ABSTRACT This study explores how the mixing structures and coating compositions of black carbon (BC) particles influence their light absorption, focusing on liquid-liquid phase separation

(LLPS), which separates organic and inorganic phases and redistributes BC from the inorganic core (Icore) to the organic coating (Ocoating). Using transmission electron microscopy and

3D-modeling, we found that the BC core’s position significantly impacts its light absorption. A BC core embedded within the Icore shows stronger light absorption at wavelengths below 600 nm

compared to the same core in the Ocoating. When Ocoating is considered as brown carbon (BrC), it reduces BC core’s light absorption at 350 nm due to shielding effect, but its overall impact

CARBON AEROSOLS Article Open access 02 June 2022 OVERESTIMATION OF BLACK CARBON LIGHT ABSORPTION DUE TO MIXING STATE HETEROGENEITY Article Open access 02 January 2024 UNIFIED THEORETICAL

FRAMEWORK FOR BLACK CARBON MIXING STATE ALLOWS GREATER ACCURACY OF CLIMATE EFFECT ESTIMATION Article Open access 10 May 2023 INTRODUCTION Black carbon (BC, also known as soot), emitted from

incomplete combustion of biomass and fossil fuel, influence global climate by absorbing solar radiation, altering cloud properties, and accelerating the melt of ice cover1,2,3. Due to the

strong light absorption and heating properties, BC became the major warming agent after greenhouse gases. The IPCC report “Climate Change 2021” showed that the effective radiative forcing of

BC is +0.11 W m–2 with the uncertainty ranges from –0.20 to +0.42 W m–2 over the global4. Significant uncertainties are primarily attributed to size distributions, chemical compositions,

and mixing states of BC particles, which depend on the chemical and microphysical evolution during atmospheric processes5,6,7,8. Climate models typically assume that BC particles are

spherical and divide them into uncoated (external‐mixing structure) or concentrically coated (core‐shell structure)9. However, these simplified assumptions fail to effectively explain the

observed optical properties of BC particles10,11,12,13, with uncertainties in light absorption enhancement (Eabs) ranging from 14% to 150%2,14,15. The reason is that the actual BC particles

have three‐dimensional agglomerates with tens to hundreds of monomers and their position embedded within the host particle is complicated, such as in the center or at the surface of host

particle16,17. Recent advancements in BC morphology and its mixing structures have provided new insights into the complex interactions within aerosols8,11,18. Once BC cores were internally

mixed with other aerosols, their morphology became more compact, leading to significant changes in their optical properties and radiative forcing11,19,20. The coatings and embedding

materials of BC particle were often considered as secondary inorganic matters (e.g., nitrates and sulfates). When BC cores are coated by these non-light-absorbing aerosols, their Eabs

fluctuates from 1.06 to 3.514,21 due to the “lensing effect”. However, this assumption may not be true in ambient air, where abundant organics mixing with secondary inorganic species can be

coating. Secondary organic aerosol (SOA) is a major component of PM2.5, contributing 30–77% of the total mass during heavy pollution events22,23. It is known that a large part of SOA behaves

optical absorption in short wavelength (<400 nm) to near infrared, which has been called as secondary brown carbon (SOABrC)24,25,26. Some studies found the Eabs of BC core decreases due

to the “shielding effect,” as the light-absorbing coating blocks more photons from reaching the BC core27,28,29. Lack et al.30 showed that the shielding effect can reduce the Eabs by 25%

across the visible spectrum, and specifically by 40% at 400 nm. They also found that coating thickness or imaginary part of complex refractive index (RI) of the BrC control their shielding

effect28,31. However, previous studies primarily focused on the core-shell structure and assumed the coating to be light-absorbing materials to account for shielding effects. This assumption

cannot reflect the real mixing structure of BC and SOABrC in the atmosphere. Many studies well recognized inorganic and organics coatings on BC particles in ambient air16,32,33. Under

relative humidity (RH) < 90%, the unique phenomenon of liquid-liquid phase separation (LLPS) that organic and inorganic species separating in individual particles can frequently occur in

ambient air34. Recent studies found that the LLPS can further cause BC redistribution in individual particles32,34. In other words, position of BC within individual particles responses to

the LLPS, driven by its higher affinity for the nonpolar organic phase compared to the electrolytic inorganic phase34. The scientific question here is: how are the optical properties of BC

influenced by double-layers coating (hereinafter referred to as LLPS) and BC redistribution? Zhang et al.32 showed that the optical absorption of the LLPS increased 8.2–9.4% compared with

core-shell structure. Furthermore, BC redistributing from inorganic to organic coating reduced 28–34% of light absorption at 550 nm32. Until now, no study has examined the coating mixture of

inorganic and brown organic aerosols (i.e., SOABrC). In this study, we analyzed transmission electron microscope (TEM) images of individual particles to determine the actual mixing

structures between BC and SOA in ambient air. A novel 3D modeling approach (Electron-Microscope-to-BC-Simulation, EMBS11) was employed to measure how the different microphysical properties

(i.e., variations in BrC coating thickness and the position of BC) influence the optical absorption of aged BC particles. Based on the unique phenomenon of LLPS, our study aims to

investigate the optical properties of actual mixing structures of BC/inorganic/organic during atmospheric aging. The focus is primarily on the shielding effects of SOABrC on aged BC

particles with LLPS. RESULTS OPTICAL PROPERTIES OF BC COATED BY NON-LIGHT-ABSORBING SOA The LLPS significantly influences the microstructure of aerosol particles by separating organic from

inorganic materials, which even redistributes BC from the Icore (Fig. 1A-iii) to the Ocoating (Fig. 1A-iv). The BC redistribution significantly alters the optical absorption of aged BC

particles, reducing light absorption by 28–34% at 550 nm32. Figure 1A shows these transformations through four distinct mixing structures: BC, CS, PS-CS, and R-CS models. To understand the

non-light-absorbing SOA (SOAclean)/SOABrC effects on light absorption of individual particles, three various thicknesses—thin, moderate and thick—were applied to both PS-CS (1.2, 7.0 and

