One Earth, Volume
7
Supplemental information
Microphysical complexity of black carbon particles
restricts their warming potential
Xiao-Feng Huang, Yan Peng, Jing Wei, Jianfei Peng, Xiao-Yu Lin, Meng-Xue Tang, Yong
Cheng, Zhengyu Men, Tiange Fang, Jinsheng Zhang, Ling-Yan He, Li-Ming Cao, Chao
Liu, Chenchong Zhang, Hongjun Mao, John H. Seinfeld, and Yuan Wang
Supplemental
Notes
1
Note
S1. Calculation of photochemical parameters.
2
The OH radical exposure is defined as the product of the OH radical concentration ([OH]) and the
3
photochemical age (
Δ
t). [OH]
Δ
t was calculated from the
concentrations of ambient isoprene and its
4
photochemical products, methyl vinyl ketone (MVK) and methacrolein (MACR).
1
Isoprene is one of the
5
main natural VOCs in the atmosphere, and its oxidation in the atmosphere is mainly produced by
6
reactions with OH radicals during the daytime. The reaction process of isoprene oxidized by OH radicals
7
in the atmosphere are:
8
Isoprene + OH → 0.63 HCHO + 0.32 MVK+0.23 MACR k
1
= 1.0 × 10
-
10
cm
-
3
s
-
1
9
MVK + OH → Products k
2
= 1.9 ×
10
-
11
cm
-
3
s
-
1
10
MACR + OH → Products k
3
= 3.3 × 10
-
11
cm
-
3
s
-
1
11
By combining the above three reactions, the chemical process of MVK+MACR/Isoprene with
12
reaction time can be expressed as:
13
!"#
$
!%&'
()*+,-.-
=
/
.
12
3
!
3
"
4
3
!
(
1
−
푒푥푝
(
푘
5
−
푘
2
)
[
푂퐻
]
∆
푡
)
+
/
.
12
3
!
3
#
4
3
!
(
1
−
푒푥푝
(
푘
5
−
푘
1
)
[
푂퐻
]
∆
푡
)
(
1
)
14
Therefore, the OH radical exposure can be calculated by Equation (1). Note the concentration of
15
isoprene, MVK and MACR was obtained from a 6000X2 PTR
-
ToF
-
MS instrument (Ionicon Analytik
16
GmbH Innsbruck, Austria) in both field measurements. The operation principle of this PTR
-
ToF
-
MS has
17
been described in the study of Zhu et al.
2
.
18
Element ratios, such as hydrogen to carbon (H:C) and oxygen to carbon (O:C), are calculated
19
based on high resolution mass spectra of organic coating measured by SP
-
AMS with the “Improved
-
20
Ambient” method. The average carbon oxidation state calculated by the equation of oxidation
21
state=2*O:C
-
H:C are used as a proxy for BC
-
containing particle photochemical age.
3,4
22
23
Note
S2. Correction of
DMA
-
SP2 data
24
Correction of collection efficiency.
The collection efficiency of particles included the pipeline
25
transmission efficiency, DMA charging efficiency, and DMA effective sampling time (
see
Fig
ure
S13).
26
Due to
Brownian motion, particles with smaller sizes can diffuse from high concentration to low
27
concentration and deposit on the tube wall. In the pipeline that passes through laminar gas, transport
28
efficiency
η
of the particle is a function of
휁
=
678
9
, where
D
is the dissipation coefficient of particles,
L
is
29
the length of the pipeline, and
Q
is the volumetric flow rate of the gas. Gormley and Kennedy gave the
30
formula for transport efficiency in laminar fugitive deposition
5
:
31
휂
=
1
−
2
.
56
휁
"
#
+
1
.
2
휁
+
0
.
177
휁
$
#
휁
<
0
.
009
(
2
)
32
휂
=
0
.
819
exp
(
−
3
.
657
휁
)
+
0
.
097
exp
(
−
22
.
3
휁
)
+
0
.
032
exp
(
−
57
휁
)
휁
>
0
.
009
(
3
)
33
According to Equations 2 and 3, the pipeline dissipation loss of each particle mobility diameter
34
(
D
p_mob
) can be calculated (Fig
ure
S13A).
