Why Soot is not Alike Soot: A Molecular/Nanostructural Approach to Low Temperature Soot Oxidation

Abstract

Due to worldwide increasingly sharpened emission regulations, the development of Gasoline Direct Injection and Diesel Direct Injection engines not only aims at the reduction of the emission of nitrogen oxides but also at the reduction of particulate emissions. Regarding present regulations, both tasks can be achieved solely with the help of exhaust after treatment systems. For the reduction of the emission of particulates, Gasoline (GPF) and diesel Particulate Filters (DPF) offer a solution and their implementation is intensely promoted. Under optimal conditions particulates retained on particulate filters are continuously oxidized with the exhaust residual oxygen so that the particulate filter (PF) is regenerated possibly without any additional intervention into the engine operating parameters.
The regeneration behavior of PF depends on the reaction rates of soot particles with oxidative reactants at exhaust gas temperatures. The reaction rates of soot particles from internal combustion engines (ICE) often are discussed in terms of order/disorder on the particle nanoscale, the concentration and kind of functional groups on the particle surfaces, and the content of (mostly polycyclic aromatic) hydrocarbons in the soot. In this work the reactivity of different kinds of soot (soot from flames, soot from ICE, carbon black) under oxidation conditions representative for PF regeneration is investigated. Soot reactivity is determined in dynamic Temperature Programmed Oxidation (TPO) experiments and the soot primary particle morphology and nanostructure is investigated by High-Resolution Transmission Electron Microscopy (HRTEM). An image analysis method based on known methods from the literature and improving some infirmities is used to evaluate morphology and nanostructural characteristics. From this, primary particle size distributions, length and separation distance distributions as well as tortuosities of fringes within the primary particle structures are obtained. Further, UV–visible spectroscopy and Raman scattering and other diagnostic techniques are used to study the properties connected to the reactivity of soot and to corroborate the experimental findings. It is found that nanostructural characteristics predominantly affect reactivity. Oxidation rates are derived from TPO and interpreted on a molecular basis from quantum chemistry calculations revealing a replication/activation oxidation mechanism.

