A custom-built flow tube reactor was used to perform a series of laboratory studies on nucleation and growth. This flow tube consisted of a 25cmlong×1cmi.d. quartz tube (19.6 mL in volume) fitted with stainless steel adapter on each end. The entrance was coupled with two union cross in line to introduce gas precursors. As shown in Fig. 1, the water vapor generated by passing N2 through water and O3 from a UVP ozone generator (model SOG-2, Analytik Jena US) were introduced into the main gas flow in the first union cross. The SA and OOMs in all experiments were generated from SO2 and α-pinene. These precurses were diluted from a gas cylinder containing 0.6 % SO2 and obtained from a gas cylinder with 50 ppmv α-pinene, respectively. The carrier flow, water vapor, O3, SO2 and α-pinene were mixed in the second union cross and then introduced into flow tube reactor. To initiate photolysis reactions in the system, a UV lamp (model 11SC-1, Analytik Jena US) with a length of 5.38 cm was installed at the entrance of the quartz tube, emitting ultraviolet light at a wavelength of 254 nm. At the exist of flow tube reactor, the temperature and RH were measured by a humidity sensor (model SHT85, Sensirion) with precision of ±1.5%. The O3 concentration was monitored by an ozone analyser (model 49i, Thermo Fisher Scientific). The concentrations of other gaseous precursors were derived from their mixing ratios, and the molecular composition of the flow tube products was not directly measured in this study.

SA and OOMs was used in this work to represent inorganic and organic components in atmosphere respectively. For pure inorganic experimental groups, H2SO4 was generated in situ via the reaction of OH radicals with SO2 in the presence of water vapor. When the SO2, O3 and H2O were mixed and introduced into the flow tube reactor, O3 underwent photolysis to produce O(1D) atoms, which then react with water vapor to generate OH radicals. These OH radicals interact with SO2, forming the HOSO2 adduct, which subsequently decomposed to produce SO3 and HO2 (Jayne et al., 1997; Lovejoy et al., 1996). In the reaction of SO3 with water vapor, two H2O molecules or one H2O dimer per SO3 molecule were required, ultimately resulting in the formation of H2SO4 (Berndt et al., 2005). For pure organic experimental groups, OOMs were produced from organic peroxides formed from oxidation reactions of α-pinene (Kirkby et al., 2016; Lee et al., 2019). α-pinene was exposed to ozone and also to hydroxyl radicals (OH) due to the unavoidable production of OH from ozone photolysis and secondary reactions. Although detailed molecular composition information could not obtained in our work, the ozonolysis pathway is generally understood to proceed via Criegee intermediates, leading to various peroxy radicals and subsequent low-volatility products (Iyer et al., 2021; Yang et al., 2025). Similarly, OH-initiated oxidation proceeds mainly via OH addition, forming peroxy radicals that further react to produce condensable organic species (Berndt et al., 2016; Kang et al., 2025). While the present study did not estimate the OH concentration and further elucidate specific mechanistic pathways, this simplification is justified because, to the best of our knowledge, no existing studies have clearly demonstrated significant differences in the hygroscopic performance of pure OOMs derived from different α-pinene oxidation pathways.

The SO2 and α-pinene concentration in experiments were regulated by setting the mixing ratio of SO2 flow rate and α-pinene flow rate to the total flow rate. The total flow rate was 3000 mLmin-1, and the residence time in flow tube reactor was about 0.4 s. The all flow rates in this flow tube reactor were set by mass flow controllers (MFCs; MFC. 1–4, model GT130D, Gas Tool Instruments Co., Ltd.; MFC. 5–7, model Sevenstar CS200, NAURA Technology Group Co., Ltd.). The conditions of 24 experimental groups conducted to research the organic contribution to new formed particles in the initial growth stage were summarized in Table S1 in the Supplement. To research the RH impacts to the initial growth process, the experiments were divided to four series conducted under RH 20 %, 40 %, 60 % and 80 %. For pure inorganic (Exp. A) and mixture groups (Exp. C–F), the concentration of SO2 was set as a constant value and the concentration of α-pinene was regulated based on the [α-pinene]/[SO2] (concentration ratio of gas precursors α-pinene and SO2, 0.1–1). The pure organic experiments (Exp. B) were conducted with much higher concentration than that in mixture experimental groups to generate sufficient 3–10 nm particles (number concentration larger than 1000 # per cm3). The temperature in all experiments was around 28 °C when the reaction was stable. O3 concentration obtained by Ozone monitor was ∼200 ppb with a regulable O2 flow rate.

