Effective densities of soot particles and their relationships with the mixing state at an urban site in the Beijing megacity in the winter of 2018

The effective density (ρ_eff) of refractory black carbon (rBC) is a key parameter relevant to its mixing state that imposes great uncertainty in evaluating the direct radiation forcing effect. In this study, a tandem differential mobility analyzer–centrifugal particle analyzer–single-particle soot photometer (DMA–CPMA–SP2) system was used to investigate the relationship between the effective density (ρ_eff) and the mixing state of rBC particles during the winter of 2018 in the Beijing megacity. During the experiment, aerosols with a known mobility diameter (D_mob) and known ρ_eff values (0.8, 1.0, 1.2, 1.4, 1.6, and 1.8 g cm⁻³) were precisely selected and measured by the SP2 to obtain their corresponding mixing states. The results showed that the ρ_eff well represented the morphological variation in rBC-containing particles. The rBC-containing particles changed from an irregular structure to a compact spherical structure with the increase in ρ_eff. A ρ_eff value of 1.4 g cm⁻³ was the morphological transition point. The morphology and ρ_eff value of the rBC-containing particles were intrinsically related to the mass ratio of non-refractory matter to rBC (M_R). As the ρ_eff values of the rBC-containing particles increased from 0.8 to 1.8 g cm⁻³, the M_R of the rBC-containing particles significantly increased from 2 up to 6–8, indicating that atmospheric aging processes were likely to lead to the reconstruction of more compact and regular particle shapes. During the observation period, the ρ_eff of the majority of rBC-containing particles was smaller than the morphology transition point independent of the pollution conditions. This suggested that the major rBC-containing particles did not have a spherical structure. Simulation based on an aggregate model considering the morphological information of the particles demonstrated that absorption enhancement of rBC-containing particles could be overestimated by ∼ 17 % by using a core–shell model. This study highlights the strong dependence of the morphology of ambient rBC-containing particles on ρ_eff and will be helpful for elucidating the microphysical characteristics of rBC and reducing uncertainty in the evaluation of rBC climate effects and health risks.

1 Introduction

Refractory black carbon (rBC) is the major light-absorbing aerosol in the atmosphere. It plays a vital role in the climate by influencing the radiative balance, cloud properties, and glaciers (Flanner et al., 2007; Ramanathan and Carmichael, 2008; Bond et al., 2013). rBC is considered to be one of the most important global warming factors (Bond et al., 2013). Additionally, as a component of PM_2.5 (particulate matter with an aerodynamic diameter less than 2.5 µm), rBC has an adverse environmental effect because it degrades visibility and harms the human respiratory system (Apte et al., 2015; Lelieveld et al., 2015; Raaschou-Nielsen et al., 2013; Dominguez-Rodriguez et al., 2015). The control of rBC emission is an immediate and win-win strategy to face climate and environmental challenges.

In the troposphere, rBC mixes with other components, such as organics, sulfate, and nitrate, through condensation, coagulation, heterogenous chemistry, or other complicated processes. Many studies have reported that the mixing state of rBC-containing particles greatly impacts the absorption ability (Shiraiwa et al., 2008; Nakayama et al., 2010; Shiraiwa et al., 2010) and hygroscopicity of rBC (Zhang et al., 2008; Moteki et al., 2012; Liu et al., 2013) based on a combination of laboratory, numerical model, and field measurement methods. However, debate exists among researchers. For instance, several studies (Lack et al., 2012; Wang et al., 2014, 2016; Wu et al., 2016) observed a large absorption enhancement of rBC caused by mixing with the coating material, whereas other studies found negligible absorption enhancement (Cappa et al., 2012; Lan et al., 2013). Liu et al. (2017) proposed that the mixing structure of rBC-containing particles depended on the proportion of coating material. When coating materials are insufficient to encapsulate rBC, they tend to attach to it and provide little absorption enhancement. Sufficient coating materials will change rBC-containing particles to a core–shell structure and significantly contribute to light absorption. Thus, the morphology of rBC-containing particles needs to be further studied to minimize the error in the estimation of rBC's absorption enhancement effect. Moreover, the morphology of rBC-containing particles causes uncertainty in evaluation of the dose deposited in the respiratory system and thus in health risk estimations (Londahl et al., 2008; Alfoldy et al., 2009).

Laboratory inspection using transmission electron microscopy (TEM) can provide visual evidence of and information on the morphology of rBC-containing particles (China et al., 2013; Adachi and Buseck, 2013; Adachi et al., 2010). The common opinion based on TEM results is that bare rBC-containing particles adopt a fractal chain-like structure that will become more compact during the aging process (Wang et al., 2017). However, the representativeness of the TEM results remains a question. Since identifying rBC-containing particles using TEM is time-consuming work, the number of rBC-containing particles observed in one TEM study often ranges between hundreds and thousands, which is a tiny fraction of the ambient rBC-containing particles. Another way to determine the morphology of rBC-containing particles is to measure a physical index, such as the effective density (ρ_eff), shape factor (χ), fractal dimension, etc. For instance, the ρ_eff is defined as the ratio of the particle mass (M_p) to the volume of its mobility-equivalent sphere. The compactness of a particle can be determined by comparing the ρ_eff with the material density (the density of particles with a solid spherical structure). For particles with the same material density, a smaller ρ_eff indicates a looser structure.

