Measurement report: Distinct size dependence and diurnal variation in organic aerosol hygroscopicity, volatility, and cloud condensation nuclei activity at a rural site in the Pearl River Delta (PRD) region, China

Organic aerosol (OA) has a significant contribution to cloud formation and hence climate change. However, high uncertainties still exist in its impact on global climate, owing to the varying physical properties affected by the complex formation and aging processes. In this study, the hygroscopicity, volatility, cloud condensation nuclei (CCN) activity, and chemical composition of particles were measured using a series of online instruments at a rural site in the Pearl River Delta (PRD) region of China in fall 2019. During the campaign, the average hygroscopicity of OA (κ_OA) increased from 0.058 at 30 nm to 0.09 at 200 nm, suggesting a higher oxidation state of OA at larger particle sizes, supported by a higher fraction of extremely low volatility OA (ELVOA) for larger size particles. Significantly different diurnal patterns of κ_OA were observed between Aitken mode particles and accumulation mode particles. For Aitken mode particles (30–100 nm), the κ_OA values showed daily minima (0.02–0.07) during daytime, while the accumulation mode exhibited a daytime peak (∼ 0.09). Coincidently, a daytime peak was observed for both aged biomass burning organic aerosol (aBBOA) and less oxygenated organic aerosol (LOOA) based on source apportionment, which was attributed to the aging processes and gas–particle partitioning through photochemical reactions. In addition, the fraction of semi-volatile OA (SVOA) was higher at all measured sizes during daytime than during nighttime. These results indicate that the formation of secondary OA (SOA) through gas–particle partitioning can generally occur at all diameters, while the aging processes of pre-existing particles are more dominated in the accumulation mode. Furthermore, we found that applying a fixed κ_OA value (0.1) could lead to an overestimation of the CCN number concentration (N_CCN) up to 12 %–19 % at 0.1 %–0.7 % supersaturation (SS), which was more obvious at higher SS during daytime. Better prediction of N_CCN could be achieved by using size-resolved diurnal κ_OA, which indicates that the size dependence and diurnal variations in κ_OA can strongly affect the N_CCN at different SS values. Our results highlight the need for accurately evaluating the atmospheric evolution of OA at different size ranges and their impact on the physicochemical properties and hence climate effects.

1 Introduction

The impact of aerosol particles on global climate is widely known, including absorbing and scattering solar radiation and acting as cloud condensation nuclei (CCN). However, the extent of their contribution to the climate forcing is still unclear. Organic aerosol (OA) as a dominant component of fine particles (Jimenez et al., 2009) may contribute the uncertainties of climate effects of particles, mainly owing to unknown sources, physical properties, formation, and aging mechanisms (Volkamer et al., 2006; Kuang et al., 2020b; Rastak et al., 2017). Numerous studies show that secondary organic aerosol (SOA) accounts for a large OA fraction in most atmospheric environments (e.g., Huang et al., 2014; Shrivastava et al., 2017; Kanakidou et al., 2005; Hallquist et al., 2009). Nevertheless, both primary OA (POA) and SOA in the ambient air remain poorly characterized in terms of the formation mechanism and atmospheric evolution, and their particle diameter can vary on a large scale. Their impact on the global climate and atmospheric chemistry is still highly uncertain.

A combination of Aerodyne aerosol mass spectrometer (AMS) or aerosol chemical species monitor (ACSM) with positive matrix factorization (PMF) is widely used for investigating the OA evolution in the atmosphere (Li et al., 2013; Huang et al., 2018, 2014; Chen et al., 2015; Jimenez et al., 2009). For instance, Qin et al. (2017) found that hydrocarbon-like OA (HOA) from traffic emission contributed up to 40 % of OA during nighttime, owing to daytime traffic restrictions on heavy vehicles in urban Guangzhou. Kuang et al. (2020a) reported a dominant contribution to oxygenated OA (OOA) through aqueous-phase reaction in the North China Plain (NCP). Guo et al. (2020) observed different SOA mechanisms between clean and pollution episodes in the Pearl River Delta (PRD) region. Nevertheless, the investigation of bulk OA is still insufficient in understanding the aerosol climate effects without the size-resolved characterization. The OA size distribution is largely dependent on its composition, sources, and aging level. Li et al. (2012) observed various mass distribution patterns for different species in airborne particulate organics and reported that dehydrated sugars, fossil-fuel-derived n-alkanes, and PAHs showed a unimodal distribution, while non-dehydrated sugars and plant wax were derived as n-alkanes which presented a bimodal pattern. In the urban region, the Aitken mode was mainly dominated by HOA owing to traffic emissions (Zhang et al., 2005b; Cai et al., 2020). In the marine atmosphere, the size distribution of fine-mode POA was found to be independent of sea salt, while coarse-mode particles tended to be internally mixed with sea salt (Gantt and Meskhidze, 2013). Similarly, the OA physical properties were also found to be size-dependent. Deng et al. (2018) reported a higher OA hygroscopicity (κ_OA≈ 0.22) at about 150 nm than that (κ_OA≈ 0.19) at sub-100 nm at a forest site. In contrast, Zhao et al. (2015) measured size-dependent hygroscopicity and chemical composition for SOA from various procedures and found that κ_OA of SOA from α-pinene photooxidation decreased from 0.17 at 50 nm to 0.07 at 200 nm, which was attributed to the higher oxidation degree for smaller particles.

The size dependence of OA properties in the aforementioned studies might exert impact on the CCN prediction, which is mainly determined by their sources and formation processes. Cai et al. (2018) found that N_CCN at 0.1 % SS was underestimated by about 10 % if a κ_OA value of 0.1 was used. A model simulation from Liu and Wang (2010) showed that an increase of about 40 %–80 % for the CCN concentration was obtained by increasing the κ value of POA from 0 to 0.1. Wang et al. (2008) reported that the uncertainties of the first indirect aerosol effect varied from −0.2 to 0.2 W m⁻² for a κ_OA value of 0 to 0.25. Rastak et al. (2017) showed that using a single-parameter framework of κ_OA in evaluating the climate effects of aerosol could lead to significant errors (about −1.02 W m⁻²), which is the same order as the climate forcing of anthropogenic aerosol during the industrial period. These results further highlight a need for the understanding of the relationship between the OA evolution processes and its impact on the CCN activity at different particle sizes.

The OA hygroscopicity and volatility can provide information about the evolution of OA, given that they are often related to the chemical composition of the particles. A positive correlation between the hygroscopicity values and the oxidation degree of OA, including the ratio of atomic oxygen to atomic carbon (O:C), the oxidation state ($\stackrel{\mathrm{‾}}{{\text{OS}}_{\text{C}}}$), or the mass fraction of $m/z$ 44 (for ${\mathrm{CO}}_{\mathrm{2}}^{+}$) ion fragments in the organic spectra (f₄₄) from chemical composition, was widely reported in the literature (Wu et al., 2013; Pajunoja et al., 2015; Chang et al., 2010). Kim et al. (2020) found that the κ_OA was positively and negatively correlated with OOA and HOA at different size ranges, respectively. Deng et al. (2019) reported a decreasing trend of κ_OA at a size range of 100–360 nm during daytime in a forest environment, suggesting the formation of biogenic SOA (BSOA) through photochemical oxidation of biogenic volatile organic compounds (BVOCs). The OA volatility, specifically saturation vapor concentration (C^∗), is linked to the gas–particle partitioning and aging processes. In general, the C^∗ value decreases with an increase in the oxidation degree and the number of atomic carbon (Donahue et al., 2011). May et al. (2013) found that most of the biomass-burning POA was semi-volatile. Saha et al. (2017) showed a lower volatility of OA in the afternoon hours using a dual-thermodenuder (TD) system, probably owing to photochemical oxidation of OA. Hong et al. (2017) derived the OA volatility distribution by a combination of the VTMDA measurement and a multi-component evaporation dynamics model and found a moderate (R≈ 0.4) correlation between the OA groups obtained by the VTDMA data and the PMF results, respectively.

