2.1 The CLOUD chamber

We conducted experiments at the CERN CLOUD chamber (Cosmics Leaving Outdoor Droplets). With a volume of 26.1 m³, the chamber is built of electropolished stainless steel and equipped with a precisely controlled gas system. The temperature inside the chamber is measured with a string of six thermocouples (TC, type K), which were mounted horizontally between the chamber wall and the center of the chamber at distances of 100, 170, 270, 400, 650 and 950 mm from the chamber wall (Hoyle et al., 2016). The temperature is controlled accurately (with a precision of ±0.1 ^∘C) at any tropospheric temperature between −65 and 30 ^∘C (in addition, the temperature can be raised to 100 ^∘C for cleaning). The chamber enables atmospheric simulations under highly stable experimental conditions with low particle wall loss and low contamination levels (more details of the CLOUD chamber can be found in Kirkby et al., 2011 and Duplissy et al., 2016). At the beginning of the campaign the CLOUD chamber was cleaned by rinsing the walls with ultra-pure water, followed by heating to 100 ^∘C and flushing at a high rate with humidified synthetic air and elevated ozone (several ppmv) (Kirkby et al., 2016). This resulted in SO₂ and H₂SO₄ concentrations that were below the detection limit (< 15 pptv and < 5 × 10⁴ cm⁻³, respectively), and total organics (largely comprising high volatility C₁–C₃ compounds) that were below 150 pptv.

The air in the chamber is ionized by galactic cosmic rays (GCRs); higher ion generation rates can be induced by a pion beam (π⁺) from the CERN Proton Synchrotron enabling controlled simulation of galactic cosmic rays throughout the troposphere. Therefore, the total ion-pair production rate in the chamber is between 2 (no beam) and 100 cm⁻³ s⁻¹ (maximum available beam intensity, Franchin et al., 2015).

2.2 Instrumentation

The main instruments employed for this study were atmospheric pressure interface time-of-flight (APi-TOF, Aerodyne Research Inc. & Tofwerk AG) mass spectrometers. The instrument has two main parts. The first is the atmospheric pressure interface (APi), where ions are transferred from atmospheric pressure to low pressures via three differentially pumped vacuum stages. Ions are focused and guided by two quadrupoles and ion lenses. The second is the time-of-flight mass analyzer (TOF), where the pressure is approximately 10⁻⁶ mbar. The sample flow from the chamber was 10 L min⁻¹, and the core-sampled flow into the APi was 0.8 L min⁻¹, with the remaining flow being discarded.

There is no direct chemical ionization in front of the instrument. The APi-TOF measures the positive or negative ions and cluster ions as they are present in the ambient atmosphere. As described above, in the CLOUD chamber ions are formed by GCRs or deliberately by the π⁺ beam, leading to ion concentrations of a few hundred to thousands per cm³, respectively. In our chamber the dominant ionizing species are NH${}_{\mathrm{4}}^{+}$ and NO${}_{\mathrm{3}}^{-}$ (see below). These ions mainly form clusters with the organic molecules, which is driven by the cluster energies. Therefore, the signals obtained do not provide a quantitative measure of the concentrations of the compounds. The higher the cluster energy with certain compounds, the higher the ion cluster concentration will be.

We calibrated the APi-TOF using trioctylammonium bis(trifluoromethylsulfonyl)imide (MTOA-B3FI, C₂₇H₅₄F₆N₂O₄S₂) to facilitate exact ion mass determination in both positive and negative ion modes. We employed two calibration methods, the first one by nebulizing MTOA-B3FI and separating cluster ions with a high-resolution ultra-fine differential mobility analyzer (UDMA) (see Steiner et al., 2014 for more information); the second one by using electrospray ionization of a MTOA-B3FI solution. The calibration with the electrospray ionization was performed three times, one for each temperature. These calibrations enabled mass/charge (m∕z) measurements with high accuracy up to 1500 Th in the positive ion mode and 900 Th in the negative ion mode.

