The 1-month continuous observations were conducted from the 9 September 2023 to the 8 October 2023 at the Central Air Quality Assurance Monitoring Station (CASA site) for the 19th Asian Games in Hangzhou. The CASA site (30.25° N, 120.24° E) is located in the western region of Hangzhou, which is one of the most developed cities in the Yangtze River Delta (YRD) (Supplement Fig. S1), and near the Qiantang River (located just 100 m away). There is an elevated road 1.9 km northeast of the site and another 3.2 km southwest of the site. The surrounding area is mainly residential and commercial, with no significant sources of pollution. The local influence at the site is primarily from residential activities and traffic emissions.

A schematic diagram of the measurement settings is shown in Fig. 1. The particles were sampled with a PM_2.5 (particulate matter with an aerodynamic diameter of ≤ 2.5 µm) cyclone inlet (8 L min⁻¹) and then passed through a Nafion dryer to reduce the relative humidity (RH) to less than 30 %. The sampling flow was split into three lines. One line was fed to an AAC-SMPS to determine the effective densities of particles with different diameters. Another line was connected to a seven-wavelength Aethalometer (Model AE-33, Magee Scientific, USA; sample flow rate of Q= 3 L min⁻¹) to measure the mass concentration of BC. The remaining flow was maintained as a bypass flow with an extra pump to ensure an accurate cutoff size. Particles with 12 logarithmically equally distributed aerodynamic sizes ranging from 200 to 1000 nm were selected by an AAC (Cambustion Ltd., UK; sheath flow rate Qsh= 9 L min⁻¹ and relaxation time resolution Rt= 2.5), and each size was sampled for 5 min. After the AAC classification, the aerosol flow was then split into three parallel lines. One line led to a condensation particle counter (CPC, Model 3772, TSI Inc., USA) to determine the concentration of the dae-selected particles. The flow rate of the CPC was decreased to 0.3 L min⁻¹, with a bypass flow of 0.7 L min⁻¹. The second line directed the flow to an AE-33. The results of the CPC and AE-33 downstream of the AAC will be discussed in other studies. In the remaining line, the particle number size distribution (PNSD) of each dae-selected particle was acquired using an SMPS, which consisted of a soft X-ray neutralizer (Model 3088, TSI Inc., USA), a DMA (Model 3081, TSI Inc., USA; sheath flow rate Qsh= 3 L min⁻¹), and a CPC (Model 3756, TSI Inc., USA; sample flow rate Qa= 0.3 L min⁻¹). The mobility diameter range was 13.8–749.9 nm with a total scan time of 4 min. The modal mobility diameter of the dae-selected particles, denoted as dm, was determined by fitting the PNSD to a lognormal distribution (Eq. S4 in the Supplement). However, owing to the low concentrations of larger particles selected by the AAC and the inability to fit the mode ρeff from ρeff distributions scanned by the SMPS, only particles with mobility diameters smaller than 600 nm were fitted to lognormal distributions. The bulk chemical composition of nonrefractory aerosols, i.e., the mass concentrations of OA, nitrate, sulfate, ammonium, and chloride, was measured via an aerosol chemical speciation monitor (ACSM; Aerodyne Research, Inc., USA). Combined with the BC mass concentration, the effective density (ρeff,cal) can be calculated as follows (Levy et al., 2013): 11ρeff,cal=∑ifiρi, where ρi and fi denote the effective density and mass fraction of chemical component i, respectively. The values of the effective density of BC and OA are discussed in Sect. 3.4.

The AAC and SMPS used in this study were calibrated with certified polystyrene latex (PSL) spheres (Thermo Fisher Scientific Inc., USA) with sizes of 152±5, 203±5, 303±8, and 508±8 nm (Fig. S2). The dae measured by the AAC was compared with the aerodynamic diameter of the PSL (dae,PSL), which was calculated from the nominal diameter (dm,PSL) and material density of the PSL (1.05 g cm⁻³). The dm determined by the SMPS was compared to the nominal diameter of the PSL. The deviations between the measured dae (dm) and dae,PSL (dm,PSL) were 3.19 % and 2.48 %, respectively. The performance of the AAC-SMPS tandem system was first validated with PSL particles, and the average effective density of 1.045 g cm⁻³ was determined, which is consistent with the material density of PSL (1.05 g cm⁻³) (Fig. S3). Then, the system was validated by ammonium sulfate (AS) and ammonium nitrate (AN) particles generated with an atomizer (Model 3079A, TSI, Inc., USA). The effective densities of the size-resolved AS and AN particles are shown in Fig. S2c. The effective densities of AS particles of different sizes are within the range of 1.68–1.82 g cm⁻³, which is consistent with previous studies (Yao et al., 2020; Lu et al., 2024). The measured average ρeff of AN particles was 1.80 g cm⁻³, which is slightly higher than the mean ρeff of 1.69±0.17 g cm⁻³ measured via DMA and a quartz crystal microbalance (QCM) (Sarangi et al., 2016).

