Particle nucleation rates were obtained using the method described in . By measuring the concentration of particles with diameters exceeding a cut-off diameter of 1.7 nm (N1.7), the nucleation rate J1.7 is defined as 1J1.7=dNdt,N=N1.7exp⁡(-kt), where k denotes the rate of particle wall loss and t the time after the initiation of new particle formation. The cut-off diameter of 1.7 nm was selected according to , being described as the critical cluster size from where nucleation occurs; thus, J1.7 constitutes an approximation of the nucleation rate. J1.7 was obtained from the wall-loss-corrected particle number concentrations, calculating the gradient between 20 % and 80 % of the maximum particle number concentration.

The water uptake behaviour of aerosol particles at sub- and supersaturated conditions can be described by the Köhler equation: 2S=aw⋅exp⁡4MwσsRTρwD(RH), where S is the water vapour saturation ratio, aw the water activity, σs the surface tension of the solution, R the ideal gas constant, T the absolute temperature, ρw the density of water, Mw the molecular mass of water, and D(RH) the diameter of a particle exposed to a certain relative humidity, RH.

At sub-saturated conditions of water vapour, the hygroscopic growth factor at a given relative humidity (GF(RH) is calculated as the ratio of the particle diameter at high RH (D(RH)) to the dry particle diameter (Ddry): 3GF(RH)=D(RH)Ddry.

At supersaturated conditions of water vapour, the critical supersaturation (SScrit) needed for a specific particle size to be activated into a cloud droplet is in focus. This point is identified as the maximum of the Köhler curve (SS versus D(RH)).

To compare water uptake at sub- and supersaturated conditions, the hygroscopicity parameter κ, introduced by , can be used. The water activity term in Eq. () can then be described in terms of κ in the following way: 41aw=1+κVsVw, where Vs is the volume of the dry particle and Vw the volume of the water in the droplet. By combining Eqs. (), () and (), the semi-empirical κ-Köhler equation can be obtained: 5S=GF(RH)3-1GF(RH)3-(1-κ)⋅exp⁡4MwσsRTρwD(RH).

For a given supersaturation (or RH for the subsaturated case), a κGF and κSScrit can be calculated.

Nitrogen oxides (NOx) and ozone (O3) levels were continuously measured with a chemiluminescent monitor (AC32M, Environnement SA) and a UV absorption ozone analyser (O342 Module, Environment S.A), respectively. The temperature (T) and RH were monitored in the centre of the bag (HC02-04 sensor; Rotronic AG, Switzerland).

During Exp. 1, 2, 4, 5, and 8–11, a proton transfer reaction time-of-flight mass spectrometer (PTR-ToF-MS 4000, Ionicon Analytik, Innsbruck, Austria; e.g. ) was employed to continuously monitor DMS concentrations. The instrument is based on a soft-ionisation technique using hydronium ions (H3O+) to ionise gas-phase compounds with proton affinities equal to or greater than that of water, which is the case for most volatile organic compounds (VOC). After the reaction with the primary ion occurs in the drift tube, the ionised compounds are detected in the ToF-MS. The PTR-ToF-MS was run with drift tube conditions of 650 V, 80 ∘C, and 2.4 mbar and, thus, an E/N number of 143 Townsend. The instrument was connected to the chamber via a 2 m long Teflon tube, wrapped in heating tape set to 60 ∘C, that was connected to the heated inlet of the instrument (temperature set to 80 ∘C). Additionally, the instrument flow rate was increased by adding a sheath flow of 200 mL min-1 to reduce sampling losses.

Data analysis was performed using the PTR-MS Viewer 3 (IONICON). Prior to the measurement campaign, a transmission calibration was carried out based on specific reaction rate constants and mass discrimination factors, as described elsewhere .

An Airmodus A11 nano Condensation Nucleus Counter (nCNC, Airmodus), consisting of a particle size magnifier (PSM, Airmodus A10) and a condensation particle counter (CPC, Airmodus A20), was used to measure particles above 1.7 nm in diameter during Exp. 5, 9, and 11. A thorough description of the instrument is given elsewhere . In short, the PSM was operated with diethylene glycol as working fluid. Supersaturated diethylene glycol leads to growth of the smallest (approximately 1 nm) particles by condensing the working fluid onto them. When the particles reach sizes of approximately 90 nm, they are guided to a condensation particle counter (using butanol as working fluid) and optically detected therein. The PSM was operated in fixed mode, counting all particles above the selected 1.7 nm threshold. The saturator flow rate was kept at 0.28 L min-1 in order to obtain the desired cut-off diameter.