Additionally, two peaks in the positive ion mode were identified as contaminants and also used for calibration purposes at the three different temperatures: C₁₀H₁₄OH⁺ and C₂₀H₂₈O₂H⁺. These peaks were present before the addition of ozone in the chamber (therefore being most likely not products of α-pinene ozonolysis) and were also detected by a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS). Both peaks appeared at the same m∕z at all three temperatures. Therefore, based on the calibrations with the UDMA, the electrospray and the two organic calibration peaks, we expect an accurate mass calibration at the three temperatures.

2.3 Experimental conditions

All ambient ion composition data reported here were obtained during nucleation experiments from pure α-pinene ozonolysis. The experiments were conducted under dark conditions, at a relative humidity (RH) of 38 % with an O₃ mixing ratio between 33 and 43 ppbv (Table 1). The APi-TOF measurements were made under both galactic cosmic ray (GCR) and π⁺ beam conditions, with ion-pair concentrations around 700 and 4000 cm⁻³, respectively.

Table 1Experiments performed at the CLOUD chamber.

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Figure 1Positive spectra at 5 ^∘C. (a) Low mass region, where primary ions from galactic cosmic rays are observed, as well as secondary ions such as NH${}_{\mathrm{4}}^{+}$, which are formed by charge transfer to contaminants. (b) Higher mass region during pure biogenic nucleation, which shows broad bands in steps of C₂₀. Most of the peaks represent clusters with NH${}_{\mathrm{4}}^{+}$.

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2.4 Quantum chemical calculations

Quantum chemical calculations were performed on the cluster ion formation from the oxidation products of α-pinene. The Gibbs free energies of formation of representative HOM clusters were calculated using the MO62X functional (Zhao and Truhlar, 2008), and the 6-31+G(d) basis set (Ditchfield, 1971) using the Gaussian09 program (Frisch et al., 2009). This method has been previously applied for clusters containing large organic molecules (Kirkby et al., 2016).

3.1 Ion composition

Under dry conditions (RH = 0 %) and GCR ionization, the main detected positive ions were N₂H⁺ and O${}_{\mathrm{2}}^{+}$. With increasing RH up to ∼ 30 % we observed the water clusters H₃O⁺, (H₂O) ⋅ H₃O⁺ and (H₂O)₂ ⋅ H₃O⁺ as well as NH${}_{\mathrm{4}}^{+}$, C₅H₅NH⁺ (protonated pyridine), Na⁺ and K⁺ (Fig. 1a). The concentrations of the precursors of some of the latter ions are expected to be very low; for example, NH₃ mixing ratios were previously found to be in the range of 0.3 pptv (at −25 ^∘C), 2 pptv (at 5 ^∘C) and 4.3 pptv (at 25 ^∘C) (Kürten et al., 2016). However, in a freshly cleaned chamber we expect ammonia levels below 1 pptv even at the higher temperatures. For the negative ions, NO${}_{\mathrm{3}}^{-}$ was the main detected background signal. Before adding any trace gas to the chamber the signal of HSO${}_{\mathrm{4}}^{-}$ was at a level of 1 % of the NO${}_{\mathrm{3}}^{-}$ signal (corresponding to < 5 × 10⁻⁴ molecules cm⁻³, Kirkby et al., 2016), excluding any contribution of sulfuric acid to nucleation in our experiments.

After initiating α-pinene ozonolysis, more than 460 different peaks from organic ions were identified in the positive spectrum. The majority of peaks were clustered with NH${}_{\mathrm{4}}^{+}$, while only 10.2 % of the identified peaks were composed of protonated organic molecules. In both cases the organic core was of the type C₇₋₁₀H₁₀₋₁₆O₁₋₁₀ for the monomer region and C₁₇₋₂₀H₂₄₋₃₂O₅₋₁₉ for the dimer region.