Table 1 Abbreviations and symbols used in this paper.

In practice, a differential mobility analyzer (DMA), aerosol particle mass (APM) analyzer (or a centrifugal particle analyzer, CPMA), and condensation particle counter (CPC) are often integrated to obtain the M_p and mobility diameter (D_mob) simultaneously. Then, the ρ_eff is calculated by Eq. (1):

$$\begin{array}{}\text{(1)}& {\mathit{\rho }}_{\text{eff}}={\displaystyle \frac{\mathrm{6}{M}_{\text{p}}}{\mathit{\pi }{D}_{\text{mob}}^{\mathrm{3}}}}.\end{array}$$

The ρ_eff is often used in laboratory studies to determine the morphology of rBC (Xue et al., 2009; Pagels et al., 2009; Zhang et al., 2008). The freshly emitted rBC-containing particles are characterized by a significantly lower ρ_eff than the rBC material density of 1.8 g cm⁻³ suggested by Bond et al. (2013). Zhang et al. (2008) observed that the ρ_eff of rBC-containing particles changed from 0.56 to 1.60 g cm⁻³ after H₂SO₄ condensation, indicating reconstruction of rBC during the condensation process, which was consistent with the TEM results. Further studies showed that BC reconstruction was caused by the surface tension of the coating material, which differed for various coating compositions (Xue et al., 2009; Pagels et al., 2009).

In the laboratory, a high concentration of rBC-containing particles is normally generated by a laminar diffusion burner, and the ρ_eff of rBC-containing particles can be reasonably studied using the DMA–CPMA–CPC system. Investigation of the ρ_eff of rBC-containing particles using a DMA–CPMA–CPC tandem system would be difficult because there are substantial non-rBC particles in the ambient atmosphere. The ρ_eff determined using this approach is only representative of the characteristic of the bulk aerosols and not the rBC-containing particles. A single-particle soot photometer (SP2) is able to distinguish rBC-containing particles from non-rBC particles at a single-particle resolution. In this study, the CPC in the regular tandem DMA–CPMA–CPC system was replaced with the SP2, and the ρ_eff of the rBC-containing particles and the non-rBC particles was detected separately. Additionally, the key parameters related to the rBC mixing state, such as the mass of the rBC core, number fraction of rBC-containing particles, and optical diameter of the rBC-containing particles, were well determined through SP2 measurement. Thus, the mixing state and ρ_eff of rBC-containing particles were obtained simultaneously using the novel tandem DMA–CPMA–SP2 system.

In this study, field measurement using a tandem DMA–CPMA–SP2 system was performed from 20 December 2018 to 4 January 2019 in the urban areas of Beijing to investigate the ρ_eff of ambient rBC-containing particles. The site is located in the tower campus of the State Key Laboratory of Atmospheric Boundary Layer Physics and Atmospheric Chemistry, Institute of Atmospheric Physics (LAPC, longitude: 116.37^∘ E; latitude: 39.97^∘ N). A more detailed description of the site can be found in the literature (Sun et al., 2016; Pan et al., 2019). Particles with different effective densities preselected by the DMA–CPMA were injected into the SP2. A comprehensive analysis was conducted with a focus on the relationship between the rBC-containing particle ρ_eff and the mixing state. To the best of our knowledge, this study is the first report of the ρ_eff of ambient rBC-containing particles. This study will help elucidate the microphysical properties of rBC-containing particles, which can reduce uncertainty in climate and health risk effect estimations.

2 Methods

2.1 Single-particle soot photometer

The detailed principle of the SP2 (Droplet Measurement Technology Inc., Boulder, CO, USA) has been reported in the literature (Shiraiwa et al., 2008; Moteki and Kondo, 2007). Briefly, due to the unique absorption ability of rBC, each single rBC-containing particle will absorb the high-intensity laser (1064 nm, TEM00 mode) produced by the SP2. Then, the rBC is heated to the boiling point and emits incandescence. The peak incandescence intensity is nearly linearly correlated with the rBC mass. By detecting the incandescence, the rBC mass in each rBC-containing particle can be determined. The scattering signal of each particle is obtained simultaneously by the SP2. Particles that only have a scattering signal are identified as non-rBC particles, whereas particles with concurrence of incandescence and a scattering signal are identified as rBC-containing particles.

The SP2 was calibrated using Aquadag aerosols (lot 9627) and a polystyrene latex sphere (PSL, Nanosphere Size Standards, Duke Scientific Corp., USA) with sizes of 203 nm (lot 185856), 303 nm (lot 189903), and 400 nm (lot 189904). Because the SP2 is more sensitive to Aquadag than ambient rBC (Laborde et al., 2013), the incandescent signal was corrected by scaling a factor of 0.75 in the ambient measurement. The total uncertainty of the rBC mass measured by the SP2 was estimated to be 30 %.

2.2 Tandem system

The tandem system in this study included a DMA (model 3085A, TSI Inc., USA), CPMA (Cambustion Ltd.), condensation particle counter (CPC, model 3775, TSI Inc., USA), and SP2. A schematic diagram of the measurement system is provided in Fig. S1.

