### Distributions of the particle size and mixing states in different combustion states

The biomass burning experiments, were performed in a combustion chamber in a laboratory environment and were conducted using dry wheat straw, wet wheat straw and dry rapeseed plants, as shown in Figure S1. Eighteen samples were directly burned in the chamber (referred to as “dry”), and four samples (referred to as “wet”) were placed in humid conditions (RH > 99%) for 30 min. A 50 cm long, 1/4-in. flexible conductive silicone tube was used for aerosol sampling, and a polytetrafluoroethylene (PTFE) tube was used for gas sampling. The residence time was very short (~ 6 s) to minimize the aging of the aerosols in the tube^{13,14}. Most carbon substances are converted to carbon dioxide and BC particles in flaming-dominated combustion, while further smoldering-dominated combustion predominantly emits carbon monoxide and organics. The flaming and smoldering combustion stages were classified using the modified combustion efficiency (MCE), which was calculated from the fire-integrated excess CO and CO_{2} mixing ratios, relative to their background values. It is defined as ({{Delta {text{CO}}_{2} } / {left( {Delta {text{CO}}_{2} + Delta {text{CO}}} right)}}), indicating different combustion states in biomass burning. An MCE value > 0.95 is normally regarded as flaming-dominant combustion, whereas an MCE value < 0.9 represents the smoldering-dominant combustion^{15,16}. The mixing ratio of CO_{2} and CO was measured using a Li-7000 CO_{2} analyzer (Li-COR Inc.) and an ultrafast CO analyzer (model AL5002, Aero-Laser GmbH). A single particle soot photometer (SP2, Droplet Measurement Technologies Inc.) was used to measure the size distribution and shell-core ratio of BC. The distributions of the particle size and mixing states are measured in the smoldering-dominated and flaming-dominated combustion states. The commonly used shell-core ratio (S/C, or *F*_{sc} = *D*_{p}/*D*_{c}) is defined as the ratio of the volume-equivalent diameter of the shell (entire particle, *D*_{p}) to the core (*D*_{c}) particles, indicating the coating states of the carbonaceous aerosols. Microscopy observations have suggested that smoldering-dominated combustion leads to a smaller BC core and thicker non-BC coating. Thus, it tends to lead to a compact fractal aggregated BC structure^{17,18,19}.

For different combustion stages, the mass size distribution of BC ensembles and the S/C ratio distribution of BC particles with fixed sizes were measured. The total masses of BC-containing particles (*M*_{p}) are described by the lognormal functions of the mass equivalent diameter (MED) and the standard deviation (*σ*). The peak of MED (*D*_{m}) is 215 nm for typical flaming-dominated combustion and 152 nm for typical smoldering-dominant combustion. The detailed parameters of the samples are shown in Table S1.

$$ M_{p} = frac{1}{{D_{p} sigma sqrt {2pi } }}e^{{ – frac{{left( {ln D_{p} – ln D_{m} } right)^{2} }}{{2sigma^{2} }}}}$$

(1)

Smoldering-dominated combustion tends to produce more thickly coated BC particles than flaming-dominated combustion. In this study, the S/C ratio distributions are described by Gaussian functions. When the MED of BC particles is 200 ± 10 nm, the measured peak values of S/C ratio (*F*_{m}) are 1.18 for the flaming-dominated stage and 1.34 for smoldering-dominated stage.

$$ Nleft( {F_{sc} } right) = frac{1}{{F_{sc} sigma sqrt {2pi } }}e^{{ – frac{{left( {F_{sc} – F_{m} } right)^{2} }}{{2sigma^{2} }}}}$$

(2)

The variations of the measured S/C ratio can be described as a function of the MCE values. The peak of the MCE-dependent S/C ratio is fitted as follows:

$$ F_{m} = – 1.73 times MCE + 2.86$$

(3)

Figure S2 shows the mass absorption cross sections (MAC) of the BC-containing aerosols was calculated using the distributions of the S/C ratio and peaks of the distributions. The absorption properties of carbonaceous aerosols were quantified using a state-of-the-art theoretical model considering more realistic particle morphologies (computational methods are introduced in the following section “Optical simulations by the aggregate model”). The deviations of the MAC between the poly-disperse and mono-disperse S/C ratios are limited to be less than 1.5%. Therefore, simulations of the BC-containing aerosols with the distributions of S/C ratios can be calculated by the peaks of the distributions.