Full text

Vol.:(0123456789)
Flow, Turbulence and Combustion (2021) 106:295–329
https://doi.org/10.1007/s10494-020-00205-2
1 3
Why Soot isnotAlike Soot: AMolecular/Nanostructural
Approach toLow Temperature Soot Oxidation
FabianHagen, etal.[full author details at the end of the article]
Received: 25 March 2020 / Accepted: 29 July 2020 / Published online: 29 August 2020
© The Author(s) 2020
Abstract
Due to worldwide increasingly sharpened emission regulations, the development of Gaso-
line Direct Injection and Diesel Direct Injection engines not only aims at the reduction of
the emission of nitrogen oxides but also at the reduction of particulate emissions. Regard-
ing present regulations, both tasks can be achieved solely with the help of exhaust after
treatment systems. For the reduction of the emission of particulates, Gasoline (GPF) and
diesel Particulate Filters (DPF) offer a solution and their implementation is intensely
promoted. Under optimal conditions particulates retained on particulate filters are con-
tinuously oxidized with the exhaust residual oxygen so that the particulate filter (PF) is
regenerated possibly without any additional intervention into the engine operating param-
eters. The regeneration behavior of PF depends on the reaction rates of soot particles with
oxidative reactants at exhaust gas temperatures. The reaction rates of soot particles from
internal combustion engines (ICE) often are discussed in terms of order/disorder on the
particle nanoscale, the concentration and kind of functional groups on the particle surfaces,
and the content of (mostly polycyclic aromatic) hydrocarbons in the soot. In this work the
reactivity of different kinds of soot (soot from flames, soot from ICE, carbon black) under
oxidation conditions representative for PF regeneration is investigated. Soot reactivity is
determined in dynamic Temperature Programmed Oxidation (TPO) experiments and the
soot primary particle morphology and nanostructure is investigated by High-Resolution
Transmission Electron Microscopy (HRTEM). An image analysis method based on known
methods from the literature and improving some infirmities is used to evaluate morphology
and nanostructural characteristics. From this, primary particle size distributions, length and
separation distance distributions as well as tortuosities of fringes within the primary par-
ticle structures are obtained. Further, UV–visible spectroscopy and Raman scattering and
other diagnostic techniques are used to study the properties connected to the reactivity of
soot and to corroborate the experimental findings. It is found that nanostructural character-
istics predominantly affect reactivity. Oxidation rates are derived from TPO and interpreted
on a molecular basis from quantum chemistry calculations revealing a replication/activa-
tion oxidation mechanism.
Keywords Soot oxidation· Particulate filters· Soot nanostructure· Soot reactivity·
Exhaust gas treatment
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1 Introduction
Due to the increasingly stringent emission regulations (The European Parliament and the
Council of the European Union 2007), the development of Gasoline (GDI) and Diesel
Direct Injection (DDI) engines aims at the reduction of particulate matter (PM) emissions
by application of Gasoline (GPF) or Diesel Particulate Filters (DPF). Particulate filters
(PF) trap soot particles present in the exhaust gases resulting in minimized PM emission.
To allow for a continuous operation of PF, the captured soot is removed periodically by a
regeneration procedure or continuously by oxidation with residual
O2
in the exhaust gas
(Fang and Lance 2004). The reaction rates of soot against oxidation by
O2
determine the
frequency and efficiency of this kind of PF-regeneration (Fang and Lance 2004; Bhardwaj
etal. 2014). The regeneration behavior of PF depends on the reaction rates of soot particles
with oxidative reactants at engine exhaust gas temperatures (573 K to approximately 1073
K). Time scales of reactions of soot in oxidation determine the reactivity of soot and the
reactivity of soot may be expressed through the reciprocal over-all rate coefficient of the
oxidation reaction.
Although a contemporary topic of intensive research, oxidation reaction rates of soot at
engine exhaust conditions are still barely predictable. Reaction rates of soot towards oxida-
tion have been widely discussed under aspects ranging from physico-chemical properties
via different morphological and nanostructural characteristics to its carbon nanostructure
(Stanmore etal. 2001; Mühlbauer etal. 2016; Lu etal. 2012; Lapuerta etal. 2012).
Results reported from various investigations indicate diverse and sometimes conflicting
influencing factors. Small soot primary particle sizes correlate with high reactivity (Stan-
more etal. 2001; Lu etal. 2012; Lapuerta etal. 2012). Large specific surface area which
correlates with small primary particle sizes is found to cause high soot reactivity (Fang and
Lance 2004; Aarna and Suuberg 1997). The specific surface area (Fang and Lance 2004)
as well as the pore structure within soot particles (Stanmore etal. 2001; Lu etal. 2012)
are linked to the diffusive infiltration of oxidant into soot particles affecting also reactiv-
ity. Accessible active surface area rather than the overall surface area determines reactivity
of soot particles (Aarna and Suuberg 1997; Neeft etal. 1997). Amongst the morphologi-
cal characteristics of primary soot particles, their size distributions and fractal dimensions
are indicators for reactivity. Sediako etal. (2017) observed changes in particle morphol-
ogy during soot oxidation by real-time environmental TEM and demonstrated a correlation
between soot aging and oxidation mode.
In addition the carbon nanostructure within primary soot particles is reported to affect
considerably the reactivity towards oxidation. Soot primary particles consist of collo-
cated packets of layered large polycyclic aromatic hydrocarbon molecules of different size
with different functional edge-groups and distorted sites that can be assigned graphene-
like characteristics (Pawlyta etal. 2015). Huang and Vander Wal (2016) demonstrated the
dependence of the nanostructure of soot particles upon partial premixing and the associ-
ated changes in the gas-phase chemistry of ethylene-air Bunsen flames. The collocation
of layered graphene-like structures measured by their length, separation distance and cur-
vature as well as defects within the crystallite structure (Bhardwaj etal. 2014; Lapuerta
etal. 2012; Vander Wal and Tomasek 2003; Pfau etal. 2018) altogether affect the reactivity
of soot. Reactivity of soot, therefore, is a consequence of both agglomerate morphology
and the nanostructure and chemical composition of primary particles (Pfau et al. 2018).
The nanostructure determines the number density of
sp2
and
sp3
-hybridized C-atoms and,
therefore, the energy level of C-atoms within these structures accessible for oxidation. The
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larger the number density of
sp3
-hybridized C-atoms and the less organized the nanostruc-
ture of soot, the higher its reactivity and oxidation rate (Vander Wal and Tomasek 2003; Su
etal. 2004; Knauer etal. 2009).
High-resolution transmission electron microscopy (HRTEM) provides information
about the nanostructural properties such as distribution of length, distance and tortuosity
of the graphene-like layers (Su etal. 2004; Knauer etal. 2009; Yehliu etal. 2011a; Palotas
etal. 1996; Sadezky etal. 2005; Sharma etal. 2000; Vander Wal etal. 2004a, b). Although
HRTEM is limited to ex-situ measurements and particles in the size range below about
10 nm as well as little contrast-forming particles are difficult to detect, it is the preferred
method to investigate the carbon nanostructure of soot (Su etal. 2004; Yehliu etal. 2011a,
b; Palotas etal. 1996; Sharma etal. 1999, 2000; Vander Wal etal. 2004a, b; Shim etal.
2000; Botero etal. 2016). Ultrafine particles with diameters in the 10 nm range or below
and highly amorphous particles are emitted from GDI engines (Czerwinski et al. 2018;
Bardi etal. 2019) and would not contribute to the fringe analysis. HRTEM images are ana-
lyzed qualitatively, manually, or with the help of computer-based image processing soft-
ware (Vander Wal etal. 2004a, b; Shim etal. 2000; Sharma etal. 1999; Botero etal. 2016;
Yehliu etal. 2011b). Large effort has been applied in recent years to improve quantitative
analyses of HRTEM of soot, compare e.g. (Vander Wal etal. 2004a, b; Shim etal. 2000;
Sharma etal. 1999; Botero etal. 2016; Yehliu etal. 2011b; Toth etal. 2013, 2015).
The objective of this work is to develop substantiated information about the oxidation
of soot with molecular oxygen on a nanoscale/molecular level to identify the predominant
parameters of soot governing its reactivity. As a remedy against some infirmities known
from literature, a HRTEM image analysis method developed to perform a quantitative and
reproducible analysis of the carbon nanostructure, has been applied to different soot and
carbon black samples. Subsequently, the nanostructure determined by the image processing
method is compared for the different soot and carbon black samples. Similar work has been
performed by Pfau etal. (2018) comparing the nanostructure af carbon black and soot-in-
oil from gasoline and diesel engines
The results are further interpreted using data obtained for the reactivity of soot and
carbon black in oxidation with oxygen derived from temperature programmed oxidation
(TPO). Further, UV–visible spectroscopy and Raman Scattering and other diagnostic
techniques are used to support the study of the reactivity of soot during oxidation. Soot
samples are inspected at different burn-out ratio providing valuable information about the
development of reactivity during particle burn-out and some evidence for the development
of oxidation models. Results are interpreted with kinetic models and oxidation rate kinet-
ics are derived from TPO and interpreted on a molecular basis from quantum chemistry
calculations.
2 Materials andMethods
2.1 Materials
In this work a vast variety of soot particles has been investigated. Soot samples were gener-
ated using a Graphite Spark Discharge Generator (GFG-3000, Palas GmbH, Germany) at a
voltage of 2500 V and a discharge frequency of 500 Hz. The argon carrier gas flow was set
to
10 nl min−1
(nl: norm liters) This soot sample will be denoted as AGFG. Downstream of
the aerosol generation, a nitrogen flow of
10 nl min−1
was used to dilute the aerosol before
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collecting it on filters. The carrier gas argon has been replaced by nitrogen at the same
flow rate to generate a further soot sample (NGFG). Additional soot samples were pre-
pared by collecting soot on quartz fiber filters downstream of a low pressure (200 mbar)
flat premixed laminar acetylene/oxygen flame (equivalence ratio
𝜙=2.7
) (ACFL) and
flat premixed iso-octane/oxygen/argon flames (
𝜙=2.3
) at pressures of 1 bar, 2 bar and
3 bar (i-OCT1, i-OCT2, i-OCT3). Flame soot samples were Soxhlet-extracted to remove
adsorbed polycyclic aromatic hydrocarbons (PAH). In addition, soot samples from a tur-
bocharged 4 cylinder research GDI engine (2.0 liters) collected close to the manifold at
medium (A22) and high (A33) engine load have been included. Sample A22_1 is obtained
from the GDI engine operated with a modified injection pressure (87.5 bar compared
to 100 bar for sample A22). Engine conditions are given in detail in Koch etal. (2020).
The ICE soot was complemented by samples from a commercial Diesel Direct Injection
engine at injection pressures of 2200 bar, 1600 bar and 1200 bar (C50_2200, C50_1600,
C50_1200). Sampling procedure and engine description is delineated in Lindner et al.
(2014). For comparison commercial carbon black samples were investigated. The carbon
blacks examined are Printex
Ⓡ
25 (P25), Printex
Ⓡ
45 (P45), Printex
Ⓡ
85 (P85) and Printex
Ⓡ
90
(P90) (Orion Engineered Carbons, Luxembourg) manufactured by the furnace carbon black
process and acetylene carbon black Alfa Aesar™(ThermoFischer Scientific Inc., USA),
100% compressed (AC100). The carbon black samples provide materials with a wide range
of mean primary particle sizes, specific surface areas and reactivity, see Table1. As com-
mercial products they are easily available and, therefore, are ideally for the investigation
presented here.
Table1 summarizes some properties of the investigated soot and carbon black samples:
The BET specific surface area (BET), the count median diameter (CMD) of the primary
Table 1 Properties of the investigated soot and carbon black samples ordered by increasing reactivity
Values of
Tmax
, the temperature of maximum oxidation rate during TPO, are derived from TPO profiles, see
Sect.2.2.1. Some soot samples exhibit multiple peaks in the TPO profiles indicated by multiple
Tmax
values
Sample (abbreviation) BET (
m2g−1
)CMD (nm) C/H (–)
X
O
2
(mol%)
Tmax
(K)
Alfa Aesar™(AC100) 70 42 22 0.69 1063
Printex
Ⓡ
25 (P25) 46 54 19 0.00 1010
Printex
Ⓡ
45 (P45) 81 31 18 1.05 965
Spark discharge soot
N2
(NGFG) 426 5 10 5.14 963/796/570
Printex
Ⓡ
90 (P90) 293 17 17 1.28 949
iso-Octane, 3 bar (i-OCT3) 62 24 7 1.56 944
Printex
Ⓡ
85 (P85) 173 16 17 1.81 937
Diesel soot (C50_1200) 409 – 7 – 935
Acetylene flame soot (ACFL) 96 15 8 4.98 924
iso-Octane, 2 bar (i-OCT2) 89 26 7 1.14 923
iso-Octane, 1 bar (i-OCT1) 94 37 6 1.32 916
Spark discharge soot Ar (AGFG) 679 3 4 – 911/796/570