The CPMA was used to select particles with a known mass based on a specific charge-to-mass ratio by imposing opposite centrifugal and electric forces on the charged aerosols inside (Olfert and Collings, 2005). The DMA was used to select particles with a known mobility diameter (D_mob) based on the particles' electromobility. The tandem DMA–CPMA system was capable of selecting particles with a known ρ_eff. The reliability of the DMA–CPMA tandem system was tested using PSL particles (ρ_eff: 1.05 g cm⁻³). In general, the tandem system overestimated the ρ_eff by 5 % with a mode ρ_eff value of 1.10 g cm⁻³, as shown in Fig. S2. The multiple charged influences (Fig. S2) were negligible.

Particles with known effective densities preselected by the DMA–CPMA system were injected into the SP2 to obtain information on the corresponding rBC. In practice, the mobility diameter selected by the DMA was set at a constant value of 240 nm. The set points of the CPMA were 5.79, 7.24, 8.69, 10.13, 11.58, and 13.03 fg, which corresponded to a ρ_eff of 0.8, 1.0, 1.2, 1.4, 1.6, and 1.8 g cm⁻³, respectively. Each CPMA set point was held for 10 min, and the duration of a whole scan turn of the six set points was 1 h. In this study, the sum of particle numbers over 10 min was used to present the temporal variation in particles with different ρ_eff values.

2.3 Data analysis

2.3.1 Determination of the bulk effective density

The number concentration of particles with six different target ρ_eff values was measured consecutively on a 10 min basis. Thus, a distribution of different effective densities could be obtained every hour. Previous studies (Qiao et al., 2018; Momenimovahed and Olfert, 2015) often used a lognormal or Gaussian function to fit the ρ_eff distribution. The ρ_eff of the bulk aerosols was determined to be the peak location of the fit function. Due to the limited ρ_eff measurement points in this study, the bulk aerosol density was calculated using a simple method as shown in Eq. (2). ρ_i denotes the ρ_eff with the maximum particle number in 1 h, and N_i denotes the number of particles with ρ_i. ρ_i−1 and ρ_i+1 denote the adjacent effective density set points of ρ_i.

$$\begin{array}{}\text{(2)}& {\mathit{\rho }}_{\text{bulk}}={\displaystyle \frac{{\mathit{\rho }}_i\times N_i+{\mathit{\rho }}_{i-\mathrm{1}}\times N_{i-\mathrm{1}}+{\mathit{\rho }}_{i+\mathrm{1}}\times N_{i+\mathrm{1}}}{N_i+N_{i-\mathrm{1}}+N_{i+\mathrm{1}}}}\end{array}$$

We tested this method to calculate the ρ_eff of PSL, as shown in Fig. S3. The ρ_eff determined using this approach was 1.09 g cm⁻³, which was very close to the given density of 1.05 g cm⁻³.

Figure 1 Time series of (a) the PM_2.5 mass concentration; (b) number counts of rBC-containing particles with different effective densities; (c) number fractions of rBC-containing particles with different effective densities; (d) number counts of non-rBC particles with different effective densities; (e) number fractions of non-rBC particles with different effective densities; (f) mass concentrations of aerosol species, including organics, sulfate, nitrate, ammonium, and chloride, in NR-PM_2.5; and (g) mass fractions of aerosol species in NR-PM_2.5 during the five episodes denoted at the top of the graph.

2.3.2 Determination of the optical diameter

For non-rBC particles, the scattering cross sections are proportional to the peak scattering intensity measured by the SP2. The optical diameter (D_opt) was calculated through the Mie theory with a refractive index of 1.48 and an assumption of a spherical structure. Since rBC-containing particles evaporate in the laser beam, leading to a decrease in the scattering cross section, a leading-edge-only (LEO) fit (Gao et al., 2007; Liu et al., 2014; Pan et al., 2017) method was used to retrieve the undisturbed peak scattering intensity. By assuming a core–shell structure and using the refractive indices determined by Taylor et al. (2015), 1.48 for coating and 2.26–1.26i for the rBC core, the D_opt of the rBC-containing particles can also be calculated based on the Mie scattering theory.

2.3.3 Determination of the shape factor and void fraction

The shape factor χ is an applicable parameter describing irregularity of a particle. When χ is equal to 1, the particle is in a regular spherical structure, whereas a larger χ indicates that the particle is more irregular. The χ of the rBC-containing particles was calculated using the following equation (Zhang et al., 2016) in this study:

$$\begin{array}{}\text{(3)}& \mathit{\chi }={\displaystyle \frac{D_{\text{mob}}\times C_{\text{C}}\left(D_{\text{mev}}\right)}{D_{\text{mev}}\times C_{\text{C}}\left(D_{\text{mob}}\right)}},\end{array}$$

where D_mob is the mobility diameter, D_mev is the mass equivalent diameter, and C_C is the Cunningham slip correction factor (Decarlo et al., 2004).

