Mixing characteristics of refractory black carbon aerosols determined by a tandem CPMA-SP 2 system at an urban site in Beijing

Black carbon aerosols play an important role in climate change by absorbing solar radiation and degrading visibility. In this study, the mixing state of refractory black carbon (rBC) at an urban site in Beijing was studied with a single particle soot photometer (SP2), as well as a tandem observation system with a centrifugal particle mass analyzer (CPMA) and 15 a differential mobility analyzer (DMA), in early summer of 2018. The results demonstrated that the mass-equivalent size distribution of rBC exhibited an approximately lognormal distribution with a mass median diameter (MMD) of 171.2 nm. When the site experienced prevailing southerly winds, the MMD of rBC increased notably by 19%. During the observational period, the ratio of the diameter of rBC-containing particles (Dp) to the rBC core (Dc) was 1.20 on average for Dc=180 nm, indicating that the majority of rBC particles were thinly coated. The Dp/Dc value exhibited a clear diurnal pattern, with a 20 maximum at 1400 LST and an enhancing rate of 0.013/h; higher Ox conditions increased the coating enhancing rate. Bare rBC particles were primarily in a fractal structure with a mass fractal dimension (Dfm) of 2.35, with limited variation during both clean and pollution periods, indicating significant impacts from on-road vehicle emissions. The morphology of rBC-containing particles varied with aging processes. The mixing state of rBC particles could be indicated by the mass ratio of non-refractory matter to rBC (MR). In the present study, rBC-containing particles were primarily found in an external fractal structure when 25 MR < 1.5 and changed to a core-shell structure when MR > 6, at which the measured scattering cross section of rBC-containing particles was consistent with that based on the Mie-scattering simulation. We found only 9% of the rBC-containing particles were in core-shell structures on clean days with a particle mass of 10 fg, and the number fraction of core-shell structures increased considerably to 32% on pollution days. Considering the morphology change, the absorption enhancement (Eabs) was 11.7% higher based on core-shell structures. This study highlights the combined effects of morphology and coating thickness 30 on the Eabs of rBC-containing particles, which will be helpful for determining the climatic effects of BC. Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2019-244 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 20 May 2019 c © Author(s) 2019. CC BY 4.0 License.

Reply: We want to exhibit the different Dp/Dc distribution during episode 1 and episode 2. We have changed the expression which may be more understandable and concise.
The Dp/Dc exhibited a unimodal distribution during episode 1 and a clear bimodal pattern during episode 2 as shown in the upper panel of Reply: Thanks, "tends" seems to be more appropriate.
L304-305: There are more recent studies on the microscopy of BC.
Reply: It's true. We update the reference now. (line 282) 135 L341: "The median MR values of the pollution day were all larger than those on the clean day for the four Mp points. This result demonstrated that rBC had more coating material during the pollution day than the clean day." Couldn't it be related to the higher RH?
Reply: A higher RH can truly increase the water content in the rBC-containing particles and thus the size as well as MR. 140 However, we have dried the rBC-containing particles before the tandem system as shown in Fig. 2(a) to avoid the influence of RH. We will write a new section to introduce the tandem system including the drying process to avoid causing misunderstanding of readers.
L380: "indicating in-cloud nucleation scavenging may be a more efficient mechanism for rBC-containing particles". Do you 145 mean removal mechanisms?
Reply: Yes, we will add "removal" to make it more clear.  In the two upper panels, the integral of the area below the curve seems to be larger than 1, is it really the normalized dN/dlogDp? Moreover, the arrows indicating the clean and polluted periods are not precise. 160 Reply: The former normalized dN/dlogDp was obtained by letting the maximum value of the histogram be 1. We have changed the calculation to let the integral of the area be 1.
The arrows have been in bold to make them more clear and extra guide line have been added to denote the clean and polluted periods. Reply: The concentrations of PM2.5 and gaseous pollutants were from a state control air quality site, provided by the China National Environmental Monitoring Centre. The state control air quality site was 2.5 km from our observation site. We think the air quality data is similar in such close distance. And we added the position of the state control air quality site in Fig. 1b. (line 186-189) 170 Reply: Yes, there is only one data point. The purpose of this calibration is to determine the laser intensity of SP2. In fact, the DMT company suggests the calibration of the scattering signal only needs one data point. Thus, we only did calibration of scattering signal using PSL with diameter of 240 nm after the experiment which showed good consistency with the calibration 185 before the experiment (varied within 3%) demonstrating the stability of the instrument. Zhang, Y. X., Zhang, Q., Cheng, Y. F., Su, H., Li, H. Y., Li, M., Zhang, X., Ding, A. J., and He, K. B.: Amplification of light absorption of black carbon associated with air pollution, Atmospheric Chemistry andPhysics, 18, 9879-9896, 10.5194/acp-18-9879-2018, 2018. 195 Reply to the comments of anonymous reviewer #3 on manuscript Entitled " Mixing characteristics of refractory black carbon aerosols determined by a tandem CPMA-SP2 system at an urban site in Beijing" 200 We appreciate very much the patient and insight comments and recommendations of the reviewer in improving this paper and our future research. Here, we will response to all the comments one by one as follows: General comments: 205 First, a full and careful proofreading is necessary to catch all the grammar and word choice errors. I have listed a bunch, but am not confident I listed them all here. In fact, after a while, I gave up listing them because this was taking too much time.
Please correct these errors before sending out for review again.
Reply:Great thanks to the reviewer to point out the grammar errors. We have changed the error places and checked the 210 manuscript several times again.
Second, there needs to be better quantification of the SP2 calibrations. To give this dataset importance in terms of the big picture, better uncertainties are necessary. The conclusions all sound reasonable as far as I can tell; but they need to be mathematically rigorous as well. 215 Reply: We have determined the uncertainty of our SP2 and the error bars have been added to the calibration figures. Also, the uncertainties of some key parameters have been evaluated.
A final big comment, there are many places in the paper that need more detail and clarifications. See my many comments 220 listed below. In general, a better description of the tandem experiments and of the models used to calculate absorption enhancements are necessary. Many other places need rewording for clarity.
Reply: We have reorganized the method section and added a part to describe the tandem system including the configuration, time, the air mass during the tandem system (Section 2.32 and line 145-176 in the manuscript). The description of the 225 calculation of absorption enhancement (Section 3 in supplementary) is added in the supplementary. Many parts of the manuscript have been rewritten to make it clearer.

