ABSTRACT
Title of dissertation: SOOT OXIDATION IN FLAMES:
NANOSTRUCTURE, MORPHOLOGY,
AND CHEMICAL KINETICS
Paul M. Anderson
Doctor of Philosophy, 2019
Dissertation directed by: Professor Peter B. Sunderland
Department of Mechanical Engineering
Soot produced from the combustion of hydrocarbons is of immense scientific
interest owing to its deleterious effects on human health and the environment. De-
spite decades of research, existing soot models are accurate across only a narrow
range of combustion conditions. A substantial portion of this inaccuracy is rooted
in the multitude of factors affecting soot oxidation that remain ill-understood.
In the current work, a novel flame system allowed soot oxidation to be observed
in isolation from competing soot formation processes. Measurements tracked evolv-
ing soot structures, oxidation rates, temperatures and gas species concentrations.
Transmission electron microscopy (TEM) was used to characterize soot structure at
aggregate, primary particle, and nanostructural scales. For this, a program called
Aerosol Image Analyzer was developed, incorporating new algorithms for process-
ing and measuring TEM images of mass-fractal aerosols, like soot. For the first
time, TEM image measurement uncertainties incorporating sample, operator, and
random effects, were quantified through gage repeatability and reproducibility anal-
ysis. Successful methods for reducing operator bias were presented, and automated
measurement methods from literature were tested and found to be unreliable. Mea-
surements of surface area by N2 adsorption validated TEM as a technique for de-
termining soot specific surface area, provided that the polydispersity and partial
sintering of primary particles is taken into account.
TEM measurements of soot undergoing oxidation showed continuously de-
creasing primary particle size distributions and increasing specific surface area.
Measurements of soot aggregate morphology found a fractal dimension of 1.74 that
was unchanged by oxidation. The breakup of aggregates by oxidative fragmenta-
tion was observed for the first time using methods that combined TEM analysis
with laser extinction. Soot nanostructure was characterized through high resolution
TEM measurements of lattice fringe length, tortuosity, orientation, and separation
distance. It was observed that primary particles could be divided into an inner 80%,
where lattice fringes showed greater graphitic order with increasing radial location,
and an outer 20%, where this trend was reversed. While oxidation proceeded in a
shrinking-sphere manner at the particle surface, the interior underwent thermal and
oxidation-induced graphitization, challenging the assumption that the nanostruc-
ture of mature soot is “locked-in.” This results in a surface nanostructure that is
effectively unchanging from the perspective of the oxidizing gases and corresponds
to a constant collision efficiency kinetics model.
SOOT OXIDATION IN FLAMES: NANOSTRUCTURE,
MORPHOLOGY, AND CHEMICAL KINETICS
by
Paul Marcus Anderson
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2019
Advisory Committee:
Professor Peter B. Sunderland, Chair/Advisor
Professor Christopher Cadou, Dean’s Representative
Professor Elaine S. Oran
Professor Arnaud Trouvé
Associate Professor Michael J. Gollner
© Copyright by
Paul Marcus Anderson
2019
Acknowledgments
I am filled with deep gratitude for the many individuals who made this work
possible. A big thank you to my advisor, Dr. Peter Sunderland, for his unflagging
support and positivity throughout this processes. Thank you to Dr. Elaine Oran,
Dr. Christopher Cadou, and Dr. Michael Gollner for giving me the chance to work
with and learn from you in many ways beyond just this dissertation, and to Dr.
Arnaud Trouvé for many helpful discussions and encouragement. Thank you to Dr.
Wen-An Chiou, Dr. Sz-Chian Liou, and the support of the Maryland NanoCenter
and its AIMLab.
Thank you to my kitchen cabinet of advisors: Ajay Singh, Haiqing Guo, and
Ahmed Khalil. You kept me from going off plenty of cliffs, and were an ever-present
source of good ideas, or at least good laughs. For as miserable as we were, we
definitely laughed a lot. Playing with lasers helps.
Thank you to the many people in the Mechanical Engineering Department and
my adoptive Fire Protection Engineering Department at Maryland who made this
a great place be each day: Evan, Xuan, Ram, Raquel, Isaac, Cara, Sara, Fernando,
Colin, Andrés, Ahmed, Conor, Yan, Dennis, Mark, Zhengyang, Yasser, Yaqoub,
Hannes, Vivek, Ryan, Ford, Kerri, Nicole, Christine, Rosa, Antoine, Mary Lou,
Sharon, and Dr. Milke.
Thank you to Sheryl Duff and James Stankevitz for giving me the inspiration
and tools early on to pursue a life of science.
Thank you for the love and support of my incredible family. Mom and Dad,
ii
you’ve given me the firm foundation. Rachel, Gene, Jacob, and Edith, you have
been a wind in my sails. Lora, Armin, David, Ryan, Emily, and Evan, you have
been an unbelievable cheering section.
Most of all, thank you to my wonderful wife, Jennifer. There is no way I
can express my gratitude that would not be an absurd understatement. You’re my
favorite, and there’s no one else I’d rather stumble through life with. Thank you
Marcus and Matthew for being my biggest, littlest fans, and for bringing joy to each
day. Never lose your sense of wonder and adventure. Not only will it serve you well,
it is what you were made for.
iii
Table of Contents
Acknowledgments ii
List of Tables vii
List of Figures viii
Nomenclature xi
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 General Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Literature Review 5
2.1 Soot Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Oxidation by O2 . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Oxidation by OH . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 Oxidation Model . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Soot Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1.1 Aggregate Measurement Methods: Non-TEM . . . . 13
2.2.1.2 Aggregate Measurement Methods: TEM . . . . . . . 14
2.2.2 Primary Particles . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2.1 Primary Particle Size Distribution . . . . . . . . . . 18
2.2.2.2 Sintering and Overlap of Primary Particles . . . . . . 20
2.2.2.3 Attempts to Automate Primary Particle Measurement 21
2.2.3 Uncertainty of TEM Morphological Measurements . . . . . . . 23
2.3 Soot Fragmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Soot Nanostructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 Description of Nanostructure . . . . . . . . . . . . . . . . . . 26
2.4.2 Dependence on Heat Treatment and Fuel Type . . . . . . . . 28
2.4.3 Nanostructure Diagnostic Methods . . . . . . . . . . . . . . . 29
2.4.3.1 Non-TEM Methods . . . . . . . . . . . . . . . . . . . 29
2.4.3.2 Selected-Area Electron Diffraction (SAED) . . . . . . 30
iv
2.4.3.3 High Resolution Transmission Electron Microscopy
(HRTEM) Lattice Fringe Analysis . . . . . . . . . . 33
2.4.4 Role of Nanostructure in Soot Oxidation . . . . . . . . . . . . 38
3 Experimental Methods 46
3.1 Ternary Flame System . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Axial Flame Velocity Measurement . . . . . . . . . . . . . . . . . . . 48
3.3 Temperature, Soot Volume Fraction, and Gas Species Measurements . 50
3.3.1 Soot Flame Temperature . . . . . . . . . . . . . . . . . . . . . 51
3.3.2 Soot Volume Fraction . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.3 Major Species Concentrations . . . . . . . . . . . . . . . . . . 54
3.3.4 Estimation of OH Radical Concentrations . . . . . . . . . . . 55
3.4 Thermophoretic Sampling of Flame Soot . . . . . . . . . . . . . . . . 55
3.5 TEM Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.5.1 Aerosol Image Analyzer Program . . . . . . . . . . . . . . . . 58
3.5.2 Primary Particle Measurement . . . . . . . . . . . . . . . . . . 60
3.5.2.1 Measurement Bias Controls . . . . . . . . . . . . . . 60
3.5.2.2 Center-Selected Edge Scoring (CSES) Algorithm . . 61
3.5.2.3 Primary Particle Overlap . . . . . . . . . . . . . . . 63
3.5.3 Soot Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5.4 Soot Aggregate Morphology . . . . . . . . . . . . . . . . . . . 69
3.5.5 Soot Fragmentation . . . . . . . . . . . . . . . . . . . . . . . . 73
3.5.6 Selected Area Electron Diffraction . . . . . . . . . . . . . . . . 73
3.5.7 HRTEM Lattice Fringe Analysis . . . . . . . . . . . . . . . . . 76
3.5.7.1 HRTEM Image Processing Procedure . . . . . . . . . 76
3.5.7.2 HRTEM Fringe Measurement . . . . . . . . . . . . . 83
3.6 Soot Oxidation Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.7 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4 Repeatability and Reproducibility of TEM Measurements and Surface Area
Validation 94
4.1 Non-Bias-Controlled Results and Study Motivation . . . . . . . . . . 95
4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2.1 Bias-controlled measurements . . . . . . . . . . . . . . . . . . 97
4.2.2 Gage R & R Analysis . . . . . . . . . . . . . . . . . . . . . . . 98
4.2.3 A simplified approach to obtaining sample confidence intervals 101
4.2.4 Automated Measurements . . . . . . . . . . . . . . . . . . . . 102
4.2.4.1 Circular Hough Transform . . . . . . . . . . . . . . . 102
4.2.4.2 Euclidean Distance Mapping . . . . . . . . . . . . . 104
4.2.5 TEM-Derived Mass Specific Surface Area . . . . . . . . . . . . 105
4.2.6 BET-Derived Mass Specific Surface Area . . . . . . . . . . . . 106
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.1 Gage R & R Results . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.2 Automated Results . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.3 Mass Specific Surface Area Results . . . . . . . . . . . . . . . 113
v
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5 Results 120
5.1 Axial Flame Velocity Results . . . . . . . . . . . . . . . . . . . . . . 120
5.2 Temperature, Soot Volume Fraction, and Gas Species Concentration
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.1 Temperature and Soot Volume Fraction . . . . . . . . . . . . . 121
5.2.2 Gas Species Concentrations . . . . . . . . . . . . . . . . . . . 123
5.3 TEM Measurement Results . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.1 Primary Particle Measurements . . . . . . . . . . . . . . . . . 124
5.3.2 Soot Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.3.3 Soot Aggregate Morphology . . . . . . . . . . . . . . . . . . . 132
5.3.4 Soot Fragmentation . . . . . . . . . . . . . . . . . . . . . . . . 137
5.3.5 Primary Particle Number Flow Rate . . . . . . . . . . . . . . 139
5.3.6 Selected Area Electron Diffraction . . . . . . . . . . . . . . . . 143
5.3.7 HRTEM Lattice Fringe Analysis Results . . . . . . . . . . . . 145
5.3.7.1 Fringe Length . . . . . . . . . . . . . . . . . . . . . . 147
5.3.7.2 Fringe Tortuosity . . . . . . . . . . . . . . . . . . . . 151
5.3.7.3 Fringe Orientation . . . . . . . . . . . . . . . . . . . 155
5.3.7.4 Fringe Separation Distance . . . . . . . . . . . . . . 159
5.3.7.5 Nanostructure at the Particle Surface . . . . . . . . . 163
5.4 Soot Oxidation Rate Expressions . . . . . . . . . . . . . . . . . . . . 166
6 Conclusions and Recommendations 170
6.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 170
6.2 Recommendations for Future Study . . . . . . . . . . . . . . . . . . . 177
A MATLAB Code 179
A.1 Center-Selected Edge Scoring . . . . . . . . . . . . . . . . . . . . . . 179
A.2 SAED Image Analysis Code . . . . . . . . . . . . . . . . . . . . . . . 183
A.3 Lattice Fringe Analysis Code . . . . . . . . . . . . . . . . . . . . . . . 189
A.3.1 BridgeGaps Function . . . . . . . . . . . . . . . . . . . . . . . 189
A.3.2 SeverBranches Function . . . . . . . . . . . . . . . . . . . . . 192
A.3.3 MeasureFringes Function . . . . . . . . . . . . . . . . . . . . . 195
A.3.4 GetFringeSeps Function . . . . . . . . . . . . . . . . . . . . . 199
B Mathematical Derivations 202
B.1 Expressions for the Diameters of Average Surface Area and Volume . 202
B.2 Expressions for Spherical Cap Height . . . . . . . . . . . . . . . . . . 205
C Supplemental Figures 207
C.1 Fractal Dimension and Pre-factor from Fitted Data . . . . . . . . . . 208
C.2 Additional Fringe Measurements at the Primary Particle Surface . . . 209
Bibliography 210
vi
List of Tables
2.1 Summary of literature reporting OH collision efficiencies with soot,
under various experimental conditions. . . . . . . . . . . . . . . . . . 10
4.1 Components of variance in the measurement of primary particle di-
ameter mean and standard deviation as quantified by Gage R & R
analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.2 Primary particle diameter mean and standard deviation of each sam-
ple using two methods for combining operator measurements. Inter-
vals are at the 95% confidence level. . . . . . . . . . . . . . . . . . . . 111
4.3 Components of variance in the skewness of the primary particle size
distribution and the mean projected overlap coefficient, as quantified
by Gage R & R analysis. . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.1 Comparison of oxidation mechanism predictions with measured oxi-
dation rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
vii
List of Figures
2.1 Common measurements on binary soot aggregate images . . . . . . . 16
2.2 Structure of crystalline graphite . . . . . . . . . . . . . . . . . . . . . 27
2.3 HRTEM image showing internal burning . . . . . . . . . . . . . . . . 42
3.1 Ternary flame system . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Soot column disruption apparatus for velocity measurement . . . . . 49
3.3 Velocity measurement video analysis method . . . . . . . . . . . . . . 49
3.4 Laser extinction system schematic . . . . . . . . . . . . . . . . . . . . 53
3.5 Thermophoretic soot sampling apparatus . . . . . . . . . . . . . . . . 56
3.6 Aerosol Image Analyzer GUI . . . . . . . . . . . . . . . . . . . . . . . 58
3.7 Screenshot of primary particles measured using the CSES algorithm . 61
3.8 Steps in the CSES algorithm . . . . . . . . . . . . . . . . . . . . . . . 62
3.9 Spherical cap and overlapping primary particle schematic . . . . . . . 68
3.10 Procedure for creating binary images of soot aggregates . . . . . . . . 71
3.11 SAED image measurement process . . . . . . . . . . . . . . . . . . . 75
3.12 Fringe image: ROI and contrast enhancement . . . . . . . . . . . . . 78
3.13 Fringe image: processing and skeletonization . . . . . . . . . . . . . . 79
3.14 Fringe segment connection . . . . . . . . . . . . . . . . . . . . . . . . 82
3.15 Fringe branch severing . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.16 Lattice fringe measurement . . . . . . . . . . . . . . . . . . . . . . . . 85
3.17 Lattice fringe separation measurement . . . . . . . . . . . . . . . . . 86
3.18 Differing reciprocal fringe separation distances . . . . . . . . . . . . . 87
3.19 Final fringe measurements in the Aerosol Image Analyzer . . . . . . . 87
3.20 Soot flame control volume for oxidation rate analysis . . . . . . . . . 89
4.1 Preliminary measurements of dp without bias controls. . . . . . . . . 96
4.2 Soot collection apparatus for BET measurement . . . . . . . . . . . . 107
4.3 Gage R & R results for dp and sdp . . . . . . . . . . . . . . . . . . . . 109
4.4 Comparison of automated and Gage R & R results for dp and sdp . . 112
4.5 Comparison of MSSA results from various methods . . . . . . . . . . 115
5.1 Soot flame velocity vs. height above burner . . . . . . . . . . . . . . . 120
5.2 Radial temperature and soot volume fraction . . . . . . . . . . . . . . 122
viii
5.3 Temperature and integrated soot volume fraction vs. HAB . . . . . . 122
5.4 Concentrations of major species and radicals vs. HAB . . . . . . . . . 124
5.5 Representative images of primary particles obtained at HABs of 10,
15, 25, and 50 mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.6 Primary particle size distributions at HAB = 10 to 30 mm . . . . . . 127
5.7 Primary particle size distributions at HAB = 35 to 50 mm . . . . . . 128
5.8 Primary particle measurements vs. HAB . . . . . . . . . . . . . . . . 129
5.9 Soot specific surface area vs. HAB . . . . . . . . . . . . . . . . . . . 131
5.10 Specific surface area overlap factor vs. HAB . . . . . . . . . . . . . . 131
5.11 Aggregate size distributions at HAB = 10 to 45 mm . . . . . . . . . . 134
5.12 Radius of gyration geometric mean vs. HAB . . . . . . . . . . . . . . 135
5.13 Fractal dimension and pre-factor vs. HAB . . . . . . . . . . . . . . . 136
5.14 Distribution of primary particles per aggregate at each HAB . . . . . 137
5.15 Geometric mean number of primary particles per aggregate and num-
ber flow rate of aggregates vs. HAB . . . . . . . . . . . . . . . . . . . 138
5.16 Primary particle number flow rate vs. HAB . . . . . . . . . . . . . . 141
5.17 Representative SAED images obtained at HAB = 10, 15, 25, and 50 mm143
5.18 SAED d-spacings and integral breadths at HAB = 10, 15, 25, and
50 mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.19 Diameters of primary particles used for fringe analysis at each HAB . 145
5.20 HRTEM images of soot obtained at HABs 10, 15, 20, and 50 mm . . 146
5.21 (a) Fringe length distribution; (b) Median fringe length vs. HAB . . . 148
5.22 Median fringe length vs. fringe radial location . . . . . . . . . . . . . 149
5.23 Change in fringe length with primary particle size, inner 80% of pri-
mary particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.24 (a) Fringe toruoisity distribution; (b) Median fringe tortuosity vs. HAB152
5.25 Median fringe tortuoisty vs. fringe radial location . . . . . . . . . . . 154
5.26 Change in fringe tortuosity with respect to primary particle size, inner
80% of primary particles . . . . . . . . . . . . . . . . . . . . . . . . . 155
5.27 (a) Fringe Non-concentricity distribution; (b) Std Dev. of fringe non-
concentricity vs. HAB . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.28 Standard deviation of fringe non-concentricity vs. fringe radial location157
5.29 Change in std. dev. of fringe non-concentricity with respect to pri-
mary particle size, inner 80% of primary particles . . . . . . . . . . . 158
5.30 (a) Fringe separation distance distribution; (b) Mean of fringe sepa-
ration vs. HAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.31 Mean fringe separation distance vs. fringe radial location . . . . . . . 161
5.32 Change in mean fringe separation distance with respect to primary
particle size, inner 80% of primary particles . . . . . . . . . . . . . . 162
5.33 Fringe length measurements within the outer 20% of primary particles 164
5.34 Change in fringe length with respect to primary particle size, outer
2 nm of the primary particle . . . . . . . . . . . . . . . . . . . . . . . 165
5.35 Measured and predicted soot oxidation rates vs. HAB . . . . . . . . . 167
B.1 Spherical cap and overlapping primary particle schematic . . . . . . . 205
ix
C.1 Fitted data to obtain fractal dimension and pre-factor at HAB = 10
to 45 mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
C.2 Additional fringe measurements within the outer 20% of the primary
particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
x
Nomenclature
Physical constants
c Speed of light in a vacuum (3.0× 108 m/s)
h Planck’s constant (6.63× 10−34 J-s)
kB Boltzmann’s constant (1.38× 10−23 J/K)
Ru Ideal gas constant (Ru = 8.314 J/mol-K)
Latin symbols
a1, a2 Limits of a bias correction distribution
Aa Projected area of an aggregate
Ai Arrhenius pre-factor for species i
Ap Cross-sectional area of a primary particle of mean diameter
B Expected value of a bias correction
C Empirical constant for determining radius of gyration
Cov 3-dimensional primary particle overlap coefficient
Cov,p Projected (2D) primary particle overlap coefficient
Cs Surface concentration of active sites
Cλ Calibration constant for bandpass filter centered at wavelength λ
CMi The i
th central moment of a size distribution
d Scale diameter in Eq.4.9
df Fringe separation distance
dhkl Distance between Bragg planes specified by Miller indices hkl
dij Distance between primary particles i and j
dp Primary particle diameter
dp Mean primary particle diameter of a sample
dp,min Specified minimum primary particle diameter
dp,max Specified maximum primary particle diameter
xi
dpg Geometric mean primary particle diameter
dpS Primary particle diameter of average surface area
dpV Primary particle diameter of average volume
Df Fractal dimension of an aggregate
EA,i Activation energy of species i
Eijk Measured difference from the mean due to random effects
E(m) Refractive index absorption function
Fov Specific surface area overlap factor
fs Local soot volume fraction
Fs Sectional integrated soot volume fraction
FS Lost surface area factor due to primary particle overlap
FV Lost volume factor due to primary particle overlap
|Gi| Magnitude of image intensity gradient at pixel i
GS Grayscale intensity of a soot flame image
hi Spherical cap height of primary particle i
I The set of overlapping primary particle pairs in an image
k Coverage factor
k(T ) Temperature dependent reaction rate
ka Projected area pre-factor
kf Fractal pre-factor
Ke Dimensionless extinction coefficient
L Maximum projected length of an aggregate (i.e. maximum caliper length)
La Crystallite layered plane diameter
Lc Crystallite layered plane stacking height
Lcam TEM camera length
Lf Fringe length
L̃f Median fringe length
xii
m mass
Mi Molar mass of species i
n Sample size
N Population size
Ṅa Number flow rate of aggregates
Ṅp Number flow rate of primary particles
Np Number of primary particles in a soot population
Np,a Number of primary particles per aggregate
Npx Number of pixels
o Number of operators
Oj Measured difference from the mean due to operator effects
pi Partial pressure of species i
Pi Measured difference from the mean due to sample effects
(PO)ij Measured difference from the mean due to sample-operator interaction effects
r Number of replicate measurements
rf Radial fringe location
r∗f Normalized radial fringe location
ri Radius of primary particle i
rox Oxidation rate per unit mass of soot
rp Mean primary particle radius
r Distance between the ithpx,i pixel and the aggregate centroid
R Radius of a diffraction ring or soot flame radius
Rg Radius of gyration of an aggregate
Rg,2D The 2D image radius of gyration of an aggregate
sY Sample standard deviation of measurand Y
S Surface area of a soot population
Sa Surface area of an aggregate
xiii
Scap Surface area of a spherical cap
Sm Mass specific surface area
Sm,0 Initial mass specific surface area
SV Volume specific surface area
S◦V Volume specific surface area of non-overlapping primary particles
S◦V,mono Volume specific surface area of monodisperse non-overlapping primary particles
t Time
T Temperature
u Standard uncertainty
v̄i Mean molecular velocity of species i
vs Soot velocity
Vcap Volume of a spherical cap
Vs Volume of a soot population
w Statistical weight equaling the inverse variance
ẇox Soot oxidation rate per unit surface area
W Maximum projected width normal to L in an aggregate
x Order of the reaction in carbon or horizontal coordinate in the object plane
xi Independent variable in a data reduction equation
y The calculated result of a data reduction equation
Y A measurand
YA,C The combined weighted mean of measurements of Y for sample A
Yijk A measured value of measurand Y from sample i, by operator j, the k
th time
z Height above burner
Greek symbols
α Projected area exponent, or statistical significance level
β An equation constant
xiv
γ Skewness of a distribution
γ̂ Point estimator of population skewness
ζ1, ζ2 Regression constants relating Cov to Cov,p
ηi Collision efficiency between species i and the soot surface
θB Bragg angle
θf,c Fringe angle of deviation from concentricity (i.e. non-concentricity)
θi Difference in intensity gradient orientation from that of a perfect circle, at pixel i
λ Bandpass filter wavelength or laser wavelength
λe DeBroglie wavelength of an electron
µY True mean of measurand Y
µ̂ Point estimator of population mean
ξ Oxidized fraction of the original carbon mass
ρs Soot density
ρsa Ratio of scattering-to-absorption cross section
σ2Y True variance of measurand Y
σ̂2 Point estimator of population variance
σ2ε True variance due to effect ε
σpg Geometric standard deviation of primary particle diameter
τf Fringe tortuosity
τ̃f Median fringe tortuosity
φS Surface area coefficient in Eq. 2.10
Ω Calibration constant in Eq.4.9
Subscripts
a Aggregate
CV Control Volume
f Fringe or Fractal
xv
g Geometric mean or gyration radius
m Mass
ov Overlap
ov, p Projected image overlap
ox Oxidation
p Primary particle
px Pixel
s Soot
sa Scattering and absorption
S Surface area
V Volume
Y Pertaining to measurand Y
Abbreviations
AIA Aerosol Image Analyzer
ANOVA Analysis of Variance
BET Brunauer-Emmett-Teller method
BSU Basic Structural Unit (of nanocrystalline carbon)
CSES Center-Selected Edge Scoring algorithm
CHT Circular Hough Transform
CPC Condensation Particle Counter
CV Control Volume
DMA Differential Mobility Analyzer
EDM Euclidian Distance Mapping
EELS Electron Energy Loss Spectroscopy
FWHM Full-Width at Half-Maximum
FT Fourier Transform
xvi
FTIR Fourier-Transform Infrared spectroscopy
Gage R & R Gage Repeatability and Reproducibility
GUI Graphical User Interface
HAB Height Above Burner
HRTEM High Resolution Transmission Electron Microscopy
LIF Laser-Induced Fluorescence
LII Laser-Induced Incandescence
MCM Monte Carlo Method of uncertainty propagation
MSSA Mass Specific Surface Area
NSC Nagle and Strickland-Constable model of soot oxidation by O2
PAH Polycyclic Aromatic Hydrocarbons
PPSD Primary Particle Size Distribution
RDG-PFA Rayleigh-Debye-Gans Polydisperse Fractal Aggregate theory
ROI Region of Interest
SAED Selected-Area Electron Diffraction
SMPS Scanning Mobility Particle Sizer
TEM Transmission Electron Microscopy
TGA Thermogravimetric Analysis
TSM Taylor Series Method of uncertainty propagation
VSSA Volume Specific Surface Area
XPS X-ray Photoelectron Spectroscopy
XRD X-ray Diffraction spectroscopy
xvii
Chapter 1: Introduction
1.1 Motivation
Soot is carbon particulate formed through the incomplete combustion of car-
bonaceous fuels. It is the byproduct of modern combustion systems including gas
and diesel engines, boilers, and coal-fired power plants. Soot produced by these pro-
cesses is enormously detrimental to human health and the environment. Anthro-
pogenic soot is responsible for cardiopulmonary, lung cancer, and ischemic heart
disease mortality [1–4]. The World Health Organization estimated that in 2012,
one in eight deaths worldwide resulted from air pollution exposure, of which soot
is a major contributor [5]. Similarly, in 2012 the U.S. Environmental Protection
Agency estimated that a 20% reduction in the soot emission limit from coal-fired
power plants and diesel vehicles would result in over 1,000 fewer premature deaths
and would avoid as much as $9 billion in health related costs annually [6].
In addition, atmospheric soot is a major contributor to climate change. It is the
strongest absorber of shortwave radiation in the atmosphere, resulting in a warming
effect that is second only to carbon dioxide [7, 8]. Additionally, soot deposits on
snow and ice reduce reflectivity, resulting in positive climate forcing [9, 10].
A thorough understanding of how soot is produced and consumed in com-
1
bustion environments is therefore of great interest to the broad fields of energy,
health, and the environment. However, current models of soot processes in flames
are incapable of predicting sooting behavior across more than a targeted set of com-
bustion environments. Improving these models will require improved models of soot
oxidation.
1.2 General Background
Soot oxidation is a heterogeneous reaction between gas-phase oxidizers and the
soot particle surface. Soot oxidation studies have been performed across a variety of
experimental conditions including premixed and diffusion flames, shock tubes, and
flow reactors. Unfortunately, as one review observed, the oxidation rates reported
by these studies vary by over 2 orders of magnitude [11]. In flames, soot formation
processes compete simultaneously with soot oxidation, making it difficult to isolate
the effects of either phenomenon.
Soot formation research has generally received greater attention than oxida-
tion. Leading models include those by Kazakov et al. [12] and Appel et al. [13] for
laminar premixed flames and those by Smooke et al. [14] and Dworkin et al. [15]
for laminar diffusion flames. The model predictions generally compare well with the
experimental environments targeted by each model. However, in a study by Mehta
and coworkers in which 36 different detailed models of gas and soot kinetics were
compared with 8 different laminar premixed and diffusion flames, no model could
accurately match the experimental soot volume fractions for all eight flames within
2
a factor of five [16]. An improved understanding of soot oxidation might enhance
the predictive capabilities of such models, and might also contribute to improved
soot formation models due to the competition between soot formation and oxidation
in flames.
In addition to oxidation kinetics, an accurate understanding of the physical
structure of soot and how it evolves in various oxidative environments is critical to a
full description of the oxidation process. Soot formation in a flame is a complex pro-
cess involving particle inception, condensation, surface growth and aggregation. The
resulting particles are chain-like aggregates of partially sintered spherules referred
to as primary particles, and the morphology is described as fractal-like [17].
The structural description of soot occurs on three scales. The largest scale per-
tains to the size and shape of the aggregate, or what is often simply referred to as the
soot ”particle.” Below that are the primary particles: spherules that group together
to form the aggregate. The aggregate and its constituent primary particles together
comprise what in most literature is referred to as the soot morphology. The third
and smallest scale deals with forms and features at the sub-primary particle level
down to the atomic scale, and is most often referred to as the soot nanostructure.
The nanostructure mediates how soot carbon atoms are presented to the attack-
ing gas-phase oxidizers, and hence is vital to understanding variations in oxidation
behavior.
The high level of attention paid to the study of soot formation over many
decades may in part be due to its truly puzzling nature. At its core, the chal-
lenge is in identifying a pathway for gas-phase polycyclic aromatic hydrocarbons
3
(PAHs) to cluster and grow into a condensed phase without violating the second
law of thermodynamics [18]. The recently proposed mechanism involving chain re-
actions of resonance-stabilized hydrocarbon radicals capable of producing growing
PAH clusters is a promising approach [19].
If the problem of soot formation is gaining focus, the question of oxidation is
becoming more complex. In addition to gas-phase kinetics, factors affecting the rate
and pathways of soot oxidation have grown to encompass: the presence of surface
oxygenates, aliphatic C-H groups, and other heteroatoms in the carbon matrix [20–
27], pore size distribution [22,28–30], aggregate morphology and fragmentation [31–
34], the size, curvature, and stacking of carbon planes [11, 35–37], and degree of
amorphousness [38]. As one longtime researcher of soot phenomena recently noted,
”The mechanism [of soot oxidation] appears to be complex, perhaps even more so
than that of soot growth” [39]. The present work hopes to help untangle the skein
of factors affecting soot oxidation and gain deeper insight into the phenomenon.
4
Chapter 2: Literature Review
2.1 Soot Oxidation
Studies of soot oxidation have been summarized in the reviews of Howard [40]
Kennedy [41], and Stanmore [30]. Soot oxidation in flames has been found to be
dominated by molecular oxygen, O2, and the hydroxyl radical, OH. Contributions
by other oxidizers including O, CO2, H2O, and NO have generally been observed to
be minor, although a recent study by Frenklach et al. [39] suggests a greater role
for oxidation by O.
2.1.1 Oxidation by O2
One of the earliest studies to isolate the oxidation of carbon by O2 was that
of Nagle and Strickland-Constable (NSC) [42]. The study measured the removal of
carbon from a heated pyrographite rod by an impinging oxygen jet. The resulting
semi-empirical model defined two types of active sites on the carbon surface with
different reactivities. The model was first order in O2 partial pressure at low oxygen
concentrations but approached zeroth order at high O2 partial pressures. Despite
little experimental resemblance to flame conditions, the NSC correlation remains a
5
widely-used model, and has become a benchmark against which new experimental
oxidation results are compared (e.g., [11, 43–46].
Another popular model of oxidation by O2 comes from Lee et al. [47] who
measured oxidation in the lean regions of a hydrocarbon diffusion flame. Unlike
NSC, their results showed a first-order dependence on O2 partial pressure. The
study did not account for oxidation by other species such as OH, or O and was
limited to a narrow range of O2 partial pressures.
Park and Appelton [48] performed shock tube measurements which generally
agreed with NSC between 1500 - 2000 K, however above 2000 K, oxidation was
underpredicted by the NSC expression. The study required short test times and
considered temperatures much higher than those of a typical flame. Roth et al. [49]
also performed shock tube experiments and obtained results comparable to Park
and Appelton.
At lower temperatures, Chan et al. [50] measured O2 oxidation between 770-
1250 K in both a post flame region similar to Lee et al., and with thermogravimetric
analysis (TGA). Their results generally agreed with Lee et al. and showed first order
O2 dependence. Neeft et al. [29] flowed oxygen over fixed-temperature (near 775 K)
beds of Printex-U and diesel soot and measured the carbon mass loss rate. They
found a reaction order in O2 partial pressure between 0.76–0.94 that depended on
the degree of burnout and sample type.
Flow reactors in combination with mobility analysis has been another tech-
nique more recently employed. Higgins et al. [51] and Ma et al. [52] extracted soot
from an ethylene coflow diffusion flame and measured the change in mobility di-
6
ameter of size-selected particles as they passed through an oxygen-filled reactor.
In both studies, the apparent kinetic rate parameters depended on the size of the
soot particles. Although a definitive reason for this could not be established, the
authors offered various possibilities including different effective densities, different
particle compositions, or different surface areas due to primary particle sintering.
More recently, Camacho et al. [53] used a similar configuration to study the O2 oxi-
dation of nascent soot. They observed oxidation rates an order of magnitude higher
than those predicted by NSC, and attributed this to the difference in nascent soot’s
structure and higher concentration of active sites as compared to mature soot.
Some researchers have noted the dependence of O2 soot oxidation rates on
soot nanostructure. Vander Wal and Tomasek [11] synthesized soot from benzene,
acetylene, and ethanol in a tube furnace, and then oxidized it in in the post flame
region of a fuel lean methane/air flame on a McKenna burner. They attributed dif-
ferent oxidation rates among the three soot types to their differing nanostructures.
The oxidation rates exceeded those predicted by NSC by as much as a factor of 5,
although the researchers ignored any oxidation by OH, assuming its concentration
was negligible due to the fuel lean condition. Song and co-workers [54] went fur-
ther and derived an empirical modification to the pre-factor in the NSC model that
was a function of fringe lengths measured from HRTEM soot images. The mathe-
matical form of the empirical factor has no physical significance, and its numerical
values have limited utility outside of the specific study from which it was derived.
Nonetheless, the work serves as a proof-of-concept as to how nanostructure can be
taken into consideration in predicting soot oxidation rates.
7
2.1.2 Oxidation by OH
In many cases, especially in fuel rich flames, OH is the principal soot ox-
idizer. Studies of soot oxidation by OH are fewer in number than those of O2,
most likely because quantifying the short-lived radical is notoriously difficult. Most
studies that have measured OH in sooting flames have used laser-induced fluores-
cence (LIF) [55–58], although others have used absorption spectroscopy [59], or
Li atom absorption [60–62]. Another approach has been to forgo direct measure-
ment altogether and infer OH concentrations based on partial equilibrium assump-
tions [43,63,64], full equilibrium [65], or some other kinetic model [49]. All of these
methods carry substantial uncertainties.
Owing to its high reactivity, the activation energy of OH with soot is generally
considered to be zero. This was supported recently in a comprehensive review of
experiments investigating OH oxidation of soot [46]. Consequently, the oxidation
rate by OH is typically expressed as a temperature-independent collision efficiency,
denoted ηOH . Fenimore and Jones [66] were the first to measure oxidation by OH.
They used a two-stage burner where soot generated in a rich premixed ethylene
flame was oxidized in a secondary lean hydrogen premixed flame. They reported
a collision efficiency of 0.1. The most commonly used collision efficiency is that of
Neoh et al. [43], who also used a premixed two-stage burner configuration. They
subtracted the O2 oxidation rate as predicted by the mechanism of NSC from the
total oxidation rate and attributed the balance to OH, whose concentrations were
calculated from partial equilibrium considerations. Flame velocities were not mea-
8
sured and oxidation was measured across a height of only 5 mm. In addition, soot
deposition prevented longer-term observations of steady flames. They measured a
collision efficiency of 0.27 when using an apparent optical diameter of the soot aggre-
gates and 0.13 when the actual particle size as determined by transmission electron
microscopy (TEM) was used.
Oxidation of soot by OH was investigated by Roth and co-workers [49] in shock
tube experiments in which soot particles were suspended in mixtures of O2/H2/Ar
gas. The group used time-resolved CO and CO2 measurements to infer the progress
of soot oxidation and in situ laser extinction to determine particle size and number
density. Combined with OH concentrations computed from the kinetic model of
Warnatz [67], the group found a collision efficiency ranging from 0.13 to 0.34 de-
pending on the gas phase mixture used, and an overall mean of 0.21. The group
concluded that these results principally agreed with the observations of Fenimore
and Jones [66] and Neoh et al. [43], despite being higher and more widely scattered.