12.8 nm) and R-CS (69.6, 139.2 and 208.8 nm) models. While our study fixed BC morphology to isolate the effects of LLPS, previous study has shown that BC particles undergo morphological

compaction during atmospheric aging35. Specifically, the capillary forces, induced by the interaction of BC with liquid coating, can lead to the compaction of BC aggregates36. This

restructuring, driven by the surface tension of the coating material, reduces the voids between monomers, potentially altering the internal structure of the BC aggregates and influencing

their optical properties. Therefore, future work should explore how surface tension gradients, induced by phase separation, might further influence BC morphology and its subsequent optical

behavior. The Absorption Ångström Exponent (AAE) reflects how light absorption of aerosol varies with wavelength37. Here we adopted wavelength at 400 nm as the starting point, which is

commonly used in field observations of aerosol optical properties30. Figure 1B displays the variations of the AAE from 400–700 nm across four particle structures with the increased SOA

thicknesses. For the CS structure, the AAE increased by 45.2% compared with the bare BC. When CS is coated by SOAclean, the AAE of PS-CS particle is positively correlated with the coating

thickness, resulting in an increase of 45.9%–50.6% compared to BC. When BC is redistributed in organic coating, its AAE exhibits a reduction ranging from 37.6% to 91.9% compared to that of

PS-CS particles. The R-CSmoderate particle, which experiences the most significant reduction in AAE, has an AAE that is only 12% of that of bare BC particle. Figure 1B shows that BC core

coated by the sulfate or multi-coatings of sulfate and SOAclean increase the AAE, suggesting that the difference of light absorption between short and long wavelengths becomes greater. On

the contrary, BC core embedded in organic coating shows one minimal AAE, suggesting that the BC redistribution either blocks short-wave absorption or enhances long-wave absorption, thereby

equalizing light absorption across 400–700 nm and reducing AAE. Once the ratio of SOA coating thickness to BC core size (TOD/DBC) is greater than 0.2432, the BC redistribution due to LLPS

can be observed. To confirm how this impact of BC position changes its optical absorption, we compared the light absorption of PS-CSmoderate and R-CSmoderate particles across 350–700 nm. The

dashed line shown in Fig. 1C represents the scenario where the SOA does not absorb radiation. The light absorption of R-CS particle is weaker than that of PS-CS particle in the near

ultraviolet band, amounting for only 84.5% of PS-CS at 400 nm. Meanwhile, the light absorption of R-CS particle at 700 nm is 1.7 times that of PS-CS particle (Fig. 1C). This Cabs change

trend of R-CS particle is similar to that of “bull horn”, which leads to a notably smaller difference in the light absorption of R-CS particle between 400 nm and 700 nm compared to the PS-CS

particle (Fig. 1C). The result confirms our conjecture that the BC redistribution blocks short-wave absorption and enhances long-wave absorption. The Cabs of PS-CS and R-CS particles

intersect at approximately 580 nm (Fig. 1C). This indicates that the light absorption of BC core centered in Icore is stronger below 600 nm, while the light absorption of BC core in the

Ocoating is slightly enhanced above 600 nm. Figure 2A shows the Eabs of CS, PS-CS and R-CS particles in the SOAclean scenario. The structures of CS and PS-CS particles show no significant

difference, and thereby their Eabs for CS and PS-CSthin should be same (Fig. 2A). For the three thicknesses of R-CS particles, an enhanced trend of light absorption is observed above 600 nm.

The result shows that entire BC particle exhibits stronger light absorption in the larger wavelength when BC core is located in organic coating. Figure 2C illustrates that the average Eabs

of R-CS particles with three different thickness at short wavelengths is lower than them of CS and PS-CS structures. The comparison further confirms our above consumption that the BC

redistribution reduces its light absorption at short wavelengths. OPTICAL PROPERTIES OF BC COATED BY LIGHT-ABSORBING SOA The above section explored the optical properties of the four mixing

structures coated by SOAclean. When we consider SOA as light-absorbing secondary BrC (SOABrC), how does the SOABrC change the optical properties of BC? The presence of SOABrC that strongly

absorbs near-ultraviolet light results in higher AAE values for PS-CS and R-CS particles (Fig. 1B). Moreover, the AAE increases significantly as the increased thickness of SOABrC. The AAE

values of CS, PS-CS, and R-CS structures are 1.3, 1.5 ± 0.2, and 3.7 ± 1.0, respectively. This increased AAE suggests that more BrC leads to a greater AAE. Figure 1C in above section shows

the variation of light absorption across the visible spectrum, controlled by the lensing effect at different BC positions. When SOA is light-absorbing BrC, its light-absorbing contribution

contains the lensing/shielding effect and the intrinsic light absorption of BrC itself. To focus on how the BC position affects light absorption, it is necessary to eliminate the intrinsic

light absorption of SOABrC. For this purpose, we define ΔCabs as the difference between the Cabs of PS-CS and R-CS particles and their corresponding particles without BC core (ΔCabs in Fig.