### Physical properties of carbonaceous aerosols

The morphologies and compositions of black carbon aerosols depend on the types of fossil fuel or biomass source, burning process, and aging processes in the atmosphere^{20,21}. Previous microscopy studies have indicated that freshly emitted BC particles consist of hundreds of small spherical primary particles combined into branched aggregates^{22,23}. The construction and morphology of these particles can be described by the well-known fractal law^{24,25}:

$$ Ns = k0left( frac{Rg}{a} right)^{Df}$$

(4)

$$ R_{g}^{2} = frac{1}{{N_{s} }}sumlimits_{i = 1}^{{N_{s} }} {r_{i}^{2} }$$

(5)

where *N*_{s} is the number of monomers in the cluster, *a* is the mean radius of the monomers, *k*_{0} is the fractal prefactor, *D*_{f} is the fractal dimension, *R*_{g} is the radius of gyration representing the deviation of the overall aggregate radius in a cluster, and *r*_{i} is the distance from the *i*th monomer to the centre of the cluster. The S/C ratio is 1.0 for bare BC particles without mixing non-BC components. The fractal dimensions (*D*_{f}) of bare and coated BC particles typically vary from 1.8 to 3.0 with a fractal prefactor of 1.2^{18}. Previous studies showed that fractal dimensions of different types of BC particles ranged from 1.8 to 2.2 and increased during aging^{19}. The sensitivity of fractal parameters on BC optical properties is investigated in Figure S3. Bond and Bergstrom reported the value of the mean radii of a BC monomer (*a)* to be in the range of 0.01–0.025 μm^{24}. In field observations, the numbers of monomers (*N*_{s}) have been observed to be in the range of 50–300, and may vary up to approximately 800^{26}.

The refractive index of a BC component is assumed to be 1.95 + 0.79i in the visible and infrared range^{24}. In the ambient environment, these refractive indices may vary across aerosol types. The real parts of the refractive indices of non-BC particles are assumed to be in the range of 1.4–1.6 and the imaginary part from 0 to 0.1^{27}. These assumed refractive indices lie in the range of typical atmospheric aerosols, such as organics, sulfate, nitrate, dust, sea salt and brown carbon components^{28,29,30,31}. In this study, the real refractive indices of the non-BC coatings were held constant at 1.55, and three values of 10^{–2}, 10^{–3}, and 10^{–4} for their imaginary refractive indices were assumed. Figure S4 indicates that the trends of the simulated values of the BC aerosols are consistent with the measurements by McMeeking et al.^{12}, a refractive index of 1.55 + 10^{−3}i for the non-BC component is suggested for the biomass burning absorption simulations. The sensitivity of the non-BC refractive indices to the BC optical properties is presented in Figure S5.

### Optical simulations by the aggregate model

Optical simulations were performed using the aggregate model parameterized by the complex particle morphology of BC at different aging scales. BC particles with bare, partly coated (thinly coated), partially encapsulated, and heavily coated states were modelled. Bare BC particles were modelled without any non-BC coating components using the diffusion limited aggregation (DLA) method, and aggregations of BC monomers were constructed with the given fractal parameters^{32}. Partly coated BC particles were constructed by the aggregation of concentric core–shell spherical monomers. The partially encapsulated morphologies of BC-containing particles were represented by aggregated BC particles partially embedded in the host non-BC particle. For the heavily coated states, compact aggregated BC particles were internally mixed with large spherical non-BC particles, and all the BC monomers were inside the non-BC particles^{33,34}. In this study, the fractal prefactor was assumed to be 1.2 and the fractal dimension was 1.8, 2.4, and 2.8 for the partly coated (including bare), partially encapsulated, and heavily coated states, respectively.

The morphologies of BC aerosols with different mixing states were modelled to initialize the superposition T-matrix method. This method uses numerically exact solution methods of Maxwell’s equations, which can be used to calculate the T-matrix descriptions of light scattering from the cluster with an appropriate superposition technique and thereby, analytically obtain the random-orientation cross sections and scattering matrices of these clusters. The superposition T-matrix method is applicable to a wide range of particle sizes and generates all of the scattering and absorption characteristics of the particles^{35,36}. The random-orientation optical results were averaged using 10 random realizations of BC particles with the same morphological parameters to reflect the overall single scattering properties.

The cross sections of absorption (*C*_{abs}) were calculated and integrated using the distributions of the particle size and S/C ratio.

$$ leftlangle {C_{abs} } rightrangle = int_{0}^{infty } {int_{1}^{infty } {C_{abs} left( {F_{sc} ,D_{p} } right),Nleft( {F_{sc} ,D_{p} } right),dF_{sc} ,dD_{p} } }$$

(6)

$$ M_{p} = frac{4}{3}pi Nleft( {D_{p} } right)left[ {int_{1}^{infty } {left( {rho_{BC} – rho_{non – BC} } right)left( {frac{{D_{p} }}{{{2}F_{sc} }}} right)^{3} Nleft( {F_{sc} } right)dF_{sc} } + rho_{non – BC} left( {frac{{D_{p} }}{2}} right)^{3} } right]$$