In this study, we investigate physical properties of OA at different size ranges and evaluate their influence on the atmospheric CCN concentration. A rural field measurement was conducted at the Heshan site in the Pearl River Delta (PRD) region, China, during fall 2019 (October and November). The hygroscopicity, volatility, size-resolved CCN activity, and chemical composition were measured by a series of online instruments. The size-resolved hygroscopicity and volatility distribution of organics were investigated. PMF was employed to analyze the sources and processes of OA. The impact of diurnal variation and size dependence of κ_OA on the N_CCN prediction at different supersaturation (SS) was assessed.

2 Measurement and methodology

2.1 Measurement site

The field measurements were conducted at the Heshan supersite in Guangdong Province, China during fall 2019 (27 September to 17 November 2019). This supersite (22^∘42^′39.1^′′ N, 112^∘55^′35.9^′′ E) is located in the southwest of the PRD region and surrounded by farms and villages, with an altitude of about 40 m. All sample particles first passed through a Nafion dryer (model MD-700, Perma Pure Inc., USA) to maintain a relative humidity (RH) lower than 30 %. The schematic diagram of the experimental setup can be found in Fig. S1 in the Supplement. Detailed descriptions of the measurement site and some instruments can be found in Cai et al. (2021a).

2.2 Instrumentation

2.2.1 Aerosol hygroscopicity and volatility measurement

Size-resolved hygroscopicity and volatility of particles were measured by a H/V-TDMA (model M3000, Bmet Inc., China). The instrument consists of two differential mobility analyzers (DMA1 and DMA2, model 3081 L, TSI Inc., USA), a Nafion humidifier (model MD-700, Perma Pure Inc., USA), a heater tube, and a condensation particle counter (CPC, model 3788, TSI Inc., USA). The instrument was operated in H- and V-mode during the measurement with a cycle time of about 3–4 h. The dried sample particles were firstly charged by an X-ray neutralizer and then classified by DMA1 at six diameters (30, 50, 80, 100, 150, and 200 nm). In the H-mode, the chosen particles with a specific dry diameter (D₀) were sequentially humidified by the Nafion humidifier to achieve 90 % of RH. A combination of DMA2 and CPC was employed to measure the size distribution of humidified particles ($D_{{\mathrm{p}}_{\text{wet}}}$). The hygroscopic growth factor (GF) at a certain dry diameter can be defined as

$$\begin{array}{}\text{(1)}& \text{GF}\left(D_{\mathrm{0}}\right)={\displaystyle \frac{D_{{\mathrm{p}}_{\text{wet}}}}{D_{\mathrm{0}}}}.\end{array}$$

In the V-mode, the selected particles from DMA1 were heated in the heater tube at 100, 150, 200, and 250 ^∘C, respectively. Similar to the H mode, the size distribution of heated particles along with particles at room temperature (25 ^∘C) was measured by the DMA2 and CPC. The volatility shrink factor (VSF) at a certain diameter and temperature is then defined as

$$\begin{array}{}\text{(2)}& \text{VSF}(T,D_{\mathrm{0}})={\displaystyle \frac{D_{\mathrm{p}}\left(T\right)}{D_{\mathrm{0}}}}.\end{array}$$

Before the campaign, standard polystyrene latex spheres (PSLs; with a size of 20, 50, and 200 nm), ammonium sulfate, and sodium chloride were used to calibrate the diameter classification of DMAs, hygroscopicity measurement, and transport efficiency of particles in the heater tube, respectively. For the H/V-TDMA data, the TDMAfit algorithm (Stolzenburg and McMurry, 2008) was applied to fit the growth factor and volatility shrink factor probability density function (GF-PDF and VSF-PDF) with various DMA transfer functions. The detailed data inversion processes can be found in Tan et al. (2013a).

2.2.2 The size-resolved CCN activity and particle number size distribution measurement

A combination of a cloud condensation nuclei counter (CCNc, model 200, DMT Inc., USA) and a scanning mobility particle sizer (SMPS, model 3938L75, TSI Inc., USA) was employed to measure size-resolved CCN activity. The supersaturation (SS) of each column (A and B) of CCNc was set to be 0.1 %, 0.2 %, and 0.4 % (for column A) and 0.7 %, 0.9 %, and 1.0 % (for column B), respectively. During the measurement, the SMPS was operated at a scanning mode. The sample particles were firstly neutralized by an X-ray neutralizer (model 3088, TSI Inc., USA) and were subsequently classified by a DMA. The classified particles were then split into three paths: one to a CPC (model 3756, TSI Inc., USA) for measurement of particle number concentration (with a flow rate of 0.6 L min⁻¹) and two to the CCNc for measurement of the CCN number concentration (N_CCN) at a specific SS (with a flow rate of 0.5 L min⁻¹).

The particle number size distribution (PNSD) in a size range of 1 nm–10 µm was measured by a suite of instruments including a diethylene glycol scanning mobility particle sizer (DEG-SMPS, model 3938E77, TSI Inc., USA), a SMPS (model 3938L75, TSI Inc., USA), and an aerodynamic particle sizer (APS, model 3321, TSI Inc., USA). The detailed description of these instruments can be found in Cai et al. (2021a). Before the measurement, the SMPSs were calibrated with PSLs (20, 50, and 200 nm), and the CCNc was calibrated with ammonium sulfate ((NH₄)₂SO₄) particles at selected SSs (0.1 %, 0.2 %, 0.4 %, 0.7 %, 0.9 %, and 1.0 %, Sect. S1 in the Supplement).

2.2.3 Aerosol chemical composition measurement

The size-resolved chemical composition of ambient aerosol particles was measured by a soot particle aerosol mass spectrometer (SP-AMS, Aerodyne Research, Inc., USA). The principle and operation of the instrument are generally the same as a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS) (Canagaratna et al., 2007). In addition to an original tungsten vaporizer (∼ 600 ^∘C), a soot-particle module which mainly contains a Nd:YAG (1064 nm) laser was integrated into the HR-ToF-AMS for vaporizing refractory species (Onasch et al., 2012). As a result, the SP-AMS can provide chemical information for non-refractory species (nitrate, sulfate, ammonium, chloride, and organics) as well as refractory species such as refractory black carbon (rBC) and several metals. During the campaign, the SP-AMS was run between V mode (only tungsten vaporizer) and SP mode (tungsten and laser vaporizers) with a time resolution of 1 min. In order to minimize disturbance caused by mode switch, 15 min averaged data are used in the present study. More details on the quantification using ionization efficiency, composition-dependent collection efficiency, and external instrument as well as software for SP-AMS data analysis could be found in Kuang et al. (2021).

Facilitated by the time-of-flight chamber in the SP-AMS, the particle mass size distribution can be measured in submicrometer size range, specifically 40 to 800 nm in vacuum aerodynamic diameter (Dva). The mass size distribution for relevant AMS species was used in this study for investigating the link between particle chemical composition and volatility/hygroscopicity. Since SP-AMS provided the size distribution versus Dva, the equation below was used to convert Dva into mobility diameter (D_p).

$$\begin{array}{}\text{(3)}& D_{\mathrm{p}}={\displaystyle \frac{D_{\text{va}}}{S\times \frac{{\mathit{\rho }}_{\mathrm{p}}}{{\mathit{\rho }}_{\mathrm{0}}}}},\end{array}$$

where S is the shape factor, ρ_p is the particle density, and ρ₀ is the density for water (1 kg m⁻³). In this study, we estimate that the particles were close to sphere due to high RH in the PRD, and thus a shape factor of 0.8 was applied. An overall particle density of 1.6 kg m⁻³ is used.

Based on high-resolution data from the SP-AMS, source apportionment was performed for organic aerosols (OAs) in the bulk PM₁ with positive matrix factorization (PMF, Paatero, 1997; Paatero and Tapper, 1994) following the instruction in Ulbrich et al. (2009). The input data, selection of solutions, mass spectral profile, and time series of each factor can be found in Kuang et al. (2021). In brief, OA measured at the Heshan site could be divided into six components with identified sources and processes, including two from primary sources and four factors corresponding to secondary formation: a hydrocarbon-like OA (HOA) contributed mainly by vehicle exhausts mixed with cooking emissions, a biomass burning OA (BBOA) related to biomass burning combustion from the surrounding villages, an aged BBOA (aBBOA), a more oxygenated OA (MOOA) from regional transport, a less oxygenated OA (LOOA) provided by daytime photochemical formation, and a nighttime-formed OA (Night-OA) related to secondary formation during nighttime.