S1). In other words, ΔCabs represents the absorption cross-section attributed solely to the lensing/shielding effect while the intrinsic light absorption of BrC was removed. By comparing the

ΔCabs of the SOABrC scenario with the Cabs of the SOAclean scenario, we can better understand the specific impact of the shielding effect of SOABrC. For PS-CS particles, the light

absorption decreases by 1.8% at 350 nm due to the SOABrC, suggesting the shielding effect of BrC coating. We noticed that the shielding effect of SOABrC on PS-CS particle is almost

negligible at wavelengths greater than 400 nm. This result is consistent with the findings of Lack et al.30, who observed that the optical behavior of thin SOABrC were more like SOAclean as

the wavelength increases. For R-CS particles, the shielding effect of BrC is more efficient at wavelengths below 500 nm, with the largest decline of 49.8% occurring at 350 nm. The result is

similar to 50% at 400 nm reported by Lack et al.30. Figure 2B, D shows that the light absorption enhancement of BrC coating highly depends on wavelength. For wavelength at 350 nm, the

R-CSthick model exhibits a Eabs peak at 42.0, which exceeds the range of 3.0–5.0 from PS-CS particles and 2.9 from CS particles. The thick BrC coating undoubtedly becomes the main source of

light absorption of R-CS particles at 350 nm. With the increase of wavelength, the light absorption of R-CS particles is reduced by 90% at 600 nm, with the most significant reduction between

350 nm and 450 nm (74% reduction) (Fig. 2D). Following the wavelength >600 nm, there is negligible contribution from BrC coating thickness to light absorption of individual particles,

and the Eabs of CS, PS-CS and R-CS particles are all close to 2.7 ± 0.7 (Fig. 2B). LIGHT ABSORPTION OF BC, BRC AND LENSING/SHIELDING EFFECT IN LLPS PARTICLES The sections above examine the

impact of SOA thickness, BC position, and SOABrC coating on light absorption of entire BC particles during the LLPS. However, AAE and ΔCabs/Cabs are both influenced by multiple

light-absorbing components within each particle. To clarify the contribution of each component, we adopted the calculation method described in Section “Optical absorption of aged BC

particles”. This method distinguishes the intrinsic light absorption of BC core and SOABrC themselves, as well as the lensing or shielding effects of sulfate and SOAclean/SOABrC. For

SOAclean scenario, there are lensing effects of sulfate and SOAclean and BC core (Fig. 3A). Because SOAclean and sulfate are non-light-absorbing materials, the light-absorbing contribution

of CS and PS-CS structures are highly similar. Therefore, CS and PS-CS structures both exhibit a higher proportion of lensing effect (red bar) at wavelength below 600 nm, at 63.8% and 64.5%,

respectively (Fig. 3A). It should be noted that lensing effects are significantly reduced at wavelength above 600 nm, with 57.1% and 56.9% of CS and PS-CS, respectively (Fig. 3A). In

conclusion, the phase separation does not significantly alter the lensing effect of LLPS particles in the SOAclean scenario. However, when BC redistributes, it has an obvious decrease on the

light absorption of LLPS particles. Compared with CS and PS-CS models, light absorption of R-CSthin model is reduced by 48.6% and 47.5%, respectively (Table S3). The reason may be related

to the sudden drop of lensing effect caused by BC redistributing to the thin SOAclean coating (Table S4). Figure 3A demonstrates that the R-CSthin particles are the only structure

predominantly influenced by BC core, the average contributions of BC core exceeding 50% across 350–700 nm. Unlike the other structures, the R-CSthin particles exhibit distinct light

absorption characteristics that the contribution of lensing effect is unstable, reaching a minimum of 19.8% at 350 nm and a maximum of 57.4% at 550 nm (Fig. 3A). As the SOAclean coatings

become thicker, the lensing effect of R-CSmoderate and R-CSthick model contributes more than 64.2% like as that of CS and PS-CS models. This result indicates that the lensing effect is more

influenced by coating thickness than by the BC position, whether it is located at the outer Ocoating or the inner Icore. Figure 3B displays the contribution of each light-absorbing component

in the scenario of SOABrC. Due to the absence of SOABrC, the contribution of light absorption in the CS structure remains unchanged and is the same as in the SOAclean scenario. As SOABrC

appears and gradually thickens, its light-absorbing contribution in the ultraviolet band becomes significant. At the wavelength of 350 nm, the contribution of SOABrC in PS-CS particles

increases from 5.2% to 49.5% as the SOABrC coating becomes thicker (Fig. 3B). For the R-CS structure, the contribution of SOABrC remains even above 96.3% at 350 nm. However, when the

wavelength increases, the light absorption of SOABrC diminishes, with contributions in PS-CSthick and R-CSthick particles dropping to less than 0.11% and 4.6% at 700 nm, respectively (Fig.

3B). Previous studies confirmed the shielding effect of light-absorbing coating in CS structure27,28,29,30. Our study found that the shielding effect in LLPS particles is more complex. A net

shielding effect under the coating of sulfate and SOABrC in the LLPS particles simultaneously required a sufficiently thick BrC coating and near-ultraviolet wavelengths. We found that the

net shielding effect occurs only at 350 nm when the thick coating of SOABrC induces BC redistribution (i.e., R-CS structures). Figure 1C illustrates that the shielding effect of BrC coating

in R-CS can reduce light absorption of BC core by 49.8% at 350 nm. Accounting for the light absorption of BrC itself and BC core, the contribution of BrC shielding effect to R-CS particles

is merely –3.0% ± 1.6%. In other words, the primary light absorption effect of BrC coating in individual particles is to enhance light absorption, while the shielding effect is only a “side

effect”. This suggests that atmospheric models should incorporate the light absorption of BrC, as well as the enhancement in light absorption caused by the mixing structure of BC and BrC.

