Introduction

Black carbon (BC) particles, also known as soot, play an important role in climate change as an effective short-lived climate forcer. BC is mainly formed by the incomplete combustion of biomass, fossil, and biofuels, and the global annual emission of BC was estimated to be 8.54 Tg in 20171. Once emitted, BC particles undergo a series of aging processes, including coagulation, gas-phase condensation, and heterogeneous reactions, consequently altering their optical, physical, and chemical properties. In the recent IPCC AR6, the effective radiative forcing of BC was estimated to be between −0.28 and 0.41 Wm−2, contributing to a temperature rise of 0.1 °C from 1750 to 20192. However, all modeling results are subject to considerable uncertainties, and understanding the aging process of BC is a critical challenge for an accurate and meaningful estimation.

The aging process of BC particles can be simply described as nascent BC (bare BC core or BC thinly coated with co-emitted compounds) gradually grown larger by coating with other non-BC components, which act like a lens focusing more light to the internal BC core, thus enhancing its light absorption3. This light absorption enhancement of BC has been confirmed in many laboratory and modeling studies4,5,6,7. However, ambient measurements have yielded inconsistent results; some studies have observed a significant enhancement in light absorption, while others have reported a much lower enhancement than the results obtained from laboratory and modeling simulations8,9,10,11,12. The discrepancies between field studies and laboratory/modeling results have sparked a debate whether climate models have overestimated the climate effects of BC13,14. Recent studies, based on simulations of mixing state of BC particles in the ambient atmosphere, proposed that the particle-to-particle heterogeneity in the environment is the main reason for the differences in the enhancement of light absorption between laboratory/modeling results and field observations15,16. A field study by Zhai et al.17 observed both large and minor BC absorption enhancement when the mass ratio between non-BC component and BC core was high and they conclude light absorption enhancement is strongly dependent on the mixing state heterogeneity in coating thickness. However, the impact of BC light absorption due to mixing state has not been fully understood, and it is difficult to incorporate BC mixing state into the global climate model due to its complexity14. Yao et al.18 have shown that a simplified representation of the mixing state of BC (and other aerosol components) may introduce significant errors in aerosol optical properties and further estimate radiative effects. Therefore, a lack of comprehensive understanding of BC heterogeneity is a great challenge in accurately representing the climate impact of BC.

In order to investigate the impact of BC mixing state on the optical properties of BC in the real ambient atmosphere, this study uses an established parameterization scheme to quantify the mixing state heterogeneity of black carbon particles18,19,20. The differences and variations in BC heterogeneity in different ambient air conditions are revealed, and the impact of particle-particle heterogeneity on the light absorption enhancement of BC is discussed.

Results and discussion

Overview of the measurement results

The field campaigns at each site lasted approximately 10 days, and the typical levels of air pollutants, temperature, and RH were summarized in Table 1 and Supplementary Fig. 1. As a typical background site, YL has much lower PM1, SO2, and NOx level compared to suburban CP and urban PKUERS. Although the median levels of O3 were similar at YL and CP, the distribution of O3 at CP was much wider compared to YL. The O3 concentration at PKUERS was the lowest among the three sites, possibly due to the combination effect of low solar radiation in winter and titration with NO in the urban atmosphere. There were no extreme events or precipitation during the campaigns, ensuring that the measurements taken at YL, CP, and PKUERS were representative of typical background, suburban, and urban conditions, respectively. The time series of BC number and mass concentration is shown in Supplementary Fig. 2, and it exhibited a consistent trend when compared to the time series of PM1 mass concentration (Fig. 2g, h, i). The mass fraction of BC particles in PM1 is between ~5 and 10%, with no statistically significant difference observed among the three sites. In the subsequent context, we will focus on the mixing state properties of BC particles.