The void volume ratio (R_void) was also used to represent the compactness of rBC-containing particles in this study. The R_void is 0 for particles with an ideal solid sphere and increases when the structure loosens. The R_void is calculated by Eq. (4):

$$\begin{array}{}\text{(4)}& R_{\text{void}}=\mathrm{1}-{\displaystyle \frac{D_{\text{me}}^{\mathrm{3}}}{D_{\text{m}}^{\mathrm{3}}}}.\end{array}$$

2.3.4 Determination of the coating thickness

The mass ratio (M_R) of coating to rBC core was used to represent the coating thickness in this study. The mass of the rBC-containing particle (M_p) was directly measured by CPMA and the mass of the rBC core (M_rBC) was measured by SP2. Then, the M_R was calculated by Eq. (5):

$$\begin{array}{}\text{(5)}& M_{\text{R}}={\displaystyle \frac{M_{\text{p}}-M_{\text{rBC}}}{M_{\text{rBC}}}}.\end{array}$$

The uncertainty of M_R was determined to be 31.6 % and the uncertainties of the major parameters used in this paper can be found in the Supplement.

3 Results

3.1 Constraining factors of effective density

The temporal variation in the number concentrations of rBC-containing and non-rBC particles and the mass concentration of non-refractory PM_2.5 (NR-PM_2.5) measured by a time-of-flight aerosol chemical speciation monitor (ToF-ACSM) are shown in Fig. 1. Four pollution events and one lasting clean episode were observed during the study period and were denoted EP 1–5. EP 3 was defined as the clean episode with a PM_2.5 mass concentration less than 10 µg cm⁻³. The PM_2.5 mass concentration was higher than 50 µg cm⁻³ during the other four pollution episodes. The backward trajectories of the five episodes are illustrated in Fig. S4. Beijing was majorly affected by the local air mass or southern polluted air mass during the pollution episodes. In contrast, the clean northwest air mass dominated in Beijing during the clean episode.

For simplicity, the effective densities of non-rBC and rBC-containing particles were called ρ_non-rBC and ρ_rBC separately. The effective density of bulk non-rBC and rBC-containing particles calculated by Eq. (2) was called ρ_non-rBC,bulk and ρ_rBC,bulk. The bulk effective density reflects the number distribution of particles with different effective densities. For example, the number fractions of non-rBC particles with lower ρ_non-rBC (0.8–1.2 g cm⁻³) were ∼ 70 % during EP 2 and EP 4, and this value was significantly lower (∼ 20 %) during EP 1 and EP 5. Correspondingly, the ρ_non-rBC,bulk was calculated to be 1.18 and 1.20 g cm⁻³ in EP 2 and EP 4, lower than 1.43 and 1.40 g cm⁻³ in EP 1 and EP 5. The variation in ρ_non-rBC was mainly caused by different non-rBC compositions in different cases since the ρ_eff of different compositions varies. The ρ_eff value of (NH₄)₂SO₄ and NH₄NO₃ particles was 1.75 g cm⁻³ (Qiao et al., 2018), whereas that of organics depended on their compositions and usually was between 0.64 and 1.49 g cm⁻³ (Malloy et al., 2009; Hallquist et al., 2009; Bahreini et al., 2005; Turpin and Lim, 2001).

Figure 2 The optical diameters of particles with different effective densities. (a) Non-rBC particles and (b) BC-containing particles. (The black lines in the middle signify the medians; the black markers in the middle denote the means; the upper and lower bounds of the box denote the 75th and 25th percentiles, respectively; and the upper and lower whiskers denote the 90th and 10th percentiles, respectively.) The blue and red dashed lines denote the average optical diameters from different assumptions of the refractive index. The grey dashed line denotes the mobility diameter (D_mob=240 nm) selected by DMA.

Turpin and Lim (2001) suggested an overall ρ_eff of 1.2 g cm⁻³ for organic aerosols in Los Angeles, and Hallquist et al. (2009) recommended a ρ_eff of 1.4 g cm⁻³ for secondary organic aerosols in the absence of direct measurement. In general, the ρ_eff values of organics are always lower than those of inorganic compounds. The lower ρ_non-rBC may indicate a higher mass fraction of organic compounds in the non-rBC particles. In fact, although the composition may slightly differ between NR-PM_2.5 and particles with D_mob=240 nm as observed in this study, the higher organic fractions in NR-PM_2.5 in EP 2 and EP 4 (66 % and 59 %) may indicate an organic dominant pollution environment and thus a higher organic fraction in particles with D_mob=240 nm consistent with the lower ρ_non-rBC,bulk in these two episodes. Furthermore, the relationship between effective density and organic fraction was assessed throughout the observation period, as shown in Fig. S5. The ρ_non-rBC,bulk value was apparently low in the high organic fraction environment during the whole observation period. The ρ_rBC,bulk was also lower in the more organic fraction condition similar to that of the non-rBC particles, which was mostly due to composition of coating matter. In this study we presumed that, first, a lower ρ_non-rBC,bulk value means a higher organic fraction in the non-rBC particles. Second, composition of non-rBC particles and the coatings of rBC-containing particles were similar.

