t)(t → ∞) =[trans](t) + [cis](t)R(rt + rc )R(rt + rc ) + rt lc + rc lt

KA/B − 1
rt lc − rc lt,+
KA/B + 1 R(rt + rc ) + rt lc + rc lt(A.24)

which reduces to the long-timescale value of Eq. A.15 when lt , lt → 0.

Appendix B
Frequency comb locking notes
This section is primarily meant to be a technical reference for those in our lab wishing to fully lockall parameters of the OPO frequency comb. In the rst section, I will briey discuss locking frep ,which is the least challenging lock, followed by the stabilization of the f0 of the idler.

B.1 Stabilization of the Repetition Rate
Since many harmonics of the repetition rate are present in the frequency comb's photocurrent signal,
one of these harmonics may be used to stabilize the comb, achieving a tighter lock. In our case,
we use the 8thharmonic of frep at ∼ 1092 MHz. This signal is mixed-down with a 1 GHz stable rf

source to 92 MHz and sent to one port of a phase-detector. A Discrete Digital Synthesizer (DDS,
AD9913 from Analog Devices), clocked to a stable 10 MHz source, provides a 92 MHz reference
signal to the other port of the phase-detector. The output of the phase-detector is then low-passed
and fed back to the slow frep actuator (stretcher piezo in the oscillator) to close the loop. This loop
can be very slow, operating with ~10s of Hz servo bandwidth, compensating for the drift of the Yb
oscillator while relying on its inherent stability at higher frequencies. Moreover, the resolution andphase-continuity of the DDS chip allows for smooth tuning of the repetition rate by ramping the
DDS output frequency to the desired value.

139

APPENDIX B. FREQUENCY COMB LOCKING NOTES

140

B.2 Locking the Carrier Envelope Oset Frequency
The error signal for locking the idler's carrier-envelope-oset frequency,

f0,i , was generated byheterodyne beating the p+i summing signal (810 nm) from the OPO with the pump supercontinuum(SC, spectrum shown in Fig. B.1). The pump input to the SC ber (NL-1050-ZERO-2) was 650
mW. With an 810 nm bandpass lter in front of the detector, the repetition rate peak (136 MHz)signal-to-noise wasSC pump only. -14.7 dBm (300 kHz RBW).

 p+i


beam only: -31.0 dBm (300 kHz RBW).

Both arms: -13 dBm (300 kHz RBW).

This yielded a (p + i) − p beatnote of amplitude -35 dBm (300 kHz RBW). From the repetition-rateonly values, we would expect a beat note of amplitude 1/2 [(−15 dBm) + (−31 dBm)] = −23 dBm.
It is likely that the poor spatial quality of the parasitic p + i beam is causing this reduction in signal.
Nonetheless, it was possible to feed this signal (through a phase detector) back to the fast and slow
piezo actuators in the OPO, resulting in the in-loop error signal shown in Fig. B.2.

B.3 The Fiber Bragg Grating
The eect of the ber bragg grating (FBG) inside the oscillator is to change both frep and f0 , since
it changes both the group delay and the group delay dispersion. By tuning the temperature of our°°FBG (total length 5 cm), the frep and f0 change by 6.3 Hz/ C and 12.2 MHz/ C, respectively. Thiscan be used as a slow servo for either frep or f0 with large dynamic range.

APPENDIX B. FREQUENCY COMB LOCKING NOTES

Figure B.1: Supercontinuum Fiber Spectrum.

141

APPENDIX B. FREQUENCY COMB LOCKING NOTES

Figure B.2: In-loop error signal from p + i beat with pump supercontinuum.

142

APPENDIX B. FREQUENCY COMB LOCKING NOTES

143

Figure B.3: Response of frep (left) and f0 (right) to ber bragg grating temperature. The data on
the right was measured by locking frep and beating the Yb oscillator with a stable cw laser at 1064nm.

Appendix C
MATLAB Code
C.1 VIPA Fringe Collection% Usesone

variable :%fringeImage

% Bad

Pixel

− the

image

from

which

to

collect

thefringes .

Locations

badPixelKernel = [1

1

1;

1

0

1;

1

1

1]/8;

fringeImageConv = fringeImage ;fringeImageConv ( isnan ( fringeImageConv ) ) = 0 ;b a d P i x e l R e p l a c e = c o n v 2 ( f r i n g e I m a g e C o n v , b a d P i x e l K e r n e l , ' same ' ) ;fringeImage ( isnan ( fringeImage )) = badPixelReplace ( isnan ( fringeImage ) ) ;fringeImage = fringeImage ' ;f i g u r e ; imagesc ( fringeImage ' ) ;% Identify

the

zero

crossings

of

the

image

windowSize = 3 0 ;fringeImageBase =f i l t e r ( ones ( 1 , windowSize ) / windowSize , 1 , . . .
fringeImage , [ ] , 1 ) ;144

APPENDIX C. MATLAB CODE145

− fringeImageBase ;fringeImageNorm = f r i n g e I m a g e

f r i n g e I m a g e N o r m 1 = f r i n g e I m a g e N o r m ( 1 : end − 1 , : ) ;f r i n g e I m a g e N o r m 2 = f r i n g e I m a g e N o r m ( 2 : end , : ) ;i d x = f i n d ( s i g n ( f r i n g e I m a g e N o r m 1 )− s i g n ( f r i n g e I m a g e N o r m 2 ) ) ;[ idxX , idxY ]= ind2sub ( s i z e ( fringeImageNorm1 ) , idx ) ;i s P e a k = (− s i g n ( f r i n g e I m a g e N o r m 1 ( i d x ( 1 : end − 1 ) ) ) + 1 ) / 2 ;m = ( f r i n g e I m a g e N o r m 2 ( i d x )− f r i n g e I m a g e N o r m 1 ( i d x ) ) ;b = f r i n g e I m a g e N o r m 1 ( i d x )−m.