Specific comments:
Line 21 -Is "enhancing rate" standard terminology? I don't know what the units are (0.013 what per hour?). 230 Reply: 1) We changed the expression of "enhancing rate" to "growth rate".
2) Dp/Dc is a dimensionless quantity, so there shouldn't be a unit for 0.013. We change to report the growth rate of Dp instead of Dp/Dc to make it clearer for readers. The growth rate of Dp now has a unit of "nm". (line 21) Line 21 -Should the "x" be a subscript in "Ox"? 235 Reply: Thanks, we have changed the mistake. (line 21) Line 65 -Is the "18.97%" number really accurate to two decimal places?
Reply: We directly cited this value from the work of , so we think it's not appropriate to change the value which we cited. 240 Line 95 -I don't understand the sentence beginning with "Anthropogenic". Reply: 1) Good advice, we would like to check such loose and correct the concentration according to the probable particle loose in the diffusion dryer. Unfortunately, our SP2 has some problems now and have been sent to the manufacturers for repairing and we can't do the test at present.
2)We waited a long time (about half an hour) after changing the regular single SP2 observation to tandem system measurement. And waiting for about 2 min every time we change the setpoint of DMA/CPMA to let the system stabilize, we 255 have added these details in the method section. (line 156, line 168).
Line 104-105 -Should show error bars/scatter in the data on Fig S1. Also should quantify how constant the laser was during the study. Also, be careful of wordingtwo data points does not ensure that the laser was constant during the study, just that the beginning and end points were similar. Without more data, it even looks like intensity may have been drifting in one 260 direction.
Reply: 1) There is a parameter called YAG power which is recorded in the housekeeping file in SP2 and reflects the laser intensity. We found the YAG power was 4.8±0.1 during the observation indicating the stable condition of the laser.
2) Yes, we agree that two data points does not ensure that the laser was constant. We reword the expression and use YAG 265 power to prove the laser was nearly constant during the study. Now: The calibration of the scattering channel and incandescence channel was also conducted after the observation, the calibration coefficient varied little (<3%) and the YAG power (laser intensity index recorded by SP2) fluctuated with 4.8±0.  Fig S2 and simplified the introduction of CPMA to make the paper more concise.
Line 136 -More precisely, the peak LII signal is what is used, not the entire LII signal. 285 Reply: Yes, we have changed the expression. Now: The LII peak-MrBC relationship is thus obtained (Fig. S1). (line 104) Line 137 -Why did you use a spline fit when earlier you state that there is a linear relationship between peak height and rBC 290 mass?
Reply: It's nearly linear relationship between LII peak height and rBC mass, but not perfectly linear. The DMT company suggested their custom to use a spline fit. The coefficient of the spline fit is exhibited in Fig S1. In fact, the coefficient of x 2 is very small. 295 Figure S3 -Should show error bars showing the scatter in the data and uncertainty in the particle mass from the CPMA. Also, if there is no calibration equation, how do you use these data? Figure S5 -Again, would be nice to see error bars showing scattering/uncertainty in the data. Reply: The coefficient of DMA-SP2 calibration and CPMA-SP2 calibration varied little (<3%). For conciseness, we don't mention the DMA-SP2 calibration since the coefficient used in this study came from the CPMA-SP2 calibration.
Line 152 -Why multiply by 1.17 and not 1.15? 310 Reply: The corrected concentration is: (the measured concentration) / (1-15%) or (the measured concentration) * 1.17. We have changed the expression to "dividing by a factor of 0.85". We have changed the expression, now: By extrapolating a lognormal function fit to the observed mass distribution, we found that rBC particles outside the detection range caused an ~15% underestimation of the rBC mass concentration. To compensate, the mass concentration of rBC was 315 corrected by dividing by a factor of 0.85 during the measurement. (line 128-129) Line 159 -This whole section should probably be edited for clarity. Specifically here, I don't understand "dividing by laster intensity". Line 161 -Again, clarity -reword "the data before a length" 320 Reply: We have reworded the method section to make it clearer.
Line 173 -How did you determine which was the most proper refractive index to use? Supplemental -What is "RCT"?
Reply: We have removed this part and directly use the refractive index from the previous research. 325 Line 182 -To be clear, the MrBC is what is measured by the SP2, correct? Section 2.3.3 needs some work for clarity.
Reply: Yes, it's directly measured by SP2. The method section has been rewritten.

330
Line 192 -Again, there is no quantification of how well the current study compares with previous studies. It looks like your data points are systematically higher than the polynomial fit by Gysel. You should quantify the relationship and tell the reader what it means for your study.
Reply: Our results are ~7% higher than the poly-fit of Gysel but lower than the results from Moteki and Kondo. These 335 differences may be result of different characteristics of Aquadag with varied lot and different instrument condition (such as the uncertainty of SP2).
Line 195 -What is the purpose of Section 2.3.5? Need more details. Where exactly do the parameters going into the Mie model come from? The Cabs variables should be defined in Table S1. 340 Reply: We have rewritten the method section and added a new section in the supplementary to describe the optical calculation.

(Section 3 in supplementary)
Line 202 -What instruments measured the gaseous pollutants? Line 207 -What measured total PM2:5 mass? Was this 345 measurement behind the cyclone? If so, was the cyclone's cut size at 2.5 microns, or something higher? These details might effect your measurement.
Reply: The concentrations of PM2.5 and gaseous pollutants were from a state control air quality site, provided by the China National Environmental Monitoring Centre. The state control air quality site was 2.5 km from our observation site. We think 350 the air quality data is similar with the air quality of our observation site in such close distance. And we added the position of the state control air quality site in Reply: Thanks. It's a good advice to examine whether the coatings are the reason for the discrepancy. We did the test and found there wasn't strong relationship between the coating thickness and the discrepancy between MAAP and SP2. Thus, we remove the part of MAAP in the manuscript. 360 Line 276 -It actually looks like the increase was on June 12, not June 13.
Reply: Yes, it's on June 12. The episode 2 that we referred here is just June 12. We conducted the tandem experiment on June 13. So, the Dp/Dc value from single SP2 measurement is only available on June 12. And we report the Dp/Dc before the tandem 390 experiment. The expression of this part has been modified. Now: The Dp/Dc distributions for the two episodes before the tandem CPMA/DMA-SP2 experiments are shown in Fig. 7. Episode 1 (June 7 2200 LST -June 8 1200 LST) occurred after a heavy rain period and is representative of clean conditions. Episode 2 (June 11 2300 LST -June 12 1200 LST) was characterized by the highest Dp/Dc value (1.4) and the highest PM2.5 concentration value (120 μg/m 3 ) during the observation period. (line 246-249) 395 Line 277 -Where does 63% come from?
Reply: 63% is cited from . The air quality in Beijing is easily influenced by the regional pollution transportation in pollution conditions Li et al., 2017). We just use this number in the previous research to 400 demonstrate our inference that the rBC-containing particles with Dp/Dc = 1.8 in the right peak of the bimodal distribution may be the result of transportation from pollution region.
Line 295 -Do you have any idea the magnitude/emission rate of fresh rBC in Beijing? If so, you could use that number for a closure study. 405 Reply: It's a good advice. It's possible to estimate the true growth rate of Dp by simultaneously considering the fresh rBC emission and the "apparent" Dp growth rate. And this true growth rate value is important in the atmospheric model.
Unfortunately, the emission data about the aging degree of rBC from different emission sectors is still lacking. We may conduct laboratory experiments to determine the rBC aging degree from varied rBC sources and try to estimate the true Dp growth rate 410 in the future.
Line 305 -This sentence is worded as if the Li et al 2003 study took images of the rBC from this study, which is obviously not correct. Were any new microscopy images taken from the current study period?