The hygroscopicity of nanoparticles was measured with a custom-designed SFCPC. The setup of SFCPC system has been described previously (Zhang et al., 2023), and only a brief summary is presented here. The aerosol particles were passed through a neutralizer (X-ray, TSI model 3080), and a nano-differential mobility analyzer (nano-DMA, TSI model 3086) was used to select charged monodisperse particles in diameter range of 3–10 nm (with intervals of 0.2 nm in the 3–4 nm range and intervals of 0.5 nm in the 4–10 nm range). Considering the negligible probability of double-charge for particles below 20 nm (Fuchs, 1963; Wiedensohler et al., 1986; Wiedensohler and Fissan, 1988), no double-charge correction was applied in the studied size range. SFCPC, which was improved from a water-based condensation particle counter (WCPC, TSI model 3788) and could change the supersaturation fast by altering the sample flow, was deployed to count the activated particle concentration (N). And an electrometer (EM, TSI model 3068B) was operated in parallel to measure the total particle concentration (Ntotal), where the counting efficiency of sampled particles (fcount) in different supersaturation (S) conditions could be obtained by N/Ntotal. S distributions of SFCPC were calibrated by tungsten oxides (WOx) particles generated from a WOx generator (Model 7.860, Grimm Aerosol Technik; Steiner, 2011), and twelve S conditions were setup to meet the requirements of κ value measurements. The effective S ranged from 7.7 % to 73.1 %, a sufficiently broad range to activate the SA and OOMs corresponding fcount in 20 %–80 %. For the measurement part, particles from flow tube reactor were selected with discrete diameters and the S could be calculated through the measured fcount. Then the κ values could be obtained from dry diameter (Dd) and its corresponding S based on κ-Köhler equation (Petters and Kreidenweis, 2007). The equation was applied following Eq. (2) in Zhang et al. (2023), in which the surface tension of water (0.072 Nm-1) was used.

The linear relationship between chemical composition and hygroscopicity of CCN sized particles has been found both in laboratory experiments and field measurements (Dusek et al., 2010; Pöhlker et al., 2023; Vogel et al., 2016; Zhou et al., 2024). Our previous work extended the linear relationship between κ and forg to 3–10 nm size range for AS and levoglucosan/sucrose mixed particles, which were generated via Electrospray from solutions with known mixing ratios (Wang et al., 2015; Zhang et al., 2023). Zhang et al. (2025) assessed the uncertainty arising from the dependence of κ on particle size, also based on Electrospray-generated particles (AS and cis-pinonic acid). In this work, we introduced κ–forg linear relationship into the mixing products from flow tube – a setup designed to simulate atmospheric processes – in order to explore the organic content in the particulate phase. Furthermore, we established size-resolved κ–forg linear relationship to eliminate the mentioned uncertainty. The application of the κ–forg linear relationship relies on the assumption of ideal internal mixing within the particles. Under our experimental conditions, for in situ freshly formed 3–10 nm particles, the characteristic mixing times are short, and organic-inorganic mixtures are likely to remain liquid and well-mixed (Cheng et al., 2015). Therefore, the ideal internal mixing assumption is reasonable. For SA-OOMs mixture, we use the κ values of pure organic (OOMs) and inorganic (SA) experiment groups to represent the hygroscopicity of the organic and inorganic component in the mixture particles, respectively. Although the organic and inorganic components in mixture may not be identical to those in pure organic and inorganic particles of the same size under the same RH due to the potential change of oxidation processes, this simplification is a necessary given the current inability to directly measure the composition and component-specific hygroscopicity of particles in the 3–10 nm size range. To further reduce uncertainties associated with the linear relationship, the κ values of pure organic and inorganic particles were taken from the fitted lines to serve as a reference baseline, as shown in Fig. S1 in the Supplement. Based on the size-resolved κ–forg linear relationship (colored solid lines) and the measured κ values (grey dashed line) of the SA-OOMs mixture, the corresponding forg values (colored dashed lines) for particles generated in the flow tube reactor were derived using Eq. (1): 1forg=κ-κinorgκorg-κinorg×100% where forg and κorg is the mass fraction and hygroscopicity of pure organics (OOMs in this work), respectively; κinorg is the hygroscopicity of pure inorganic component (SA in this work); κ is the hygroscopicity of the measured particles nucleation and growth process in flow tube reactor.