Moreover, the SOABrC in R-CS particles with the coating thickness at 69.6 nm, 139.2 nm, and 208.8 nm has similar shielding effects, with Cabs at –0.83 e–2 μm² (Fig. S2). To further verify

the robustness of our conclusions, we conducted sensitivity analyses on both BC core size (considering additional scenarios of 58 nm and 88 nm alongside the originally modeled 116 nm) and

the complex refractive index of BrC (introducing a highly light-absorbing BrC coating scenario in addition to the SOABrC and SOAclean scenarios. THE SHIELDING EFFECT OF BRC COATING ON BC

CORES OF VARYING SIZES We conducted sensitivity analyses to evaluate the shielding effect of BrC coating on BC cores of varying sizes. The results indicate that as the BC core size

decreases, the shielding effect becomes more pronounced at shorter wavelengths, particularly in R-CSthick particles (Tables S5 and S6). This is attributed to the relatively thicker BrC

coating surrounding smaller BC cores (Fig. S3, using R-CSthick particles as an example), which enhances the occurrence of the shielding effect. However, despite these variations, the overall

magnitude of the shielding effect remains relatively stable. The shielding effect exhibits only minor fluctuations, ranging from –3.0% ± 1.6% for BCESD = 116 nm to –1.4% ± 1.3% for BCESD = 

88 and 58 nm (Tables S5 and S6). These findings reinforce the conclusion that the primary role of BrC coatings in LLPS particles is to enhance light absorption rather than significantly

contribute to the shielding effect. IMPACT OF LIGHT ABSORPTION OF BRC COATING ON ITS SHIELDING EFFECT To explore the role of BrC coatings with varying complex refractive indices, we

introduced a highly light-absorbing SOA scenario. The results indicate that the shielding effect primarily occurs in redistributed (R-CS) particles, consistent with the findings from the

weakly light-absorbing SOA (SOABrC) scenario. The maximum shielding effect remains limited to –4.9% at 350 nm and gradually diminishes with increasing wavelength, eventually transitioning

into a lensing effect. Furthermore, highly light-absorbing BrC coatings in LLPS particles consistently dominate light absorption, contributing more than 89.3% at wavelengths below 500 nm.

Although minor variations in the refractive index introduce slight differences in the shielding effect at shorter wavelengths, the overall conclusion remains robust: BrC coatings in LLPS

particles primarily enhance light absorption rather than significantly contributing to the shielding effect. Results from Sections “The shielding effect of BrC coating on BC cores of varying

sizes” and “Impact of light absorption of BrC coating on its shielding effect” confirm that while these factors may slightly influence the occurrence of the shielding effect, the magnitude

of the shielding effect remains stable, reinforcing the conclusion that BrC coatings in LLPS particles primarily enhance light absorption. These findings suggest that the net contribution of

the shielding effect may be less significant than previously reported in the core-shell structure of individual particles containing BC, inorganic components, and secondary BrC. DISCUSSION

In this study, we classified four typical structures (e.g., bare BC, core-shell, phase-separated core-shell and redistributed) in LLPS particles to explore their subtle impact on the optical

properties of individual BC-containing particles. The size distributions and RIs of BC, sulfate, SOAclean and SOABrC were used to build mixing structures of BC-containing particles and

further calculate their optical properties. Our study shows that the BC position in individual particles significantly influences light absorption of BC. In CS and PS-CS models, the AAE is

1.33–1.39 across the 400–700 nm when BC core is situated within the Icore. The light absorptions of both CS and PS-CS decrease following the increased wavelength. However, AAE exhibits a

minimal value at 0.11–0.85 when BC core is embedded within the Ocoating. The variation trend of light absorption of the R-CS structure resembles that of a “bull horn”, where Cabs initially

decreases and then increases as the wavelength increases. This result suggests that BC distribution blocks short-wave absorption while enhancing long-wave absorption. Therefore, BC core

within the Icore and Ocoating exhibits higher light absorption below and above 600 nm, respectively. The variation of BC-containing particle’s light absorption arises from lensing effects of

sulfate and SOAclean, suggesting the lensing effect contributes the majority of their light absorption for CS and PS-CS particles. We also found that transition from the PS-CS to the

R-CSthin structure leads to significant fluctuations of light absorption with the contribution of lensing effect from 19.8% at 350 nm to 57.4% at 550 nm. We introduce a scenario of

light-absorbing SOA to discuss the impact of BrC coating on light absorption of LLPS particles. The shielding effect decreases light absorption by 1.8% at 350 nm in PS-CS model (Fig. 4). The

optical behavior of thin SOABrC is more like SOAclean and the shielding effect become more negligible above 400 nm. Following the increased thickness of SOABrC, it becomes the major

contribution of light absorption. The highest Eabs of R-CS structure is up to 12 times at wavelength of 350 nm compared with CS structure. Meanwhile, the BrC coating significantly reduces

light absorption of BC core by 49.8% at 350 nm in R-CS structure (Fig. 4). Therefore, the interaction between BC and BrC mixtures is more intricate than the previous reports, and the

core-shell model alone is inadequate to cover the actual optical properties of aerosol particles in the atmosphere. This study highlights that light absorption and shielding effect of aged

BC particles not only depend on the details of mixing structure of BC-containing particles but also involve the coating components (e.g., BrC) in the atmosphere. METHODS SAMPLE COLLECTION

AND MICROSCOPIC ANALYSES Aerosol particle samples were collected from four distinct locations to capture a range of environmental conditions. These included Mount Wudang in central China

(32°23′N, 111°02′E), at 862 meters, rural areas in northeastern China—Tongyu, Jilin (44°25′N, 122°52′E), and Yucheng, Shandong (36°57′N, 116°36′E) and a polar site in the Svalbard Arctic