2.3 Methodology

2.3.1 Estimates of hygroscopicity

The hygroscopicity parameter κ can be obtained under subsaturation conditions by the H/V-TDMA measurement and supersaturation conditions by the CCNc measurement. The κ value (κ_HTDMA) can be estimated from the growth factor measured by the H/V-TDMA (Petters and Kreidenweis, 2007):

$$\begin{array}{}\text{(4)}& {\mathit{\kappa }}_{\text{HTDMA}}=({\text{GF}}^{\mathrm{3}}-\mathrm{1})\left[{\displaystyle \frac{\mathrm{1}}{\text{RH}}}\exp \left({\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{\text{s/a}}{M}_{\mathrm{w}}}{RT{\mathit{\rho }}_{\mathrm{w}}{D}_{\mathrm{p}}}}-\mathrm{1}\right)\right],\end{array}$$

where σ_s/a is the surface tension of the solution–air interface and the solution is temporarily assumed to be pure water (0.0728 N m⁻¹ at 298.15 K), M_w is the molecular weight of water (0.018 kg mol⁻¹), R is the universal gas constant (8.314 $\mathrm{J}{\mathrm{mol}}^{-\mathrm{1}}{\mathrm{K}}^{-\mathrm{1}}$), T is the thermodynamic temperature in kelvin (298.15 K), ρ_w is the density of water (about 997.04 kg m⁻³ at 298.15 K), and D_p is the particle diameter in meters.

For the CCNc measurement, the κ value (κ_CCN) is calculated from the critical supersaturation (S_c) and the critical diameter (D₅₀) by the following equation (Petters and Kreidenweis, 2007):

$$\begin{array}{}\text{(5)}& {\mathit{\kappa }}_{\text{CCN}}={\displaystyle \frac{\mathrm{4}{A}^{\mathrm{3}}}{\mathrm{27}{D}_{\mathrm{50}}^{\mathrm{3}}(\ln S_{\mathrm{c}}{)}^{\mathrm{2}}}},A={\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{\text{s/a}}{M}_{\mathrm{w}}}{RT{\mathit{\rho }}_{\mathrm{w}}}}.\end{array}$$

The critical diameter, D₅₀, is defined as the diameter at which 50 % of the particles are activated at a specific SS and can be obtained from the N_CCN and N_CN measured by the CCNc and SMPS system:

$$\begin{array}{}\text{(6)}& {\displaystyle \frac{N_{\text{CCN}}}{N_{\text{CN}}}}={\displaystyle \frac{B}{\mathrm{1}+{\left(\frac{D_{\mathrm{p}}}{D_{\mathrm{50}}}\right)}^C}},\end{array}$$

where the B and C are fitting coefficients.

2.3.2 Derivation of the size-resolved hygroscopicity of organic matter

The size-resolved chemical composition is adopted to derive the size-dependent hygroscopicity of organic matter (κ_OA). However, the AMS cannot provide sufficient information of the size-resolved species, especially for small size particles (< 100 nm) owing to the low mass concentration. Thalman et al. (2017) proposed a method to reconstruct the size-resolved chemical composition, which combines a time-resolved bulk mass concentration and an average mass distribution. Nevertheless, the variation in mass distribution was not considered in this method. In this study, a bimodal lognormal distribution function method was adopted, and the 1 h average mass distribution was fitted to obtain the reconstructed size-resolved chemical composition. The average mass distribution with bimodal lognormal fitted modes of each species was shown in Fig. S2 in the Supplement.

According to the ZSR mixing rule (Zdanovskii, 1948; Stokes and Robinson, 1966), the hygroscopicity of particles (κ_AMS) can be calculated based on the SP-AMS measurement, assuming an internal mixing state for all particles:

$$\begin{array}{}\text{(7)}& {\mathit{\kappa }}_{\text{AMS}}=\sum _i{\mathit{\kappa }}_i{\mathit{\epsilon }}_i,\end{array}$$

where κ_i is the κ value of each component and ε_i is the volume fraction of corresponding species in particles. The mole concentrations of the inorganic species are estimated based on the ${\mathrm{NH}}_{\mathrm{4}}^{+}$, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, and ${\mathrm{NO}}_{\mathrm{3}}^{-}$ measured by the AMS (Gysel et al., 2007).

$$\begin{array}{}\text{(8)}& {\displaystyle }\begin{array}{rl}& n_{{\mathrm{NH}}_{\mathrm{4}}{\mathrm{NO}}_{\mathrm{3}}}=n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}\\ & n_{{\mathrm{H}}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}=max(\mathrm{0},N_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}}-n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}+n_{{\mathrm{NO}}_{\mathrm{3}}^{-}})\\ & n_{{\mathrm{NH}}_{\mathrm{4}}{\mathrm{HSO}}_{\mathrm{4}}}=min\left(\mathrm{2}{n}_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}}-n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}+n_{{\mathrm{NO}}_{\mathrm{3}}^{-}},n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}\right.\\ & \left.-n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}\right)\\ & n_{({\mathrm{NH}}_{\mathrm{4}}{)}_{\mathrm{2}}{\mathrm{SO}}_{\mathrm{4}}}=max\left(n_{{\mathrm{NH}}_{\mathrm{4}}^{+}}-n_{{\mathrm{NO}}_{\mathrm{3}}^{-}}-n_{{\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}},\mathrm{0}\right)\\ & n_{{\mathrm{HNO}}_{\mathrm{3}}}=\mathrm{0}\end{array}\end{array}$$

Here n denotes the number of moles of each component (${\mathrm{NH}}_{\mathrm{4}}^{+}$, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, and ${\mathrm{NO}}_{\mathrm{3}}^{-}$), and ε_org and ε_BC were obtained from mass concentration measured by the SP-AMS. The density and κ value of each component are listed in Table 1.

Table 1 The density and the κ value of the related species used in this study.

^a From Gysel et al. (2007). ^b From (Cai et al., 2018). ^c From Deng et al. (2019). ^d Assumed to be 0.

The κ_OA can be calculated based on the size-resolved chemical composition and H/V-TMDA measurement using the following equation:

$$\begin{array}{}\text{(9)}& {\mathit{\kappa }}_{\text{OA}}={\displaystyle \frac{{\mathit{\kappa }}_{\text{HTDMA}}-\left({\mathit{\kappa }}_{\text{inorgsalt}}{\mathit{\epsilon }}_{\text{inorgsalt}}+{\mathit{\kappa }}_{\text{BC}}{\mathit{\epsilon }}_{\text{BC}}\right)}{{\mathit{\epsilon }}_{\text{org}}}}.\end{array}$$

Table 2 Thermophysical properties of each component used in the multi-component evaporation dynamics model.

^a From Hong et al. (2017). ^b From Riipinen et al. (2010). ^c From Riipinen et al. (2010). ^d The ΔH_vap values of organics are obtained from the sensitivity test shown in Fig. S4, and the values of inorganic species are from Hong et al. (2017). ^e Obtained from the sensitivity test shown in Fig. S4.