To better understand the morphological impacts on ρ_eff, the optical diameters (D_opt) of non-rBC and rBC-containing particles were compared to those of D_mob, as shown in Fig. 2. The particle shapes are spherical if D_mob is the same as D_opt since the structure is assumed to be spherical in the D_opt calculation through Mie theory. For non-rBC particles with a ρ_non-rBC larger than 1.4 g cm⁻³ D_mob and D_opt are nearly the same. For non-rBC particles with a ρ_non-rBC=1.0 or 1.2 g cm⁻³ the D_opt is slightly lower than the D_mob. The refractive indices for (NH₄)₂SO₄, NaCl, and secondary organic aerosols have been determined to be 1.51, 1.53, and 1.44–1.5, respectively (Nakayama et al., 2010; Schnaiter et al., 2003; Toon et al., 1976). An even lower refractive index (1.42) was found for ambient non-rBC particles (Zhang et al., 2018). The constant refractive index of 1.48 may underestimate the D_opt of non-rBC particles with lower ρ_non-rBC since the refractive indices of organic aerosols may be lower than those of inorganics. Different refractive index assumptions were used to calculate the D_opt, as denoted by the red and blue dashed lines in Fig. 2. When the variation in the refractive indices was taken into account, the D_opt was considered to be the same as the D_mob for non-rBC particles with a ρ_non-rBC=1.0 or 1.2 g cm⁻³. For non-rBC particles with a ρ_non-rBC of 0.8 g cm⁻³, the lower D_opt may be caused by the lower refractive indices for some specific compounds or the nonspherical morphology. However, the fraction of this non-rBC was negligible, as shown in Fig. 1. Thus, the non-rBC particles mostly adopted a spherical structure.

The mean D_opt was 179, 197, and 214 nm for rBC-containing particles with a ρ_rBC=0.8, 1.0, and 1.2 g cm⁻³, respectively, which were significantly lower than the D_mob values. This decrease could not be explained by variation in the refractive indices, as shown in Fig. 2b, indicating that the morphologies of these rBC-containing particles were not spherical. The D_opt was the same as the D_mob when the ρ_rBC was equal to 1.6 or 1.8 g cm⁻³, suggesting that the particles approximate to spherical structure. rBC-containing particles with a ρ_rBC=1.4 g cm⁻³ were placed at the morphological transition point. The differences between the 75th and 25th percentiles of the D_opt were larger for the rBC-containing particles than for the non-rBC particles, as denoted by the box length. This larger difference may be caused by the complex morphology of rBC-containing particles compared to that of non-rBC particles. In general, the non-rBC particles mostly had a spherical structure, and the ρ_non-rBC was majorly influenced by the composition. A lower fraction of organics contributed to the increase in the ρ_non-rBC. The ρ_rBC was controlled by the combined effect of the morphology and coating composition. A fractal structure and a more organic coating tend to decrease the ρ_rBC.

Figure 3 The shape factor and void fraction of BC-containing particles under different effective densities.

3.2 The relationship between the morphology and effective density of rBC-containing particles

Figure 3 depicts the variations in the χ and R_void values as a function of ρ_rBC. χ is a physical index representing the regularity of a particle; the theoretical χ for a spherical particle is 1 regardless of the void inside, and a larger χ means a more irregular particle (Decarlo et al., 2004). In practice, the χ of rBC-containing particles ranges from 1 to 4 (Table 2) mostly due to the combustion material, combustion temperature, aging degree, etc. The largest χ (1.4) observed in this study was lower than that of freshly emitted rBC-containing particles from a diesel truck (χ=2.1), methane flame (χ=1.87), and propane flame (χ=4.0) and was in the range (χ=1–2.8) of rBC-containing particles with different aging degrees (Qiu et al., 2014; Peng et al., 2016). Zhang et al. (2016) suggested that the ρ_rBC of thinly coated rBC-containing particles was 0.3 g cm⁻³. Direct measurements of vehicle exhaust always obtain a ρ_rBC of 0.3–0.5 g cm⁻³ (Momenimovahed and Olfert, 2015). Because the lower detection limit of ρ_rBC was set to 0.8 g cm⁻³, fresh rBC-containing particles might not have been observed in this study. Indeed, the rBC-containing particles observed in this study were actually aged rBC-containing particles with moderate irregularity.

Figure 4 Variation in mass ratio (M_R) of coatings to rBC as a function of ρ_rBC.

Table 2 Brief summary of the effective density and dynamic shape factor of rBC-containing particles.

^* The effective density and shape factor counted in this table are for rBC-containing particles with a $D_{\text{mob}}=\mathrm{240}\pm \mathrm{20}$ nm.

The χ values showed a decreasing trend with the increasing ρ_rBC, indicating a more regular shape for rBC-containing particles with a larger ρ_rBC, which was consistent with previous studies (Qiu et al., 2014; Peng et al., 2016). When the ρ_rBC is less than 1.4 g cm⁻³, the χ decreases significantly with the increase in ρ_rBC. However, χ varies slowly between 1 and 1.1 when the ρ_rBC is larger than 1.4 g cm⁻³. A similar variation trend was also found for R_void. R_void decreases significantly from 0.5 to 0.1 and varies slowly between 0.1 and 0 when the ρ_rBC is larger than 1.4 g cm⁻³. These results are similar to those from the comparison between D_opt and D_mob; the morphology of rBC-containing particles changed from an irregular and loose structure to a compact spherical structure with the increasing ρ_rBC. Thus, a ρ_rBC of 1.4 g cm⁻³ may be the morphological transition point in this study. Using a smog chamber, Peng et al. (2016) also observed a change in the ρ_rBC from ∼ 0.5 to 1.4 g cm⁻³ during the aging process and found that rBC-containing particles with a ρ_rBC=1.4 g cm⁻³ had a χ∼1.