35
Fuchs
et al
.
6
used convective
-
diffusion and kinetic models to calculate the ion migration rate and
36
establish a charge distribution model. Wiedensohler
et al.
7
developed and revised the Fuchs charge
37
distribution model. The calculation formula for the proportion of particles with charge
n
can be calculated
38
by:
39
:
%
:
&'&()
=
10
;
<
=
*
,
%
(
?@A
!,
B
%-
)
*
.
*
/
,
D
(
4
)
40
where
d
nm
is the particle diameter. The coefficient
a
i,n
is constant, where
a
0,1
to
a
5,1
of single positively
41
charged particles are [
-
2.3484, 0.6044, 0.4800, 0.0013,
-
0.1553, 0.0320]. According to Equation 4 and
42
the above parameters, the proportion of each particle size with single positive charge in this study can
43
be calculated (Fig
ure
S13B).
44
The ability of DMA to separate particles of different
D
p_mob
is expressed by the transfer function.
45
The transfer function describes the probability of particles that enters the DMA via the aerosol inlet will
46
leave via the sampling flow, given that its electric mobility (
Z
p
).
8
For an ideal cylindrical DMA, its transfer
47
function exhibits a triangular distribution with height a=1 and relative FWHM
β
.
The particles with
48
mobility of
Z
p
-
β
Z
p
*
-
Z
p
+
β
Z
p
* can pass through the channel when the characteristic electric mobility is
49
Z
p
*. The
Z
p
* and
β
can be calculated by
9
:
50
푍
+
∗
=
9
0
1
×
?G
H
2
"
2
!
I
2
68"
(
5
)
51
훽
=
9
(
9
0
1
(
6
)
52
where
Q
a
and
Q
sh
are the aerosol sample gas flow and sheath gas flow, respectively. The r
1
, r
2
, and
L
53
are the inner electrode radius, outer electrode radius, and length of the cylindrical DMA, respectively.
54
The
V
is the electrode voltage.
55
In this study, the flow rates of the DMA sample gas and sheath gas were set to 0.42 L min
-
1
and 4.2
56
L min
-
1
, respectively. Based on Equations 4 and 5, it can be calculated that the relative FWHM of the
57
transfer function of DMA is 0.1. When the characteristic electric mobility is
Z
p
*, the particles with the
58
electric mobility of 0.9
Z
p
*
-
1.1
Z
p
* have a probability to pass through the channel. Therefore, the passage
59
efficiency
α
p
of particles with electric mobility
Z
p
can be calculated by:
60
훼
+
=
55
J
3
∗
4
5/
J
3
J
3
∗
푍
+
>
푍
+
∗
(
7
)
61
훼
+
=
5/
J
3
4
K
J
3
∗
J
3
∗
푍
+
<
푍
+
∗
(
8
)
62
The effective sampling time of each
D
p_mob
during the whole sampling period was equal to the
63
average transfer efficiency multiplied by the sampling period time (Fig
ure
S13C).
64
Correction of delay time.
After the particles were selected by DMA, a time difference existed between
65
the counting for the
condensation particle counter (
CPC, TSI Inc.) and SP2. The DMA
-
CPC and DMA
-
66
SP2 systems were used to measure the delay in response time by adjusting the concentration of
67
fullerene soot. The delay time in this study was 10 s.
68
Correction of multi
-
charged particles.
DMA selected the
D
p_mob
through different electric mobility,
69
whereas large particles with multiple charges may have the same electric mobility as small single
-
70
charged particles. A demarcating line was constructed to identify and correct multi
-
charged particles.
71
The number and mass concentration distribution of the BC core in each
D
p_mob
bin and each
D
c
bin
72
shows a significant multi
-
mode distribution (Fig
ure
S14A), and it can be observed that there are obvious
73
inflection points for the
D
c
distribution under the fixed
D
p_mob
value
(Fig. S14B). Then, fitting the inflection
74
points under every
D
p_mob
bin can determine demarcating lines (Fig
ure
S14A), and based on
75
demarcating lines, we divided the particles into three modes. For Mode 1,
D
p_mob
<
D
c
, which was divided
76
into multi
-
charged particles. For Mode 2,
D
p_mob
is slightly larger than
D
c
, which was considered to be
77
thinly coated. For Mode 3,
D
p_mob
is much larger than
D
c
, which was considered to be more thickly
78
coated.