A scanning mobility particle sizer (SMPS, TSI model 3938) was used to measure the dry particle number size distributions. The electrostatic classifier (EC, TSI model 3082) was either connected to a nano differential mobility analyser (DMA; TSI model 3085A) for sizes between 2 and 65 nm or a long DMA (TSI model 3081) for the size range 10–422 nm. Initially, the nano DMA was used and switched to the long DMA when particles grew out of the size range. The DMAs were connected to a nano water-based condensation particle counter (WCPC, TSI model 3788). The SMPS data analysis was performed with the Aerosol Instrument Manager (AIM) version 10.2.0.11, using the corrections for diffusion losses and multiple charges. A sheath to aerosol flow ratio of 10:1 was chosen (nano SMPS: 15:1.5 L min-1; long SMPS: 6:0.6 L min-1). A silica gel diffusion dryer was used to ensure a RH < 10 % at the inlet of the SMPS.

In order to retrieve particle properties, such as hygroscopicity, representative for the main particle mode, we used the size distributions measured with SMPS over time. A log-normal distribution was fitted to the SMPS data at every time step. The mean and standard deviation of the particle number size distribution were retrieved from the fit. A particle size was classified as representative for the major particle population in the chamber when it was within the fitted mean ±1 SD of the SMPS size distribution. All mean values presented in the manuscript refer to the time when particle properties were measured within the main growth mode. An example for the limits found for Exp. 5 is shown in Fig. S1 in the Supplement.

The hygroscopic growth of 10–150 nm (dry size) particles was measured with two separate humidified tandem differential mobility analysers (HTDMAs) at a constant RH of 80 %. In brief, an HTDMA consists of two DMAs, a CPC, and a humidifier in between the two DMAs. The first DMA is used to select a monodisperse sample from the dry polydisperse particle population, which is then exposed to a selected RH. The size distribution of the humidified particles is then measured with the second DMA, followed by the CPC. In this way, the hygroscopic growth factor GF(RH) can be retrieved (Eq. ). The hygroscopic growth of particles with Ddry=10, 15, and 20 nm particles was measured with a custom built “nano-HTDMA”, described in more detail in, for example, and . In short, the nano-HTDMA system consists of two nano-DMAs (TSI, model 3085) and a water-based CPC (TSI, model 3785) to count the particles. A silica gel diffusion drier was placed in front of the first DMA to make sure the particles entered the instrument with RH < 10 %. The DMAs were operated in an open-loop system, with a sample flow of 1 L min-1 and a sheath flow of 10 L min-1. To ensure stable conditions through the particle sizing, the sample flow and the sheath air inside the second DMA were humidified separately. The measured GFs were then corrected to the target RH of 80 %, assuming a constant hygroscopicity parameter κ within small deviation around the target humidity (±1.5 %), as in . Ammonium sulfate particles (Sigma Aldrich, purity ≥99.0 %) were used to calibrate the instrument for offsets in dry size selection. After taking into account the uncertainties of all devices influencing particle sizing, the uncertainty in the GFs can be estimated to be at maximum 2.5 %. The hygroscopic growth of particles with Ddry=30, 50, 80, 100, and 150 nm was measured with a commercially available HTDMA (Brechtel, Model 3002, ), from now on termed “long-HTDMA”. A diffusion drier at the inlet ensured that particles entered the instrument at RH < 10 %. The aerosol flow of the first and second DMA were 0.8 and 0.5 L min-1, respectively, while the sheath flows were 5 L min-1 in both systems. The instrument was calibrated using ammonium sulfate (Sigma Aldrich, purity >99.95 %) particles. The overall uncertainty in GF (80 %) is estimated to be below 3 %, based on the combination of instrumental uncertainty (estimated to be 2 % sizing accuracy and 1 % RH uncertainty) and comparison to theoretical values calculated with Köhler theory (max. 2 % for the chosen size range).