We found that rBC-containing particles had a larger χ value and R_void at the condition when ρ_non-rBC,bulk is smaller, especially for irregular particles (Fig. 3a). This may imply that different coating composition played a different role in the morphology reconstruction of rBC-containing particles because ρ_non-rBC,bulk reflected the composition of non-rBC, which may relate to the coating composition of rBC to some degree (Fig. S6). The rBC-containing particles could reach a compact spherical structure when the ρ_rBC was 1.2 g cm⁻³ with an χ of 1.05 and a R_void of 0.08 when 1.1 g cm${}^{-\mathrm{3}}<{\mathit{\rho }}_{\text{non-rBC,bulk}}<\mathrm{1.3}$ g cm⁻³, whereas the morphological transition of ρ_rBC was higher for rBC-containing particles at a higher ρ_non-rBC,bulk condition.

3.3 Mass ratio of coatings to the rBC core of rBC-containing particles with different ρ_eff values

The mass ratio (M_R) of the coating to the rBC core is used to represent the coating thickness in this study. The coating thickness is an index of the aging degree of rBC-containing particles since condensation and coagulation will lead to an increase in the coating thickness during the aging process. As shown in Fig. 4, rBC-containing particles with larger ρ_rBC values had more coating. This phenomenon explains the morphological change that occurs with an increasing ρ_rBC. The surface tension imposed by the coating was found to shrink the rBC core (Zhang et al., 2016). After coating, rBC-containing particles with larger hygroscopicity more easily obtain surface water, which enlarges the surface tension and shrinks the rBC-containing particles to a more compact structure (Zhang et al., 2008). Moreover, the coatings are able to fill the void of rBC-containing particles, resulting in a more compact structure (Pagels et al., 2009). Thus, increasing the coating makes rBC-containing particles more compact, and the compact structure leads to a larger effective density, as observed.

Recently, studies using different methods have proven the occurrence of morphological change of rBC-containing particles with an increase in the coating thickness. Peng et al. (2016) observed that rBC-containing particles changed to a compact spherical structure when the ratio of the coating thickness to the rBC core diameter reached 0.8–1, corresponding to a M_R of 4.5–6.5. By comparing the measured and modeled scattering cross sections of rBC-containing particles, Liu et al. (2017) found that the measured scattering cross section agreed well with the core–shell model prediction when the M_R was larger than 3, suggesting adoption of a spherical morphology by rBC-containing particles with a large M_R. The morphology of rBC-containing particles seems to change to be spherical at a certain M_R point. In this study, the M_R was nearly invariant and fluctuated between 6 and 8 when the ρ_eff was larger than 1.4 g cm⁻³, suggesting that the rBC-containing particles were mostly spherical in structure when the M_R was larger than 6–8.

In the real atmosphere, the variant temperature and relative humidity may also contribute to the morphological variation in rBC-containing particles, which makes the morphological transition M_R point more complicated and thus different from that reported in previous studies. However, an agreement has been reached concerning the mechanism by which the morphology changes with the increasing coating thickness. A M_R of 7 was determined to be the morphological transition point in Beijing in winter. The morphological transition M_R or volume ratio may be very useful for parameterization in atmospheric models. Thus, more observations are needed to explore the variation in and constraining factors of the morphological transition M_R.

Figure 5 Number distributions of rBC-containing particles (black lines) and non-rBC particles (blue lines) with different effective densities during different episodes. The black dashed line denotes the effective density of bulk rBC-containing particles, and the blue dashed line denotes the effective density of bulk non-rBC particles.

Previous studies have always used a shell ∕ core ratio (S ∕ C) to represent the coating thickness. The M_R of rBC-containing particles with a ρ_rBC=0.8 g cm⁻³ averaged 2.0, corresponding to an S ∕ C of 1.5, and the M_R of rBC-containing particles with a ρ_rBC=1.4 g cm⁻³ averaged 7.0, corresponding to an S ∕ C of 2.15. Typically, the S ∕ C ratio of freshly emitted BC observed at urban sites was lower than 1.2 (Liu et al., 2014; Laborde et al., 2013). In this study, rBC-containing particles with a ρ_rBC of 0.8 g cm⁻³ were characterized as having an irregular and loose structure with χ=1.4 and R_void=0.5. Since the ρ_rBC increased with the increase in the M_R or S ∕ C, the observed average S ∕ C = 1.2 at the urban site suggested that most rBC-containing particles at the urban site might have a ρ_rBC lower than 0.8 g cm⁻³ and thus a more irregular structure.