2.3.3 Volatility data

During the heating process, some particles could be lost between DMA₁ and DMA₂ due to complete evaporation (CV), thermophoresis, and Brownian diffusion (Philippin et al., 2004). Owing to these losses, the V-mode measurement does not represent the actual volatility distribution of the monodisperse particles. The sodium chloride (NaCl) particles, which do not evaporate at the set temperature in this measurement, were used to determine the particle losses owing to thermophoretic forces and diffusion. The size- and temperature-dependent transmission efficiency (η(D_pT)) of NaCl in the heater was shown in Fig. S3 in the Supplement. Thus, the number fraction of the CV group (NF_CV(D_pT)) at a certain diameter and temperature can be calculated using the following equation (Cheung et al., 2016):

$$\begin{array}{}\text{(10)}& {\text{NF}}_{\text{CV}}(D_{\mathrm{p}},T)=\mathrm{1}-{\displaystyle \frac{N^{\prime }(D_{\mathrm{p}},T)}{N\left(D_{\mathrm{p}}\right)\mathit{\eta }(D_{\mathrm{p}},T)}},\end{array}$$

where N^′(D_pT) is the number concentration of particles at a specific diameter and temperature after heating, which was measured by the CPC in the H/V-TDMA. The N(D_p) is the number concentration of particles with a diameter D_p before heating, which was provided by the SMPS measurement. The volume fraction remaining (VFR) after heating for the measured particles can be obtained according to the following equation:

$$\begin{array}{}\text{(11)}& \begin{array}{rl}\text{VFR}(D_{\mathrm{p}},T)=& \sum _i{\text{VSF}}_i^{\mathrm{3}}(D_{\mathrm{p}},T){\text{NF}}_i\left(D_{\mathrm{p}}T\right)\\ & \times \left[\mathrm{1}-{\text{NF}}_{\text{CV}}(D_{\mathrm{p}},T)\right],\end{array}\end{array}$$

where i represents the ith VSF bin, and NF_i is the number fraction of particles with VSF_i, which is calculated based on the VSF-PDF (c(VSFD_pT)):

$$\begin{array}{}\text{(12)}& {\text{NF}}_i=\underset{{\text{VSF}}_i}{\overset{{\text{VSF}}_{i+\mathrm{1}}}{\int }}c(\text{VSF},D_{\mathrm{p}},T)\mathrm{d}\text{VSF}.\end{array}$$

The mass fraction remaining (MFR) was assumed to be proportional to VFR, assuming that the density of particles was constant before and after heating.

2.3.4 Multi-component evaporation dynamics model

Based on the volatility basis set (VBS) framework (Donahue et al., 2011), the organic matter was classified into three organic groups based on the saturation concentration (C^∗(T_ref), T_ref = 298.15 K): extremely low-volatility organic aerosol (ELVOA, C^∗ = 10⁻⁵ µg m⁻³), low-volatility organic aerosol (LVOA, C^∗ = 10⁻² µg m⁻³), and semi-volatile organic aerosol (SVOA, C^∗ = 10 µg m⁻³).

A multi-component evaporation dynamics model described by Lee et al. (2011) was used to simulate the evaporation of particles in the heated tube of the H/V-TDMA by solving the mass transfer regime equation, in order to obtain the size-resolved distribution of the aforementioned three OA groups. The MFR, residence time (about 4.11 s) in the heater tube, temperature of the heater tube, particle number concentration, particle sizes, chemical composition, and thermophysical properties of each species (Table 2) were input into the model. The particles were assumed to be internally mixed with organic and inorganic species, including three organic groups, NH₄NO₃, (NH₄)₂SO₄, and black carbon (BC). The mass transfer of each component i between the aerosol and gas phases in the transition regime was calculated from the following equation:

$$\begin{array}{}\text{(13)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{d}{m}_{\mathrm{p},i}}{\mathrm{d}t}}=& \mathrm{2}\mathit{\pi }{D}_i{D}_{\mathrm{p}}f\left(\mathit{Kn}\mathit{\alpha }\right)(C_{i,\mathrm{g}}\\ & -f_i{C}_i^{\ast }\left(T\right)\exp \left({\displaystyle \frac{\mathrm{4}{\mathit{\sigma }}_{\text{s/a}}{M}_i}{D_{\mathrm{p}}{\mathit{\rho }}_{i}RT}}\right))\\ {\displaystyle \frac{\mathrm{d}{C}_{i,\mathrm{g}}}{\mathrm{d}t}}=& -{\displaystyle \frac{\mathrm{d}{m}_{\mathrm{p},i}}{\mathrm{d}t}}{N}_{\mathrm{p}}\left(D_{\mathrm{p}}\right),\end{array}\end{array}$$

where m_p,i (µg) is the mass of species i in a single particle, C_i,g (µg m⁻³) is its gas-phase concentration, D_i (m² s⁻¹) is the diffusion coefficient for species i in air, D_p (m) is the particle diameter, f(Kn,α) is a correction term to account for non-continuum mass transfer depending on Knudsen number (Kn) and mass accommodation coefficient (α), f_i is the mole fraction of species i, $C_i^{\ast }\left(T\right)$ is the saturation concentration at temperature (T) of the heater tube, M_i (kg mol⁻¹) is the molecular weight of species i, ρ_i (kg m⁻³) is its density, and N_p(D_p) (cm⁻³) is the number concentration of particles with a diameter D_p.

The correction term f(Kn,α) is determined by the following equation (Seinfeld and Pandis, 2016):

$$\begin{array}{}\text{(14)}& \begin{array}{rl}& f(\mathit{Kn},\mathit{\alpha })={\displaystyle \frac{\mathrm{1}+\mathit{Kn}}{\mathrm{1}+\mathrm{2}\mathit{Kn}(\mathrm{1}+\mathit{Kn})/\mathit{\alpha }}}\\ & \mathit{Kn}={\displaystyle \frac{\mathrm{2}{\mathit{\lambda }}_i}{D_{\mathrm{p}}}},\end{array}\end{array}$$

where λ_i is the mean free path of species i in the air, which is defined as ${\mathit{\lambda }}_i=\frac{\mathrm{2}{D}_i}{c_i}$. The c_i is the mean speed of species i and $c_i=\sqrt{\frac{\mathrm{8}RT}{\mathit{\pi }{M}_i}}$.

The temperature-dependent $C_i^{\ast }\left(T\right)$ is estimated from the Clausius–Clapeyron equation:

$$\begin{array}{}\text{(15)}& C_i^{\ast }\left(T\right)=C_i^{\ast }\left(T_{\text{ref}}\right)\exp \left[{\displaystyle \frac{\mathrm{\Delta }{H}_{\text{vap},i}}{R}}\left({\displaystyle \frac{\mathrm{1}}{T_{\text{ref}}}}-{\displaystyle \frac{\mathrm{1}}{T}}\right)\right]{\displaystyle \frac{T_{\text{ref}}}{T}},\end{array}$$

where ΔH_vap,i (kJ mol⁻¹) is the enthalpy of vaporization. The known mass fractions of NH₄NO₃, (NH₄)₂SO₄, and BC were calculated based on the SP-AMS measurement. The time step of the model was set to be 10⁻³ s. The characteristics of each species were listed in Table 2. The mass fraction of each organic group in different particle sizes was derived by minimizing the squared residual (SSR) values, $\text{SSR}=\sum _{T_i=T_{\mathrm{1}}}^{T_{\mathrm{5}}}\left[{\text{MFR}}_{\text{model}}\right(T_i,D_{\mathrm{p}})-{\text{MFR}}_{\text{measured}}(T_i,D_{\mathrm{p}}){]}^{\mathrm{2}}$. The non-linear constrained optimization function “fmincon” in MATLAB (version 2016a, Mathworks Inc.) was used to obtain the optimal fitted result. A constraint of $\sum f_{i,\text{inorganics}}+\sum f_{i,\text{organics}}=\mathrm{1}$ is used.