The ability of particles to act as cloud condensation nuclei (CCN) was monitored with a continuous-flow streamwise thermal-gradient ccn chamber (CFSTGC, CCN-100 from Droplet Measurement Technologies; ). The CCN instrument was operated following the Scanning Mobility CCN Analysis (SMCA) described in to increase the temporal resolution. In short, we measured the critical dry diameter, Dp,c, of mobility size-selected aerosols. Aerosol-laden air from AURA was dried using diffusion dryers (RH < 10 %) before entering the electrostatic classifier. The classifier consisted of a long-DMA (TSI model 3081) and an aerosol neutraliser (X-ray source, TSI model 3087). A scanning voltage was applied (scan time 120 s up and 15 s down), and the mono-disperse outlet stream of the DMA was directed to both the CCNc and CPC (TSI model 3010). Time was synchronised daily. The CCN supersaturation was initially set high (∼1.4 %), since the newly formed aerosols were small in the beginning. As the particle size distribution grew to larger sizes, the supersaturation of the CCNc was decreased to ∼0.2 %, which is representative for supersaturations found in the marine environment . Scan time alignment, multiple charge correction, quality control, and sigmoidal fitting of the activation curves (CCN/CN vs. Dp) were done using the “SMCAProcessor.xls” file, available at http://nenes.eas.gatech.edu/Experiments/SMCA.html (last access: 1 February 2019). The supersaturation of the CCN column was calibrated on 11 March 2019 using atomised ammonium sulfate (99.9999 % purity, 33 mg in 500 mL MilliQ). The measured Dp,c was used as input to the “Köhler curves” module of the Extended AIM Aerosol Thermodynamics Model to estimate the supersaturation (http://www.aim.env.uea.ac.uk/aim/kohler/kohler2.php, last access: 13 March 2019). A schematic of the SMCA calibration setup and a calibration curve performed with ammonium sulfate are shown in Figs. S2 and S3.

A high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS, Aerodyne Research Inc.) was used to measure the chemical composition of the particles in real time. The instrument setup is described in detail in . The instrument was employed as described in . HR-ToF-AMS data were processed in Igor Pro 8 by the data analysis software packages SQUIRREL (version 1.62) and PIKA (version 1.22). The PIKA default HR-ToF-AMS collection efficiency (CE) of 1 was used. The MSA calibration as presented in was applied to quantify particulate MSA. Unit-mass resolution efficient particle time-of-flight (ePToF) data were exported for the MSA tracer ion m/z 79 and sulfate tracer ion m/z 80. This sulfate tracer ion was selected, because MSA only contributes 0.04⋅(m/z79) to the m/z 80 signal. The relationship between vacuum aerodynamic diameters, as retrieved from ePToF data and mobility diameters for spherical particles, used in the measurement of the water uptake, can be calculated according to : 6ρp=dvadmρ0, where dva is the vacuum aerodynamic diameter, dm is the electric mobility diameter, ρ0 is standard density (1 g cm-3), and ρp is the density of the particle. The particles were assumed to have no voids, which results in the density of the particle being equal to the density of the material. PToF time series were smoothed using a 15-point (i.e. 15 min) moving average to decrease short-term fluctuations.

The Gaussian09 program was used to obtain the molecular cluster structures and to calculate the vibrational frequencies. The ωB97X-D functional was employed, as it has been shown to exhibit low errors in the binding energies of atmospheric molecular clusters compared to higher level CCSD(T) calculations (). The calculations were performed using the 6-31++G(d,p) basis set, which has shown good agreement with basis sets of significantly larger sizes ().

The ORCA program version 4.0.0 was used to calculate the single point energy (i.e. the electronic energy of a molecule for a certain arrangement of the atoms in the molecule) of all the clusters using DLPNO-CCSD(T0) () with an aug-cc-pVTZ basis set. The aug-cc-pVTZ/C and aug-cc-pVTZ/JK auxiliary basis sets were used for density fitting and Coulomb or exchange fitting. We have recently demonstrated that this level of theory yields total and relative binding energy results in good agreement with higher level, explicitly correlated, coupled cluster calculations on a test set of 45 cluster structures and sulfuric acid hydrates (). All the thermochemical parameters have been calculated at 298.15 K and 1 atm.