In the negative spectrum we identified more than 530 HOMs, of which ∼ 62 % corresponded to organic clusters with NO${}_{\mathrm{3}}^{-}$ or, to a lesser degree, HNO₃ ⋅ NO${}_{\mathrm{3}}^{-}$. The rest of the peaks were negatively charged organic molecules. In general, the organic core of the molecules was of the type C₇₋₁₀H₉₋₁₆O₃₋₁₂ in the monomer region and C₁₇₋₂₀H₁₉₋₃₂O₁₀₋₂₀ in the dimer region. For brevity we refer to the monomer, dimer (and n-mer) as C₁₀, C₂₀ (and C_10n), respectively. Here, the subscript indicates the maximum number of carbon atoms in these molecules, even though the bands include species with slightly fewer carbon atoms.

Figure 2Comparison of the negative ion composition during α-pinene ozonolysis in CLOUD and during nighttime in the boreal forest at Hyytiälä (Finland). (a) CLOUD spectrum on a logarithmic scale. (b) CLOUD spectrum on a linear scale. (c) Typical nighttime spectrum from the boreal forest at Hyytiälä (Finland), adapted from Ehn et al. (2010).

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3.1.2 Negative spectrum

In the negative spectra, the monomer, dimer, and trimer bands are observed during nucleation (Fig. 2). Monomers and dimers have similar signal intensities, whereas the trimer intensity is at least 10 times lower (Fig. 2a and b). The trimer signal is reduced since it is a cluster of two gas phase species (C₁₀ + C₂₀). Additionally, a lower transmission in the APi-TOF may also be a reason for the reduced signal.

Figure 3Positive (a–c) and negative (d–f) mass spectra during pure biogenic nucleation induced by ozonolysis of α-pinene at three temperatures: 25 ^∘C (a, d), 5 ^∘C (b, e) and −25 ^∘C (c, f). A progressive shift towards a lower oxygen content and lower masses is observed in all bands as the temperature decreases. Moreover, the appearance of C₃₀ species can be seen in the positive spectrum at the lowest temperature (c).

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In Fig. 2, we compare the CLOUD negative-ion spectrum with the one from nocturnal atmospheric measurements from the boreal forest at Hyytiälä as reported by Ehn et al. (2010). Figure 2a and b show the negative spectrum of α-pinene ozonolysis in the CLOUD chamber on logarithmic and linear scales, respectively. Figure 2c shows the Hyytiälä spectrum for comparison. Although the figure shows unit mass resolution, the high-resolution analysis confirms the identical composition for the main peaks: C₈H₁₂O₇ ⋅ NO${}_{\mathrm{3}}^{-}$, C₁₀H₁₄O₇ ⋅ NO${}_{\mathrm{3}}^{-}$, C₁₀H₁₄O₈ ⋅ NO${}_{\mathrm{3}}^{-}$, C₁₀H₁₄O₉ ⋅ NO${}_{\mathrm{3}}^{-}$, C₁₀H₁₆O₁₀ ⋅ NO${}_{\mathrm{3}}^{-}$ and C₁₀H₁₄O₁₁ ⋅ NO${}_{\mathrm{3}}^{-}$ (marked in the monomer region), and C₁₉H₂₈O₁₁ ⋅ NO₃, C₁₉H₂₈O₁₂ ⋅ NO₃, C₂₀H₃₀O₁₂ ⋅ NO${}_{\mathrm{3}}^{-}$, C₁₉H₂₈O₁₄ ⋅ NO${}_{\mathrm{3}}^{-}$, C₂₀H₃₀O₁₄ ⋅ NO${}_{\mathrm{3}}^{-}$, C₂₀H₃₂O₁₅ ⋅ NO${}_{\mathrm{3}}^{-}$, C₂₀H₃₀O₁₆ ⋅ NO${}_{\mathrm{3}}^{-}$, C₂₀H₃₀O₁₇ ⋅ NO${}_{\mathrm{3}}^{-}$ and C₂₀H₃₀O₁₈ ⋅ NO${}_{\mathrm{3}}^{-}$ (marked in the dimer region). The close correspondence in terms of composition of the main HOMs from the lab and the field both in the monomer and dimer region indicates a close reproduction of the atmospheric nighttime conditions at Hyytiälä by the CLOUD experiment. In both cases the ion composition was dominated by HOMs clustered with NO${}_{\mathrm{3}}^{-}$. However, Ehn et al. (2010) did not report nocturnal nucleation, possibly because of a higher ambient condensation sink than in the CLOUD chamber.