The RF models were built with the “RandomForestRegressor” function provided by “scikit-learn” in a Python environment (Pedregosa et al., 2011). In the RF models, the independent variables are the size-resolved effective densities of particles with different diameters. The explanatory variables are the mass fractions of the main components of PM_2.5, i.e., OA, (NH4)2SO₄, NH₄NO₃, NH₄Cl, and BC. The RF model was trained with a portion of the samples drawn from the whole dataset, while the remaining samples were used for model validation. To obtain an optimal RF model, the hyperparameters for the RF model were tuned via the “GridSearchCV” function from the scikit-learn library (Song et al., 2022a). The coefficient of determination (R2) was used to evaluate the performance of the ML model. The best hyperparameters (n_estimators, min_samples_split, max_features, bootstrap, and max-samples) of the RF model and R2 values for particles of different sizes are listed in Table S1 in the Supplement. The SHAP approach was implemented via the “shap” Python package.

The regional-scale transport patterns were investigated via back-trajectory calculations with the open-source MeteoInfo software developed by Wang (2019). The model was run 48 h backward every hour from an altitude of 5 m above the site. The NCEP Global Data Assimilation System (GDAS) model with a grid resolution of 1° × 1° and a run time of 48 h each day from August to October 2023 was used in the calculations, followed by K-means clustering to investigate sources of air masses, which has been widely used in previous studies (Xu et al., 2023). All of the data in this study are shown in Beijing time (BJT).

The average ρeff values for particles with aerodynamic diameters of 200, 235, 277, 326, 384, 452, and 531 nm were 1.47±0.09, 1.50±0.09, 1.52±0.08, 1.55±0.08, 1.58±0.08, 1.60±0.08, and 1.63±0.10 g cm⁻³, respectively (Fig. 2). The distribution of ρeff was fitted to a unimodal Gaussian distribution, whereas some previous studies have reported a bimodal distribution, i.e., a mode with a higher peak value and larger effective density, denoted as the main-density mode and another mode with lower peak value and lower effective density denoted as the sub-density mode. The unimodal distribution denotes an internally mixed aerosol composition, whereas the bimodal distribution with a second, below-unity density peak indicates externally mixed BC (Qiao et al., 2018; Ma et al., 2020; Zhou et al., 2022; Xie et al., 2024). In many studies, the frequency of the bimodal distribution is not comparable and largely depends on the distance between the observation points and the emission sources (Zhou et al., 2022; Wu et al., 2023; Xie et al., 2024). The occurrence of the sub-density mode is greater at sites close to the emission source. The sub-density particles predominated near the street with higher traffic emissions, whereas the main-density particles dominated in the rural background (Rissler et al., 2014). A lower frequency of sub-density events indicates that the particles are more likely to be in an internal mixing state. BC, a major product of fossil fuel and biomass combustion, is a tracer of primary emissions (Briggs and Long, 2016). On the one hand, the bimodal distribution may not have been detected due to the absence of fresh BC. The diameter of fresh BC mainly ranges from 50 to 120 nm (Bond et al., 2013), which is much smaller than the selected particles in our study. On the other hand, a previous study indicated that when the ratio of the mass concentration of BC to PM_2.5 is less than 20 %, particles with diameters of between 50 and 350 nm are predominantly in an internal mixing state (Wu et al., 2023). Moreover, the relatively low number concentration of soot particles may be masked by the overwhelming abundance of dominant-mode particles, making them difficult to detect in the number size distribution (Yin et al., 2015). Unfortunately, we did not measure the chemical composition of particles of different sizes, and the bulk chemical composition revealed that the average proportion of BC to PM_2.5 was only 11 % in our study. Therefore, only a unimodal Gaussian fit of ρeff was identified, indicating that the particles in Hangzhou tend to be internally mixed.