The modeled MFR is strongly dependent on the values of vaporization enthalpy (ΔH_vap) and mass accommodation coefficient (α) (Lee et al., 2010, 2011). Thus, a sensitivity test is performed to determine the ΔH_vap of OA and α based on the campaign average data (Fig. S4 in the Supplement). A linear relationship was adopted between ΔH_vap and ${\log }_{\mathrm{10}}{C}_i^{\ast }\left(T_{\text{ref}}\right)$, ΔH_vap = $-a\cdot {\log }_{\mathrm{10}}{C}_i^{\ast }\left(T_{\text{ref}}\right)+b$, where a and b are fitting parameters (Epstein et al., 2010). The a and b values are set to be [0, 4, 8, 12] and [50, 80, 100, 150, 200] in the sensitivity test, respectively, along with α = [0.01, 0.09, 0.1, 0.5, 0.7, 0.9, 1]. The results show that the measured MFR was reproduced well (with the lowest SSR of 0.0205, Fig. S5 in the Supplement) by using ΔH_vap = 80 kJ mol⁻¹ with α of 0.09, 0.1, and 0.7, respectively. For simplicity, ΔH_vap = 80 kJ mol⁻¹ and α = 0.09 are considered to be the best estimation and adopted in the simulation of the whole campaign datasets. The extracted α value was consistent with the values (α≤0.1) reported previously (Saha et al., 2015; Park et al., 2013; Saleh et al., 2008; Cappa and Jimenez, 2010), indicating significant resistance to mass transfer during evaporation. In addition, the ΔH_vap of OA is of the same magnitude (80–150 kJ mol⁻¹) as reported in the literature (Hong et al., 2017; Saha et al., 2017; Riipinen et al., 2010).

Note that the decomposition of particles during the heating process is ignored in the model. Kiyoura and Urano (1970) suggested that ammonium sulfate would decompose to ammonium bisulfate (NH₄HSO₄) or triammonium hydrogen sulfate (NH₄)₃H(SO₄)₂ and ammonia (NH₃) when heated to around 160–180 ^∘C. Wang and Hildebrandt Ruiz (2018) also observed thermal decomposition of organics and ammonium sulfate during evaporation by using a filter inlet for gases and aerosols chemical-ionization mass spectrometer (FIGAERO-CIMS). It suggests that, besides sublimation, decomposition might occur during evaporation of particles. However, the mechanisms of decomposition are complex and remain unclear, which is difficult to simulate in our model. We roughly estimated uncertainty caused by the decomposition and found that ignoring the decomposition of organics would lead to an underestimation of SVOA, while the decomposition of (NH₄)₂SO₄ played a minor role in the simulation (Sect. S2 in the Supplement). However, the exact effects are still highly uncertain. We hence exclude the decomposition of particles from the model for simplicity.

Figure 1 The temporal profile of the measured variables during the campaign. (a) Particle number size distribution; (b) PM₁ chemical composition measured by the SP-AMS along with mass concentration of PM_2.5; (c) mass fraction of each species; (d) wind speed and direction. The color code in (d) represents the wind direction.

3 Results and discussion

3.1 Overview

Figure 1 shows the temporal profile of PNSD (a), aerosol chemical composition and total mass concentration of PM_2.5 (b), mass fraction of each component (c), and wind speed and direction (d) during the measurements. Note that the SP-AMS measurement started on 12 October. According to the PNSD data, a total number of 20 new particle formation (NPF) events were observed during the whole campaign. The background particles mainly exhibited unimodal distribution, which peaked at a size range of about 80–150 nm. The average particle number concentration (N_CN) in the size range of 3–1000 nm was about 12 700 cm⁻³, much lower than that from the rural measurement (18 150 cm⁻³) in 2006 in the PRD region (Rose et al., 2010). A wide accumulation mode was observed during the period with a prevalent north wind direction, implying that the air mass from the north could bring pollutants from the city cluster around Guangzhou to the measurement site.

Figure 2 The temporal profile of GF-PDF at the measured diameters (30, 50, 80, 100, 150, and 200 nm). The color code denotes the probability density, and the red solid line represents the mean GF (GF_mean).

Table 3 The average and standard deviation values (mean ± SD) of N_CCN, AR, D₅₀, and κ_CCN at 0.1 %, 0.2 %, 0.4 %, 0.7 %, 0.9 %, and 1.0 % SS during the campaign.

The chemical composition and the corresponding mass fraction measured by the SP-AMS (Fig. 1b and c) were consistent with those of PNSD, which showed a significantly high mass concentration of organics when the wind was from the north. The average mass fraction of PM₁ was dominated by organics (51.8 %), followed by sulfate (17.5 %), nitrate (10.2 %), BC (9.9 %), ammonium (8.8 %), and chloride (1.7 %). The mass concentration of organics varied from 3.3 to 123.4 µg m⁻³, with an average value of 20.3 µg m⁻³, lower than the value (25.7 µg m⁻³) reported in Guangzhou City (Qin et al., 2017), but significantly higher than that was observed (4.1 µg m⁻³) in Hong Kong (Lee et al., 2013). The mass distribution of the chemical species at the Heshan site was similar to that measured in inland China (Chen et al., 2015; Huang et al., 2014), which was dominated by organics from anthropogenic emissions. A distinguished and reproducible diurnal pattern of the mass fraction was observed during the measurement (Fig. 1c), implying that the particle composition was more affected by local emission or photochemical production than other pathways. Organics showed a diurnal pattern with bimodal peaks in the afternoon and evening, which will be discussed later in Sect. 3.3. The temporal profile of GF-PDF (Fig. 2) measured by the H/V-TDMA was consistent with that of chemical composition, which showed a significant diurnal pattern. This suggested that particles at all diameters could be affected by atmospheric chemical processes and local emissions, which will be further discussed in Sect. 3.3. The H/V-TDMA data from 18–26 October and 29 October to 3 November were not available due to instrumental failure. In general, the GF-PDF exhibited a bimodal distribution for particles larger than 30 nm, with a significant more-hygroscopic (MH, GF > 1.33) or less-hygroscopic (LH, 1.11 < GF < 1.33) mode and a less obvious non-hygroscopic mode (NH, GF < 1.11), indicating that these particles were partly externally mixed. The NH mode with primary emissions (e.g., fresh black carbon and some organics) was more obvious in a size range of 50–150 nm than others, suggesting that these particles were more affected by local anthropogenic emissions. The above observation was supported by the size distribution of the BC mass faction (Fig. S7 in the Supplement), which peaked at a size range of about 50–150 nm. Besides, the MH mode shifted to a higher GF value with an increase in particle sizes, implying that larger particles were more aged with a higher fraction of inorganic salt (Fig. S7) and well separated from the freshly emitted counterparts. A similar phenomenal pattern was previously observed in the urban environment, including the PRD region (Hong et al., 2018; Cai et al., 2017; Jiang et al., 2016; Tan et al., 2013b), the North China Plain (Liu et al., 2011; Ma et al., 2016), and other city regions around the world (Yuan et al., 2020; Mochida et al., 2006; Massling et al., 2005).