We have recently reported the application of a systematic sampling technique to obtain the molecular structures of sulfuric acid–water clusters and carboxylic acid–water clusters . Here, we utilise the same method to thoroughly sample the rich potential energy surface of the methanesulfonic acid (MSA)–water clusters. The following procedure was applied:

Water molecules are placed around all the exterior atoms of the cluster.

Atmospheric ageing of DMS-derived secondary aerosols was simulated by prolonged exposure to OH radicals at different temperatures and RH. We first consider the water uptake at sub- and supersaturated water vapour conditions at 293 K for both dry and humid conditions. Figure  illustrates the water uptake behaviour in the form of κ values obtained from hygroscopic growth and CCN measurements overlaid on particle number size distributions during Exp. 5 (humid conditions) and Exp. 7 (dry conditions). In both cases, clear nucleation events are visible, with particles growing up to approximately 150 nm in diameter within the first 10 h. As mentioned in , an additional growth mode is observed, and from Fig. 2, it seems to be more pronounced at dry compared to humid conditions (Fig. a vs. b).

κ values are only presented for times when the selected dry diameter was within the boundary chosen to represent the main growth mode (see description in Sect. ). The colour code describes the magnitude of κ, where dark blue colours represent low values and light blue colours high values. Mean κ values during the main particle growth mode for 80 nm particles (dry size), as retrieved from long-HTDMA measurements in Exp. 5 and 7, were κ=0.52 ± 0.03 and κ=0.54 ± 0.03, respectively. These were calculated from GF (80 %) results of 1.42 ± 0.02 and 1.44 ± 0.02. κ values derived for other particle sizes are presented in Table , and the GF (80 %) results are presented in Table S3. In comparison, κ values from CCNc measurements for dry particles of approximately 80 nm yielded κ=0.50 ± 0.03 and κ=0.54 ± 0.06 for Exp. 5 and 7, respectively (all mean κ values from CCNc are presented in Table S4). Thus, for this size, mean κ values at sub- and supersaturated water vapour conditions are well comparable and agree within the standard variations of the measurements. Figure S6 shows the derived mean κ values as a function of all measured dry particle diameters for Exp. 5 and 7. There is no systematic trend in the variation of κ with particle diameter for κ values calculated from GFs, while an increase in κ with particle size can be seen for κ values calculated from CCNc data. Such a size trend can be expected from Köhler theory; for comparison, the κ value for ammonium sulfate varies from 0.51 to 0.63 over the particle size range 20–100 nm (calculated using UManSysprop at 293 K, ). Mean κ values during the main particle growth mode are consistent across instruments and supersaturations. Agreement between κ values derived for the same particle size from measurements at sub- and supersaturation is not necessarily expected, as shown by several earlier studies for organic and inorganic particles e.g..

Following the evolution of κ for a certain size, in Fig.  it can be seen that the values increase over time, meaning that hygroscopicity increases with ageing by exposure to OH radicals and UV light, indicating slight changes in chemical composition. In Exp. 7, performed under dry conditions (Fig. a), dry 80 nm particles could first be measured approximately 4 h after the start of the experiment, showing κ values of 0.50, which increased to κ values of 0.58 at about 7 h after the start of the experiment. Similarly, in Exp. 5, performed under humid conditions (Fig. b), the κ value for dry 80 nm particles changed from 0.51 to 0.63 (measured at approximately 4 and 8 h after the start of the experiment). Similar trends were observed in Exp. 8 and 10, performed at different temperatures and shown in the Supplement.