Oxidation by OH was also examined in a number of studies in laminar hy-
drocarbon diffusion flames at atmospheric pressure [56, 60, 68–70]. Though largely
supporting the OH findings by Neoh et al. and the O2 findings by NSC, the range
of collision efficiencies was wide both within and among these studies, ranging from
0.01 to 0.38, with many authors suggesting that particle reactivity and/or density
of active sites changed with time. Studies by Kim and coworkers [61, 62] examined
oxidation over pressures ranging from 0.1 - 8.0 atm, and found the OH collision
efficiency to be nearly independent of pressure. Table 2.1 lists the OH collision
efficiencies reported in all the known experimental studies of soot oxidation by OH.
9
Table 2.1: Summary of literature reporting OH collision efficiencies with soot, under
various experimental conditions.
Study Condition ηOH
Fenimore and Jones, 1967 [66] premixed flame 0.1
Mulcahy and Young, 1975 [71] graphite in low temp flow reactor 0.04 - 0.08
Neoh, 1980 [43] premixed flame 0.13
Garo et al., 1990 [68] diffusion flame 0.01 - 0.1
Roth et al., 1991 [49] shock tube 0.13 - 0.34
Puri, et al., 1994, 1995 [69,70] diffusion flame 0.03 - 0.38
Haudiquert, et al., 1997 [56] diffusion flame 0.01 - 0.11
Xu, et al., 2003 [60] diffusion flame 0.14
Kim, et al., 2004 [61] diffusion flame 0.13
Kim, et al., 2004 [61] diffusion and partially premixed flames 0.12
Guo, et al., 2016 [46] meta-analysis of past experiments 0.10
2.1.3 Oxidation Model
Kinetic models of soot oxidation are often reported in the following form:
rox = SmCSk(T )f(pO , pOH, ...) (2.1)2
where rox is the oxidation rate per unit mass of soot, Sm is the specific surface area,
CS is the surface concentration of active sites, k(T ), is a temperature dependent
reaction rate usually in an Arrhenius form, and f(pO , pOH, . . .) is a function de-2
scribing the dependence of the reaction rate on the partial pressures on the various
reactants. It is clear from this expression that knowing the available surface area
and active site concentration at a given moment is just as important as choosing
the correct Arrhenius parameters in predicting oxidative behavior.
As oxidation proceeds, the change in the available mass specific surface area,
10
Sm, is most simply expressed as a function of the conversion, ξ, or the fraction of
the original amount of carbon which has been oxidized:
Sm = Sm,0(1− ξ)x (2.2)
Here Sm,0 is the initial specific surface area (i.e. when ξ = 0) and x is the reaction
order in carbon. The simplest application of the above expression is what is variously
referred to as the shrinking sphere or shrinking core model for which the value of x is
2/3. (A value of 1/3 is used if consumed material is computed using diameter rather
than surface area). The model assumes all oxidation occurs on the smooth outer
surface of spherical particles of constant density which shrink isotropically. This
model has been used to derive oxidation rates by several groups (e.g. [11, 51, 72]).
However, apart from some notable exceptions [29, 73], most studies to evaluate
this model, have observed effects such as surface porosity and burning from the
interior of the particle outward, that cannot be accounted for by the shrinking
sphere model [22,23,28,74,75].
A more nuanced approach considers three regimes of soot oxidation: full pene-
tration of the oxidizer into soot pores resulting in reactions on all surfaces (regime I),
partial penetration and internal burning by the oxidizer (regime II), and reactions
only at the outer surface of the soot particles (regime III). The circumstances under
which each of these regimes applies has been the subject of some debate. Stanmore
et al. [30] found that a regime II situation applied to a study oxidizing diesel soot
in a 500◦C dry-air furnace [76]. Ma et al. [52] studied soot oxidation by O2 in a flow
reactor from 600 - 900◦C and found a regime change from I to II above about 675◦C.
11
On the other hand, several groups have suggested that internal burning (regime I) is
present at significantly higher temperatures (T=1500◦C) [77,78]. The above studies
also discussed additional factors affecting specific surface area, including the opening
of occluded pore space after removal of surface layers and the reduction of surface
area due to sintering of primary particles.
2.2 Soot Morphology
Soot morphology affects a wide array of properties including light scattering,
absorption, and radiation [79–84], particle mobility [85–88], and reactive surface
availability [89–92]. It comes as no surprise then that the structure of soot and
its measurement methods have been the topic of considerable research for many
decades.
2.2.1 Aggregates
The fractal description of aerosols formed by diffusion limited cluster aggrega-
tion, such as soot, was first introduced in 1979 by Forrest and Wittan [93]. Fractal
aggregates are scale-invariant and can be mathematically described by the relation-
ship: ( )D
R fg
Np,a = kf (2.3)
rp
where Np,a is the number of primary particles per aggregate, kf is the fractal pre-
factor, Rg is the radius of gyration of the aggregate, rp is the mean primary particle
radius, and Df is the fractal dimension of the aggregate.
12
2.2.1.1 Aggregate Measurement Methods: Non-TEM
Researchers have employed a variety of methods to measure the terms found
in expression 2.3 above. Angular light scattering has seen widespread use and has
the major advantages of being unobtrusive and able to be performed in-situ [43,
94–97]. A disadvantage is that it requires optical access to the flame, which is not
always available in combustion environments of interest. In addition, light scattering
measurements are affected by the distribution of primary particle and aggregate sizes
as well as fractal dimension [98]. Mobility analysis is an increasingly common aerosol
measurement approach, especially within the last decade [52, 53, 86, 99–102]. A
major advantage of this method is that freshly generated flame soot can be sampled,
processed, and analyzed continuously in a single in-line system. The downside is
that the technique only directly measures the mobility diameter of a soot particle.
Mobility measurements are related to other morphological parameters of interest
by empirical expressions that require assumptions about the dispersity of primary
particle sizes, and degree of sintering [103]. In addition, mobility measurements
must be coupled with primary particle measurements obtained from an alternative
technique (e.g. TEM) to accurately estimate soot surface area; (see for example
Refs [52, 88]).
For studies of oxidation, soot surface area is the structural quantity of great-
est interest since the heterogeneous reaction is mediated by the particulate surface.
Gas adsorption techniques are commonly employed to measure soot specific surface
area as well as surface porosity. The Brunauer-Emmett-Teller (BET) method [104]
13
has been used extensively [76, 77, 105, 106]; thermogravimetric analysis (TGA) less
so [107–109]. BET is the more accurate of the two but requires soot quantities
in excess of 100 mg, while TGA requires substantially less (∼30 mg) [107]. Still,
collecting even this smaller amount is often impractical in many combustion en-
vironments, especially for experiments examining oxidation where soot burnout is
expected.
2.2.1.2 Aggregate Measurement Methods: TEM
The use of transmission electron microscopy (TEM) to quantify soot morpho-
logical details was spurred forward by Dobbins and Megaridis who pioneered the
technique of thermophoretic sampling of soot directly from a flame onto a copper
TEM grid [110]. Thermophoretic deposition is driven by the temperature gradient
between the hot soot-laden gases and the relatively cold surface presented by the
probe carrying the TEM grid. Contact with the cold probe effectively freezes the
chemistry of the soot particles. The probe must remain in-flame long enough for
sufficient soot deposition to occur, but not so long as to cause significant heating of
the probe. Typical sampling times are on the order of 10-100 ms. Sample grids are
then imaged using TEM.
In many cases, TEM is the preferred method for measuring soot morphology,
as it allows features to be directly assessed from the soot aggregate images. However,
since TEM images are 2-dimensional projections, techniques are required to extract
the desired 3-dimensional characteristics. From both theoretical considerations [111]
14
and experiments using stereo-pair imaging and different viewing angles [90,98,112],
the following expression, first proposed by Medalia and Heckman [113], relates the
number of primary particles in an aggregate, Np,a, and the aggregate’s projected
area Aa: ( )α
Aa
Np,a = ka (2.4)
Ap
The term Ap is the projected area of a primary particle of mean diameter. The
projected area pre-factor, ka and projected area exponent α are empirically derived
either from simulation or experiment. For soot, values in the literature for ka range
from 1.0 - 1.44, while α ranges from 1.08 - 1.15 [90,96,98,112,114–116].
Recently, Moran et al. [117] performed simulations of soot aggregates com-
prised of polydisperse primary particles and found that Eq. 2.4 is more accurate
when Ap is replaced with cross-sectional area of a particle of average surface area.
Since the latter is larger than Ap, this implies that using Ap in Eq. 2.4 will overes-
timate Np,a. However, this finding is in direct conflict with another recent study of
simulated aggregates by Martos et al. [116], which found that Np,a was consistently
underpredicted when literature values for the parameters in Eq. 2.4 were used. This
led them to suggest a higher value for α than is common. Notably, Martos and
co-workers did not consider the effect of polydispersity. Nonetheless, the lack of
consensus for how Eq. 2.4 should be adjusted leads the current author to apply it
in its unaltered form.
Several methods have been put forth for determining an aggregate’s radius of
gyration from its TEM projection. The 2-dimensional radius of gyration, Rg,2D can
15
Figure 2.1: Morphological measurements commonly performed on binary soot ag-
gregate images: Projected area, Aa, maximum projected length, L, and maximum
projected width normal to L, W .
be computed directly from a binary aggregate image, such as that shown in Fig. 2.1
using: √√√√ 1 ∑NpxR = r2g,2D px,i (2.5)Npx i=1
where rpx,i is the distance between the i
th pixel and the aggregate centroid, and Npx
is the number of pixels in the aggregate. Several authors have uncritically assumed
an equivalence of Rg,2D with Rg [81, 118]. However this has been demonstrated to
be an poor assumption. Using simulated aggregates, Köylü et al. [90] found Rg
to be greater than Rg,2D by a factor of 1.24. Similarly, simulations by Martos et
al. [116] suggested the relationship: Rg = R
B
g,2D + ARg,2D, where A = 3.73 × 10−5
and B = 2.79.
As an alternative characteristic length, several authors have suggested using
the geometric mean of L, the aggregate’s maximum projected length, and W , the
16
√
maximum projected width normal to L, (i.e. LW ) [90, 119, 120]. This could
be directly substituted for Rg in Eq. 2.3. In principal, this would not affect the
derived value of Df , only the pre-factor, which would then be designated KLW .
√
Alternatively, LW could be related back to Rg with the relationship suggested by
Köylü et al. [90]:
√
LW
Rg = (2.6)
β
where β is a constant equal to 2.34. However, caution should be exercised in the
application of the above equation, since β is not truly constant, but has a compli-
cated dependence on both the aggregate fractal dimension and number of primary
particles [90,121].
The final approach to deriving an aggregate’s radius of gyration requires mea-
suring only the maximum projected length, L, from the TEM image. Both experi-
mental [90,122] and numerical studies [111,114,117,121] have indicated that Rg can
be inferred from L using:
L
Rg = (2.7)
2C
Although the empirical constant C varies from 1.39 to 1.78 in these papers, C = 1.5
appears to be a consensus value [89, 117,118,123,124]. Köylü et al. [90] found that
the scaling of Rg with L was less sensitive to changes in Np,a than was the scaling
√
of Rg with LW . Similarly, Moran et al. [117] performed simulations of soot that
were polydisperse at both the aggregate and primary particle level, and found that
C remained nearly constant around 1.5 (maximum deviation < 10%) across a wide
range polydispersity levels. A similar maximum deviation around a mean value of
17
C = 1.45 was observed in simulated aggregates of monodisperse primary particles
by Wozniak et al. [121].
Regardless of the method used to obtain Rg, once it and Np,a have been calcu-
lated for a large number of aggregates, the fractal dimension and pre-factor in Eq. 2.3
can be obtained by applying a least-squares fit to a plot of ln(Np,a) vs. ln(Rg/rp),
where Df corresponds to the slope, and the intercept corresponds to ln(kf ). Values
of Df for combustion soot as determined by this method have ranged from 1.47
to 1.93 [96, 98, 112, 115, 118, 123, 125–127], which encompasses the theoretical value
of 1.78 for diffusion limited cluster aggregation [103]. It should be noted that this
method does not determine the fractal parameters for individual aggregates, but
rather yields a global fractal dimension and pre-factor for an entire sample.
2.2.2 Primary Particles
2.2.2.1 Primary Particle Size Distribution
Accurate knowledge of the size distribution of the primary particles that make
up soot aggregates is critical to quantifying a wide range of aerosol properties. Pri-
mary particle size is needed to derive optical properties from Rayleigh–Debye–Gans
fractal aggregate theory [79–81], and charging efficiency in electrical mobility anal-
ysis depends on primary particle size [85, 88]. Morphological properties, such as
fractal dimension, surface area, and volume, also depend on primary particle size
distribution [89,90,128].
Manual analysis of TEM images is the most common method for measuring
18
primary particle size, and the results are often used to calibrate or validate other
measurements. De Iuliis et al. [97] employed manual TEM measurements to vali-
date the results of three-angle scattering and extinction. Laser induced incandes-
cence (LII) measurements of primary particle size have often relied on manual TEM
measurements to calibrate [129] or validate results [130, 131]. However, a recent
comparison of TEM and LII primary particle measurements by Kholghy et al. [132]
showed that additional factors such as shielding and bridging of particles due to high
aerosol concentration can complicate validation. Attempts at automating the TEM
measurement process have also relied on manual measurements to calibrate [133] or
validate results [134,135].
Despite its importance, knowledge of the distribution of primary particle sizes
may not be readily available. This may be due to small sample sizes resulting
from he manual nature of the TEM measurement (see for example [98, 112]), or
because other methods (e.g. mobility analysis) were used instead. In these cases,
simplifications such as monodisperse primary particles in single point contact with
one another are common [49,52,61,62,119,136–138]. However, when measured, the
distribution of soot primary particles has generally been found to approach either
a normal [22,115,118,127,138–140] or lognormal [97,119,130,133,134] distribution.
Not accounting for this polydispersity can greatly alter surface area estimates [141,
142].
19
2.2.2.2 Sintering and Overlap of Primary Particles
Likewise, in most combustion environments, substantial sintering, or overlap,
between primary particles makes the point-contact assumption difficult to justify.
This can have a substantial impact on the estimation of surface area and aggregate
fractal parameters. Neoh and coworkers observed that assuming single-point contact
between primary particles overestimated the total surface area by 60% as compared
to the BET external surface area [77]. Using simulated aggregates, Oh and Sorensen
found that both fractal dimension (Df ) and prefactor (kf ) increased with the degree
of primary particle overlap [111]. Lapuerta et al. [143], similarly saw a significant
increase in kf as overlap increased in simulated aggregates, but at the same time
found Df to decrease. Johnsson et al. [144] showed that not accounting for overlap
could result in as much as a 51% overestimation of primary particle size derived from
LII measurements. Simulations by Yon et al. [145] demonstrated that scattering and
absorption properties of soot are significantly affected by primary particle overlap.
To account for the effect of primary particle overlap in extracting morphology
from TEM images, Brasil et al. [114] introduced a parameter Cov,p, which they
termed the projected image overlap coefficient and defined it:
dp − dij
Cov,p = (2.8)
dp
The term dij is the distance between primary particles i and j, and dp is their
average diameter. Unfortunately, a 2D TEM image cannot distinguish between
partially sintered primary particles and those that appear overlapped due to shad-
20
owing by primary particles on a different vertical plane. Using simulated aggregates
with monodisperse primary particles and a fractal dimension of 1.78, Brasil and
co-workers established the following relationship between the projected overlap and
the true three dimensional particle overlap Cov:
Cov = ζ1Cov,p − ζ2 (2.9)
Values of ζ1 = 1.1 ± 0.1 and ζ2 = 0.2 ± 0.02 were shown to hold for Cov values
between 0 and 0.33. Wozniak et al. [121] arrived at the same linear relationship
from their own simulations, with similar regression constants of ζ1 = 1.27±0.01 and
ζ2 = 0.27± 0.01.
To find the true aggregate surface area accounting for overlap, Sa, Brasil et
al. [114] suggested the following correction to the surface area with no overlap, Sa,0:
Sa = [1− φSCov(1− 1/Np,a)]Sa,0 (2.10)
where a value of φS = 1.3 comes from a fit of the group’s simulation results. Gwaze
and coworkers [115] employed the method of Brasil et al. on soot aggregates from
wood combustion. While the results were reasonable, they were not validated against
other techniques. Bau et al. [89] also applied the method to estimate the surface
areas of various solid oxide nanoparticles and found good agreement with BET
values.
2.2.2.3 Attempts to Automate Primary Particle Measurement
Given the large number of measurements needed to quantify morphological
properties with statistical significance, and the laborious nature of manually obtain-
21
ing them, there is a strong incentive to automate the TEM measurement process.
Most attempts at automating measurement of primary particles have followed one
of two approaches. The first is built around the Hough Transform [146], a well-
known algorithm that identifies pre-defined geometries, such as a line or circle, by
the strength of features in a parameter space. Grishin et al. [134] were the first to
apply the Circular Hough Transform (CHT) to fractal aggregates. Because the algo-
rithm relies on accurate edge detection, primary particle detection was restricted to
the perimeter of a binarized aggregate image. Other studies [135,147], extended the
technique to interrogate the interior of an aggregate using a combination of image
self-subtraction and Canny edge detection [148]. Canny edge detection is known
for its ability to detect weak edges and is therefore thought to be well-suited to
discerning primary particles in the interior of a soot aggregate. A drawback of the
CHT approach is that it requires accurate pre-knowledge of several input param-
eters, including the range of primary particle diameters and the CHT sensitivity
level.
The second automation method is based upon Euclidean distance mapping
(EDM) of a binarized aggregate image [133,149]. EDM is a technique whereby pixels
within a binarized image object are assigned grayscale intensities corresponding to
their distance from the object’s nearest edge. The procedure outlined by Bescond
et al. [133] involves thresholding the EDM image of an aggregate at a specific pixel
intensity, then inverting and repeating the EDM-threshold sequence. Repeating this
process across all possible threshold levels, a sigmoidal function emerges relating the
number of white pixels remaining after processing, to threshold value. Following
22
calibration, this can be translated into a primary particle size distribution function.
The EDM approach has the advantage of not requiring an assumed geometry
or size range for detection. However, its results must be calibrated against manual
TEM measurements, and the shape of the size distribution must be assumed. Addi-
tionally, one must assume that the calibration holds across samples with potentially
dissimilar morphologies.
2.2.3 Uncertainty of TEM Morphological Measurements
Despite its importance and use as a calibration/validation source, uncertain-
ties associated with manual TEM soot measurements have received little attention.
If reported at all, the standard uncertainty of the mean primary particle diameter is
typically < 3% and represents the standard deviation of the mean of a single mea-
surement replicate by a single operator on a single sample (e.g., [22,119,126,133]).
A study by Kondo, Aizawa, Kook, & Pickett [150] observed that different operators,
especially those with less experience, were the greatest source of fluctuation among
primary particle measurements. However, to date there has been no formal attempt
to quantify the uncertainty of TEM soot measurements resulting from different op-
erators, samples, and measurement replicates. In addition, opportunities for bias
are introduced at nearly every stage of the measurement process. These include bias
in choosing which regions of the TEM grid to investigate, which aggregates to image
from those regions, which images to select for measurement, which image areas and
primary particles to consider, and how to best interpret the size of a given primary
23
particle. With a few exceptions [25, 121, 151, 152], studies rarely employ safeguards
against operator bias.
2.3 Soot Fragmentation
More recently, increasing attention has been given to soot fragmentation as a
controlling step in the prediction of soot burnout and particle size distributions [32].
While oxidation is the general process by which carbon atoms are subtracted from
soot particles, fragmentation refers to the breakup of aggregates into smaller pieces.
It is generally hypothesized that fragmentation is the result of oxidation by O2 either
at the narrow bridging between primary particles or within the primaries where
internal burning increases porosity and eventually breaks the particle apart [153].
Oxidation-induced soot fragmentation was first experimentally observed in the
2-stage burner studied by Neoh et al. [77]. Soot and exhaust gases generated by
a CH4-O2 premixed flame were mixed with a secondary stream of O2 and then
oxidized in a flat flame burner. Overall equivalence ratios were controlled by the
amount of secondary gas supplied. Measurements were performed using light scat-
tering and absorption techniques. They found that in fuel-lean and slightly fuel-rich
flames, soot number concentrations increased as oxidation progressed, while they
remained constant in more fuel-rich flames. They concluded that internal burning
by the additional O2 in leaner flames resulted in breakup of aggregates at points of
structural weakness. More recently, Echavarria et al. [78] and Ghiassi et al. [153]
used an experimental configuration similar to Ref. [77] to study soot fragmentation.
24
Measurements were made using a scanning mobility particle sizer (SMPS), and
a condensation particle counter (CPC) coupled to a differential mobility analyzer
(DMA). Like Neoh and coworkers, the results of Echavarria’s group linked increased
fragmentation to greater O2 concentration. However, the results of Ghiassi et al.
suggested that reduced temperature was more important to fragmentation than the
amount of oxygen.
For diffusion flames, Garo et al. [68] used light scattering and extinction meth-
ods to measure soot in a CH4-air laminar diffusion flame and observed an increased
number density of soot aggregates near 75% of total soot burnout. Noting that
this effect was more prevalent in regions with higher O2/OH ratios, they concluded
that fragmentation had occurred due to internal burning by molecular oxygen. In a
different study, Zhang and Kook [154] analyzed in-cylinder diesel soot using TEM.
They found that a drop in the radius of gyration of soot aggregates near cylinder
walls was consistent with fragmentation due to flame-wall interactions.
Recent numerical studies have also investigated soot fragmentation. Harris and
Maricq [155] modeled diesel exhaust soot and found that including fragmentation
in the model significantly improved the soot size distribution prediction. Mueller
and co-workers [156] modeled the premixed flames measured in Ref. [77] as well
as the partially premixed counterflow diffusion flames studied in Ref. [157]. The
fragmentation model agreed well with the premixed flame measurements, while no
fragmentation was predicted in the counterflow flame. The authors concluded that
this is because the soot is completely oxidized by OH before reaching O2 rich re-
gions. Counterflow diffusion flames were both measured and modeled by Sirignano
25
et al. [32], who found that fragmentation greatly affects the particle size distribution
by inhibiting coagulation and aggregate growth.
2.4 Soot Nanostructure
2.4.1 Description of Nanostructure
Seeking to explain the wide variability of soot oxidation rates reported in the
literature, much recent research has focused on the role that nanostructure may
play in the rates and modes of soot oxidation. The fine structure of mature soot is
comprised of short segments of layered graphene planes, held together by van der
Waals forces [41, 158, 159], and often seen grouped into short stacks, referred to as
crystallites. The stacked carbon layers are randomly rotated with respect to each
other along the c-axis (the axis normal to the layered planes), an arrangement re-
ferred to as turbostratic [76,160–163]. This contrasts with polycrystalline graphite,
whose layered planes are aligned with respect to each other. This results in a much
closer interlayer d002 spacing for graphite (3.354 Å), than for soot which typically
ranges from 3.5 Å- 3.9 Å [76, 161, 162, 164–170]. An illustration of this interlayer
spacing within crystalline graphite is shown in Fig.2.2(a).
The crystallites within a soot primary particle are typically arranged in a
core-shell structure. The central core, a region approximately 4-6 nm in diame-
ter [158, 171], contains randomly oriented crystallites as well as more amorphous
material, while the outer shell is comprised of crystallites whose layered planes
are often preferentially oriented perpendicular to the radius of the primary par-
26
Figure 2.2: Structure of a crystalline graphite. The unit cell (shaded region) is
defined by the primitive vectors a, b, and c, where a = b in the case of a hexagonal
structure. The c vector is twice the interlayer spacing because the ABA layering
of graphite requires 3 planes to define the unit cell. (a) A 3-dimensional crystallite
with interlayer spacing d002. In a turbostratic configuration, layered planes will be
rotated randomly about the c-axis and d002 will be greater than that of graphite. (b)
A single layered plane showing lattice spacings between the (110) and (100) Bragg
planes.
ticle [119, 158, 161, 162, 166, 172, 173]. This preference tends to become more pro-
nounced with increasing radial distance [174, 175]. Curvature of the carbon layer
planes, arising from five- and seven-membered rings within the aromatic matrix, is
also a nanostructure feature of interest, and some have observed curvature to in-
crease near the primary particle core [11]. Additional carbon material, not organized
into any periodic structure, may also be present, helping to partially adjoin neigh-
boring crystallites [176]. Discontinuities and misalignments between layers produce
microporous voids which can substantially increase the surface area of a primary par-
ticle above that of a smooth surface [177]. Opening of these pores during oxidation
can further increase the specific surface area beyond the smooth-surface model [76].
27
The nanostructural features of flame-generated soot are the result of a com-
plicated process of soot formation that begins with the first appearance of polyaro-
matic hydrocarbons (PAH) clusters. These PAHs grow by various pathways such
as hydrogen abstraction carbon addition (HACA) [178, 179], and form nucleated
particles of nascent soot which further grow through surface reactions, PAH con-
densation and particle coalescence [18]. In the high temperatures of the flame, the
nascent soot sheds hydrogen, and the carbon layer planes further carbonize and form
graphitic crystallites [162,180]. The resulting carbonized primary particles are con-
joined within larger aggregates and are what is referred to as ”mature” soot [181].
It is generally thought that once carbonization has occurred, the carbon layers are
no longer able to reorganize at ordinary flame temperatures (<1800 ‰), and the
nanostructure is essentially ”locked in” [182]. As such, the mature soot nanostruc-
ture reflects the nucleation and growth environment.
2.4.2 Dependence on Heat Treatment and Fuel Type
Within this general picture there is substantial variability in soot nanostruc-
ture that depends primarily on the thermal history of the particles and to a lesser
degree, on fuel type. Various studies have demonstrated that thermal annealing of
soots and carbon blacks, through heat treatment, reduces plane defects and pro-
motes carbon plane layer growth. This latter structural change is most commonly
referred to as graphitization [162,164,183]. As the temperature of the heat treatment
increases, relative alignment between carbon layers improves, resulting in interlayer
28
spacings that decrease toward that of graphite [160,184]. Higher temperatures also
cause crystallites to grow both in the size of their carbon layer planes and in the num-
ber of stacked layers [183]. Importantly, these thermally-induced structural changes
are present even at the sub-microsecond time scales relevant to soot formation and
oxidation in flames [185–187].
Fuel type has also been shown to affect soot nanostructure. Vander Wal et
al. [182] found that fuel type influenced the curvature of the carbon layer planes,
an effect that could be enhanced or suppressed depending on the temperature and
duration of heat treatment. Alfé et al. [24] observed that cycloalkanes and aro-
matic fuels produced soot with a more ordered nanostructure than that produced
by straight alkanes and ethylene. Lapuerta et al. [25] observed that the nanostruc-
ture of biodiesel soot exhibited greater order and a higher degree of graphitization
than diesel soot produced under the same conditions. Apicella et al. [188] found
that the carbon layer planes in soot from a methane flame were much smaller than
what is typically found in ethylene and benzene flame soot [170].
2.4.3 Nanostructure Diagnostic Methods
2.4.3.1 Non-TEM Methods
A wide array of diagnostic techniques can be used to extract nanostruc-
tural features of soot. X-ray diffraction (XRD) is one of the most commonly used
tools [23, 76, 160, 164, 167, 173, 189]. Using the positions and widths of peaks in an
XRD pattern, one can estimate the average crystallite interlayer (d002) spacing, lay-
29
ered plane diameter, La, and stacking height, Lc [173]. Similar information can be
obtained from Raman spectroscopy. Here the intensity ratio of spectral bands corre-
sponding to graphitic and defect structures (G band and D bands, respectively), can
be used to estimate La [190–193], as well as provide information about the degree
of graphitic ordering within a specimen [22,25,27,189,194].
Other methods gage the degree of graphitization by probing the carbon bond-
ing states. X-ray photoelectron spectroscopy (XPS) is used to measure the relative
prevalence of carbon hybridization states sp2 and sp3. The former bonding state
is indicative of graphitic content while the latter is generally interpreted as de-
fect sites within the graphitic network [73, 74, 195–197]. Likewise, electron energy
loss spectroscopy (EELS) can assess graphitization based on the different energy
losses of electrons passing through the sample, indicative of sp2 versus sp3 hybridiza-
tion [37,76,188,195,198]. A similar task can be performed using Fourier Transform
infrared spectroscopy (FTIR) on the basis of absorption by C=C bonds as opposed
to hydrogenated or oxygenated bonds [76,199,200].
2.4.3.2 Selected-Area Electron Diffraction (SAED)
As with morphology, TEM imaging is indispensable for revealing information
about soot nanostructure. Different information may be obtained by operating the
instrument in either diffraction mode, or in high resolution mode (HRTEM). In
diffraction analysis, the incoming electron beam is thought of as a plane wave whose
wavelength, λe, is the electron DeBroglie wavelength, which is a function of the
30
beam energy. The wave is elastically scattered by the atoms in the specimen. If
the specimen possesses atomic planes at regular spacings, dhkl, and the polar angle
between the beam and the plane is at θB, satisfying the Bragg condition,
2dhkl sin θB = nλe (2.11)
where n is an integer, then waves re-scattered at θB, (the Bragg angle), will con-
structively interfere. In polycrystalline materials such as soots and carbon blacks,
crystallites are oriented randomly with respect to the incoming electron beam. This
ensures many crystalline domains will be oriented at the correct polar angle with re-
spect to the beam to produce constructive interference. The random orientation will
also ensure that the re-scattered waves will emanate equally over all 2π azimuthal
angles from the specimen. The diffracted waves will trace out a cone in space and
arrive in a ringed pattern at the TEM projection plane. The distance from the spec-
imen to the projection plane is referred to as the camera length. The relationship
between the cone half-angle 2θB, the camera length Lcam, and the diffraction ring
radius R at the projection plane is
R
tan 2θB = (2.12)
Lcam
Combining Eq. 2.11 & 2.12, and assuming R Lcam, yields
λeLcam
dhkl = (2.13)
R
The d-spacing, dhkl, is the distance between the Bragg planes specified by Miller
indices hkl, which identify the direction normal to the plane with respect to the
unit cell of the crystal lattice. If Lcam is known from calibration of a specimen
31
with known lattice spacings, the d-spacings of an unknown specimen are readily
determined by measuring R from the diffraction image. The d-spacings d002, d100,
and d110 illustrated in Fig. 2.2 produce the most prominent rings in typical soot
specimens.
In the technique of selected area electron diffraction (SAED), only the portion
of the specimen that is visible through the selected area aperture (also called a field-
limiting aperture) contributes to the diffraction pattern. In the case of soot, one
can probe the crystalline structure within an area as small as a single primary parti-
cle. The average spacing between various Bragg planes is easily measured from the
diffraction peaks and can be translated into first- and second-neighbor interatomic
distances of the sp2 carbons [193, 201]. Distance between the (002) basal planes
can be compared to known values of pure graphite (Fig. 2.2) to infer degree of
graphitization [189]. A greater portion of the electron beam will be diffracted with
increasing crystallinity, an effect observable in the integrated intensity of diffrac-
tion peaks [22, 162]. Similarly, diffraction peak broadness reflects the dispersity of
diffracting layer spacings, and hence indicates relative amorphousness of the speci-
men [168,176,201–203]. Broadness of a diffraction peak is typically reported as the
full-width at half maximum (FWHM) of a peak curve, or as the integral breadth,
defined as ratio of the integrated intensity to the peak maximum.
The SAED technique is limited by a number of uncertainties affecting the
terms found in Eq 2.13. The first originates from the energetic variability of the
electrons, which are produced in a TEM by either field emission or thermionic
emission. This variation in energy translates into an wavelength bandwidth that is
32
wider than what is typically seen from X-ray sources [162]. Electromagnetic lenses
used in a TEM can produce elliptical distortions in diffraction rings, making the
camera length non-uniform, and changes in lens currents can also affect the camera
length value [202].
2.4.3.3 High Resolution Transmission Electron Microscopy (HRTEM)
Lattice Fringe Analysis
A commonality among all the nanostructure diagnostic techniques thusfar
mentioned, is that they can only yield specimen-averaged quantities. In contrast,
HRTEM provides nanostructural information that can be spatially resolved across
the projected soot image. This information comes in the form of lattice fringes
formed by the interference between the direct and scattered electron waves. It
should be noted that the structures visible in an HRTEM image of soot are not the
graphene planes themselves, but rather the fringes resulting from this phase con-
trast phenomenon [203]. Adding to the challenge of interpreting HRTEM images
are the irregularities inherent to soot, such as overlapping and curved carbon layers,
amorphous content, and contrast variations [204]. Nonetheless, on-axis lattice fringe
images can provide information about the orientation, spacing, and extent of the
local lattice structure [203]. For over 20 years, researchers have developed methods
to process and extract quantitative structural information from the lattice fringe
images of carbonaceous materials.
All methods of lattice fringe image analysis can be broadly organized into two
33
steps: An image processing procedure that identifies and isolates fringe objects,
and algorithms to meaningfully quantify the size, shape, and arrangement of these
fringes within the carbon nanomaterial. Davis et al. [21] were the first to apply
quantitative lattice fringe analysis to pulverized coal during combustion. After ap-
plying a Fourier transform (FT) filter to remove structures lacking the characteristic
periodicity of turbostratic carbons, the group measured average fringe lengths and
relative amounts of crystalline structure. In the analysis of soot HRTEM images,
Palotas et al. [205] obtained binary images of the fringe structure by similarly apply-
ing a bandpass filter in the frequency domain, followed by a reverse transform and
then thresholding. Measurements including the length, orientation, and circularity
of fringes as well as interplanar spacing were then extracted from the binary images.
Sharma et al. [206] argued that a bandpass filter removed information that
had value but lacked periodicity. Using a step filter in Fourier space, they were able
remove noise while retaining both periodic stacks and non-periodic single layers.
Following an inverse FT, binarization, and skeletonization, an algorithm was applied
that removed Y and T shaped fringe linkages and then reconnected those fringes that
conformed to a set of geometric parameters. Measurements of fringe length, stacking
dimension, and interlayer spacing were obtained. Interlayer spacing calculations
were restricted to fringe pairs within tolerances that included parallelism (±10◦),
and perpendicular distance (0.355 ± 0.025 nm). Shim et al. [175] similarly used a
process involving FT filtering, binarization, skeletonization, linkage separation and
fringe reconnection. Fringes shorter than 1.5 nm were discarded and average fringe
lengths, tortuosity, and apparent crystalline fraction were calculated. They defined
34
tortuosity as the fringe length divided by the diagonal length of a box bounding the
fringe. Additionally, they developed a method to characterize the orientational order
of the lattice fringes. Investigating the nanostructure of carbon particles formed by
laser pyrolysis, Galvez et al. [199] followed a similar process, but applied a top-
hat filter prior to binarization to reduce intensity variations, and threw out fringes
shorter than the size of a single aromatic ring (0.25 nm). They also identified stacked
crystallite structures, so-called basic structural units (BSUs) [207], on the basis of
fringe spacing and similar fringe orientations and tortuosities.
Yehliu et al. [208], provided a very detailed description of their method for
processing and measuring HRTEM images of soot. Following an inversion of the
image grayscale, a region of interest (ROI) around a primary particle was manually
selected. Defining an ROI improved operations that rely on image statistics, such
as contrast enhancement, since areas outside the ROI were not included in the
statistical treatment. After ROI selection, contrast was enhanced, high frequency
noise was attenuated by a Gaussian lowpass filter in the frequency domain, and
uneven illumination was ameliorated through a top-hat filter. After thresholding to
binarize the image, a morphological opening and closing operation was performed in
place of the linkage separation and fringe reconnection steps of previous works [175,
206]. Fringes touching the ROI border were removed, the image was skeletonized,
and fringes shorter than 0.5 nm were eliminated. Following the work of Ref. [209],
distributions of fringe length and tortuosity were automatically calculated while
fringe separation distribution was determined from the manual selection of fringe
pairs in the image. Here, as in most other studies, tortuosity was defined as the
35
fringe length divided by the distance between fringe endpoints.
Several researchers have since followed the process outlined by Yehliu et al. [208],
with or without minor modifications [35,74,118,210,211]. Botero et al. [210], consol-
idated the steps of image inversion and top-hat filtering via a bottom-hat transfor-
mation, and they automated the fringe separation distance calculation while taking
fringe orientations into account. They selected 0.483 nm as the minimum allowable
fringe length as this is the corresponds to the length of two aromatic rings.
Other approaches include those by Wang et al. [212] who applied HRTEM
analysis to coals. Rather than calculating tortuosity, they presented an image anal-
ysis method that measured the individual angles between fringe segments. From
this they produced a distribution not only of fringe lengths, but of fringe curvatures
as an accumulation of individual segment angles. In another approach, Pré and
coworkers [213], attempted to glean surface nanopore information from HRTEM
images of activated carbons. Extending the work of Refs. [199, 207], they merged
nearby BSUs with similar orientations into what they termed continuous domains.
They assumed that the non-organized regions separated from these domains were
probable locations of nanopores, and then correlated the size distributions of spaces
between ensembles of fringes, BSUs, and continuous domains, to the pore size dis-
tributions obtained from Nitrogen adsorption isotherms.
