The experimental setup includes a nanoparticle generation system, a humidification system, and a FTIR analysis system. Particles are aerosolized by an atomizer (model 255, Met One), dried by a diffusion dryer (model 3062, TSI), sorted into a specific electrical mobility diameter (Dem) by a differential mobility analyzer (DMA; model 3082, TSI), and finally deposited onto a 3 cm × 3 cm zinc selenide (ZnSe) substrate inside a cylinder sample cell with a radius of 3 cm and a length of 4 cm through a cone-shaped hole (Fig. 1). The sheath-to-sample flow ratio of the DMA is set to be 10 : 1 (the sheath flow is 10 L min-1, and the sample flow is 1 L min-1), which can produce an effective mobility for the measured aerosols with sizes ranging from 14.9 to 673.2 nm. We only selected nanoparticles with Dem values of ∼ 100 nm for deposition. After a deposition time of ∼ 12 h, the substrate is sealed inside the sample cell to obtain a stable RH condition for subsequent analysis. There are about 100 000 nanoparticles deposited onto the substrate. For the 100 nm nanoparticle, its hydration characteristic mainly depends on its chemical composition, and the Kelvin effect is negligible (Cruz and Pandis, 2000; Lee et al., 1998). The enrichment of the nanoparticles is to improve the signal of FTIR measurement because the hygroscopic signal of a single nanoparticle is too weak to be measured by the FTIR method. Since the chemical composition is not changed during the deposition, this deposition process can obtain the same results as those for a single particle.

The humidification system can provide a specific RH for the sample cell (Kuai et al., 2020). A RH sensor (HC2-S, Rotronic AG, Switzerland) with an accuracy of ±0.8 % for a 0 %–100 % RH range is mounted at the inlet of the sample cell. The RH downstream of the DMA varies over 16.52 % to 18.74 %, which is well below the efflorescence relative humidity (ERH) of AS (about ∼32 % RH) (Fig. S1 in the Supplement). As a result, the initial states of all nanoparticles are in dry conditions.

The FTIR spectrometer (Tensor 27, Bruker Optics, Germany) starts to take absorption spectra of the samples approximately 5 min after the injection of each designated RH. This time interval is used to stabilize the atmospheric condition, especially the RH, inside the sample cell. The FTIR spectrometer is equipped with a KBr beam splitter and a liquid-nitrogen-cooled mercury cadmium telluride (MCT) detector for measuring the absorption spectra of the samples. A He–Ne laser metrology keeps the FTIR instrument in a good optical alignment. The FTIR spectrometer saves middle infrared (MIR) spectra from 800 to 4000 cm-1 with a spectral resolution of 4 cm-1 and a repeat time of 64 scans. An air conditioner is run uninterruptedly to keep the laboratory at a constant temperature of ∼ 25 ∘C.

In this study, all chemical reagents are produced by the Aladdin Reagent Inc. (reagent grade, 99.8 % purity), and the water is obtained from an ultrapure water system (Direct-Q 3, Millipore). Table 1 summarizes all chemical compounds and their concentrations used in the experiment. The density, solubility, and molecular mass of all chemical compounds are prescribed based on the CRC Handbook of Chemistry and Physics (Lide, 2007). All single chemical compounds are dissolved individually in ultrapure water with a concentration of 4.0 g L-1. All mixed solutions (including AS/SN and AS/OA) are generated by mixing the two corresponding single compounds with a mass ratio of 1 : 1. As a result, both AS/SN and AS/OA nanoparticles are internally mixed nanoparticles.

AS is selected as a representative of inorganic salt, and OA is an important water-soluble organic compound contained in atmospheric aerosols. We select AS as a representative of inorganic salt because it is a significant constituent of the submicron-scale aerosol in the atmosphere. In addition to an important water-soluble organic compound contained in atmospheric aerosols (Wang et al., 2019), OA is also the dominant dicarboxylic acid in both urban and remote atmospheric aerosols (Richard et al., 2020).

Figure 2 shows the FTIR spectral absorption characteristics of the AS nanoparticles under humidity conditions from 50 % to 90 %. Figure 3 shows the predicted Mwater/M0 and the measured hygroscopic properties of 100 nm AS nanoparticles as a function of RH during the hygroscopic growth process. The strong absorption peaks observed at 3250 and 1112 cm-1 at the initial RH of 50 % are the stretching vibration peak of OH and the symmetrical stretching vibration peak of SO42-, respectively (Wang et al., 2017; Nájera and Horn, 2009; Gopalakrishnan et al., 2005). The areas of OH and SO42- absorption peaks reflect the liquid water content and the concentration of SO42- contained in the AS nanoparticles. With the increase in RH between 50 % and 79 %, the SO42- absorption peak (1112 cm-1) starts to shift toward red slowly (Fig. 3), which indicates that liquid water molecules have been attached to the surface of the solid AS nanoparticles, and the SO42- is then bonded with these liquid water molecules to form a hydrogen bond during this hygroscopic growth process (Yeşilbaş and Boily, 2016). In the meantime, the position and the area of the OH absorption peak do not change significantly, indicating that no hygroscopic growth of the AS nanoparticles occurs for the RH between 50 % and 79 % (Wang et al., 2019; Tang et al., 2016; Nájera and Horn, 2009; Martin, 2000). It is worth noting that the SO42- has two different absorption peaks in solid and aqueous AS nanoparticles and Fig. 3 only presents the area of SO42- absorption peak in aqueous AS nanoparticles. As a result, the area of OH absorption peak is zero for the RH between 50 % and 79 % since no hygroscopic growth occurs in this RH range.