Diesel soot (C50_1600) 453 – 7 – 906
GDI soot (A22) – 28 – – 895/570
GDI soot (A
22_1)
– 45 – – 895/795
GDI soot (A33) – 23 – – 891
Diesel soot (C50_2200) 284 – 6 – 786
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particle size distribution approximated by a log-normal distribution, the C/H atomic ratio
and the oxygen mole fraction
XO2
determined by elemental analysis and the temperature of
maximum reaction rate (
Tmax
) during TPO.
Tmax
is widely used to indicate the reactivity
towards oxidation, where low temperatures are linked to high reactivity and vice versa, see
following sections.
As can be noticed from Table1, the properties of the investigated soot and carbon
black samples are spread over a wide range in magnitude. The listed soot samples were
chosen deliberately to harden or exclude correlations of the reactivity against oxidation
with different morphological, chemical and nanostructural properties. Some correlations
between properties, e.g. reactivity indicated by
Tmax
, the temperature of maximum oxida-
tion rate during TPO, with specific surface area and mean primary particle size, differ from
those given in the literature, see GDI and carbon black soot samples. Equally well, e.g.
the relationship between specific surface area and mean primary particle size differs from
the expected one (the higher the specific surface area the lower the mean primary particle
size), see the Printex
Ⓡ
samples. On the other hand, some properties between different sam-
ples are similar, so that conflicting results can be explained by widening the spectrum of
influencing factors and identifying those with highest weight.
The various applied analytical methods for the investigation of the soot samples, see
Sect.2.2, require varying sample amounts. Due to the different origin of the soot (com-
mercial carbon black, soot from ICE, soot from flames), only varying quantities were avail-
able for the experiments. Therefore, not every method could be applied fully to the entity
of soot samples, which particularly applies to the soot samples from ICE. However, due to
the similarity with respect to measured morphological and nanostructural properties, these
samples were withheld in the discussion for comparison.
The emission of soot from ICE depends significantly on operation conditions such as
injection pressure, injection timing, multiple injection patterns, load etc., resulting in soot
which is not alike soot when looking at some bulk properties. However, soot from ICE is
similar to flame generated soot or carbon black with respect to morphological and nano-
structural properties and, therefore, is alike these kinds of soot with respect to reactiv-
ity against oxidation. Vice versa, alike soot with respect to some bulk properties exhibits
diverse nanostructure and reactivity. For the above reasons, the wide range of soot samples
including soot from ICE was considered in the tests, though the application of the full diag-
nostic and analytic methods to all these samples was limited.
2.2 Applied Methods
The elemental analysis of the elements carbon, nitrogen and hydrogen was performed using
a Vario Micro Cube elemental analyzer (Elementar Analysensysteme GmbH, Germany).
The measurement system is equipped with thermal conductivity (TCD) and infrared (IR)
detectors. The soot sample mass was 2.5 mg for each measurement.
Specific surface areas were measured using a BELSORP-mini (BEL Japan Inc., Japan)
volumetric adsorption measurement instrument with nitrogen physisorption at 77 K. Prior
to the measurements, the apparatus was calibrated using internal standards. Soot samples
were outgassed in vacuum at 378.15 K before the measurements. The resulting isotherms
were analyzed conforming to the latest IUPAC recommendations with respect to the BET
surfaces.
UV–visible spectroscopy was performed with soot particle suspensions in N-methyl-pyrro-
lidone (NMP). Apicella etal. (2004) mention, that NMP is a suitable solvent to achieve stable
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suspensions of carbon-rich, solid materials. Sample preparation was carried out by mixing
sample and solvent, followed by dispersing with an ultrasonic homogenizer (Bandelin, Sono-
plus HD3200, Germany) for 10 minutes. The spectral response of the solvent NMP in the UV
limits the visualization of the spectra to a region of 280–800 nm. UV–visible spectra were
measured in the absorbance mode on a Chirascan (Applied Photophysics, UK) spectrometer
and the Cary 300 UV–visible spectrometer (Agilent, USA) using 1 cm quartz cuvettes. Each
sample was measured four times, while the cuvette was refilled before each measurement.
2.2.1 Oxidation Rates
The oxidation rates of the soot samples were measured through temperature programmed
oxidation (TPO) employing thermogravimetric analysis (TGA) (Koch etal. 2020; Hagen
etal. 2020). Dynamic, non-isothermal measurements were performed with a TG 209 F1
Libra thermo balance (Netzsch Gerätebau GmbH, Germany) at a heating rate of 5
K min−1
.
The soot samples with a sample mass of
2±0.2 mg
were oxidized under an atmosphere
consisting of 5 %vol
O2
and 95 %vol
N2
at atmospheric pressure. The thermo balance was
temperature-calibrated with reference to the melting points of In, Sn, Bi, Zn, Al and Ag.
In addition to virgin soot, soot samples at different burn-out ratios (mostly 0%, 20%, 60%,
80%, 90%) have been investigated.
Complementary to the dynamic TPO-experiments, soot samples were also oxidized
stepwise to mass losses of 20%, 60%, 80% and 90%. During these experiments soot sam-
ples were heated up in the thermobalance under inert conditions (
N2
) applying a heating
rate of
200 K min−1
. After attaining the reaction temperature of 1073 K, soot samples were
oxidized with a mixture of 5% by volume of
O2
in
N2
under isothermal conditions until the
desired mass loss and cooled down under inert conditions. After each oxidation step part of
the sample was examined with regard to the reactivity of the primary particles by TPO and
by HRTEM analysis and the remaining sample was used for the subsequent oxidation step.
As far as reaction mechanisms based on elementary reactions are not available, the oxi-
dation of soot may be described with the help of global over-all kinetic expressions. To
deduce kinetic parameters for the oxidation of soot with excess of oxygen from the TPO
profiles, a reacting-volume model of the form
is applied, where
msoot
means the actual soot mass,
pO2
is the oxygen pressure and
Nact
the
number density of sites accessible for oxidation with the reaction order m and n, respec-
tively.
k(1)
ox
is the corresponding reaction rate coefficient. For
O2
in excess,
pO2
can be
regarded being constant and according to the reacting-volume model
Nact
can be approxi-
mated assuming
Nact ∝msoot
. This results in
Introducing
𝛼=msoot∕m0soot
gives
When performing TPO experiments with a constant heating rate
𝛽
=
dT
dt
the rate equation
can be rewritten as
(1)
dm
soot
dt
=−k(1)
ox
⋅pm
O2
⋅Nn
act
(2)
dm
soot
dt
=−k(2)
ox
⋅mn
soot
.
(3)
d
𝛼
dt
=−k(3)
ox
⋅𝛼n
.
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The rate coefficient
k(4)
ox
contains the heating rate and in case of
n≠1
the initial mass
m0soot
. Therefore, all TPO experiments are performed with a constant initial mass of 2 mg
and a constant heating rate of
5 K min−1
to compare rate coefficients. The temperature
dependency of the rate coefficient is expressed with the help of a simple Arrhenius
approach
k
(4)
ox =k(4)
0ox
⋅exp
[
−Ea
R
⋅
T]
where
Ea
is the apparent activation energy of the over-all
reaction. The reactivity of soot may be expressed through the reciprocal rate coefficient
k(4)
ox
.
The three-parameter rate coefficient can be obtained by numerical integration of the
model equation Eq.4 and fitting it to measured TPO profiles with the help of non-linear
regression, e.g. via the method of Levenberg-Marquardt. As alternative the easily to meas-
ure temperature
Tmax
at the maximum change
d𝛼
dT
can be used to describe reactivity. Figure1
exhibits TPO-profiles computed for
k(4)
0ox
=4.0 ⋅106K
−1
and
Ea=100 kJ mol−1
. The left
branch of the TPO-profiles until the maximum is determined by the temperature depend-
ency of the oxidation rate while the right branch of the rate is limited by the depletion of
the soot mass.
Tmax
, the temperature of maximum oxidation rate during TPO (indicated
by the broken line), is correlated approximately linearly to the apparent activation energy
meaning that low
Tmax
indicates high reactivity and vice versa (e.g.
Tmax =6.0
⋅
Ea+30
for
k(4)
ox
=4.0 ⋅10
6
K
−1
,
n=1
and
Ea
in
kJ ⋅mol−1
).
2.2.2 Raman Microscopy
The Raman spectra of soot samples were obtained using a Renishaw inVia Raman Micro-
scope with Fiber Optic Probe (FOP) equipped with a Nd:YAG laser (532 nm, laser power
150 mW). Spectra were recorded from 50 to
2000 cm−1
. For the detection a grid with
1800 mm−1
spacing and a CCD detector with an objective of 100fold magnification was
employed.
Raman spectra of soot can be characterized by a 5-peaks structure (Hagen etal. 2020;
Ferrari and Robertson 2000) containing a G-peak at about
1580 cm−1
(graphite band, G),
(4)
d
𝛼
dT
=−k(4)
ox
⋅𝛼n=k(4)
0ox
⋅exp
[
−
Ea
R⋅T
]
⋅𝛼n
.
Fig. 1 Calculated TPO-profiles
according to Eq.4 at differ-
ent reaction order n using
k(4)
0ox
=4.0 ⋅106K−
1
and
Ea=
100 kJ mol
−1
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see Fig.2. This band is attributed to an ideal graphitic lattice and caused by the relative
motion of
sp2
carbon atoms (
E2g
-symmetry). The D-peak at about
1355 cm−1
is a breathing
mode of the carbons in six-membered rings (
A1g
-symmetry). This mode becomes active
only in presence of disorder (defect or disordered bands, D1). A peak at about
1620 cm−1
refers to disordered graphitic structures (D2,
E2g
-symmetry), whereas the peak at about
1500 cm−1
(D3) is attributed to amorphous carbon. Finally the peak at about
1200 cm−1
(D4,
A1g
-symmetry) is attributed to
sp2
and
sp3
carbon atoms not necessarily in six-mem-
bered rings. To reproduce the spectra a 5-band-fitting procedure according to Sadezky
et al. (2005), Ferrari and Robertson (2000) has been applied, which is demonstrated in
Fig.2. The figure displays the measured spectrum (symbols) and the intensity of the D1- to
D4 and G-peaks as well as the fitted spectrum (gray line). This allows the estimation of the
relative intensities of D- and G-bands providing qualitative information about the abun-
dance of graphitic ordered structures and disordered regions and the content of amorphous
carbon. High values of the intensity ratio
ID1∕IG
indicate predominance of low ordered
graphene-like structures with small extension whereas low values suggest well ordered,
graphitic graphene-like structures of large extension.
2.2.3 HRTEM Image Preparation andProcessing
In preparation of HRTEM recordings, soot samples were mixed with ultra-pure water,
stirred by ultrasound and dispersed onto a carbon-coated TEM copper grid. HRTEM
images were acquired using a Philips CM200 transmission electron microscope (Ther-
moFischer Scientific Inc., USA), operated at 200 kV and a magnification of 380.000 result-
ing in a spatial resolution of
0.0283 nm px−1
.
Size distributions of primary soot particles have been determined from HRTEM images
of soot particle aggregates applying a MATLAB-procedure, the single steps of which are
illustrated in Fig.3. After reading the TEM images, appropriate scaling and selection of a
Fig. 2 Raman spectrum of the i-OCT3 sample and 5 band fitting procedure for identification of D- and
G-bands. Symbols represent measured spectrum, gray line the fit (
R2
=0.9947
with
n=482
data points)
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region of interest a Gaussian low-pass filter is applied, to remove background noise. These
steps are followed by binarization as well as edge enhancement and a Hough transforma-
tion to detect circular objects.
The Hough transformation leads to the detection of an excessive number of circular
objects not all being primary particles. Therefore, different operations are applied to extract
circles representing actual particles with their accurate diameter. The outlines of detected
circles are compared to edge structures extracted from the original image. Overlapping cir-
cles are then ranked and deleted according to their congruity with those edge structures,
leaving only well-fitting circles. At last, size distributions of the detected primary soot
particles and fractal dimensions
Df
are calculated. The fractal dimension according to the
minimum bounding rectange (MBR) method is given by
with the circular area
App
, the aggregate area
Aa
and the width W and length L of the
aggregate. The exponent
𝛼
is taken from Köylü etal. (1995),
𝛼=1.09
. Size distribu-
tions are based on the evaluation of about five exposures and 100–500 primary particles
each. The procedure has been tested with synthetically generated size distributions before
application.
The essential steps of HRTEM image processing to evaluate the primary particle nano-
structures are filtering in the Fourier space, binarization, skeletonizing elements, post-pro-
cessing of the skeletons and analysis of fringe length, tortuosity and separation distance of
the fringes (Shim etal. 2000; Sharma etal. 1999; Yehliu etal. 2011b). For binarization the
choice of a suitable, global threshold (TH) still represents an unsatisfied challenge. While
the evaluation of fringe length and tortuosity is well established, the calculation of the sep-
aration distance still contains uncertainties and difficulties.
(5)
D
f=d