A number of studies have compared measurements obtained from lattice fringe
analysis to those obtained from non-TEM methods. Taken in aggregate, one can
observe several trends. First, unless the range of allowable fringe separation dis-
tances is restricted a priori to the characteristic range of turbostratic carbon (see
36
section 2.4.1)(e.g. by means of an FT filter or calculation window) the fringe sepa-
ration distance obtained from HRTEM images is substantially higher than the d002
lattice spacing given by XRD. This discrepancy serves as a reminder to not confuse
lattice fringes with the carbon layers themselves. Nonetheless, relative differences
in fringe spacings can be used to distinguish between specimens possessing differ-
ent lattice spacings and degrees of graphitization [209, 214]. Generally speaking,
if separations between 0.3 and 0.6 nm are permitted, the fringe separation dis-
tance will follow a symmetric bell-shaped distribution with a mean between 0.38
and 0.45 nm [24, 118, 199, 207, 210, 215]. The 0.6 nm upperbound is often chosen
because van der Waals forces are negligible beyond this distance (see [24, 169, 210].
Additionally, upperbounds below this value can often be seen to truncate the fringe
separation distribution (see for example [209,214]).
Comparison of HRTEM fringe analysis with Raman spectroscopy has shown
mixed results. Sampling soot from premixed benzene and ethylene flames, Apicella
et al. [192] saw excellent agreement between the mean fringe length determined
by Raman spectroscopy and that found by HRTEM lattice fringe analysis. Their
analysis assumed an equivalence between the Raman measured crystallite diameter,
La, and HRTEM fringe length, Lf , an assumption of dubious validity. Parent et
al. [193], also found reasonable agreement in the absolute values of La and Lf in air-
craft soot produced at different engine thrusts, but noted that the two measurement
techniques yielded trends in opposite directions. Studies by Vander Wal et al. [183]
and Yehliu et al. [214] on various soots and carbon blacks did not attempt to ex-
tract crystallite size from Raman measurements. However, they did see a monotonic
37
relationship between the ratio of the graphitic and defect band intensities, and the
mean or median fringe lengths measured by HRTEM. Song et al. [22] also measured
both of these quantities for biodiesel soots. The general trend was similar but not
monotonic.
Various other validations of the HRTEM method are scattered about the liter-
ature. Using XPS, Gaddam et al. [74] found a nearly constant sp2/sp3 ratio during
oxidation of a carbon black, which was consistent with the constant distribution
breadth of fringe length measured by HRTEM. Yehliu et al. [214] observed that
mean fringe separation distance increased with mean tortuosity. They took this
both as evidence that curved structures inhibit stacked layer development and as
validation of their tortuosity measurement method.
2.4.4 Role of Nanostructure in Soot Oxidation
Broadly speaking, soot reactivity increases with nanostructural disorder as
measured by the various techniques outlined in Section 2.4.3 (see, for example,
trends in Refs. [22, 31, 35, 73, 211]). This is because the carbon atoms comprising a
soot particle are not a homogeneous population, but rather participate in a variety
of bonding structures affecting their reactivity. The rates and pathways of soot
oxidation therefore depend on the relative prevalence and accessibility of differently
bound carbons, which in turn is dictated by the nanostructure.
The most important reactivity variation is between the vastly more reac-
tive carbons found on the edges of a layered plane than those lying on the basal
38
plane [216] (see Fig. 2.2). This bifurcation correlates to the empirically derived two-
site model by Nagle and Strickland-Constable discussed in Section 2.1.1. An edge
site carbon has an unpaired sp2 electron, which can facilitate the chemisorption of
oxygen, a critical step in the transformation of soot carbon into a gaseous carbon
oxide [20,216]. Edge sites can also host impurities common in combustion environ-
ments such as Fe, Zn, and Cu that can catalyze the oxidation reaction [20,27]. Sur-
face edge sites are more likely to terminate in oxygenated or hydrogenated groups,
both of which can enhance oxidation rates [22–24,26,217]. Lastly, edge site carbons
are more prone to oxidative attack than basal plan carbons simply by virtue of their
greater physical exposure to the gas phase.
Rosner and Allendorf [218] observed the reactivity of isotropic graphite to
O2 was over 100 times that of pyrolitic graphite, and attributed this to the relative
abundance of edge sites in the former. The reactivity of edge site carbons in graphene
can be 100 - 1000 times that of basal plane carbons [216]. It follows then, that since
the ratio of edge site to basal plane carbons decreases with increasing crystallite
size, the overall soot reactivity should decrease as well.
Other nanostructural features will also increase carbon reactivity above that
of a relatively inert graphene plane. The presence of 5- and 7-membered rings in-
duces curvature in a carbon plane. This curvature creates bond strain, weakening
the C-C bond and effectively reducing the oxidation activation energy [11]. The
carbon planes, nominally sp2 hybridized, will also possess a small admixture of sp3
characterization due to curvature [74, 219]. The presence of sp3 hybridized amor-
phous carbon will also increase reactivity, owing to its lower C-C bond dissociation
39
energies [21, 73,220].
Numerous studies have demonstrated the interdependence between soot nanos-
tructure and oxidation. Ishiguro et al. [76] observed the progressive oxidation of
diesel soot in a dry-air furnace at 500◦C. Comparing BET surface areas with those
measured by TEM, the group found porosity increased by over a factor of 4 as ox-
idation progressed. At the same time, the nanostructure became more ordered by
certain measures. Using XRD, they detected an increase in crystallite size in the
stacking dimension and a decrease in layered plane spacing during oxidation, while
in-plane carbon layer growth was inferred from EELS and FTIR measurements. By
considering the comparative weakness of inter-layer van der Waals forces to the cova-
lent bonds holding edge-site carbons, and in light of the carbon layer plane growth,
the researchers concluded that primary particle mass loss was due primarily to the
stripping of outer shell crystallite segments, rather than the dissociation of carbon
atoms from layer plane edges.
Palotas et al. [165] used HRTEM to analyze the nanostructure of commercial
carbon blacks undergoing oxidation in a TGA at temperatures of 575◦C and 680◦C.
They similarly observed a decrease in interlayer spacing as oxidation progressed,
due mostly to the disappearance of the widest spacings in the distribution. The
standard deviation of interlayer spacings also decreased with oxidation while the
fraction of each primary particle containing crystallite structures increased. They
interpreted all of these results as an increased order in the carbon structure due to
oxidation.
Vander Wal and Tomasek [11] took soot synthesized from benzene, acetylene,
40
and ethanol in a tube furnace, and oxidized it in the 750◦C post flame region of a
McKenna burner. They used HRTEM to measure the different initial nanostructures
of the three soots which then translated into different oxidation rates. Benzene soot
was characterized by short, disordered fringes and few discernible crystallites. It
showed an oxidation rate approximately 5 times that predicted by the NSC model.
They attributed this to the high proportion of edge to basal plane sites in the
short graphene segments. In contrast, acetylene soot displayed long, weakly curved,
concentric lattice fringes and oxidized much more slowly (although still faster than
NSC would predict). This, they concluded, was due to the fewer exposed edge sites
and the minimal bond strain imposed on the basal plane carbons. Lastly, ethanol
soot, which exhibited longer fringes than benzene soot but greater curvature than
acetylene soot, showed an oxidation rate as high as that for the benzene soot. They
concluded that weakly held carbons in the strain-inducing curved planes was the
determining factor in the high reactivity.
Raj et al. [37] compared the oxidation of two different model soots: one com-
posed primarily of planar PAH segments (Printex-U), and one composed mostly of
curved PAHs (Fullerene soot). Using a TGA at air temperatures ranging from 200
- 800◦C and different heating rates, they found the activation energy for the curved
soot to be 26 kJ/mol lower than for the planar soot. This was true in spite of there
being a higher H/C ratio in the planar soot, which normally correlates to higher ox-
idation rates. They interpreted this as showing the dominant role of PAH curvature
in oxidative reactivity. This interpretation was bolstered by quantum chemistry
calculations that demonstrated consistently lower energy barriers for the oxidation
41
pathways of curved PAH than for planar PAH.
Gaddam et al. [74] observed the changing nanostructure of 5 different model
carbons oxidized in a flow reactor (400 - 550◦C) and a TGA (490 - 650◦C). Using
various methods (XPS, HRTEM, BET, and Raman spectroscopy) they tracked how
nanostructural changes impacted the mode and rate of oxidation. The initial nanos-
tructure of R250 carbon black contained loosely concentric fringes of varying lengths
with slightly more disorder near a primary particle’s core. The nanostructure was
largely unchanged by oxidation which proceeded at a nearly constant rate and pro-
gressed outward from the particle’s core. As in Ref. [23], the internal burning mode
was dramatically apparent from the HRTEM images as seen in Fig. 2.3.
Different behavior was observed in arc-
generated soot owing to its largely amor-
phous initial structure. The amorphous
carbon made for fast initial oxidation but
also provided material for oxidation-induced
graphitization, which in turn, slowed oxi-
dation. (Oxidation-induced graphitization
is understood to occur by the removal of
Figure 2.3: HRTEM image show-
cross-links, interstitial atoms such as non- ing internal burning within a primary
particle. (Image From Ref. [74])
sp2 carbon, or strained bonds within the car-
bon matrix. This frees graphene segments to realign and create longer carbon
planes [21, 221, 222]. Radicals produced during oxidation would also serve as sites
for carbon plane growth [222]). M1300 carbon black, on the other hand, showed
42
a highly curved but non-concentric fringe arrangement. Oxidation started at sites
of curvature which then opened into pores, exposing ever greater numbers of reac-
tive edge site carbons producing an exponentially increasing oxidation rate. Lastly,
multi-walled carbon nanotubes and carbon onions, which began with highly graphi-
tized nanostructures, oxidized more slowly than the other model carbons. Oxidation
occurred almost exclusively at edge sites and did little to affect the nanostructure.
The presence of oxygenated functional groups and aliphatic C-H groups on
the soot surface can greatly affect the way nanostructure evolves, especially during
initial oxidation, which in turn impacts oxidation at later stages. Highlighting the
importance of oxygenated surface functional groups, Song et al. [22] compared the
oxidation of biodiesel soot with that of diesel produced by the Fischer-Tropsh pro-
cess (F-T soot). The soot samples were oxidized in a TGA with 500◦C air and were
analyzed with a bevy of techniques including HRTEM, SAED, Raman spectroscopy,
EELS, and FTIR. Biodiesel soot, initially exhibited shrinking sphere oxidation dom-
inated by oxygenated surface functional groups. This gave way to internal burning
made accessible by the opening of micropores while the remaining outer layers un-
derwent oxidation-induced graphitization. By contrast, smaller presence of oxygen
functional groups in F-T soot resulted in slower oxidation and no evidence of inter-
nal burning. The shrinking core model held throughout and there was little change
in fringe lengths or reorganization of the carbon layers as oxidation progressed.
Other studies have shown the effect of surface oxygenates to be less important.
Seong and Boehman [223] characterized soot from a turbocharged diesel engine using
XPS, HRTEM, Raman spectroscopy, and XRD. In contrast to Song et al. [22], they
43
found surface oxygen content to have little impact on oxidation rates. Instead,
reactivity was increased by the presence of metallic compounds from the engine
lubricant, and also possibly by increasing nanostructural disorder. Wang et al. [26]
similarly found oxygenated surface functional groups to be much less important to
the reactivity of in-cylinder diesel soot than aliphatic C–H surface functional groups.
There is scarce literature exploring the link between soot oxidation and nanos-
tructure in actual flames. Notwithstanding the work of Vander Wal and Tomasek [11],
the papers surveyed here thus far, all oxidized soot in furnaces, TGA’s, or flow re-
actors at colder temperatures and longer times than are found in flames. Moreover,
the only oxidizer considered has been O2. This is a major gap in the literature. Two
very recent studies by Li et al. [118] and Botero et al. [215] tracked the evolution
of soot within co-flow diffusion flames of varying fuels. Observations of oxidation
effects were limited to regions near the flame tip where soot growth no longer dom-
inated. Li and coworkers saw a slight increase in fringe length near the flame tip
but offered no explanation. In this region, tortuosity increased due to the oxidation
of straighter outer layers, which left behind a less-ordered core. Fringe separation
distance was seen to fluctuate throughout the flame, for which several reasons were
given, none as convincing to the present author as simple statistical variation.
In addition to measuring at different flame locations, Botero et al. [215] ana-
lyzed fringe structure at various radial locations within the primary particles. Once
nascent particles had begun to coalesce and show surface growth, fringe length con-
sistently increased and tortuosity decreased with radial location, indicating graphi-
tization as the soot matured, even as oxidation began to dominate. Near the tip
44
of the flame, oxidation was concentrated on the particle surface. Fringe length and
fringe stacking decreased, and fringe separation distance increased, but this was
predominantly limited to the outer shell of the primary particles. Near the core, a
slight decrease in tortuosity and increase in fringe stacking was observable, which the
authors interpreted as evidence of heat-induced graphitization. Interestingly, else-
where in the flame, the authors found that the nanostructure in the core changed
very little, suggesting molecular immobility in this region.
45
Chapter 3: Experimental Methods
3.1 Ternary Flame System
Measurements were performed in the
ternary flame system shown in Fig. 3.1.
Here, a column of soot generated by a propy-
lene/air co-flowing diffusion flame, passes
through the center of a ring burner support-
ing a hydrogen diffusion flame. The hydro-
gen flame supplies heat and oxidizing species
to the soot column, producing a soot flame.
This configuration enables soot oxidation,
occurring within the soot flame, to be ob-
served in a diffusion flame environment in
a region far separated from competing soot
formation processes.
Figure 3.1: Ternary flame system.
The soot-generating propylene/air lam-
inar diffusion flame was produced using a Santoro-style co-flow burner [94], consist-
ing of concentric brass tubes with inner diameters of 14 and 101.6 mm. Propylene
46
(99.5% purity) flowed through the inner tube at 2.1 mg/s surrounded by a 1.18 g/s
co-flow of air. Plug flow for the co-flowing air was achieved by injecting the air into
the bottom of the outer brass tube where it flowed past 3 mm glass beads followed
by a ceramic honeycomb with 1.5 mm square cells. The surface of the honeycomb
sat 4 mm below the top of fuel port. The vertical column of soot produced by the
co-flow flame was axisymmetric with a luminous length of ∼50 mm.
A brass ring burner with inner and outer diameter of 10.2 mm and 38.1 mm,
and a height of 20.8 mm was centered over the soot column with its top face posi-
tioned 80 mm above the co-flow fuel port. Hydrogen (99.9995% purity) flowed at
1.48 mg/s into the ring burner plenum and exited through 41 jets measuring 0.41
mm in diameter encircling the ring center at a radius of 7.6 mm. As the soot col-
umn passed through the center of the ring burner and into the H2 flame, it ignited,
producing a soot flame that was steady, optically thin, and axisymmetric. The flow
of gases supplied to the flame system were each controlled with a pressure regu-
lator and need valve, and were measured with rotameters calibrated with a soap
bubble meter. Additional details of the ternary flame system can be found in the
dissertation work of Guo [224], and in work published by this group in [225].
Temperature measurements using a K-type thermocouple on the flame axis
at the ring burner entrance were below 300◦C, indicating that at this height, most
of the gaseous products of the propylene flame had been diffusively replaced by N2
and O2. This means that very few carbonaceous gas species were carried to the soot
flame to that would otherwise have contributed to soot formation. Observations
and measurements to characterize soot oxidation were performed in the soot flame,
47
which had a luminous length of ∼70 mm. The diameter of the soot flame ranged
between 1 − 4 mm, narrowing as height above the ring burner increased. The
open accessibility of the soot flame facilitated optical diagnostics and soot and gas
sampling.
3.2 Axial Flame Velocity Measurement
Given the narrow width of the soot flame (1 - 4 mm), velocities were assumed
to be radially uniform. It was also expected that the soot particles would follow
the local gas velocities which are high enough to dominate over any thermophoresis
effects in the axial direction.
The axial velocity of the flame was determined by using high frame rate video
to track a brief disruption to the soot column as it traveled upward. To create a con-
sistent, minimally obtrusive, but trackable perturbation, a device was constructed
which quickly swung a small steel rod with a wedge-shaped profile (0.6 × 3 mm)
through the upward-traveling soot column. The motion of the steel rod was actuated
by a solenoid piston connected to a 4-bar linkage (See Fig. 3.2), and interrupted the
column for ∼2 ms at a location 35 mm above the propylene fuel port. The resulting
disturbance to the flame was recorded with video (Casio EX-FH100) at 420 frames
per second with a 0.45 mm spatial resolution.
Flame velocity was determined by tracking the axial location of the point of
minimum pixel intensity along the centerline of the soot flame. Video analysis was
facilitated by a program developed in MATLAB and is depicted in Fig. 3.3. Video
48
Figure 3.2: Soot column disruption apparatus for velocity measurement.
Figure 3.3: Velocity measurement video analysis method. (a1-a3) A perturbation
to the soot flame is seen as a gap in the luminous soot traveling axially. (b1-b3)
The perturbation, identified as the local minimum intensity along the soot flame
centerline, is tracked in each frame. (c1-c3) The evolving plot of axial location of
local minimum vs. time measured in frames.
49
was first converted from the RGB color format into 8-bit grayscale. The centerline
of the soot flame was detected as the column of pixels oriented parallel to the flame
axis with the maximum overall pixel intensity (Fig. 3.3 a1-a3). Gaussian smoothing
was applied to the centerline intensities using a 5 pixel window to eliminate noise.
Intensities along the centerline were displayed as a plot of intensity vs. axial height
above burner. Upon detection of a disturbance to the flame, the program tracked the
axial location of the point of minimum intensity along the smoothed centerline above
the ring burner as it moved from one frame to the next (Fig. 3.3 b1-b3). The axial
location of the local minimum was plotted against time (Fig. 3.3 c1-c3), to which a
polynomial line was fit. First, 2nd, and 3rd order polynomial fits were considered.
An expression for axial velocity vs. height above burner was then determined by
taking the 1st derivative of the fitted lines.
3.3 Temperature, Soot Volume Fraction, and Gas Species Measure-
ments
Measurements within the soot flame of temperature, soot volume fraction, and
gas species concentrations were reported in detail in the dissertation of Guo [224].
The essential aspects of the methods used and additional details relevant to the
preset study are provided here.
50
3.3.1 Soot Flame Temperature
Temperatures in the soot flame were measured using ratio pyrometry as de-
scribed by Guo et al. [226]. Images of the soot flame were obtained at wavelengths
of 450, 650, and 900 nm using a modified Nikon D700 camera in combination with
three bandpass filters. The camera was modified by removing both the infrared cut
filter to reach the 900 nm wavelength, and the anti-aliasing filter to improve focus.
Spatial resolution in the object plane was 21 µm. The camera was calibrated using
a blackbody furnace (Oriel 67032) at temperatures ranging 900 – 1200 ◦C, yielding
a calibration constant, Cλ, for each bandpass filter. The line-of-sight images of the
axisymmetric soot flame were averaged across the flame axis, and then processed
by Abel deconvolution yielding radial grayscale intensities, GS at each wavelength.
The local soot temperature, T , was then measured from each pairwise combination
of wavelength filters (denoted here by subscripts 1 and 2), using:
hc(1/λ1 − 1/λ2)
T = (3.1)
kB ln(Cλ1GS1/Cλ2GS2)
where c is the speed of light, h is Planck’s constant, kB is the Boltzmann constant,
and λ is each filter’s central wavelength. The soot temperature was assumed to be
equal to the local gas temperature, which is reasonable for soot primary particle
diameters within the typical 20 - 50 nm range [227]. Local temperatures were
taken as the average of the three temperatures obtained from each line pair. The
difference between the average temperature and any of the line pairs was lower than
50 K. Temperatures obtained using the ratio pyrometry method outlined here are
51
estimated to have an uncertainty of ± 50 K [226].
3.3.2 Soot Volume Fraction
Soot volume fraction was measured using the laser extinction method of Guo
et al. [226], who validated the method against a well-studied reference flame. A
schematic of the laser extinction system is given in Fig. 3.4. The beam from a
7 mW He-Ne laser (Melles Griot 25LHR171) at a 632.8 nm wavelength expands
through a stationary diffuser (Thorlabs DG20-220), and then a vibrating diffuser
(Thorlabs DG20-600) to reduce speckling. An off-axis parabolic mirror collimates
the beam to 100 mm before it passes through the soot flame. After the flame, a
filter (Andover ANDV12564) retains only light at the laser wavelength, the beam
is decollimated, attenuated to avoid camera saturation, and sent through a pinhole
to remove off-axis light. The camera, which is the same as that used for tempera-
ture measurements, was focused on the soot flame’s object plane and had a spatial
resolution of 34 µm. Abel deconvolution can be used to convert the line-of-site
images of the laser, whose attenuation follows the Beer-Lambert law, to local radial
soot volume fractions, fs(r) [228]. Since radial soot transport was observed to be
non-negligible in ∫the soot flame, the sectional integrated soot volume fraction, Fs,∞
defined as Fs = 2πrfs(r)dr at each height, was used instead of the centerline0
soot volume fraction(fs). Fortunately, Fs can also be calculated directly from the
line-of-site laser images, thereby ∫avoiding noise introduced by deconvolution, using:R
λ − ln[GS
◦(x)/GS(x)]dx
F Rs = (3.2)
Ke
52
Figure 3.4: Schematic of the laser extinction system. Image taken from Ref [226].
Here λ is the laser wavelength, R is the soot flame radius, x is the horizontal
coordinate in the object plane, and GS(x) is the line-of-site grayscale images divided
by the camera shutter time. The superscript (◦) denotes the reference image (i.e.
the “flame off, laser on” image) which was approximated by linearly interpolating
the grayscales of the soot free regions in the “flame on, laser on” image. The
denominator in Eq. 3.2 is the volumetric dimensionless extinction coefficient, which
can be represented as:
Ke = 6πE(m)(1 + ρsa) (3.3)
where E(m) is the refractive index absorption function and ρsa is the ratio of
scattering-to-absorption cross section [79, 229]. In modeling the extinction of light
by soot, primary particles are commonly thought of as independent absorbers, for
which scattering effects are negligible [230–232]. Hence, a value of ρsa = 0, was
adopted for the present work. Soot was assumed to have a refractive index of
53
m = 1.57− 0.56i [233], which corresponds to E(m) = 0.26 [81]. For the laser wave-
length λ =632.8 nm, soot primary particles are significantly smaller (dp ≈ 30 nm)
than the Rayleigh limit (πdp/λ < 0.3) [234]. Therefore, both temperature and
soot volume fraction calculations assume soot satisfies the Rayleigh scattering ap-
proximation. Uncertainties of ±5% (95% confidence) are expected for values of
Fs > 3× 10−5 mm2, and ±10% otherwise.
3.3.3 Major Species Concentrations
Concentrations of the gases H2, O2, N2, CO, CO2, were measured in the soot
flame using gas chromatography while concentrations of H2O were measured by
desiccant gravimetry. Gas was sampled isokinetically at various axial locations
within the flame using a radiatively cooled stainless steel probe with a 2.1 mm
diameter, in a manner similar to Refs. [136, 137, 235]. The probe was connected to
a vacuum pump regulated by a rotameter, and the flow rate required for isokinetic
conditions was determined from the local measured temperature (Sec. 3.3.1) and
flow velocity (Sec. 3.2).
Water concentration was determined by passing soot-filtered flame gases through
a water-cooled stainless steel trap filled with Drierite desiccant, and then measuring
the increase in water trap weight. For other stable species, filtered gases were drawn
into a gas chromatograph (GC) (Hewlett-Packard 5890) with a thermal conductiv-
ity detector. Helium was used as the carrier gas for N2, O2, CO2, and CO, while
argon was used as the carrier gas for H2, because helium and hydrogen have similar
54
thermal conductivities. The relative concentration of each gaseous compound was
calculated by first calibrating the GC with different volumes of known gas mixtures.
All concentration uncertainties were estimated at ±10%.
3.3.4 Estimation of OH Radical Concentrations
For the purposes of analyzing the chemical kinetics of soot oxidation, radical
concentrations were estimated based on an assumption of full equilibrium. This
choice was prompted by two major considerations. First, it has been shown that
diffusion flames approach full equilibrium in fuel lean regions, and the soot flame
studied here is fuel lean at all heights [224]. Second, the presence of soot has been
shown to reduce hydroxyl concentrations from superequilibrium by serving as a sink
for the radical pool [69]. Using the measured temperatures and major species con-
centrations as inputs, concentrations of the radicals O, H, and OH were calculated
using the equilibrium solver in CHEMKIN [236], assuming constant pressure and
enthalpy. The thermodynamic properties of each species were taken from the default
thermodynamic database in CHEMKIN Ver. 4.0.
3.4 Thermophoretic Sampling of Flame Soot
A schematic of the apparatus constructed for thermophoretic sampling is
shown in Fig. 3.5 A double-acting pneumatic cylinder with a 7.9 mm (5/16 inch)
bore and 7.62 cm (3 inch) stroke (Bimba 0073-DXP) was connected to 5-port
solenoid-actuated control valve (Motion Industries LTV-115DD) with 60 psi sup-
55
Figure 3.5: Pneumatic and electrical schematic of the thermophoretic soot sampling
apparatus. (TR) is a normally-closed, timed-open relay, and (S) is a manual switch.
ply air. The control valve was switched by a normally-closed, timed-open relay
(SSAC TRDU24A3), set to a time delay of 0.1 s. The cylinder piston was connected
to a roller carriage (8.26 × 3.18 cm), shuttling it along a track while carrying the
thermophoretic sampling probe to the flame. The brass probe measured 53 × 5 ×
0.65 mm and had a rounded tip. The entire assembly was mounted to an aluminum
plate with a stainless steel wind shield mounted on the end nearest the flame.
All soot sampled from the soot flame was collected on a 200 mesh copper
grid with a lacey carbon support film (Electron Microscopy Sciences LC200-Cu).
Attachment of the TEM grid to the probe was done by laying the grid flat against
the probe’s surface at its rounded end, and then applying a very small amount of
rubber cement onto the edge of the grid farthest from the probe tip. Upon actuation,
the roller carriage travels a distance of 7.62 cm along the track, inserting the TEM
grid directly into the soot flame, and then retracting. The probe dwells a total of
56
about 90 ms in the flame. Soot samples were obtained withing the soot flame at
10 different heights above the ring burner: 10, 13, 15, 20, 25, 30, 35, 40, 45, and
50 mm.
3.5 TEM Measurements
Soot images were obtained on a JEOL-2100 LaB6 transmission electron mi-
croscope at the University of Maryland NanoCenter’s AIMLab. For all measure-
ments, the TEM was operated with an electron beam accelerating voltage of 200
kV. Coordinates on the TEM grid plane to be considered for analysis were randomly
generated using MATLAB prior to imaging with the TEM. The coordinate generat-
ing program was constrained to produce equal numbers of coordinates in each grid
quadrant. Imaging was only considered at regions centered at these coordinates. If
no soot aggregates were present at the specified location, analysis simply contin-
ued with the next randomly generated coordinate. If soot was present, no attempt
was made to center the viewing window on any particular image element. Both
bright field and diffraction pattern images in the TEM were calibrated against a
gold diffraction grating replica (Ted Pella, part no. 607). The standard uncertainty
of the length scale was estimated to be 0.8% at magnifications between 2,000 and
200,000, and 0.2% at higher magnifications. Images were obtained with an Orius
SC1000A1 CCD camera using Gatan Digital Micrograph V3.22 software and saved
as 8-bit .tif files.
57
3.5.1 Aerosol Image Analyzer Program
The extensive use of TEM methods in the present work made the choice of
software for quantitative image analysis critical. The NIH software ImageJ is com-
monly used and freely available [237]. Gatan Digital Micrograph is also widely
used, especially in diffraction pattern analysis. Ultimately, these off-the-shelf soft-
wares were found to be lacking for the unique and heavily quantitative needs of the
present study. Instead, a custom software, named Aerosol Image Analyzer (AIA),
was developed by the author using MATLAB. This choice was made based on MAT-
LAB’s extensive image processing functions and the author’s long experience with
the platform.
Figure 3.6: Aerosol Image Analyzer GUI. (a) Image viewing and processing GUI.
(b) User-defined image processing procedure. (c) Measurements GUI. (d) Tabs for
switching between measurement of primary particles, aggregates, and lattice fringes.
58
The graphical user interface (GUI) of the AIA program can be broken into
two components: a image viewing and processing GUI, and a GUI for performing
measurements. These components are shown in Fig. 3.6. In the image viewing and
processing GUI (Fig. 3.6a) the user can perform typical file management functions
(open, save, etc.), and can interact with the image in customary ways (pan, zoom,
crop). The interface is designed to support the rapid creation and testing of complex
image processing procedures, allowing the user to converge on an optimal set of
image processing steps to achieve a consistent result (Fig. 3.6b). The user may
select from 33 common image processing operations native to MATLAB along with
3 custom functions (detailed in Sec. 3.5.7). Individual parameters for each image
processing operation can be changed directly within the GUI, and operations can
be quickly added, removed, and re-ordered. When running the procedure, the user
can elect to step through and see the effects of each operation, or simply run the
procedure to completion. Procedures can be named and saved for use in future
sessions.
The measurements GUI (Fig. 3.6c) contains a number of utilities, such as the
ability to easily specify the image resolution by clicking the image scale bar, creating
regions of interest that can be saved with the image, and changing program default
settings. Other features include auto-detection of image polarity (i.e. whether the
image foreground is light or dark with respect to the background), and the ability
to toggle between original and processed images while holding measurements on-
screen. The controls for measuring aggregates, primary particles, and lattice fringes
are split into three tabs (Fig. 3.6d). Measurement results are displayed in tables
59
embedded within each tab and can be directly exported to Excel. The controls
also allow measurements on the image to be individually or collectively displayed,
hidden, or deleted. Past measurements of primary particles that have been saved
elsewhere (as in Excel) can even be re-displayed on the current image by copying
and pasting the past measurements into the embedded table.
3.5.2 Primary Particle Measurement
3.5.2.1 Measurement Bias Controls
The primary particle size distribution (PPSD) was measured from TEM im-
ages obtained at each sampled location within the soot flame. At least 20 images
were obtained at each flame location and magnifications ranged between 6,000 and
60,000. To avoid image selection bias, 10 images were randomly drawn from each
image set. To mitigate bias in selecting which primary particles to measure, the AIA
program generated 5 randomly placed 140 × 140 nm regions of interest (ROIs) on
each image. The operator then measured every element within each ROI that could
be reasonably deemed a primary particle using a semi-automated algorithm called
center-selected edge scoring (CSES) which is detailed in Sec. 3.5.2.2. If not satisfied
with the algorithm’s output, the operator could reject it and remeasure with CSES
by selecting a different pixel and/or restricting the diameter range. Alternatively,
the operator could remeasure the primary particle manually by drawing the desired
circle on the image.
This measurement procedure has several benefits. First, the semi-automation
60
Figure 3.7: Screenshot of the Aerosol Image Analyzer program showing primary
particles measured using the CSES algorithm within randomly generated ROIs.
speeds up the measurement process fivefold, as will be shown in following section.
In addition, it is expected to reduce bias since it quantifies image features uniformly.
At the same time, the operator’s best judgment is retained since the semi-automated
results may be overridden. Figure 3.7 shows a typical soot aggregate, whose primary
particles have been measured using the CSES algorithm within random ROIs.
3.5.2.2 Center-Selected Edge Scoring (CSES) Algorithm
Existing attempts at automating or semi-automating primary particle size
measurement generally rely on Circular Hough Transform (CHT) or Euclidean dis-
tance mapping (EDM) algorithms as discussed in Sec. 2.2.2.3. As will be shown in
Sec. 4.3.2, the available automation algorithms found in the literature do not ac-
curately assess PPSD. In addition, they are incapable of measuring overlap among
61
Figure 3.8: Steps in the CSES algorithm. A low magnification image is shown to
clearly illustrate individual pixels. (a) Pixels of candidate center points around an
operator-selected pixel. (b) Grayscale intensity gradient map with vectors denoting
gradients. (c) The magnitude and orientation (shown by vectors) of the gradient of
a candidate circle’s edge pixels.
primary particles.
One of the reasons that both CHT and EDM algorithms have performed
poorly, is because they rely on detectable edges in an image to infer circular fea-
tures. By contrast, center-selected edge scoring (CSES) begins from an estimate of
a primary particle’s center point, and then, like a manual operator, considers image
features over the entire circumference of a primary particle, not just those parts de-
tectable as “edges.” Figure 3.8 outlines this process. The operator manually selects
a point on the image that is judged to be the center of a primary particle. A square
neighborhood of pixels around the selected point is calculated (Fig. 3.8a). Candi-
dates for a best-fit circle are those within an operator-specified diameter range, dp,min
to dp,max, centered at any pixel within this neighborhood. A neighborhood measur-
ing 1 + 2[round(0.025dp,max + 1)] on a side was found to match operators’ intuitive
expectations for candidate center point tolerance. Using a 3 Ö 3 Sobel filter, the
algorithm computes a gradient map of the grayscale intensity at each image pixel
(Fig. 3.8b). For each candidate circle, all pixels in the gradient map are eliminated
62
except those that comprise the candidate circle’s circumference (Fig. 3.8c). The fit
of each circle is scored using the magnitude of the image intensity gradient, |Gi|, at
each pixel i, and the difference in its gradient orientation from that of a perfectly
circular primary particle, θi according to:
Npx
1 ∑
Score = |Gi| cos θi (3.4)
Npx i=1
where Npx is the number of circumference pixels. The best-fit circle is chosen as
that with the greatest score, according to Eq. 3.4. The CSES code is provided in
Appendix A.1. Though developed using soot TEM images, the CSES algorithm
has application to any aerosol that is spheroidal or comprised of spheroidal primary
particles.
CSES also has the feature of being substantially faster than the traditional
primary particle measurement. The time per primary particle needed to perform
measurements using CSES was compared to a manual measurement on the same
images in ImageJ. Twice measuring 100 primary particles on two randomly selected
image sets, CSES was found to require a little less than 20% of the operator time
required by manual measurement. This improvement comes from the fact that a
pixel can be selected at a perceived center point much more quickly than a circle
can be drawn to fit a perceived circumference.
3.5.2.3 Primary Particle Overlap
The partial sintering of primary particles reduces the overall volume and sur-
face area of a soot population relative to the single-point-contact primary particle
63
model. Partial sintering is measured as overlap of adjacent primary particles in a
2-dimensional TEM image as described in Sec. 2.2.2.2. Once all the primary par-
ticles on a TEM image have been measured as outlined in Sec. 3.5.2.2, the AIA
program evaluates each pair of primary particles on the 2D image. Particles are
deemed overlapping if the distance between their two centerpoints is less than their
combined radii. The projected overlap coefficient, Cov,p is then calculated for each
overlapping pair per Eq. 2.8.
3.5.3 Soot Surface Area
Soot surface area derived from the TEM images is calculated in terms of the
volume specific surface area (VSSA). Ignoring the effect of overlap for the moment,
the surface area of a population of Np spherical primary particles in single point
contact is:
S◦ = Npπd
2
pS (3.5)
where dpS is the diameter of average surface area. Similarly, the population’s volume
can be expressed in terms of the diameter of average volume, dpV :
◦ N
3
pπdpV
V = (3.6)
6
Combining Eq. 3.5 and 3.6 the volume specific surface area for a polydisperse pop-
ulation of primary particles in single point contact, S◦V , can be expressed as:
6d2pS
S◦V = (3.7)d3pV
Determination of dpS and dpV will be discussed momentarily, however, they need not
be calculated if the assumption of monodisperse primary particles is applied. In this
64
case Eq. 3.7 simply reduces to:
S◦V,mono = 6/dp (3.8)
A more thoroughgoing VSSA model takes both polydispersity and overlap
of primary particles into consideration. The factors FS and FV are introduced to
respectively account for surface area and volume lost to primary particle overlap.
They may be combined into a single VSSA overlap factor, Fov:
Fov = FS/FV (3.9)
Now the VSSA can be expressed as:
6F 2ovdpS
SV = (3.10)
d3pV
If one assumes the distribution of dp to be either normal or lognormal, expres-
sions for dpS and dpV are readily obtained from the second and third moments of
the distribution [117, 141, 142, 238–241]. However, while a lognormal size distribu-
tion for soot aggregates is generally a safe assumption [141, 241], primary particles
have been observed with distributions of varying levels of symmetry and modal-
ity [18,22,97,115,118,119,127,130,133,134,138–140,242,243]. It would be valuable,
therefore, to have expressions for dpS and dpV that hold regardless of the distribution.