415
Reply: There was no new microscopy images taken from current study. The literature cited here is to support the argument that bare rBC is in a fractal structure. We have changed the expression to make it clearer and added some new literatures. Now: This significant discrepancy indicates bare rBC was in a fractal structure consistent with the previous research from electron microscopic image that bare rBC was in a fractal chain-like structure (Li et al., 2003;Adachi and Buseck, 2013;. Reply: Yes, it's from Peng et al 2016, we cite this literature in order to support the argument that the rBC-containing particles 425 tend to become more compact with the coating increasing. The effective densities are the parameters in Peng's literature to support this argument. However, we think this sentence may confuse the readers and thus we changed the expression in the manuscript. Now: Different techniques have been used to explore the morphology of rBC-containing particles in ambient and laboratory measurements Peng et al., 2016;. It is generally agreed that the morphology of rBC-430 containing particles will become more compact with the aging process or with increasing coating thickness. Reply: What we mean is the wet scavenging may be a more efficient removal mechanism for larger rBC-containing particles.
We have changed the expression. Thanks for reminding. 445

Technical corrections
Great thanks for the patient and careful comments about the technical corrections from the reviewer, we have corrected the technical corrections pointed by the reviewer and carefully checked the manuscript again and again. Thanks again for the 450 reviewer for improving this paper.
Line 44 -should be "into the atmosphere" Line 45 -need a comma after condensation Reply: Now: After being emitted into the atmosphere, BC particles tend to mix with other substances through coagulation, 455 condensation, and other photochemical process, which significantly changes BC's cloud condensation nuclei activity as well as its light absorption ability (Liu et al., 2013;Bond and Bergstrom, 2006).

(line 41-44)
Line 83-84 -reword: the data are not analyzed in the discussion section, they are presented Reply: Now: A tandem experiment combining a centrifugal particle mass analyzer (CPMA, Cambustion Ltd.) and a differential 460 mobility analyzer (DMA, model 3085A, TSI Inc., USA) with a SP2 were performed during two typical cases, focusing on BC- By extrapolating a lognormal function fit to the observed mass distribution, we found that rBC particles outside the detection 490 range caused an ~15% underestimation of the rBC mass concentration. (line 126-128) Line 156 -is intracavity a noun?
Line 164-165 -reword "description ... described" Line 170 -the densities are not defined in the text nor in Table S1  495 Line 174 -add "respectively" to the sentence Line 207 -Don't use "this" as the subject of a sentence.
Reply: Former:" The mass concentration of rBC was 1.21 ± 0.73 μg/m 3 on average, accounting for 3.5 ± 2.4% of PM2.5 on an hourly basis. This was comparable to the previous filter-based measurement in Beijing, with an average fraction of 3.2% in the summer of 2010 (Zhang et al., 2013)." Now: The mass concentration of rBC was 1.21 ± 0.73 μg/m 3 on average, accounting for 3.5 ± 2.4% of PM2.5 on an hourly 510 basis, which was comparable to the previous filter-based measurement in Beijing, with an average fraction of 3.2% in the summer of 2010 (Zhang et al., 2013). (line 186-188) Line 209-210 -reword, I don't think this is actually a sentence Reply: It has been deleted. 515 Line 232 -MED or MMD?
Reply: It's MED.  only reported the average MED and standard deviation of MED in winter and summer but not MMD, but these MED value also show a summer-low-winter-high trend.

520
Line 242 -combination should be combined Reply: Now: The diurnal cycle reached a peak plateau between 0300-0700 LST and it decreased gradually in the afternoon, which was Black carbon (BC) aerosol is one of the principal light-absorbing aerosols in the atmosphere. BC is regarded as one of the most important components contributing to global warming (Bond et al., 2013). BC has a much shorter lifetime than CO2.
Thus, BC's radiative perturbation on a regional scale may be different from globally averaged estimates. It has been reported 595 that BC's direct radiative forcing can reach an order of +10 W m -2 over East and South Asia (Bond et al., 2013). BC aerosols can also influence the climate by altering cloud properties, such as the evaporation of cloud droplets, cloud lifetime and albedo (Ramanathan et al., 2001;Ramanathan and Carmichael, 2008). Ding et al. (2016) determined that the existence of BC in the upper mixing layer could absorb downward solar radiation, impeding the development of the boundary layer, which aggravates air pollution. Moreover, BC aerosols have detrimental health effects. BC and organic carbon are regarded as the most toxic 600 pollutants in PM2.5 and lead to as many as ~3 million premature deaths worldwide (Adler et al., 2010;Apte et al., 2015).
BC is typically emitted from the incomplete combustion of fossil fuels and biomass. After being emitted into the atmosphere, BC particles tend to mix with other substances through coagulation, condensation, and other photochemical processes that significantly change BC's cloud condensation nuclei activity as well as its light absorption ability (Bond et al., 2013;Liu et al., 2013). The model results suggest that after BC's core is surrounded by a well-mixed shell, its direct absorption radiative 605 forcing could be 50% higher than that of BC in an external mixing structure (Jacobson, 2001). Such an absorption enhancement phenomenon is interpreted as exhibiting a "lensing effect", in which a non-absorbing coating causes more radiation to interact with the BC core and thus more light is absorbed. This absorption enhancement effect has been proven in laboratory studies (Schnaiter et al., 2005). Shiraiwa et al. (2010) reported that the absorption enhancement of BC in a core-shell structure increased with coating thickness and reached a factor as high as 2. Nevertheless, field observation results demonstrated large 610 discrepancies (6 to 40%) in the absorption enhancement of aged BC particles Lack et al., 2012). The discrepancies could be attributed to the complex mixing state of BC in the real atmosphere, which depends on the coating composition, the coating amount and the size of the BC core and structure. Bond et al. (2013) regarded the mixing state of BC as one of the most important uncertainties in evaluating BC direct radiative forcing. Furthermore, freshly emitted BC is initially hydrophobic. Mixing BC with other soluble materials will significantly increase BC-containing particles' hygroscopicity and 615 thus their ability to become cloud condensation nuclei (Bond et al., 2013;Popovicheva et al., 2011). This ability is associated with the wet deposition rate and consequently influences the lifetime and spatial distribution of BC particles in the atmosphere.
For these reasons, more observations are needed to determine the specific spatial and temporal distribution of BC's mixing state, which would be helpful for minimizing the uncertainty in evaluating BC's climatic and environmental effects.
China's economy has grown rapidly in recent decades, accompanied by the substantial emission of pollutant precursors. Annual 620 emissions of BC in China are reported to have increased from 0.87 Tg in 1980 to 1.88 Tg in 2009, comprising half of the total emissions in Asia and an average of 18.97% of the global BC emissions during this period . Such substantial BC emissions greatly influence the regional climate and environment (Ding et al., 2016;Menon et al., 2002).
Although temporal/spatial variations in BC and the corresponding optical properties of aged BC have been recently reported (Cao et al., 2007;Cao et al., 2004;Zhang et al., 2009), the number of observational studies on BC's mixing state remains 625 insufficient. Recently, single particle soot photometer (SP2) has been used as a reliable instrument for estimating the mixing state of BC due to its single particle resolution and high accuracy. Several studies have used SP2 to investigate BC's mixing state in China (Gong et al., 2016;Huang et al., 2012;. Most studies have primarily focused on the variability of BC's mixing state on severe haze days during winter because of the extremely high concentrations of particle matter and low visibility. In summer, higher radiation and high hydroxyl radical concentrations favor photochemical 630 reactions and thus contribute to the condensation aging of BC. By using a smog chamber, Peng et al. (2016) found that the amount of BC-containing particles increased rapidly owing to the photochemical aging of the BC coating materials from Beijing's urban environment, even in relatively clean conditions. Cheng et al. (2012) noted that the changing rate of BC from an external to internal mixing state can reach up to 20%/ h in summer. Thus, the mixing state of BC should also be carefully considered on relatively clean days during summer. 635 In this study, we used an SP2 to investigate BC in the urban areas of Beijing, China, during early summer, focusing on the size distribution and mixing state of BC-containing particles. Field experiments using a tandem system consisting of a centrifugal particle mass analyzer (CPMA, Cambustion Ltd.) and a differential mobility analyzer (DMA, model 3085A, TSI Inc., USA) with an SP2 were performed during two typical cases, focusing on BC-containing particles' microphysical properties. Various techniques have been developed to quantify the mass concentration of BC aerosols, including optical, thermal, thermal-optical 640 and photoacoustic methods. For the SP2, the mass concentration of BC was measured on the basis of incandescent signal emissions; therefore, refractory black carbon (rBC) was used. The abbreviations and symbols used in this paper are listed in Table S1.  (Fig. 1b). Anthropogenic emissions from the experimental campus were negligible. Thus, this site can 650 well represent the urban conditions in Beijing.