3.4 The morphology of bulk rBC-containing particles

The number distributions of ρ_rBC and ρ_non-rBC were counted to evaluate the morphological characteristics of the bulk rBC-containing particles in the ambient environment, as shown in Fig. 5. Generally, the ρ_rBC and ρ_non-rBC number distributions exhibited a unimodal distribution except for the ρ_rBC distribution in EP 3 (the clean period). Observations of rBC-containing particles indicated that the coating thickness distribution always exhibited a clear bimodal pattern (Liu et al., 2014; Wu et al., 2017). rBC-containing particles were observed with a thin coating, which was mostly attributed to local traffic emissions, and with a thick coating, which might be the result of biomass emissions or the aging process. The aged rBC-containing particles with a ρ_rBC>0.8 g cm⁻³ observed in this study may exactly correspond to the rBC-containing particles with a thick coating and thus exhibit a unimodal pattern. We speculate that the ρ_rBC number distribution will exhibit a bimodal pattern if the detection limit is sufficiently low and the left peak in the expected bimodal pattern corresponds to the rBC-containing particles with thin coatings. The ρ_rBC distribution in EP 3 may be influenced by the thinly coated rBC-containing particles, which might be present in relatively higher numbers during the clean period.

Figure 6 Number fractions of rBC-containing particles in the total particles (rBC-containing and non-rBC particles) under different effective densities.

Figure 7 (a) The scattering cross section of BC-containing particles at the 1064 nm wavelength predicted by different models and measured by the SP2 under different effective densities. (b) The mass absorption cross section at the 532 nm wavelength predicted by different models under different effective densities. Model 3 was used with various assumptions of the core fractal dimension (D_f=2.0, 2.2, 2.4, 2.6, and 2.8) as denoted in the graph.

The ρ_rBC,bulk and ρ_non-rBC,bulk were separately estimated to be 1.21 and 1.39 g cm⁻³, respectively, throughout the observation period. Notably, due to the detection limit, the ρ_rBC,bulk in this study was determined for aged rBC-containing particles, and the true ρ_rBC,bulk was expected to be lower if fresh rBC-containing particles were taken into consideration. However, even for these aged rBC-containing particles, the morphology was mostly in a fractal structure because the ρ_rBC,bulk (1.21 g cm⁻³) was smaller than the morphological transition ρ_rBC (1.40 g cm⁻³). Wang et al. (2017) proved that only 12 % of rBC-containing particles were in an embedded structure and that 88 % of rBC-containing particles were in a bare or partly coated structure at urban sites through direct TEM observation. Our results provided evidence for the irregularity of rBC-containing particles based on assessment of more particle numbers.

The ρ_eff was separately counted in the five episodes, as shown in Fig. 5, to investigate variation in ρ_eff under different pollution situations. The ρ_rBC,bulk was 1.37, 1.01, 1.15, 1.01, and 1.21 g cm⁻³ during EP 1–5, and the corresponding ρ_non-rBC,bulk was 1.43, 1.18, 1.40, 1.20, and 1.40 g cm⁻³, respectively. According to Fig. 3a, the morphological transition ρ_rBC points were 1.2 g cm⁻³ in EP 2 and EP 4 and 1.4 g cm⁻³ in EP 1, EP 3, and EP 5 due to the different ρ_non-rBC,bulk values. The ρ_rBC,bulk in the five episodes was lower than that of the morphological transition ρ_rBC regardless of the pollution conditions, indicating that a substantial number of rBC-containing particles were in a fractal structure even under pollution conditions. However, the ρ_rBC,bulk in EP3 was smaller than that in EP1 and EP5, which might suggest a more compact structure of rBC-containing particles in pollution conditions since the morphological transition ρ_rBC was similar during these three episodes.

The number fraction of rBC-containing particles in the total measured particles (rBC-containing and non-rBC particles) increased with the decrease in the ρ_eff, as shown in Fig. 6. rBC-containing particles only accounted for 10 %–20 % of particles with a ρ_eff=1.6 g cm⁻³, whereas this fraction significantly increased to ∼ 60 % for particles with a ρ_eff=0.8 g cm⁻³. The data from the five episodes all followed the same tendency, and the maximum number fraction of rBC-containing particles was reached when the ρ_eff was equal to 0.8 g cm⁻³. A power function was used to fit the data and showed that the number fraction of rBC would be 100 % if the ρ_eff were less than 0.73 g cm⁻³. Rissler et al. (2014) observed a bimodal ρ_eff distribution of ambient aerosols. The ρ_eff of aerosols in the two peaks ranged separately from 0.30 to 0.80 and 1.28 to 1.46 g cm⁻³. The mass of aerosols with a ρ_eff of 0.30–0.80 g cm⁻³ only lost 10 % after being heated to 300 ^∘C, indicating that most of these particles were fresh rBC-containing particles, which was consistent with our inference. Thus, if the measurement site was located in an area with enough fresh BC emission, the bimodal ρ_eff distribution of ambient aerosols was often observed (Qiao et al., 2018; Liu et al., 2015; Rissler et al., 2014) since the ρ_eff of fresh rBC-containing particles was sufficiently small with no disturbance by non-rBC particles. However, as shown in Fig. 6, the ρ_eff distributions of non-rBC and aged rBC-containing particles overlapped and could not be distinguished through a simple DMA–APM/CPMA–CPC system. Our study suggested that the second peak often observed in previous ρ_eff measurements was actually a mixture of non-rBC and aged rBC-containing particles. Rissler et al. (2014) used “dense” particles to describe particles with a ρ_eff of 1.28–1.46 g cm⁻³. This expression might be not very accurate since nearly 10 %–40 % of the particles were aged rBC-containing particles with a fractal structure (χ=1–1.2).