3.2 Temperature dependence

Experiments at three different temperatures (25, 5 and −25 ^∘C) were conducted at similar relative humidity and ozone mixing ratios (Table 1 and Fig. 3). Mass defect plots are shown for the same data in Fig. 4. The mass defect is the difference between the exact and the integer mass and is shown on the y axis versus the mass/charge on the x axis. Each point represents a distinct atomic composition of a molecule or cluster. Although the observations described in the following are valid for both polarities, the trends at the three temperatures are better seen in the positive mass spectra due to a higher sensitivity at high m∕z.

The first point to note is the change in the distribution of the signal intensity seen in Fig. 3 (height of the peaks) and in Fig. 4 (size of the dots) with temperature. In the positive ion mode, the dimer band has the highest intensity at 25 and 5 ^∘C (see also Fig. 1b), while at −25 ^∘C the intensity of the monomer becomes comparable to that of the dimer. This indicates a reduced rate of dimer formation at −25 ^∘C, or that the intensity of the ion signal depends on both the concentration of the neutral compound and on the stability of the ion cluster. Although the monomer concentration is higher than that of the dimers (Tröstl et al., 2016), the C₂₀ ions are the more stable ion clusters as they can form more easily two hydrogen bonds with NH${}_{\mathrm{4}}^{+}$ (see Sect. 3.3). Thus, positive clusters formed from monomers may not be stable enough at higher temperatures. Moreover, charge transfer to dimers is also favored.

The data also show a “shift” in all band distributions towards higher masses with increasing temperature, denoting a higher concentration of the more highly oxygenated molecules and the appearance of progressively more oxygenated compounds at higher temperatures. The shift is even more pronounced in the higher mass bands, as clearly seen in the C₄₀ band of the positive ion mode in Fig. 3a–c. In this case the combination of two HOM dimers to a C₄₀ cluster essentially doubles the shift of the band towards higher mass/charge at higher temperatures compared to the C₂₀ band. Moreover, the width of each band increases with temperature, as clearly seen in the positive ion mode in Fig. 4, especially for the C₄₀ band. At high temperatures, the production of more highly oxygenated HOMs seems to increase the possible combinations of clusters, resulting in a wider band distribution.

Table 2Signal weighted average O : C ratios for positive and negative spectra at 25, 5 and −25 ^∘C.

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Figure 4Mass defect plots with the color code denoting the O : C ratio (of the organic core) at 25, 5 and −25 ^∘C for positive (a–c) and negative ion mode (d–f). A lower O : C ratio is observed in the positive ion mode than in the negative ion mode. The intensity of the main peaks (linearly proportional to the size of the dots) changes with temperature for both polarities due to a lower degree of oxygenation at lower temperature.

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This trend in the spectra indicates that the unimolecular autoxidation reaction accelerates at higher temperatures in competition to the bimolecular termination reactions with HO₂ and RO₂. This is expected. If unimolecular and bimolecular reactions are competitive, the unimolecular process will have a much higher barrier because the pre-exponential term for a unimolecular process is a vibrational frequency while the pre-exponential term for the bimolecular process is at most the bimolecular collision frequency, which is 4 orders of magnitude lower. Quantum chemical calculations determine activation energies between 22.56 and 29.46 kcal mol⁻¹ for the autoxidation of different RO₂ radicals from α-pinene (Rissanen et al., 2015). Thus, such a high barrier will strongly reduce the autoxidation rate at the low temperatures.

The change in the rate of autoxidation is also reflected in the O : C ratio, both in the positive ion mode (Fig. 4a–c), and the negative ion mode (Fig. 4d–f), showing a clear increase with increasing temperature. The average O : C ratios (weighted by the peak intensities) are presented in Table 2 for both polarities and the three temperatures, for all the identified peaks (total) and separately for the monomer and dimer bands. For a temperature change from 25 to −25 ^∘C the O : C ratio decreases for monomers, dimers and total number of peaks. At high masses (e.g., for the C₃₀ and C₄₀ bands), the O : C ratio may be slightly biased since accurate identification of the molecules is less straightforward: as an example, C₃₉H₅₆O₂₅ ⋅ NH${}_{\mathrm{4}}^{+}$ has an exact mass-to-charge ratio of 942.34 Th (O ∕ C = 0.64), which is very similar to C₄₀H₆₀O₂₄ ⋅ NH${}_{\mathrm{4}}^{+}$ at 942.38 Th (O ∕ C = 0.60). However, such possible misidentification would not influence the calculated total O ∕ C by more than 0.05, and the main conclusions presented here remain robust.