To further investigate this change in hygroscopicity as a result of ageing, we extracted size-selected ePToF data from the HR-ToF-AMS. Figure  illustrates the temporal evolution of m/z 79 and 80, representative for MSA and ammonium sulfate, respectively. Only data for particles with an aerodynamic diameter of approximately 126 nm are illustrated, as these correspond to particles with a mobility diameter of 80 nm, assuming that particles were spherical and composed of approximately 50 % MSA and 50 % ammonium sulfate, thus having a density of approximately 1.6 g cm-3 (density of MSA: 1.48 g cm-3, density of ammonium sulfate: 1.77 g cm-3; according to Sigma-Aldrich). This assumption is based on bulk chemical composition data from HR-ToF-AMS, presented in Fig. S7. Only results for Exp. 5 (wet conditions) and Exp. 6 (dry conditions) are shown, as the signal on the chosen marker ions was highest during these experiments; thus, best PToF data analysis could be performed. The black lines in Fig.  denote the ratio of m/z 79 to 80, and the vertical grey, dashed lines depict the time interval when this selected size was present within the main particle growth mode. When performing a linear regression to the ratio of m/z 79 to 80, when the ion signal was above 0.2 (threshold chosen to be less influenced by noise), a slow decrease is visible, indicating an increased fraction of ammonium sulfate in the particles with time (red solid lines in Fig. ) under both dry and humid conditions. During this campaign, the HR-ToF-AMS was not set up in a way to resolve size-selected properties at low aerosol mass concentration, as only 30 s were spent on ePToF data acquisition for each 1 min data point. Thus, these results have to be treated with care, and further experiments targeting the size-selected chemical composition of secondary particles formed from the oxidation of DMS are needed to obtain a more detailed understanding of changes in the chemical composition of DMS-derived products.

Previous HTDMA measurements of pure MSA particles at 293 K yielded GF (90 %) = 1.57 for a dry particle size of 100 nm , which translates to κ=0.36 and GF (80 %) = 1.33 (recalculated using κ-Köhler theory). predicted the supersaturation needed to activate MSA particles at 293.15 K with dry sizes between 20 and 200 nm with the AIOMFAC model, finding a κ value of 0.55 for 80 nm particles (critical supersaturations presented in the Supplement of and recalculated using κ-Köhler theory). Lower κ values of 0.40 for 80 nm particles were modelled for ammonium–MSA . In comparison, κ values for 80 nm ammonium sulfate particles are 0.59 and 0.62, according to the UManSysProp thermodynamic model , for subsaturated (GF (80 nm, 80 %)) and supersaturated (80 nm dry size) conditions, respectively. Assuming particles are composed of 50 % MSA and 50 % ammonium sulfate, as indicated by the HTR-ToF-MS results in this study, mixed κ values can be retrieved using the modelled data of the single substances, yielding 0.57 and 0.59 for 80 nm particles using ammonium sulfate results at sub- and supersaturated conditions, respectively. Our mean κ results are considerably higher than those for pure MSA from HTDMA measurements, presented earlier by and being closest to AIOMFAC κ values for MSA while being lower than the ammonium sulfate values from UManSysProp. The range of κ values measured within this study is consistent with the hygroscopicity of a mixture of MSA and ammonium sulfate. As the hygroscopicity of ammonium sulfate is larger than that of MSA, a change in chemical composition during ageing leading to a higher fraction of ammonium sulfate in the particles could be responsible for the measured increase in hygroscopicity over time.

Experiments at 258, 273, and 293 K and high relative humidity were carried out to explore how the hygroscopicity and CCN activation potential are affected by the temperature during particle formation and subsequent ageing. Similar to the results at 293 K, the hygroscopicity of the particles formed at 258 and 273 K increases with ageing (see Figs. S8 and S9). Figure a illustrates mean GF (80 %) as measured by nano- and long-HTDMA, and Fig. b illustrates mean κ values as calculated from HTDMA and CCNc results for the three different temperatures. The mean values are calculated from the time period when a certain size was measured in the main growth mode, as described in Sect. . Only data for humid experiments are shown, i.e. Exp. 2–5 and 8–11. Table  shows mean κ values for each experiment (mean GF (80 %) values and mean κ values from the CCNc are presented in Table S4). When comparing results at 293 K in Fig. a, it is evident that GF (80 %) values are smaller for smaller sizes. This difference disappears when κ values are compared (spherical symbols), indicating that this difference originates from the Kelvin term that is more important for particles of approximately 15 nm in dry size compared to those of approximately 80 nm. GF (80 %) values in the long-HTDMA range seem comparable at all temperatures, while the nano-HTDMA shows a tendency for smaller GF (80 %) at 293 K compared to 258 K. When comparing HTDMA data in Fig. b, which illustrates κ values, this general trend of less hygroscopic particles at 293 K compared to 258 K is also visible. Figure b additionally illustrates κ values as derived from CCNc measurements (square symbols). Generally, the ranges of the CCNc results are more scattered, but they overlap with HTDMA results. The majority of the herein presented experimental κ values lie in the range of modelled values for MSA and ammonium–MSA, as found by (theoretical values depicted in Fig. b); the experimental κ values at 258 K for small particles exceed the modelled MSA results and are more comparable with the theoretical κ values for ammonium sulfate.