3.5 Optical properties of rBC-containing particles with different ρ_eff values

Since the morphology of rBC-containing particles was mostly in a fractal structure as discussed above, the simple core–shell structure treatment in the atmospheric model might cause bias in the optical property estimate of rBC-containing particles. An aggregate model was established, and the optical properties were calculated by solving Maxwell's equation based on the superposition T-matrix method (Wu et al., 2018). As shown in Fig. 7a, large discrepancies in the scattering cross sections (σ_SC) between the core–shell model and measurement were found in the small ρ_rBC range, indicating the strong impact of morphology on optical properties. An aggregate model can better capture the σ_SC characteristics than a perfect shell–core model when the ρ_rBC is smaller than 1.4 g cm⁻³. When the ρ_rBC is 0.8 g cm⁻³, the σ_SC predicted by the aggregate model with a rBC core fractal dimension (D_f) of 2.0–2.2 agrees well with the measurement. With an increase in the ρ_rBC, the measured σ_SC is consistent with the predicted value from the aggregate model obtained using the larger rBC core fractal dimension. This result may imply that the rBC core becomes more compact and regular with an increase in the ρ_rBC or coating thickness consistent with the laboratory results (Pagels et al., 2009; Xue et al., 2009).

Figure 7b exhibits the estimated mass absorption cross sections (MACs) from different models. The overestimation of the MAC using the core–shell structure averaged 16.7 % compared to that of the aggregate model when the ρ_rBC was less than 1.4 g cm⁻³. Additionally, the measured σ_SC with a ρ_rBC=1.6 g cm⁻³ was similar to the predicted values of models 1 and 2, indicating a near-spherical structure of the rBC-containing particles. However, the MAC predicted by models 1 and 2 varied. Although laboratory studies proved that the rBC core shrank after coating, an irregular rBC core was often observed even in thickly coated cases in the ambient measurement (Adachi et al., 2010; Zhang et al., 2016), suggesting that model 2 might be closer to the realistic thickly coated situation. Since model 1 overestimated the MAC by 7.4 % with a ρ_rBC=1.6 g cm⁻³ compared to that of model 2, the morphology of the rBC core should also be considered, even in cases with a large ρ_rBC or thickly coated condition. In general, the commonly observed light absorption enhancement in pollution conditions cannot simply be attributed to the “lensing effect”. The morphological change of rBC-containing particles and the BC core may also play an important role in light absorption enhancement.

4 Conclusion

A novel tandem DMA–CPMA–SP2 system was used to investigate the effective density of rBC-containing particles (ρ_rBC) and their relationship with the rBC mixing state in Beijing. Aerosols with the same mobility diameter (240 nm) and different ρ_eff values (0.8, 1.0, 1.2, 1.4, 1.6, and 1.8 g cm⁻³) were preselected by the DMA–CPMA system and injected into the SP2 to obtain the corresponding mixing state. The results showed that the ρ_rBC could reflect the morphology of rBC-containing particles. The dynamic shape factor of rBC-containing particles decreased from 1.4 to 1 with the increase in the ρ_rBC, indicating that the morphology of the rBC-containing particles changed from an irregular loose structure to a compact spherical structure. rBC-containing particles with ρ_rBC values of 0.8, 1.0, and 1.2 g cm⁻³ mostly adopted a nonspherical structure, whereas those with ρ_rBC values of 1.6 and 1.8 g cm⁻³ had a spherical structure. The ρ_rBC=1.4 g cm⁻³ was determined to be the morphological transition point in this study. The mass ratio (M_R) of the coatings to the rBC core was calculated for rBC-containing particles with different ρ_rBC values. The M_R gradually increased from 2 to 6–8 with the increase in the ρ_rBC when its measure was less than 1.4 g cm⁻³ and stayed invariant when the ρ_rBC was larger than 1.4 g cm⁻³, suggesting that the increased coating thickness during the aging process was the cause of morphological changes and that the rBC-containing particles tended to be spherical when the M_R was larger than 6–8 in the winter in Beijing.

The morphological characteristics of the bulk ambient rBC-containing particles were investigated by calculating the bulk effective density of rBC-containing particles (ρ_rBC,bulk) considering the number distribution of ρ_rBC. The ρ_rBC,bulk averaged 1.21 g cm⁻³ during the whole observation period and was lower than the morphological transition ρ_rBC regardless of the pollution conditions. The ρ_rBC,bulk was overestimated due to the lower detection limit in this study (set to 0.8 g cm⁻³), which was larger than the ρ_rBC of freshly emitted rBC-containing particles. However, the ρ_rBC,bulk was still lower than the morphological transition ρ_rBC, suggesting that the rBC-containing particles were mostly not in a core–shell structure in the ambient condition. An aggregate model considering the morphological information of rBC-containing particles was approved to better represent and to evaluate the optical properties of rBC-containing particles. Generally, the core–shell model overestimated light absorption compared to that of the aggregate model by 16.7 % for rBC-containing particles with a ρ_rBC=0.8–1.4 g cm⁻³. This study revealed that a substantial number of rBC-containing particles were in an irregular structure in the ambient atmosphere and highlighted the importance of morphology for optical property estimates. A proper parameterization considering rBC-containing particle morphological changes with M_R and a morphology-dependent optical model may help reduce the uncertainty in atmospheric modeling.