Table 3 summarizes the N_CCN, activation ratio (AR), D₅₀, and κ_CCN values at 0.1 %, 0.2 %, 0.4 %, 0.7 %, 0.9 %, and 1.0 % SS during the campaign. The activation ratio is defined as the ratio of N_CCN to N_CN, that is, $\text{AR}=N_{\text{CCN}}/N_{\text{CN}}$. The average N_CCN at 0.1 %, 0.2 %, 0.4 %, 0.7 %, 0.9 %, and 1.0 % SS was about 2507, 4322, 5854, 6834, 7497, and 7862 cm⁻³, respectively. The N_CCN at 0.7 % SS was lower than that measured (7900 cm⁻³ at 0.7 % SS) in urban Guangzhou (Cai et al., 2018) and at a suburban site (14 400 cm⁻³ at 0.864 % SS) in the North China Plain (Zhang et al., 2020) but significantly higher than that measured at an urban site (2776 cm⁻³ at 0.68 % SS) in São Paulo, Brazil (Almeida et al., 2014). The average AR at the above six SS values was 0.20, 0.34, 0.45, 0.52, 0.57, and 0.60. The AR at 0.7 % SS was lower than the measured value (0.64 at 0.7 % SS) in urban Guangzhou (Cai et al., 2018), while the corresponding D₅₀ (52.56 nm) was lower than that (58.45 nm) in the Guangzhou campaign, implying a higher CCN activity at this site. Thus, the lower AR in this fall campaign suggested that particles were more centered at smaller sizes, which might be attributed to frequently occurring NPF at the Heshan site. The average κ values obtained using the HTDMA fall in a range of 0.1–0.17 at 30–200 nm (Fig. S8a in the Supplement), which were possibly attributed to a high fraction of organic matter (Fig. S7). The κ_AMS is slightly higher than the κ_HTDMA, and the differences become larger with decreasing particle sizes. This was probably due to the overestimated κ_OA at a small size range, which will be discussed in the next section. The hygroscopicity parameter κ values obtained by the CCNc method were 0.48, 0.47, 0.31, 0.22, 0.20, and 0.20 at the above SS values, which were much higher than those measured by the HTDMA in this study. This significant discrepancy between the measured κ_CCN and κ_HTDMA values might suggest that the water uptake behavior is different under super- and sub-saturation conditions, which is likely attributed to the surfactant effect. It was reported that organic matter in the particles could serve as a surfactant and lower surface tension by about 0.01–0.032 N m⁻¹, leading to a higher CCN activity and thus a higher κ_CCN (Petters and Kreidenweis, 2013; Ovadnevaite et al., 2017; Liu et al., 2018). According to Eqs. (4) and (5), the κ_CCN was more susceptibly affected by the value of surface tension than that of κ_HTDMA, which would lead to the discrepancy between κ_CCN and κ_HTDMA values. The surfactant effect is closely related to the presence of liquid–liquid phase separation (LLPS) for organic-containing particles at high RH (Renbaum-Wolff et al., 2016; Ruehl and Wilson, 2014). Once LLPS occurred, the organic film on the droplet surface would decrease surface tension and enhance water uptake. For particles of organic–inorganic mixture, the LLPS can occur when the O:C is lower than 0.8 (Bertram et al., 2011; Song et al., 2012a, b; Schill and Tolbert, 2013). The average O:C obtained using AMS is about 0.53 in this campaign, suggesting that the LLPS likely occurred at supersaturation conditions. Meanwhile, the variation in the discrepancy between κ_CCN and κ_HTDMA is statistically insignificant during clean and polluted periods (Fig. S8b and c), implying that the surfactant effect was hardly affected by pollution conditions. Note that surface tension effect is not the only factor which leads to a higher κ_CCN. It was found that κ_CCN could be higher than κ_HTDMA, since the existence of the slightly soluble compounds inhibits water uptake under subsaturation conditions (Zhao et al., 2016; Pajunoja et al., 2015; Dusek et al., 2011; Petters et al., 2009; Hong et al., 2014; Hansen et al., 2015). Other factors, such as different parameters used in the CCNc and HTMDA calibration and function groups associated with the carbon chain, can lead to a gap between κ_HTDMA and κ_CCN (Rose et al., 2008; Wex et al., 2009). More future work is needed to better understand this water uptake mechanism and to improve the prediction of aerosol–cloud–climate interactions.

Figure 3 The average mass fraction distribution of SVOA, LVOA, and ELVOA at the measured diameters (30, 50, 80, 100, 150, and 200 nm) and average size-resolved hygroscopicity of organic aerosol (κ_OA) with the upper and lower error bars (in red).

3.2 The average size-resolved hygroscopicity and volatility of OA

The composition of organics could vary on a large scale with diameters due to different sources and aging processes, which would further affect their properties. Figure 3 presents the average size-resolved hygroscopicity and volatility of OA. The κ_OA values (vertical red lines in Fig. 3) ranged from 0.058 to 0.09, within the range (0.05–0.15 at 100 nm) previously reported in the PRD region (Hong et al., 2018) and slightly higher than that (0.03–0.06 at 250 nm) at a mountain site in Germany (Wu et al., 2013). In general, the κ_OA values increased with particle sizes from 0.058 at 30 nm to 0.09 at 150 and 200 nm, similar to the feature observed in urban and forest environments (Kim et al., 2020; Deng et al., 2019). The increases in the κ_OA values with particle sizes could be explained by the oxidation level of organic aerosols (Massoli et al., 2010; Lambe et al., 2011; Xu et al., 2021). Specifically, the hygroscopicity of OA was often found to be positively correlated to its oxidation level (Mei et al., 2013; Lambe et al., 2011), which was usually represented by f₄₄, $\mathrm{O}/\mathrm{C}$ ratio, or $\stackrel{\mathrm{‾}}{{\text{OS}}_{\mathrm{c}}}$. Thus, the higher κ_OA values at larger particle diameters in this study might correspond to a higher aging degree of these particles, and this was confirmed by the increasing trend of f₄₄ with particle diameters, i.e., the increasing fraction of ${\mathrm{CO}}_{\mathrm{2}}^{+}$ in OA in large particles (Fig. S9 in the Supplement). Previous field studies also indicated that f₄₄ increased with particle diameters (Kim et al., 2020; Cai et al., 2018), leading to a higher κ_OA value.

Besides the hygroscopicity of OA, we observed the size dependence of volatility. As shown in Fig. 3, the mass fraction of ELVOA increases from 0.16 to 0.30 with the particle diameter, indicating that the particles could be more aged at larger diameters, consistent with the higher κ_OA values as discussed above. The ELVOA fraction in this campaign was higher than that in Beijing in summer (0.13) measured by a thermodenuder (TD) coupled to an AMS (Xu et al., 2019), but similar to that in Athens (0.3) using a similar TD system (Louvaris et al., 2017). The SVOA generally contributed 42 %–57 % to the OA at all measured sizes, comparable to the values reported in Centreville and Raleigh (66 %–75 %, Saha et al., 2017), Beijing (64 %, Xu et al., 2019), and Mexico City (39 %–73 %, Cappa and Jimenez, 2010). Note that the relationship between volatility and oxidation state of OA is not usually strong. Saha et al. (2017) reported weak correlations (R < 0.3) between the mean volatility ($\stackrel{\mathrm{‾}}{C^{\ast }}$) and the mean oxidation state ($\stackrel{\mathrm{‾}}{{\text{OS}}_{\text{C}}}$). Hong et al. (2017) also found that the volatility distribution of OA derived from the combined V-TDMA and evaporation dynamic model could not be fully explained by the organic factions determined by the PMF analysis based on the AMS data. This is probably because the volatility was dependent on not only the $\stackrel{\mathrm{‾}}{{\text{OS}}_{\text{C}}}$ but also the number of atomic carbon (Donahue et al., 2011). In spite of this, the size-resolved volatility distribution can provide a rough estimate of the aging degree of OA.

Figure 4 The campaign average diurnal variation in mass fraction of organics and f₄₄ in bulk PM₁ (a), the κ values at 200 nm obtained by HTDMA (κ_HTDMA) and AMS (κ_AMS) measurements (b), and the PNSD (c) and mass distribution of organics (d). The shaded area represents standard deviation.

Figure 5 The diurnal variation (displayed in boxplot) mass concentration of the deconvolved OA factors from PMF analysis of AMS data, including more oxygenated OA (MOOA), less oxygenated OA (LOOA), aged biomass burning OA (aBBOA), hydrocarbon-like OA (HOA), biomass burning OA (BBOA), and nighttime OA (night-OA).

3.3 The diurnal variation in OA hygroscopicity and volatility

As discussed in Sect. 3.2, the hygroscopicity and volatility of OA could vary on a large range with particle diameters, which might be attributed to photochemical reactions and the OA sources. In this section, the diurnal variation in hygroscopicity and volatility of OA at different particle sizes was investigated, in combination with the PMF results. In general, the mass fraction of organics showed an obvious diurnal pattern during the whole campaign, with two peaks at about 14:00 and 19:00 LT (Fig. 4a), implying significant impacts of photochemical reactions and local emissions. Based on the PMF results (Fig. 5), the afternoon peak was attributed to secondary organic aerosol (SOA) formation (aBBOA and LOOA) during daytime, while the evening peak was explained by local residential activity (e.g., biomass burning and cooking, HOA and BBOA), as will be discussed later. A similar late-afternoon peak was observed in Hong Kong (Lee et al., 2013), where the OA enhancement was mainly contributed by traffic emissions. The f₄₄ remained at a high level during daytime, consistent with strong photochemical reactions. A similar diurnal pattern was observed in the urban and suburban regions (Hong et al., 2018; Hu et al., 2016; Thalman et al., 2017), suggesting the consistent aging processes of pre-existing OA. In contrast, Deng et al. (2019) reported a relatively low OA oxidation state during daytime in a forest environment, which could be explained by the SOA formation through photochemical oxidation of BVOCs.