Such expressions may be derived from the so-called central moments (or moments
about the mean) of the distribution. The general equation for the ith central moment
CMi, of a continuous distribution of variable x, with probability density function
f(x) and mean value µ is: ∫ ∞
CMi = (x− µ)if(x)dx (3.11)
−∞
65
The second central moment corresponds to the variance σ2, of the distribution, while
the third central moment is equal to the skewness of the distribution γ, multiplied
by the cube of its standard deviation. For a sample population of primary particles
with mean diameter dp and standard deviation sdp , the diameter of average surface
area is found by:
2
d = (s2 + d )1/2pS d p (3.12)p
The diameter of average volume incorporates the skewness of the sampled population
of primary particles, γdp , and is given by the expression
3
dpV = (γ s
3 + 3d s2dp d + d )
1/3 (3.13)
p p dp p
The summary variables dpS and dpV are now defined in terms of known statistical
parameters. Surprisingly, while expressions for dpV are available in the literature
for known distributions as mentioned above, the author has yet to encounter the
distribution-agnostic Eq. 3.13. Hence, its derivation, along with that for dpS, is
presented in Appendix B.1.
At this point, the only remaining values needed for calculating the VSSA are
FS and FV . One approach would be to assume that the volume lost to primary
particle overlap is negligible, and then estimate the lost surface area factor from the
coefficient of Eq. 2.10. Together these are:
FS = 1− φSCov (3.14a)
FV = 1 (3.14b)
where φS = 1.3 [114]. Note that unlike Eq. 2.10, the number of primary particles
66
in an aggregate, Np,a, is not present in this expression for FS because specific sur-
face area at the population level rather than at the aggregate level is of interest.
This approach has been taken by several researchers [89, 124], however there are
drawbacks. For one, this expression for FS comes from a simulation of aggregates
comprised of monodisperse primary particles; the effect of polydispersity has never
been investigated. Second, Eq. 3.14 assumes only surface area loss, however, volume
lost to partial sintering may not be negligible.
To overcome many of these drawbacks, a methodology that accommodates a
polydisperse primary particle population was developed for the present work. The
approach begins by estimating the true 3D overlap, Cov, from the 2D TEM image
using the linear function Cov = ζ1Cov,p− ζ2, which was introduced earlier as Eq. 2.9.
The values of ζ1 = 1.27± 0.01 and ζ2 = 0.27± 0.01 from Wozniak et al. [121] were
chosen for the present study. The negative intercept of Eq. 2.9 reflects the fact
that some of the overlap observed in the 2D image is due to shadowing by out-of-
plane primary particles rather than to a true material overlap. In other words, a
positive mean value of Cov,p will be measured on a TEM image even at the limit of
Cov = 0. Hence, Eq. 2.9 is necessarily a population-averaged expression and cannot
be applied to individual primary particle pairs, as doing so would lead to a non-
physical, negative overlap for small values of Cov,p. Therefore, the values of Cov,p,
obtained according to Sec. 3.5.2.3, are averaged to give Cov,p and then supplied to
Eq. 2.9, yielding a global Cov for the sample.
Using this sample-averaged Cov, the lost surface area and volume can be cal-
culated in terms of the size of the spherical cap consumed by the partial merger of
67
Figure 3.9: (a) Spherical cap (b) Overlapping primary particles of different sizes.
each overlapping pair. For a sphere of radius r, the surface area and volume of a
spherical cap of height h, as depicted in Fig. 3.9a, are given respectively by:
Scap = 2πrh (3.15)
and
1
V 2cap = πh (3r − h) (3.16)
3
To apply these relationships to overlapping primary particles, consider Fig. 3.9b.
The spherical cap height hi can be computed from the known terms ri, rj, and Cov
according to:
C2ov(ri + rj)− 2rjCovhi = (3.17)
2(Cov − 1)
By swapping subscripts i and j, the value for hj can be computed from the same
expression, or from its relation to hi:
hj = Cov(ri + rj)− hi (3.18)
Derivations of Eq. 3.17 and 3.18 are provided in Appendix B.2.
68
Combining Eq. 3.5 and 3.1∑5, FS can be calculated from:
2 (rihi + rjhj)
− (i,j)∈IFS = 1 (3.19a)
N d2p pS
where I is the set of overlapping primary particle pairs. Similarly, by combining
Eq. 3.6 and 3.16, an expression ∑for FV is obtained:
2 (h2i (3ri − hi) + h2j(3rj − hj))
− (i,j)∈IFV = 1 (3.19b)
N d3p pV
The approach embodied by Eqs. 3.15 - 3.19 is not without its limitations.
For one, despite not relying on Eq. 3.14, which assumes monodisperse primary
particles and aggregates with a 1.78 fractal dimension, it still depends on Eq. 2.9 to
estimate Cov, which is built on the very same assumptions. Additionally, the method
shown here analyzes each overlapping pair in isolation. This does not take into
consideration cases in which the overlapping region of multiple pairs occupy the same
physical space. Such situations certainly exist in real aggregates, especially those
with larger fractal dimensions (i.e. less chain-like). This simplification, therefore,
would tend to overestimate the surface area and volume consumed by partially
merged primary particles, resulting in a net effect of slightly underestimating the
VSSA.
3.5.4 Soot Aggregate Morphology
At the scale of the aggregate, soot exhibits a mass fractal morphology, de-
scribed by the power law relationship: N = k (R /r )Dfp,a f g p , which was introduced
earlier as Eq. 2.3, and is sometimes termed the ”fractal equation.” This equation
69
relates the parameters most often used to quantify soot morphology: the number
of primary particles in the aggregate, Np,a, the of radius of gyration, Rg, fractal
dimension, Df , and fractal pre-factor, kf .
Formally identical to the fractal equation, Eq. 2.4, Np,a = ka(A
α
a/Ap) , is used
to extract Np,a from the 2D TEM soot images. From a consideration of the reviewed
literature (Sec. 2.2.1.2), the present analysis adopts the values of ka = 1.15 ± 0.04
and α = 1.09 ± 0.36, from the work of Köylü et al. [90], which was found to be
the most compelling. Likewise, for determination of Rg in the current study, the
literature shows good evidence for the robustness of the expression Rg = L/2C,
(Eq. 2.7), where C = 1.5± 0.05.
At least 20 TEM images of soot aggregates were obtained at each sampled
location within the soot flame. Magnifications ranged from 5,000 and 8,000. No
fewer than 10 images were randomly selected from each image set for measurement.
More images were chosen if 10 was insufficient to achieve a statistically significant
number of aggregates (ideally > 250). Soot deposition was so sparse on the TEM
grid sampled at HAB = 50 mm that an insufficient number of aggregates could be
imaged. Consequently, soot morphology was not analyzed at this flame location.
Before they can be measured, images of soot aggregates must first be bina-
rized. This step is reasonably straight-forward if the image background is relatively
homogeneous, as is the case with a TEM grid with a carbon film substrate. However,
since carbon film interferes with HRTEM and SAED measurements, a lacey carbon
substrate was used in the present study. Unfortunately, while a human operator
can easily distinguish between a soot aggregate and a lacey carbon support, they
70
Figure 3.10: Procedure for creating binary images of soot aggregates. (a) Original
TEM image. (b) Result of image background removal and binarization process. (c)
Locations for aggregate - background separation are manually identified. (d) Result
of manual separation of aggregate from background. (e) Measured aggregates. (f)
Non-aggregate objects removed from image.
are virtually indistinguishable by background removal algorithms, especially near
the dark edges of the carbon lace. To circumvent this difficulty, the AIA program
was equipped with a tool that effectively allows the operator to manually snip the
aggregate away from the carbon lace wherever this problem exists within the image.
The steps for producing binary images of discrete aggregates is illustrated in
Fig. 3.10. Starting from the initial TEM image (Fig. 3.10a), a process is followed that
removes as much of the image background as possible without deleting any portions
of the aggregates themselves, and then performs image binarization (Fig. 3.10b).
71
Several methods for removing the background of TEM images have been suggested
in the literature [134, 244], however the greatest success was achieved here using
a general procedure of edge-preserved smoothing (e.g., median filtering), contrast
enhancement followed by a rolling-ball transform, and lastly, manual thresholding.
The size of the structural element used in the rolling ball transform and the manual
thresholding level often had to be adjusted by trial and error to achieve optimal
results. Even with optimized background removal, artifacts from the lacey carbon
substrate were usually present in the binary image. The next step, therefore, was to
cut away points of connection between aggregate and substrate. This was accom-
plished using the aforementioned manual cutting tool within the AIA program. The
operator can mark the locations for the image cut on either the binary image or on
the original image as shown in Fig. 3.10c. Once soot aggregates were adequately
separated from non-aggregate objects (i.e. 8-pixel connectivity was severed), as in
Fig. 3.10d, the operator could measure aggregates (Fig. 3.10e) and eliminate all
non-aggregate objects in the image (Fig. 3.10f).
The AIA program performs the following measurements on each the binary
aggregate object on the image resulting from the above procedure. The projected
aggregate area, Aa, is simply determined from the number of pixels comprising
the discrete binary object, and the maximum projected length, L, is calculated as
the maximum Feret diameter. For comparison purposes, functions within the AIA
program were also written to calculate the projected radius of gyration, Rg,2D, per
Eq. 2.5, and the maximum width W , normal to L, for use in Eq. 2.6.
72
3.5.5 Soot Fragmentation
Soot fragmentation refers to the breakup of larger aggregates into smaller
pieces. If this phenomenon is present within the soot flame, one should observe an
increase in the overall number flow rate of aggregates as well as a decrease in the
average number of primary particles per aggregate. Averaging the results of Eq. 2.4
across a large sample of TEM aggregate images will produce an estimate of the
mean number of primary particles per aggregate, Np,a. If the size distribution of
aggregates is lognormal, as is typical [241], the geometric mean number of primary
particles in an aggregate, Npg,a, will be the statistic of interest.
Combining the sectional integrated soot volume fraction, Fs, and soot flame
velocity, vs, with the diameter of average primary particle volume found by Eq. 3.13,
the total number flow rate of aggregates, Ṅa can be calculated at any given height
using:
6vsFs
Ṅa = (3.20)
N 3p,aFV πdpV
Here FV is the lost volume factor due to primary particle overlap, discussed in
Sec. 3.5.3.
3.5.6 Selected Area Electron Diffraction
Soot aggregates considered for SAED analysis were identified at random loca-
tions on the TEM grid. For a chosen aggregate, a portion that was suspended away
from the lacey carbon support structure was imaged at a magnification of 300,000.
A 20µm diameter selected area aperture was inserted into the beam path, eliminat-
73
ing any possible diffraction signal from the amorphous lacey carbon film. To make
comparisons of SAED measurements as meaningful as possible, similar volumes of
soot were used to generate diffraction patterns from each sample. This was done by
first centering the viewing window on a section of the aggregate in which primary
particles were not stacked along the electron beam axis (i.e. at a location where the
aggregate was only one primary particle thick). Additionally, the sample was also
positioned such that soot occupied at least ∼90% of the area viewed through the
aperture. Diffraction pattern images were captured over a 1 s exposure time at a
scale of 0.017036 nm−1/px.
For each diffraction pattern image (e.g. Fig 3.11a), the center point was deter-
mined using Digital Micrograph’s Find Center tool, and a binary mask to exclude
the beam blocker from image analysis(Fig. 3.11b) was generated using the PolyROI
tool in the AIA program (Sec. 3.5.1). Quantitative analysis of the SAED images was
performed using the following steps, which were executed using the MATLAB code
given in Appendix A.2. Ignoring pixels covered by the beam blocker, the average
intensity of the image as a function of radius was computed, producing a radial in-
tensity profile (Fig. 3.11c). The profile was smoothed until two minima between the
diffraction rings were identified. The first inflection point following the initial decay
of the direct electron beam was chosen as starting location for diffraction analysis.
Labar [245] has observed that in the absence of amorphous material, the back-
ground signal of an SAED image will follow a lognormal curve. Hence, background
illumination from the direct beam was first estimated by fitting a lognormal func-
tion to the background points, which were taken to be the first inflection point,
74
Figure 3.11: SAED image measurement process. (a) Original diffraction pattern
image with lattice spacings identified by their Miller indices. (b) Beam blocker
mask; only diffraction pattern pixels corresponding to white pixels on the mask are
analyzed. (c) (—) Radially averaged diffraction pattern, (- -) lognormal fit of the
background signal, (∗) points used in lognormal curve fit. (d) (—) Diffraction peaks
with first estimate of background removed, (- -) spline fit to refine the background
signal estimate, (∗) points used in the spline curve fit. (e) (—) Radially averaged
diffraction pattern, (- -) combined lognormal-spline fit of the background signal. (f)
Final net diffraction peaks with noted locations of maxima (H).
the inter-ring minima, and the end point of the radial intensity profile (Fig. 3.11c).
The background estimate was subtracted from the original diffraction image and
was then refined by fitting a spline curve to the local minima, inflection and end
points on the net diffraction profile. (Fig. 3.11d). The lognormal and spline curves
were combined into a final background estimate (Fig. 3.11e), which was subtracted
from the original diffraction curve, leaving only the diffraction peaks produced by
75
the d002, d100, and d110 lattice spacings. (Fig. 3.11f).
3.5.7 HRTEM Lattice Fringe Analysis
Capture of high resolution soot images was carried out using the general
methodology outlined in Section 3.5. Images were obtained at magnifications of
either 300,000 (0.0421 nm/px) or 400,000 (0.0307 nm/px). Each image was pro-
cessed using a procedure that resulted in a binary image in which lattice fringes
appeared as skeletonized segments. The procedure follows the general roadmap
provided by Yehliu et al. [208] and Botero et al. [210], with some improved al-
gorithms for connecting segments belonging to the same fringe and for breaking
spurious fringe branches. The steps of the procedure are: ROI creation, contrast
enhancement, Gaussian filtering, bottom-hat filtering, thresholding, skeletonization,
fringe connection, branch severing, and removal of segments below a size threshold.
The details of each step are given below. Once a skeletonized fringe image was ob-
tained, analysis was performed yielding measurements of fringe length, tortuosity,
inter-fringe separation distance, deviation from concentric orientation, and fringe
radial location.
3.5.7.1 HRTEM Image Processing Procedure
ROI Creation
In the first image processing step, a region of interest (ROI) was manually
created by drawing a closed polygon (Fig. 3.12a) on the image using Aerosol Image
76
Analyzer’s Draw Polygonal ROI tool. ROIs were drawn such that they encompassed
only individual primary particles and excluded regions of overlap with neighboring
primary particles. This was done because overlapping primaries tend to produce a
complicated fringe pattern that is unrepresentative of either primary particle’s fringe
structure. In addition to restricting measurements to a desired region, creation of
an ROI allows regions outside of it to be ignored, which quickens subsequent image
processing steps and improves the results of operations relying on image statistics,
such as contrast enhancement and thresholding.
Contrast Enhancement
Image contrast within the ROI was enhanced using the histogram equalization
method and was implemented using MATLAB’s histeq function. Histogram equal-
ization enhances contrast by reducing an image’s grayscale intensity histogram to a
fewer number of discrete levels whose distribution is approximately flat. Experience
found that a contrast-enhanced image containing only five discrete gray levels pro-
duced the best results. Figure 3.12 shows the grayscale histograms for the example
image before and after contrast enhancement.
Gaussian Filtering
The next step, Gaussian low-pass filtering, removed high frequency noise from
the image, and utilized the 2-D Gaussian filtering function imgaussfilt in MATLAB.
The Gaussian filter is defined by two user-supplied parameters: The filter size is
specified as an odd number of pixels and determines the size of the square Gaussian
77
Figure 3.12: (a) Original image with user-drawn ROI. (b) Grayscale his-
togram of (a) (ROI only). (c) Fringe image after contrast enhancement.
(d) Grayscale histogram of (c).
kernel, while the standard deviation effectively determines the cut-off frequency of
the filter. Although the standard deviation is specified in the spatial domain, the
filtering in performed in the frequency domain after Fourier transformation of the
kernel. Best results were obtained with a filter sizes of 7 and 9 px for 3×105 and
78
Figure 3.13: Lattice fringe image resulting from successive image pro-
cessing operations: (a) Gaussian filtering, (b) Bottom-hat filtering, (c)
Thresholding, (d) Skeletonization.
4×105 magnifications, respectively (approximately 0.3 nm) and a standard deviation
of 3 px. Results of the Gaussian filter for the example image are given in Fig. 3.13a.
Bottom-hat Filtering
Bottom-hat filtering, (also called black top-hat filtering) was used to correct
uneven image illumination and bring fringes into greater relief against the back-
79
ground. It also had an inverting effect, so that lattice fringes, appearing dark in the
raw image, are light against a dark background in the processed image. The filter
operates by subtracting an image from its morphological closing using a structur-
ing element [246]. This was implemented here using MATLAB’s imbothat function.
Best results were obtained using a 4 or 5 px (∼0.15 nm) disk-shaped structuring
element. Results of this operation for the example image are shown in Fig. 3.13b.
Thresholding
Thresholding produces a binary image by setting all pixels with grayscale
values above a certain threshold to 1, and all others to 0. Thresholding of the
bottom-hat-filtered image was performed using Otsu’s method (MATLAB functions
graythresh and im2bw) which chooses a threshold based on the image’s grayscale
distribution [246]. The resulting binary image shows the lattice fringes as white
objects of varying sizes, as seen in the example image in Fig. 3.13c.
Skeletonization
Skeletonization reduces each binary object down to a single-pixel-width center-
line. The operation preserves the positions and essential structures of each object.
Skeletonization facilitates quantitative analysis of the fringe objects, as will be seen.
Skeletonization was performed using MATLAB’s thin morphological operation. The
skeletonize operation, which uses a slightly different algorithm, was also tested but
was more prone to producing spurious artifacts. Figure 3.13d shows the skeletonized
example image.
80
Fringe Connection
The series of operations leading to a skeletonized fringe image inevitably sep-
arates structures that would properly be interpreted as belonging to a single fringe
object. To reunite such structures, a fringe connecting algorithm called BridgeGaps
was developed. The function, whose code is provided in Appendix A.3.1, connects
segments whose endpoints are within a user-defined proximity and orientation toler-
ance. After identifying the endpoints of each segment, the algorithm calculates the
orientation of the two ends. Around a given endpoint, the algorithm evaluates a re-
gion whose radius equals the user-specified proximity (Fig. 3.14a). If a neighboring
segment terminates within that region, its ending orientation is compared to that
of the original segment. If the two orientations differ by 180◦ ± the user-supplied
tolerance, and the two endpoints are not part of the same segment, a line is drawn
connecting the two segment endpoints (Fig. 3.14b). Best results were obtained with
a 7 or 9 px proximity (for 3×105 and 4×105 magnifications, respectively), and a 30◦
orientation tolerance.
Branch Severing
Fringes in the skeletonized image that are linked together or that branch in
different directions, cannot be properly measured. Hence, all such linkages must be
severed. The SeverBranches function was developed to accomplish this; (code in
Appendix A.3.2). The function begins by identifying each branch point in the image.
Then, a square interrogation window, whose size is specified by the user, is centered
81
Figure 3.14: Connection of segments belonging to the same fringe. For
clarity, pixel colors have been inverted. (a) Identification of segment end-
points (red pixels) within a user-defined proximity. (b) The two segments
whose ends are oriented roughly opposite one another are connected. The
orientation difference with the second segment within proximity did not
meet a user-defined tolerance, so was not connected.
at each branch point (Fig. 3.15a). The orientation of each branching segment with
respect to the branch point is defined by the location at which each segment crosses
the window boundary. The pair of branching segments whose orientation difference
is closest to 180◦ remains connected; all other branches are severed such that they
loose 8-pixel connectivity (Fig. 3.15b). The function was found to be most successful
with an interrogation window size of 7 and 9 px for 3×105 and 4×105 magnifications,
respectively.
Small Segment Removal
The last image processing step was the removal of small segments below a
size threshold. This was accomplished using MATLAB’s bwareaopen function. The
size threshold used was approximately 0.3 nm, which corresponds to 7 and 10 px
82
Figure 3.15: Severing a branched line segment. For clarity, pixel colors
have been inverted. (a) Angles between each branching segment are
measured at the border (blue pixels) of an interrogation window centered
on the branch point (red pixel). The pair of branches closest to 180◦
apart and will remain connected. (b) The spurious branch is severed in
the resulting image.
for images magnified 3×105 and 4×105, respectively. It should be noted that the
size threshold here refers simply to the number of pixels in a segment, and is only
equivalent to the fringe length in the case of a perfectly horizontal or vertical fringe.
3.5.7.2 HRTEM Fringe Measurement
Individual Fringes
Before the skeletonized fringe image can be measured, the primary particle to
which the fringes belong must be identified. This was performed manually on the
original HRTEM image using Aerosol Image Analyzer’s manual circle measurement
tool, as shown in Fig. 3.16a. Defining the primary particle enables the computation
of each fringe’s orientation and radial location within the primary.
Figure 3.16 illustrates the measurements of fringe radial location, non-concentricity,
83
length, and tortuosity. These quantities were obtained using the MeasureFringes
code provided in Appendix A.3.3. The function begins by calculating the centroid
and orientation of each fringe object not touching the ROI border. Radial location,
rf , is then simply the distance between the primary particle’s center point and the
fringe centroid. Non-concentricity, θf,c, as defined here, is a fringe’s angular devia-
tion from an orientation perpendicular to a radial line running through its centroid,
(Fig. 3.16b). This is consistent with the definition used in the work of Shim et.
al [175], although they they went further to define a polar order parameter. The
measure of non-concentricity was found to be sufficient for the present work. Fringe
length, Lf , is calculated as the sum of the distances between the center points of
√
adjacent pixels in a fringe, which can be either 1 px or 2 px, (Fig. 3.16c). Fringes
shorter than a user-specified minimum length are not considered. For this study, a
minimum fringe length of 0.483 nm was chosen, as it corresponds to the length of
two aromatic rings [210]. Lastly, fringe tortuosity, τf , is the fringe length divided by
the linear distance between the fringe’s endpoints. For a perfect line, τf = 1, while
for all other geometries, τf > 1.
Fringe Separation Distance
To calculate the separation distances between stacked lattice fringes, the func-
tion GetFringeSeps was developed. The code is given in Appendix A.3.4. The
function only considers fringe pairs separated within a user-specified range. A sep-
aration range of 0.3 - 0.6 nm was used in the current work because this range was
found to encompass the distribution of fringe separation values without truncation
84
Figure 3.16: (a) Primary particle identified on the original image. (b)
The given fringe is located at rf within the primary particle, and its
orientation deviates from perfect concentricity by angle θf,c. (c) Fringe
length (green line) is approximated by segments connecting pixel centers.
Tortuosity is the ratio of fringe length to endpoint distance.
or inclusion of outliers. In addition, as others have noted [24,169,210], 0.6 nm marks
a good upperbound, since van der Waals forces are negligible beyond this distance.
For each fringe identified in the prior step of fringe measurement, the algorithm
determines the fringe’s major axis (i.e. the axis defining its orientation) and isolates
a region the width of the maximum allowed separation distance (i.e. 0.6 nm) on
either side of the major axis as shown in Fig. 3.17a and b. The Euclidean distance of
each pixel within this region to the nearest pixel of the reference fringe is computed.
Then, the locations of the pixels of each neighboring fringe are determined within
this Euclidean distance map (EDM). This is illustrated in Fig. 3.17c, where the
Euclidean distance of each pixel away from the reference fringe is displayed as a
grayscale intensity. A fringe’s overall separation distance from the reference fringe
is calculated as the average of the Euclidean distances of its pixels. The separation
distance between a given fringe pair is the average of the two separation distances
85
Figure 3.17: (a) Fringes identified on the original image. (b) Isolated
region for analysis around the reference fringe (blue). (c) Neighboring
fringes (green) superimposed over a grayscale map of the Euclidean dis-
tance from the reference fringe.
calculated when each fringe in a pair serves as the reference fringe.
Fringe pairs must also meet two criteria for parallelism. First, the orientations
of the reference fringe and of the neighboring fringe may differ by no more than
a user-supplied tolerance. If part of the neighboring fringe extends beyond the
measurement window, only the portion of the fringe within the window is considered
in the analysis. An orientation tolerance of ±30◦ was used in the present study. A
second measure of parallelism comes from the fact that the calculated distance from
fringe i to fringe j will generally not be the same as that of j to i. To illustrate this,
consider the two artificial fringes shown in Fig 3.18a. While the overall orientation
of the two fringes’ major axes is parallel, the contours of the two fringes clearly are
not. Consequently, the fringe separation distance is 46% larger when calculated from
fringe i to j than when calculated from j to i. If this artificial fringe image were to
represent an image obtained at a magnification of 4×105, this would be a 0.14 nm
difference in the fringe separation distance. This discrepancy can be visualized in
the different Euclidean distance map images that are generated depending on which
86
Figure 3.18: (a) The major axes fringes i and j are parallel however
their contours are not. (b) Visualization of the EDM from fringe i. (c)
Visualization of the EDM from fringe j.
of the two fringes is serving as the reference fringe (Fig. 3.18b and c). In the present
work, for a fringe separation measurement to be retained, the fringe pair must
reciprocally calculate the same separation distance within a tolerance of ±0.05 nm.
Figure 3.19: Final measured fringes as displayed in the Aerosol Image
Analyzer software. The program identified the fringes in yellow as neigh-
bors to the fringe shown in blue.
If a given fringe pair meets all of the above criteria (separation distance, ori-
entation difference, and reciprocal separation difference all within allowable ranges
87
and tolerances), the fringe separation between the two fringes is included in the
output of the GetFringeSeps function. An example of the final fringe measurements
displayed by the AIA program are seen in Fig. 3.19. The user can verify the results
of GetFringeSeps by clicking on a fringe object within the AIA program. The pro-
gram highlights in yellow the neighboring fringes that meet the criteria for pairing
with the clicked fringe (in blue), as shown in the figure.
3.6 Soot Oxidation Rate
Once measurements within the soot flame have been obtained per this Methods
section, the soot oxidation rate may be determined and analyzed with respect to
changing soot morphology, nanostructure, temperature and gas composition. The
soot oxidation rate is derived as follows. Consider a control volume (CV) around
the soot flame as depicted in Fig. 3.20. Soot enters the CV with a mass flow rate
of ṁs,1, resides within the CV for time ∆t, and then exits with mass flow rate ṁs,2.
The change in soot mass within the CV is given by:
∆ms = (ṁs,1 − ṁs,2)∆t (3.21)
The radius of the control volume, RCV , is constant and is sufficiently large to radially
encompass all of the soot at each axial location within the soot flame. The height
of the CV is simply the product of the soot velocity vs and ∆t.
The volume of soot within the control volume is:
∫ RCV
Vs,CV = ∆tvs 2πrfs(r)dr (3.22)
0
88
Figure 3.20: The soot flame control volume used in soot oxidation rate analysis.
The integral term in Eq. 3.22 is the sectional integrated soot volume fraction, Fs,
whose value is experimentally determined via Eq. 3.2. The surface area of soot
within the CV is then given by:
Ss,CV = ∆tVs,CVSV (3.23)
where SV is the volume specific surface area, determined from Eq. 3.10.
The soot oxidation rate per unit of soot surface area within the control volume
can be expressed as:
−∆ms
ẇox = lim (3.24)
∆t→0 Ss,CV ∆t
Recognizing that ṁs = ρsvsFs, combining Eq. 3.21-3.24, and taking the limit ∆t→ 0
the expression for the soot oxidation rate per unit surface area becomes:
−ρs d(vsFs)
ẇox = (3.25)
vsFsSV dt
Once the overall soot oxidation rate is known, the next task is to determine
the reaction kinetic parameters for the two principal oxidizers, O2 and OH. Owing
to the small size of soot primary particles, the rate of soot oxidation is thought to
89
be limited by the chemical kinetics of the heterogeneous reactions, rather than by
the rate of diffusion of gas phase oxidizers to the soot surface [247]. The reactions
for soot oxidation by O2 and OH are:
Cs + O2 −→ 2CO + products (3.26)
Cs + OH −→ CO + products (3.27)
Rate expressions will be sought for these two reactions. Assuming that oxidizing
species i has a constant activation energy EA,i and a constant collision efficiency ηi
with the soot surface, the reaction rate can be w(ritten i)n the Arrhenius form:
ηi[i]v̄imC,i −EA,i
ẇox,i = exp (3.28)
4 RuT
where [i] and v̄i are respectively the mole concentration and mean molecular velocity
of species i, mC,i is the mass of carbon removed per mole of reactive collision between
i and the soot surface (e.g. 12 g/mol for OH), T is temperature, and Ru is the
universal gas constant. Assuming species velocities follow a Maxwell-Boltzmann
distribution, v̄i is: ( )1/2
8RuT
v̄i = (3.29)
πMi
where Mi is the species i molar mass. After applying the ideal gas law, combining
Eq. 3.28 and 3.29, and grouping constants, the following expression is obtained for
the oxidation of soot by species i: ( )
ẇ = A p T−1/2
−EA,i
ox,i i i exp (3.30)
RuT
where Ai is the Arrhenius pre-factor, and pi is the partial pressure of species i. In
the case of OH, the activation energy is understood to be zero [46], and the OH
90
collision efficiency is commonly written separately from the rest of the Arrhenius
pre-factor. In this case, Eq. 3.30 reduces to:
ẇox,OH = η
−1/2
OHAOHpOHT (3.31)
For OH, the remaining pre-factor term, AOH, is equal to 0.0127 s-K
1/2/m. Note that
the assumption of constant collision efficiency for both oxidizers implies a constant
surface concentration of active sites (i.e. CS =const. in Eq. 2.1). However, this is by
no means a given, as evidenced by the multitude of studies indicating changing soot
reactivities depending on factors such as nanostructure, prevalence of heteroatoms,
etc. (See Sec. 2.4.4). For the present study, a constant ηi shall be treated as a null
hypothesis, which will be evaluated in light of nanostructural measurements and of
the goodness-of-fit of proposed reaction rate expressions.
In experiments involving only one oxidizer, typically molecular oxygen, the
reaction rate parameters EA,i and Ai may be obtained from the slope and intercept
of a plot of Ki vs. 1/T obtain(ed by rearr)anging Eq. 3.30:
ẇ 1/2ox,iT −EA,i 1
Ki = ln = + lnAi (3.32)
pi Ru T
However, in flames, the presence of multiple oxidizers complicates straightforward
determination of the reaction rate parameters. For the present study, the measured
soot oxidation rate will be compared against predictions of a combination of the
Nagle and Strickland-Constable mechanism for O2 [42] and the OH mechanism of
Neoh et al [43], as well as the optimized expressions suggested by Guo et al. [46].
Then, an attempt will be made at determining rate expressions optimized against
only the measurements in the present study. This will be done by varying the values
91
of EO2 , AO2 , and ηOH across the ranges of published values for these parameters
and maximizing the coefficient of determination between measured and predicted
oxidation rates.
3.7 Uncertainty Analysis
The uncertainty of a quantity calculated from a data reduction equation that
combines multiple independent variables, is obtained from the Taylor Series method
(TSM) of uncertainty propagation [248,249]:
∑( )2
u2
∂y
(y) = u2(xi) (3.33)
∂x
i i
Here, u(y) is the combined standard uncertainty for a result y = y(x1, x2, . . . xn),
and u(xi) is the elemental standard uncertainty of each independent variable xi.
The TSM method assumes a symmetric confidence interval around y, and requires
that all elemental uncertainty distributions are known and symmetric. In cases in
which these assumptions or requirements cannot be met, the Monte Carlo method
(MCM) of uncertainty propagation is used instead [249,250].
Regardless of whether TSM or MCM is used, the elemental uncertainty of each
independent variable must include both random (precision) and systematic (bias)
uncertainties. As discussed earlier in Sec. 2.2.3, uncertainties stemming from op-
erator bias and sample variation are difficult to estimate because a measurement
capability analysis of TEM-derived aerosol morphology is currently lacking from
the literature. To address this gap in knowledge, and to generate a robust esti-
mate of measurement uncertainties in the current work, a detailed repeatability and
92
reproducibility study (Gage R & R) is presented in Chapter 4.
Whenever possible, the uncertainties obtained from Gage R & R analysis will
be used in the confidence intervals reported in the present work. When this cannot
be done, u(xi) will be obtained from a statistical analysis of multiple measurements.
Other uncertainties will be adopted from the best available estimates in the litera-
ture. All uncertainties in the present work are reported at the 95% confidence level
unless preceded by the modifier standard, indicating the value represents a single
standard deviation.
93
Chapter 4: Repeatability and Reproducibility of TEM Measurements
and Surface Area Validation
This chapter presents a study of the repeatability and reproducibility of soot
primary particle and surface area measurements obtained from TEM image analy-
sis. The purpose is fourfold. First, although TEM is used widely to measure the
size and structure of aerosols, a measurement system analysis of TEM used for this
purpose is lacking from the literature. This study fills this gap in knowledge. Sec-
ond, the present work employs several methods intended to reduce operator bias,
(see Sec. 3.5.2.1), and an assessment of their efficacy is needed. Third, multiple
methods of automating the measurement of primary particle size distributions from
TEM images have been presented in the literature. If these methods are reliable,
they would greatly accelerate one of the more time-consuming components of TEM
aerosol analysis. This study evaluates their capabilities. Lastly, validation of the
soot surface area measurement method presented in Sec. 3.5.3 is needed. Validation
is performed here against the BET surface adsorption method.
94
4.1 Non-Bias-Controlled Results and Study Motivation
Prior to the development of the Aerosol Image Analyzer software (see Sec. 3.5.1),
measurements of soot primary particle diameter from TEM images were performed
manually in ImageJ [237]. In the course of performing these measurements, sub-
stantial discrepancies were observed in the results obtained by two equally-qualified
operators. Figure 4.1a shows the results of measurements performed by the two
operators on the same five image sets. No attempts were made to randomize which
images were analyzed, which regions within each image to measure, or how many
measurements to make; all such decisions were left to the judgment of the opera-
tor. The error bars shown in Fig. 4.1 represent the uncertainty at 95% confidence
that can be attributed to non-operator effects (i.e. image resolution and statistical
variance). The percent difference in the mean primary particle size for each sample
ranged from 11% - 33%, and a consistent operator bias is readily observable.
To test that this observation was repeatable, and to better gage its magnitude,
a formal follow-up test was performed with three operators. The operators measured
primary particle diameters on image sets of two samples collected from the soot flame
at a 13 mm height above burner. The operators were instructed to measure at least
300 primary particles per image set, but were not told which images within each
set to select, or which regions therein to measure. The results, shown in Fig. 4.1b,
again demonstrate considerable variability that cannot be attributed to statistical
precision alone. Indeed, there is no overlap of 95% confidence intervals among
any of the operators for any of the 7 samples considered across both tests, and
95
Figure 4.1: Preliminary measurements of mean primary particle diameter without
bias controls. Both an initial test (a), and a follow-up test (b) show substantial
variability between operators, and a consistent operator bias. Error bars reflect the
precision of the mean at the 95% confidence level.
the consistent relative trend among the operators confirms the significant between-
operator effect. In the follow-up test (Fig. 4.1b),the overall fluctuation, calculated
as the measurement range over its average, was 18.9% and 17.6% for samples 6
and 7, respectively. This is comparable with the fluctuation of primary particle
measurements across all operators reported by Kondo et al. [150].
Since operator bias is clearly present in primary particle measurements ob-
tained using traditional methods, it is fair to inquire into the efficacy of the bias
mitigation techniques employed in the present work (Sec. 3.5.2.1). Moreover, it
would be valuable to quantify the overall uncertainty of TEM-measured primary
particle size distributions, accounting for repeatability as well as variation across
samples and operators. To these ends, a gage repeatability and reproducibility
(Gage R & R) study was undertaken to produce a statistically robust estimate of
96
the true uncertainty associated with TEM measurements of soot primary particles.
We are also interested in evaluating the ability of several automated mea-
surement methods presented in the literature to accurately measure soot primary
particle size distributions. Using the Gage R & R results as the baseline, three auto-
mated methods are evaluated: two employing a Circular Hough Transform (CHT)
algorithm and one utilizing Euclidean distance mapping (EDM).
Finally, with a firm understanding of the sources and magnitudes of TEM
measurement uncertainties, analysis is extended to the important measurement of
soot surface area. The mass-specific surface areas derived from TEM analysis are
compared to results obtained by the BET method, which is a widely-recognized
standard for measuring nanoparticle surface area.