Single-particle soot photometer (SP2)
A single particle soot photometer (SP2, Droplet Measurement Technology, Inc., Boulder, CO, USA) was used to determine the size distribution and mixing state of rBC particles in the atmosphere. In the SP2 measuring chamber, an intensive continuous intracavity Nd:YAG laser beam is generated (1064 nm, TEM00 mode). After an rBC-containing particle crosses 655 the beam, it is heated to incandesce by sequentially absorbing the laser power. The maximum incandescence intensity (or the peak height of the incandescence signal) is approximately linearly correlated with rBC's mass, irrespective of the presence of non-BC material or the rBC's morphology. The SP2 was calibrated to determine the relationship between the incandescence peak height and the mass of rBC particles using Aquadag aerosols (Acheson Inc., USA). Fig. 2b illustrates the schematic diagram of the calibration system. During calibration, monodisperse Aquadag aerosols were generated with an atomizer (model 660 3072, TSI Inc., USA) and dried using a diffusion dryer. Then, Aquadag aerosols with known mass (MrBC) were selected with a CPMA and injected into the SP2 to obtain the corresponding laser-induced incandescence (LII) signal. A recent study (Laborde et al., 2012) demonstrated that the mass of rBC particles could be underestimated when using Aquadag aerosol as the calibration material. We performed a correction by multiplying by a factor of 0.75 for LII peak height during the calibration, as described in . The LII peak-MrBC relationship was thus obtained (Fig. S1). The 665 uncertainty of the derived rBC mass was estimated to be 20%, which corresponds to an uncertainty of ~6% of the mass equivalent size (Dc, = √ 6 * π * 3 ) by using a 1.8 g cm -3 density for rBC material density (Bond et al., 2013).
In addition to the incandescence channel, SP2 also has scattering channels to directly measure the scattering cross section (σmeasured) of every single particle. However, for rBC-containing particles, the particles will evaporate during the measurement since rBC can absorb the laser energy, which results in a decrease in the rBC-containing particles' sizes and thus a decrease in 670 the σmeasured. The leading-edge only (LEO) fitting method was invented to obtain the scattering cross section of the initial rBCcontaining particles before evaporation (Gao et al., 2007). With the σmeasured and Dc, the diameter (Dp) of the rBC-containing particle can be obtained using Mie theory with refractive indices of 2.26-1.26i for the rBC  and 1.48-0i for the coatings  by assuming a core-shell structure. Thus, the coating thickness of rBC can be directly determined by SP2, as denoted by the shell/core ratio (Dp/ Dc). The Dp derivation method based on LEO fitting has been widely 675 used Shiraiwa et al., 2008;Laborde et al., 2013), and  estimated that the core-shell assumption will cause <6% uncertainty in the derived Dp/Dc. The scattering signal of SP2 was calibrated using polystyrene latex spheres (PSL, Nanosphere Size Standards, Duke Scientific Corp., USA) with known sizes (203±3 nm: Lot #185856; 303±3 nm: Lot #189903; 400±3 nm: Lot #189904), as shown in Fig. S2. The calibration of the scattering channel and the incandescence channel was also conducted after the observation. The calibration coefficient varied little (<3%) and 680 the YAG power (laser intensity index recorded by the SP2) fluctuated by 4.8±0.1, indicating the stable condition of the SP2 during the observation period.
The detection efficiency of the SP2 was determined by comparing the number concentrations of Aquadag as simultaneously measured by the SP2 and a condensation particle counter (CPC, model 3775, TSI Inc., USA). For large particles, the SP2 detection efficiency was approximately unity and decreased gradually for smaller rBC particles (Fig. S3). For rBC with Dc< 685 70 nm, the detection efficiency of the SP2 fell significantly below 60%. The mass concentrations of rBC may be underestimated because of the low detection efficiency of for smaller rBC particles. By extrapolating a lognormal function fit to the observed mass distribution, we found that rBC particles outside the detection range caused an ~15% underestimation of the rBC mass concentration. To compensate, the mass concentration of rBC was corrected by dividing by a factor of 0.85 during the measurement. 690 In general, the SP2 can directly measure the mass of the rBC core (MrBC) and thus the mass equivalent diameter (Dc).
Additionally, the scattering cross section (σmeasured) can be directly obtained by the SP2, and the diameter of the rBC-containing particle (Dp) can be derived using Mie theory.

Experiment
Two kinds of measurements were conducted in this study: a regular single SP2 observation to provide the number/mass size 695 distribution and coating thickness of the rBC-containing particles and a tandem CPMA/DMA-SP2 experiment to study the microphysical properties of the rBC-containing particles.