ln

Aa
App

𝛼

∕d

ln

L⋅W
rpp
,
Fig. 3 Procedure for evaluation of primary particle size distributions from HRTM images and example
from i-OCT3 soot. Measured size distribution (right diagram) is approximated by a log-normal distribution
with
CMD =24 nm
and
𝜎g
=1.2
. HRTEM of an exemplary aggregate is also given
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The single steps of the procedure used in this work are depicted in Fig.4, see also Koch
etal. (2020). The single computing steps are given in the left part of the figure and illus-
trated with the help of corresponding HRTEM images (right part). The imported 16-bit
HRTEM images are saved as gray scale matrices. The images are inverted, top-hat trans-
formed and their spatial resolution is calculated (yellow framed rectangles). In order to
reduce the background noise resulting from optical distortion of the HRTEM images, the
use of a Gaussian low-pass filter is an established method (Botero etal. 2016; Gonzalez
and Woods 2008). In addition to removing small background structures, larger structures
are reduced in size (Sharma etal. 1999). This leads to a loss of carbon fringe layers or a
separation of structures. To counteract this effect, an image comparison is implemented in
the algorithm. By comparing filtered and unfiltered images only structures present in the
filtered image are kept but then replaced by the original unfiltered structure (green framed
rectangles). As a result, background noise is significantly reduced while fringes maintain
shape and size.
Binarization separates pixels into two different categories due to their intensity. The
use of top-hat transformation is an established method to prepare an image for bina-
rization. Differences in exposure within an image make a global threshold (TH) unfit
for this task. According to a TH, the intensity
I={0, 1}
(
I=1
foreground,
I=0
back-
ground) is assigned to every pixel during binarization. The determination of a suitable
TH is considered as crucial for image processing (Yehliu etal. 2011b; Gonzalez and
Woods 2008; Galvez etal. 2002; Serra 1989). An ideal TH is achieved when pixel inten-
sities show a bimodal distribution. Then, the TH value is equal to the local minimum
Fig. 4 Procedure for evaluation of the nanostructure of primary particles
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in between the two maxima of the distribution. In HRTEM images, these modes would
represent graphene-like structures and background, respectively. The intensity distribu-
tions of HRTEM images, however, are unimodal.
Applying the well-known Otsu threshold method (Jähne 2002) to the unimodal inten-
sity distributions resulting from HRTEM images of soot primary particles, no suitable
TH could be found. Therefore, a method was developed in this study, using a TH value
that causes a minimal alteration of the graphene-like structures when changing its value.
For this, the number of pixels per object has been calculated versus the value of the
TH. The resulting histograms were fitted by a two parameter
𝛾
-function. The obtained
functions exhibit regions in the parameter space (shape parameter and scale parameter)
where the number of pixels changes only little with changing TH value. This transition
region characterizes an ideal TH value for binarization where fringes are optimal sepa-
rated from background pixels. As part of this development 215 HRTEM images have
been analyzed. Only 19 of them (
≈
8%) did not result in reasonable TH values. Fur-
ther testing with the use of a different transmission electron microscope (FEI
TITAN3
(80–300) (ThermoFischer Scientific Inc., USA), at 300 kV) also confirmed the method.
Skeletonizing the elements reduces all objects to lines with a width of one pixel. This
prepares the image for calculating length L, Euclidian end point distance e and, hence,
tortuosity
T=L∕e
of fringes. In this study, the objects are skeletonized by a Zhang-
Suen algorithm (Zhang and Suen 1984). Subsequently, a number is assigned to every
object. Branches within the skeletonized structures, which are joined by branch point
(BPs) originate from applying the skeletonization algorithm. The BP analysis aims at
creating a continuous main structure by deleting branches not belonging to this main
graphene-like structure. For this, Yehliu etal. (2011b) use a morphological opening and
closing method. This method leads to an incomplete removal of branches of the carbon
nanostructures investigated in this study. Therefore, each BP is analyzed individually
using a similar procedure as introduced by Shim etal. (2000) as well as Sharma etal.
(1999), (blue framed rectangles).
The fringe length results from counting the pixels of a structure while pixels are
assigned different lengths according to their connection to neighboring pixels. A straight
link between two pixels results in a length of
L=1 px
while a diagonal connection is
equal to the length of
L=√2 px
. Tortuosity T describes the ratio of fringe length and
Euclidian distance and, hence, the curvature of fringes. The separation distance D, on
the other hand, is used to indicate the short-range order of fringes, see Fig. 4, (gray
framed rectangles). The algorithm developed in this study allows an automated deter-
mination of both structural parameters. Prior to analyzing the nanostructure of soot and
carbon blacks the developed image processing procedure programmed also in MATLAB
has been validated by analyzing manually created, characteristic reference structures.
This led to a maximum deviation of 3% concerning the length of the detected structures.
For evaluation of the nanostructure 20 to 50 soot primary particles from different expo-
sures and up to 5000 fringes were analyzed.
The length L, spacing D and tortuosity T of the fringes reflect a relationship to the
corresponding properties of the graphene-like layers in the primary soot particles, so
that “fringe” and “graphene-like layer” are used synonymously in the following. It
should also be noted, that ultrafine particles with sizes in the 10 nm range and below
and particularly amorphous particles emitted from GDI engines (Czerwinski etal. 2018;
Bardi etal. 2019) are hardly accessible for this kind of analysis.
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2.2.4 Quantum Chemistry Calculations
For interpretation of the oxidation rates obtained from TPO-measurements quantum-
chemistry estimations have been performed. Applying these methods, calculations have
to be restricted to comparatively small molecules to obtain reliable results. Therefore,
model molecules which represent carbon structures in soot primary particles are used
for this kind of calculations, see e.g. Sendt and Haynes (2011), Edwards etal. (2013,
2014).
Soot primary particles are built up of layered graphene-like structures consisting of
large polycyclic aromatic hydrocarbons, partially equipped with functional groups and
aliphatic side chains. Particularly in the state of incipient soot, smaller structures are
linked via aliphatic bridges, see e.g. D’Anna (2009). The primary attack of
O2
at tem-
peratures of about 900 K occurs at aliphatic side chains or aliphatic bridges rather than
at aromatic C-H-sites. According to Mehl etal. (2011), Zhang and McKinnon (1995),
the respective rate coefficients differ by more than one order of magnitude. It is then
likely, that aliphatic side chains and aliphatic bridges are stripped from the polycyclic
aromatic structures first and the much slower activation of the remaining polycyclic aro-
matic structures constitutes the rate limiting step. Therefore, and because the amount
of carbon fixed in these side chains and aliphatic bridges is low compared to that con-
tained in the graphene-like structures, the polycyclic aromatic hydrocarbon pyrene has
been used as a model molecule for graphene-like layers in soot primary particles in this
work. The estimated rate coefficients presented in Sect.3.4, therefore, are limited to
activation/degradation reactions of this polycyclic structure. The hydrogen content of
the investigated soot samples, which is even considerable for the soot sample with the
lowest reactivity (AC100, see Table1), is less compared to pyrene. However, consider-
ing the large extension of the polycyclic aromatic structures in the soot primary parti-
cles, the decrease of the hydrogen content with increasing size of the structures and the
focus on the activation/degradation reactions of these structures, the choice of pyrene as
a model molecule is justified.
The reactions of pyrene with molecular oxygen are investigated for developing
kinetic models and oxidation rate kinetics. To determine the molecular properties of
reactants, transition states and products of the different species occurring in the pyr-
ene/
O2
system, the Gaussian 03/09 (Frisch etal. 2016) and the Gaussian-4 (G4) (Curtiss
etal. 2007) program suites have been employed. The hybrid density functional method
DFT (B3LYP), which combines the three parameter Becke exchange functional B3 with
the Lee-Yang-Parr nonlocal correlation functional (LYP), with a double polarized set,
6-311G(d,p), is used to optimize geometries (Becke 1993; Lee etal. 1988; Montgomery
etal. 1994). The use of DFT (B3LYP) is affordable and permits handling of large mol-
ecules at low computational costs. This method, when combined with isodesmic reac-
tions, delivers good accuracy for thermodynamic data. B3LYP/6-311G(d,p) is chosen
because it is reported to yield accurate geometry and reasonable energies and vibration
frequencies at reasonable computational expense (Durant 1996; Andino etal. 1996).
B3LYP has been validated previously by comparing results with higher level methods
and its application for large molecules and radicals has produced reasonable results
(Sebbar etal. 2008, 2015, 2011). Only transition state structures differ sometimes from
other methods due to the differences in structures calculated by B3LYP.
The reaction rate coefficients for the primary reactions of pyrene with oxygen were
calculated and compared with data from literature (Manion etal. 2015) when available.
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Kinetic parameters are determined as a function of temperature from the calculated
thermochemical parameters using chemical activation analysis. Kinetic parameters are
obtained from canonical transition state theory (TST) calculations.
3 Results andDiscussion
3.1 TPO‑Results
TPO-profiles for a subset of soot samples from Table1 are given in Fig. 5. The figure
contains the experimental results (symbols) and the calculated profiles derived from Eq.4
and the fitting procedure introduced in Sect.2.2.1 (solid lines) using the kinetic param-
eters given in Table2. In Table2
Xi
means the mass fraction of the different soot types
in the samples (NGFG, AGFG). The calculated values and the given digits represent the
95% confidence interval from regression. As can be extracted from Fig.5 and Table2,
oxidation rates of the soot and carbon black samples are spread over a wide range of
Tmax
.
The apparent activation energies cover a range from
≈95
to
≈175 kJ mol−1
except for a
low temperature peak appearing at about 570 K for NGFG and AGFG. Similar values
for the over-all activation energies (
≈150 kJ mol−1
) of the ICE soot samples (C50_1200,
C50_1600, C50_2200, A22) are reported in Zöllner etal. (2017). The A22 soot sample
exhibits a low temperature peak at about 430 K (also present in the TPO of ACFL) which
can be identified as evolution of volatiles by oxidizing the samples after heating them up
under inert atmosphere up to about 800 K. The spark discharge generated soot samples
show three peaks in the TPO profiles at about 570 K, 790 K and 910 K. The estimation of
kinetic parameters works best when treating these samples as consisting of three independ-
ent kinds of soot, denoted as
AGFG(1)
,
AGFG(2)
and
AGFG(3)
and same for NGFG (Hagen
etal. 2020). The A22 sample suggestively also exhibits the peak at 570 K.
Treating soot samples such as AGFG or NGFG as consisting of three independ-