When the RH reaches 79 %, the position of the SO42- absorption peak has shifted from 1102 to 1097 cm-1 and its area increases abruptly from 0 to 0.38. In the meantime, the position of the OH absorption peak is still the same as that in initial humidity conditions (50 %), but its area increases abruptly from 0.18 to 0.67 (Fig. 3). The area of the OH absorption peak can be used to ascertain the phase transition of nanoparticles since it is sensitive to the surrounding chemical environment (Braban et al., 2003). The abrupt increase in the area of the OH absorption peak indicates the phase transition of AS; i.e., the AS nanoparticles have absorbed water rapidly and transformed from the crystalline phase to the aqueous phase. According to the E-AIM predictions and the results from previous studies (Estillore et al., 2016; Cruz and Pandis, 2000; Tang, 1982), this process is called the deliquescence, and the RH at this stage is referred to as the deliquescence RH (DRH). When deliquescence occurs, NH4+ molecules hydrated with SO42- are replaced with H2O molecules, which leads to the redshift of the SO42- absorption peak (Dong et al., 2007). Tang (1982), Cruz and Pandis (2000), and Estillore et al. (2016) have used photonic microscopes to observe the hygroscopic growth properties of large-size AS particles. Our method and the particle size are different from previous studies, but we obtained a DRH (about 79 % ± 0.8 %) consistent with those in Tang (1982), Cruz and Pandis (2000), and Estillore et al. (2016), where the DRH for AS was found to be 79 % ± 1 % or 80 % ± 0.4 %. This is because the hydration characteristics of nanoparticles mainly depend on their chemical composition, and the Kelvin effect is negligible. Lee et al. (1998) concluded that, for particles with Dve values larger than 100 nm, their critical hydration characteristics are essentially independent of the particle size and are similar to the condensation of water on a flat surface (Lee et al., 1998).

The AS nanoparticles continue to be humidified after deliquescence, resulting in a further increase in the area of the OH absorption peak due to continuous water uptake. However, the position of the SO42- absorption peak remains constant regardless of RH, indicating that the AS nanoparticles are still in the aqueous phase after deliquescence. With a further increase in RH, the volume of AS nanoparticles increases due to the increase in liquid water content, but the mass of AS nanoparticles remains constant, resulting in a decrease in SO42- concentration. As a result, we observe a decrease in the area of the SO42- absorption peak starting from ∼ 83 % RH.

Figure 4 is the same as Fig. 2 but for the OA nanoparticles. The results for the OA nanoparticle differ from those for AS. The FTIR spectral absorption characteristics of SN, AS/SN, and AS/OA nanoparticles under humidity conditions from 50 % to 90 % are shown in Figs. S2, S3, and S4, respectively. Throughout its hygroscopic growth process, the OH absorption peak at 3250 cm-1 was not detected, indicating that liquid water is not absorbed by the OA. Previous studies conclude that, for the dihydrate crystalline state of OA particles, its deliquescence point is larger than 97% RH (Peng et al., 2001) but, for the amorphous state of OA particle, it starts to uptake water above 45 % RH (Mikhailov et al., 2009). From this point of view, the OA particles in this study could be in the dihydrate crystalline state, and our findings are consistent with those of Jing et al. (2016) and Ma et al. (2019).

Figure 5 compares the Mwater/M0 (Mwater is the mass of liquid water in the nanoparticles; M0 is the initial mass of nanoparticles) ratio predicted by the E-AIM (UNIFAC model) (http://www.aim.env.uea.ac.uk/aim/aim.php, last access: 20 May 2021) and the measured hygroscopic properties from the FTIR spectra with the method described in Sect. 2.3 for the AS, AS/OA, and AS/SN nanoparticles during the hygroscopic growth process from 50 % to 90 % (RH). The results show that the predicted and measured Mwater/M0 results for both pure and mixed nanoparticles are generally in good agreement during the whole hygroscopic growth process, indicating consistent water uptake between the predictions and the measurements with the increase in RH.