The results of pure inorganic groups and organic groups were shown in Fig. 2. The hygroscopicity of 3–10 nm SA particles formed by the oxidation products of SO2 have significant size dependence. κ values would decrease with Dd, from 0.413±0.011 for 3 nm to 0.209±0.004 for 10 nm under RH=20%. It should be noted that the quartz tube was replaced for every single experiment group to eliminate the potential contamination between experiments. Moreover, prior to the hygroscopicity measurements, the oxidation products of SO2 were characterized using an iodide chemical ionization mass spectrometry (Vocus AIM), which detected no significant organic compound signals in the gas phase (Fig. S2 in the Supplement). Therefore, this decreasing trend cannot be attributed to organic contamination. Considering the sulfuric acid and water binary nucleation is the basic mechanism for the SA particle formation, the water molecules plays a significant role through hydration (Kulmala et al., 1998; Lee et al., 2019; Stolzenburg et al., 2023; Yu et al., 2017). The initial formation of H2SO4⚫H2O molecular clusters is followed by rapid addition of further H2O molecules and these stepwise hydrates process ultimately leads to particles covered with water during growth (Couling et al., 2003; Matsubara et al., 2009). The measured particles were thought as (H2SO4)m-(H2O)n rather than pure H2SO4. Consequently, the decreasing trend of κ with particle size may be explained by the increasing water content, which lowers the particles' water uptake capacity relative to their dry mass.

Hygroscopicity of SA particles also revealed a consistent decrease with rising RH: at RH=80%, κ values declined to 0.361±0.013 for 3 nm and 0.171±0.011 for 10 nm particles, decreasing 13 % and 18 % compared to RH=20%. This demonstrates that SA particles exhibit reduced hygroscopicity under higher humidity conditions. Although bases such as ammonia/amine could in principle suppress the hygroscopicity of SA particles (Yishake et al., 2025), the κ of an SA-ammonia/amine mixture would be expected to increase with RH, because a higher SA fraction (more acidic) is expected at higher RH (Chen et al., 2018). This κ–RH dependence is opposite to the trend observed in our study. Moreover, there was no identified source of bases in our system, so ammonia contamination can largely be ruled out. Furthermore, previous studies have shown that the average number of water molecules hydrating each H2SO4 molecule increases with RH (Kurtén et al., 2007; Temelso et al., 2012; Zollner et al., 2012). Therefore, the observed decrease in hygroscopicity can be attributed to the particles already containing more water at higher RH, resulting in a reduced capacity for additional water uptake.

The κ values reported in previous studies are summarized in Table 1. The measured hygroscopicity results in this work are much lower than those reported in previous studies (0.68–0.9, Petters and Kreidenweis, 2007; Shantz et al., 2008; Sullivan et al., 2010), which predicted by thermodynamic model in 30–80 nm based on the model parameters provided by Clegg et al. (1998). The hygroscopicity of newly formed sulfuric acid nanoparticles in CLOUD chamber was examined by a nano hygroscopicity tandem differential mobility analyser (nano-HTDMA) and the reported κ values were 0.64±0.02 and 0.52±0.02 for 10 and 15 nm, respectively (Kim et al., 2016). The reported variation trend in particle size aligns with our findings but the κ values were much larger than that in this work. While both Kim et al. (2016) and our study report κ values of the oxidation products of SO2, the measurement methods used are fundamentally different. Kim et al. (2016) employed a nano-HTDMA, which measures hygroscopic growth under subsaturated conditions. In contrast, our SFCPC method derives κ values by activating particles under supersaturated conditions. As discussed in previous studies, the measurement condition can induce inherently different κ values (Biskos et al., 2009; Massling et al., 2023). Specifically, SA particles are expected to exhibit comparably higher hygroscopic growth under subsaturated conditions and lower CCN activity at supersaturation. Therefore, this methodological difference is likely the primary factor contributing to this discrepancy in κ values. In addition, for sub-10 nm particles, the enhanced Kelvin effect (compared to that for larger CCN-size particles) dramatically raises the energy barrier for vapor condensation, directly contributing to suppressed hygroscopicity. Furthermore, the potential size-dependent influence on phase state may reflect a tendency for nanoparticles to remain in a liquid or mixed phase (Cheng et al., 2015). These nano-size effects on the thermodynamic and physical properties of aerosol particles are likely significant contributing factors in explaining the distinctively lower κ values observed in our study. As far as we know, direct measurements of the κ of sulfuric acid particles remain limited in the literature, and our results is the first measurement under supersaturation condition in 3–10 nm range.