79
Extrapolation of the size range.
Due to the limitation of the DMA selection range, we extrapolated the
80
size range (
D
p_mob
larger than 580 nm) to PM
1
in this study. First, we performed a bimodal lognormal fit
81
to the concentration distribution under fixed
D
p_mob
. According to the evolution of the fitting peaks for
82
Mode2 and Mode3 under different
D
p_mob
bins, we can further extrapolate the concentration distribution
83
of the two modes (Fig
ure
S15A). The correlation coefficient R
2
=0.95 by comparing the observed data
84
and the fitting data, and the size distribution after extrapolation can reproduce the data measured by
85
SP2 only (Fig
ure
S15B). Furthermore, the BC mass concentration time series after correction was more
86
consistent with the values measured by the SP2 and the SP
-
AMS (
see
Fig
ure
S16, A and B).
87
According to the distribution after extrapolation, we can calculate the
M
R
,
ρ
eff
and the mass fraction
88
of non
-
spherical particles (
F
non
-
spherical
)
of each
D
c
in the
D
p_mob
range of 70 nm
-
580 nm and 70 nm
-
89
820 nm, respectively. Then the
D
c
-
resolved ratio of 70
-
820 nm values to 70
-
580 nm values can be
90
calculated as the correction coefficient (Equation 9).
91
푐표푟푟
=
L
5,
6
7",
%-
L
5,
6
.7,
%-
(
9
)
92
where the
x
is the value of
M
R
,
ρ
eff
, and
F
non
-
spherical
.
93
Finally, we multiplied the original size
-
resolved mixing state by the correction coefficient.
94
95
96
Note
S3. Calculation of density and shape of BC
-
containing particles.
97
1) Determining
ρ
eff
for fully fresh and aged particles under each
D
c
bin: We compared the
D
c
vs.
98
D
p_mob
distribution of demarcating lines with other studies. The demarcating line between Mode1 and
99
Mode2 (Line
Mode1
-
Mode2
) is consistent with fresh particles measured in other studies
10
-
19
within ± 20%
100
deviation (Fig
ure
S14C). Thus, we assumed that the particles are not coated (
M
R,0
=0, and the particle
101
mass equivalent diameter is equal to the
BC core mass equivalent diameter) at the demarcating line
102
between Mode1 and Mode2 (Fig
ure
S14C). The effective density of Line
Mode1
-
Mode2
(
ρ
eff,0
) can be
103
obtained from Equation 10.
104
퐷
+
_
N-
=
J
O
899
O
-(&82*()
#
×
퐷
+
_
N*P
(
10
)
105
where the
D
p_me
is the mass
-
equivalent diameter of each particle. The
ρ
material
is the material density
106
of each particle. Furthermore, we calculated the sensitivity of the
M
R
value for this demarcating line on
107
the mixing state calculation by assuming
M
R,0
= 0~1, respectively (Fig
ure
S17). The results show that,
108
even if we assume the
M
R,0
of the demarcating line is 1 instead of 0, the uncertainty of
M
R
and
ρ
eff
are
109
less than 10%, and the
M
R
and
ρ
eff
still show the dependence on
D
c
.
110
The demarcating line between Mode2 and Mode3 (Line
Mode2
-
Mode3
) is consistent with the criteria for
111
near
-
spherical in other studies
11,12,20
-
23
within ± 20% deviation (Fig
ure
S14D). Thus, we assumed that
112
the morphology is spherical for particles at the demarcating line between Mode2 and Mode3 (Fig
ure
113
S14D). The effective density of Line
Mode2
-
Mode3
(
ρ
eff,2
) can be calculated as the volume
-
weighted average
114
of the
ρ
material
of components, where assumed the particle mobility diameter is equal to the particle mass
115
equivalent diameter.