Single SP2 measurement
The regular single SP2 observations were conducted from May 30 to June 7 and June 9 to June 12. An aerosol sampling inlet was placed at 4 m above the ground. A PM2.5 cyclone (URG-2000-30ENS-1) was used to selectively measure particles with 700 an aerodynamic diameter smaller than 2.5 µm because rBC particles are typically present in the submicron mode. The systematic configuration of the rBC measurements is presented in Fig. 2a. A supporting pump with a flow rate of 9.6 L/min was used to guarantee a total inlet flow rate of 10 L/min (the demanding flow rate of a PM2.5 cyclone) and to minimize particle loss in the tube. The residence time of the sampling flow was estimated to be ~17 s. Then, the sample air was dried by passing through a Nafion dryer (MD-700-24S, TSI) at a flow rate of 0.4 lpm. The dried sample was measured with the SP2 and CPC. 705

Tandem CPMA/DMA-SP2 measurement
The tandem CPMA/DMA-SP2 experiments were conducted on June 8 and 13. June 8 is representative of a clean period, when the concentrations of PM2.5 and O3 averaged 20 μg/m 3 and 60 ppbv, respectively. Beijing was mainly affected by a clean northern air mass on June 8 (Fig. S5). June 13 is representative of a polluted period when the hourly mass concentration of PM2.5 exceeded 110 μg/m 3 ; the air mass was from the southern polluted area of Beijing, where many heavy industries are 710 located. Thus, the tandem CPMA/DMA-SP2 experiment was conducted on June 8 and 13 to study the detailed physical characteristics of rBC under different pollution conditions. As shown in Fig. 2(a), the tandem system was similar to the regular single SP2 observation system. The difference is the neutralizer, and a DMA or CPMA were added in front of the SP2, as denoted by the orange dashed line. Specifically, in the DMA-SP2 system, particles were first selected by DMA to obtain particles with known mobility diameters (Dmob). Then, the 715 monodispersed particles were injected into the SP2 to obtain the corresponding information. In practice, we set three Dmob setpoints (Dmob = 200 nm, 250 nm, 300 nm). The duration of one setpoint is ~20 min, and we recorded data 2 min after we changed the setpoint to allow the system to stabilize. The purpose of the DMA-SP2 system is to obtain the effective density of bare rBC. Bare rBC is defined as rBC with Dp/Dc ≈ 1, and the effective density of bare rBC was calculated according to the following equation: 720 = 6 3 (5) In principle, the measured effective density is the same as the material density if the particle has an ideal spherical shape with no void space. Thus, the effective density is an indicator of particle compactness, as it compares the effective density and the material density. Several studies that include the coupling of DMA with APM or CPMA have been conducted to determine the ρeff-Dmob relationship of Aquadag rBC samples in the laboratory Gysel et al., 2011). The 725 relationship between the ρeff and Dmob of Aquadag is presented in Fig. S4. The ρeff obtained using the DMA-SP2 system in this study agreed well with previous research.
In the CPMA-SP2 system, particles with known mass (Mp) selected by CPMA were injected into the SP2, and the Mp setpoints were 1 fg, 2 fg, 5 fg and 10 fg. The duration of one setpoint was ~20 min, and we waited 2 min after we changed the setpoints to record a measurement. The purpose of the CPMA-SP2 system is to obtain morphological information about rBC-containing 730 particles with different coating degrees. Using a tandem CPMA-SP2 system, the mass of an rBC-containing particle (Mp) and of the rBC core (MrBC) can be simultaneously obtained. The coating thickness can be represented by the mass ratio of the coating to the rBC core (MR = (Mp-MrBC)/MrBC) without any assumptions. Knowing Mp and MrBC, the scattering cross section of rBC-containing particles can be calculated through Mie theory with refractive indices of 2.26-1.26i for the rBC and 1.48i for the coatings by assuming a core-shell structure and a coating density of 1.5 g/cm 3 . The calculated scattering cross section 735 (σmodel) can be compared to the σmeasured by SP2, which can reflect the morphological characteristic of rBC-containing particles; this comparison will be further discussed in section 4.1.2.

Concentrations of PM2.5, rBC and pollutant gases 740
The temporal variations in the concentrations of PM2.5, rBC and gaseous pollutants (O3, NO2) during the project are presented in Fig. 3. The regular pollutant concentrations, including PM2.5 (1405-F, ThermoFisher Scientific), NO2 (42c, ThermoFisher Scientific) and O3 (49i, ThermoFisher Scientific), were obtained from a state control air quality site (2.5 km from LAPC), provided by the China National Environmental Monitoring Centre. The mass concentration of PM2.5 ranged between 5 and 120 μg/m 3 on a daily basis during the observation period. The mixing ratios of both NO2 and O3 exhibited obvious opposite 745 diurnal variations. The maximum O3 concentration appeared at 1400 LST on June 2 with a value of 145 ppbv, reflecting high atmospheric oxidant levels and strong photochemistry during the observation period. The mass concentration of rBC was 1.21 ± 0.73 μg/m 3 on average, accounting for 3.5 ± 2.4% of PM2.5 on an hourly basis, which was comparable to the previous filter-based measurement in Beijing, with an average fraction of 3.2% in the summer of 2010 (Zhang et al., 2013). The mass concentration of rBC also exhibited a clear diurnal variation, with a maximum at night and a minimum at noon. 750 During the period from June 1 to June 6, the meteorological conditions were characterized by low relative humidity (RH < 40%) and strong solar radiation and were favorable for ozone formation. The mixing ratio of ozone was relatively high from June 1 to 6. On June 7, a heavy rainfall event occurred, and most of the major pollutants decreased due to significant wet scavenging. The mass concentration of PM2.5 decreased from 65 to 10 μg/m 3 , and the mass concentration of rBC decreased from 2.63 to 0.2 μg/m 3 from 0300-0700 LST on June 7. The pollutant concentration remained at a low level from June 7 to 8. 755 After June 9, the ambient RH increased to 80%. Under high humidity conditions, the mass concentration of PM2.5 experienced steady growth, increasing from 10 to 120 μg/m 3 and staying at a high level from June 12 to 13. Thus, the tandem DMA/CPMA-SP2 observations were conducted separately on June 8 and June 13, which separately represented the different PM2.5 pollution conditions.