We also compared the ρeff values of the particles with those reported in other studies (Fig. 3). Notably, in this study, particles with aerodynamic diameters were selected by the AAC; however, generally, the particle mobility diameter has been selected in previous studies. Therefore, the mobility diameters reported in previous studies were first converted to aerodynamic diameters for comparison with the results of our study. The results revealed that the particle ρeff in most urban regions has a unimodal distribution, with relatively high densities ranging from 1.2 to 1.8 g cm⁻³ (Yin et al., 2015; Xie et al., 2017; Lin et al., 2018; Lu et al., 2024). The bimodal distribution of particle ρeff was found primarily in remote areas and near highways (Rissler et al., 2014; Ma et al., 2017; Ma et al., 2020; Zhou et al., 2022; Xie et al., 2024). Specifically, in the bimodal distribution, the main-density mode corresponds to a higher ρeff and increases with increasing particle size, which is similar to that in urban areas. In contrast, the ρeff of the sub-density mode was generally less than 1 g cm⁻³ and decreased with increasing particle diameter. The difference between urban and rural sites can be attributed to differences in the mixing state of the particles. Due to effective secondary organic aerosol formation and emissions from various sources, particles tend to mix internally in urban areas (Ching et al., 2019), leading to a unimodal distribution. Additionally, traffic emissions promote the occurrence of bimodal distributions, and it has been reported that particles are more externally mixed in street canyons and near highways (Rissler et al., 2014; Riemer et al., 2019). At rural sites, the high frequency of the bimodal distribution was determined when the observation site was influenced by local emissions (Zhou et al., 2022).

Figure 4 shows the diurnal cycle of ρeff for particles with diameters of 200 and 531 nm, along with the meteorological parameters and mass fractions of different chemical compositions of bulk particles. The diurnal variations in ρeff of the seven dae-selected particles are shown in Fig. S4. The results indicated that, in comparison with larger particles, smaller particles (dae < 350 nm) exhibit more pronounced diurnal variations in ρeff, typically showing lower values during the day and higher values at night (Fig. 4a). From 07:00 to 09:00 BJT, with increasing fresh BC and hydrocarbon-like organic aerosols (HOAs) from vehicle emissions (Fig. 4b), the ρeff of small particles decreases significantly. The volatile and gas–particle partitioning properties of (NH₄)₂SO₄ and NH₄Cl are dependent on the ambient temperature and RH (Sun et al., 2012). Although the atmospheric oxidative capacity increases later (Fig. S5), the photochemical production of HNO₃ cannot compensate for evaporative loss under relatively high temperatures (Zhang et al., 2015). The mass fraction of nitrate decreased continuously from 07:00 to 13:00 BJT. Moreover, SOA formation increased significantly during this period. As a result, the fraction of the high material component decreased, whereas OAs with low material density accumulated, leading to a decrease in ρeff. Although the mass fraction of secondary inorganic particles subsequently remained relatively low, ongoing atmospheric aging may cause more small particles to have a spherical morphology (Wang et al., 2017, 2021). This explains why the ρeff of fine particles gradually increased between 13:00 and 17:00 BJT, even though the proportion of high-density components, such as secondary inorganic components, did not significantly increase. After 17:00 BJT, the ρeff values of the small particles did not decrease with increasing BC (Fig. S6f) and POA (Fig. S6g) emissions. Instead, it continued to rise, reaching a peak at 23:00 BJT, after which it remained relatively stable. During this period, the increasing RH and decreasing temperature facilitated the redistribution of HNO₃ into the particulate phase (Sun et al., 2018; Kuang et al., 2021) and promoted the liquid-phase formation of nitrates on aerosol surfaces (Wang et al., 2020). This led to a dramatic increase in the proportion of SIA, especially for nitrates (Fig. S6d); therefore, the ρeff of the small particles did not decrease despite the decrease in the concentration of primary emitted particles such as BC and HOA.

In addition, compared to small particles, the diurnal variation in the effective density of large particles is less pronounced (Fig. S4). The decreasing trend during the period from 07:00 to 13:00 BJT becomes less obvious, primarily because larger particles have longer residence times in the atmosphere and are less influenced by fresh emissions, resulting in a more stable chemical composition (Zhai et al., 2017; Xie et al., 2024). Overall, the effective density of large particles shows a slight increase throughout the day. This may be related to the increase in RH at night. which facilitates the formation of SIA, as has been discussed before. However, compared with smaller particles, larger particles exhibit reduced surface reactions and a decreased adsorption capacity due to their lower specific surface area (Okuda, 2013). As a result, the ρeff of larger particles was less sensitive to changes in temperature and RH.