The calculated κ_HTDMA and κ_AMS (the blue and red lines in Fig. 4b, respectively) values at 200 nm based on Eqs. (4) and (7) both reached minimum during daytime, which was consistent with high OA fractions. This may be explained by lower hygroscopicity of OA than inorganics as found in previous studies (Pajunoja et al., 2015; Zhao et al., 2015; Kuang et al., 2020b) as well as the low κ_i values shown in Table 1. Although OA in a higher oxidation state could be hydrophilic (Massoli et al., 2010), the primary OA is usually considered to be hydrophobic substances, and their mixture would be less hygroscopic (usually with average κ = 0.1). The κ_AMS values were generally consistent with those of the κ_HTDMA during daytime while the overestimated κ_OA was observed during nighttime. This implies a lower κ_OA value than 0.1 at 200 nm during the nighttime, probably due to less oxidation processes at night than those under the sunlight.

The average diurnal profile of PNSD is shown in Fig. 4c. Besides a stable accumulation mode peaking at around 100 nm, a significantly growing mode of particle number from 20 to 80 nm was observed from 12:00 to 20:00 LT, which could be attributed to the frequently occurring NPF during the campaign (Fig. 1a).

The size-resolved diurnal variations in κ_OA were explored in Fig. 6. Note that the κ_OA values are presented in 2 h resolution due to the low data coverage (Figs. 1 and 2). In general, a significantly different pattern was observed between the Aitken mode and the accumulation mode. For Aitken mode particles (30–100 nm), the κ_OA values were higher (0.05–0.1) before dawn than those (0.02–0.07) during daytime, while this trend began to overturn at 150 and 200 nm, where the κ_OA values peaked at noon (∼ 0.09, Fig. 6). As reported in literature, the hygroscopicity of organics was partly dependent on the aging degree (Liu et al., 2021; Zhao et al., 2016; Kim et al., 2020). The diurnal characteristics of the size-resolved κ_OA indicate that the OA in small particles (30–100 nm) was fresh and became aged in large particles. For the same campaign, Kuang et al. (2021) reported the bulk κ_OA of PM₁ based on aerosol optical hygroscopicity measurements, which could provide high-time-resolution data of κ_OA. The relationship between κ_OA and different OA factors was investigated, which showed a negative correlation (R = −0.25) between LOOA and κ_OA and a positive correlation (R = 0.35) between aBBOA and κ_OA. Thus, the decrease in κ_OA for Aitken mode particles during daytime might be attributed to the daytime formation of LOOA through gas–particle partitioning (Fig. 5). A similar phenomenon was reported by Deng et al. (2019) in a forest environment, which might be attributed to the photochemical reactions of BVOCs. Therefore, OA in small particles might be less aged and was primarily contributed by photochemical oxidation of VOCs. In contrast, it is likely that the accumulation mode particles became aged through photochemical oxidation during daylight, as evidenced by higher fractions of ELVOA at 200 nm and higher κ_OA (Figs. 6 and 7) during daytime. According to the PMF analysis, the daytime formation of aBBOA likely resulted from the aging processes of primary OA or biomass-burning-related precursors (Fig. 5). As suggested by Kuang et al. (2021), the daytime formation of aBBOA (Fig. 5) would lead to an increase in κ_OA, which likely explained the noontime κ_OA peak at 150 and 200 nm. It suggested that the OA in the accumulation mode was more influenced by the aging processes through photochemical reactions (leading to aBBOA formation).

Figure 6 The average (solid line) and standard deviation (shaded area) diurnal variation in κ_OA at different particle diameters.

Figure 7 The size-resolved volatility distribution during daytime (08:00–16:00 LT) and nighttime (20:00 to 04:00 LT) based on the median time of each cycle owing to the limited time resolution.

The average size-resolved volatility distribution of OA during daytime (08:00 to 16:00 LT) and nighttime (20:00 to 04:00 LT) was demonstrated in Fig. 7. A higher fraction of semi-volatile organic aerosol (SVOA) was observed at six measured sizes (30, 50, 80, 100, 150, and 200 nm) during daytime. SVOA was usually related to primary emission (e.g., traffic, biomass burning) and gas–particle partitioning (Donahue et al., 2012; Jathar et al., 2020; Hong et al., 2017; Saha et al., 2017). Two primary emission factors, BBOA and HOA, remained at a relative low level during daytime, suggesting that the higher fraction of SVOA during daylight might originate more from gas–particle partitioning. Note that gas–particle partitioning (leading to LOOA formation) could occur at all measured diameters, as shown by the higher daytime fractions of SVOA (Fig. 7). In summary, the above results indicate that the negative effect of LOOA on κ_OA might exist at all diameters, while the positive effect of aBBOA was more dominant at larger particle sizes.

Meanwhile, the decreasing trend of κ_OA was observed from 18:00 to 24:00 at 80 and 100 nm, which might be related to the high mass fraction of OA from primary emissions (HOA and BBOA, Fig. 5), owing to their hydrophobic nature. These two primary factors were associated with traffic emissions, cooking, and biomass burning. Zhang et al. (2005b) constructed the size distribution of HOA based on the size-resolved $m/z$ 44 and 57 from the AMS measurement and showed that HOA was dominant (∼ 75 %) in ultrafine particles (D_va < 100 nm). The size-resolved PMF results from Sun et al. (2012) also indicated a high mass fraction of HOA (0.3–0.4) in Aitken mode particles. The mass distribution of BC could be used to represent the distribution of primary OA (Cubison et al., 2008; Wang et al., 2010; Zhang et al., 2005a) due to similar source origins for BC and HOA/BBOA. The average mass fraction of BC peaked at about 80–100 nm (Fig. S7a), suggesting that HOA and BBOA might be dominant at this size range. The BC peaks at 80 and 100 nm were consistent with those of the SVOA mass fraction (Fig. 3), which was attributed to biomass burning as similar characteristics for the BC peak were shown in other studies (May et al., 2013; Huffman et al., 2009; Donahue et al., 2011). Furthermore, this conclusion was supported by the hygroscopicity measurements as a significant NH mode for 80–100 nm particles was found (Fig. 2). Overall, these results highlight that the diurnal variation in physicochemical properties of OA could vary in a large range with particle diameters, and further investigation is needed.

3.4 Implication for CCN activity

The CCN activity and its prediction are essential in global climate modeling and evaluation. A κ_OA value of 0.1–0.15 was widely adopted in the prediction of N_CCN based on aerosol chemical composition (Meng et al., 2014; Wang et al., 2010; Almeida et al., 2014). As discussed in Sect. 3.3, the κ_OA values might be dependent on particle sizes and vary diurnally, which in turn affect N_CCN. Here, different κ_OA values were adopted to predict N_CCN, and the impact of κ_OA on N_CCN was investigated through comparison between the predicted and measured N_CCN. Note that we only discussed the N_CCN at 0.1 %, 0.2 %, 0.4 %, and 0.7 % SS, since the D₅₀ at higher SS (0.9 % and 1.0 %) was within a narrow range (35–60 nm).

Figure 8 The average diurnal variation in ${\mathit{\delta }}_{N_{\text{CCN}}}$ at 0.1 %, 0.2 %, 0.4 %, and 0.7 % SS based on fixed κ_OA (a), SR κ_OA (b), and SR diurnal κ_OA (c).