(7)

where *C*_{abs}*(F*_{sc}*,D*_{p}*)* is the absorption cross sections of the individual BC particles. *N(F*_{sc}*,D*_{p}*)* is the number of the individual BC particles with fixed shell-core ratio (*F*_{sc}) and particle size (*D*_{p}). The mass density of BC (*ρ*_{BC}) is assumed to be 1.8 g/cm^{3} according to the review of measurement by Bond and Bergstrom^{24}, and the mass density of the non-BC components (*ρ*_{non-BC}) is estimated to be 1.05 g/cm^{3}^{37}. The sensitivity of the density of the non-BC components in the individual BC-containing particles (1.0–1.2 g/m^{3}) to the MAC of the BC aerosols at different combustion stages is investigated, as shown in Figure S6. (leftlangle {C_{abs} } rightrangle) is obtained by integration of the absorption cross sections of all BC particles with different sizes and S/C ratios. The single scattering albedo (SSA) is defined as (leftlangle {SSA} rightrangle = frac{{leftlangle {C_{{s{text{ca}}}} } rightrangle }}{{leftlangle {C_{abs} } rightrangle { + }leftlangle {C_{sca} } rightrangle }} ), where *C*_{abs} and *C*_{sca} are the cross sections for absorption and scattering, respectively.

The mass absorption cross sections of the BC aerosols were further normalized, which were defined as the cross section per unit mass of the particles. The normalization of the absorption cross sections is defined by the BC mass.

$$ MAC = frac{{leftlangle {C_{abs} } rightrangle }}{{frac{4}{3}pi rho_{BC} int_{0}^{infty } {int_{1}^{infty } {left( {frac{{D_{p} }}{{2F_{sc} }}} right)^{{3}} Nleft( {F_{sc} ,D_{p} } right),dF_{sc} dD_{p} } } }} $$

(8)

The *E*_{abs} is defined as the MAC between the BC aerosol ensembles including coated BC particles with the specific peak values of S/C ratio in the range of *F*_{m} > 1 and the BC aerosol ensembles are all bare BC particles with *F*_{m} = 1 ((E_{abs} = {{MAC_{{F_{m} > 1}} } mathord{left/ {vphantom {{MAC_{{F_{m} > 1}} } {MAC_{{F_{m} = 1}} }}} right. kern-nulldelimiterspace} {MAC_{{F_{m} = 1}} }} )).

The Ångström exponent (ÅE) over a wavelength interval (left[ {lambda_{1} ,lambda_{2} } right] ) is defined as

$$ Amathop Alimits^{o} E = – frac{{ln frac{{leftlangle {C_{abs} left( {lambda_{1} } right)} rightrangle }}{{leftlangle {C_{abs} left( {lambda_{2} } right)} rightrangle }}}}{{ln frac{{lambda_{1} }}{{lambda_{2} }}}} $$

(9)

Previous measurements indicated that the absorption ÅE values (AÅE) are near 1 (the theoretical value for black carbon) for AErosol RObotic NETwork-measured (AERONET) aerosol columns dominated by urban-industrial aerosol and larger AÅE values are observed for biomass burning aerosols^{12}. The sensitivity of the incident wavelength on BC optical properties is presented in Figure S7, and the SSA and AÅE are shown in Figure S8.

The radiative properties of BC aerosols in climate models are commonly obtained based on the morphological simplification of spheres for the different mixing states, which are generally calculated using the Mie core–shell model. However, large discrepancies have been measured and simulated between the aggregates and the equivalent sphere approximations due to their complex morphologies, components and multiple scattering^{38,39,40}.

The S/C ratio has been generally used in previous measurements of BC aerosols, because of the widely adopted Mie method. Therefore, in this study, the S/C ratio is applied for the comparisons of the aggregate model using the T-matrix method with the corresponding measurements by previous studies. In fact, the volume/mass fractions of BC and non-BC particles have also been used in previous studies^{37}. For example, the S/C ratio can be directly calculated by the mass ratio of non-BC and BC components in individual BC-containing particles (*M*_{R} = *M*_{non-BC}/*M*_{BC}, non-BC mass *M*_{non-BC}, and BC mass *M*_{BC}) as *F*_{sc} in the following equation:

$$ F_{sc} = sqrt[3]{{frac{{M_{R} rho_{BC} }}{{rho_{non – BC} }}{ + 1}}} $$

(10)

In the core–shell model calculated using Mie theory, the volume-equivalent radius of BC (*R*_{BC}) is related to their masses and their aggregated morphologies, according to the following equation:

$$ R_{BC} = sqrt[3]{{frac{{M_{BC} }}{{frac{4}{3}pi rho_{BC} }}}} = sqrt[3]{{N_{s} }}a $$

(11)

The thickness of the non-BC (*T*_{non-BC}) shell is

$$ T_{non – BC} = sqrt[3]{{frac{3}{4pi }left( {frac{{M_{BC} }}{{rho_{BC} }} + frac{{M_{non – BC} }}{{rho_{non – BC} }}} right)}} – R_{BC} $$

(12)

The mixing states of BC particles are quantified by the augmentation of the non-BC thickness. For bare BC particles, the thickness of the non-BC coating is zero. Thicker coating of non-BC components leads to larger values of the S/C ratio. Multi-scattering of fractal aggregated BC monomers in the individual BC-containing particles is not considered by the morphological simplifications of the single core–shell sphere model, and BC particles with inclusions, which are frequently found by microscopy measurements, may have significant effects on estimating the absorption enhancements of BC aerosols^{41}.