4.2 Methods
4.2.1 Bias-controlled measurements
With the ring burner used to produce the ternary flame removed, three soot
samples were thermophoretically drawn from the propylene/air co-flow diffusion
flame on separate days at a height of 10 cm above the co-flow fuel port. The soot
was deposited onto 200 mesh copper TEM grids with a standard carbon support
film (Electron Microscopy Sciences CF200-Cu). Coordinates for imaging on the
TEM grid plane were randomly generated. If soot was present at a coordinate, an
image was recorded with no attempt to center the viewing window on any partic-
ular image element. Individual aggregates were identified in the images and then
97
randomly chosen for analysis. Four independent operators, three of whom made
the preliminary measurements, performed image analysis using the Aerosol Image
Analyzer program. The program randomly selected 100 × 100 pixel regions of in-
terest (ROIs) on each soot aggregate image. To ensure that more weight was not
given to primary particles of smaller aggregates, the number of ROIs was propor-
tional to an automated estimate of the aggregate’s projected area. Operators were
directed to measure every element within these ROIs they considered to reasonably
constitute a primary particle using the semi-automated CSES algorithm, detailed in
Sec. 3.5.2.2. If not satisfied with the algorithm’s output, the operator could reject it
and remeasure by selecting a different pixel or restricting the diameter range. The
semi-automated measurement therefore reflects an operator’s best judgment, but is
also expected to reduce bias since it quantifies image features uniformly. The in-
struction to measure every discernible primary particle within an ROI was included
to both inhibit selection bias by the operator, and to get the best estimate of pri-
mary particle overlap. Each operator performed 2 replicate measurements on each
sample’s image set, yielding a total of 24 measurement sets with an average of 290
measured primary particles per set. The randomly chosen images and ROIs used
for a given replicate were the same for all operators.
4.2.2 Gage R & R Analysis
The true uncertainty of the TEM measurement method described above and
the extent to which it eliminates operator bias, was assessed through analysis of
98
variance (ANOVA) gage repeatability and reproducibility analysis. Since operators
performed the measurement the same number of times on the same set of samples,
and assuming the operators represent random selections from a population of all
possible operators, the appropriate Gage R & R model is a balanced two-factor
crossed random model with interaction [251]:
Yijk = µY + Pi +Oj + (PO)ij + Eijk (4.1)
Here, Yijk is the measured value of sample i, by operator j, the k
th time, and µY
is the true mean of the measurand Y from the population of all samples producible
by the given process (in this case, the co-flow flame). The terms Pi, Oj, (PO)ij,
and Eijk, are jointly independent normal random variables with means of zero and
variances σ2 , σ2 2 2P O, σPO, and σE. These correspond to the variation away from µY
due to effects of sample, operator, sample-operator interaction, and random error,
respectively. If an F-test determines the sample-operator interaction to be negligible,
the term (PO) 2ij may be dropped from Eq. 4.1, and one may assume σPO = 0. This
model is termed a balanced two-factor crossed random model with no interaction.
The variances σ2 2O and σPO sum to yield the reproducibility, σ
2
Repro, while σ
2
E
is the repeatability, σ2Repeat. The variance of the measurement system, σ
2
M (also
referred to as the Total Gage R & R), is then:
σ2M = σ
2
Repro + σ
2
Repeat (4.2)
and the total observed variance can be written as:
σ2 2 2Tot = σP + σM (4.3)
99
The model given in Eq. 4.1 assumes overall repeatability uncertainty is greater
than measurement resolution. The measurands here are the mean, dp, and standard
deviation, sdp , of the distribution, not the individual primary particle measure-
ments. The resolution of dp and sdp estimated from n measured primary particle
√
diameters a√re given by their respective standard deviations: sd = sdp/ n andp
ss = sdp/ 2(n− 1). The latter expression assumes a normal distribution of pri-dp
mary particles, however uncertainty due to any divergence from normality is ex-
pected to be negligible compared to other sources of uncertainty.
The values of these variances and µY found with Gage R & R analysis are
point estimators (so denoted σ̂2) of the true values, and are themselves subject to
uncertainty. Uncertainty distributions for these terms were simulated following the
generalized inference approach of Hamada and Weerahandi [252]. Sampling from
these distributions, Monte Carlo methods were employed following the approach
outlined in Ref. [253] to compute confidence intervals for the both the means and
standard deviations of the measured size distributions.
To combine operator measurements and obtain confidence intervals for each
sample, a balanced one factor random ANOVA model is used:
YAjk = µY +OA Aj + EAjk (4.4)
For a given sample A, YAjk is the k
th replicate measurement by operator j, and
µY is the true mean of the measurand YA. The terms OAj and EAjk represent theA
deviation of the measurement away from the true mean of sample A due to operator
and random effects, respectively. Since the sample is fixed, and OAj and EAjk are
100
assumed to be normally distributed about a mean of zero, µY also represents theA
true value of µY , for which the best estimate, µ̂Y , is the mean of all measurements,A A
YA∗∗, for the sample. The confidence interval for YA is then found from
√
YA = µ̂Y ± s2OFA 1−α:1,o−1/ro, (4.5)
∑
where s2O = (r/(o − 1))
o
j=1(YAj∗ − YA∗∗)2 is the mean squares for o operators
each performing r replicates, YAj∗ is the mean of measurements by operator j, and
F1−α:1,o−1/ro is the F -statistic at significance level α, having 1 and o− 1 degrees of
freedom [251].
4.2.3 A simplified approach to obtaining sample confidence intervals
As a practical matter, it would be desirable to estimate the uncertainty of a
sample’s primary particle distribution without the relatively large number of repli-
cates required by ANOVA. One approach treats the combination of operator results
as an inter-laboratory evaluation in which operators are equally competent and sub-
ject to independent random and systematic effects [254]. The measurements of each
operator j for a given sample are pooled, and the resulting distribution will have
a mean and standard deviation with standard random uncertainties, equal to sdp,j
and ss , as given in Section 4.2.2. For a given sample A, the measured value Ydp,j Aj
(here either dp or sdp) from each operator j may then be combined using a weighted
mean, where the weight is defined as wAj = 1/s
2
Y . The combined result, YA,C , isAj
then: ∑∑j wAjYAjYA,C = (4.6)
j wAj
101
for which the standard uncertainty is:
1
uY = √A,C ∑ (4.7)
j wAj
If the interval 2uY of this combined mean fails to encompass a non-negligibleA,C
fraction of operator results, an expanded confidence interval that includes an addi-
tive bias correction with its own expectation value and uncertainty distribution is
appropriate. Since each operator’s results are believed to be equally probable, this
correction is assumed to follow a rectangular distribution on the interval (−a1, a2),
where −a1 =minj(YAj)− YA,C and a2 = maxj(YAj)− YA,C . The expected value for
√
this correction is B = (a2− a1)/2 with a standard uncertainty uB = (a2 + a1)/ 12.
Finally, the confidence interval for the measurand YA is:
YA = (YA,C +B)± k(u2 + u2 )1/2Y B (4.8)A,C
where a value of 2 for the coverage factor k corresponds to a 95% confidence level.
4.2.4 Automated Measurements
4.2.4.1 Circular Hough Transform
The different methods proposed in the literature for automating primary par-
ticle measurement was touched upon in Sec. 2.2.2.3. Here, three different automated
measurement methods were applied to the TEM image sets obtained in Sec. 4.2.1.
The first, proposed by Grishin et al. [134], applies CHT to binarized images of soot
aggregates, and will be referred to as the binary-CHT method. Techniques for au-
tomating the image binarization step have been proposed [134,244], however, as with
102
the soot sampled on carbon lacey grids (3.5.4), automated procedures were found
to be incapable of reliably separating aggregate from background. The greatest suc-
cess was obtained with a general procedure that employed edge-preserved smoothing
(e.g., median filtering) and contrast enhancement followed by background removal
via a rolling-ball transform and then manual thresholding. Grishin et al., [134] used
a modified CHT algorithm to reduce processor load and eliminate falsely identi-
fied primary particles produced by convex fragments on the aggregate border. As
these were not issues in our implementation, we used the unmodified CHT found in
MATLAB’s imfindcircles function.
The second method, suggested by Kook et al. [135], also uses the CHT algo-
rithm, however with different pre-processing. First, the image undergoes inversion
and self-subtraction to enhance contrast between aggregate and background. Pri-
mary particle edges are then enhanced by negative Laplacian filtering, after which
Canny edge detection is applied. We used the MATLAB script provided by Kook
et al. [135], which also utilizes the imfindcircles function. This method is referred
to here as the Canny-CHT method.
Both CHT methods require the user to specify a diameter range and a sensi-
tivity level. The sensitivity level is a value between 0 to 1, where higher sensitivities
interpret more image features as circular. The Canny-CHT method also requires
specified values for self-subtraction level and negative Laplacian filter shape param-
eter. Kook et al. [135] observed that parameter values, especially the lower-bound
diameter, and CHT sensitivity, substantially affected results. Without knowledge
of the primary particle size distribution a priori, the choice of parameter values
103
represents a source of uncertainty for all CHT methods. In practice, one would
likely estimate the diameter range manually before performing automated analy-
sis. Therefore, the diameter ranges found from the Gage R & R measurements
were used as inputs to both CHT algorithms. For the binary-CHT method, the
sensitivity value was varied, based on personal experience, between 0.8 and 0.92.
For the Canny-CHT method, parameter ranges were adopted from those that Kook
and co-workers [135] found to optimally detect soot primary particles produced by
five different diesel combustion facilities. Sensitivity ranged from 0.75–0.79, self-
subtraction level ranged from 0.8–1.2, and alpha was 0.1. Each of the input param-
eters to both CHT algorithms were then varied individually to assess sensitivity of
the response variables.
4.2.4.2 Euclidean Distance Mapping
The EDM method of Bescond et al. [133] was evaluated. This approach has
the advantage of requiring no input parameters, however results must be calibrated
and a distribution shape assumed. Bescond and co-workers assumed a lognormal
distribution and computed calibration parameters that adequately fit EDM results
from soot produced by both an aircraft engine and an ethylene laminar diffusion
flame. Given the very different types of soot produced by these systems, the calibra-
tion is expected to be robust and was applied to the present study. Measurement
was performed in the NIH software ImageJ using the plug-in provided by Bescond
104
et al. [133]. The resulting measurementswere expectedto follow a sigmoidal curve:  − −1ln d ln dpgS(d)  − β lnσ= 1 + exp pg  (4.9)S(0) Ω
The left-hand side of this equation is the normalized average aggregate surface area
after the EDM transformation at scale diameter, d, itself a function of the EDM
threshold value. The calibration constants are β = 1.90 ± 0.03 and Ω = 0.80 ±
0.03 [133]. The geometric mean, dpg , and geometric standard deviation, σpg, were
determined from a fit of the sigmoidal curve to the data, and were then converted
to their arithmetic values for comparison to results from other methods.
4.2.5 TEM-Derived Mass Specific Surface Area
To obtain robust confidence intervals for the mass specific surface area (MSSA)
of each of the three samples, the Gage R & R analysis presented in Sec. 4.2.2 was
extended to two additional measurands: the skewness of the primary particle size
distribution, γdp and the mean projected overlap coefficient, Cov,p. To compare the
two different methods presented in Sec. 3.5.3 for calculating the lost surface area
and volume due to overlap, FS and FV , were calculated using both Eq. 3.14, and
Eq. 3.19. As an additional comparison, MSSA was also calculated using the two
simplifications common in the literature: primary particles in single point contact
(i.e. no overlap), and monodisperse primary particles in single point contact. After
obtaining the volume specific surface area, SV , per Eq. 3.10, or via the simplified
Eqs. 3.7 and 3.8, the MSSA is simply:
Sm = SV /ρs (4.10)
105
The soot density, ρs, represents an additional source of uncertainty. In the
surveyed literature, which considers soot from a range fuels and flame types, the
value of ρs varies between 1.46 and 2.05 g/cm
3 [127,128,255–259]. No studies report
the density of soot from a propylene/air flame, however a good estimate can be
obtained using soot from flames of unsaturated aliphatic hydrocarbons. Combining
the values from such studies (i.e. Refs. [127,255–258]) in an inter-laboratory evalua-
tion as described in Sec. 4.2.3, yields ρs = 1.85±0.15 g/cm3. The MSSA confidence
intervals were obtained by propagating the independent elemental uncertainties (i.e.
those corresponding to dp, sdp , γdp , Cov,p, and ρs) obtained either from Gage R & R
analysis or from literature using the law of uncertainty propagation, (Eq. 3.33).
4.2.6 BET-Derived Mass Specific Surface Area
BET analysis was employed to characterize the porosity of the mature soot
produced by the co-flow flame and to validate the method of measuring soot surface
area from TEM images. To collect soot in bulk for BET analysis, a square copper
plate, 1.6 mm thick with 12.7 cm sides, was suspended 10 cm above the co-flow
fuel port, the same location from which the samples for TEM analysis were drawn.
A 6 mm hole in the center of the plate was positioned on the soot column axis.
Ultrafine particulates followed exhaust gas streamlines through the hole and onto a
0.2 µm filter (Sigma-Aldrich Z269212) connected to a vacuum pump, while larger
soot particles accumulated on the cold plate. For each of three samples taken,
approximately 200 mg of soot was collected from the filter and plate. Attempts were
106
made to collect soot at the exit of the soot flame as well, however, the quantity of
soot available at this location was insufficient for BET analysis. Bulk soot collection
was performed at the same time that TEM samples were obtained.
BET surface area and t-plot external
surface area measurements by adsorption of
N2 were performed on a Micrometrics ASAP
2020 porosimeter at the University of Mary-
land NanoCenter’s FabLab. The t-plot exter-
nal surface area method is based on the as-
sumption that in a certain region of the adsorp-
tion isotherm, micropores (<2 nm) are already
filled, and the remaining external surface fol-
lows a linear pressure dependence. Absent any
micropores in the aggregates, these two sur- Figure 4.2: Soot collection appara-
tus for BET measurement.
faces areas should show good agreement [260].
The porosimeter t-plot analysis also estimates the specific volume of surface micro-
pores, which can then be used to calculate the porosity (i.e. the void fraction) of
the sample.
The uncertainties of BET and t-plot surface areas reported by commercial
porosimeters typically only consider the goodness of fits to the plotted isotherm
data. However, there are far more sources of error beyond this [261]. For the
work here, adsorption-derived MSSA values will be assigned either the combined
uncertainty of the porosimeter and soot mass (via Eq. 3.33), or the known relative
107
standard uncertainty for adsorption methods of ±5% [262], whichever is greater.
4.3 Results
4.3.1 Gage R & R Results
The mean primary particle diameter, dp, and standard deviation, sdp , for each
measurement replicate is given in Fig 4.3, with the corresponding Gage R & R re-
sults in Table 4.1. An F-test (α = 5%), determined that sample-operator interaction
was negligible for both dp, and sdp , (p = 0.156 and 0.102, respectively). Hence, a
balanced two-factor crossed random model with no interaction holds. Repeatabil-
ity variances exceeded the variance due to individual measurement precisions which
were s2 ≈ 0.6 and s2s ≈ 0.3. This justifies the assumption that measurementdp dp
resolution is subsumed within overall repeatability [263]. It is also clear from the
differences in replicate measurements in Fig 4.3 that inhomogeneities in the sample
account for some of the repeatability uncertainty. A follow-up test, in which 2 oper-
ators performed 5 replicate measurements on the same group of ROIs on successive
days, found that inhomogeneities accounted for about two-thirds of the overall re-
peatability variance. In contrast to the finding of Kondo et al. [150], there was no
discernible trend in results based on the experience level of the operator.
Sampling from the variance distributions produced by the generalized inference
method, Monte Carlo simulations were used to construct 95% confidence intervals
for key metrics. The true mean of all primary particle diameter means producible
by this process, (that is, the mean of means), µd , is 32.5 ± 5.9 nm (± 18%), andp
108
Table 4.1: Components of variance in the measurement of primary particle diameter
mean and standard deviation as quantified by Gage R & R analysis.
µ̂d σ̂d
Variance Component p p
Variance % Variance Variance % Variance
σ̂2P 4.82 57.4% 2.03 48.1%
σ̂2O 0.53 6.3% 1.82 43.1%
σ̂2E 3.05 36.3% 0.37 8.8%
σ̂2M 3.58 42.6% 2.19 51.9%
σ̂2Tot 8.4 100% 4.22 100%
the true mean of the standard deviation, µs , is 12.3 ± 4.3 nm (± 35%). Thedp
values of µdp and σdp of a specific sample for which a single measurement has been
performed may be known within ± 14%, and ± 33%, respectively. The confidence
intervals for µdp and σdp for any unmeasured sample produced by this process are
32.5 ± 8.9 nm (± 27%) and 12.3 ± 6.7 nm (± 54%), respectively, however a larger
number of samples beyond the three used here would likely narrow these intervals.
Figure 4.3: Primary particle diameter mean and standard deviation for each Gage
R & R replicate.
109
For both dp, and sdp , the total variance is almost evenly split between sample
and measurement system effects. Nearly all the measurement system variation for
dp is due to repeatability - only 6.3% of the overall variance is attributable to oper-
ator effect. This is strong evidence that randomization and CSES semi-automation
were effective in reducing operator bias. This claim is bolstered through a direct
comparison of the fluctuation in measurements with and without bias controls. As
reported earlier in Sec. 4.1, the non-bias controlled measurements of 2nd preliminary
test fluctuated 18.9% and 17.6% for each of two samples across three operators.
With bias-controls in place for the Gage R & R study, however, measurements by
these same operators (Gage R & R operators 1,3 and 4) fluctuated only 4.9%, 9.8%,
and 7.5% for each of the three samples. This amounts to a 59.5% reduction in the
average fluctuation of measurements across the same set of operators.
In contrast, operator effects account for 43.1% of the overall variance of sdp .
An inspection of operator measurements on identical image regions revealed that
operators showed a clear preference for the range of primary particle diameters that
they were willing to consider. This makes sense considering that primary particle
range is the only user-adjustable parameter involved in CSES.
The two methods for combining operator measurements for each sample, pro-
duced comparable results as shown in Table 4.2. The approach outlined in Eqs. 4.6-
4.8 therefore offers a way to estimate the values and uncertainties of µdp and σdp
in the absence of a large number of measurement replicates. Additionally, if mea-
surements by multiple operators cannot be obtained, replicate measurements by a
single operator utilizing bias limiting methods may serve as an adequate surrogate.
110
Table 4.2: Primary particle diameter mean and standard deviation of each sample
using two methods for combining operator measurements. Intervals are at the 95%
confidence level.
dp sd
Sample p
Eq. 4.5 Eqs. 4.6-4.8 Eq. 4.5 Eqs. 4.6-4.8
1 31.1 ± 4.3% 31.3 ± 4.4% 12.5 ± 17.1% 12.6 ± 15.0%
2 35.1 ± 8.1% 35.7 ± 6.5% 13.6 ± 13.8% 13.7 ± 14.4%
3 31.3 ± 9.8% 31.5 ± 8.4% 10.8 ± 25.7% 11.2 ± 20.7%
The overall uncertainty of the combined result of r replicates on given sample A,
could then be estimated following Sec. 4.2.3, by combining σ2O from Table 4.1 with
Eq. 4.7, yielding: ( ∑ )r 1/2
uY = 1/ wAk + σ̂
2
O (4.11)A,C
k=1
where now, the term in the summation corresponds to wAk = 1/σ̂
2
E. If σ̂
2
E can
be considered to be constant across replicates, as is often the case, then Eq. 4.11
simplifies to: ( )1/2
σ̂2
u = EY + σ̂
2 (4.12)
A,C r O
As before, if 2uY does not encompass the value of YA from most measurementA,C
replicates, Eq. 4.8 can be applied.
4.3.2 Automated Results
The three automated methods were applied to each of the 37, 41, and 73 ag-
gregate images of samples 1, 2, and 3, respectively. The Gage R & R measurements
found diameters ranging 6 – 79 nm, 8 – 86 nm, and 8 – 82 nm for these three samples.
These ranges were supplied as inputs to the two CHT-based algorithms. The re-
111
Figure 4.4: Primary particle diameter mean and standard deviation for each sample
as found by CSES (Gage R & R), binary-CHT (CHT1), Canny-CHT (CHT2), and
Euclidean distance mapping (EDM) methods.
maining parameters for each algorithm were varied as discussed in Sec. 4.2.4.1. The
results of all three automated measurements are shown in Fig. 4.4 alongside the Gage
R & R results combined across operators using Eq. 4.5. Both CHT-based algorithms
drastically underpredicted µ̂dp for all three samples. The binary-CHT method also
substantially underestimated σ̂dp , while the Canny-CHT method generally matched
the Gage R & R σ̂dp results. While performing better than CHT, the EDM method
consistently overpredicted µ̂dp . For σ̂dp , the results are statistically equivalent to the
Canny-CHT results. Inaccuracy of the EDM results can be credited to the model’s
assumed calibration values and lognormal distribution. The latter is questionable
given that the distributions found from the semi-automated measurements almost
uniformly failed standard tests for both normality and lognormality.
The error bars in Fig. 4.4 are at the 95% confidence level. For the CHT
112
results, the error bars reflect the statistical precision of the mean combined with
uncertainty caused by varying input parameters other than diameter range. Error
bars for the EDM method include the published uncertainty of the calibration con-
stants [133], and uncertainty in the sigmoidal fits, but do not consider repeatability
and reproducibility uncertainty of the calibration.
The two CHT methods showed sensitivity to several of the input parameters,
most prominently, the lower-bound diameter. For the binary-CHT method, the
value of µ̂dp rose 1 nm for each 1 nm increase in dp,min, and for Canny-CHT, µ̂dp
increased at twice that rate. This large dependence on dp,min is problematic. To force
either CHT method to yield a value for µ̂dp that matches the Gage R & R results for
all three samples, a value for dp,min between 17 and 19 nm must be specified. There
is no practical reason to choose an input value within this range without having
foreknowledge of the distribution. Choice of such a value would also truncate the
bottom 16% of the distribution. One possibility for overcoming this difficulty is
through a weighted scoring scheme for the Hough Transform that is a function of
diameter.
4.3.3 Mass Specific Surface Area Results
The Gage R & R results for the skewness of the primary particle size distri-
bution, γdp , and the mean projected overlap coefficient Cov,p are given in Table 4.3.
As was the case with dp and sdp , sample-operator interaction was found to be negli-
gible for both γdp and Cov,p, (p = 0.055 and 0.255, respectively). Hence, σ̂
2
PO is not
113
Table 4.3: Components of variance in the skewness of the primary particle size
distribution and the mean projected overlap coefficient, as quantified by Gage R & R
analysis.
γ̂d Cov,p
Variance Component p
Variance % Variance Variance % Variance
σ̂2P 0.016 14.8% 5.7× 10−6 0.7%
σ̂2O 0.031 29.6% 7.4× 10−4 83.5%
σ̂2E 0.059 55.6% 1.4× 10−4 15.8%
σ̂2M 0.090 85.2% 8.8× 10−4 99.4%
σ̂2Tot 0.106 100% 8.9× 10−4 100%
included in the analysis. Sample effects have a much weaker impact on the overall
variance here than what was found for dp and sdp , and in the case of Cov,p, sample
effects are essentially zero. Another striking result is the heavy influence of operator
on Cov,p measurements, where σ̂
2
O accounts for nearly 84% of the overall variance.
Clearly, the magnitude of primary particle overlap that can be interpreted from a
TEM image varies greatly from one operator to the next. The true mean of the pri-
mary particle distribution skewness, µγ , is 0.717 ± 0.485 (± 67%), while the truedp
mean of the mean projected overlap coefficient, µC , is 0.277± 0.045 (± 16%).ov,p
Mass specific surface area was measured for each of the three soot samples
using two nitrogen adsorption methods, and four TEM methods, as previously in-
troduced. The results are presented in Fig. 4.5. The external surface area measured
by the t-plot method for each sample was 9%, 12%, and 12% lower than the BET
surface area for each respective sample. In other words, on average, 11% of the total
surface area accessible to the adsorbing N2 molecules, came from micropores on the
soot surface. The porosities (i.e. void fraction) determined by t-plot analysis were
114
Figure 4.5: Mass specific surface area of the 3 soot samples as determined from the
BET and t-plot adsorption methods, and from 4 different TEM methods.
relatively low; 1.5%, 1.7%, and 1.7%, for samples 1, 2, and 3, respectively.
Of the TEM-based methods, two approaches modeled soot as partially-sintered,
polydisperse primary particles (Eq. 3.10). The only difference was how each calcu-
lates the reduction in VSSA due to overlap. The method utilizing Eq. 3.14, was de-
rived from monodisperse simulations and assumed no volume lost to overlap, while
the method of Eq. 3.19 calculated both the surface area and volume lost within each
overlapping primary particle pair. There was a negligible difference (< 1%) between
the MSSA results from these two methods, so for all practical purposes they are
equivalent. The two remaining TEM methods modeled soot as non-sintered primary
particles that were and either polydisperse, (Eq. 3.7), or monodisperse, (Eq. 3.8).
Both methods produced MSSA results that were substantially larger than the mod-
els taking overlap into account. On average, MSSA derived from Eq. 3.7 and Eq. 3.8
were respectively 12% and 44% greater than the models with overlap.
115
While the monodisperse model (Eq. 3.8) clearly overstates the true soot surface
area, the remaining models warrant greater scrutiny. The model of polydisperse
primary particles in point-contact (Eq. 3.7) gives a result that is, on average, 5%
greater than the BET surface area and 18% greater than the t-plot external surface
area. The MSSA values calculated from the models of partially-sintered polydisperse
primary particles fall, on average, in between those from BET and t-plot methods:
(6% below BET and 5% above t-plot). Since pores on aggregate surfaces are not
included in models for image derived surface area, one might expect the TEM results
to hew more closely to the t-plot values, however no such trend is apparent here.
For the purpose of modeling soot oxidation, we are most interested in the sur-
face area that is accessible to oxidizing gases. At high flame temperatures (>1000
K) oxidizing gases are not expected to fully penetrate micropores [30], defined as
pores less than 2 nm wide [260]. Hence the available surface area for oxidation in the
soot flame is expected to fall somewhere between the values reported by BET and
t-plot analyses. The TEM measurements incorporating overlap and polydispersity
of primary particles best meet this criteria, and are therefore assessed as the best
TEM-based method for evaluating soot surface area. At the same time, broad state-
ments about the ”correctness” of this approach are cautioned against. For one, even
with operator bias minimized, TEM-based MSSA measurements consistently have
uncertainties of ± ∼ 20%, when repeatability and reproducibility is included. This
is reflected in the error bars of Fig. 4.5. Hence, for the measurement performed here,
all polydisperse models are ”valid” in a statistical sense, even if models accounting
for overlap are preferable on both empirical and theoretical grounds. Additionally, if
116
oxidation should result in the further opening of surface pores, or make the interior
of soot particles available to oxidizers, the validity of any TEM-based method falls
into question.
4.4 Conclusions
The method of Gage R & R was applied to the measurement of soot primary
particle size distributions from TEM images. Uncertainties stemming from the
sample, operator, and random effect were quantified, and the effectiveness of bias
minimization was assessed. The Gage R & R results also served as the baseline
against for evaluating the performance of different automated TEM measurement
methods. Lastly, soot surface area was determined from TEM images using four
different models and compared to the BET and t-plot adsorption methods. This
study revealed several important findings:
1. Uncertainties in TEM soot measurements are substantially greater
than generally acknowledged. Monte Carlo sampling of Gage R & R
variance distributions found that 95% confidence intervals for a single estimate
of µdp and σdp for a given sample were ± 14% and ± 33%, respectively. If
sample-to-sample variation is taken into account, these uncertainties grow to
± 18% and ± 35%. These are substantially greater than the < ± 3% [22,119,
126, 133] and < ± 5% [115, 133] often reported for µdp and σdp , respectively,
which do not consider variation due to the measurement method. The 95%
confidence of µdp and σdp for any single unmeasured sample producible by
117
the co-flow flame is ± 27% and ± 54%, respectively. Uncertainties can be
reduced by combining measurements across operators (Eqs. 4.6-4.8) or across
replicates of a single operator (Eq. 4.11). Doing so incorporates an estimate
of repeatability and reproducibility uncertainties without demanding a large
number of replicates.
2. Bias minimization was successful. Efforts to minimize operator bias
through randomized image regions and use of the CSES algorithm were largely
successful, especially for measurements of mean primary particle diameter.
Operator effect accounted for only 6.3% of the total variance of µ̂dp , and the
measurement fluctuation of dp, which averaged 18% without bias controls,
dropped to 7.4% among the same operators once bias controls were in place.
For σ̂dp , operator effects still accounted for 43.1% of the overall variance, indi-
cating that even with bias controls, operators showed a preference in the range
of primary particles they were willing to consider.
3. Automated methods of primary particle size distribution measure-
ments were unreliable. All three automated methods that were considered
failed to produce results consistent with the Gage R & R measurements. The
EDM method came closest, but consistently overestimated µ̂dp . A calibra-
tion tailored to the soot produced by a specific process might improve this
method’s performance, although the need to assume a distribution shape will
remain a source of uncertainty. On the other hand, both CHT methods greatly
underestimated µ̂dp and the binary-CHT method also underestimated σ̂dp . In-
118
accuracies in the CHT methods are mostly attributable to a high sensitivity
to the algorithms’ lower-bound diameter input. Less sensitivity to this and
other input parameters is needed to make this approach robust enough to use
broadly. Given the difficulties presented by existing automated techniques, the
semi-automated CSES algorithm (or if unavailable, manual measurements),
with randomization to reduce bias, constitutes the best method for evaluating
soot primary particle size distributions from TEM images.
4. TEM image measurement of primary particles, accounting for poly-
dispersity and overlap, is a valid method for estimating soot surface
area. The soot surface area accessible to flame oxidizers is expected to fall
between the t-plot external surface area, which does not include additional
area within micropores, and the BET surface area, which does. Both TEM
methods modeling primary particles as partially-sintered and polydisperse (i.e.
utilizing Eq. 3.14 or Eq. 3.19) met this criterion. Modeling primary particles
as polydisperse, but not partially sintered (i.e. no overlap), also gave reason-
able results, but were consistently higher than the target range for validity.
The model of monodisperse primary particles in single point contact, though
prevalent in the literature, vastly overstated the soot surface area and should
be dispensed with.
119
Chapter 5: Results
5.1 Axial Flame Velocity Results
Soot flame velocity was determined by tracking the axial motion of a deliberate
perturbation to the flame using high frame rate video. Videos were captured on four
different occasions, and three disturbances were analyzed from each video for a total
of 12 video sections analyzed. From this, a total of 135 data points were obtained.
The axial location vs. time data was most accurately represented by a 2nd order
polynomial fit. The corresponding plot of velocity vs. height above burner (HAB)
is presented in Fig. 5.1.
Figure 5.1: Soot flame velocity vs. height above burner.
120
Soot flame velocity is seen to increase with height above burner due to buoy-
ancy. The soot velocity, vs at a given height above burner, z, is then determined
from the linear best fit of the data, vs = az + b, where a = 0.012 ± 0.0021 and
b = 1.657± 0.168. Velocities calculated in this manner have an uncertainty of ±9%.
5.2 Temperature, Soot Volume Fraction, and Gas Species Concen-
tration Results
Measurements within the soot flame of temperature, soot volume fraction, and
gas species concentrations were reported in detail in the dissertation of Guo [224].
Key results and additional discussion relevant to the preset study are provided here.
5.2.1 Temperature and Soot Volume Fraction
Figure 5.2 shows the radial profiles of temperature and soot volume fraction at
selected locations within the soot flame. At a given HAB, temperatures were nearly
uniform in the radial direction. At a given height, the radial temperature differed by
no more than 150 K. Temperatures are somewhat lower where soot volume fractions
peak, due to soot radiative heat loss. The soot volume fraction results indicate a
hollow soot column.
Figure 5.3 plots soot flame temperature and integrated soot volume fraction
against height above burner. Temperatures at each height were taken as the radial
average of temperatures at locations whose soot volume fraction exceeded half the
local maximum. This can be considered the temperature at which most soot oxi-
121
Figure 5.2: Radial temperature and soot volume fraction at heights of 13, 30, and
45 mm. Figure from Ref. [224].
Figure 5.3: Temperature and integrated soot volume fraction at each HAB. Figure
from Ref. [224].
122
dation occurred at each height. Values ranged from 1500 K at 50 mm to a peak of
1725 K at 13 mm. Integrated soot volume fraction, Fs, continuously decreased with
height due to oxidation, dropping from 1.1× 10−4 to 8.1× 10−6 mm2. Normalizing
Fs by the soot flame cross-sectional area yields an average soot volume fraction, fs,
between 1-15 ppm.
5.2.2 Gas Species Concentrations
Major species concentrations measured by gas chromatography and radical
species, estimated from an assumption of full equilibrium, are provided in Fig. 5.4.
Critical to the present study are concentrations of O2 and OH. The former has a
peak mole fraction of 10% at an HAB of 10 mm due to the entrained air from co-flow
flame below. It quickly drops to its minimum of 0.8% at a height of 20 mm due to
consumption by the hydrogen flame and soot. It climbs steadily thereafter as O2
diffuses from the air.
The OH radical reaches a peak mole fraction of 0.055% at heights of 13 and
15 mm above the ring burner, corresponding with the peak flame temperatures.
Thereafter it falls steadily until reaching a mole fraction of 0.007% at 50 mm. Un-
certainty in OH concentration is estimated at±40% as propagated from temperature
and species measurement uncertainties.
123
Figure 5.4: Species concentrations vs. height above burner. (a) Measured stable
species. (b) Estimated radical species. Figures from Ref. [224].
5.3 TEM Measurement Results
5.3.1 Primary Particle Measurements
Soot primary particles underwent both qualitative and quantitative changes
as oxidation progressed with increasing height above burner. TEM images repre-
sentative of soot at heights of 10, 15, 25, and 50 mm are shown in Figure 5.5, and
illustrate a clear progression in primary particle structure. The primary particles
at HAB = 10 mm are large, spherical, and well-defined, As height increases, they
grow progressively smaller, and more poorly defined. By HAB = 50 mm, there is a
clear loss of sphericity, which some have suggested corresponds to exposure of the
amorphous primary particle core [264].
Primary particle measurements were performed on TEM images obtained at
each sampled location within the soot flame. An average of 495 primary particles,
124
Figure 5.5: Representative images of primary particles obtained at HABs of 10, 15,
25, and 50 mm.
and no fewer than 355, were measured on each image set. At several locations in
the flame, multiple samples were obtained; four were taken at HAB = 10 mm, while
two samples were retrieved at both HAB = 13 and 40 mm. Values reported are the
sample averages at these locations. The sample-to-sample variation was consistent
with that reported in the Gage R & R study (Ch. 4).
The primary particle size distributions (PPSD) for samples obtained at each
HAB are provided in Figs. 5.6 and 5.7. PPSDs shift downward with increasing
HAB, as primary particles of all sizes shrink from oxidation. The shape of the
125
distribution also changes. An Anderson-Darling test for normality, which is robust
for both symmetric and asymmetric distributions [265], was administered for each
data set. At flame locations 20 mm and below, PPSDs most closely follow a normal
distribution while above 20 mm, with the exception of HAB = 45 mm, distributions
are better characterized as lognormal.
The distributions of primary particle diameters are summarized by their mean,
standard deviation, and skewness, while distributions of overlap between primary
particles are summarized by the mean projected overlap coefficient. The best es-
timates for each of these measured terms, respectively denoted µ̂dp , σ̂dp , γ̂dp , and
Cov,p, are plotted against height above burner Fig. 5.8.
As the soot column travels upward, mean primary particle diameter and stan-
dard deviation steadily decrease due to surface oxidation. Distribution skewness
shows an increasing trend with HAB, consistent with the evolution from normal
to lognormal shape. Primary particle overlap shows a slight decreasing trend as
oxidation proceeds. This suggests that primary particles are oxidizing in place with
respect to each other, rather than compacting due to oxidative sintering. This
contrasts with a study of furnace-oxidized soot which did observe compaction [52].
The uncertainties reflected in the error bars in Fig. 5.8, were obtained from
the results of Gage R & R analysis and thus take into consideration variation due
to different samples, operators, and replicate measurements. The relative standard
uncertainties for µ̂dp , σ̂dp , γ̂dp , Cov,p from a single measurement on a single sample are
9.0%, 17.5%, 34%, and 8.1%, respectively. Note that applying Gage R & R results
in this way assumes Gage linearity, which is a reasonable, but not assured, assump-
126
Figure 5.6: PPSDs at heights above burner of 10 to 30 mm.
127
Figure 5.7: PPSDs at heights above burner of 35 to 50 mm.
128
Figure 5.8: Primary particle measurements vs. height above burner. (a) Mean
primary particle diameter. (b) Standard deviation of primary particle diameter.
(c) Skewness of primary particle diameter. (d) Mean projected overlap coefficient.
129
tion. The proportions of these uncertainties stemming from sample, replicate, and
operator are those given in Tables 4.1 and 4.3. For flame locations in which multiple
samples were obtained, the uncertainty was reduced following Eq. 4.11, but with σ̂2P
now used to compute the summation term. The error bars for γ̂dp , and Cov,p appear
particularly large, owing to the relatively narrow range of results and to the large
repeatability and reproducibility uncertainties inherent in these measurements.