Size distribution of rBC 760
The number and mass distribution as a function of the Dc are illustrated in Fig. 4. As presented, the mass median diameter (MMD) was 171.2 nm during the project. A brief summary of the SP2 observations in China is presented in Table 1. Most previous studies focused on the rBC characteristics in winter when a larger MMD (~200-230 nm) was obtained (Zhang et al., 2013;Huang et al., 2012;Gong et al., 2016) than in this study. A similar MMD (180 nm) was reported in urban Shenzhen during a summer observation period (Lan et al., 2013), and a higher MMD (210-222 nm) was 765 reported in winter.  also found a winter-high-summer-low trend for rBC sizes in London, with Dc=149±22 nm in winter and 120±6 nm in summer. Laboratory studies have proven that MMD is highly dependent on combustion conditions  and material. Thus, MMD is a suitable indicator of the sources of rBC. Several studies have suggested that the MMD of rBC from biomass burning and coal is much larger than that from traffic emissions Schwarz et al., 2008). Huang et al. (2012) found the MMD observed at rural sites to be much larger than that observed at urban sites 770 because urban sites are primarily affected by rBC emitted from traffic sources and rural sites are more influenced by rBC from coal combustion. The seasonal trends in MMD may be partially explained by the different rBC sources in summer and winter. After the two rain events (June 4 and June 7), the MMD decreased significantly from 186 nm to 170 nm and from 183 nm to 159 nm, respectively, as shown in Fig. 3.  observed that the rBC core size distribution shifted to smaller sizes after a biomass burning plume passed through a precipitating cloud, attributing this shift to the preferential nucleation scavenging of larger rBC cores. By counting the MMD on non-rainy days and rainy days,  also found that 780 the MMD decreased from 164±21 nm to 145±25 nm. The decrease in MMD after rain events can be explained by the preferential wet scavenging of the larger rBC-containing particles.
A pollutant rose plot of MMD versus wind speed and wind direction is presented in Fig. 6a. The MMD of rBC was ~160 nm at low wind speed conditions and exhibited a significant increase with increasing southeast wind speed. The maximum MMD exceeded 190 nm when the wind speed was greater than 10 m/s. Fig. 6b presents the correlation between wind speed and 785 MMD. A southerly wind period was selected when the wind direction was 135-225°, and a northerly wind period was the time when the wind direction was 325-45°. The MMD exhibited little correlation with wind speed and varied little between the south and northerly wind periods when the wind speeds were less than 2 m/s, as local rBC emissions were predominant. An MMD of 150-160 nm during low wind speed periods may be characteristic of the local sources. The MMD had a strong positive correlation with the wind speed during the southerly wind period (r 2 =0.93), suggesting that the rBC from the south 790 was larger, which may be the result of the different rBC sources in the southern polluted region. Since the air mass from the north is always clean, the local rBC emissions may be the main contributors to the total rBC concentration in the northerly wind period. Thus, the MMD may be more influenced by local emissions and show a weak correlation with the wind speed during northerly wind periods.

Temporal variation of Dp/Dc
The Dp/Dc for a given single rBC-containing particle was calculated using the LEO fitting method. Herein, rBC cores with Dc=180 ± 10 nm were selected because the low scattering signal of small rBC is easily influenced by signal noise (Dp/Dc indicates the Dp/Dc with Dc=180 ± 10 nm in the following discussion if not specified). The Dp/Dc variation during the investigation time is illustrated in Fig. 7. In general, Dp/Dc was 1.20±0.05 on average during the investigation, which is 800 consistent with observations (1.15) during the summer in Paris (Laborde et al., 2013). rBC sources and the aging process significantly influenced the Dp/Dc of rBC. The rBC from traffic is reported to be relatively uncoated , whereas the rBC emitted by biomass burning is found to be moderately coated, with a Dp/Dc=1.2-1.4 . Moreover, Dp/Dc increases with the aging process, and a larger Dp/Dc (1.6) was found in an aged continental air mass (Shiraiwa et al., 2008). The relatively low Dp/Dc value further supports the argument that rBC was primarily emitted from on-road vehicles 805 during the summer in Beijing.
The Dp/Dc distributions for the two episodes before the tandem CPMA/DMA-SP2 experiments are shown in Fig. 7. Episode 1 (June 7 2200 LST -June 8 1200 LST) occurred after a heavy rain period and is representative of clean conditions. Episode 2 (June 11 2300 LST -June 12 1200 LST) was characterized by the highest Dp/Dc value (1.4) and the highest PM2.5 concentration value (120 μg/m 3 ) during the observation period. The Dp/Dc exhibited a unimodal distribution during episode 1 and a clear 810 bimodal pattern during episode 2, as shown in the upper panel of Fig. 7. The peak of the unimodal distribution and the left peak of the bimodal pattern correspond to a Dp/Dc value of ~1.05, and the right peak of the bimodal pattern corresponds to a Dp/Dc value of ~1.8. The rBC-containing particles with Dp/Dc = 1.05 may be freshly emitted by the local traffic.  demonstrated that 63% of the rBC was estimated to be transported from outside of Beijing during previous pollution events, and the rBC-containing particles from regional transportation were characterized by having more coating material. The 815 rBC-containing particles with Dp/Dc = 1.8 in the right peak of the bimodal distribution may be the result of transportation from polluted regions.

Diurnal variation in Dp/Dc
The temporal variation in Dp/Dc exhibited a clear day-high and night-low pattern. Fig. 8 exhibits the diurnal trend of Dp/Dc. 820 The mean Dp/Dc increased during the daytime, with a peak (1.2) at 1400 LST and a minimum (1.12) at 0600 LST. Dp/Dc was controlled by the competing effects of emissions and aging because freshly emitted thinly coated rBC tends to decrease Dp/Dc and the aging process tends to increase Dp/Dc. The increasing trend of Dp/Dc during the day could be explained by the prevailing aging process, whereas the decreasing trend at night can be explained by the prevailing emissions process, as the photochemical condensation aging during the day was much faster than the coagulation aging at night (Riemer et al., 2004;Chen et al., 825 2017).By measuring the Dp from 0600-1400 LST, the Dp growth rate was calculated to be 2.34 nm/h. A larger Dp growth rate was found in the period with a high Ox concentration, which may be favorable for the formation of coating material on rBC.
The photochemical process and condensation aging have proven to be very efficient during the day. Using a smog chamber, (Peng et al., 2016) found that the Dp growth rate of rBC-containing particles could reach 26 nm/h in Beijing's urban area.
Although the photochemical process and condensation may rapidly increase the Dp, the difference between the present study 830 and the smog chamber results indicated that the "apparent" Dp growth rate in the ambient measurement was relatively low given the continuous freshly emitted rBC in urban Beijing. Thus, the Dp/Dc was always at a low level, resulting in little light absorption enhancement during the summer. By coupling DMA and SP2, the mass and the mobility diameter of bare rBC (Dp/Dc ≈ 1) can be obtained simultaneously, and therefore, the effective density (ρeff) can be calculated. The ρeff of the ambient bare rBC was measured on a clean day (June 8) and a polluted day (June 13). The ρeff of bare rBC at 200-300 nm ranged from 0.41-0.29 g/cm 3 , which was much smaller than 840 the material density of rBC (1.8 g/cm 3 ). This significant discrepancy indicates that bare rBC was in a fractal structure consistent with the previous research from electron microscopic images, which showed that bare rBC was in a fractal chain-like structure (Adachi and Buseck, 2013;Li et al., 2003;. ρeff showed no evident difference between the pollution day and the clean day because the bare rBC particles were freshly emitted and only affected by local sources. A power law is always used to describe the fractal-like aggregates of particles: Mp∝Dmob Dfm Park et al., 2004), where Dfm 845 is defined as the mass fractal dimension that is an indicator of particle compactness. The value of Dfm is 3 for ideal spherical particles and less than 3 for fractal particles. Based on the equation for ρeff, the following relationship can be found: ρeff ∝Dmob Dfm-3 . Thus, a larger bare rBC had a smaller ρeff, which was consistent with the results in Fig. 9. A power function was used to fit the observed data. ρeff ∝Dmob -0.65 and ρeff∝Dmob -0.6 were found separately on clean and polluted days, corresponding to the mass fractal dimensions of 2.35 and 2.4, respectively. These mass fractal dimensions from the summer in Beijing are 850 similar to the observations (Dfm=2.3) from urban Tokyo  and the diesel exhaust measurement (Dfm=2.35) (Park et al., 2004), suggesting that the freshly emitted bare rBC particles originated primarily from traffic sources.
Traffic may contribute a majority of the fresh rBC during both polluted and clean periods in the summer.