With the results derived from the FTIR measurements, we calculated the GFs for both pure and mixed nanoparticles via Eq. (7) and investigated their variabilities with respect to the changes in RH. Figure 6 compares the measured and predicted GFs for both pure and mixed nanoparticles under the humidity conditions from 50 % to 90 %. The measured and predicted GFs are in good agreement through the whole humidity range. The GFs can be obtained precisely using the H-TDMA technique via a direct measurement of the aerosol diameter. In this study, the GFs for both pure and mixed nanoparticles are calculated with liquid water content and the relative masses of dry nanoparticles obtained from FTIR measurements. Though with different methods, the GFs for both pure and mixed nanoparticles in this study are in good agreement with those from previous studies (Jing et al., 2016; Braban et al., 2003).

The GF curves can be used to investigate the sensitivity of particle volume to RH. At the RH of 79 ± 0.8 %, deliquescence occurs, the diameters of AS nanoparticles grow sharply by up to a factor of approximately 1.48 and transform from the crystalline to aqueous phase. At the RH of 85 ± 0.8 %, the GF for AS is 1.65 ± 0.05, which is slightly higher than the values deduced with the H-TDMA (about 1.49; Cruz and Pandis, 2000) and Environmental Scanning Electron Microscope (about 1.50; Matsumura and Hayashi, 2007) but is close to the value deduced with the E-AIM (about 1.60).

Since both the AS/SN and AS/OA mixed nanoparticles have lower DRHs than that of the AS and absorb liquid water below their DRHs, their GF curves differ from that of the pure AS particles. Although OA particles do not absorb water, OA and AS in the AS/OA aqueous solution can react with each other via the following pathway (Miñambres et al., 2013): R1(NH4)2SO4+H2C2O4→NH4HSO4+NH4HC2O4. This reaction can be identified in Fig. S5, where the absorption peak at 1245 cm-1 is the stretching vibration peak of HSO4-. As a result, a lower DRH for the mixed nanoparticles relative to the pure AS can be attributed to the formation of NH4HSO4, which has a lower DRH (about 40 %) than the pure AS (80 %) (Tang and Munkelwitz, 1994). All the above findings are in good agreement with those in Seinfeld and Pandis (2016), which measure GFs with the H-TDMA.

The 2D IR spectra based on the spectral variations induced by the deliquescence of pure AS between 50 %–90 % RH are shown in Fig. 7. The correlation maps for the OA nanoparticles are not shown because they do not absorb water and thus present no deliquescence transition during hygroscopic growth processes. In the synchronous correlation maps, one main red–positive auto-peak of (3250, 1097 cm-1) was observed for the AS nanoparticles in the 50 %–90 % RH range, which indicates simultaneous increases in the spectral intensities of OH and SO42- absorption peaks. This means that the liquid water and SO42- in the aqueous AS nanoparticles increase simultaneously during hygroscopic growth processes. Furthermore, two main blue–negative auto-peaks of (1112, 1097 cm-1) and (3250, 1112 cm-1) were also observed for the AS nanoparticles. The blue–negative auto-peak of (1112, 1097 cm-1) indicates that the spectral intensity of the OH absorption peak increases with RH, while the spectral intensity of the SO42- absorption peak in the solid AS nanoparticles decreases with RH. It also indicates that the SO42- components in solid and aqueous AS nanoparticles can transform into each other, and the decrease in SO42- in solid AS nanoparticles results in an increase in SO42- in aqueous AS nanoparticles. This behavior can be explained by the fact that NH4+ particles hydrated with SO42- are replaced by H2O molecules with an increase in RH.

The asynchronous map indicates the sequential changes in the spectral intensities in response to the hygroscopic activities. As shown in the asynchronous correlation maps in Fig. 7, two main red–positive auto-peaks of (3250, 1097 cm-1) and (1112, 1097 cm-1) and two main blue–negative auto-peaks of (3250, 1112 cm-1) and (1097, 1112 cm-1) were observed for the AS nanoparticles, which indicates that spectral intensities of the absorption peaks changed in the order of 1112 > 3250 > 1097 cm-1. The decrease in SO42- in the solid AS nanoparticles does not result in a simultaneous increase in SO42- in the aqueous AS nanoparticles during the AS deliquescence transition. The former process occurred predominantly before the later process. This suggests an intriguing possibility of the existence of an intermediate state between the solid and aqueous AS nanoparticles. Meanwhile, the water uptake occurred predominantly before the decrease in SO42- in the solid AS nanoparticles during the AS deliquescence transition. We speculate that the surface-limited process may control the transport of liquid water to the AS nanoparticles or, in other words, the surface-limited process determines the hygroscopic behavior of AS nanoparticles (Leng et al., 2015).