In general, the ρeff values of particles are influenced mainly by their chemical composition and morphology, which are driven by their atmospheric oxidative capacity, RH, and temperature. Two episodes were identified to further explore the evolution of the particle ρeff (Fig. S7). Episode 1 (EP1) and episode 2 (EP2) occurred from 18:00 BJT on the 9 September to 18:00 BJT on the 12 September and from 17:00 BJT on the 23 September to 12:00 BJT on the 30 September, respectively, with the remaining period defined as the clean period (CP). The PM_2.5 concentrations of EP1 and EP2 were significantly greater than that of CP (11.4 µg m⁻³), with average concentrations of 27.9 and 44.7 µg m⁻³, respectively. EP1 was dominated solely by organic components, which accounted for 64.1±8.0 % on average, whereas EP2 was dominated by organic and nitrate components, which accounted for 40.0±13.5 % and 29.4±12.9 %, respectively.

The average size-resolved effective densities and bulk chemical compositions under different pollution conditions are shown in Fig. 5. The ρeff values of all of the particles increased with increasing particle size except during EP2. Interestingly, the ρeff of the particles during EP1 (1.47–1.61 g cm⁻³) was smaller than that during CP, which is similar to previous observations in the North China Plain (Zhou et al., 2022), indicating that the compositions of particles of the same size are different under different pollution levels. The proportion of OAs reached 64.1 %, significantly higher than that during CP (49.3%). Previous studies have reported that the effective density of organic materials is between 1.2 and 1.4 g cm⁻³, which is lower than that of inorganic materials (Levy et al., 2013). Therefore, the small ρeff values of all of the particles during EP1 could be attributed to the high proportion of OAs. Additionally, air mass cluster analysis indicated that the pollution during EP1 was influenced primarily by regional transport, with a shorter transportation distance than that during CP (Fig. 5d). As a result, the particles had not fully aged and remained in a relatively fractal structure, leading to a lower effective particle density during EP1.

Another interesting phenomenon is that the ρeff of the particles did not increase with increasing particle size during EP2. For particles smaller than 400 nm, the average ρeff (1.51–1.55 g cm⁻³) was greater than that of CP (1.40–1.51 g cm⁻³), whereas for particles larger than 400 nm, the average ρeff (1.54–1.56 g cm⁻³) was lower than that of CP (1.56–1.64 g cm⁻³). We attempt to explain this phenomenon from two perspectives. First, a small particle size results in a large specific surface area, which promotes the formation of secondary inorganic components. As shown in Fig. 5b, the proportion of secondary inorganic compounds during EP2 was as high as 53.2 %, which was much higher than the 37.3 % observed during CP. Secondary nitrate was the most prominent component, contributing 29.2 %. The diurnal variations in size-resolved particles during different periods are shown in Fig. S8. During EP2, from 13:00 to 19:00 BJT, the ρeff of small particles was significantly greater than that during CP. This difference gradually decreased over time, from a peak of 7.3 % at 13:00 BJT to 4.7 % at 07:00 BJT. This suggests that nitrate formation on small particles was more pronounced during EP2. A previous study revealed that the formation of atmospheric nitrate under high temperatures was due to enhanced heterogeneous processes associated with the aerosol water concentration (Wang et al., 2020). The heterogeneous hydrolysis of N₂O₅ was the main mechanism of nitrate formation at night, which was also promoted by high RH and low temperature (Liu et al., 2020). Our observations revealed that the RH and temperature were 81.6 % and 26.4 °C, respectively, during EP2, which were significantly higher than the respective values of 78.3 % and 23.8 °C during CP. These results are favorable for nitrate formation on small particles during EP2. Additionally, during EP2, the air mass passing over regions such as Jiangsu and northern Zhejiang carried a high load of anthropogenic pollutants, including SO₂ (Fig. 5c). All of these factors resulted in higher precursor concentrations and enhanced the formation of secondary inorganic compounds, particularly on smaller particles. Consequently, the ρeff of the particles during EP2 remained relatively unchanged with increasing particle size.