Figure 5Comparison of the positive ion mode spectrum measured (blue), the C₄₀ band obtained by the combination of all C₂₀ molecules (light gray), and the C₄₀ band obtained by combination of only the C₂₀ molecules with O ∕ C ≥ 0.4 (dark gray). The low or absent signals at the lower masses obtained by permutation suggest that only the highly oxygenated dimers are able to cluster and form C₄₀.

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The O : C ratios are higher for the negative ions than for the positive ions at any of the three temperatures. Although some of the organic cores are the same in the positive and negative ion mode, the intensity of the peaks of the most oxygenated species is higher in the negative spectra. While the measured O : C ratio ranges between 0.4 and 1.2 in the negative ion mode, it is between 0.1 and 1.2 in the positive ion mode. An O : C ratio of 0.1, which was detected only in the positive ion mode, corresponds to monomers and dimers with two oxygen atoms. The presence of molecules with such low oxygen content was also confirmed with a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS), at least in the monomer region. Ions with O : C ratio less than 0.3 are probably from the main known oxidation products like pinonaldehyde, pinonic acid, etc., but also from minor products like pinene oxide and other not yet identified compounds. It is likely that these molecules, which were detected only in the positive mode, contribute only to the growth of the newly formed particles (if at all) rather than to nucleation, owing to their high volatility (Tröstl et al., 2016). In this sense, the positive spectrum could reveal both the molecules that participate in the new particle formation and those that contribute to growth. The differences in the O : C ratios between the two polarities are a result of the affinities of the organic molecules to form clusters either with NO${}_{\mathrm{3}}^{-}$ or NH${}_{\mathrm{4}}^{+}$, which, in turn, depends on the molecular structure and the functional groups. Hyttinen et al. (2015) reported the binding energies of selected highly oxygenated products of cyclohexene detected by a nitrate CIMS, finding that the addition of OOH groups to the HOM strengthens the binding of the organic core with NO${}_{\mathrm{3}}^{-}$. Even when the number of H-bonds between NO${}_{\mathrm{3}}^{-}$ and HOM remains the same, the addition of more oxygen atoms to the organic compound could strengthen the binding with the NO${}_{\mathrm{3}}^{-}$ ion. Thus, the less oxygenated HOMs were not detected in those experiments, neither in ours, in the negative mode. The binding energies were calculated for the positive mode HOMs–NH${}_{\mathrm{4}}^{+}$ and are discussed in Sect. 3.3.

We also tested to which extent the formation of the C₄₀ band could be reproduced by permutation of the potential C₂₀ molecules weighted by the dimer signal intensity. Figure 5 shows the measured spectrum (blue) and two types of modeled tetramers: one combining all peaks from the C₂₀ band (light gray) and one combining only those peaks with an organic core with O ∕ C ≥ 0.4 – i.e., likely representing non-volatile C₂₀ molecules (dark gray). The better agreement of the latter modeled mass spectrum of the tetramer band with the measured one suggests that only the molecules with O ∕ C ≥ 0.4 are able to form the tetramer cluster. This would mean that C₂₀ molecules with 2–7 oxygen atoms are likely not to contribute to the nucleation, but only to the growth of the newly formed particles. One has to note that the comparison of modeled and measured spectra relies on the assumption that the charge distribution of dimers is also reflected in the tetramers.