ent soot types raises the hypothesis that different reactive parts of primary particles
in the soot aggregates are oxidized independently and the oxidation rate is a linear
Fig. 5 TPO profiles of soot samples from Table1, experimental results (symbols), calculated profiles (solid
lines) derived from Eq.4 and the fitting procedure introduced in Sect.2.2.1 using the kinetic parameters
given in Table2
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combination of the oxidation rates of the different soot types. This can be verified by
the oxidation of soot sample A22_1 illustrated in Fig.6 which contains the experimen-
tal oxidation rates of the sample (red symbols). The experimental TPO profile contains
two major peaks at about 790 K and 890 K and includes features also exhibited by those
of A22 and the most prominent peak of AGFG. The TPO profile calculated by a lin-
ear combination of these two TPO profiles (0.74*AGFG (green line) + 0.33*A22 (blue
line)) is indicated by the red solid line. The low temperature peak at about 450 K which
represents the evolution of volatiles is excluded in the combination.
From the TPO experiments and the properties of the soot samples given in Table1
no clear basic causes for the differences in reactivity are obvious. Comparatively small
Table 2 Kinetic parameters
according to Eq.4 estimated
using least squares minimization
for soot samples from Table1
Sample
k(4)
0ox
(
K−1
)
Ea
(
kJ mol−1
)n (–)
Xi
(mass%)
Tmax
(K)
AC100
7.2 ⋅106
173.0 1.0 100 1063
P25
4.5 ⋅106
160.0 1.0 100 1010
NGFG(3)
5.5 ⋅106
152.1 1.0 60.4 963
NGFG(2)
3.8 ⋅104
96.4 0.95 20.8 796
NGFG(1)
19.5 39.9 1.25 18.8 570
i-OCT3
4.2 ⋅106
150.0 1.0 100 944
P85
4.25 ⋅106
149.0 0.75 100 937
C50_1200
1.0
⋅
107
158.0 0.6 100 935
ACFL
4.2 ⋅106
143.0 1.0 100 924
C50_1600
1.0 ⋅107
155.0 0.6 100 906
A22
4.2
⋅
106
142.0 1.2 100 895
AGFG(2)
3.8 ⋅104
96.4 1.2 48.0 796
AGFG(3)
5.5 ⋅106
152.1 1.0 15.0 911
AGFG(1)
19.5 39.9 1.2 38.0 570
C50_2200
4.5 ⋅106
125.0 0.6 100 786
Fig. 6 Experimental TPO profile
of the soot sample A22_1 (red
symbols) and calculated profile
(red solid line) using a linear
combination of the TPO profiles
of A22 and AGFG
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soot primary particle sizes are not well correlated with high reactivity in all samples,
compare e.g. P45 with a CMD of 31 nm with A22 with a CMD of 28 nm and a differ-
ence in
Tmax
of about 70 K. Similarly, large specific surface areas which correlate with
small primary particle sizes cause different reactivity, compare e.g. NGFG with a BET
surface of about
425 m2g−1
and AGFG with about
680 m2g−1
and a difference in
Tmax
for
the most prominent TPO peak of about 160 K. Also the content of volatiles present e.g.
in the samples A22, A22_1 and ACFL obviously does not lead to comparable reactivity.
If the oxygen content in the soot samples indicates the presence of functional groups at
the surface of soot particles, also no clear correlation is found between reactivity and
functional groups. Soot samples with alike bulk properties, e.g. P25, i-OCT1, A22 with
a CMD of
≈30 nm
or NGFG, C50_1200, C50_1600 with a BET of about
420 m2g−2
are
unalike with respect to reactivity (widely varying
Tmax
, temperature of maximum oxida-
tion rate during TPO). Vice versa, soot samples with alike reactivity, e.g. P90, i-OCT3,
P85, C50_1200 with
Tmax ≈940 K
are unalike with respect to bulk properties such
as CMD or BET. Therefore, the basic causes for the dependency of reactivity on soot
properties as stressed e.g. in Fang and Lance (2004), Stanmore etal. (2001), Lu etal.
(2012), Lapuerta etal. (2012), Aarna and Suuberg (1997), Neeft etal. (1997) have to be
extended to morphological and nanostructural aspects of the soot primary particles.
3.2 Morphology andNanostructures ofSoot Primary Particles
Primary particle size distributions of some soot samples are given in Fig.7. The size dis-
tributions all resemble logarithmic normal size distributions which are also indicated in
the diagrams (dashed lines). The mean particle sizes differ for the single samples, whereas
the variances and fractal dimensions are similar. Similar size distributions are obtained for
other soot samples listed in Table1. As discussed in the previous section, no clear correla-
tion between mean particle size and reactivity expressed via
Tmax
is observable from the
size distributions.
In contrast to this, the distribution of fringe lengths and separation distances in the pri-
mary particles exhibit a clear correlation to
Tmax
. The lower
Tmax
(the higher the reactiv-
ity), the smaller the fringe lengths and the wider the distribution of the fringe separation
distance, see Figs. 8 and 9. Small fringe lengths are correlated to wide distributions of
the separation distance and vice versa. For the most reactive soot sample (AGFG) fringe
lengths range up to 3 nm and the separation distances range up to 0.6 nm. The fringe length
distribution for the least reactive soot sample (AC100) ranges up to higher than 7 nm with
small separation distances (up to 0.45 nm) and a much narrower distribution of those dis-
tances. For comparison: The extension of a
C6
-unit in graphite is 0.380 nm and the separa-
tion distance of the graphene layers in graphite amounts to 0.335 nm.
The shape of the determined fringe length frequency distributions corresponds well
with findings of other studies (Pfau et al. 2018; Yehliu etal. 2011a, b; Palotas et al.
1996; Rinkenburger et al. 2017). The fringe length distributions appear as approxi-
mately resembling Poisson-distributions or exponential distributions. These distributions
are one-parameter distributions and, therefore, the mean fringe length seems to be suffi-
cient for characterizing the distributions. The mean fringe lengths quantified in this study
[
0.45 nm <Lf<0.7 nm
, compare e.g.
≈0.9 nm
(Pfau etal. 2018)] are slightly smaller than
those calculated in the literature. This is most likely due to the comparatively high fre-
quency of short structures (
<0.5 nm
). Particularly short structures are reconstructed in the
algorithm due to the newly introduced image comparing procedure. Another reason for this
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could be the manual selection of regions of interest (ROI) favoring images with high con-
trast (Yehliu etal. 2011a, b; Palotas etal. 1996; Wan etal. 2018). The image processing
algorithm used here analyzes full frame HRTEM images (
120 nm ×120 nm
) including also
short structures with comparably less contrast.
The slope of the fringe length distribution with a logarithmic scale on the frequency
axis is larger for the highly reactive sample (AGFG) than that of the less reactive sample
(ACFL). This indicates a broader distribution for ACFL, though in the evaluated image
fringes with large lengths have not been detected. Missing of large fringe lengths could be
by chance due to the selection of the region of interest in the image. A broader distribu-
tion of the fringe length corresponds to a narrower distribution of the separation distances,
which has been measured for this image.
The resulting structure-reactivity correlation is depicted in Fig. 10, where the mean
fringe length of the primary particles is plotted versus
Tmax
. The error bars in the plot are
due to the evaluation of up to 5000 structures from primary particles in different HRTEM
images and represent the variation of the evaluated mean lengths from different primary
particles. The correlation is approximated by a linear fit in Fig.10. The correlation depicted
in Fig.10 holds for the different types of soot obtained from different sources, e.g. flame
soot, carbon blacks, engine soot and spark discharge generated soot.
UV–visible absorption spectra affirm qualitatively the structure-reactivity correla-
tion, see Fig.11. The shape of the spectra is similar to that resulting from soot analyzed
Fig. 7 Primary particle size distributions and morphological properties of soot samples from Table1 calcu-
lated with the procedure outlined in Sect.2.2.3; dashed curves correspond to fitted log-normal distributions
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in Apicella etal. (2004). All soot samples exhibit highest absorption at 290 nm, which
decreases towards larger wavelengths. The decay is lowest for the soot sample with low-
est reactivity (AC100,
Tmax =1063 K
). For P25 (
Tmax =1010 K
) after an initially steep
decrease of the normalized absorption, a slightly steeper decrease compared with AC100
at larger wavelengths is observed. For the highly reactive soot samples AGFG, ACFL and
i-OCT3 with
Tmax
around 911 K to 944 K after an initially steep decrease, the normalized
absorbance decays similarly at larger wavelengths, however, somehow steeper than for the
low reactive soot samples. For the latter samples different absorbance of molecular feature
at 450-500 nm, least pronounced for ACFL, and slight shift of contained bands occurs.
The fringe length L is a measure for the spatial extension of graphene-like layers in
the primary particles. Along with an increase of the extension of a graphene-like layer,
the contribution of planar
sp2
-bonded carbon atoms and thereby
𝜋
-electrons rises. Large
contributions of
𝜋
-electrons corresponding to large extension of graphene-like layers cause
a redshift of absorption and only a smooth decline of the absorption functions with increas-
ing wavelength (Apicella et al. 2004). Small contributions of
𝜋
-electrons cause a steep
decrease. Relative to the total number of electrons, large mean fringe lengths (AC100) pro-
vide the largest number density of
𝜋
-electrons and only smooth decline of the absorption
function whereas small mean fringe lengths (AGFG) provide the smallest number density
of
𝜋
-electrons and a steep decrease of the absorption function. This is reflected plotting the
Fig. 8 Fringe length distributions of primary particles from soot samples from Table1 evaluated with the
procedure outlined in Sect.2.2.3
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Fig. 9 Fringe separation distances distributions of primary particles from soot samples from Table1 evalu-
ated with the procedure outlined in Sect.2.2.3
Fig. 10 Correlation of mean
fringe length
Lf
of the soot pri-
mary particles versus
Tmax
for the
soot samples from Table1
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ratio of the absorption function at different wavelengths versus
Tmax
, the temperature of
maximum oxidation rate during TPO, or the fringe lengths, see Fig.12. Again the resulting
correlations are approximately linear. The error bars in the plot are due to the evaluation of
up to four spectra from different portions of the same soot sample.
As exemplified by Fig.6 the oxidation rates of soot samples with multiple
Tmax
are
reproduced by a linear combination of the oxidation rates of different soot types with the
respective
Tmax
(or
Tmax
in the respective range). The interpretation of this behavior is that
the single soot types are oxidized independently. If the extension of the fringe layers is the
essential parameter describing the reactivity, the linear combination should also apply to
Fig. 11 Normalized UV–vis
spectra of soot samples from
Table1
Fig. 12 Ratio R of the absorption function at 290 nm to that at 500 nm versus
Tmax
and mean fringe length,
resp., of soot samples from Table1
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the distributions of the fringe length. This is demonstrated in Fig.13 for the soot sample
A22_1, the TPO profile of which is given in Fig.6. The figure contains a HRTEM image
including some primary particles of that sample (left) and the distribution of the fringe
length evaluated from that image (upper right). The fringe length distribution of an artifi-
cial mixture with 0.74*AGFG + 0.33*A22 composed by a linear combination of the distri-
butions of AGFG and A22 is given in the lower right part of Fig.13. The two distributions
show a reasonable correspondence. Due to the shape of the fringe length distributions no