Ocean (78°550′N, 11°560′E). Detailed sampling data, meteorological conditions, and other relevant information for each location are documented in Table S1. Individual particle samples were

collected onto copper TEM grids coated with a carbon film using a sampler at a flow rate of 1.0 L min–1. These TEM grids were analyzed using a JEM-2100 TEM (by JEOL, Japan) equipped with an

energy-dispersive X-ray spectrometry system (EDS, by Oxford Instruments, U.K.). TEM analysis showed morphology and mixing states of individual aerosol particles, while the EDS system

provided the details of elemental composition and the proportional weights of these elements. SHAPE MODEL GENERATION AND OPTICAL CALCULATION The LLPS may occur in aged BC particles

containing organic/inorganic aerosols under the RH < 90%. This process may result in BC redistribution, which migrates BC toward the organic phase. Zhang et al.32 found that the ratio of

SOA coating thickness to BC core size (TOD/DBC) influences the BC redistribution. When TOD/DBC is 0.24–1.8, most BC cores locate in organic coating (named as Ocoating). Conversely, most BC

cores locate in inorganic cores (named as Icore) under the TOD/DBC < 0.12. Here, we used the TOD/DBC of 0.01–0.12 and 0.24–1.8 for modeling BC-in-Icore and BC-in-Ocoating particles,

respectively. TEM identified four LLPS structures of individual BC particle (Table 1): bare BC model, basic core-shell model (CS, BC within the Icore without Ocoating), phase-separated

core-shell model (PS-CS, BC within the Icore), and redistributed model (R-CS, BC within the Ocoating). Our study categorized three thicknesses (thin, moderate, and thick) of the Ocoating for

both the PS-CS (TOD/DBC = 0.01, 0.06 and 0.11, respectively) and R-CS model (TOD/DBC = 0.6, 1.2 and 1.8, respectively). Except the SOA thickness, the diameters of BC core and sulfate core

kept constant, set as 116 nm32 and 432 nm32, respectively (the above diameters are all equivalent spherical diameters, ESD). To isolate the effects of LLPS-induced coating properties and BC

redistribution on the optical properties of BC particles, we also fixed the fractal dimension of BC to 2.1635 in all simulations. This approach ensures that the observed optical changes are

directly attributable to LLPS effects, without interference from potential morphological changes in the BC core that could independently influence light absorption. Luo et al.38 indicated

that variations in the imaginary RI of BC across different bands can be negligible. Consequently, this study assigned a constant value of 0.7139 to the imaginary RI of BC, while the RI of

SOABrC varies at different wavelengths (for more details, see Table S1). This EMBS model enables the flexible creation of aged BC particles including complex morphologies and mixing

structures to efficiently compute their optical properties under the incident light wavelengths (_λ_). The DDA model is critical to maintain the condition |m|kd <0.5, where “m” is the RI

and “k” is 2_π_/_λ_. To ensure accuracy within DDA, the dipole size used in this study is maintained well below the size of a monomer. Further details on this methodology are available in

Wang et al.11. OPTICAL ABSORPTION OF AGED BC PARTICLES When SOA is not light-absorbing and acts as scattering material (hereinafter called SOAclean), the _E_abs is calculated as:

$${E}_{{abs}{{\_}}{all}}=\frac{{C}_{{ab}{s}{{\_}}{{BC}}+{lens}}}{{C}_{{{ab}{s}{{\_}}{{BC}}}}}$$ (1) where Eabs_all is the sum of all light-absorbing components of individual particle

including BC core, lensing effect of Icore and SOAclean. Cabs_BC is absorption cross section for fresh BC core without any coating. Cabs_lens is light absorption of lensing effect. The

contributions of BC and lensing effect of Icore and SOAclean are as follow: $${f}_{{abs}{{\_}}{BC}}=\frac{{C}_{{ab}{s}{{\_}}{{BC}}}}{{C}_{{ab}{s}{{\_}}{{BC}}+{lens}}}$$ (2)

$${f}_{{abs}{{\_}}{lens}}=\frac{{C}_{{ab}{s}{{\_}}{{lens}}}}{{C}_{{ab}{s}{{\_}}{{BC}}+{lens}}}$$ (3) For the scenario of SOABrC, there are two different versions of Eabs which refer to Lack

et al.40 (Fig. S1 provides a visual representation of formula 4 and 5): $${E}_{{abs}{{\_}}{all}}=\frac{{C}_{{ab}{s}{{\_}}{{BC}}+ {\rm

lens/shield}\,+\,{{\rm{SOA}}}_{{\rm{BrC}}}}}{{C}_{{ab}{s}{{\_}}{{BC}}}}$$ (4) $${E}_{{abs}{{\_}}{No}{{\rm{SOA}}}_{{\rm{BrC}}}}=\frac{{C}_{{ab}{s}{{\_}}{{BC}}+{\rm

lens/shield}+\,{{\rm{SOA}}}_{{\rm{BrC}}}}-{C}_{{ab}{s}{{\_}}{{{\rm{SOA}}}_{{\rm{BrC}}}}}}{{C}_{{ab}{s}{{\_}}{{BC}}}}$$ (5) In these equations, where Eabs_all is the sum of all

light-absorbing components of individual particle including BC core, lensing or shielding effect of Icore and SOABrC and the intrinsic absorption of SOABrC. It’s worth noting that the

lensing and shielding effects discussed in our study refer to the combined influence of sulfate and SOA, resulting in net enhancement or attenuation of light absorption. Eabs_NoSOA (BrC)

means the whole individual particle except the intrinsic absorption of SOABrC. Cabs_BC + lens/shield + SOA (BrC) denotes the absorption cross-section of BC core coated with sulfate and