These two observations (change in signal distribution and band “shift”) are not only valid for positive and negative ions, but also for the neutral molecules as observed by two nitrate chemical-ionization atmospheric-pressure-interface time-of-flight mass spectrometers (CI-APi-TOF; Aerodyne Research Inc. and Tofwerk AG). This confirms that there is indeed a change in the HOM composition with different temperature rather than a charge redistribution effect, which would only be observed for the ions (APi-TOF). The detailed analysis of the neutral molecules detected by these CI-APi-TOFs will be the subject of another paper and is not discussed here.

A third distinctive trend in the positive mode spectra at the three temperatures is the increase in signal intensity of the C₃₀ band at −25 ^∘C. The increase in the signal of the trimer also seems to occur in the negative ion mode when comparing Fig. 3d and f. For this polarity, data from two campaigns were combined (Table 1). To avoid a bias by possible differences in the APi-TOF settings, we only compare the temperatures from the same campaign, CLOUD 10, therefore experiments at 25 and −25 ^∘C. The increase in the trimer signal may be due to greater stability of the monomer–dimer clusters or even of three C₁₀ molecules at low temperatures, as further discussed below.

3.3 Quantum chemical calculations

Three points were addressed in the quantum chemical calculations to elucidate the most likely formation pathway for the first clusters, and its temperature dependence. These included (i) the stability of the organic cores with NO${}_{\mathrm{3}}^{-}$ and NH${}_{\mathrm{4}}^{+}$ depending on the binding functional group, (ii) the difference between charged and neutral clusters in terms of clustering energies, and finally (iii) the possible nature of clusters in the dimer and trimer region.

Figure 6Quantum chemical calculations of the free energy related to the cluster formation between NH${}_{\mathrm{4}}^{+}$ and three structurally similar molecules with different functional groups: (a) acetaldehyde, (b) acetic acid and (c) peracetic acid.

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The calculations showed that among the different functional groups the best interacting groups with NO${}_{\mathrm{3}}^{-}$ are in order of importance carboxylic acids (R–C(= O)–OH), hydroxyls (R–OH), peroxy acids (R–C(= O)–O–OH), hydroperoxides (R–O–OH) and carbonyls (R–(R^′–) C = O). On the other hand, NH${}_{\mathrm{4}}^{+}$ preferably forms a hydrogen bond with the carbonyl group independent of which functional group the carbonyl group is linked to; Fig. 6 shows examples of NH${}_{\mathrm{4}}^{+}$ clusters with corresponding free energies of formation for carbonyls (ΔG = −17.98 kcal mol⁻¹), carboxylic acid (ΔG = −17.32 kcal mol⁻¹) and peroxy acid (ΔG = −17.46 kcal mol⁻¹). For the three examples shown, the interaction of one hydrogen from NH${}_{\mathrm{4}}^{+}$ with a C = O group is already very stable with a free energy of cluster ion formation close to −18 kcal mol⁻¹.

To evaluate the effect of the presence of a second C = O on the binding of the organic compound with NH${}_{\mathrm{4}}^{+}$, we performed a series of calculations with a set of surrogates containing two C = O groups separated by different numbers of atoms, as shown in Fig. 7. The addition of a second functional group allows the formation of an additional hydrogen bond, increasing the stability of the cluster considerably (almost 2-fold) from about −18 to −34.07 kcal mol⁻¹, whereby the position of the second functional group to form an optimal hydrogen bond (with a 180^∘ angle for N–H–O) strongly influences the stability of the cluster, as can be seen in Fig. 7. Thus, optimal separation and conformational flexibility of functional groups is needed to enable effective formation of two hydrogen bonds with NH${}_{\mathrm{4}}^{+}$. This could be an explanation for the observation that the signal intensity is higher for dimers than for monomers, as dimers can more easily form two optimal hydrogen bonds with NH${}_{\mathrm{4}}^{+}$.

Figure 7Quantum chemical calculations for different organic molecules with a carbonyl as the interacting functional group with NH${}_{\mathrm{4}}^{+}$. Increasing the interacting groups from one to two increases the stability of the cluster. The distance between the interacting groups also influences the cluster stability.

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Table 3Gibbs free energies of cluster formation ΔG at three different temperatures. ΔG for the molecules C₁₀H₁₄O₇ (C₁₀) and C₂₀H₃₀O₁₄ (C₂₀) forming neutral, as well as negative and positive ion clusters.