polydisperse distribution as in the TPO profiles for the linear combination is expected.
This behavior can be verified also for other mixtures as given in Fig.14. The figure con-
tains the experimental TPO profile (red symbols) of a prepared 1:1 mixture of the P25
and i-OCT3 samples and a TPO profile composed from the TPO profiles of these soot
samples (red solid line). The upper right part of the figure displays an exemplary HRTEM
image including some primary particles of that mixture. Finally, the fringe length distribu-
tion evaluated from up to 5000 fringes from mixed primary particles in different HRTEM
images of that mixture (lower right) and that calculated from the linear combination of the
distributions of P25 and i-OCT3 (lower left) is displayed. In difference to Fig.13 the figure
contains the HRTEM and the fringe length distributions of the prepared mixture from the
respective experiments. Again a good agreement between the two distributions is observed.
An intermediate conclusion—as argued by e.g. Bhardwaj etal. (2014), Lapuerta etal.
(2012), Vander Wal and Tomasek (2003)—is that the nanostructure of the soot primary
particles essentially determines their reactivity against oxidation. A simple reactivity-nano-
structure relation approximately linearly correlates the mean length of the fringes in the
primary particles with
Tmax
. Furthermore, oxidation rates of soot samples with differently
reactive components can be linearly combined to the apparent oxidation rate.
3.3 Stepwise Oxidation ofSoot
If the extension of the fringe layers is the essential property that determines reactivity, the
reactivity of soot should increase with deceasing length of the fringes. Decreasing length
of the fringes is expected during oxidation of soot particles and, therefore, the reactivity
should increase during oxidation.
Fig. 13 HRTEM image of primary particles of the sample A22_1 (left), distribution of the fringe length of
that sample (upper right) and that calculated from the linear combination of the distributions of AGFG and
A22 (lower right)
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To test this hypothesis, different soot samples were oxidized as described in Sect.2.2.1
repeatedly with oxygen under isothermal conditions at 1073 K. After each oxidation stage
with mass decreases of 20%, 60%, 80% and 90% soot primary particles were examined
with regard to their reactivity by TPO and HRTEM analysis.
Figure15 shows the TPO profiles of two soot samples from these test series (i-OCT3
and P25). The figure demonstrates the decrease in
Tmax
, i.e. increase in reactivity, with
increasing mass loss due to oxidation, which is more pronounced for the more reactive
carbon blacks (i-OCT3: 944 K to 860 K, P25: 1010 K to 964 K, AC100: 1063 K to 1052
K ) than for the less reactive ones. The temperature at maximum oxidation rate,
Tmax
, is
dependent on the kinetics of oxidation and connected to the apparent activation energy
of the oxidation, compare Sect.2.2.1. A change of
Tmax
by 10 K results in a change
of the activation energy of about
1.5 kJ mol−1
. The decrease of
Tmax
with proceeding
burn-out is steeper at burn-out ratios larger than 60% compared with lower burn-out
ratios. The analysis of the nanostructure of the primary particles from these two soot
samples confirms this development, as given in Figs.16 and17. The decrease in
Tmax
from 944 K of the untreated sample i-OCT3 to approx. 860 K during oxidation up to a
mass decrease of 90% is associated with a significant decrease in the expansion of the
graphene-like layers in the primary particles (Fig.16, left part). It is interesting that the
size distribution of the primary particles hardly changes during the stepwise oxidation
(Fig.16, right part), suggesting an internal burning mode rather than a shrinking core
mode. The same trend can be seen for the sample P25 in Fig.17 and ACFL and AC100
Fig. 14 TPO profile of a prepared mixture with 0.5*P25 + 0.5*i-OCT3 (upper left), HRTEM image of pri-
mary particles of that mixture (upper right), distribution of the fringe length from the HRTEM image of
that mixture (lower right) and that calculated from the linear combination of the distributions of P25 and
i-OCT3 (lower left)
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(not depicted here). At the prevailing large time scales for the oxidation of soot diffusion
rates of oxygen into the structures of the primary particles well competes with chemical
reaction rates. Similar behavior has also been observed in the oxidation of soot cata-
lyzed with
Fe2O3
under similar conditions (Reichert etal. 2010) and in flames (Schäfer
etal. 1995).
Fig. 15 TPO profiles of i-OCT3 (left) and P25 (right) at stepwise oxidation
Fig. 16 Fringe length distribution of primary particles from i-OCT3 and primary particle size distribution
at stepwise oxidation
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Similar interesting features can be extracted from Raman scattering results given in
Fig.18. The figure displays stacked Raman spectra of primary particles from i-OCT3 at
stepwise oxidation (left) and the evaluation of
ID1∕
I
G
according to the procedure described
in Sect.2.2.2 (right).1 The graphite band (G band) at about
1580 cm−1
is attributed to an
ideal graphitic lattice and indicates highly ordered structures. The D1-peak at about
1355 cm−1
becomes active only in presence of disordered graphene-like structures. The
estimation of the relative intensities of D1- and G-bands using the 5 band fitting proce-
dure, therefore, provides qualitative information about the abundance of graphitic ordered
structures and disordered regions in the primary particles. High values of
ID1
∕I
G
indicate
predominance of low ordered graphene-like structures with small extension whereas low
values suggest well ordered, graphitic graphene-like structures of large extension.
The spectra of i-OCT3 at different burn-out ratios in Fig.18 give a qualitative picture
of the evolution of the intensity ratio, and the quantitative evaluation is displayed in the
right part of Fig.18. The intensity ratio
ID1∕IG
is initially high for virgin soot i-OCT3 and
decreases to about less than half and decreases further slightly with progressing oxidation
until a burn-out ratio of 80%. At higher burn-out ratio it increases again, indicating that the
Fig. 17 Fringe length distribution of primary particles from P25 and primary particle size distribution at
stepwise oxidation
1 The 5 band fitting procedure for i-OCT3 at a burn-out ratio of 0% indicating the D1- and G-peaks is dem-
onstrated in Fig.2, to keep the figure clear, the fitting procedure is not indicated in Fig.18.
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318
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relative abundance of ordered regions within the primary particles increases on account of
the disordered amorphous regions. At high burn-out ratios also the highly ordered struc-
tures decompose. This behavior suggests that the very reactive, disordered structures are
first oxidized, while the less reactive structures, whose reactivity nevertheless increases
during the oxidation, see Fig.15, are later oxidized and degraded finally to smaller struc-
tures. Similar trends can be found for e.g. AGFG and NGFG, where the different reactivity
against oxidation can be traced back to the relative abundance of ordered and disordered
graphene layer structures and is reflected by the Raman spectra of these soot types (Hagen
etal. 2020).
3.4 Mechanistic Interpretation
As discussed in Sect.2.2.4, in this work as well as in similar work from literature, see e.g.
Sendt and Haynes (2011), Edwards etal. (2013, (2014), Frenklach and Mebel (2020), the
mechanistic interpretation of the oxidation of soot is based on model molecules. These
are supposed to depict the graphene-like structures in the primary soot particles omitting
interactions between the single layers. The employed model molecules—in this work pyr-
ene—are approximations with regard to the energy levels of the individual carbon atoms in
the graphene-like structures. However, they facilitate the identification of essential reaction
pathways for reactions of the graphene-like layers with
O2
and for estimating and compar-
ing reaction rate coefficients. These limitations restrict the focus of the following discus-
sion to clearly identifiable trends.
The experimental results discussed in the previous sections reveal that the property
determining reactivity is predominantly the fringe length of graphene layers. The larger
the fringe length the lower the reactivity. Soot types with different reactivity are charac-
terized by different fringe sizes. Different soot types combined in a soot primary particle
contain regions of different fringe length which are oxidized independently leading to mul-
tiple peaks in the TPO traces with different
Tmax
, see Sect. 3.2. The independent oxida-
tion of graphene layers of different reactivity suggests, that after primary activation of a
graphene-like structure the further degradation proceeds at higher reaction rate than the
activation of additional layers. Another experimental result is the increasing reactivity of
Fig. 18 Raman spectra of primary particles from i-OCT3 (left) at stepwise oxidation and evaluation of
ID1∕IG
according to the procedure described in Sect.2.2.2 (right)
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the graphene layers with proceeding oxidation, see Sect.3.3. The mechanistic interpreta-
tion of the experiments given in the following is intended to reflect these results.
The primary attack of
O2
on the graphene-like layers - represented by the pyrene model
molecule—can take place on edge C-H sites in a sequence of three edge C-H-sites as
depicted in the energy diagram Fig.19.2 The attack of
O2
at internal carbon atoms or at
edge carbon atoms or at C-H-sites in sequences with only two edge C-H-sites, which may
result in different energy barriers, is not detailed here, because it is followed by a complex
reaction system contributing little to the degradation of the polycyclic structure. The
energy diagram illustrates the attack of
O2
on pyrene A4 via abstraction of a hydrogen from
a C-H-site forming a pyrenyl radical, A4J + OOH. The H-abstraction occurs via transition
state TS1 representing an energy barrier of
307.1 kJ mol−1
relative to pyrene and
O2
. The
respective rate coefficient fitted to the format
k
0⋅exp
[
−
Ea
R⋅T
]
is given in Table3.
The experimental reaction rate coefficients according to Eq.4 are in the order of magni-
tude of
k
(4)
ox ≈5⋅106⋅exp
[
−150
R
⋅
T]
K−
1
, see Table2, with
Ea
in
kJ mol−1
. Considering the
heating rate of
5 K min−1
, this results in rate coefficients at 900 K (which is the temperature
range for maximum conversion rates) of
k(3)
ox(900K)
≈8⋅10−
4
s−1
. The corresponding time
scale then amounts to about 20 min. The reaction rate coefficient of the H-abstraction,
reaction (1), amounts to
1.1
⋅1012 ⋅exp
[
−
325.3
R
⋅
T]
cm3mol−1s−1
. Assuming constant
O2
con-
centration of 5 %vol this results in
k(1)
(900K)
≈1⋅10−13 s−
1
. Compared with the measured rate
coefficients for the oxidation of soot the rate coefficient for the activation of the graphene
Fig. 19 Energy diagram for the primary attack of
O2
at pyrene and follow-up reactions with
O2
via reaction
path a (blue), reaction path b (green) and reaction path c (red); structures of the involved species are also
indicated in the diagram
2 To facilitate reading of the energy diagrams, all structures of the molecules involved in the oxidation
reactions are also displayed. For simplicity abbreviations are used for the structures. Here Ax means x six-
membered rings, Ax
⋅
or AxJ describes the corresponding radical,
⋅
or J is a radical site, D stands for a
double-bond and Y means a cyclic structure. TS is a transition state structure.
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Table 3 Reaction rate parameters for the reactions given in Figs.19, 20, 21, 22, 23
Reaction No.
k0
(in
cm3
, mol, s)
Ea
[
kJ mol−1
]
k(900 K)
(in
cm3
, mol,
s)
Activation by
O2