SOABrC. Cabs_SOA (BrC) is the light absorption of PS-CS and R-CS structures without BC core, which represents the intrinsic absorption of SOABrC. To identify the light absorption

contribution of each component in the individual particle, the calculation of absorption cross-section and corresponding fraction as follow:

$${C}_{{abs}{{\_}}{lens}/{shield}\,+\,{{\rm{SOA}}}_{{\rm{BrC}}}}=({E}_{{ab}{s}{{\_}}{{all}}}-1)\times {C}_{{ab}{s}{{\_}}{{BC}}}$$ (6) Formula (6) means the absorption cross-section of

sulfate and SOABrC, including the net lensing or shielding effect and intrinsic absorption of SOABrC.

$${C}_{{abs}{{\_}}{lens}/{Shield}}=({E}_{{ab}{s}{{\_}}{{no}{{\rm{SOA}}}_{{\rm{BrC}}}}}-1)\times {C}_{{ab}{s}{{\_}}{{BC}}}$$ (7) This equation means the net lensing/shielding effect of

sulfate and SOABrC. $${f}_{{abs}{{\_}}{BC}}=\frac{{C}_{{ab}{s}{{\_}}{{BC}}}}{{C}_{{ab}{s}{{\_}}{{all}}}}$$ (8) $${f}_{{abs}{{\_}}{\rm lens/shield}} = \frac{{C}_{{ab}{s}{{\_}}{\rm

lens/shield}}}{{C}_{{ab}{s}{{\_}}{{all}}}}$$ (9) $${f}_{{abs}{{\_}}{{\rm{SOA}}}_{{\rm{BrC}}}} = 1 - {f}_{{ab}{s}{{\_}}{{BC}}} - {f}_{{ab}{s}{{\_}}{\rm lens/shield}}$$ (10) These equations

mean the fraction of absorption due to BC, net lensing/shielding effect, and intrinsic absorption of SOABrC, respectively. SENSITIVITY ANALYSIS OF BRC COATING ON BC CORES OF VARYING SIZES

Observations indicate that BC particles can reach diameters as large as 300 nm, with some studies even reporting coarse BC particles exceeding 1 µm41,42. However, such large particles are

typically removed efficiently during long-range transport through dry and wet deposition. In contrast, LLPS primarily occurs in humid environments with abundant organic and inorganic

components, such as background sites where aerosols have undergone atmospheric aging. Smaller BC particles, due to their higher surface area-to-volume ratio, exhibit a greater tendency to

interact with organic coatings. Field measurements of LLPS phenomenon further confirm that BC cores with diameters below 240 nm are more likely to redistribute from the inorganic core to the

organic coating32, with a dominant BC core size of 116 nm observed at rural sites32. Based on these observations, this study assumes a BC core diameter of 116 nm to align with real-world

conditions and accurately assess the influence of secondary organic coatings within the LLPS particle. To further investigate the effect of BC core sizes on optical properties, additional

sensitivity analyses were conducted, considering BC core sizes of 58 nm (50% of 116 nm) and 88 nm (~75% of 116 nm) in addition to the originally modeled 116 nm. SENSITIVITY ANALYSIS OF THE

SHIELDING EFFECT OF BRC COATING WITH VARYING COMPLEX REFRACTIVE INDICES To assess the impact of BrC coatings with different light-absorbing properties, we introduced a new scenario of highly

light-absorbing SOA, in addition to the two scenarios from the original study—weakly light-absorbing SOA (SOABrC) and non-light-absorbing SOA (SOAclean)—forming three distinct scenarios. By

varying the complex refractive index parameters, we systematically investigated the shielding effect of BrC coatings on BC particle. Table S2 summarizes the complex refractive indices of

SOA across different wavelengths, where the “higher absorption” scenario corresponds to the newly introduced highly light-absorbing SOA scenario. Given that secondary BrC is generally weaker

in light absorption than BC and considering other sensitivity analyses on LLPS microphysical parameters (e.g., BC position and SOA coating thickness), the highly light-absorbing SOA

scenario was ultimately excluded. For the light absorption of BrC coating, only the weakly light-absorbing (SOABrC) and non-light-absorbing (SOAclean) scenarios were retained. This decision

is further supported by the observation that the shielding effect trends and magnitudes remained similar between the two light-absorbing SOA scenarios, reinforcing the conclusion that BrC

coatings in LLPS particles mainly enhance light absorption rather than acting as a significant shielding shell. DATA AVAILABILITY The data for figures are available on figshare at

https://doi.org/10.6084/m9.figshare.27013879.v1. For EMBS, refer to https://doi.org/10.1029/2021JD034620. All data needed to evaluate the conclusions in the paper are present in the paper

and/or the Supplementary Information. REFERENCES * Gustafsson, Ö. & Ramanathan, V. Convergence on climate warming by black carbon aerosols. _Proc. Natl Acad. Sci. USA_ 113, 4243–4245

(2016). Article  CAS  Google Scholar  * Fierce, L. et al. Radiative absorption enhancements by black carbon controlled by particle-to-particle heterogeneity in composition. _Proc. Natl Acad.