5.3.2 Soot Surface Area
Volume specific surface area (VSSA) was calculated assuming a model of par-
tially sintered, polydisperse primary particles (Eq. 3.10). This model was shown
in Ch. 4 to best match results obtained from well-established surface adsorption
methods. That chapter also showed the equivalence of the two approaches (Eq. 3.14
vs. 3.19) for calculating the terms in the VSSA overlap factor, Fov (Eq. 3.9). The
approach of Eq. 3.14 was used here due to its mathematical simplicity.
The VSSA along with the associated mass specific surface area (MSSA) are
plotted against HAB in Fig. 5.9, and Fov vs. HAB is given in Fig. 5.10. Specific
surface area increases with height above burner due to the steady reduction in pri-
mary particle size. MSSA rises from 62 g/m2 at HAB = 10 mm, a value comparable
to those measured in Chapter 4, to a peak of 119 g/m2 at HAB = 45 mm. Specific
surface area drops going from 45 mm to 50 mm. The difference is certainly within
the experimental error, so this drop may simply be statistical. Another possibility is
that primary particles are coalescing into larger units as has been observed by stud-
130
Figure 5.9: (a) Volume specific surface area, and (b) Mass specific surface area vs.
height above burner.
Figure 5.10: Specific surface area overlap factor vs. height above burner.
131
ies in an environmental TEM [264]. The error bars shown account for repeatability
and reproducibility and are about ±18% for VSSA and ±23% for MSSA.
Looking at Fig. 5.10, overlap factor increases with HAB, consistent with the
drop of overlap coefficient seen in Fig. 5.8). Fov grows from 0.86 low in the flame to
a peak of 0.93 at HAB = 40 and 45 mm. In other words, the reduction in specific
surface area goes from 14% to 7% with respect to a point-contact, model of primary
particles. Uncertainty in Fov at the 95% confidence level is ∼ ±9%.
5.3.3 Soot Aggregate Morphology
Soot morphology was measured from TEM images obtained at each sampled
location within the soot flame. At least 279 aggregates were analyzed from each
sample’s image set, with the exception of the sample at HAB = 40 mm, from which
only 104 aggregates were measured due to their sparse deposition on the TEM grid.
In the case of HAB = 50 mm, the TEM grid was too sparsely populated to obtain a
sufficient number of aggregate images, so this flame location was omitted from soot
morphology analysis.
To estimate the sources and magnitudes of the uncertainties of TEM-derived
morphology, the operators and samples used in the Gage R & R study of Chapter 4
were again employed. Sets of 12, 15, and 20 aggregate images were randomly selected
from each of the three respective samples. Each operator was instructed to create
a binary image of each aggregate using the image processing tools available in the
Aerosol Image Analyzer program. Some guidance was given to the operators in this
132
regard, but the image processing procedure and parameters used were ultimately
left to the operator’s best judgment. Once a binary representation of each aggregate
was produced to the satisfaction of the operator, the maximum projected length, L,
and projected aggregate area Aa were measured.
Gage R & R analysis of these measurements revealed that the magnitude of
uncertainties due to random and operator effects were negligible (< 2%) compared to
sample variation. Knowing this, a single operator measured the balance of aggregate
images for the three samples, a total of 37, 41, and 73 aggregates, respectively. From
this, standard uncertainties of 5% and 10% were determined for the means of L
and Aa, respectively. These elemental uncertainties, combined with the published
uncertainties of empirical constants, were used to derive the 95% confidence intervals
given in the results below, following the methodology of Sec. 3.7.
Using the maximum projected length as the characteristic aggregate size, his-
tograms of the soot aggregate size distribution at each HAB were generated, and are
presented in Fig. 5.11. Without exception, the size distributions were lognormal.
Hence, a lognormal fit to each histogram is also plotted, and the geometric mean,
Lg, is listed with each plot. No major trend stands out, however there does appear
to be a shift in the distributions at heights of 35 mm and above. In these locations,
the size distributions are bunched toward lower values of L. Likewise, Lg, though
fluctuating across flame locations, appears to be systematically lower for HAB =
35 to 45 mm than elsewhere in the flame. The significance of this will be examined
further when fragmentation is discussed in Sec. 5.3.4.
Figure 5.12 presents the geometric mean of the radius of gyration, calculated
133
Figure 5.11: Soot aggregate size distributions based on the maximum projected
length, at different heights above burner.
134
at each HAB using the three methods presented in Sec. 2.2.1.2. The first method,
(denoted 2DRg) simply calculates the 2-dimensional radius of gyration from a binary
image of the aggregate, according to Eq. 2.5. The two other methods estimate a
√
3-dimensional value of Rg using the empirical formulas: Rg = LW/β, (Eq. 2.6),
where β = 2.34 and Rg = L/2C, (Eq. 2.7), where C = 1.5. Uncertainties are ±11%.
From Fig. 5.12, the two empirical formulas give essentially the same result, and are
consistently higher than the value of 2DRg by a factor of 1.2±0.02. This is very near
the factor of 1.24 found from simulated aggregates by Köylü et al. [90]. In general,
the radius of gyration is essentially constant from HAB = 10 to 30 mm, and then
decreases steadily beginning at HAB = 35 mm.
Figure 5.12: Radius of gyration geometric mean vs. height above burner.
The number of primary particles in each aggregate, Np,a, was determined us-
ing Eq. 2.4. Then, for each HAB, the fractal dimension, Df , and pre-factor, kf , as
defined by Eq. 2.3, were determined from the slope and intercept of a least-squares
135
Figure 5.13: (a) Soot aggregate fractal dimension, and (b) pre-factor vs. height
above burner.
fit of ln(Np,a) vs. ln(Rg/rp). The fitted plots at each HAB are provided in Ap-
pendix C.1. The value of Rg calculated from Eq. 2.7 was used in this analysis.
The fractal parameters at each HAB are shown in Fig. 5.13. Both Df and kf are
very typical for flame generated soot [96,98,112,115,118,123,125–127]. The mean
value of Df is 1.74, which is very close to 1.78, the theoretical value for diffusion
limited cluster aggregation [103]. Df is essentially constant, with a percent differ-
ence no greater than 5.7% between any two points in the flame. This is in contrast
with groups such as Li et al. [118], who found fractal dimension to increase as soot
matured and began to oxidize in a co-flowing flame. They interpreted this as com-
paction of the aggregates. Ma et al. [52] similarly observed aggregate compaction
due to oxidation in a flow reactor, although a fractal analysis was not performed.
The pre-factor, kf , may trend mildly downward as HAB increases, with the most
136
pronounced drop at HAB = 35 mm. This corresponds with the reductions in L and
Rg already noted at this flame location.
5.3.4 Soot Fragmentation
If soot aggregates undergo fragmentation at a particular point within the flame,
this should be detected as drop in the geometric mean number of primary particles
per aggregate, Npg,a, and should coincide with a shift in the probability distribution
of Np,a. Additionally, the total number flow rate of aggregates, Ṅa, should increase
at the same flame location.
Figure 5.14: Probability distribution of the number of primary particles per aggre-
gate at each height above burner.
The probability distributions of Np,a at each sampled flame location are given
in Fig. 5.14. The plotted distributions are shaded from dark to light as HAB in-
creases from 10 to 30 mm. Within this range, the distribution becomes steadily less
137
weighted toward aggregates with small Np,a and more weighted towards aggregates
with greater Np,a. However, the trend is broken at a height of 35 mm and thereafter,
which are plotted as lines in Fig. 5.14. At HAB = 35 mm the distribution shifts
back toward a greater percentage of aggregates with a small number of primary par-
ticles. This is indicative of large-scale fragmentation occurring across the aggregate
population.
The pattern is mirrored in the plot of Npg,a vs. HAB in Fig. 5.15a, which
exhibits a large drop in Npg,a at 35 mm. Figure 5.15b paints a corroborating picture,
with a jump in Ṅa beginning at 35 mm.
Figure 5.15: (a) Geometric mean number of primary particles per aggregate vs.
height above burner. (b) Total number flow rate of aggregates vs. height above
burner.
The increase in Npg,a, seen here in the lower regions of the soot flame, has
also been observed by Li et al. [118] who attributed the trend to agglomeration by
138
aggregates, though offered no justification for this interpretation. Given that the
large drop in Ṅa from HAB 10 - 13 mm coincides with the region of greatest soot
oxidation (see Fig. 5.3), this drop (and the attendant increase in Npg,a) would seem
to have more to do with the burnout of very small aggregates, than with aggregate
agglomeration.
The decrease in Npg,a, Lg, Rg, and kf , along with the increase in Ṅa, all begin-
ning at HAB = 35 mm is strong evidence that this location in the flame marks the
onset of large-scale aggregate fragmentation. The residence time at this point in the
flame is 19 ms. It is unclear why this should be the critical point for fragmentation
to occur, as there are no major shifts in temperature or species concentrations at this
location. However, given the lack of evidence for internal burning of soot primary
particles (see Sec. 5.3.7), we can surmise that the mode of fragmentation is through
the destruction of structurally weak points in the aggregate through surface oxida-
tion, rather than through internal burning by O2 that consumes material between
primary particles from the inside out. To the best of the author’s knowledge, this
is the first successful detection of soot fragmentation from the statistical analysis of
TEM images.
5.3.5 Primary Particle Number Flow Rate
Though an analysis of the number flow rate of soot primary particles was
not originally planned, and investigation yielded results that merit attention. The
primary particle number flow rate, Ṅp is simply the product of the number flow rate
139
of aggregates and the mean number of primaries per aggregate:
Ṅp = ṄaNp,a (5.1)
Generally, we should expect Ṅp to continuously decrease as soot is consumed during
its upward journey above the ring burner. Indeed, this is the trend from HAB = 10
to 20 mm, as seen in Fig. 5.16. However, an unexpected jump in Ṅp occurs at HAB =
25 mm, after which the downward trend resumes, but now at systematically higher
values of Ṅp. This would suggest that individual primary particles begin to break
apart into smaller primaries beginning at HAB = 25 mm. Moreover, the remnants
of this sundering would have to retain a sphere-like character enough for an operator
to perceive them as primary particles. There is no obvious mechanism for this sort of
fragmentation at the primary particle level. One might expect that this phenomenon
would be preceded by some form of internal burning, however no evidence of this is
apparent in the HRTEM images (see Sec. 5.3.7). Nonetheless, some circumstantial
evidence for primary particle fragmentation does exist. There is a sizable drop in µ̂dp
at HAB = 25 mm (Fig. 5.8a), and this location in the flame does mark the shift from
a normal to a lognormal primary particle size distribution (Fig. 5.6). Qualitatively,
primary particle asphericity becomes visually more pronounced beginning at 25 mm
above the ring burner, which might be the result of spherical primary particles being
broken apart.
Looking for other possible explanations, one might investigate the validity
of the assumptions employed in the calculation of Ṅp, namely, the assumptions of
non-porous spherical primary particles, and of constant dimensionless extinction
140
Figure 5.16: Primary particle number flow rate vs. height above burner.
coefficient, Ke. If primary particles have a high level of porosity, the volume per
primary particle as determined from TEM images as the diameter of average volume,
dpv, will be overstated. This would lead to fewer observed primary particles for a
given soot volume fraction than are actually present. However, for this to be the
origin of the trends in Fig. 5.16, porosity would need to be high near the base of the
flame, with primary particles suddenly becoming non-porous at HAB = 25 mm and
above. Apart from violating common sense, this scenario does not comport with the
available data. Adsorption measurements of the mature soot generated by co-flow
burner showed void fractions less than 2% (Sec. 4.3.3), therefore, soot below HAB
= 25 mm is unlikely to be highly porous. Moreover, HRTEM images show little
evidence of primary particle porosity at any point in the flame.
Turning to the 2nd assumption, for variations in the dimensionless extinc-
tion coefficient to explain the jump in Ṅp, the value of Ke would need to increase
141
sharply at HAB = 25 mm. That is, if Ke is greater than was assumed at 25 mm and
above, the soot volume fraction at those locations is actually smaller than what was
measured. Recall that Ke = 6πE(m)(1 + ρsa), (Eq. 3.3), where ρsa is the ratio of
scattering-to-absorption cross-section. An increase in Ke could come about though
an increase in the relative influence of scattering of the incoming laser light. The in-
clusion of scattering in the soot extinction model can be accommodated through
Rayleigh-Debye-Gans Polydisperse Fractal Aggregate theory (RDG-PFA), which
considers the effects not only of individual primary particles, but also of their mem-
bership within aggregates of various sizes and fractal dimensions [79–81, 229, 266].
Unfortunately, RDG-PFA predicts that ρsa will increase with greater aggregate size,
which would exacerbate, rather than the resolve the present issue. Indeed, if one
assumes that aggregates meet the size criterion of 2πRg/λ ≤ 3 [80], which for the
present case is quite reasonable, RDG-PFA predicts a value of ρsa at HAB = 25 mm
that is almost 60% less than at HAB = 10 mm.
Other factors that may affect Ke, include the extent of primary particle over-
lap and between-particle necking, [145], intra-aggregate multiple scattering, [267],
primary particle asphericity, [268], and degree of graphitization [269]. However, the
effects of such factors is generally much smaller than the first-order scattering effects
predicted by RDG-PFA. At this point, the inconsistencies in the measured number
of primary particles will have to remain an avenue for future research.
142
5.3.6 Selected Area Electron Diffraction
A total of 8 diffraction pattern images were taken from soot samples obtained
at HABs of 10, 15, 25, and 50 mm in the soot flame. Figure 5.17 shows representative
SAED images from each location, and Fig. 5.18 plots the d-spacings and integral
breadths for the d002, d100, and d110 lattice spacings at each HAB. Error bars were
calculated by pooling the relative variances across measurements at each HAB.
Figure 5.17: Representative SAED images obtained at HABs of 10, 15, 25, and
50 mm.
Figure 5.18a shows that overall, the d-spacings are constant throughout the
soot flame. The average values for the d002, d100, and d110 lattice spacings are 3.85,
143
2.08, and 1.21 Å. The interlayer d002 spacing is near the higher end of the 3.5 Å-
3.9 Å range that is typical for soot [76, 161, 162, 164–170, 189, 193, 201]. The d110,
and d100 spacings respectively correspond to first and second-neighbor interatomic
distances of 1.4 Åand 2.42 Å, which is just slightly below the interatomic distances
in crystalline graphite, but is not uncommon in soot due to the presence of bond-
shortening 5-membered carbon rings [201].
Figure 5.18: (a) d-spacings and (b) integral breadths for the d002, d100, and d110
lattice spacings obtained at HABs of 10, 15, 25, and 50 mm.
Qualitatively, the rings in the SAED image at 25 mm appear more sharply
defined that in the other images. This may correspond to the lower d002 and d110
integral breadths at this height. However, the only difference in Fig. 5.18b that has
statistical significance is the d100 increase from HAB = 25 to 50 mm. In principal, an
144
increased integral breadth can indicate a broadening of the probability distribution
of lattice plane spacings. This could correspond to an increasing percentage of
the soot exhibiting an amorphous-like nanostructure. However, a single data point
showing a statistically significant shift is scant evidence for a change in the soot
nanostructure. In summary, the SAED images do not indicate any sort of global
change to the soot nanostructure as it undergoes oxidation in the soot flame.
5.3.7 HRTEM Lattice Fringe Analysis Results
Lattice fringe analysis was performed
on 6 randomly selected high resolution
images from each sampled height above
burner (HAB). Typically, only one pri-
mary particle was present in each image,
although in some cases two or thee could
be clearly identified. The lattice fringes
from each individually identifiable primary
particle were measured separately, follow- Figure 5.19: Diameters of primary par-
ticles used for fringe analysis at each
ing the image processing and fringe mea- HAB. The fitted line serves to guide
the eyes.
surement procedures detailed in Sec. 3.5.7.
By this method, between 2,000 and 7,500 lattice fringes were measured at each HAB,
from a total of 87 different primary particles. Having been randomly selected, the
measured primary particles cover a broad range of diameters as shown in Fig. 5.19.
145
146
Figure 5.20: Representative HRTEM images of soot obtained at heights above burner of 10, 15, 20, and 50 mm. Magnification
is 400,000 for all images.
However, the overall trend matches that of the formal measurement of dp vs. HAB
reported in Sec. 5.3.1.
Figure 5.20 shows HRTEM images representative of soot at heights of 10, 15,
25, and 50 mm. A number of general observations can be made of the images
obtained at all sampled flame locations. For all samples, lattice fringes are generally
oriented concentrically and increase in average length as one moves radially outward.
Fringes near the primary particle core show less order in their arrangement. As is
somewhat evident in the image at HAB = 50 mm, primary particles higher in the
flame are less-perfectly circular than at lower locations. There were no images that
showed evidence of internal burning; (compare to Fig. 2.3).
5.3.7.1 Fringe Length
Lattice fringe length distributions were right-skewed and could be best approxi-
mated as lognormal, although lognormal fits uniformly underpredicted the sharpness
of the distribution peak as exemplified in Fig. 5.21a. Fringe length distributions,
as a whole, remained largely unchanged from one HAB to another. The most dis-
similar distributions, as determined from a pairwise Kruskal-Wallis test, were those
at HAB = 25 and 45 mm, which are plotted together in Fig. 5.21a. Figure 5.21b
reveals no obvious overarching relationship between median fringe length, L̃f , and
HAB, although there is a statistically significant rise in L̃f from 35 to 45 mm above
the burner, followed by a significant drop from 45 to 50 mm. Since the uncertainty
of the median is poorly defined for non-normal distributions, the 95% confidence
147
Figure 5.21: (a) Histograms and lognormal fits of the two most dissimilar fringe
length distributions illustrate the range of Lf variation within the soot flame. (b)
Median fringe length vs. height above burner.
intervals reported in Fig. 5.21b, and for all other medians in this Results section,
were determined by bootstrapping the sample data [270].
Things become more interesting when fringes are scrutinized with respect to
their host primary particles. Consider Fig. 5.22a which shows, at three different
HABs, how the median fringe length changes with respect to radial location, rf ,
within the host primary particle. To calculate medians, fringes were radially grouped
into successive 1 nm-wide rings. Only radial locations with at least 30 measurements
were included in the plot. While there is considerable random variability from one
radial location to the next, the general trend is of increasing L̃f as one moves
farther from the primary particle center, followed by decreasing L̃f at larger radial
locations. Grouping results by HAB obscures the correlation between fringe
length and radial location, due to the diversity of primary particle sizes analyzed.
148
Figure 5.22: (a) Plots from 3 different HABs showing typical contours of median
fringe length vs. radial fringe location. (b) Median fringe length vs. radial fringe
location normalized by primary particle radius. Fringe length drops near a primary
particle’s outer edge due to surface oxidation.
A clearer picture is obtained when the radial location of each fringe is normalized
by the radius of its host primary particle. Figure 5.22b shows L̃f measured at each
normalized radial location, r∗f . For this calculation, fringes were grouped together in
successive rings with normalized widths of 0.05. At a given value of r∗f , there was no
significant difference in the fringe lengths based on height above burner, therefore
measurements from all HABs were combined to form the plot. Fringes at radial
locations outside the user-identified primary particle (due to noncircularity) were
included in the r∗f = 1 median calculation. Figure 5.22b shows that fringe length
grows with increasing radial distance, up 80% of the primary particle radius. Fringe
149
length drops sharply, however, within the outer 20% of the primary particle. This
can be interpreted as the shortening of the carbon layers due to surface oxidation.
If the lengths of non-surface fringes grow with radius, but their median value
remains essentially constant (Fig. 5.21b) even as primary particles shrink (Fig. 5.19),
it must be that fringes within the bulk of the primary particle grow as the surface
oxidizes. To investigate this, the median fringe length at each radial location between
1 and 15 nm was evaluated against the diameter of the host primary particle, dp.
For the analysis, diameters were rounded to the nearest nm and the outer 20% of
each primary particle, where fringe length was clearly affected by oxidation, was
excluded. Figure 5.23a plots L̃f against dp for radial locations of 2, 6, 11, and
15 nm. Two trends are apparent. First, for any given radial location, fringe length
generally increases as primary particle size decreases. Second, the sensitivity of this
relationship becomes more pronounced at larger radial locations.
Figure 5.23b plots the average rate of change of L̃f with respect to dp at
each radial location. Not only is the relationship between ∆L̃f and ∆dp uniformly
negative, but the further one gets from the center of the primary particle, the
more greatly fringe length grows in response to a reduction in primary particle
size. Moreover there appears to be two regimes of fringe length growth. The first
occurs within the core of a primary particle (rf between ∼0 and 12 nm), where
∆L̃f/∆dp decreases modestly as rf increases. The second regime shows a much
steeper change of ∆L̃f/∆dp with respect to rf and occurs nearer to the primary
particle surface, which is undergoing oxidation.
The two regimes point to two modes of carbon layer graphitization. The first
150
Figure 5.23: (a) Median fringe length vs. primary particle diameter for selected
fringe radial locations. (b) Change in median fringe length with respect to primary
particle diameter at each fringe radial location. To exclude surface oxidation effects,
only fringes within the core 80% of the primary particle were used in the analysis.
arises everywhere within the primary particle as a result of thermal annealing. The
effect appears to be weaker near the particle core where the atomic structure is more
securely locked into place within the carbon matrix - an observation also made in
the flame studied by Botero et al. [215]. The second mode is induced by surface
oxidation, which removes cross-links and interstitial material at the outer shell of
the particle, freeing the carbon planes beneath it to realign and expand while still
out of reach of oxidizing gases.
5.3.7.2 Fringe Tortuosity
Fringe tortuosity at each height above burner exhibited a highly skewed distri-
bution. While some authors have attempted to fit a lognormal curve to tortuosity
151
Figure 5.24: (a) Histograms and lognormal fits of the two most dissimilar fringe
tortuosity distributions illustrate the range of variation of τf within the soot flame
(b) Median fringe tortuosity vs. height above burner.
data [118,210], in the current work, no distribution shape could be found that rea-
sonably fit the data. As with fringe length, the tortuosity distribution held relatively
unchanged within the soot flame. Histograms for the two most dissimilar distribu-
tions, (at HAB = 20 and 50 mm as determined by a pairwise Kruskal-Wallis test),
are shown in Fig. 5.24a. Lognormal fits are also plotted for comparison. Substantial
scatter is seen in the plot of median tortuosity, τ̃f vs. HAB given in Fig. 5.24b.
A statistically significant spike in τ̃f occurs at HAB =15 mm, followed by an even
greater drop at HAB = 20 mm. There also may be an upward trend in τ̃f from
HAB = 40 to 50 mm. Possible explanations for these features will be discussed
below.
At all locations in the soot flame, a strong relationship exists between fringe
tortuosity and fringe radial location within the host primary particle. Figure 5.25
152
plots median tortuosity against fringe radial location, rf , at select HABs, as well
as against normalized radial location, r∗f . Radial groupings for the calculation of
medians were the same as those used in the fringe length analysis. Fringe tortuos-
ity consistently decreases with increasing distance from the primary particle core,
although a slight upturn may occur at the very surface. This indicates that the de-
gree of graphitization increases with increasing radius, consistent with fringe length
results. However, unlike fringe lengths, which dropped sharply near the primary
particle surface due to oxidation, there is no dramatic change in tortuosity within
the outer shell. This difference is understandable considering the mechanisms re-
sponsible for each effect. Fringe lengths are reduced predominantly by oxidation
of highly reactive edge site carbons. An increase in curvature, on the other hand,
would come about through the removal of a far less reactive basal plane carbon,
followed by a re-alignment of the carbon plane to incorporate the new 5-carbon
ring. At the same time, curvature reducing mechanisms would also be in effect,
such as the removal of a carbon from a 5- or 7-membered ring, both of which would
tend to relax the curvature of the carbon plane. Due to the bond strain present in
these odd-numbered rings, these carbons are also more reactive than basal carbon.
The cumulative effect is that tortuosity, overall, changes very little due to oxidation.
The slight increase in τ̃f at the primary particle surface is therefore most likely an
artifact of decreasing fringe length rather than a result of increasing curvature.
The median fringe tortuosity at each radial location between 1 and 15 nm was
evaluated against the diameter of the host primary particle, dp. Consistent with the
analysis performed on fringe lengths, diameters were rounded to the nearest nm, and
153
Figure 5.25: (a) Plots from 3 different HABs showing typical contours of median
fringe tortuosity vs. radial fringe location. (b) Median fringe tortuosity vs. radial
fringe location normalized by primary particle radius.
the outer 20% of each primary particle was excluded to avoid confounding trends due
to surface oxidation. Figure 5.26 plots the average rate of change of τ̃f with respect
to dp at each radial location. The plot shows that throughout the bulk of the primary
particle, ∆τ̃f/∆dp is small, but generally in positive territory. This means that at
any given radial location, fringes tend to straighten (i.e. τf decreases) as primary
particle size is reduced. This corroborates the graphitization by thermal annealing
already observed, in which fringe elongation accompanied decreasing particle size.
The data point at r = 15 nm may indicate that the effect on tortuosity is heightened
nearer to the surface oxidation zone, but there is insufficient data to make a strong
154
Figure 5.26: Change in median fringe tortuosity with respect to change in primary
particle diameter at different fringe radial locations. To exclude surface oxidation
effects, only fringes within the core 80% of the primary particle were used in the
analysis.
claim. Similarly, the two negative data points at rf = 1 and 11 nm are more likely the
result of statistical variation than to any special factors occurring at these locations.
5.3.7.3 Fringe Orientation
The soot produced by the propylene co-flow diffusion flame exhibited a loosely
concentric arrangement of lattice fringes about the primary particle core. This struc-
ture is common among combustion soot from short-chained hydrocarbons [119,158,
162, 175]. The histograms in Fig. 5.27a are for the two most dissimilar distribu-
tions of non-concentricity, which occur at HAB = 15 and 25 mm as determined
by a pairwise Kruskal-Wallis test. Distributions changed very little within the soot
flame, and all HABs displayed a distribution peak near 0◦, which is indicative of a
155
Figure 5.27: (a) Histograms and normal fits of the two the most dissimilar fringe
non-concentricity distributions illustrate the variation of θf,c distributions within
the soot flame. (b) Standard deviation of fringe non-concentricity vs. height above
burner.
concentric fringe arrangement. The distributions can be reasonable approximated
as normal, as shown by the plotted fits, although the approximation is worse near
the distribution tails.
The extent of orientational order within this concentric fringe arrangement
can be quantified by the standard deviation of the fringe non-concentricity, with
lower standard deviations signifying greater order. The standard deviation of fringe
non-concentricity, sθ at each HAB is plotted in Fig. 5.27b. The data is fairly wellf,c
scattered about a mean sθ of about 36. Although there may appear to be a subtlef,c
trend of rising sθ as HAB increases, the correlation is not significant (p=0.14).f,c
All measured samples exhibited a reduction in sθ as one moves radiallyf,c
outward within the host primary particle. This is exemplified in Fig. 5.28a for
156
Figure 5.28: (a) Plots from 3 different HABs showing typical contours of the stan-
dard deviation of fringe non-concentricity vs. radial fringe location. (b) Standard
deviation of fringe non-concentricity vs. radial fringe location normalized by primary
particle radius.
three heights above burner. Statistics were calculated within the same radial group-
ings as was done for fringe length and tortuosity analysis. Measurements from all
HABs were combined and normalized against host primary particle radius to create
Fig. 5.28b. Here, sθ trends downward as r
∗
f increases. This matches observationsf,c
by Shim et. al [175] who reported a higher polar order parameter as one moved
radially from the particle nucleus. The downward slope continues until r∗f = 0.9, at
which point, the trend reverses. The higher orientational disorder near the primary
particle center is consistent with randomly distributed PAH clusters, typical in the
cores of flame-generated soots [158,181, 271]. A small but unmistakable increase in
157
Figure 5.29: Change in the standard deviation of fringe non-concentricity with re-
spect to change in primary particle diameter at each fringe radial location. To
exclude surface oxidation effects, only fringes within the core 80% of the primary
particle were used in the analysis.
disorder is present at the oxidizing outer shell of the primary particle. This indi-
cates an increase in carbon plane mobility near the surface, as well as a weakening
attachment to the underlying layers. The mobility of carbon planes near the pri-
mary particle surface is both consistent with and necessary for the oxidation-induced
graphitization inferred from fringe length measurements in Sec. 5.3.7.1.
To see the effect of primary particle size on fringe orientation, the standard
deviation of fringe non-concentricity, sθ , at radial locations from 1 to 15 nm wasf,c
evaluated with respect to diameter of the host primary particle, dp. As was done for
fringe length and tortuosity analysis, diameters were rounded to the nearest nm, and
the outer 20% of each primary particle was excluded to eliminate surface oxidation
effects. Figure 5.29 plots the average rate of change of sθ with respect to d at eachf,c p
radial location. Similar to the tortuosity results, ∆sθ /∆dp, is small but positivef,c
158
in in most locations. This means that in response to a reduction in primary particle
size, fringes at a given radial location become more concentric (i.e. ∆sθ < 0). Thisf,c
is consistent with the picture painted thus far of thermally-induced graphitization
within the bulk of the primary particle. The jump in ∆sθ /∆df,c p at rf = 14 nm is
also consistent with the oxidation-induced graphitization suspected just below the
surface layers. As cross-links between layers are removed by oxidation, the carbon
layers beneath are free to grow and concentrically realign. Although the data point
at rf = 15 nm casts doubt on this interpretation, it may be close enough to the
surface here for carbon plane mobility to increase orientational disorder, as discussed
in the paragraphs above.
5.3.7.4 Fringe Separation Distance
The final HRTEM measurement to consider is the fringe separation distance,
df . Distributions of df appeared nearly symmetric, although lognormal fits were
uniformly superior to normal fits. Nonetheless, means will be used as the sum-
mary statistic, consistent with existing literature (e.g. [118,208,210,210,214]). Fig-
ure 5.30a shows the histograms and lognormal fits of df from HAB = 13 and 20 mm,
which were the least similar data sets as determined from a pairwise Kruskal-Wallis
test. The plot of df vs. HAB in Fig. 5.30b shows large amount of statistical
scatter without any obvious trend. The overall mean value of df across all sam-
ples was 0.427 nm, which is falls right in the middle of the range of typical val-
ues [24, 118,199,207,210,215].
159
Figure 5.30: (a) Histograms and lognormal fits of the two the most dissimilar fringe
separation distributions illustrate the range of df variation within the soot flame.
(b) Mean fringe separation distance vs. height above burner.
Clearer patterns are observable when fringe separation distance is shown with
respect to fringe radial location, which was taken as the average radial location of
the fringes in each pair. As with prior analyses, fringes were radially grouped into
successive 1 nm-wide rings, and only radial locations with at least 30 measurements
were considered. Figure. 5.31a shows the relationship between df and radial rf at
three different heights above burner, and Fig. 5.31b shows df combined across HABs
vs. radial location normalized by primary particle radius. The basic pattern that
emerges is of df that is high near the primary particle core, but that drops with
increasing r until r∗f f = 0.8 at which point df rises until reaching the particle surface.
Relatively large fringe separations near the primary particle center followed
by closer fringes away from the center, again aligns with the core-shell soot model
in which an amorphous nucleus is surrounded by increasingly graphitized carbon
160
Figure 5.31: (a) Plots from 3 different HABs showing typical contours of the mean
fringe separation distance vs. radial fringe location. (b) Mean fringe separation
distance vs. radial fringe location normalized by primary particle radius.
layers (e.g. [119, 158, 161, 162, 166, 172, 173]). This model holds until the inflection
point at r∗f = 0.8, which precisely matches the start of the surface oxidation region
ascertained from fringe length analysis. Here we see that the effect of oxidation is
a widening distance between carbon layers. This would result in weaker coupling
to neighboring layered planes, permitting greater fringe mobility, as was concluded
from fringe orientation measurements. This lends further support to the theory
of oxidation-induced graphitization just below the oxidation region, since fringe
mobility is an ingredient of this graphitization mode.
The mean fringe separation distance at each radial location between 1 and
161
Figure 5.32: Change in the mean fringe separation distance with respect to change
in primary particle diameter at each fringe radial location. To exclude surface
oxidation effects, only fringes within the core 80% of the primary particle were used
in the analysis.
15 nm was evaluated against the primary particle diameter, dp. As before, diameters
were rounded to the nearest nm, and the outer 20% of each primary particle was
excluded to avoid surface oxidation effects. Figure 5.32 plots the average rate of
change of df with respect to dp at each radial location. For each plotted point,
∆df/∆dp is positive, meaning that as dp shrinks, df decreases as well. This comports
with results of Lf , τf , and θf,c, which indicate thermally-induced graphitization
within the bulk of the primary particle, as oxidation proceeds on the surface.
Lastly, several authors have argued that fringes with greater tortuosity will
produce larger fringe separations distances by inhibiting stacked layer develop-
ment [209, 214]. While we observe regions in which both tortuosity and separation
distance decrease due to graphitization, an analysis of individual fringes found no
162
correlation between tortuosity and separation distance.
5.3.7.5 Nanostructure at the Particle Surface
A threefold summary of the HRTEM data analyzed thusfar can now be made.
First, there is no evidence of internal burning or major pore openings within soot
primary particles. Instead, oxidation appears to proceed inward from the particle
surface in a shrinking sphere manner. Second, primary particles can be divided into
an inner radial 80%, in which lattice fringes display greater order and graphitization
with increasing radius, and an outer 20% in which this trend reverses due to surface
oxidation. Third, while oxidation is happening at the soot surface, shrinking the
primary particles, graphitization is occurring in the particle interior, as evidenced
by the growing, straightening, re-orienting, and compaction of lattice fringes.
We now turn our attention to the affects of oxidation on nanostructure within
the outer 20% of the primary particles. Section 2.4.4 detailed the myriad ways
in which soot nanostructure affects its ability to be oxidized. Not only does the
nanostructure dictate how carbons with varying reactivities become accessible to
gas-phase oxidizers, but changes to the nanostructure can alter these reactivities.
Since oxidation is essentially isolated to the outer primary particle shell, changes to
nanostructure within this region will directly inform the approach that should be
taken in analyzing chemical kinetics with the gas phase.
For fringe lengths, a different picture emerges at the primary particle surface
than in the bulk. As was done in Sec. 5.3.7.1, Fig. 5.33a plots the median fringe
163
Figure 5.33: Fringe lengths near the primary particle surface. To highlight surface
oxidation effects, only fringes within the outer 20% of the primary particle were used
in the analysis. (a) Median fringe length vs. height above burner. (b) Change in
median fringe length with respect to primary particle diameter at each fringe radial
location.
length against height above burner and Fig. 5.33b plots the average rate of change
of L̃f with respect to dp at each radial location. However, now only the outer 20% of
each primary particle is included in the analysis. Figure 5.33a shows no correlation
between L̃f and HAB, and notwithstanding the dips at heights of 25 and 50 mm, L̃f
stays essentially constant at about 1.0 nm. In contrast to Fig. 5.23, in Fig. 5.33b,
values for ∆L̃f/∆dp are uniformly positive, indicating that fringes at a given radial
location near the particle surface shorten in response to a drop in primary particle
size. This means, for example, that at a radial location of 10 nm, L̃f will be greater
in a 12 nm radius primary particle than in one with an 11 nm radius. This is
consistent with an environment of surface oxidation. The effect appears to lessen in
magnitude with increasing radial fringe location. One possible explanation for this
164
is that for primary particles with larger radii, the outer 20% includes some regions
that are undergoing graphitization, thereby offsetting the fringe shortening effect of
oxidation. Indeed, if the analysis is restricted to the outer 2 nm of each primary
particle, the downward trend in Fig. 5.33b largely disappears, (Fig. 5.34).
The other lattice fringe measure-
ments are equally independent of both
soot flame location and primary particle
size. These results are included in Ap-
pendix C.2. Taken together, the data
shows that while fringe lengths are shorter
as one moves radially inward, the char-
acter of the carbon layers encountered by
Figure 5.34: Change in median fringe
the gas phase at the surface remains es- length with respect to primary particle
diameter at each fringe radial location.
sentially constant due to prior thermal and Analysis restricted to the outer 2 nm
of each primary particle.
oxidation-induced graphitization, even as
the primary particles shrink.
Obviously, this trend cannot continue indefinitely. Eventually, the primary
particles will be so small that one or more of the following will be forced to occur:
1. The carbon layers decrease in size, increasing the percentage of edge to basal
plane carbons; 2. Curvature of the carbon layers increases, raising the proportion
of the more reactive odd-member-ring carbons; 3. The primary particles lose their
spherical shape, increasing the specific surface area. All of these transformations
would result in an increase of the effective soot reactivity. In a shrinking-sphere
165
situation, these effects should become especially pronounced as the primary particle
diameter approaches the lattice fringe length. In the flame system investigated here,
the ratio of mean primary particle diameter to median fringe length never goes below
about 20. Only the 3rd effect, increasing asphericity, has been qualitatively observed.
Interestingly, the presence of this effect may be responsible for the other two having
not been observed. That is, the loss of sphericity may precede the curving and
shortening of fringes such that primary particles exhibiting these latter features are
no longer recognizable as such by a TEM operator.