A4 +O2
→
A4J +OOH
(1)
1.1
⋅
1012
325.3
1.5
⋅
10−7
Activation by radicals

A4 +OOH
→
A4J +H2O2
(2)
1.1
⋅
109
65.0
1.9 ⋅105

A4 +OH
→
A4J +H2O
(3)
1.9 ⋅1012
−4.96
3.7 ⋅1012

A4 +O→A4J +OH
(4)
3.2 ⋅1011
49.8
4.1 ⋅108
Follow-up reactions (path a, b, c)

A4J +O2
→
A4OOJ
(5)
8.4 ⋅109
138.8
7.3 ⋅101

A4OOJ →A4JDO +O
(6)
6.4 ⋅1013
91.2
3.2 ⋅108

A4OOJ →A4OJDO
(7)
6.4 ⋅1013
89.9
3.8 ⋅108

A4OOJ →A4JYC2O2
(8)
6.9 ⋅1012
206.2
7.4 ⋅100
Follow-up reactions (path a1)

A4JDO +O2
→
A4DOO2J
(9)
2.2 ⋅105
70.6
1.75 ⋅101

A4DOO2J →A4JDOYC2O2
(10)
1.3 ⋅1012
72.5
8.1 ⋅107

A4JDOYC2O2 →A3JDODODO
(11)
1.5 ⋅1013
−3.58
2.4 ⋅1013

A3JDODODO →A3JDODO +CO
(12)
1.9 ⋅1013
237.6
3.2 ⋅10−1

A3JDODO →A3J +2CO
(13)
3.6
⋅
1014
221.1
5.3
⋅
101
Follow-up reactions (path a2)

A4JDO +O→A4OJDO
(14)
2.0 ⋅1011
−11.9
1.0 ⋅1012

A4OJDO →A4JDOYC2O
(15)
7.5 ⋅1011
−12.8
4.2 ⋅1012

A4JDOYC2O →A3YC5OCJDO
(16)
2.9 ⋅1013
113.5
7.7 ⋅106

A3YC5OCJDO →A3C2JCOCO
(17)
5.2 ⋅1013
175.4
3.4 ⋅103

A3C2JCOCO
→
A3C2JCO +CO
(18)
9.4 ⋅1014
306.3
1.5 ⋅10−3

A3C2JCO →A3JYC5DO1
(19)
4.0 ⋅1013
23.3
1.8 ⋅1012

A3JYC5DO1 →A3JYC5DO3
(20)
2.1
⋅
1013
257.0
2.5
⋅
10−2

A3JYC5DO3 →A3CJ +CO
(21)
2.4 ⋅1014
212.6
1.0 ⋅102
Follow-up reactions (path bc1)

A4OJDO →A3YC6JODO
(22)
5.9 ⋅1012
29.4
1.1 ⋅1011

A3YC6JODO
→
A3CCDOCJDO
(23)
1.1 ⋅1013
143.9
4.9 ⋅104

A4JYC2O2 →A3CCDOCJDO
(24)
6.9 ⋅1013
−251.8
2.8 ⋅1028

A3CCDOCJDO →A3JCCDO +CO
(25)
1.9 ⋅1016
83.7
2.6 ⋅1011

A3JCCDO
→
A3CCJDO
(26)
4.3 ⋅1012
−11.5
2.0 ⋅1013

A3CCJDO →A3CJ +CO
(27)
2.0
⋅
1012
215.9
6.0
⋅
10−1
Follow-up reactions (path bc11, bc12)

A3CJ +O→A3JCDO
(28)
1.5
⋅
1011
−117.9
1.0
⋅
1018

A3JCDO →A3CJDO
(29)
4.1 ⋅1013
266.2
1.4 ⋅10−2

A3CJDO
→
A3J +CO
(30)
2.3 ⋅1012
9.3
6.6 ⋅1011

A3CJ +O2
→
A3COOJ
(31)
4.6 ⋅104
−26.8
1.7
⋅
106

A3COOJ →A3JYCO2
(32)
2.7 ⋅1013
72.9
1.5 ⋅109

A3JYCO2
→
A3YCJO2
(33)
6.4 ⋅1012
310.6
6.0 ⋅10
−
6

A3YCJO2
→
A3J +CO2
(34)
1.8
⋅
1012
−147.4
6.6
⋅
1020
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321
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surrogate molecule via the attack of
O2
is several orders of magnitude lower and seems too
small to make this step appear as the predominant channel for the degradation of the model
molecule. An alternative activation reaction would be the H-abstraction by radicals such as
O, OH or OOH, see Table3, reaction (2)–(4). The rate coefficient for e.g. the H-abstraction
by O at 900 K is
k(4)
(900K)
≈4⋅108s−
1
. A concentration of O about
2.5 ⋅10−11 mol cm−3
results in a time scale for this reaction of about 100 seconds, which is comparable to the
experimental time scales.
Figure19 contains also the energy diagram for the attack of
O2
on the pyrenyl radical,
A4J +
O2
→
A4OOJ, reaction (5). which constitutes another possibility of activation. The
rate coefficient for this reaction at 900 K is
k(5)
(900K)
≈7⋅101cm3mol−1s−
1
and assuming
constant
O2
concentration of 5 %vol this results in
k(5)
(900K)
≈5⋅10−5s−
1
, which is is several
orders of magnitude larger than
k(1)
(900K)
. Depending on the history of soot during formation
or finishing treatment, soot contains radical sites in variable density in the graphene-like
structures (Yamanaka etal. 2005). Compared with the model molecule A4, where just one
radical site A4J is viewed, graphene-like structures in soot primary particles contain mul-
tiple radical sites, so that the reaction rate of oxygen with radical sites in graphene-like
structures in soot primary particles may be a multiple of the rate of reaction (5) resulting in
reasonably smaller time scales. When lumping together the reaction rates of the three acti-
vation channels, reaction (1), reactions (2)–(4) and reaction (5), the resulting reaction rate
comes close to the experimental ones.
The consecutive reaction of A4J with
O2
leads to A4OOJ providing three parallel path-
ways to A4JDO + O (reaction path a), A4JYC2O2 (reaction bath b) and A4OJDO (reaction
path c), see Fig. 19. This opens pathways to further degradation via
A4JDO +O2
(a1),
A4JDO + O (a2), A4OJDO and A4JYC2O2 (bc1). The energy diagrams for these reaction
pathways are given in Figs.20, 21, and 22. The respective reaction rate coefficients are
contained in Table3.
As can be seen in Fig. 20, the consecutive reactions in reaction path a1, reaction
(9)–(13), end with the radical species A3J, which is a polycyclic radical with one ring less
compared with A4J, and 2 molecules of CO. The bottleneck reaction of this sequence is
reaction (9), see rate coefficients listed in Table3. Assuming again constant
O2
concen-
tration of 5 %vol the rate coefficient of this reaction is
k(9)
(900K)
≈5⋅10−5s−
1
, which is by
orders of magnitude larger than that of reaction (1). Assuming again multiple sites acces-
sible for oxidation, the reaction sequence contributes considerably to the degradation of
graphene-like structures.
The alternative pathways a2, reaction (14)–(21), see Fig.21, and bc1 reaction (22)–(27),
see Fig.22, form the species A3CJ and CO. The corresponding rate coefficients of these
reactions listed in Table3 are also large compared with the rate coefficient of the pri-
mary activation reaction and illustrate a considerable contribution to the degradation of
graphene-like structures. The species A3CJ is further converted by the attack of O and
O2
Table 3 (continued)
Reaction No.
k0
(in
cm3
, mol, s)
Ea
[
kJ mol−1
]
k(900 K)
(in
cm3
, mol,
s)