The relative contributions and absolute concentrations of organics, nitrate, sulfate, ammonia, chloride, and MSA are illustrated in Fig. S7 for experiments performed at 273 and 293 K. Absolute concentrations show that, in general, the aerosol mass loading was small and that the organic contribution was comparable during all experiments. As previously discussed in and , we cannot conclude on the exact origin of the organic signal. A thorough analysis of the organic mass spectra revealed that the organic mass signal is composed of the sum of many low-intensity fragments that we cannot attribute to a specific source (see example organic mass spectrum for Exp. 5). It cannot be entirely excluded that it is due to contamination from previous experiments. It could, however, also derive from biases due to the complex fragmentation during ionisation and uncertainties arising from the calibration with MSA. Additionally, instrumental memory effects have previously been documented for the AMS e.g.. Two ionisation efficiency calibrations before and after the experiments could neither exclude nor completely prove memory effects. If the organic signal stems from uncertainties in the analysis, it will not influence hygroscopicity. In the case that the organic signal is real, the herein presented hygroscopicity results represent lower estimates of the inorganic aerosol hygroscopicity, as κ values for organics in the range 0–0.2 can be expected, which would lead to a decrease of the κ values measured for an organic–inorganic mixture.

The chemical composition of the aerosol particles could not be measured at 258 K due to the low mass produced during these experiments. Experiments 8 and 9 were carried out at 273 K, but no obvious difference was found compared to the experiments carried out at 293 K. Figure  illustrates mean κ values colour coded by the MSA to sulfate ratio measured by the HR-ToF-AMS at 293 and 273 K. We selected κ values for dry particles of 80 and 100 nm (long-HTDMA), as these sizes are more representative of the size range analysed by the HR-ToF-AMS (typically PM1). Tabular values of MSA / SO42- are given in Table S5. The MSA / SO42- ratio is highest in Exp. 1 and 7, which were performed at 293 K and dry conditions, reaching values above 3. These high values at dry and warm conditions were already discussed in . Contrarily, Exp. 6, which was also carried out at 293 K and dry conditions, shows a small MSA / SO42- ratio of 1.3. This difference could potentially originate from the higher RH values of 13.7 ± 1.7 in Exp. 6 compared to RH below 10 % in Exp. 1 and 7. At 293 K and high humidity conditions, the MSA / SO42- ratios vary from 2.7 to 1.4, where experiments at low H2O2 concentrations yield high values and experiments at high H2O2 conditions yield low values. At 273 K and high humidity conditions, the values during experiments with high or low H2O2 coincide, yielding ratios of 1.5. As seen in Fig. , the κ values at 273 K vary most, while their MSA / SO42- ratios are the same. At 293 K, on the other hand, the MSA / SO42- ratios vary from 3 to 1.4, as discussed above, but no clear trend is observed in the κ values, i.e. higher κ values are associated with both high and low MSA / SO42- ratios.

To the best of our knowledge, there are no previous measurements of the water uptake of MSA or ammonium–MSA particles at 258 or 273 K. When using the UManSysProp thermodynamic model to calculate κ values for ammonium sulfate particles at 293 and 258 K, only small variations are found. κ values of 0.59 and 0.58 at 293 and 258 K, respectively, are found based on hygroscopic growth, while κ values of 0.63 and 0.59 at 293 and 258 K, respectively, are found based on CCN activation potential. This is consistent with previous findings showing that the water activity of ammonium sulfate in this temperature range is quite constant . Due to the similarities between ammonium sulfate and MSA, we thus expect that the temperature dependence of the water uptake of MSA is also negligible.