Table 1 Summarization of field campaigns at three sites.
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BC particles are emitted from various sources and undergo distinct atmospheric processes, leading to significant regional differences in their mixing states. In this study, Fig. 1 presents the histogram of the mixing state index χ measured under three different ambient atmospheres, each displaying a distinct distribution. We found that the heterogeneity of BC was a ubiquitous phenomenon as different BC-containing particles have different non-BC to BC ratios. The background station YL exhibited a mode of χ around 0.62, which fell in the middle range among the three sites. Additionally, the distribution ranged from 0.25 to 0.71, suggesting that the BC observed in the high-altitude background site had been influenced by multiple sources. On the contrary, the histograms of χ in urban (PKUERS) and suburban (CP) environments were narrower, indicating that BC sources in both regions had relatively single and steady profiles. The value of χ at PKUERS ranged from 0.5 to 0.75, consistent with the result observed in the winter of 2016 in Beijing20. Moreover, the χ distribution at the PKUERS site skewed to the left of the histogram mode at CP, indicating a more homogeneous mixing of BC in the polluted urban atmosphere. This can be attributed to the fact that BC had undergone more complete aging processes under heavily polluted atmospheric conditions, resulting in less variation in coating fraction among different black carbon particles.

Fig. 1: Frequency histograms of the BC mixing state index.
figure 1

Frequency histograms of the BC mixing state index χ at YL (a), CP (b), and PKUERS (c).

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In the high-altitude background site YL station, the main source of BC was long-range transport from surrounding regions or vertical upwelling from emissions at lower altitudes21,22. The heterogeneities of BC from different air masses behave distinctively. The value of χ was around 0.7 in the early stage (March 23 to 29, 2015) of the field campaign, which subsequently dropped to 0.3 towards the end of the campaign. χ and PM1 show similar trends during the campaign (Fig. 3a, g). According to back trajectory results, the observed high PM1 concentration was attributable to air masses transported from South Asia, where biomass burning events occurred frequently over that period, while no dominant source was identified during other times23. The high χ observed during the early campaign implies that BC mixed more homogeneously from a single strong source rather than multiple sources. At the later stage of the campaign, χ was lower and became noisier. Regarding the diversity of single particles, Dα shows a slight downward trend, which is similar to χ, being higher at the start and lower at the end. For population diversity parameter, Dγ and χ exhibit a noisy pattern observed in the later stage at YL, while no obvious trends were observed before March 28, 2015. As Dγ was determined by the bulk mass fraction of non-BC to BC mass ratio, the overall ratio of them changed significantly over that time in a clean background atmosphere. We found the mixing state index of BC (χ) under background conditions was dominated by the difference in BC material contribution at the population level, especially at the end of the campaign. To address the issue of noisy data in the later stages of the campaign, primarily arising from the low number/mass concentration of BC-containing particles, potentially resulting in statistically insignificant results, we opted to exclude data points with less than 0.10 μg m−3 of BC (equivalent to ~2 μg m−3 of PM1) in the subsequent analysis. Additionally, χ showed a similar trend with Fthick in Fig. 2a, g, suggesting Fthick may represent the heterogeneity of BC to some extent.

Fig. 2: Time series of BC mixing state parameters during the measurements.
figure 2

Time series of the BC mixing state parameters (χ, Dα, Dγ, and Fthick) and PM1 mass concentrations at YL (a, d, g), CP (b, e, h), and PKUERS (c, f, i) sites.

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In suburban site CP, it was found that the variation of χ was smaller in comparison to the variations at YL, as shown in Fig. 2b. There was also no significant contrast in χ when the ambient air was clean or moderately polluted, suggesting the pollution level in suburban atmosphere did not have a direct impact on mixing state of BC. However, both Dα and Dγ in Fig. 2e were slightly higher on clean days than under polluted conditions, and they exhibited a clear diurnal variation, also shown in Fig. 3. The value of χ decreased from midnight until 7 am, reaching its minimum value at that time. It then gradually increased till 3 pm, after which it remained relatively high until midnight. The diurnal cycle of χ was the opposite of the mass concentration of thinly coated BC (fresh BC), suggesting that primary emissions dominated the heterogeneity in this region. When primary emissions (e.g., vehicle emissions) were active, the concentration of fresh BC increased dramatically. There was a significant difference in the coating mass fraction between fresh BC particles and background BC, which had undergone a high degree of aging. This difference increases the mixing state heterogeneity of BC (lower χ).