A3JYCO2
→
A3JDCO2
(35)
2.3 ⋅1012
240.9
2.3 ⋅10−2

A3JDCO2
→
A3J*B +CO2
(36)
4.0 ⋅1014
88.3
2.9 ⋅109

A3J*B →A3J
(37)
1.7 ⋅1013
192.8
1.1 ⋅102
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to A3J releasing CO and
CO2
via reaction path bc11 and bc12. The corresponding energy
diagrams are given in Fig.23 and the rate coefficients are also contained in Table3. The
follow-up reactions via reaction path a,b,c and a1, a2 in combination with bc1 and bc11,
bc12 form a replication reaction scheme leading to the degradation of one six-membered
Fig. 20 Energy diagram for the follow-up reactions via reaction path a1; structures of the involved species
are also indicated in the diagram
Fig. 21 Energy diagram for the follow-up reactions via reaction path a2; structures of the involved species
are also indicated in the diagram
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Fig. 22 Energy diagram for the follow-up reactions via reaction path bc1; structures of the involved species
are also indicated in the diagram
Fig. 23 Energy diagram for the follow-up reactions via reaction path bc11 and bc12; structures of the
involved species are also indicated in the diagram
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ring after the other (AnJ
→
A(n − 1)J) releasing CO,
CO2
and also via reaction (6) oxy-
gen atoms. In addition, the activation reaction (1) delivers OOH, being together with O a
potential candidate for activating aromatic ring systems via reaction (2) and (4) with a low
energy barrier.
The discussion of the reaction paths presented here does not claim completeness. How-
ever, the developed activation/replication mechanism explains some experimental phenom-
ena such as the increase in reactivity with increasing burn-out, the independent oxidation
of differently reactive compartments in the soot or the increase in ordered structures at the
expense of disordered/disturbed reactive structures, see Sect.3.3. The primary attack of
O2
at graphene-like layers via reaction (1) at temperatures in the range of 900 K contributes
only little because of the high activation energy causing extremely low reaction rates. In
contrast to this an alternative activation reaction via radicals such as O, OH or OOH pro-
vides sufficiently high reaction rates at radical concentrations as low as
1⋅10−11 mol cm−3
.
Reactions (1) and (6) in the sequence of follow up reactions delivers OOH and O, so that
the oxidation of graphene-like structures includes formation of activating species. Addi-
tionally, O, OH and OOH may be produced via reactions in the gas phase. Another pos-
sibility of activation constitutes the reaction of
O2
with radical C-atoms requiring much
lower activation energies, see reaction (5) in Table3. The concentration of these “active”
sites depends on the kind of soot and correlates with the method of synthesis. Flame gener-
ated soot and engine soot contain radical C-atoms in different concentration (Yamanaka
etal. 2005) than e.g. thermally aged soot (P25, AC100) and exhibit, therefore, different
reactivity. Graphene-like structures in soot primary particles contain more edge active sites
than the model molecule A4J, which can be attacked in parallel multiplying the degrada-
tion rate of these structures.
In summary, the mechanism given in Table3 describes an activation/replicating mecha-
nism AnJ
→
A(n − 1)J where the rates of the follow-up reactions are sufficiently high com-
pared with the initial activation of the graphene-like structure by
O2
. The self-activation
would explain the independent oxidation of different containments within the primary par-
ticles. The oxidation rate depends on the initial concentration of radical C-atoms in the gra-
phene-like structures in the soot and on the concentration of the radical pool of O, OH and
OOH. Considering the different activation steps via the attack of
O2
and radicals at A4 and
the attack of
O2
at AJ and their different reaction rates as discussed above, the experimental
time scales for the oxidation can be reproduced with that replication/activation mechanism.
For deriving the reaction rate expression in Eq.4 the density of “active” sites constituted
by C-H-sites or radical sites was assumed to be proportional to the soot mass. For gra-
phene-like structures, the ratio of edge C-H-sites to total carbon atoms in the graphene-like
layers increases with decreasing extension of the layers. The density af active sites, there-
fore, increases with decreasing size of the layers enhancing the reaction rates for reactions
of type (1)–(5). Then the reactivity increases with decreasing extension of the graphene-
like layers, which is the case for progressing oxidation of the primary soot particles. Also,
the ratio of C-H-sites to the total carbon atoms depends on the hydrogen content of the
soot and generally a higher hydrogen content leads to higher reactivity (see Table1). The
same arguments hold for the degradation of graphene-like layers via the reaction of
O2
with
disordered/disturbed structures in the primary particles such as large graphene-like struc-
tures partially equipped with functional groups, aliphatic side chains and aliphatic bridges.
The reactivity will be higher, the higher the relative concentration of distorted/reactive
structures within the graphene-like layers. In addition, the stability of a graphene-like layer
with or without radical/active site increases with its extension. An extended ring system
facilitates the stabilization of the intermediate stage by conjugation (hyper-conjugation).
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Therefore, a distribution of activation energies for reactions (1)–(5) results depending on
the stability of the activated graphene-like layers and thus on the layer extension. This sup-
ports again the findings of Sect.3.3, that the reactivity increases with proceeding oxida-
tion, viz. decreasing extension of the graphene-like layers.
While the investigation presented in this work identifies the predominant parameters
determining the reactivity of “pure” soot the oxidation of soot in GPFs may be additionally
affected by metals or metal oxides present in the emitted soot. This aspect opens the field
of catalytic reactions of metal(oxides), which cannot be covered her. However, some prin-
ciples developed in this work may be transferred also to catalytic oxidation, since recent
studies show that initial graphene-like structures are shortened by adding catalytic addi-
tives (Rinkenburger etal. 2017).
4 Conclusions
The reactivity of soot from flames, soot from IC-engines, carbon blacks under oxidation
conditions representative for GPF regeneration has been investigated. Soot reactivity is
determined in dynamic TPO experiments and the soot primary particle nanostructure is
investigated by HRTEM. Further, UV–visible spectroscopy and Raman scattering and
other diagnostic techniques are used to study the properties connected to the reactivity of
soot and to corroborate the experimental findings. It is found that nanostructural character-
istics predominantly affect reactivity.
From the TPO experiments and the bulk properties of the soot samples no clear basic
causes for the differences in reactivity of the different kinds of soot are obvious. Small soot
primary particle sizes are not well correlated with high reactivity and also large specific
surface area which correlates with small primary particle sizes causes different reactivity.
Also the content of volatiles present in the different samples, the C/H-ratio and the oxygen
content do not lead to comparable reactivity. Soot samples with alike bulk properties, e.g.
P25, i-OCT1, A22 with a CMD of
≈30 nm
or NGFG, C50_1200, C50_1600 with a BET
of about
420 m2
⋅
g−2
are unalike with respect to reactivity (widely varying
Tmax
, tempera-
ture of maximum oxidation rate during TPO). Vice versa, soot samples with alike reactiv-
ity, e.g. P90, i-OCT3, P85, C50_1200 with
Tmax ≈940 K
are unalike with respect to bulk
properties such as CMD or BET.
In contrast to this, the nanostructural properties clearly affect the reactivity of the inves-
tigated soot samples. The distribution of fringe lengths and separation distances in the
primary particles exhibit a clear correlation to reactivity. The smaller the fringe lengths
and the wider the distribution of the fringe separation distance, the higher the reactivity.
Small fringe lengths are connected to wide distributions of the separation distance and vice
versa. The nanostructure of the soot primary particles essentially determines their reactiv-
ity against oxidation and a simple reactivity-nanostructure relation linearly correlates the
mean length of the fringes in the primary particles with
Tmax
, the temperature of maximum
oxidation rate during TPO. UV–visible absorption spectra affirm qualitatively the struc-
ture-reactivity correlation.
The oxidation rates of soot samples with multiple
Tmax
can be reproduced by a linear
combination of the oxidation rates of different soot samples with
Tmax
in the respective
range. The conclusion from this behavior is that different compartments in the soot pri-
mary particles are oxidized independently governed by their reactivity. The extension
of the fringe layers is the essential parameter describing the reactivity. Therefore, the
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nanostructure of soot primary particles containing different compartments with different
reactivity can be composed also by a linear combination.
The reactivity of soot particles increases during oxidation. As the soot mass decreases
due to oxidation the extension of the fringes decreases leading to an increase of reactiv-
ity according to the structure-reactivity correlation. This effect is more pronounced for the
more reactive carbon blacks than for the less reactive ones. The size distribution of the
primary particles hardly changes during stepwise oxidation suggesting an internal burning
mode rather than a shrinking core mode under the employed conditions.
The mechanistic interpretation on the basis of quantum-chemistry estimations reveals
a replication/activation mechanism which explains the experimental phenomena and the
interpretation of reactivity on the basis of the nanostructural analyses.
Acknowledgements The authors are very grateful to the Deutsche Forschungsgemeinschaft for financial
support within the project Partikelreaktivität (TR470/7-1, KO4830/2-1, SU249/6-1). Also, the authors
would like to thank Prof. Dagmar Gerthsen and Dr. Heike Störmer from the Laboratory for Electron Micros-
copy (Karlsruhe Institute of Technology (KIT)) for everlasting help in preparing and interpreting electron
microscopy images. Dr. Amin Velji, KIT deserves thanks for his constant support and willingness to dis-
cuss. The authors are obliged to Prof. Sven Kureti and Marlis Zimmermann from the Chair of Reaction
Engineering at Technical University of Freiberg for preparing the Raman spectra of soot samples. Finally,
the authors thank Dr. Puneet Verma from Queensland University of Technology for his help in the initial
stages of development of the microstructure analysis code.
Funding Open Access funding provided by Project DEAL. This study was funded by Deutsche Forschun-
gsgemeinschaft (Grant Numbers TR470/7-1, KO4830/2-1, SU249/6-1).
Compliance with Ethical Standards
Conflict of interest The authors declare that they have no conflict of interest.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License,
which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com-
mons licence, and indicate if changes were made. The images or other third party material in this article
are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the
material. If material is not included in the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly
from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.
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Aliations
FabianHagen1· FabianHardock1· SergejKoch2· NadiaSebbar1·
HenningBockhorn1· AlexandraLoukou1· HeikoKubach2· RainerSuntz3·
DimosthenisTrimis1· ThomasKoch2
* Henning Bockhorn
henning.bockhorn@kit.edu
1 Division ofCombustion Technology, Engler-Bunte-Institute, Karlsruhe Institute ofTechnology,
Engler-Bunte-Ring 1, 76131Karlsruhe, Germany
2 Institut für Kolbenmaschinen, Karlsruhe Institute ofTechnology, Rintheimer Querallee 2,
76131Karlsruhe, Germany
3 Institute ofChemical Technology andPolymer Chemistry, Karlruhe Institute ofTechnology,
Engesserstr. 18/20, 76131Karlsruhe, Germany
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2.
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4.
5.
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