5.4 Soot Oxidation Rate Expressions
From the TEM measurements, there are several key results of direct relevance
to the analysis of the chemical kinetics of soot oxidation. First, there are no changes
to the soot morphology or global nanostructure that would greatly affect soot optical
properties. Second, for the current flame system, observations are best represented
by a shrinking sphere model, with oxidation restricted to the outer soot surface.
Third, the nanostructure encountered by the gas-phase is effectively constant, even
as material is removed through oxidation.
The first two results align with assumptions embedded in the measurements of
soot volume fraction and specific surface area. This should strengthen confidence in
these measurements, and in the soot oxidation rates derived from them. The third
result comports with the assumption of a constant concentration of active sites on the
soot surface. From this, we conclude that the null hypothesis of constant collision
166
efficiencies between oxidizers and the soot surface cannot be rejected. The soot
oxidation analysis can therefore proceed as presented in Sec. 3.6 without alteration.
The overall soot oxidation rate at each sampled location in the soot flame, is
presented in Fig. 5.35a. These results update those reported by Guo [224], based
on refinements to the specific surface area and soot flame velocity measurements in
the present work. The soot oxidation rate reaches a peak of 5.7 g/m2-s at 13 mm,
coinciding with the location of peak temperature and OH concentration. Oxidation
rate falls to a low of 0.3 g/m2-s shortly thereafter, at HAB = 20 mm which coincides
with the location of minimum O2. Uncertainties in the values of ẇox ranged between
±20% and ±60%, and were calculated from the elemental uncertainties of each of
the terms in Eq. 3.25 following the method outlined in Ref. [272].
Figure 5.35: (a) Measured soot oxidation rate vs. height above burner. (b) Com-
parison of measured soot oxidation rates with those predicted by mechanisms of
NSC + Neoh et al. [42, 43], and the optimized mechanism of Guo et al. [46]
167
In Fig. 5.35b, the measured oxidation rate is plotted alongside the predicted
rates of two different mechanisms. The first prediction combines of the two most
commonly used mechanisms for oxidation by O2 and OH, which are those by Nagle
and Strickland-Constable (NSC) [42] and Neoh et al. [43], respectively. For all but
the data point at 10 mm, NSC + Neoh greatly overpredicts the oxidation rate. Apart
from the extreme difference at HAB = 20 mm (600%), the largest overprediction
is 220% occurring at 25 mm. Overall, the average prediction is 137% greater than
the measured values. The optimized expression derived from the meta-analysis of
Guo et al, [46], does substantially better. The largest underprediction is 73% at at
10 mm, and apart from the overshoot at 20 mm (200%), the largest overprediction
is only 30%, occurring at 25 mm.
Table 5.1 lists these mechanisms, as well as two others, with the R2 value of a
fit of the predicted oxidation rates to the line of ẇox,meas = ẇox,predict. The combined
prediction of Lee + Neoh [43, 47], yields a very similar result to that of Guo et
al. [46].
Table 5.1: Comparison of oxidation mechanism predictions with measured oxidation
rates.
Mechanism η 1/2OH AO2 (s-K /m) EA,O2 (kJ/mol) R
2
NSC + Neoh [42,43] 0.13 (multiple sub-expressions) 0.11
Lee + Neoh [43,47] 0.13 1.071 164.4 0.60
Guo et al. [46] 0.1 15.8 195 0.69
O2 only 0 0.03 97 0.99
168
Interestingly, an optimum fit to the data is obtained when oxidation by OH
is ignored entirely. The resulting O2 pre-factor and activation energy are far below
literature values suggested for mature soot. (See values and reviews in Refs. [47,50,
51, 273–275]. The value for EA,O2 of 31.3 kJ/mol used by the ABF soot formation
model [13] is derived from reactions with phenyl, not soot [276]).
A far more likely scenario is that OH is at superequilibrium quantities at the
lowest points in the soot flame, and higher in the flame, the available surface area
begins to deviate from that of hard, spherical primary particles. Indeed, differences
between measured and predicted rates disappear at heights of 10 and 13 mm if OH
exists at superequilibrium ratios of 10 and 1.5, at these respective locations. Even
in the presence of soot, these are common superequilibrium ratios, especially near
the flame sheet [69,70,277]. Likewise, beginning at a height of 35 mm, if the specific
surface area increases by only 30% above the hard sphere model due to loss of
sphericity and the opening of micropores, then discrepancies between predicted and
measured values are largely rectified. This too is reasonable - recall, the BET surface
area was 11% greater than the external surface area even before entering the soot
flame, (Sec. 4.3.3). If OH superequilibrium and increased specific surface are present
in the soot flame as described here, the Guo et al. mechanism [46] would yield an
R2 value of 0.95, while the R2 from the Lee + Neoh mechanism would be 0.93.
Intriguingly, in this hypothesized scenario, the location where the specific surface
area begins to increase, corresponds with the onset of aggregate fragmentation.
169
Chapter 6: Conclusions and Recommendations
6.1 Summary and Conclusions
A study has been performed investigating the nanostructure, morphology and
gas-phase kinetics of soot oxidized in a unique ternary flame system. In this system,
a column of soot is generated to maturity in a propylene-air co-flow diffusion flame,
after which it enters a hydrogen diffusion flame. This creates a soot flame where,
owing to the absence of hydrocarbons, soot oxidation may be observed without
competing soot formation processes, a confounding factor which past studies of soot
oxidation in flames have had to account for.
Within the soot flame, detailed measurements were performed, tracking the
evolving soot structure, oxidation rate, temperature, and gas species concentrations.
Transmission electron microscopy (TEM) was instrumental in characterizing soot
structure at three levels of increasing resolution. At the lowest magnifications, soot
particles appeared as fractal aggregates comprised of sphere-like primary particles.
At the next level, size distributions and partial sintering of primary particles were
measured. Lastly, at the highest resolutions, lattice fringes were measured, revealing
the organization of carbon layered planes with respect to height in the soot flame
and position within the primary particles.
170
To efficiently process and measure TEM images of soot across this broad scale,
a program was developed in MATLAB called the Aerosol Image Analyzer (AIA).
The program provides a convenient environment to rapidly test, optimize, and save
image processing procedures needed for repeatable quantitative analysis. It also
contains several new algorithms used to improve the speed and accuracy of mea-
surements relevant to soot and other aerosols. An innovative algorithm, known as
Center-Selected Edge Scoring (CSES) was used to semi-automatically measure the
diameters of individual primary particles. CSES operates as an inverse to tradi-
tional circle detection algorithms which depend on accurate edge detection. CSES
instead begins with a user-estimated center point and measures the gradients of all
pixels on a candidate circle’s circumference, not just those detectable as edges. The
algorithm gives accurate results that represent an operator’s best judgment, but is
also five times faster than manual measurement.
Early on, large discrepancies in TEM measurements showed a clear need to
reduce operator bias, obtain better estimates of TEM measurement uncertainties,
and validate the proposed method for determining specific surface area from TEM
images. This prompted the gage repeatability and reproducibility study presented in
Chapter 4. This study produced four key results. First, robust uncertainty estimates
for primary particle size distributions and specific surface areas were calculated, ac-
counting for variations among samples, operators, and measurements replicates.
These uncertainties, which were substantially greater than generally acknowledged
in literature, were put to use thereafter in the analysis of soot flame measurements.
Second, the study revealed that efforts to minimize bias through randomization and
171
use of the CSES algorithm were successful. Third, automated methods from the
literature for measuring primary particle size distributions were found to be unreli-
able. Lastly, through comparison with surface area measurements by N2 adsorption,
it was determined that measurement of primary particles on TEM images was a valid
method for estimating soot surface area, provided that polydispersity and overlap
among primary particles was taken into consideration.
Measurements in the soot flame found that the primary particle diameter
mean and standard deviation decreased with increasing height in the flame, as a
result of surface oxidation. In addition, primary particle asphericity became more
apparent at higher flame locations. A shift in the size distributions from a normal
to lognormal shape was observed, beginning a height of at 25 mm. Partial sintering
between primary particles, observed as overlap on the TEM images, was seen to
slightly decrease as height above burner increased, indicating in-place oxidation of
primary particles rather than compaction due to oxidative sintering.
Primary particle size distribution and overlap was also used to determine the
volume specific surface area (VSSA) of soot at each sampled location in the flame.
Distribution-agnostic expressions for VSSA were derived that accounted for poly-
dispersity of the primary particle population as well as the volume and surface area
consumed by partial sintering. Two methods for estimating the volume and sur-
face area lost to overlap were evaluated and found to give equivalent results. VSSA
increased by as much as 90% with increasing height in the soot flame.
Soot aggregates were characterized by their maximum projected length L, ra-
dius of gyration Rg, number of constituent primary particles Np,a, fractal dimension
172
Df , and pre-factor kf . Aggregate size distributions were found to be consistently
lognormal. Two different methods for calculating 3-dimensional Rg were found to
be in agreement, and their relation to 2-dimensional Rg was consistent with past
studies. The fractal dimension was essentially constant throughout the soot flame
with a mean value of 1.74, which is typical for soot.
Several morphological metrics pointed to the onset of soot fragmentation be-
ginning at a height of 35 mm. At this location in the flame, there was a shift in
the distribution of L, a sharp drop in the geometric mean value of Rg, and a mild
drop in kf . However, even more direct evidence for soot fragmentation came from
two complementary methods. From TEM imaging alone, the number of primary
particles per aggregate was found to dramatically drop at a height of 35 mm. A
second method combined TEM, soot volume fraction, and velocity measurements
to compute the total number flow rate of aggregates, which was seen to suddenly
increase at 35 mm. Taken together, this is strong evidence for soot fragmentation,
and is the first detection of this phenomenon using the methods presented here.
An interesting result was found in the overall number flow rate of primary
particles, which sees a sharp, unexpected increase at 25 mm in the soot flame. This
observation is surprising, as it would imply that in addition to aggregate fragmen-
tation, primary particle fragmentation also occurs, but in such a way that the its
remnants retain enough sphericity to be detected as primary particles by an op-
erator. While this seems implausible, alternative possibilities, including changes
in porosity or to soot optical properties, could not explain the observations. This
curious result therefore remains an open question.
173
High magnification TEM analysis was performed in both selected area elec-
tron diffraction (SAED) mode, and bright field HRTEM mode. The two methods are
complementary in that the former reveals information about the specimen-averaged
distribution of atomic spacings that cannot be observed by HRTEM, while the latter
provides information about soot nanostructure that is spatially resolved within the
projected image. The d-spacings and integral breadths determined at four flame lo-
cations by SAED were typical for soot and did not indicate a changing nanostructure
on a global scale.
HRTEM lattice fringe analysis provided a wealth of information about how
soot nanostructure changes with respect to the location within the primary parti-
cle and in the soot flame. Measurements of fringe length, tortuosity, orientation,
and separation distance revealed that primary particles could be radially divided
into two regions: an inner 80% where nanostructural order increases as one moves
radially outward from the center of a primary particle, and an outer 20% where
this trend reverses. Greater nanostructural order was interpreted from longer fringe
lengths, lower tortuosities, greater fringe concentricity, and shorter fringe separa-
tion distances. These are all hallmarks of mature soot that has already undergone
graphitization.
Since primary particles decreased in diameter with increasing height above
burner, and the nanostructure showed greater disorder near the primary particle
core, it was expected that the fringe analysis would also show an average decrease in
the indicators of graphitization with increasing height in the flame. Surprisingly this
was not the case; median and average values of fringe measurements showed little
174
correlation with location in the soot flame. Instead, analysis found that within the
outer 20% of primary particles, oxidation by the gas phase stripped away material in
a shrinking-sphere manner, while the inner 80%, which was out of reach of oxidizing
gases, underwent further graphitization. Additionally, there was evidence for two
graphitization modes. The first occurred within the bulk of the primary particle due
to thermal annealing. The second mode was more dramatic and occurred just below
the oxidizing surface. This was interpreted as graphitization induced by oxidation at
the outer shell, which removed cross links and interstitial material, allowing carbon
planes beneath it to grow and realign. Analysis of HRTEM images found no evidence
of internal burning or major pore openings within soot primary particles, however a
deviation from perfect sphericity did appear to accompany increasing height in the
soot flame.
The ongoing graphitization within primary particle interiors is consistent with
the unchanging overall nanostructure suggested by SAED measurements. It also
challenges the assumption that once soot reaches maturity, the nanostructure is
essentially ”locked in,” and cannot be altered at typical flame temperatures and
residence times. Instead, while the overall character of the nanostructure remains
unaltered (i.e. the soot retains concentric layers of increasing order), graphitization
remains ongoing, even in mature soot, in ways that are consequential to the reactive
chemistry. In this study, ongoing graphitization in the primary particle core resulted
in an unchanging nanostructure being presented to the oxidizing gas phase. Conse-
quently, analysis of oxidation kinetics proceeded with an assumption of a constant
surface concentration of active sites, implying constant collision efficiencies for the
175
oxidizers O2 and OH.
Soot oxidation rates per unit of soot surface area were obtained by combin-
ing measurements of soot volume fraction, velocity, and specific surface area. The
integrated soot volume fraction at each height within the soot flame was measured
using laser extinction at 632.8 nm. Velocity was determined using high frame rate
video to track perturbations to the soot flame as they traveled axially upward. Spe-
cific surface area was obtained from measured TEM images of primary particles as
described above. The resulting soot oxidation rates ranged from 0.3 - 5.7 g/m2-s
within the soot flame.
Soot flame temperatures were found using ratio pyrometry with a modified
commercial digital camera at wavelengths of 450, 650, and 900 nm, followed by Abel
deconvolution. Gas chromatography was used to derive major species concentrations
from isokinetically sampled gases, while water concentration was determined from
desiccant gravimetry. Radical concentrations were estimated from full equilibrium
at local temperatures and stoichiometry.
Measured soot oxidation rates were compared to predictions of several mech-
anisms. The combined mechanism of Nagle and Strickland-Constable (NSC) [42]
for O2, and of Neoh et al., [43] for OH, though arguably the most prevalent rate
expressions in the literature, gave very poor predictions of the oxidation observed in
the present study. Most of this difference can be ascribed to the NSC expression’s
overprediction of oxidation by O2. The mechanisms of Lee et al. [47] combined
with Neoh [43], gave far better predictions, and the optimized rate expressions by
Guo [46], did better still. In addition, very reasonable changes to the assumptions
176
of equilibrium OH low in the flame and hard-sphere surface areas high in the flame
would largely reconcile observations with the predictions of these latter two mecha-
nisms.
6.2 Recommendations for Future Study
There are several avenues worthy of further investigation. First, the present
work has assumed soot optical properties and density to be constant. However, this
may not be the case. For example, first order calculations using RDG-PFA theory
suggest that scattering may play a larger role in laser extinction than was assumed
here. If so, changes to primary particle and aggregate sizes could lead to changing
optical properties, which would in-turn affect observed oxidation rates. This line
of inquiry may also shed light on the increase in primary particle number flow rate
observed in Sec. 5.3.5.
Second, it would be useful to investigate whether the hard-sphere assumption
in calculating soot surface area holds after substantial oxidation. One way this could
be determined is by increasing soot production in the co-flow flame, or by lowering
the intensity of the hydrogen flame such that sufficient quantities of soot for BET
analysis could be obtained at the soot flame exit. Moreover, if increases in BET
specific surface area could be correlated to changes in TEM images, for example
by changes in the ratio of projected image perimeter to area, this could provide a
valuable means of refining surface area estimations from TEM images.
Third, as was discussed in the literature review, soot nanostructure is known
177
to be a function fuel type. An investigation using the same ternary flame system but
with soot generated from different fuels (e.g. aromatics), producing very different
nanostructures would be valuable toward understanding how nanostructure affects
oxidation behavior. Similarly, the ternary flame system could be used to examine
the oxidation of soot at varying degrees of maturity. Less mature soot could be
produced by placing a wire mesh into the co-flow flame to quench it.
Lastly, a direct measurement of the OH radical in the soot flame, such as by
laser induced fluorescence, would be invaluable. If deviations from the assumed
equilibrium condition were observed, this would go a long way toward validating or
invalidating some of the oxidation mechanisms considered in the present work.
178
Appendix A: MATLAB Code
A.1 Center-Selected Edge Scoring
f unc t i on [ CenterPt , Radius , Score ]= CSES(Img , DiaRange , Po lar i ty , Cl ickedPt )
% CSES Fit the bes t c i r c l e to an image us ing Center−Se l e c t ed Edge Scor ing
%
% Uses Center−Se l e c t ed Edge Scor ing (CSES) to f i nd the best− f i t c i r c l e on
% the input image with a diameter with in DiaRange and a cen t e rpo in t in the
% neighborhood o f Cl ickedPt
%
% Input arguments :
% Img The image matrix on which a c i r c l e i s to be found
% DiaRange A vecto r array g iv ing the range o f d iameters to eva luate
% f o r a best− f i t c i r c l e on IMG.
% Po la r i t y I n t e n s i t y o f the image foreground with r e sp e c t to the
% background . Allowed va lues : ’ br ight ’ or ’ dark ’
% ClickedPt A vecto r array [ x , y ] o f the po int c l i c k e d in the Image by
% the user . This w i l l be the cente r o f the p i x e l neighborhood
% that w i l l s e rve as candidate c en t e rpo i n t s f o r the best f i t
% c i r c l e . Note : x i n c r e a s e s from l e f t to r ight , y i n c r e a s e s
% from top to bottom o f the image
%
% Output arguments :
% CenterPt Center po int o f the bes t f i t c i r c l e
% Radius Radius o f the best f i t c i r c l e
% Score CSES goodness−of− f i t s c o r e o f the bes t f i t c i r c l e
%
% Date Vers ion Author Notes
% 10/02/14 1 .00 Paul M. Anderson I n i t i a l r e l e a s e
% 12/15/16 1 .01 Paul M. Anderson U t i l i z e s c i r c l e masks generated by
% midpoint c i r c l e a lgor i thm
% 01/28/18 1 .02 Paul M. Anderson C i r c l e masks r e f e r en c ed with
% l i n e a r index ing to improve speed
% and memory . C i r c l e s with even
% diameters cente red at p i x e l
% corne r s .
179
load ( ’ CSESCircleMasks . mat ’ , ’Masks ’ )
i f strcmp ( Po lar i ty , ’ b r i gh t ’ ) % I f foreground i s br ight , f i r s t i nv e r t image
Img = imcomplement ( Img ) ;
end
[ ImgGrads .Mag, ImgGrads . Orient ] = CalcEdges ( Img ) ;
% Get o r i g i n a l image dimensions
[ h ,w] = s i z e ( ImgGrads .Mag ) ;
RadRange = DiaRange . / 2 ;
r min = min (RadRange ) ;
r max = max(RadRange ) ;
% S i z e o f the p i x e l neighborhood surrounding the Cl ickedPt . P i x e l s with in
% the neighborhood w i l l be eva luated as c en t e rpo i n t s f o r a best f i t c i r c l e .
% Example : CenterPtNeighb = 1 w i l l c on s id e r a 3x3 matrix with Cl ickedPt at
% i t s center , 2 w i l l c on s i d e r a 5x5 matrix , e t c . From exper i ence , the
% f o l l ow i ng expr e s s i on y i e l d s a CenterPtNeighb that meets user i n t u i t i o n .
CtrPtNeighb = round (0 . 05* r max+1);
% r max w i l l be the sma l l e r o f the input r max or the rad iu s o f the l a r g e s t
% c i r c l e that can be drawn at a cente r o f ( Cl ickedPt +/− CtrPtNeighb )
% without going beyond the image boundar ies
r max = min ( [ Cl ickedPt (1)−CtrPtNeighb −0.5 , w−ClickedPt (1)−CtrPtNeighb+0.5 , . . .
Cl ickedPt (2)−CtrPtNeighb −0.5 , h−ClickedPt (2)−CtrPtNeighb+0.5 , r max ] ) ;
d min = c e i l (2* r min ) ;
d max = f l o o r (2* r max ) ;
i f d min > d max
PromptText =’The minimum rad iu s i s too l a r g e f o r t h i s image l o c a t i o n . ’ ;
u iwa i t (msgbox (PromptText , ’CSES Error ’ , ’modal ’ ) ) ;
Radius = −1; CenterPt = [ ] ; Score = 0 ;
re turn
end
nDiams = d max − d min + 1 ; %Number o f d iameters that w i l l be eva luated
% Calcu la te d i s t anc e from ClickedPt needed f o r eva lua t i on window
Of f s e t = int16 (min ( [ Cl ickedPt (1)−1 ,w−ClickedPt (1 ) , Cl ickedPt (2)−1 , . . .
h−ClickedPt (2 ) , (Masks . S i z e (1)−1)/2 , (Masks . S i z e ( 2 ) −1 )/2 ] ) ) ;
% Make sub−matr i ce s o f the image ’ s magnitude and o r i e n t a t i o n matr i ce s
SubMatMags = ImgGrads .Mag( Cl ickedPt (2)−Of f s e t : Cl ickedPt (2)+Of f se t , . . .
Cl ickedPt (1)−Of f s e t : Cl ickedPt (1)+ Of f s e t ) ;
180
SubMatOrients = ImgGrads . Orient ( Cl ickedPt (2)−Of f s e t : Cl ickedPt (2)+Of f se t , . . .
Cl ickedPt (1)−Of f s e t : Cl ickedPt (1)+ Of f s e t ) ;
[ hSub ,wSub]= s i z e (SubMatMags ) ;
% I f the sub−matr i ce s are sma l l e r than the c i r c l e mask matr ices , pad the
% sub−matr i ce s to equal the dimensions o f the c i r c l e mask matr i ce s
i f hSub < Masks . S i z e (1 )
xPad = (Masks . S i z e (2)−wSub )/2 ;
yPad = (Masks . S i z e (1)−hSub ) /2 ;
SubMatMags = padarray (SubMatMags , [ yPad , xPad ] , ’ both ’ ) ;
SubMatOrients = padarray ( SubMatOrients , [ yPad , xPad ] , ’ both ’ ) ;
hSub=s i z e (SubMatMags , 1 ) ;
end
kMin = f i nd (Masks . Diams==d min ) ;
kMax = f i nd (Masks . Diams==d max ) ;
PixIdx = Masks . PixIdx (kMin : kMax ) ;
Or ients = Masks . Thetas (kMin : kMax ) ;
Diams = Masks . Diams (kMin : kMax ) ;
nP ixe l s = Masks . nP ixe l s (kMin : kMax ) ;
% Var iab l e s to hold the best− f i t c i r c l e data
BestScore = 0 ; BestCtrDel = [ 0 , 0 ] ; BestDiam = 0 ;
% For each p o s s i b l e c en t e rpo in t ( i . e . a l l po in t s in neighborhood )
f o r xDel = −CtrPtNeighb : CtrPtNeighb
f o r yDel = −CtrPtNeighb : CtrPtNeighb
f o r k = 1 : nDiams
% s h i f t columns that i n d i c e s to r e f e r to
TheseIdx = PixIdx{k} + hSub*xDel + yDel ;
EdgeMags = SubMatMags( TheseIdx ) ;
EdgeOrients = SubMatOrients ( TheseIdx ) ;
DeltaTheta = EdgeOrients − Orients {k } ;
Or i entScore s = cos ( DeltaTheta ) ;
Th i sC i r c l eSco r e = (sum(EdgeMags .* OrientScore s ) )/ nP ixe l s ( k ) ;
i f Th i sC i r c l eSco r e > BestScore
BestScore = Th i sC i r c l eSco r e ;
BestCtrDel = [ xDel , yDel ] ;
BestDiam = Diams (k ) ;
end
end
181
end
end
CenterPt = [ Cl ickedPt (1)+BestCtrDel ( 1 ) , Cl ickedPt (2)+BestCtrDel ( 2 ) ] ;
i f mod(BestDiam , 2) == 0 % i f bes t c i r c l e has even diameter
CenterPt = CenterPt + 0 . 5 ;
end
Radius = BestDiam /2 ;
Score = BestScore ;
182
A.2 SAED Image Analysis Code
f unc t i on [DP]= AnalyzeDi f fPatt (CtrPt , PadImgTF , CurveFitType , DiffImg ,MaskImg)
% ANALYZEDIFFPATT Measure f e a t u r e s o f a concent r i c−r i ng d i f f r a c t i o n pattern
% Input Arguments
% CtrPt Center po int [ px ] o f the o r i g i n a l d i f f r a c t i o n pattern image
% PadImgTF 1 i f you want to pad the d i f f r a c t i o n patern image to make i t
% square p r i o r to ana ly s i s , 0 to keep i t as− i s .
% Dif fImg The d i f f r a c t i o n pattern image
% MaskImg Beam blocke r image mask
% Sca l e D i f f r a c t i o n pattern image s c a l e [nm−1/px ]
% Output Arguments
% DP A s t ru c tu r e va r i a b l e with the f o l l ow i ng f i e l d s :
% r Each rad iu s [ px ] at which the i n t e n s i t y o f the raw
% d i f f r a c t i o n pattern i s c i r c um f e r e n t i a l l y averaged ,
% y i e l d i n g DP gross
% gro s s The g ro s s d i f f r a c t i o n pattern p r o f i l e : the average
% i n t e n s i t y o f the raw d i f f r a c t i o n pattern image at each r
% r r Only those va lue s o f r l a r g e r than the l o c t i o n o f the
% f i r s t i n f l e c t i o n po int in DP gross
% r BkgPts Radius va lue s o f the s e l e c t e d po in t s o f the backgrnd s i g n a l
% A BkgPts Values o f the background i n t e n s i t y at each r BkPts
% BkgFit Curve f i t ob j e c t f i t t e d to the s e l e c t e d background po in t s
% BkgCurve The best f i t background image curve , eva luated at each r r
% net The d i f f r a c t i o n pattern p r o f i l e with the background removed
% pks The va lue s o f DP net at each l o c a l peak
% l o c s The va lues o f r r at which pks occur [ px ]
% FWHM The f u l l −width , ha l f−maximums o f each peak [nm−1]
% dSpacing The l a t t i c e d−spac ing ( in Angstroms ) cor re spond ing to the
% l o c a t i o n o f each peak
% In t en s i t y The in t e g r a t ed i n t e n s i t y o f each peak [ a . u . ]
% Breadth The i n t e g r a l breadth o f each peak [nm−1]
% Paul M. Anderson , 2018
warning ( ’ o f f ’ , ’ images : i n i t S i z e : adjustingMag ’ ) ;
RefineFitTF = true ; % Ref ine i n i t i a l f i t with a s p l i n e f i t
NumValleys = 2 ; % Number o f l o c a l minima to be found in Dif f Img
load ( ’ CSESCircleMasks . mat ’ , ’Masks ’ )
dMax = 1500 ;
DiaRange = [10 , dMax ] ;
183
% Get o r i g i n a l image dimensions
[ h ,w] = s i z e ( Dif f Img ) ;
i f PadImgTF
% Pad the image to make i t square
PadSize = round ( (w−h ) / 2 ) ;
Dif f Img = padarray ( DiffImg , [ PadSize , 0 ] , ’ both ’ ) ;
MaskImg = padarray (MaskImg , [ PadSize , 0 ] , 2 5 5 , ’ both ’ ) ;
[ h ,w] = s i z e ( Dif f Img ) ;
CtrPt (2 ) = CtrPt (2)+PadSize ;
e l s e
PadSize = 0 ;
end
RadRange = DiaRange . / 2 ;
r min = min (RadRange ) ;
r max = max(RadRange ) ;
% r max i s sma l l e r o f input r max or rad iu s o f the l a r g e s t c i r c l e that can
% be drawn centered at CtrPt without going beyond the image boundar ies
r max=min ( [ CtrPt (1)−0.5 ,w−CtrPt (1)+0.5 , CtrPt (2)−0.5 ,h−CtrPt (2)+0.5 , r max ] ) ;
d min = c e i l (2* r min ) ;
d max = f l o o r (2* r max ) ;
i f d min > d max
PromptText =’The minimum rad iu s i s too l a r g e f o r t h i s image l o c a t i o n . ’ ;
u iwa i t (msgbox (PromptText , ’ Error ’ , ’modal ’ ) ) ;
r e turn
end
nDiams = d max − d min + 1 ; %Number o f d iameters that w i l l be eva luated
% Calcu la te d i s t anc e from CtrPt needed f o r eva lua t i on window
Of f s e t = int16 (min ( [ CtrPt (1)−1 ,w−CtrPt ( 1 ) , CtrPt (2)−1 ,h−CtrPt ( 2 ) , . . .
(Masks . S i z e (1)−1)/2 , (Masks . S i z e ( 2 ) −1 )/2 ] ) ) ;
% Make sub−matr i ce s o f the D i f f r a c t i o n pattern image and beam blocke r mask
SubDiffImg = Dif fImg (CtrPt(2)−Of f s e t : CtrPt (2)+Of f se t , . . .
CtrPt (1)−Of f s e t : CtrPt (1)+ Of f s e t ) ;
SubMaskImg = MaskImg(CtrPt(2)−Of f s e t : CtrPt (2)+Of f se t , . . .
CtrPt (1)−Of f s e t : CtrPt (1)+ Of f s e t ) ;
[ hSub ,wSub]= s i z e ( SubDiffImg ) ;
% I f the sub−matr i ce s are sma l l e r than the c i r c l e mask matr ices , pad the
% sub−matr i ce s to equal the dimensions o f the c i r c l e mask matr i ce s
184
i f hSub < Masks . S i z e (1 )
xPad = (Masks . S i z e (2)−wSub )/2 ;
yPad = (Masks . S i z e (1)−hSub ) /2 ;
SubDiffImg = padarray ( SubDiffImg , [ yPad , xPad ] , ’ both ’ ) ;
SubMaskImg = padarray (SubMaskImg , [ yPad , xPad ] , ’ both ’ ) ;
hSub=s i z e ( SubDiffImg , 1 ) ;
end
kMin = f i nd (Masks . Diams==d min ) ;
kMax = f i nd (Masks . Diams==d max ) ;
PixIdx = Masks . PixIdx (kMin : kMax ) ;
Diams = Masks . Diams (kMin : kMax ) ;
r = ze ro s (nDiams , 1 ) ;
DP gross = ze ro s (nDiams , 1 ) ;
f o r k = 1 : nDiams
Dif f ImgVals = SubDiffImg ( PixIdx{k } ) ;
MaskImgVals = SubMaskImg( PixIdx{k } ) ;
MaskedDiffImgVals = uint32 ( Dif f ImgVals ) . * uint32 (MaskImgVals ) ;
nP ixe l s = numel ( f i nd (MaskedDiffImgVals ) ) ;
r ( k ) = Diams (k ) / 2 ;
DP gross ( k ) = sum(MaskedDiffImgVals )/ nPixe l s ;
end
% Force program to ignore f a l s e minima near the d i r e c t beam
DP gross (1:170)=max( DP gross ) ;
MaxDP=255;
rSca l ed = r * Sca l e ;
% Get the l o c t i o n s o f l o c a l minima between peaks as we l l as the i n f l e c t i o n
% point o f the curve near the d i r e c t e l e c t r on beam
[ Val leyIdx , In f l xPt Idx ] = GetVal leys ( DP gross , NumValleys ) ;
EndIdx = f i nd ( r==600); % Perform ana l y s i s out to r=600:
%Use i n f l e c t i o n point , v a l l e y points , & end point as po in t s f o r curve f i t
r BkgPts = ve r t ca t ( r ( In f l xPt Idx ) , r ( Val l eyIdx ) , r (EndIdx ) ) ;
A BkgPts = ve r t ca t ( DP gross ( In f l xPt Idx ) , DP gross ( Val leyIdx ) , . . .
DP gross (EndIdx ) ) ;
switch CurveFitType
case ’Lognorm ’
% Use a lognormal curve to f i t the background
185
opts = f i t o p t i o n s ( ’Method ’ , ’ Nonl inearLeastSquares ’ , . . .
’ Lower ’ , [0 ,− In f ,− I n f ] , . . .
’ Upper ’ , [ In f , In f , I n f ] , . . .
’ S t a r tpo in t ’ , [ 10ˆ11 , −25 ,10 ] ) ;
f = f i t t y p e ( ’ ( a/x )* exp (−(( l og (x)−b)/ c )ˆ2) ’ , ’ opt ions ’ , opts ) ;
BkgFit = f i t ( r BkgPts , A BkgPts , f ) ;
b = f e v a l ( BkgFit , r ) ;
case ’PowerLaw ’
% Use a power law curve to f i t the background
BkgFit = f i t ( r BkgPts , A BkgPts , ’ power2 ’ ) ;
b = f e v a l ( BkgFit , r ) ; % eva luate the curve at each value o f r
case ’ Sp l in e ’
% Use a s p l i n e to f i t the background
BkgFit = f i t ( r BkgPts , A BkgPts , ’ smooth ingsp l ine ’ , . . .
’ SmoothingParam ’ , 0 . 0 0 1 ) ;
b = f e v a l ( BkgFit , r ) ; % eva luate the curve at each value o f r
o therw i s e
msgbox ( ’We did not r e cogn i z e that curve f i t type ID . Aborting . ’ )
r e turn
end
Star t Idx = In f l xPt Idx ;
% Only analyze the r e l e van t po r t i on s o f the d i f f r a c t i o n pattern
r r = r ( Star t Idx : EndIdx ) ; r rS ca l ed = r r * Sca l e ;
AA = DP gross ( Star t Idx : EndIdx ) ;
BkgCurve1 = b( Star t Idx : EndIdx ) ;
% D i f f e r e n c e between d i f f r a c t i o n pattern image & 1 s t background es t imate
DP net1 = AA−BkgCurve1 ;
i f RefineFitTF
% Find the minima o f the 1 s t e s t imate o f the net d i f f r a c t i o n pattern
ValleyTF = i s l o c a lm i n (DP net1 , ’MaxNumExtrema ’ ,2 , ’ MinSeparation ’ , 8 0 ) ;
Val l eyIdx = f i nd (ValleyTF ) ;
r BkgPts2 = ve r t c a t ( r r ( 1 ) , r r ( Val l eyIdx ) , r r ( end ) ) ;
A BkgPts2 = ve r t c a t (DP net1 ( 1 ) , DP net1 ( Val leyIdx ) , DP net1 ( end ) ) ;
% Use a s p l i n e to f i t the background
BkgFit2 = f i t ( r BkgPts2 , A BkgPts2 , ’ smooth ingsp l ine ’ , . . .
’ SmoothingParam ’ , 0 . 1 ) ;
BkgCurve2 = f e v a l ( BkgFit2 , r r ) ; % eva luate the curve at each r r
% D i f f e r e n c e between net d i f f r a c t i o n pattern & background
186
DP net2 = DP net1−BkgCurve2 ;
DP net2 (DP net2<0)=0; % Set negat ive net va lue s to zero
e l s e
BkgCurve2 = ze ro s ( s i z e (BkgCurve1 ) ) ;
DP net2 = DP net1 ;
end
% Get l o c a t i o n s and FWHMs o f d i f f r a c t i o n peaks
[ pks , l o c s , widths , proms ] = f indpeaks (DP net2 , rr , ’ MinPeakDistance ’ ,50 , . . .
’MinPeakProminence ’ , 2 , ’ Annotate ’ , ’ ex t ent s ’ , ’ WidthReference ’ , ’ halfprom ’ ) ;
npks = length ( pks ) ;
% Get the l o c a t i o n s o f minima between peaks , f o r use as i n t e g r a t i o n l im i t s
ValleyTF = i s l o c a lm i n (DP net2 , ’MaxNumExtrema ’ ,2 , ’ MinSeparation ’ , 8 0 ) ;
Val l eyIdx = f i nd (ValleyTF ) ;
IntLimIdx = ve r t ca t (1 , Val leyIdx , l ength (DP net2 ) ) ;
dSpacing = 10 . / ( l o c s ( 1 : l ength ( pks ) ) . * Sca l e ) ; %d−spac ing in Angstroms
FWHM = widths .* Sca l e ; % Full−width ha l f−maximums in nm−1
% Calcu la te the i n t e g r a t ed i n t en s i t y , i n t e g r a l breadth
I n t e n s i t y = ze ro s ( l ength ( pks ) , 1 ) ;
Breadth = ze ro s ( l ength ( pks ) , 1 ) ;
f o r k = 1 : l ength ( pks )
I n t e n s i t y (k ) = trapz (DP net2 ( IntLimIdx (k ) : IntLimIdx (k+1)))* Sca l e ;
Breadth (k ) = ( I n t e n s i t y (k )/ pks (k ) ) ;
end
% Output everyth ing as a s t r u c tu r e v a r i a b l e
DP = s t r u c t ( ’ r ’ , r , ’ g r o s s ’ , DP gross , ’ r r ’ , rr , ’ r BkgPts ’ , r BkgPts , . . .