Fig. 3: Diurnal variations of BC mixing state parameters.
figure 3

Diurnal cycles of the BC mixing state index χ and fresh BC number concentration (a), the average particle species diversity Dα (b), and the bulk population species diversity Dγ and the fraction of thickly coated BC particles (c) at CP site. The shading represents the interquartile range of the observation.

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Dα and Dγ exhibit similar diurnal trends, with higher levels at night and lower levels during daytime (Fig. 3b, c). However, their patterns were not identical. Dα presents a continuous downward trend from 0 am to 9 am, reaching its lowest point around 10 am and then beginning to rise again. On the other hand, Dγ exhibits a sharp downward trend from 7 am to 12 pm and stays at a lower level until 1 pm. During the night, between evening and morning rush hour, Dγ maintained a relative stable level, suggesting the mass fraction of BC to the overall particle mass did not change much. The population diversity parameter Dγ strongly depends on the fraction of thickly coated BC, which is inferred by a contrary trend of daily variations between Dγ and Fthick in Fig. 3c.

The fresh BC (thinly coated) became aged and transformed into thickly coated BC after the morning rush hour, reducing the diversity of BC particles. As the day progressed, the proportion of thickly coated BC continued to increase, reaching its peak in the afternoon. It was likely due to the joint effect of photochemical aging and the weakening of primary emissions. During the evening rush hour (5 pm to 9 pm), accompanied by slower photochemical activities, the proportion of Fthick increased, leading to a slight increase in the heterogeneity (lower χ) of BC particles.

During the campaign at urban site PKUERS, three pollution episodes were encountered, and the corresponding χ value increased during the period with high PM. The diurnal cycle of χ at the PKUERS shares some similarities with those at the CP site, with minimum value in the morning rush hour and gradually increasing to the maximum value in the afternoon (Supplementary Fig. 3). But their nighttime behaviors were different: χ remained a lower value at PKU during nighttime, while CP kept in a higher level. A possible explanation for the discrepancy is the seasonal difference. Besides vehicle emissions, biomass burning and coal combustions produced a considerable amount of BC in winter in Beijing, resulting in a less homogeneous mixing state of BC than BC from vehicle emissions in rush hours. In contrast to χ, Dα and Dγ were slightly higher on clean days. The trough of Dα and Dγ coincided with the peak of χ at PKUERS (Fig. 2b, e) and CP (Fig. 3c, i), whereas χ and Dα at the YL site share a similar trend (Fig. 2a, d), suggesting that the dominant factor was not the same in different regions.

In urban and suburban areas, the heterogeneity of BC (χ) not only depends on the air pollution level but also relies on primary BC sources, for example, vehicle emissions and aging processes, and displays a clear diurnal variation. Whereas under background conditions like the YL site, χ strongly depends on the original of air masses; when air masses came from long-range transport of polluted region, χ increased, meaning the BC mixed more homogeneously.

The relationship between BC diversities and Fthick

Figure 4 shows the correlation between the BC mixing state index χ with the thickly coated fraction Fthick. The χ was strongly correlated with Fthick at YL. At the beginning of the campaign (blue points in Fig. 4a), whose particles originated from long-range transport, χ and Fthick exhibit an even better correlation. When the air was clean at the end of the measurement, χ and Fthick were distributed more scattered but still increased simultaneously. However, χ and Fthick have a weak correlation at CP (Fig. 4b). The variation of Fthick during the campaign ranged from 0.1 to 0.65, but χ only changed from 0.4 to 0.6. The weak correlation suggests χ did not vary significantly when Fthick changed over a large range in environments like CP. At night (dark red and blue in Fig. 4b), Fthick was relatively small and had a greater variability, suggesting that CP site were influenced by complex nighttime BC emissions. At PKUERS, χ was moderately correlated with Fthick. The distribution of χ is more scattered when Fthick is small. Low Fthick also matched the period with a low level of air pollution, suggesting BC particles mixed less homogenous. In spite of different degrees of correlation between χ and Fthick, χ generally shows an upward trend with Fthick in all cases measured in this study.