The N_CCN at a certain SS can be calculated using PNSD and D₅₀:

$$\begin{array}{}\text{(16)}& N_{\text{CCN},\mathrm{p}}\left(\text{SS}\right)=\underset{D_{\mathrm{50}}}{\overset{\mathrm{\infty }}{\int }}{n}_i\mathrm{d}\log D_{{\mathrm{p}}_i},\end{array}$$

where n_i is the particle distribution function at $D_{{\mathrm{p}}_i}$, and D₅₀ is determined from the κ_AMS using Eqs. (5) and (7). The D₅₀ at 0.1 %, 0.2 %, 0.4 %, and 0.7 % SS ranged from about 130–160, 90–110, 60–80, and 45–60 nm, respectively. Three κ_OA schemes were proposed to predict N_CCN: (1) fixed κ_OA, where κ_OA was assumed to be 0.1 for all size particles; (2) size-resolved κ_OA (SR κ_OA), where κ_OA was taken from average size-resolved κ_OA (κ_OA at 50, 80, 100, and 150 nm for 0.7 %, 0.4 %, 0.2 %, and 0.1 % SS, respectively) in Sect. 3.2; and (3) size-resolved diurnal κ_OA (SR diurnal κ_OA), where κ_OA was the average diurnal value of κ_OA at each diameter (κ_OA at 50, 80, 100, and 150 nm for 0.7 %, 0.4 %, 0.2 %, and 0.1 % SS, respectively) as shown in Sect. 3.3. The κ_AMS was calculated based on the chemical composition at the corresponding D₅₀ range. Note that the N_CCN prediction based on the SR diurnal κ_OA scheme was presented in 2 h time resolution, and the particles were assumed to be internally mixed in Eq. (16). The internal mixing assumption could slightly increase the predicted N_CCN by about 6 %–10 % (Sect. S3 in the Supplement). As aforementioned, organics can increase the CCN activity by decreasing surface tension, which might lead to significant discrepancy between κ_HTDMA and κ_CCN in this campaign (Fig. S8). In addition, this effect could result in a significant underestimation of N_CCN (Ovadnevaite et al., 2017; Liu et al., 2018; Good et al., 2010; Noziere, 2016).

Here, we evaluate the surface tension effect by comparing κ_HTDMA and κ_CCN as a function of σ_s/a (Fig. S10 in the Supplement). The κ_CCN reached κ_HTDMA when the σ_s/a values were set to be about 0.059 N m⁻¹ at 0.7 %, 0.9 %, and 1.0 % SS; 0.053 N m⁻¹ at 0.4 % SS; 0.047 N m⁻¹ at 0.2 % SS; and 0.049 N m⁻¹ at 0.1 % SS. Thus, we adopted σ_s/a values of 0.049, 0.047, 0.053, and 0.059 N m⁻¹ to predict N_CCN at 0.1 %, 0.2 %, 0.4 %, and 0.7 % SS, respectively. In general, the N_CCN prediction could be significantly improved by considering the surfactant effect (Fig. S12 in the Supplement). The N_CCN was slightly overestimated by using reduced σ_s/a values, which was probably due to using a fixed κ_OA value. This bias could be corrected by adopting the SR κ_OA scheme (Fig. S13 in the Supplement).

The deviation of the N_CCN prediction (${\mathit{\delta }}_{N_{\text{CCN}}}$) at a certain SS is defined as (Cai et al., 2021b)

$$\begin{array}{}\text{(17)}& {\mathit{\delta }}_{N_{\text{CCN}}}\left(\text{SS}\right)={\displaystyle \frac{N_{\text{CCN},\mathrm{m}}\left(\text{SS}\right)-N_{\text{CCN},\mathrm{p}}\left(\text{SS}\right)}{N_{\text{CCN},\mathrm{m}}\left(\text{SS}\right)}}\mathrm{100}\mathit{\%},\end{array}$$

where N_CCN,m(SS) is the measured N_CCN at a specific SS. A negative ${\mathit{\delta }}_{N_{\text{CCN}}}$ indicates an overestimate of N_CCN, and vice versa.

Figure 8 shows the ${\mathit{\delta }}_{N_{\text{CCN}}}$ at different SS values for the three κ_OA schemes. The fixed κ_OA scheme generally gave a negative value of ${\mathit{\delta }}_{N_{\text{CCN}}}$ (−0.18 to −0.02) at 0.7 % SS, indicating an N_CCN overestimation, due to lower κ_OA values for smaller particles. A significant diurnal pattern of ${\mathit{\delta }}_{N_{\text{CCN}}}$ was observed at all SS values. The ${\mathit{\delta }}_{N_{\text{CCN}}}$ was relatively higher during daytime at 0.1 % SS, while an opposite pattern was shown at high SS, consistent with the size-dependent variation in κ_OA (Fig. 6). Hence, the fixed κ_OA scheme could lead to an obvious discrepancy in the N_CCN prediction as SS increased. The results based on the SR κ_OA scheme showed that the minimum ${\mathit{\delta }}_{N_{\text{CCN}}}$ value at 0.7 % SS increased from −0.18 in the fixed κ_OA scheme to −0.08, indicating the improvement for the N_CCN prediction at high SS (Fig. 8b). However, only minor improvement was observed at SS lower than 0.4 % because of the low employed κ_OA (about 0.08), which was close to the κ_OA value (0.1) adopted in the fixed κ_OA scheme. A significant difference of ${\mathit{\delta }}_{N_{\text{CCN}}}$ was still observed in the diurnal pattern at high and low SS, implying the impact of the diurnal variation in κ_OA on the N_CCN prediction. To further investigate this impact, the SR diurnal κ_OA scheme was employed to calculate ${\mathit{\delta }}_{N_{\text{CCN}}}$, and the results were shown in Fig. 8c. The ${\mathit{\delta }}_{N_{\text{CCN}}}$ value at 0.7 % SS varied from −0.04 to 0.09 with an average value of 0, whereas it ranged from 0 to 0.11 at 0.1 % SS. Hence, the discrepancies of ${\mathit{\delta }}_{N_{\text{CCN}}}$ among different SS values became minor compared to the other two schemes as a relatively flat diurnal pattern of ${\mathit{\delta }}_{N_{\text{CCN}}}$ was observed at all SS values. It implies that better prediction of N_CCN could be achieved by considering the diurnal variation and the size dependence of κ_OA.

4 Conclusions

A rural field measurement was conducted at the Heshan supersite in the PRD region of China during October and November 2019. We investigated the diurnal variation and size dependence in the hygroscopicity and volatility of OA in combination with the PMF analysis of the AMS data. The impacts of OA on the CCN number concentration at different SS values were discussed for various given size-dependent κ_OA values.

In general, the average κ_OA values varied from 0.058 at 30 nm to 0.09 at 200 nm, indicating a higher oxidation degree of OA at larger sizes than at smaller sizes. This is consistent with particle volatility: the mass fraction of ELVOA increased (0.16–0.30) with increasing particle diameters.

Our results suggest that the formation and aging processes of OA might vary with particle sizes. An oppositely diurnal pattern of κ_OA was observed between Aitken mode (30–100 nm) and accumulation mode (150 and 200 nm) particles, suggesting different atmospheric evolution processes of OA at different diameters. The gas–particle partitioning could decrease the κ_OA, while the aging processes of preexisting particles could enhance the hygroscopicity of OA. For Aitken mode particles (30–100 nm), the κ_OA values reached a minimum (0.02–0.07) during daytime. Meanwhile, a daytime peak was observed for the κ_OA value (∼ 0.09) in the accumulation mode (150 and 200 nm), suggesting that the aging processes of preexisting particles were more dominant at accumulation mode particles. In addition, the mass faction of SVOA was higher during daytime at all measured diameters, implying that the formation of LOOA through gas–particle partitioning was independent of particle diameters.

The impact of the size-resolved diurnal variation in κ_OA on the N_CCN was investigated. The use of fixed κ_OA (κ_OA = 0.1) overestimated the N_CCN up to 18 % at 0.7 % SS. The diurnal deviation became obvious at 0.7 % SS and minor at 0.1 % SS during daytime, owing to the size-dependent variation in κ_OA. The N_CCN prediction at 0.7 % SS was improved if the SR κ_OA scheme was used, while the diurnal variation in ${\mathit{\delta }}_{N_{\text{CCN}}}$ still existed. Better predictions can be obtained by using SR diurnal κ_OA. Our results highlight that the physical properties of OA can vary in a large range at different size ranges due to the formation and aging processes, and the size-resolved diurnal variation in κ_OA plays an important role in the N_CCN prediction at different SS values. Further studies on the size-resolved physicochemical properties of OA should be performed in different environments to better understand their impact on cloud formation and hence climate.