The chemical composition of a particle is the main factor affecting its ρeff. Inorganic components, such as NH₄NO₃ and (NH₄)₂SO₄, have higher densities than organic compounds and BC. Therefore, variations in aerosol chemical composition can partly explain the observed trend in effective densities. Typically, the size-resolved chemical composition is measured via an aerosol mass spectrometer (Zhang et al., 2005) and single-particle mass spectrometry (Zhai et al., 2017). Due to limitations in the measurement techniques, the size-resolved chemical composition of particles is not accurately measured in most studies. Here, the SHAP method was used to explore the response of different chemical components at every measured particle size on the ρeff of the particles. A cross-validation was used to evaluate the model performance, and the results suggested that the RF model performed well for particles smaller than 350 nm, with an overall R2 score of greater than 0.55 (Table S1). In contrast, the correlation for larger particles was weaker, possibly because the chemical component variability in larger particles was smaller, resulting in inadequate modeling of these particles. For small particles, organics, NH₄NO₃, and NH₄Cl are the most important chemical components affecting their ρeff values (Fig. 6). Specifically, the contribution of the organic proportion was the greatest, with an average contribution of 42.9 %. However, this response is negative, indicating that the ρeff of smaller particles decreases with an increasing proportion of organics. NH₄NO₃ and NH₄Cl, which account for 32.2 % and 12.7 %, respectively, were positively correlated with ρeff, suggesting that the increase in the proportion of these components mainly leads to a significant increase in the ρeff of the small particles.

Considering the difficulty of measuring the size-resolved chemical components of particles, this study attempted to calculate the size-resolved composition according to the size-resolved ρeff. According to Eq. (1), the effective densities of the ambient OA and BC are needed. For simplicity, the particles were assumed to consist of three components, e.g., OA, SIA, and BC. The value of 1.77 g cm⁻³ for SIA was adopted in this study. Material density values in the range of 0.3–2 g cm⁻³ for BC and 1.2–1.8 g cm⁻³ for OA were used in the sensitivity test. A step length of 0.02 g cm⁻³ was adopted for both the BC density and OA density. The mean ρeff is the number-concentration-weighted average density of particles of different sizes. The optimal values of OA and BC were determined by comparing the calculated bulk ρeff with the average ρeff for particles with diameters in the range of 200–532 nm. As a result, density values of 1.20 g cm⁻³ for OA and 1.77 g cm⁻³ for BC were determined. The BC density of 1.77 g cm⁻³ can be attributed to the coating of nitrate, as nitrate contributed the most to the mass fraction of PM_2.5. The ρeff values of BC were reported to be in the range of 1.62–1.77 g cm⁻³ for particles with aerodynamic diameters of 200, 350, and 500 nm in Shanghai, indicating a coating of NH₄NO₃ and/or (NH₄)₂SO₄ (Wang et al., 2021). The mean ρeff can be fitted well by applying the results of OA and BC, with an R2 of 0.56 (Fig. 7a).

We apply the fitted densities of OA and BC to Eq. (1). Then, the equation is expressed as follows: 21ρeff=fOAρOA+fBCρBC+fSIAρSIA, where ρOA is 1.2 g cm⁻³, ρBC is 1.77 g cm⁻³, and ρSIA is 1.77 g cm⁻³. ρeff is the size-resolved ρeff measured by the AAC-SMPS. A series of fractions of OA, BC, and SIA were set to calculate ρeff via Eq. (2), and the fractions of OA, BC, and SIA were adjusted until the difference between the calculated and measured ρeff values was the minimum value and within an acceptable range (0.5 %). Consequently, the scatterplots and time series of the size-resolved proportions of OAs during the observation were determined, as shown in Fig. 7. The slope between the measured and calculated mass fractions of OAs reaches 0.65 for particles with dae < 350 nm, indicating that this method can be used to deduce the chemical composition effectively. However, for larger particles (dae > 350 nm), the OA and SIA fractions can be reproduced well only during EP2 (Fig. S9), indicating that this simplified method to deduce the chemical composition is not suitable for particles with diameters larger than 350 nm unless the pollution process is dominated by OA and nitrate. We must acknowledge that this calculation would be more rigorous if size-resolved chemical composition data were available. Here, we propose this method, which remains applicable if size-resolved chemical composition measurements become available in future studies. Moreover, we also conducted a sensitivity analysis, which revealed that the fitting results are more sensitive to the density of BC than to that of OA (Fig. S10). For 200 nm particles, when the BC density was 1.77 g cm⁻³, the fitting results exhibited a higher tolerance to variations in the OA density. However, as the particle size increased, this tolerance decreased. Therefore, when inferring the chemical composition from effective density, it is more important to accurately constrain the densities of OA and BC for larger particles.