*idxX ;

idxX = −b . /m;% Identify

the

peaks

for

each

row

of

the

image

t h e P e a k s A n d V a l l e y s X = ( idxX ( 1 : end −1)+idxX ( 2 : end ) ) / 2 ;t h e P e a k s A n d V a l l e y s Y = idxY ( 1 : end − 1 ) ;d e l t a Y = idxY ( 1 : end −1)− idxY ( 2 : end ) ;t h e P e a k s X = t h e P e a k s A n d V a l l e y s X ( ( i s P e a k == 1 ) & ( d e l t a Y == 0 ) ) ;t h e P e a k s Y = t h e P e a k s A n d V a l l e y s Y ( ( i s P e a k == 1 ) & ( d e l t a Y == 0 ) ) ;% Group

the

rows

( and

sort

them )[ uniqueRows , i a , i c ]= u n i q u e ( thePeaksY ) ;% Iterate

uniqe

% a

over

the

rows ,

fringefringesX = {};fringesY = {};fori= 1 : l e n g t h ( uni queRows )selecting

peaks

and

addingthemtoAPPENDIX C. MATLAB CODE

146

i d x = f i n d ( t h e P e a k s Y == uniqueR ows ( i ) ) ;forj = 1: length ( idx )if

i == 1f r i n g e s X { i , j } = thePeaksX ( i d x ( j ) ) ;f r i n g e s Y { i , j } = thePeaksY ( i d x ( j ) ) ;else
fringeMatchIdx =
for

[];

k = 1: s i z e ( fringesX , 2 )if~ i s e m p t y ( f r i n g e s X { i −1 , k } ) &( a b s ( f r i n g e s X { i −1 , k }...

− thePeaksX ( i d x ( j ) ) ) < 1 )fringeMatchIdx = k ;break ;
end
end

if

isempty ( fringeMatchIdx )f r i n g e s X { i , end +1} = t h e P e a k s X ( i d x ( j ) ) ;f r i n g e s Y { i , end +1} = t h e P e a k s Y ( i d x ( j ) ) ;else
f r i n g e s X { i , f r i n g e M a t c h I d x } = thePeaksX ( i d x ( j ) ) ;f r i n g e s Y { i , f r i n g e M a t c h I d x } = thePeaksY ( i d x ( j ) ) ;
end

end
end
end
%f i g u r e ; i m a g e s c ( f r i n g e I m a g e N o r m ' ) ; h o l don ;APPENDIX C. MATLAB CODE147

%s c a t t e r ( [ f r i n g e s X { : } ] , [ f r i n g e s Y { : } ] , ' . k ' ) ;% Saveforthefringes

to

be

used

i

= 1 : numel ( f r i n g e s X ) ;ifisempty ( f r i n g e s X { i })laser

f r i n g e s X { i } = NaN ;end
ifisempty ( f r i n g e s Y { i })f r i n g e s Y { i } = NaN ;end
endfringesXmat = cell2mat ( fringesX ) ;fringesYmat = cell2mat ( fringesY ) ;

% Get

the

minimum x

element

from

each

fringef r i n g e s S t a r t X = min ( f r i n g e s X m a t , [ ] , 1 ) ;[~ , idx ]= sort ( fringesStartX );% SortthefringesbyfringesStartX

fringesXmatSorted = fringesXmat ( : , idx ) ;fringesYmatSorted = fringesYmat ( : , idx ) ;% Remove% thatdofringes
not

that

have

at

croppedFringesX =[];croppedFringesY =[];fringeHighThresh = 0

*

do

not

least

cover
100

at

least

pointss i z e ( fringeImage ' , 1 ) ;

half

of

the

screenandAPPENDIX C. MATLAB CODE
fringeLowThresh = 1
for

i

*

148

s i z e ( fringeImage ' , 1 ) ;= 1 : s i z e ( fringesXmatSorted , 2 )ifsum ( ~ i s n a n ( f r i n g e s X m a t S o r t e d ( : , i ) ) ) > 50 &&...

max ( f r i n g e s Y m a t S o r t e d ( : , i ) ) > f r i n g e H i g h T h r e s h &&min ( f r i n g e s Y m a t S o r t e d ( : , i ) ) < f r i n g e L o w T h r e s h
c r o p p e d F r i n g e s X ( : , end +1) = f r i n g e s X m a t S o r t e d ( : , i ) ;c r o p p e d F r i n g e s Y ( : , end +1) = f r i n g e s Y m a t S o r t e d ( : , i ) ;end
end% Savethefringes

to

be

used

later

f r i n g e X = newFringesX ;f r i n g e Y = newFringesY ;fringeImageSize =% Plotthefringess i z e ( fringeImage ' ) ;

for

the

user

f i g u r e ; imagesc ( fringeImageNorm ' ) ; holdon ;f r i n g e s O d d X = f r i n g e X ( : , 1 : 2 : end ) ;f r i n g e s O d d Y = f r i n g e Y ( : , 1 : 2 : end ) ;f r i n g e s E v e n X = f r i n g e s X ( : , 2 : 2 : end ) ;f r i n g e s E v e n Y = f r i n g e s Y ( : , 2 : 2 : end ) ;s c a t t e r ( fringesOddX ( : ) , fringesOddY ( : ) , ' . k ' ) ;s c a t t e r ( fringesEvenX ( : ) , fringesEvenY ( : ) , ' . r ' ) ;...

Bibliography[1] J. Troe.

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