’ A BkgPts ’ , A BkgPts , ’ BkgFit ’ , BkgFit , ’ BkgCurve ’ ,BkgCurve1 , . . .
’ net ’ , DP net2 , ’ pks ’ , pks , ’ l o c s ’ , l o c s , ’ dSpacing ’ , dSpacing , . . .
’FWHM’ ,FWHM, ’ I n t e n s i t y ’ , I n t en s i t y , ’ Breadth ’ , Breadth ) ;
% Plot everyth ing a l l on one g iant amazing p l o t !
TotBkgCurve = BkgCurve1 + BkgCurve2 ;
f i g u r e ; hAx4 = axes ;
p l o t (hAx4 , rSca led , DP gross /MaxDP, ’b ’ , r BkgPts*Scale , A BkgPts/MaxDP, . . .
’ * r ’ , r rSca l ed , TotBkgCurve/MaxDP, ’−−r ’ ) ; hold on ;
p l o t (hAx4 , r rSca l ed , DP net2/MaxDP, ’ k ’ ) ;
p l o t (hAx4 , l o c s *Scale , ( pks+1)/MaxDP, ’ vb ’ , ’ MarkerFaceColor ’ , ’ g ’ ) ;
p l o t (hAx4 , r rS ca l ed ( IntLimIdx ( 1 : npks+1)) , . . .
DP net2 ( IntLimIdx ( 1 : npks+1))/MaxDP, ’ or ’ ) ;
t i t l e ( ImgID , ’ I n t e r p r e t e r ’ , ’ none ’ ) ;
l egend ( ’ Gross D i f f r a c t i o n Pattern ’ , ’ Background Points ’ , . . .
’ Background Fit ’ , ’ Net D i f f r a c t i o n Pattern ’ , . . .
187
’ D i f f r a c t i o n Peak Maxima ’ , ’ L imits o f I n t e g r a t i on ’ , ’ Gaussian Fit ’ ) ;
end
func t i on [ Val leyIdx , In f l xPt Idx ] = GetVal leys (A, NumValleys )
% Input arguments
% A The d i f f r a c t i o n pattern i n t e n s i t y p r o f i l e
% NumValleys The t o t a l number o f minima expected in the d i f f pattern
% Output arguements
% Val leyIdx Ind i c e s o f the l o c a t i o n s o f minima in A
% In f lxPt Idx Index o f the l o c a t i o n o f the 1 s t i n f l e c t i o n po int in the
% d i f f r a c t i o n pattern curve
KeepLooping = true ;
n = 0 ;
whi l e KeepLooping
% Keep smoothing raw data un t i l the re are no f a l s e minima
A = smoothdata (A, ’movmean ’ ,2+n ) ;
ValleyTF = i s l o c a lm i n (A) ;
n = n+1;
i f sum(ValleyTF ) <= NumValleys | | n == 100
KeepLooping = f a l s e ;
end
end
Val leyIdx = f i nd (ValleyTF ) ;
Y = d i f f (A, 2 ) ; % 2nd d e r i v a t i v e o f the curve
In f l xPt Idx = f i nd (Y>0 ,1) ; % Find the f i r s t i n f l e c t i o n po int in the curve
end
188
A.3 Lattice Fringe Analysis Code
A.3.1 BridgeGaps Function
f unc t i on BridgedImg = BridgeGaps (BWImg, Prox , AngTol )
% BRIDGEGAPS Connect l i n e segments meeting c r i t e r i a
% Connects l i n e segments whose endpoints are with in a given proximity
% and whose o r i e n t a t i o n s are with in a given t o l e r an c e
%
% Input Arguments :
% BWImg A binary image o f s k e l e t on i z e d l i n e segments
% Prox The maximum proximity between endpoints with in which
% l i n e segments w i l l be cons ide r ed f o r connect ion
% AngTol The maximum d i f f e r e n c e in ang l e s made by the ends o f
% each l i n e segment a l lowed f o r connect ion
%
% Output Arguments :
% BridgedImg The o r i g i n a l image with l i n e s drawn connect ing l i n e
% segments meeting c r i t e r i a
%
% Paul M. Anderson , 2017
% Covert ang le t o l e r an c e to rad ians
AngTol = AngTol* pi /180 ;
% Or i en ta t i on s around a 5x5 bounding box
Ang = [2 . 3 562 2 .0344 1 .5708 1 .1071 0 . 7 854 ; . . .
2 .6779 0 0 0 0 . 4 636 ; . . .
3 .1416 0 0 0 0 ; . . .
3 .6052 0 0 0 5 . 8 195 ; . . .
3 .9270 4 .2487 4 .7124 5 .1760 5 . 4 9 7 8 ] ;
% Create a mask with in which ne ighbor ing endpoints w i l l be eva luated f o r
% br idg ing . Note that s i n c e endpoints are eva luated in order o f ascending
% l i n e a r index , to avoid eva lua t ing the same endpoint pa i r twice , the mask
% only cover s those po in t s r ep r e s en t i ng l i n e a r i n d i c i e s g r e a t e r than the
% candidate endpoint . This g i v e s the mask a s em i c i r c l e− l i k e shape
hMask = 2*Prox+1; wMask = hMask ;
[ xx , yy ] = meshgrid ( 1 :wMask , 1 : hMask ) ;
ProxMask = f a l s e (hMask ,wMask ) ;
% Create a mask with 1 ’ s at p i x e l s with in Prox o f the c en t e rpo in t
ProxMask = ProxMask | hypot ( xx − ( Prox+1) , yy − ( Prox+1)) <= Prox ;
% Zero−out the r i gh t h a l f o f the c i r c u l a r mask
ProxMask ( : , 1 : Prox )=0;
% Zero−out the p i x e l s d i r e c t l y above above and in c l ud ing the cente r
189
ProxMask ( 1 : Prox+1,Prox+1)=0;
% Don ’ t evau la te l i n e segments sma l l e r than 4 p i x e l s
Img = bwareaopen (BWImg, 4 , 8 ) ;
% Pad image to accomodate masking near image boundar ies
BridgedImg = padarray ( Img , [ Prox , Prox ] , ’ both ’ ) ;
EndPtImg = bwmorph( BridgedImg , ’ endpoint ’ , i n f ) ;
% For reasons unknown , bwmorph oc ca s i ona l y f i n d s endpoints at b lack p i x e l s
EndPtImg = EndPtImg & BridgedImg ;
% Id en t i f y endpoints and l a b e l each segment
[ row , c o l ] = f i nd (EndPtImg ) ;
[ h ,w] = s i z e (EndPtImg ) ;
Ind = sub2ind ( [ h ,w] , row , c o l ) ;
LabMat = labe lmat r i x (bwconncomp( BridgedImg ) ) ;
% Determine the o r i e n t a t i o n o f the end o f each l i n e segment
EndAng = ze ro s ( numel ( row ) , 1 ) ;
f o r n=1:numel ( row )
EndSegImg = BridgedImg ( row (n)−2: row (n)+2 , c o l (n)−2: c o l (n )+2);
D = bwdi s tgeodes i c (EndSegImg , 3 , 3 ) ;
D(˜ i s f i n i t e (D))=0; % Zero out any NaN and In f
D( 2 : end−1 ,2: end−1)=0; % In t e r e s t e d in only the border p i x e l s
% Or ientat ion o f the 1 s t p i x e l that t r a c e s back to the sub image border
EndAng(n) = Ang( f i nd (D==min(D(D>0 ) ) , 1 ) ) ;
end
% Evaluate each endpoint f o r b r idg ing
f o r n=1:numel ( row )
SubImg = BridgedImg ( row (n)−Prox : row (n)+Prox , c o l (n)−Prox : c o l (n)+Prox ) ;
SubEndPtImg = EndPtImg( row (n)−Prox : row (n)+Prox , c o l (n)−Prox : c o l (n)+Prox ) ;
SubEndPtImg(ProxMask == 0) = 0 ; % mask the sub endpoint image
[ SubRow , SubCol ] = f i nd (SubEndPtImg ) ;
f o r m = 1 : numel (SubRow)
% Convert back to rows & co l s o f padded image
r = row (n)+(SubRow(m)−(Prox+1)) ;
c = co l (n)+(SubCol (m)−(Prox+1)) ;
% I f the 2 endpoints aren ’ t part o f the same segment , eva luate
i f LabMat( r , c)˜=LabMat( row (n ) , c o l (n ) )
Idx = sub2ind ( [ h ,w] , r , c ) ;
Ang2 = EndAng( f i nd ( Ind==Idx ) ) ;
AngDiff = abs (EndAng(n)−Ang2 ) ;
i f abs ( AngDiff − pi ) <= AngTol % Meets connect ion c r i t e r i a
BridgedImg=l i n e p t ( BridgedImg , r , c , row (n ) , c o l (n ) ) ;
end
190
end
end
end
% Remove padding from BridgedImg
BridgedImg = BridgedImg (Prox+1:h−Prox , Prox+1:w−Prox ) ;
% Add back in the smal l l i n e segments that were removed
BridgedImg = BridgedImg | BWImg;
191
A.3.2 SeverBranches Function
f unc t i on [ OutImg , BranchMarkers ] = SeverBranches (BWImg, SubImgSize )
% SEVERBRANCHES Sever spur ious branches from l i n e segments
% Compares l i n e segment o r i e n t a t i o n s at each branchpoint o f a
% sk e l e t on i z e d image to determine which segments are spur i ous branches
% from the primary l i n e segment . Severs the branches and marks the
% remaining por t i on .
%
% Input arguments :
% BWImg The binary s k e l e t on i z e d image to be eva luated
% SubImgSize The l ength o f a s i d e o f the square r eg i on cente red
% at each branchpoint . The ang le between the reg ion ’ s
% cente r and a segment ’ s l o c a t i o n on the reg ion ’ s
% border determines i t s o r i e n t a t i o n . Must be odd .
%
% Output Arguments :
% OutImg BWImg with branches severed ( no branch 8−c onne c t i v i t y )
% BranchMarkers A binary matrix the same s i z e as OutImg with 1 ’ s
% marking a p i x e l with in each severed branch
%
% Paul M. Anderson , 2017
OutImg = BWImg;
BranchMarkers = f a l s e ( s i z e (BWImg) ) ;
% Create an image conta in ing only branchpoints , and get t h e i r c oo rd ina t e s
BranchPtImg = bwmorph(BWImg, ’ branchpoints ’ ) ;
[ row , c o l ] = f i nd (BranchPtImg ) ;
% Ensure the i n t e r r o g a t i o n window i s always the c o r r e c t s i z e
c = 0.5+SubImgSize /2 ;
a = f l o o r ( c )−1;
b = c e i l ( c )−1;
% Create a matrix the s i z e o f SubImg in which each c e l l ’ s va lue
% i s i t s ang le with r e sp e c t the the matrix cente r
[X,Y] = meshgrid (−(c−1) :( c−1) ,−(c−1) :( c−1)) ;
Ang = f l i p ( atan2 (Y,X) ) ;
Ang(Ang<0)=Ang(Ang<0)+2*pi ;
nBranchPts = numel ( row ) ;
nPrevBranchPts = 0 ;
%Keep loop ing un t i l the number o f branchpoints in the image s tops changing
whi l e nBranchPts ˜= nPrevBranchPts
192
nPrevBranchPts = nBranchPts ;
f o r Ind=1:nBranchPts
% I f the i n t e r r o g a t i o n window does not c r o s s the image boundar ies
i f row ( Ind)−a > 0 && row ( Ind)+b <= s i z e (BWImg, 1 ) && co l ( Ind)−a . . .
> 0 && co l ( Ind)+b <= s i z e (BWImg, 2 )
% Create a sub−image centered at the g iven branchpoint
SubImg=OutImg( row ( Ind)−a : row ( Ind)+b , c o l ( Ind)−a : c o l ( Ind)+b ) ;
% Id en t i f y and index the endpoint o f each segment in SubImg
SegmtEnds = bwmorph(SubImg , ’ endpoints ’ , i n f ) ;
EndInds = f i nd ( SegmtEnds ) ;
% The ang le o f each segment at the edge o f the SubImg
SegmtAngs = Ang( EndInds ) ;
% Ca lcu la te the d i f f e r e n c e between the o r en t a t i on s o f each
% pa i r i ng o f SubImg segments
n = numel ( SegmtAngs ) ;
AngDif fs = ze ro s (n ) ;
f o r i = 1 : n−1
f o r j = i +1:n
AngDif fs ( i , j )=abs ( SegmtAngs ( i )−SegmtAngs ( j ) ) ;
end
end
Or ients = abs ( AngDif fs − pi ) ;
% Retain the segment pa i r whose ang le d i f f i s c l o s e s t to p i
[ ˜ , MinInd]=min ( Or ients ( : ) ) ;
[ i , j ]= ind2sub ( [ n , n ] , MinInd ) ;
KeptInds = f a l s e (n , 1 ) ;
KeptInds ( i ) = true ; KeptInds ( j ) = true ;
% Calc the d i s t from the endpoints o f the r e t a i n ab l e segments
% to a l l other pts on l i n e
D = bwdi s tgeodes i c (SubImg , EndInds ( KeptInds ) ) ;
SubD = D( c−1: c+1,c−1: c+1); % The cente r 3x3 p i x e l s o f D
SubD(SubD>=D( c , c ))=0; % Sever the spur i ous branches in D
SubD = SubD>0; % Convert c en te r p i x e l s to binary
SubImg( c−1: c+1,c−1: c+1) = SubD ; % rep l a c e severed cente r p i x e l s
SubImg( c , c)=true ; %Make sure the branchpoint i t s e l f i s r e t a i n ed
SubMarker = f a l s e ( s i z e (SubImg ) ) ;
SubMarker ( EndInds (˜ KeptInds ))=1; % Mark the spur i ous branches
% In s e r t the broken SubImg in to the o r i g i n a l image and the
193
% marker in to the BranchMarkers matrix
OutImg( row ( Ind)−a : row ( Ind)+b , c o l ( Ind)−a : c o l ( Ind)+b) = SubImg ;
BranchMarkers ( row ( Ind)−a : row ( Ind)+b , c o l ( Ind)−a : c o l ( Ind)+b) . . .
= SubMarker ;
end
end
% Check the number o f branchpoints remaining in the image
BranchPtImg = bwmorph(OutImg , ’ branchpoints ’ ) ;
[ row , c o l ] = f i nd (BranchPtImg ) ;
nBranchPts = numel ( row ) ;
end
end
194
A.3.3 MeasureFringes Function
f unc t i on [ FringeData , FringeCoords ] = MeasureFringes (BWImg, . . .
MinFringeLength , PolyLines , ImgAxes , CtrPt )
% MEASUREFRINGES Perform measurements on s k e l e t on i z e d l a t t i c e f r i n g e s
%
% Input Arguments :
% BWImg A binary image o f the s k e l e t on i z e d f r i n g e segments
% MinFringeLength In p i x e l s . Segments sho r t e r than t h i s w i l l not be
% inc luded in the output measurement
% PolyLines Line ob j e c t s r ep r e s en t i ng the ROI
% ImgAxes The axes ob j e c t cu r r en t l y d i s p l ay i ng the image
% CtrPt Centerpoint o f the primary p a r t i c l e to which the f r i n g e
% segments belong
%
% Output Arguments :
% FringeData A matrix conta in ing the computed length , t o r tuo s i t y ,
% non−c on c en t r i c i t y , and r a d i a l l o c a t i o n o f each f r i n g e
% FringeCoords Coordinates o f each f r i ng e ’ s p i x e l s
%
% Paul M. Anderson , 2017
% Ignore a l l the b&w ob j e c t s touching the ROI i f the re i s an ROI , or
% touching the image border i f the re i s no ROI
i f isempty ( PolyLines )
BWImg = imc learborder (BWImg) ;
e l s e
% Coordinates o f ROI v e r t i c e s
Pos = horzcat ( PolyLines . XData ’ , PolyLines . YData ’ ) ;
hPoly = impoly ( ImgAxes , Pos ) ;
LineMask = createMask ( hPoly ) ;
d e l e t e ( hPoly ) ;
LineMask = bwmorph(LineMask , ’ remove ’ ) ; % Just ROI polygon border
BWImg(LineMask )=1; %Burn the ROI polygon border in to the image
Marker = f a l s e ( s i z e (BWImg) ) ;
[ I , J ] = f i nd ( LineMask , 1 ) ; %Coords o f 1 s t p i x e l on ROI polygon border
Marker ( I , J)=true ; % Tag the ROI border p i x e l
% Img o f only the white p i x e l s on or 8−connected to the ROI border
BorderFringeImg = imrecons t ruc t (Marker ,BWImg) ;
% Img with the white p i x e l s on or 8−connected to the ROI border removed
BWImg = l o g i c a l (BWImg − BorderFringeImg ) ;
end
% Id en t i f y each unique f r i n g e in the s k e l e t on i z e d image
CC = bwconncomp(BWImg, 8 ) ;
s = reg ionprops (CC, ’ Centroid ’ , ’ Or i enta t i on ’ , ’ Extrema ’ ) ;
195
% Create a l a b e l matrix
LMat = labe lmat r i x (CC) ;
%Pr ea l l o c a t e
EndPtDists = ze ro s (CC. NumObjects , 1 ) ;
FringeLengths = ze ro s (CC. NumObjects , 1 ) ;
gDi s t s = c e l l (CC. NumObjects , 1 ) ;
FringeCoords = c e l l (CC. NumObjects , 1 ) ;
Fr ingeOr ient s = ze ro s (CC. NumObjects , 1 ) ;
FringeRadDists = ze ro s (CC. NumObjects , 1 ) ;
UserCance l led = f a l s e ;
% I f indeed we have f r i n g e s . . .
i f CC. NumObjects > 0
wb = waitbar (0 , ’ ’ , ’Name ’ , ’ Measuring f r i n g e s . . . ’ , . . .
’ CreateCancelBtn ’ , ’ setappdata ( gcbf , ’ ’ c anc e l i ng ’ ’ , 1 ) ’ ) ;
RightTopPts = ze ro s (CC. NumObjects , 2 ) ;
% Loop through each unique f r i n g e ob j e c t
f o r f = 1 :CC. NumObjects
% Check f o r c l i c k o f waitbar ’ s Cancel button
i f getappdata (wb, ’ c anc e l i ng ’ )
UserCance l led = true ;
break ;
end
% Update waitbar every 5 th time through the loop
i f mod( f ,5)==0
waitbar ( f /CC. NumObjects ,wb, s p r i n t f . . .
( ’%d o f %d candidate f r i n g e s eva luated ’ , f ,CC. NumObjects ) ) ;
end
% Find the endpoints o f f r i n g e f
TempImg = LMat == f ;
[ row , c o l ]= f i nd (bwmorph(TempImg , ’ endpoints ’ ) ) ;
RightTopPts ( f , : ) = s ( f ) . Extrema ( 8 , : ) ;
% Ignore s i n g l e p i x e l s and ob j e c t s l a ck ing endpoints ( e . g . c i r c l e s )
i f numel ( row ) > 1
% Calcu la te the f r i n g e l ength
gDis t s { f } = bwdi s tgeodes i c (TempImg , c o l ( 1 ) , row (1 ) , . . .
’ quasi−euc l i d ean ’ ) ;
196
gDis t s { f } = gDis t s { f }(˜ i snan ( gDis t s { f } ) ) ;
% Sort the Fringe p i x e l i n d i c e s so that they are in order o f
% i n c r e a s i n g d i s t anc e from the s t a r t i n g p i x e l
[ ˜ , SortIdx ]= so r t ( gDi s t s { f } ) ;
[ i , j ] = ind2sub (CC. ImageSize ,CC. P i x e l I dxL i s t { f }( SortIdx ) ) ;
% Since bwd i s tgeodes i c te rminates at the c en t e r s o f the
% endpoint p i x e l s , must extend to the t rue f r i n g e termina
i = [ 1 . 5 * i (1)−0.5* i ( 2 ) ; i ; 1 .5* i ( end )−0.5* i ( end−1) ] ;
j = [ 1 . 5 * j (1)−0.5* j ( 2 ) ; j ; 1 .5* j ( end )−0.5* j ( end−1) ] ;
Fr ingeLengths ( f ) = max( gDis t s { f }) + sq r t ( ( i (1)− i ( 2 ) )ˆ2 . . .
+ ( j (1)− j ( 2 ) ) ˆ 2 ) + sq r t ( ( i ( end)− i ( end−1))ˆ2 . . .
+ ( j ( end)− j ( end−1))ˆ2) ;
% Compute the d i s t anc e between the f r i n g e termina
EndPtDists ( f ) = sq r t ( ( i (1)− i ( end ))ˆ2+( j (1)− j ( end ) ) ˆ 2 ) ;
FringeCoords { f } = [ i , j ] ; %Record t h i s f r i ng e ’ s x , y coo rd ina t e s
% Fringe c en t r o id
c = s ( f ) . Centroid ;
x = c(1)−CtrPt ( 1 ) ; y = CtrPt(2)− c ( 2 ) ;
% Radial d i s t o f f r i n g e from CtrPt o f primary p a r t i c l e
FringeRadDists ( f ) = hypot (x , y ) ;
% Compute the f r i ng e ’ s d ev i a t i on from pe r f e c t c o n c e n t r i c i t y
Theta=atand (y/x ) ; % Angle o f the r a d i a l vec to r from the x−ax i s
i f ( y*x)>0 % I f f r i n g e i s in 1 s t or 3 rd un i t c i r c l e quadrant
% Angle between the r a d i a l vec to r and t h i s f r i n g e
Fr ingeOr ient s ( f ) = 90 − Theta + s ( f ) . Or i enta t i on ;
e l s e % I f f r i n g e i s in 2nd or 4 th un i t c i r c l e quadrant
Fr ingeOr ient s ( f ) = s ( f ) . Or i entat i on − Theta − 90 ;
end
% Ensure ang le btwn +/−90
i f Fr ingeOr ients ( f ) > 90
Fr ingeOr ient s ( f ) = Fr ingeOr ient s ( f ) − 180 ;
e l s e i f Fr ingeOr ient s ( f ) < −90
Fr ingeOr ient s ( f ) = Fr ingeOr ient s ( f ) + 180 ;
end
end
end
d e l e t e (wb ) ; % de l e t e the waitbar f i g u r e
i f UserCance l led
197
s e t ( hObject , ’ Enable ’ , ’ on ’ ) ; % re−enable the Measure Fr inges button
e l s e
% Retain data o f only those ob j e c t s meeting f r i n g e c r i t e r i a
KeptFringes = FringeLengths >= MinFringeLength ;
FringeLengths = FringeLengths ( KeptFringes ) ;
Fr ingeOr ient s = Fr ingeOr ient s ( KeptFringes ) ;
FringeRadDists = FringeRadDists ( KeptFringes ) ;
EndPtDists = EndPtDists ( KeptFringes ) ;
Fr ingeTorts = FringeLengths . / EndPtDists ;
FringeData = horzcat ( FringeLengths , FringeTorts , Fr ingeOrients , . . .
FringeRadDists ) ;
FringeCoords = FringeCoords ( KeptFringes ) ;
end
end
198
A.3.4 GetFringeSeps Function
f unc t i on FringeSeps = GetFringeSeps (CC, MinFringeLength , SepTol , . . .
OrientTol , RecipTol )
% GETFRINGESEPS Calcu la te f r i n g e s epa ra t i on d i s t an c e s
%
% Input Arguments :
% CC Connected components s t r u c tu r e o f ob j e c t s on image
% MinFringeLength Minumum a l l owab l e f r i n g e length , [ px ]
% SepTol A two−element array with the a l l owab l e range [ min max ]
% o f f r i n g e s epa ra t i on d i s t an c e s [ px ]
% OrientTol Fr inge o r i e n t a t i o n d i f f e r e n c e t o l e r an c e ( degs )
% RecipTol Tolerance w/ in which f r i n g e pa i r s must r e c i p r o c a l l y
% c a l c u l a t e the same sepa ra t i on d i s t [ px ]
%
% Output Arguements :
% FringeSeps A matrix conta in ing the ID numbers o f i d e n t i f i e d f r i n g e
% pa i r s and t h e i r s epa ra t i on d i s t an c e s in p i x e l s
%
% Paul M. Anderson , 2017
% Create a l a b e l matrix
LMat = labe lmat r i x (CC) ;
FringeImg = LMat > 0 ; % Image conta in ing only the measured f r i n g e s
FringeSeps = [ ] ;
W = 2*max( SepTol )+1; % Mask width f o r i d e n t i f y i n g ne ighbor ing f r i n g e s
% Calcu la te geometr ic p r op e r t i e s o f each f r i n g e
s = reg ionprops (CC, ’ Centroid ’ , ’ Or i enta t i on ’ , ’ MajorAxisLength ’ ) ;
wb = waitbar (0 , ’ ’ , ’Name ’ , ’ Ca l cu l a t ing f r i n g e s epa ra t i on d i s t an c e s . . . ’ , . . .
’ CreateCancelBtn ’ , ’ setappdata ( gcbf , ’ ’ c anc e l i ng ’ ’ , 1 ) ’ ) ;
n = 0 ;
f o r f = 1 :CC. NumObjects % f o r each f r i n g e in the image
% Check f o r c l i c k o f waitbar ’ s Cancel button
i f getappdata (wb, ’ c anc e l i ng ’ )
Fr ingeSeps = 0 ;
break ;
end
% Update waitbar every 5 th time through the loop
i f mod( f ,5)==0
waitbar ( f /CC. NumObjects ,wb, s p r i n t f . . .
( ’%d o f %d f r i n g e s eva luated ’ , f ,CC. NumObjects ) ) ;
199
end
% Create an image with j u s t t h i s f r i n g e
ThisFringeImg = LMat == f ;
% Get the Euc l id ian d i s t anc e o f a l l p i x e l s from th i s f r i n g e
dImg = bwdist ( ThisFringeImg ) ;
% Create a r e c tangu l a r mask s yme t r i c a l l y cente red on the major ax i s
% o f the g iven f r i n g e
L = s ( f ) . MajorAxisLength ;
theta = s ( f ) . Or i entat i on ;
x = s ( f ) . Centroid (1 ) + 0 . 5* (L* cosd ( theta )* [ −1 ;1 ;1 ; −1 ] . . .
+ W* s ind ( theta )* [ −1 ; −1 ; 1 ; 1 ] ) ;
y = s ( f ) . Centroid (2 ) + 0 . 5* (L* s ind ( theta )* [ 1 ; −1 ; −1 ;1 ] . . .
+ W* cosd ( theta )* [ −1 ; −1 ; 1 ; 1 ] ) ;
FringeMask = poly2mask (x , y ,CC. ImageSize ( 1 ) ,CC. ImageSize ( 2 ) ) ;
NeighbFringes = FringeImg ;
NeighbFringes ( FringeMask == 0) = 0 ;
% El iminate the cur rent f r i n g e keeping only i t s ne ighbor ing f r i n g e s
NeighbFringes ( ThisFringeImg == 1) = 0 ;
NeighbLMat = LMat ;
NeighbLMat ( NeighbFringes == 0) = 0 ;
% get the l eng th s o f each masked neighbor f r i n g e
NeighbIDs = unique (NeighbLMat ) ;
NeighbIDs = NeighbIDs (NeighbIDs >0);
NeighbLengths = ze ro s ( numel ( NeighbIDs ) , 1 ) ;
gDi s t s = c e l l ( numel ( NeighbIDs ) , 1 ) ;
f o r j = 1 : numel ( NeighbIDs )
% Image o f j u s t t h i s masked neighbor f r i n g e
ThisNeighbImg = NeighbLMat == NeighbIDs ( j ) ;
% Shor t e s t d i s t from each p i x e l in t h i s ne ighbor to r e f f r i n g e
SepDists = dImg( ThisNeighbImg ) ;
MeanSepDist = mean( SepDists ) ;
[ row , c o l ]= f i nd (bwmorph(ThisNeighbImg , ’ endpoints ’ ) ) ;
% Ignore s i n g l e p i x e l s and ob j e c t s l a ck ing endpoints ( e . g . c i r c l e s )
i f numel ( row ) > 1
% Calcu la te the f r i n g e l ength
gDis t s { j } = bwdi s tgeodes i c ( ThisNeighbImg , c o l ( 1 ) , row (1 ) , . . .
’ quasi−euc l i d ean ’ ) ;
gDi s t s { j } = gDis t s { j }(˜ i snan ( gDis t s { j } ) ) ;
NeighbLengths ( j ) = max( gDis t s { j })+1;
end
ThisNeighb = reg ionprops ( ThisNeighbImg , ’ Or i enta t i on ’ ) ;
i f l ength ( ThisNeighb ) > 1
% I f the FringeMask cuts the ne ighbor ing f r i n g e in to mu l t ip l e
% se c t i on s , use the e n t i r e ne ighbor ing f r i n g e to measure the
% o r i e n t a t i o n d i f f e r e n c e
200
Or i en tD i f f = abs ( s ( NeighbIDs ( j ) ) . Or ientat ion−s ( f ) . Or i entat i on ) ;
e l s e
% Otherwise use only the por t i on o f the ne ighbor ing f r i n g e
% that i s with in the FringeMask
Or i en tD i f f = abs ( ThisNeighb . Or ientat ion−s ( f ) . Or i entat i on ) ;
end
% i f t h i s ne ighbor ing f r i n g e i s l onge r than MinFringeLength ,
% i s w/ in the o r i e n t a t i o n t o l e r an c e with r e sp e c t to the r e f e r e n c e
% f r i ng e , and has an avg s epa ra t i on d i s t anc e w/ in the to l e rance ,
% record the average f r i n g e d i s t & the IDs o f the two f r i n g e s
i f NeighbLengths ( j ) >= MinFringeLength && MeanSepDist >= SepTol (1 ) . . .
&& MeanSepDist <= SepTol (2 ) && Or i en tD i f f <=OrientTol
n=n+1;
FringeSeps (n , : ) = [ f , double ( NeighbIDs ( j ) ) , MeanSepDist ] ;
end
end
end
d e l e t e (wb ) ; % de l e t e the waitbar f i g u r e
% I f f r i n g e s were found and the user didn ’ t cance l . . .
i f ˜ isempty ( FringeSeps ) && ˜FringeSeps (1)==0
% Sort so that the l a r g e r ID# of each f r i n g e pa i r s i s in column 2
FringeSeps = horzcat (min ( FringeSeps ( : , 1 : 2 ) , [ ] , 2 ) , . . .
max( FringeSeps ( : , 1 : 2 ) , [ ] , 2 ) , Fr ingeSeps ( : , 3 ) ) ;
Fr ingeSeps = sort rows ( FringeSeps ) ; % Sort ascending based on column 1
% Get the row ID o f each r e c i p r o c a l f r i n g e pa i r
[ ˜ , ia1 ,˜ ]= unique ( FringeSeps ( : , 1 : 2 ) , ’ rows ’ , ’ f i r s t ’ ) ;
[ ˜ , ia2 ,˜ ]= unique ( FringeSeps ( : , 1 : 2 ) , ’ rows ’ , ’ l a s t ’ ) ;
% Average the f r i n g e s epa r a t i on s o f each r e c i p r o c a l f r i n g e pa i r
AvgFringeSeps = ( FringeSeps ( ia1 ,3)+ FringeSeps ( ia2 , 3 ) ) / 2 ;
% El iminate any f r i n g e pa i r s that do not r e c i p r o c a l l y c a l c u l a t e
% the same sepa ra t i on d i s t ance with in a s p e c i f i e d t o l e r an c e
k = abs ( FringeSeps ( ia1 ,3)−FringeSeps ( ia2 ,3))<RecipTol ;
AvgFringeSeps = AvgFringeSeps (k ) ;
% Return the unique f r i n g e pa i r s with averaged s epa ra t i on d i s t an c e s
FringeIDs = FringeSeps ( ia1 , 1 : 2 ) ;
Fr ingeSeps = horzcat ( FringeIDs (k , : ) , AvgFringeSeps ) ;
end
201
Appendix B: Mathematical Derivations
B.1 Expressions for the Diameters of Average Surface Area and Vol-
ume
The ith moment of a continuous distribution function of random variable x is
defined as: ∫ ∞
Mi ≡ xif(x)dx (B.1)
−∞
Now consider a discrete size distribution function of a population of primary particle
diameters, f(dp), defined such that f(dp) equals the number of primary particles in
the population with diameter dp. The zeroth moment of f(dp) then is simply the
total number of primary particles:
∑
M0 = f(dp) = Np (B.2)
dp
The mean primary particle diameter is by definition:
1 ∑
µdp = dpf(dp) (B.3)Np
dp
which is simply the ratio of the first to the zeroth moments:
M1
µdp = (B.4)M0
202
The diameters of average surface area and volume can be similarly defined using the
second and third moments of the distrib(ution,)respectively [141]:1/2
M2
µd = (B.5)pS M0
and ( )1/3
M3
µd = (B.6)pV M0
The general equation for the ith central moment CMi, of a continuous distri-
bution of random variable x was giv∫en in Eq. 3.11:∞
CM = (x− µ)ii f(x)dx (B.7)
−∞
In discrete form with f(dp) defined as above, the second central moment is simply
the variance of the population of primary particles:
2 1
∑
σd = CM2 = (dp − µ 2dp) f(dp) (B.8)p Np
dp
Expanding the polynomial and rearranging, Eq. B.8 can be written a∑ ∑ ∑ 
s:
2 1σd = d
2
pf(dp)− 2µdp dpf(dp) + µ2 f(d )d (B.9)p N p pp
dp dp dp
which from the definition of the moments of the distribution is:
1 [ ]
σ2d = M2 − 2µdpM1 + µ2d M (B.10)p N p 0p
Using the relationships given by Eq. B.2 - B.5, and solving for µd :pS
µ = (σ2 2 1/2d d + µd ) (B.11)pS p p
Writing this in terms of the sample population variables defined in the text yields
Eq. 3.12:
d = (s2
2
pS d + dp )
1/2 (B.12)
p
203
Now consider that the skewness of a distribution is defined as the third central
moment divided by the standard deviation cubed. For the distribution of primary
particles this is: ∑
CM 1/Np d (dp − µdp)3f(dp)3
γdp = =
p (B.13)
σ3d σ
3
p dp
Expanding the polynomial and applying the definitions of the moments of the dis-
tribution, as was done for σdp above gives:
[ ]
γ σ3
1
dp d = M3 − 3µdpM2 + 3µ2d M 3p p 1 − µN d
M (B.14)
p 0
p
Using the relationships given by Eq. B.2 - B.6, and solving for µd :pV
µd = (γdpσ
3 2 3 1/3
pV d + 3µ σ + µ ) (B.15)p dp dp dp
Writing this in terms of sample population variables defined in the text yields
Eq. 3.13:
3
dpV = (γdps
3 2 1/3
d + 3dpsd + dp ) (B.16)p p
204
B.2 Expressions for Spherical Cap Height
Begin with the spherical cap and overlapping primary particle schematic:
Figure B.1: (a) Spherical cap (b) Overlapping primary particles of different sizes.
Assuming the centers of spheres i and j are both situated on a plane normal
to the viewer, then the overlap coefficient, Cov is equivalent to the projected overlap
coefficient in Eq. 2.8:
dp − dij
Cov = (B.17)
dp
Since the mean primary particle diameter dp for spheres i and j is simply ri + rj,
Eq. B.17 can be rewritten solving for dij:
dij = (ri + rj)(1− Cov) (B.18)
which from Fig. B.1 is also:
dij = ri − hi + rj − hj (B.19)
205
equating Eq. B.18 and B.19 and solving for hj yields Eq. 3.18:
hj = Cov(ri + rj)− hi (B.20)
Next, by the Pythagorean theorem, the following two expressions are both
equivalent to length a, and therefore to each other:
r2 − (r − h )2i i i = r2j − (rj − hj)2 (B.21)
Expanding the polynomials and rearranging gives:
2r h − h2i i i = 2rjhj − h2j (B.22)
Substituting hj from Eq. B.20 into Eq. B.22, solving for hi, and simplifying produces
equation Eq. 3.17:
C2ov(ri + rj)− 2rjCovhi = (B.23)
2(Cov − 1)
206
Appendix C: Supplemental Figures
This page intensionally left blank
207
C.1 Fractal Dimension and Pre-factor from Fitted Data
Figure C.1: Least-squares fits of ln(Np,a) vs. ln(Rg/rp) data, yielding a global
aggregate fractal dimension, Df and pre-factor, kf , at each height above burner.
208
C.2 Additional Fringe Measurements at the Primary Particle Surface
Figure C.2: Additional lattice fringe measurements. To highlight surface oxida-
tion effects, only fringes within the outer 20% of the primary particle were used
in the analysis. (a)-(c) Median fringe tortuosity, standard deviation of fringe non-
concentricity, and mean fringe separation distance vs. height above burner. (e)-(f)
Change in median fringe tortuosity, standard deviation of fringe non-concentricity,
and mean fringe separation distance with respect to primary particle diameter vs.
fringe radial location.
209
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