Fig. 4: Relationships between BC mixing state parameters.
figure 4

Scatter plots between the BC mixing state index χ and Fthick at YL (a) color-coded by date, at CP (b) color-coded by hour of day, and at PKUERS (c) color-coded by PM1 mass concentration.

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According to the calculation steps for χ provided in Table 1, BC diversity parameters in terms of both single particles (Dα) and population (Dγ) codetermine the heterogeneity of BC mixing state χ. Although the χ increases with Fthick at three sites (Fig. 4), three regions have totally different relationships between BC diversities (Dα or Dγ) with Fthick during campaign periods, as shown in Fig. 5. At YL, single particle diversity parameter Dα positively correlated with Fthick, but the relationship between population diversity parameter (Dγ) was not apparent. However, in urban and suburban atmosphere, both Dα and Dγ show a negative linear relationship with Fthick. The discrepancy implies that the dominant factor of BC heterogeneity was different under disparate atmosphere, but all associated with Fthick. In addition to Fthick, RBC was also a commonly used parameter describing the bulk property of BC mixing state. RBC and Fthick exhibit a strong positive correlation at CP and PKUERS but no relationship at YL at all (Supplementary Fig. 4). As both RBC and χ were correlated well with Fthick at PKUERS, RBC and χ exhibit a strong correlation (Supplementary Fig. 5), which was also reported in a previous study in winter of 2016 in Beijing. However, RBC and χ distributed very scattered in the summer of 2017 in Beijing, and they concluded RBC cannot used as a metric to predict the variation of χ in summer20. Intuitively, both Fthick and RBC will increase simultaneously when VOCs or any other gas phase precursors condensed on pre-existing BC-containing particles, making BC particle grow larger, like cases in urban or suburban area. Since BC had many distinct sources and had undergone atmospheric processing at varying extents, RBC and Fthick may not be closely related for all ambient conditions, just like the case observed at YL station. As Dγ was directly related to RBC, the relationship between Dγ and Fthick was opposite with it between RBC and Fthick (Fig. 5e, d, f and Supplementary Fig. 4).

Fig. 5: Relationships between BC diversities and number fraction of thickly-coated BC.
figure 5

Scatter plots between BC diversities (Dα and Dγ) and Fthick at YL (a, d), CP (b, e), and PKUERS (c, f), color-coded by PM1 mass concentration.

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The impact of heterogeneity of BC on light absorption enhancement

Figure 6 shows the time series of the light absorption enhancement (Eabs) and the mass ratio of coating material to BC (RBC) during the campaign period at YL. Eabs exhibits two distinct stages, corresponding to the two periods discussed in “Methods: Background site (YL)”: the period affected by transported pollution and the period with a clean background. Data after April 1, 2015, were removed as the extremely low BC concentration. Eabs was higher before March 28, 2015, fluctuating around 1.3. After that, Eabs began to decline and eventually dropped to less than 1.2. However, no consistent pattern was observed in the time series of RBC with Eabs, contradicting the power relationship proposed by Chakrabarty and Heinson12. Eabs and RBC initially exhibited nearly identical trends at the beginning of the campaign. However, after March 28, 2015, they started to diverge, with RBC showing more pronounced fluctuations. This indicates that simply attributing the changes in Eabs to the influence of RBC is inadequate and agrees with the findings of Cappa et al.8 that trends of Eabs and RBC do not always exhibit a consistent pattern.

Fig. 6: Times series of BC light absorption enhancement and coating mass ratio.
figure 6

Time series plot of Eabs and RBC at YL site.