Different from the SA results, the OOMs particles formed by the oxidation products of α-pinene have almost constant κ values in the 3–10 nm diameter range. As shown in Fig. 2b, κ of the pure organic group under 20 % RH is ∼0.065. This result indicates that the OOMs particles exhibit non-hygroscopicity compared to SA particles and its hygroscopicity has no significant dependence on particle diameter. While the detailed chemical composition of OOMs in these nanoparticles may vary with size due to volatility-dependent partitioning and the Kelvin effect, the observed constancy in κ suggests that the effective hygroscopic properties of the condensing mixture do not change significantly within this size range. This finding is consistent with Frosch et al. (2011), who also observed almost constant κ values (0.11±0.02) for 50–150 nm particles from α-pinene oxidation. However, to our knowledge, research on particle size dependence is very rare, and no studies have specifically examined the hygroscopicity of α-pinene oxidation particles in the 3–10 nm size range. Alfarra et al. (2013) measured the hygroscopicity of particles formed from α-pinene oxidation via both OH radicals and O3 using CCNC. Our results align closely with their reported κ values (0.1–0.16), which were also observed under supersaturation conditions. Furthermore, numerous studies have investigated the hygroscopicity of α-pinene oxidation products using CCNC or HTDMA, reporting a wide range of κ values (0.03–0.19, Cain et al., 2021; Duplissy et al., 2011; Engelhart et al., 2008; Massoli et al., 2010; Razafindrambinina et al., 2022; Wang et al., 2019; Zhao et al., 2016). All experimental results reported here fall within the established range of values found in existing publications.

Contrasting with the negligible size dependence, the measured κ values of OOMs exhibited a pronounced increase with RH, rising by 57 % from 20 % to 80 % RH. This finding aligns with Razafindrambinina et al. (2022), who reported higher κ values for laboratory-generated α-pinene oxidation products under humid conditions (κ=0.191 at 75 %–80 % RH) compared to dry conditions (κ=0.130 at RH<10%). Similarly, Luo et al. (2024) observed that the molecular composition of α-pinene oxidation products evolves with increasing RH. While direct molecular-level speciation from our measurements is unavailable, previous studies on α-pinene oxidation systems provide an explanatory framework. The work of Yuan et al. (2017) suggests that in the presence of water vapor, particles formation may promote the generation of more stable Criegee intermediates, leading to the production of more hygroscopic materials in monoterpene systems. This is supported by evidence of increased formation of oxygenated functional groups, such as multifunctional carboxylic acids, under humid conditions (Poulain et al., 2010). The hygroscopicity of such compounds is intrinsically higher, as the κ increases with the functionality in the following order: (-CH3 or -NH2) < (-OH) < (-COOH or C=C or C=O) (Han et al., 2022). Consequently, the observed increase in κ values at higher RH in this study is attributed to the likely formation of more hygroscopic components.

The forg values of 3–10 nm particles was determined using the κ–forg linear relationship as described in Sect. 2.3. Figure 3 presents the retrieved forg results for four experimental groups with varying [α-pinene]/[SO2] ratios under 20 % RH. For 3–10 nm SA-OOMs mixed particles, the median mass fraction of OOMs increased from 7.9 % to 36.9 % as the [α-pinene]/[SO2] ratio increased from 0.1 to 1. Considering that ozone was always excessive in the flow tube reactor, the oxidation products of α-pinene are expected to increase with rising precursor concentration. Consequently, the organic content in the particle phase should be proportional to the concentration of condensable OOMs in the gas phase. This significant increasing trend has also been reported in previous studies. Li et al. (2022) observed that the ratio of particulate organics to sulphate in urban field measurements was positively correlated with the ratio of gaseous condensable organic oxidation products to sulfuric acid. Comprehensive modelling study demonstrated that terpene-rich air masses containing abundant low volatility oxidation products substantially enhanced the condensational growth of nano-particles and dominated the initial growth stage in sub-10 nm, with contribution as high as 95 % (Huang et al., 2016). Our experimental results align with these findings, demonstrating that increased organic precursor concentrations significantly elevates the contribution of OOMs to the growth of 3–10 nm particles.