Morphology of rBC-containing particles with increasing coating thickness 855
The morphological characteristics of rBC-containing particles were investigated by comparing the σmeasured and σmodel using a CPMA-SP2 system first proposed by . The comparison of σmeasured and σmodel as a function of MR for a particle mass of 10 fg is illustrated in Fig. 10a. σmeasured/σmodel =1 implies that the scattering cross section measured by SP2 is the same as the model prediction under the assumption of a core-shell structure; thus, the rBC-containing particle was likely a core-shell structure. When the rBC was bare (MR ≈ 0), the rBC was in a fractal structure, as discussed in section 4.1.1. With increasing 860 MR, the σmeasured/σmodel gradually decreased until MR=1.5, indicating that the coating material may not be sufficient to encapsulate rBC and that the rBC-containing particles tended not to be away from a core-shell structure. Liu et al. (2017) showed that rBC-containing particles with MR<1.5 primarily presented an external structure. When 1.5<MR<6, the σmeasured/σmodel steadily increased, which implied that the shape of rBC-containing particles gradually transformed to become more compact, with a core-shell-like structure, in this stage. When MR>6, the σmeasured/σmodel was equal to 1, indicating that the 865 rBC-containing particles were in a core-shell-like structure in this stage. Similar phenomena were found in the relationship of σmeasured/σmodel and MR for particle masses of 5 fg, as illustrated in Fig. 10b. However, when MR ≈ 0.1, the σmeasured was consistent with the model prediction for a particle mass of 5 fg. This is because the scattering signal was not sensitive to the irregularity of smaller-sized particles . Therefore, a Mie theory-based core-shell model could capture the main morphological features. 870 Different techniques have been used to explore the morphology of rBC-containing particles in ambient and laboratory measurements Peng et al., 2016;. It is generally agreed that the morphology of rBCcontaining particles will become more compact with the aging process or with increasing coating thickness. However, this study reveals that the morphology transform may only be true when the coating is thick enough (MR>1.5), and the coatings may only attach to rBC and slightly influence rBC-containing particles' morphology when the coating is not thick enough 875 (MR<1.5).
Based on the relationship between the σmeasured/σmodel and MR, the rBC-containing particles are classified into three groups: external stage (0<MR<1.5), transit stage (1.5<MR<6) and core-shell stage (MR>6). A similar variation between the σmeasured/σmodel and MR was also found by . The MR transition point from the transit stage and core-shell stage determined by  is slightly lower than that in this study. Liu et al. (2017) found that the MR 880 transition point varied among different rBC sources. In addition to rBC sources, the environmental conditions during the aging process of rBC-containing particles, such as temperature and humidity, may also influence the rBC-containing particle morphology. We determined the MR transition point in Beijing in summer. More work needs to be done in the future to better quantify MR in different situations.
The combined CPMA and SP2 measurements were conducted separately on a clean day (June 8) and a polluted day (June 13). 885 Fig. 11(a) presents the average MR for different CPMA setpoints (1 fg, 2 fg, 5 fg, and 10 fg) on June 8 and June 13. The average MR is 0.77 for Mp =1 fg and 5.29 for Mp =10 fg on the clean day, whereas the average MR is 0.84 for Mp =1 fg and 7.28 for Mp =10 fg on the pollution day. The average MR values of the polluted day were all larger than those on the clean day for the four Mp points. This result demonstrated that rBC had more coating material on the polluted day than on the clean day. Based on the MR transition points discussed above, the rBC-containing particles were classified into three stages as shown in Fig. 11(b). 890 The rBC-containing particles with Mp=1 fg were primarily in the external mixing stage regardless of the pollution conditions.
With an increase in Mp, more rBC-containing particles were in the transition or core-shell stage. On the clean day, 28% of the rBC-containing particles were in the core-shell stage, when Mp=10 fg. However, on the pollution day, 45% of the rBCcontaining particles were in the core-shell stage, when Mp=10 fg. This phenomenon implied that most rBC-containing particles are not in an ideal core-shell structure on clean days, whereas more rBC-containing particles were in a core-shell structure 895 with thicker coatings on the pollution day.

Implications of rBC-containing particle morphology for light absorption
The morphology of rBC-containing particles varied with MR. A simple core-shell model, as always used in the previous research to determine optical properties, will certainly cause bias. Based on the classification of the rBC-containing particles according to the relationship between σmeasured/σmodel and MR, Liu et al. (2017) proposed a simple morphology-dependent 900 scheme in which the rBC-containing particles at the external stage were considered to have no absorption enhancement (Eabs) and the rBC-containing particles at the core-shell stage were considered to have the same Eabs from Mie theory under the assumption of a perfect core-shell structure. The Eabs at the transit stage was calculated by the interpolation of Eabs between the external and core-shell stages. A graphical and detailed description of the calculation of Eabs can be found in Fig. S6. Liu et al. (2017) proved that this morphology-dependent scheme is in good agreement with the measured Eabs. Thus, the Eabs at 550 nm 905 wavelength with Dc=180±10 nm was calculated separately using the core-shell model and the morphology-dependent scheme to quantify the uncertainty of using a core-shell model, as shown in Fig. 12. Eabs was 1.15, on average, using the core-shell model but was only 1.03 using the new scheme. The Eabs determined by the core-shell model was overestimated 11.7% because the observed averaged coating thickness (Dp/Dc=1.2) determined from single SP2 measurements corresponded to MR=0.37, suggesting that the coating material was not sufficient and most of the rBC-containing particles were not in a core-shell 910 structure in summer in Beijing. Thus, it is necessary to consider the morphology of rBC-containing particles when calculating their optical properties.