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The scatter plot in Fig. 7 illustrates the correlation between Eabs and RBC during the campaign period at the YL site. As RBC increases, Eabs has an upward tendency but is more scattered. When RBC is less than 1, Eabs is mainly around 1.1, indicating that the absorption enhancement effect caused by the coating is not significant at low RBC level. When RBC increases to approximately 3, Eabs ranges from 1.1 to 1.3, suggesting that there are differences in the absorption enhancement effect under the same RBC. As RBC keeps increasing, the range of Eabs variation is even larger. Colors in Fig. 7 reveal that Eabs is larger with less heterogeneity of BC (larger χ) at a constant RBC value. Therefore, the light absorption enhancement of BC estimated based only on RBC can be biased without considering the mixing state.

Fig. 7: Relationship between BC light absorption enhancement and coating mass ratio.
figure 7

Scatter plot between Eabs and RBC at YL, color-coded with the BC mixing state χ.

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The data measured at YL were binned into intervals of χ value with the increment of 0.2 and fitted with a power function for each bin. As shown in Fig. 8a, power functions can map Eabs and RBC well for a small range of χ but are all lower than the case when BC particles were mixed homogeneously (gray line). As the value of χ gets larger, the increasing rate of Eabs with respect to RBC also becomes larger. The relative deviation of Eabs in Fig. 8b is increasing with respect to RBC and levels off at a large RBC value (logarithmic scale on the bottom axis). When RBC is less than 2, the overestimation of Eabs due to BC heterogeneity is less than 10%, while Eabs can be overestimated by 24% when RBC increases to ~10. This paper quantifies the influence of mixing state heterogeneity of BC on Eabs in the ambient atmosphere and finds that this effect becomes more pronounced with increasing levels of RBC.

Fig. 8: Deviation of BC light absorption enhancement due to mixing state heterogeneity.
figure 8

a Data in Fig. 6 are binned into intervals of χ value with the increment of 0.2. Solid gray line was the case when all BC particles were mixed homogeneously with χ = 1. Dotted lines were the fitting line of binned data with power laws. b The relative deviation of Eabs with RBC at YL between two extreme cases, which are homogeneous mixing (χ = 1; gray) and the most heterogeneous case observed at YL (0.2 < χ < 0.4; blue).

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For results at CP and PKUERS, the variation of χ was small compared with them at YL, and therefore Eabs only varies a small range for a fixed RBC (Fig. 9). RBC at two sites has a similar magnitude but is slightly higher in a more polluted environment: RBC at CP spans from 1 to 5, while it at PKUERS ranges from 2 to 7. The relationship between RBC and Eabs is more pronounced and exhibits a power relationship in both regions since χ did not change significantly at either CP or PKUERS. However, Eabs of BC at both sites were smaller than in cases where BC was mixed homogeneously with other components. Scatter plots in Fig. 8 show narrower distributions at urban and suburban sites, compared with the result at background site YL. In other words, Eabs varies less with the same RBC but still indicates that the light absorption of BC is amplified by coating materials. At PKUERS with larger χ in general, Eabs is higher than CP with a similar RBC range. Our observational results provide empirical evidence aligning with previous theoretical studies, showing that the overestimation of black carbon’s (BC) light absorption is influenced by mixing state heterogeneity. This finding bridges the gap observed between modeled and actual field-measured Eabs, resolving a key discrepancy in existing research8,15,16. All results indicate that the Eabs of BC is overestimated if not considering the heterogeneity of BC. Therefore, the most current models simply assigned a fixed enhancement factor to BC absorption by assuming BC particles were coated uniformly may result in overestimating its absorption and radiative effect.

Fig. 9: Less variations in BC light absorption enhancement in suburban and urban environments.
figure 9

Scatter plots between Eabs and RBC with CP data (a) and PKUERS data (b). Data were color-coded with χ. Orange and red lines are data fitted with power functions, and gray lines assume all BC-containing particles were mixed homogeneously at two sites.

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Methods

Description of ambient monitoring sites

In this study, extensive field campaigns were carried out at three distinct sites, each representing a specific atmospheric environment: background, suburban, and urban. The geographical positions of these sites are depicted in Supplementary Fig. 6.