At the same time, our results reveal that the organic content of large particles is generally higher than that of smaller particles (coloured scatter points in Fig. 3). To further investigate the size-dependent effect on the chemical composition of nano-particles, the experimental data were analysed by categorizing particles into three distinct size ranges (3–5, 5–7, and 7–10 nm). Figure 4 shows the results from Exp. C and Exp. F, which had the lowest and highest [α-pinene]/[SO2] ratios of 0.1 and 1, respectively. The forg values for 3–5, 5–7, and 7–10 nm SA-OOMs particles in Exp. C are 5.7 %, 9.8 % and 11.3 %, respectively. Similarly, particles formed in Exp. F contained 27.5 %, 39.5 %, and 43.2 % organics, respectively. These results indicate that the forg exhibited a consistent increase with Dd across the range of the precursors mixing ratios examined in this work. Furthermore, these findings demonstrate that α-pinene oxidation products contributed progressively more to particulate phase in the SA-OOMs system as particle size increased.

Several studies have also investigated the chemical composition of newly formed particles in the initial growth stage. Kim et al. (2016) employed nano-HTDMA measurements in the CLOUD chamber to determine κ values, from which volume fractions were derived through linear relationships. Their work revealed that the volume fraction of dimethylamine sulphate in sulfuric acid-dimethylamine systems increased substantially from 0.20–0.29 for 10 nm particles to 0.58–0.92 at 15 nm. Similarly, Keskinen et al. (2013) observed a progressive enhancement in organic volume fraction from 0.4 at 2 nm to 0.9 at 63 nm, while noting the existing measurement challenges for particles between 2–15 nm where chemical characterization remains particularly difficult. More recently, Li et al. (2022) achieved direct measurements of size-resolved molecular composition using TDCIMS, demonstrating a clear increase in organic mass fraction with particle diameter across the 8–40 nm range in urban Beijing. Other studies have also indicated that particle growth mechanisms exhibit a dependence on particle size (Riipinen et al., 2012). The contribution of SA decreased as particle size increased (Xiao et al., 2015), while organic compounds increasingly dominated the growth process, showing a strong size-dependent effect (Riccobono et al., 2012). Our experimental results align well with these previous studies, confirming that organic contributions to nanoparticle growth exhibit consistent size dependence, while additionally providing novel composition data for freshly nucleated particles as small as 3 nm, thereby extending the current understanding of early particle growth.

To investigate the effect of humidity on the initial growth of newly formed particles, we increased RH from 20 % to 80 % and measured the organic content across this range. The retrieved forg values were similarly grouped by particle size, following the same methodology as in the size-dependence analysis. The results from all RH experimental groups (20 %–80 %) were compared with those under 20 % RH to examine the relative change in organic contribution with increasing RH (Fig. 5). The enhancement of organic contribution to particle growth by humidity exhibits a marked difference between particles below and above 5 nm. Taking Exp. D as an example, the forg for 3–5 nm particles began to increase from 60 % RH, with a relative increment reaching approximately 47 % at 80 % RH. For particles in the 5–7 and 7–10 nm size ranges, forg exhibited a sharp increase starting at 40 % RH and remained almost stable within the 40 %–80 % RH range. Compared to the condition at 20 % RH, the organic contribution to particle growth was enhanced by about 52 % and 81 %, respectively. We speculate that these behaviours arise from the competing influences of humidity on the physicochemical properties of α-pinene oxidation products and the Kelvin effect. For such small nanoparticles, the partitioning of a molecule into the particulate phase is influenced by both its volatility and the Kelvin effect (Riipinen et al., 2012). Previous molecular measurements in both gas and particle phases have reported increased yields at elevated RH (Poulain et al., 2010). Concurrently, Surdu et al. (2023) observed that α-pinene oxidation products become more volatile under humid conditions. The relative stability of forg in the 3–5 nm particles at low RH condition may thus be explained by a balance between these two competing mechanisms, where the heightened Kelvin effect presents a significant barrier to condensation. For larger particles, the diminished Kelvin effect facilitates the condensation of organic compounds, allowing even more volatile products to contribute to nanoparticle growth. The distinct response patterns, where the enhancement occurred gradually for 3–5 nm particles but sharply for larger particles, suggest that the Kelvin effect plays a more dominant role for the smallest particle growth at lower RH. Overall, increased RH enhances the organic contribution by altering the properties of α-pinene oxidation products, with a more pronounced effect observed for larger particles.