Supplemental Information
for
Observations of a Correlation between Primary Particle and
Aggregate Size for Soot Particles
Ramin Dastanpour*, Steven N. Rogak
Department of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia,
Canada
*
Corresponding author email: r.dastanpour@alumni.ubc.ca
Linear and power fits to dp-da data presented in Figure 2 of the manuscript
Results obtained from fitting correlations in the forms of 𝑑𝑝 = 𝑐 (constant primary average
particle size for all aggregate sizes) and 𝑑𝑝 = 𝑎. 𝑑𝐴𝑏 (power fit) to the data presented in
Figure 2 of the main manuscript are summarized in Table S1.
Table S1: Curve fitting results for data presented in Fig. 2 of the main manuscript
Source
Fit type
𝒅𝒑 = 𝒄
𝒅𝒑 = 𝒂. 𝒅𝒃𝑨
*
GDI
c = 19.93 (19.26, 20.6)
a = 5.22 (4.32, 6.12)
R-square: -2.22e-16
b = 0.30 (0.26, 0.33)
R-square: 0.349
HDPI
c = 24.45 (23.84, 25.06)
a = 6.49 (5.46, 7.52)
R-square: 1.776e-15
b = 0.29 (0.26, 0.32)
R-square: 0.327
Aviation gas
c = 27.21 (25.8, 28.63)
a = 5.01 (3.36, 6.66)
turbine
R-square: -2.22e-16
b = 0.39 (0.32, 0.46)
R-square: 0.282
Inverted burner
c = 31.19 (29.54, 32.85)
a = 6.05 (2.94, 9.17)
R-square: -2.22e-16
b = 0.29 (0.20, 0.38)
R-square: 0.195
* Values in all brackets are 95% confidence bounds.
According to these results, assuming a constant average primary particle size for the whole
ensemble of the aggregates in each combustion source is erroneous. Instead, power fits all
resulted in better fits and all have lower bounds (95% confidence) greater than 0.2 for b (b
is the slope of a linear fit in log-scale).
Notes for shielding effect simulations
Two shielding criteria were used. As an extreme criteria, the first shielding case used in
this simulation assumes primary particles as opaque objects. Particles are assumed to be
excluded from measurements when more than 50% for their projected area is shielded by
other particles. Second shielding case assumed in this simulation better represents practical
image processing measurements. It assumes primary particles to be partially transparent.
TEM images show that the primary particles are usually still detectable when they are
shielded by one monomer. Otherwise, their detection probability is reduced. Considering
this, in the second case if more than 1/2 of the area of the primary particle is completely
shielded (with more than one monomer above it) it is assumed that the monomer size
cannot be measured from TEM images.
Figures S1 and S2 compare ∆𝑁𝑝 and ∆𝑑𝑝 , defined by equations 4-5 in the main article, for
the two shielding cases assumed in this model. Shielding effect on the measurement of
primary particle polydispersity is also investigated by the normalized parameter defined by
equation S1 and is illustrated in Figure S3.
∆𝜎𝑔 =
𝜎𝑔,𝑚𝑒𝑎𝑠 − 𝜎𝑔,𝑎𝑐𝑡
𝜎𝑔,𝑎𝑐𝑡
(S1)
As shown in these figures, the difference between “measured” and “actual” 𝑁𝑝 , 𝑑𝑝 , and 𝜎𝑔
in practical measurements (case2) is smaller than the extreme case (case1). This conforms
that the effect of shielding on practical measurement of primary particle size from TEM
images results is a slight overestimation of dp. However, this overestimation is less than
1% of the actual primary particle diameter; and is negligible comparing to 4-6 times
changes in monomer size with aggregate size, as illustrated in Figure 2 in the main article.
Figure S1: Effect of shielding on the number of primary particles detectable on projected images
Figure S2: Effect of shielding on the average primary particle diameter in individual aggregates detectable on projected images
Figure S3: Effect of shielding on the polydispersity of the primary particles in individual aggregates
measured from projected images
Notes for image processing program
In order to extract morphological parameters of soot particles from TEM images, a semiautomatic image processing program was developed in MATLAB. The first version of this
program was developed in our group by Arka Soewono (Soewono, 2008). Its performance
has been enhanced for accurate measurement of soot morphology at different
magnifications.
The operation of this program can be divided into three sections. First, images are loaded
and morphological parameters are extracted from these images in units of pixel (or squared
pixel). Then, these measured parameters are scaled with the size of the pixels (nm/pixel)
to acquire desired units (nm for length and nm2 for area). Finally, these results are exported
and further processed to produce the desired representations.
TEM images are loaded by the program (Fig. S4-a). The user crops each image to select
the desired aggregate (Fig. S4-b). The aggregate’s morphological parameters are measured
by transforming the cropped grayscale image into a binary image by setting a threshold
level for the brightness of the image. To compensate for the effect of high levels of
background intensity fluctuations usually present in images taken at high magnifications,
the operator can draw a freehand boundary around the aggregate, but not necessarily close
to it (Fig. S4-c). The threshold level will only be changed in the selected region and after a
background intensity correction is applied to the cropped image. Projected area, maximum
length and width, gyration radius, and projected area equivalent diameter of the aggregates
are measured from the final binary image (Fig. S4-d). Particle perimeter is also measured
using the aggregate edge obtained from the binary image. The detected particle edge is
super-imposed onto the cropped image and is used to make sure that the binary image is
produced accurately (Fig. S4-e). Primary particle sizing is performed manually. The
accuracy of the primary particle sizing is enhanced by breaking large aggregates into
multiple sections. Considering that the primary particle is not a perfect sphere, its diameter
is measured by averaging its size in two different directions (Fig. S4-f).
Figure S4: TEM image processing steps
Image scale is determined either automatically, using automatic detection of the image
magnification, or by using the scale bar. All measured parameters are stored in a
spreadsheet. Size distribution parameters (mean, geometric mean, standard deviation, and
geometric standard deviation) of the primary particles and aggregates are calculated and
histograms are plotted by the post processing part of the program.
Upon request, this image processing program can be shared with other researchers for
morphology characterisation of soot particles from TEM images.