Background site (YL)

The Yulong Snow Mountain in Lijiang, Yunnan, China, was chosen as the representative background condition for this study. The ambient monitoring station (YL; 27.23 °N, 100.25 °E, 3410 m above sea level) was located in the transitional zone from high to low terrain at the southeastern edge of the Qinghai-Tibet Plateau. Its location connected South Asia and Southeast Asia with the Yungui and Tibet Plateau regions of China, creating a potential pathway for the transport of atmospheric pollutants from South Asia and Southeast Asia into China. The field campaign at the YL background site was conducted from March 23 to April 4, 2015, coinciding with the pre-monsoon season in the region. Previous studies have documented frequent occurrences of biomass-burning events in South Asia and Southeast Asia during this season, and the resulting air masses, influenced by the prevailing southwest monsoon winds, were observed to be transported to the Qinghai-Tibet Plateau24,25,26,27.

Suburban site (CP)

The suburban site (CP; 40.24 °N, 116.19 °E) was situated on the roof of the main teaching building (~12 m above ground) at Changping Campus, Peking University, Beijing, China. The campaign at CP took place between May 16 and 25, 2016, during which the average temperature was recorded as 21.8 °C and the relative humidity (RH) was 38.8%. CP, as a typical suburban site, was affected by both natural sources and urban anthropogenic activities28,29. The site was located approximately 38 km northwest of central Beijing, with mountainous regions surrounding it on the east, north, and west, covered by extensive green vegetation. Notably, there were no prominent industrial sources in the nearby vicinity.

Urban site (PKUERS)

The Peking University Urban Atmospheric Environment Monitoring Station (PKUERS; 39.99 °N, 116.31 °E) was located on the rooftop of an academic building (~20 m above ground) at the main campus of Peking University in the northwest of Beijing, China, was selected as the urban location for this study. The campaign took place from January 21 to February 3, 2015, with an average temperature of 0.8 °C and a RH of 27.6%. The prevailing wind direction during the campaign was from the north, and the wind speeds remained generally low, averaging at 2.2 m s−1. It is worth noting that there were no obvious emission sources in the vicinity of the site, except for Zhongguancun North Street, which was around 200 m east of the site. The traffic restrictions were slightly stricter within the Fifth Ring Road in Beijing, where PKUERS were located. For example, heavy-duty trucks were prohibited from entering the area enclosed by the Fifth Ring Road except between midnight (23:00) and the following day morning (6:00). The PKUERS has been actively monitoring ambient air quality for over a decade, equipped with a range of advanced instruments. The data obtained from this site have provided valuable insights into air pollution in Beijing, as evidenced by previous studies9,29,30,31.

Instrumentation

The refractory BC (rBC, or just BC) containing particles were measured by a Differential Mobility Analyzer (DMA, Model 3081, TSI Incorporated, Shoreview, MN, USA)–Single Particle Soot Photometer (SP2, Droplet Measurement Technologies, Longmont, CO, USA) tandem system, and the system setup was illustrated in Supplementary Fig. 7. The detailed description of the DMA-SP2 has been discussed in Zhao et al.32 and Zhao et al.19. Briefly, the DMA scans aerosol size (electrical mobility diameter, Dp) from 12.3 to 749.9 nm in a 5-min cycle, and the SP2 filters out BC-containing particles as BC-containing particles are heated to the point of incandescence when passing through a 1064 nm Nd:YAG laser beam. The induced incandescence signal is nearly proportional to the amount of refractory material (mainly BC). Then, the mass of the BC content (core) can be used to calculate the mass equivalent diameter (DMEV or Dc for simplicity) for each BC-containing particle by assuming a density of 1.8 g cm−3. The SP2 was calibrated using Aquadag, and a correction factor of 0.75 was applied to account for the higher sensitivity of SP2 to Aquadag compared to ambient BC particles33. The delay time between the DMA and SP2 was synchronized by the pulse generated by the voltage retrace of the DMA. The correction for the effect of multiple charging was applied using the method proposed by Zhao et al.32. BC-containing particles were distinguished as attached-type and coated-type following steps proposed by Dahlkötter et al.34. Only coated-type BC particles (>85%) were the subsequent analysis assuming them to be spherical particles. Based on the calibration, the lower detection limit for single BC mass was determined to be 0.32 fg, corresponding to a Dc of 69.7 nm. Therefore, only particles with Dc greater than 69.7 nm were discussed in the subsequent analysis.