116
2) Fitting effective density curve under each
D
c
bin: For Mode2, we performed linear fit based on
117
the
ρ
eff,0
and
ρ
eff,2
. For Mode3, the effective density curve was calculated according to the volume
118
weighting (Fig
ure
S18A).
119
3) Selecting the optimal effective density curve: In this study, we calculated different effective
120
density curves (Fig
ure
S18C) by increasing the effective density of the particles at the peak (
ρ
eff,1
) of
121
Mode2 in steps of 0.04 until
ρ
eff,1
=
ρ
materials,1
, and then increasing the
M
R,0
in steps of 0.1 until
M
R,0
= 1.
122
By comparing the calculated bulk
-
average
ρ
eff
/
ρ
materials
under different density curves and the observed
123
bulk
-
average
ρ
eff
/
ρ
materials
in Fig
ure
S3, we selected the optimal curve that best correlates the bulk
-
124
averaged
M
R
measured by DMA
-
SP2 with SP
-
AMS (Fig
ure
S16C).
125
Supplemental items
126
127
Figure S1. Schematic of the sampling system.
T
he dotted line represents the SP2 sample flow, and
128
the red line represents the DMA
-
SP2 tandem system sample flow.
129
130
Figure S2. Location of the sampling sites and air masses transport analysis.
The backward
131
trajectory and clustering of air masses during sampling at (A) PKUSZ
-
Autumn, (B) PKUSZ
-
Winter and
132
(C) YMK
-
Autumn. The main air mass transport pathways are represented by colors: Southeast Coastal
133
Transport Pathway (blue lines), Northern China Transport Pathway (red lines), Intra
-
Guangdong
134
Transport Pathway (green lines) and Southwestern Coastal Transport Pathway (yellow line). (D)
135
Location of the measurement sites.
136
137
Figure S3. PSCF analysis of OVOCS (divided into anthropogenic and biomass burning sources),
138
V and Zn elements, and water
-
soluble inorganic K
+
in PM
2.5
.
139
140
141
Figure S4. The standard deviation (SD) of
log
10
(
M
R
) during the field observation at the PKUSZ
142
and YMK sites.
(A and B) The SD of
log
10
(
M
R
) time series at PKUSZ and YMK, respectively. (C) The
143
SD as the function of NOx and OH exposure at the PKUSZ site. (D) The SD as the function of NOx and
144
carbon oxidation state at the PKUSZ site.
145
146
Figure S5.
Time series of particle density during the field observation at the PKUSZ site.
147
148
Figure S6. Measured variation and evolution of BC microphysics during the field observation at
149
different sites.
(A
-
C) The size
-
resolved
M
R
, effective density, and the fraction of non
-
spherical particles
150
as a function of bulk
-
averaged
M
R
at an urban site in Autumn. (D
-
F) The size
-
resolved
M
R
, effective
151
density, and fraction of non
-
spherical particles as a function of bulk
-
averaged
M
R
at a regional site in
152
Autumn. The lines and markers represent the size
-
resolved values for particles with D
c
in 100
-
120 nm
153
(blue), 150
-
170 nm (grey), and 280
-
300 nm (red), respectively. The dashed lines represent the slopes
154
of microphysics changes for particles.
155
156
Figure S7. Measured variation and evolution of BC microphysics during the field observation
157
for different emission processes.
(A
-
C) The size
-
resolved
M
R
, effective density and fraction of non
-
158
spherical particles as a function of bulk
-
averaged
M
R
for industrial emissions + biomass burning. (D
-
F)
159
The size
-
resolved
M
R
, effective density, and fraction of non
-
spherical particles as a function of bulk
-
160
averaged
M
R
for ship emissions. The lines and markers represent the size
-
resolved values for particles
161
with D
c
in 100
-
120 nm (blue), 150
-
170 nm (grey), and 280
-
300 nm (red), respectively. The dashed lines
162
represent the slopes of microphysics changes for particles.
163
164
Figure S8.
Simulated
E
abs
of particles for different core diameter (
D
c
) and
M
R
using the core
-
shell model.
165