The above 2D IR spectroscopic results verify that the hygroscopic growth of AS nanoparticles may include the following phase transition micro-dynamics stages at the molecular level: the first stage (adsorption) pertains to the attachment of liquid water molecules to the surface of the solid (NH4)2SO4 (Yeşilbaş and Boily, 2016), which would cause a decrease in the solid (NH4)2SO4; then the NH4+ particles hydrated with SO42- are gradually replaced by the H2O molecules, and finally, the AS nanoparticles become fully liquid droplets. Although the hygroscopic growth characteristics observed in this study are similar to those in previous studies (Cruz and Pandis, 2000), the 2D IR spectroscopic technique captured a more complex processes and the intermediate state during the hygroscopic growth of AS nanoparticles (Tang et al., 1977, 1994).

Figure 8 is the same as Fig. 7 but for AS/SN mixed nanoparticles. In the synchronous correlation maps, one main red–positive auto-peak of (3250, 1097 cm-1) and two blue–negative auto-peaks of (1320, 1112 cm-1) and (3250, 1112 cm-1) were observed in the RH range from 50 %–90 %. The red–positive auto-peak of (3250, 1097 cm-1) indicates the simultaneous increase in the spectral intensities of OH and SO42- absorption peaks. The blue–negative auto-peaks of (1320, 1112 cm-1) and (3250, 1112 cm-1) indicate that the spectral intensities of the NO3- and the OH absorption peaks increase with RH, while the spectral intensity of SO42- absorption peak in solid AS/SN mixed nanoparticles decreases with RH. This can be explained by the fact that the NH4+ or Na+ hydrated with SO42- and NO3- is replaced by H2O molecules with the increase in RH. In the asynchronous correlation map, three main red–positive auto-peaks of (3250, 1097 cm-1), (1097, 1112 cm-1), and (1320, 1097 cm-1) and two main blue–negative auto-peaks of (3250, 1320 cm-1) and (1112, 1097 cm-1) were observed, which indicates that the spectral intensities of the absorption peaks change in the order of 1320 < 3250 > 1097 > 1112 cm-1. This means that the increase in NO3- occurred predominantly before the increase in SO42- in the aqueous AS/SN mixed nanoparticles because the SN has a lower DRH (RH = 74.3 ± 0.4 %) relative to that of AS (Seinfeld and Pandis, 2016; Tang and Munkelwitz, 1993). Meanwhile, the decrease in SO42- in solid AS/SN mixed nanoparticles occurred predominantly after the increase in SO42- in the aqueous AS/SN mixed nanoparticles, which suggests an intermediate state between the aqueous SO42- and solid SO42- states. Furthermore, the hydrolysis reaction mechanism for the AS in AS/SN mixed nanoparticles differs from that for the pure AS nanoparticles. This is because NO3- absorbs water at a lower RH than that of pure AS nanoparticles, which enhances the dissolution of the pure AS in the AS/SN mixed nanoparticles. Therefore, the NH4+ hydrated with the SO42- is replaced by the H2O molecules. This process continues till the AS/SN mixed nanoparticles become fully liquid droplets (Jing et al., 2016).

Figure 9 is the same as Fig. 8 but for the AS/OA mixed nanoparticles. In the synchronous correlation map, one main red–positive auto-peak of (3250, 1080 cm-1) and two main blue–negative auto-peaks of (1112, 1080 cm-1) and (3250, 1112 cm-1) were observed in the RH range from 50 %–90 %. The wavenumber of 1080 cm-1 is the SO42- absorption peak in the aqueous AS/OA mixed nanoparticles. The red–positive auto-peak of (3250, 1080 cm-1) indicates the simultaneous increase in the spectral intensities of OH and SO42- absorption peaks. The blue–negative auto-peak of (1112, 1080 cm-1) indicates that the SO42- in solid and aqueous AS/OA nanoparticles can transform into each other, and the decrease in SO42- in solid AS/OA nanoparticles results in the increase in SO42- in aqueous AS/OA nanoparticles. The blue–negative auto-peak of (3250, 1112 cm-1) indicates that the spectral intensity of the OH absorption peak increases with RH, while the intensity of the SO42- absorption peak in solid AS/OA nanoparticles decreases with RH. In the asynchronous correlation map, one main red–positive auto-peak of (3250, 1080 cm-1) and one main blue–negative auto-peak of (3250, 1112 cm-1) were observed, which indicates that the spectral intensities of the absorption peaks change in the order of 1112 > 3250 > 1080 cm-1. This sequential order of occurrence is consistent with that of the pure AS nanoparticles during the hygroscopic growth process. This is because OA does not absorb water, and thus the hydrolysis reaction mechanism of AS in AS/OA mixed nanoparticles is similar to that of the pure AS nanoparticles. With current measurements, we cannot judge if the hygroscopic growth processes of AS and AS/OA have the same intermediate states.