Non-refractory chemical compositions of ambient aerosols were measured by a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS; Aerodyne Research Inc., Billerica, MA, USA). The detailed setup of the instrument and data processing methods were reported in Zheng et al.27. The mass concentration of submicron particles (PM1) was estimated by the sum of non-refractory components and refractory BC, serving as an indicator of the air pollution level.

The mixing ratio of trace gases was measured by gas analyzers (43i for SO2, 42i for NOx; 49i for O3; Thermo Fisher Scientific, Waltham, MA, USA), and meteorology conditions, including temperature, RH, wind speed and wind direction, were measured by sensors manufactured by Met One Instruments Inc., USA.

Description of BC mixing states

Fraction of thickly coated BC (Fthick)

Different amounts of coating on BC-containing particles can lead to varied responses in the SP2, as indicated by the lag time between the peaks of the scattering signal and the incandescence signal35,36. The lag time histogram exhibited two modes for this study, and the split point between the two modes ranged from 1.2 to 1.6 μs. BC-containing particles with a larger lag time were classified as thickly coated BC, whereas particles with a smaller lag time were considered as thinly coated BC. The fraction of thickly coated BC within a specific timeframe is denoted as Fthick. Thinly coated BC can be considered fresh BC, whereas thickly coated BC represents aged BC. The classification result for this dataset has been confirmed in our previous study37. This parameter does not require any assumption and complex calculation, and can be compared with many studies38,39,40,41,42.

Mass ratio of non-BC component relative to BC (RBC)

The mass ratio of non-BC component relative to BC (RBC) is a widely used bulk property characterizing the BC mixing state11,43. We assume that the fraction of each species within the BC coating was proportional to their ambient concentrations, and the densities of each component was obtained in Barnard et al.44. The mass of non-BC components within individual BC-containing particle was estimated with the coating volume, chemical compositions, and the respective density for each species.

Mixing state index of BC (χ)

This study employed the BC mixing state index (χ) developed in previous study to quantify the heterogeneity of BC mixing state18,19,20. This method utilized the concept of diversity from ecology45, and simplified the BC mixing system into a binary system by considering only BC and non-BC components. The BC mixing state index χ can be calculated using the equations listed in Table 2, and it is determined by Dα and Dγ jointly. Dα represents the average particle species diversity parameter, which reflects the diversity of BC mixing states on a single particle level. In contrast, Dγ is a parameter representing the bulk population species diversity. By definition, Dγ is determined by the mass ratio of BC to the total mass, ranging from 1 to 2, while Dα ranges from 1 to Dγ. Consequently, χ varies between 0 to 1. χ = 0 indicates that BC and non-BC components are mixed nearly as external-mixing, while χ = 1 implies that they are mixed homogeneously. Similar to χ, the diversity parameters of BC, either on single particle level (Dα) or population level (Dγ), are lower (close to 1) indicating a higher level of diversity in the mixing of BC.

Table 2 Variables and equations for calculating the BC mixing state index χ19.
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Light absorption enhancement of BC

The light absorption of both overall BC-containing particles and the corresponding BC cores was calculated using Mie theory at 550 nm46. In this study, a perfect core-shell model was assumed, where the BC core and the entire particle were considered spherical, with the core positioned at the center of the particle. The refractive index (RI) of BC core was set to 1.95 – 0.79i47, which is close to the value of engine-emitted BC in visible wavelengths reported by a recent study. The RI of coating material was determined as the volume average of RI of various chemical species reported in the literature44. The light absorption coefficient of BC cores and BC-containing particles were obtained by integrating particle number concentration measured by the DMA-SP2 system across the entire size range (e.g., size distributions for each campaign are shown in Supplementary Fig. 8), and the absorption enhancement (Eabs) of BC-containing particle was derived by the ratio of light absorption of the overall particle and BC core only.