Sci. USA_ 117, 5196–5203 (2020). Article  CAS  Google Scholar  * Bond, T. C. et al. Bounding the role of black carbon in the climate system: a scientific assessment. _J. Geophys. Res._ 118,

5380–5552 (2013). Article  CAS  Google Scholar  * Intergovernmental Panel on Climate Change. _Climate Change 2021—The Physical Science Basis: Working Group I Contribution to the Sixth

Assessment Report of the Intergovernmental Panel on Climate Change_ (Cambridge University Press, 2023). * Wu, Y., Cheng, T., Zheng, L. & Chen, H. Black carbon radiative forcing at TOA

decreased during aging. _Sci. Rep._ 6, 38592 (2016). Article  CAS  Google Scholar  * Shen, W. et al. Evaluating BC aging processes in the community atmosphere model version 6 (CAM6). _J.

Geophys. Res._ 128, e2022JD037427 (2023). Article  Google Scholar  * Riemer, N., Ault, A. P., West, M., Craig, R. L. & Curtis, J. H. Aerosol mixing state: measurements, modeling, and

impacts. _Rev. Geophys._ 57, 187–249 (2019). Article  Google Scholar  * Wang, J. et al. Unified theoretical framework for black carbon mixing state allows greater accuracy of climate effect

estimation. _Nat. Commun._ 14, 2703 (2023). Article  CAS  Google Scholar  * Jacobson, M. Z. Strong radiative heating due to the mixing state of black carbon in atmospheric aerosols. _Nature_

409, 695–697 (2001). Article  CAS  Google Scholar  * Zhao, G., Tan, T., Zhu, Y., Hu, M. & Zhao, C. Method to quantify black carbon aerosol light absorption enhancement with a mixing

state index. _Atmos. Chem. Phys._ 21, 18055–18063 (2021). Article  CAS  Google Scholar  * Wang, Y. et al. Constructing shapes and mixing structures of black carbon particles with

applications to optical calculations. _J. Geophys. Res._ 126, e2021JD034620 (2021). Article  CAS  Google Scholar  * Wu, Y. et al. Light absorption enhancement of black carbon aerosol

constrained by particle morphology. _Environ. Sci. Technol._ 52, 6912–6919 (2018). Article  CAS  Google Scholar  * Matsui, H., Hamilton, D. S. & Mahowald, N. M. Black carbon radiative

effects highly sensitive to emitted particle size when resolving mixing-state diversity. _Nat. Commun._ 9, 3446 (2018). Article  Google Scholar  * Cappa, C. D. et al. Radiative absorption

enhancements due to the mixing state of atmospheric black carbon. _Science_ 337, 1078–1081 (2012). Article  CAS  Google Scholar  * McMeeking, G. R. et al. Impacts of nonrefractory material

on light absorption by aerosols emitted from biomass burning. _J. Geophys. Res_. 119, 12272–12286 (2014). Article  Google Scholar  * Adachi, K., Chung, S. H. & Buseck, P. R. Shapes of

soot aerosol particles and implications for their effects on climate. _J. Geophys. Res._ 115, D15206 (2010). Google Scholar  * Li, W. et al. A conceptual framework for mixing structures in

individual aerosol particles. _J. Geophys. Res._ 121, 13784–13798 (2016). Article  Google Scholar  * China, S., Mazzoleni, C., Gorkowski, K., Aiken, A. C. & Dubey, M. K. Morphology and

mixing state of individual freshly emitted wildfire carbonaceous particles. _Nat. Commun._ 4, 2122 (2013). Article  Google Scholar  * Zhang, R. et al. Variability in morphology,

hygroscopicity, and optical properties of soot aerosols during atmospheric processing. _Proc. Natl Acad. Sci. USA_ 105, 10291–10296 (2008). Article  CAS  Google Scholar  * Huang, X. et al.

Microphysical complexity of black carbon particles restricts their warming potential. _One Earth_ 7, 136–145 (2024). Article  Google Scholar  * Mikhailov, E. F., Vlasenko, S. S., Podgorny,

I. A., Ramanathan, V. & Corrigan, C. E. Optical properties of soot–water drop agglomerates: an experimental study. _J. Geophys. Res._ 111, 2005JD006389 (2006). Article  Google Scholar  *

Guo, S. et al. Elucidating severe urban haze formation in China. _Proc. Natl Acad. Sci. USA_ 111, 17373–17378 (2014). Article  CAS  Google Scholar  * Huang, R. et al. High secondary aerosol

contribution to particulate pollution during haze events in China. _Nature_ 514, 218–222 (2014). Article  CAS  Google Scholar  * Moise, T., Flores, J. M. & Rudich, Y. Optical properties

of secondary organic aerosols and their changes by chemical processes. _Chem. Rev._ 115, 4400–4439 (2015). Article  CAS  Google Scholar  * Flores, J. M. et al. Evolution of the complex

refractive index in the UV spectral region in ageing secondary organic aerosol. _Atmos. Chem. Phys._ 14, 5793–5806 (2014). Article  Google Scholar  * Laskin, A., Laskin, J. & Nizkorodov,

S. A. Chemistry of atmospheric brown carbon. _Chem. Rev._ 115, 4335–4382 (2015). Article  CAS  Google Scholar  * Luo, J., Zhang, Y., Wang, F. & Zhang, Q. Effects of brown coatings on

the absorption enhancement of black carbon: a numerical investigation. _Atmos. Chem. Phys._ 18, 16897–16914 (2018). Article  CAS  Google Scholar  * Saleh, R. et al. Contribution of brown

carbon and lensing to the direct radiative effect of carbonaceous aerosols from biomass and biofuel burning emissions. _J. Geophys. Res._ 120, 10285–10296 (2015). Article  Google Scholar  *

Zhang, X., Mao, M., Chen, H., Yin, Y. & Tang, S. Lensing effect of black carbon with brown coatings: dominant microphysics and parameterization. _J. Geophys. Res._ 126, e2020JD033549