Conclusion
The mixing characteristics of rBC-containing particles were investigated in Beijing during the early summer of 2018 using a single particle soot photometer (SP2). The rBC had an approximately log-normal distribution as a function of the mass 915 equivalent diameter (Dc), characterized by a mass median diameter (MMD) of 171.2 nm, which is consistent with previous urban measurements. The mass size distribution was highly associated with the meteorological conditions. Heavy rain events caused the rBC mass size distribution to be smaller, indicating that wet scavenging may be a more efficient removal mechanism for larger rBC-containing particles. The mass size distribution of rBC shifted to larger sizes when southerly winds prevailed, which was primarily caused by the different rBC sources in the south. 920 The Dp/Dc was 1.20 on average, with Dc=180 nm during the investigation period, indicating a low coating thickness of rBC during the summer. Dp/Dc exhibited a clear diurnal pattern with a peak at 1400 LST, increasing from 0600 to 1400 LST at a Dp growth rate of 2.34 nm/h, with Dc=180 nm during the day. The growth rate was much higher in high Ox periods. However, this growth rate was significantly lower than that in the smog chamber results, with a growth rate of 26 nm/h, because the continuously emitted fresh rBC lowered the Dp/Dc in ambient measurements. Although photochemical aging may be very 925 efficient, with continuously emitted fresh rBC, the Dp/Dc increase in the ambient air was very slow, indicating that the rBCcontaining particles were primarily at a low Dp/Dc level in summer. A tandem measurement system with a differential mobility analyzer (DMA) and a centrifugal particle mass analyzer (CPMA) were coupled with an SP2 to investigate the detailed characteristics of rBC-containing particles in summer. The results showed that the effective density of bare rBC (Dp/Dc=1) was determined to be 0.41-0.30 g/cm 3 for Dc=200-300 nm. These effective 930 densities were significantly lower than the rBC material density (1.8 g/cm 3 ), suggesting that the bare rBC was in a fractal structure. The corresponding mass fractal dimension (Dfm) was 2.35, which agrees well with the Dfm of the direct measurement from vehicles, and was unchanged regardless of pollution, indicating that traffic emissions are a major source of fresh bare rBC on both clean and polluted days during the summer in Beijing. With increasing coating thickness, the morphology of rBC changed from a fractal structure to a compact core-shell structure. When MR (Mcoat/MrBC) <1.5, rBC-containing particles were 935 in an external structure. When MR>6, rBC-containing particles were in a core-shell structure. When 1.5<MR<6, the rBCcontaining particles were in a transition stage.
Based on the core-shell model and Mie theory, a new morphology-dependent absorption enhancement (Eabs) scheme was proposed and applied to the ambient measurements. A simulation showed that the Eabsaveraged 1.03 with Dc=180 nm at a wavelength of 550 nm in the summer. The core-shell model overestimated the Eabs by 11.7%. 940

Data availability
To request the data given in this study, please contact Dr. Xiaole Pan at the Institute of Atmospheric Physics, Chinese Academy of Sciences, via email (panxiaole@mail.iap.ac.cn).             σmodel Scattering cross section of rBC-containing particles calculated using the Mie theory Section 1 Calibration 1165 Figure S1: The calibration of the incandescence channel. The data of incandescence peak and rBC mass is fitted using a poly function (y = ax 2 +bx+c). The coefficient of the poly function varied little (<2%) before and after the observation indicating the stability of the incandescence channel. The scatter of incandescence intensity caused 25% uncertainty, resulting in an uncertainty of the derived BC mass of 20%, which causes an uncertainty of mass equivalent diameter of ~6%.
1170 Figure S2: The calibration of the scattering channel. The calibration factor varied little (<3%) before and after the observation indicating the stability of the scattering channel. The calibration is done using PSLwith multiple sizes (203 nm, 240 nm 300 nm, 400 nm) before the observation. And the calibration is done only with PSL with 240 nm after the observation. Figure S3: The calibration curve for the detection efficiency of SP2. For rBC with diameter > 70 nm, the detection efficiency 1175 is larger than 80%. Figure S4: The calibration of the DMA-SP2 system. An DMA-SP2 system can determine the effective density of rBC. We test our DMA-SP2 system by measuring the effective density of aquadag and comparing the result with previous research. Our results are ~7% higher than the poly-fit of Gysel but lower than the results from Moteki and Kondo. These differences may be 1180 result of different characteristics of Aquadag with varied lot and different instrument condition (such as the uncertainty of SP2).

Section 2 Backward trajectory
An WRF-Flexpart model (https://www.flexpart.eu) was used to analyze where the air mass was from. The 1°*1° FNL data (rda.ucar.edu/) was used as the input meteorological data to WRF. WRF can produce meteorological data with higher 1200 resolution which was used as the input data for Flexpart. Air samples were released at 100m above ground level at the observation site (longitude: 116.37°E; latitude: 39.97°N) and the simulation time of backward trajectory is 3 days.
On the clean days (06/07, 06/08) the air mass was from the north of Beijing where there is little pollutant emission. Since the north air mass is clean, the local emitted pollutant may be dominant.
On the pollution day (06/12, 06/13), the air mass was majorly from the south polluted area. The pollutant transportation may 1205 paly an important role in pollution day.

Figure S5
The backward trajectories at clean days (06/07, 06/08) and polluted days (06/12, 06/13), the map is the built-in map of the IGOR software (https://www.wavemetrics.com/). 1210 Section 3 Absorption enhancement calculation 3.1 Description of morphology-dependent model 1215 The absorption enhancement (Eab) of a single rBC-containing particle is calculated as the ratio of absorption cross section of rBC-containing particle (Cabs,p) and absorption cross section of rBC core (Cabs,rBC) using Mie theory assuming a core-shell structure with refractive indices of 2.26+1.26i for rBC core and 1.48 for coatings. _ ℎ = , , Considering rBC-containing particle is not in an ideal core-shell structure as discussed in section 4.1.2, the rBC-containing 1220 particles was classified into external, transition and core-shell stage based on the MR range. The rBC-containing particles with an external mixing state were considered to have no absorption enhancement, and the rBC-containing particles at the coreshell stage were considered to have a core-shell structure and the same Eabs from Mie-theory under the assumption of a perfect core-shell structure. The Eabs in the transition period was calculated by the interpolation of Eabs between the external and internal stage, which can be explained as the following equation: 1225 6−1.5 _ ℎ ℎ ≥ 6 * ( − 1.5) + 1 when 1.5 < < 6 The reliability of this morphology-dependent model has been proven by comparing the Eabs derived from the model and measuring the Eabs .

Applying the morphology-dependent model
The Dp and Dc can be directly obtained in the single SP2 measurement. With the rBC density of 1.8 g/cm 3 and assuming a coating density of 1.5 g/cm 3 , the MR of every single rBC-containing particle can be calculated in the ambient measurement.
Thus, the relationship of the morphology-dependent model between MR and Eabs can be used. We calculated the Eabs of every single rBC-containing particle with Dc =180 nm in one hour and reported the average Eabs in Fig. 12. 1240