(2021). Article  CAS  Google Scholar  * Lack, D. A. & Cappa, C. D. Impact of brown and clear carbon on light absorption enhancement, single scatter albedo and absorption wavelength

dependence of black carbon. _Atmos. Chem. Phys._ 10, 4207–4220 (2010). Article  CAS  Google Scholar  * Zhu, S., Zhang, H., Zhou, C., Wei, X. & Liu, Y. Optical properties of mixed black

and brown carbon aerosols. _Opt. Express_ 30, 33588–33602 (2022). Article  CAS  Google Scholar  * Zhang, J. et al. Liquid-liquid phase separation reduces radiative absorption by aged black

carbon aerosols. _Commun. Earth Environ._ 3, 128 (2022). Article  Google Scholar  * Li, W. et al. Microscopic evidence for phase separation of organic species and inorganic salts in fine

ambient aerosol particles. _Environ. Sci. Technol._ 55, 2234–2242 (2021). Article  CAS  Google Scholar  * Brunamonti, S., Krieger, U. K., Marcolli, C. & Peter, T. Redistribution of black

carbon in aerosol particles undergoing liquid-liquid phase separation. _Geophys. Res. Lett._ 42, 2532–2539 (2015). Article  CAS  Google Scholar  * Wang, Y. et al. Fractal dimensions and

mixing structures of soot particles during atmospheric processing. _Environ. Sci. Technol. Lett._ 4, 487–493 (2017). Article  CAS  Google Scholar  * China Morphology and mixing state of aged

soot particles at a remote marine free troposphere site: implications for optical properties. _Geophys. Res. Lett._ 42, 1243–1250 (_2015_). Article  CAS  Google Scholar  * Liu, C., Chung,

C. E., Yin, Y. & Schnaiter, M. The absorption Ångström exponent of black carbon: from numerical aspects. _Atmos. Chem. Phys._ 18, 6259–6273 (2018). Article  CAS  Google Scholar  * Luo,

J., Zhang, Y. M. & Zhang, Q. X. Effects of black carbon morphology on brown carbon absorption estimation: from numerical aspects. _Geosci. Model Dev._ 14, 2113–2126 (2021). Article  CAS

  Google Scholar  * Bond, T. C. & Bergstrom, R. W. Light absorption by carbonaceous particles: an investigative review. _Aerosol Sci. Technol._ 40, 27–67 (2007). Article  Google Scholar

  * Lack, D. A. et al. Brown carbon and internal mixing in biomass burning particles. _Proc. Natl Acad. Sci. USA_ 109, 14802–14807 (2012). Article  CAS  Google Scholar  * Wang, J. et al.

Significant contribution of coarse black carbon particles to light absorption in north China plain. _Environ. Sci. Technol. Lett._ 9, 134–139 (2022). Article  CAS  Google Scholar  *

Chakrabarty, R. K. et al. Soot super aggregates from flaming wildfires and their direct radiative forcing. _Sci. Rep._ 4, 5508 (2014). Article  CAS  Google Scholar  Download references

ACKNOWLEDGEMENTS This work was funded by the National Natural Science Foundation of China (42075096), the National Key Research and Development Program of China (2023YFC3706301), and

Research Funding of the School of Earth Sciences of Zhejiang University. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Key Laboratory of Geoscience Big Data and Deep Resource of Zhejiang

Province, Department of Atmospheric Sciences, School of Earth Sciences, Zhejiang University, Hangzhou, 310027, China Zexuan Zhang, Yuanyuan Wang, Xiyao Chen, Shupeng Zhu, Dantong Liu & 

Weijun Li * College of Sciences, China Jiliang University, Hangzhou, 310018, China Liang Xu * Department of Earth and Environmental Sciences, The University of Manchester, Manchester, UK

Zhonghua Zheng * Department of Science and Environmental Studies, The Education University of Hong Kong, Hong Kong, China Joseph Ching Authors * Zexuan Zhang View author publications You can

also search for this author inPubMed Google Scholar * Yuanyuan Wang View author publications You can also search for this author inPubMed Google Scholar * Xiyao Chen View author

publications You can also search for this author inPubMed Google Scholar * Liang Xu View author publications You can also search for this author inPubMed Google Scholar * Zhonghua Zheng View

author publications You can also search for this author inPubMed Google Scholar * Joseph Ching View author publications You can also search for this author inPubMed Google Scholar * Shupeng

Zhu View author publications You can also search for this author inPubMed Google Scholar * Dantong Liu View author publications You can also search for this author inPubMed Google Scholar *

Weijun Li View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS W.L. and Z.Z. conceived the study, led the overall scientific questions, and

wrote the manuscript. Z.Z. conducted the optical calculations. Z.Z. and W.L. contributed the data analysis. Y.W., X.C., L.X., Z.Z., J.C., S.Z., D.L. and W.L. reviewed and commented on the

paper. CORRESPONDING AUTHOR Correspondence to Weijun Li. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PUBLISHER’S NOTE Springer

Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION RIGHTS AND PERMISSIONS OPEN

ACCESS This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and

reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you

modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in

this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative

Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a

copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Zhang, Z., Wang, Y., Chen, X. _et al._ Absorption

enhancement and shielding effect of brown organic coating on black carbon aerosols. _npj Clim Atmos Sci_ 8, 102 (2025). https://doi.org/10.1038/s41612-025-00989-y Download citation *

Received: 28 September 2024 * Accepted: 01 March 2025 * Published: 13 March 2025 * DOI: https://doi.org/10.1038/s41612-025-00989-y SHARE THIS ARTICLE Anyone you share the following link with

will be able to read this content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt

content-sharing initiative