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As shown by Kirkby et al. (2016), ions increase the nucleation rates by 1–2 orders of magnitudes compared to neutral nucleation. This is expected due to the strong electrostatic interaction between charged clusters. To understand how the stability difference relates to the increase in the nucleation rate, the ΔG of charged and neutral clusters were compared. For this, C₁₀H₁₄O₇ and C₂₀H₃₀O₁₄ were selected as representative molecules of the monomer and dimer region, respectively (Kirkby et al., 2016). Table 3 shows the calculated free energies of formation (ΔG) of neutral, positive and negative clusters from these C₁₀ and C₂₀ molecules at the three temperatures of the experiment. Results show that at 5 ^∘C, for example, ΔG of the neutral dimer (C₁₀ + C₁₀) is −5.76 kcal mol⁻¹ while it decreases to −20.9 kcal mol⁻¹ when a neutral and a negative ion form a cluster (C₁₀ + C${}_{\mathrm{10}}^{-}$). Similarly, trimers show a substantial increase in stability when they are charged – i.e., from −2.1 to −19.9 kcal mol⁻¹, for the neutral and negative cases, respectively. The reduced values of ΔG for the charged clusters (positive and negative) indicate a substantial decrease in the evaporation rate compared to that for neutral clusters, and, therefore, higher stability. Comparing the NH${}_{\mathrm{4}}^{+}$ and NO${}_{\mathrm{3}}^{-}$ clusters, the energies of formation for the monomer are −22.5 and −25.9 kcal mol⁻¹, respectively, showing slightly higher stability for the negative cluster. Inversely, the covalently bound dimer showed greater stability for the positive ion (−30.9 kcal mol⁻¹) compared to the negative ion (−25.6 kcal mol⁻¹).

The temperature dependence of cluster formation is shown in Fig. 8 for the positive ion clusters. The blue and brown solid lines represent the needed ΔG for evaporation–collision equilibrium at 0.3 and 1 pptv HOM mixing ratio, respectively, calculated as described by Ortega et al. (2012). The markers show the calculated formation enthalpies ΔG for each of the possible clusters. For all cases, the trend shows an evident decrease in ΔG with decreasing temperature, with a correspondingly reduced evaporation rate.

Figure 8Quantum chemical calculations of Gibbs free energies for cluster formation at −25, 5 and 25 ^∘C. Solid lines represent the required ΔG for equilibrium between evaporation and collision rates at 0.3 and 1 pptv of the HOM mixing ratio, respectively. Markers show the ΔG for each cluster (organic core clustered with NH${}_{\mathrm{4}}^{+}$) at the three temperatures. C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$ (black circles) represent the monomer, C₂₀ ⋅ NH${}_{\mathrm{4}}^{+}$ (red circles) represent the covalently bound dimer, C₁₀C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$ (green circles) represent the dimer formed by the clustering of two monomers and C₁₀C₂₀ ⋅ NH${}_{\mathrm{4}}^{+}$ (purple circles) denote the preferential pathway for the trimer cluster (see Table 3).

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At all three temperatures, the monomer cluster C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$ falls well below the equilibrium lines, indicating high stability. Even though the difference between −25 and 25 ^∘C is just −1.6 kcal mol⁻¹ in free energy, it is enough to produce a substantial difference in the intensity of the band, increasing the signal at least 8-fold at −25 ^∘C (as discussed in Sect. 3.2). In the case of the dimers, we consider the possibility of their formation by collision of a monomer C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$ with another C₁₀ (resulting in a C₁₀C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$ cluster) or the dimer as C₂₀ ⋅ NH${}_{\mathrm{4}}^{+}$ cluster. The calculations show clearly that the cluster C₁₀C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$ is not stable at any of the three temperatures (green line). In contrast, the covalently bound C₂₀ forms very stable positive and negative ion clusters (see Table 3). Trimers are mainly observed at lower temperatures. Since the C₁₀C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$ cluster is not very stable, we discard the possibility of a trimer formation of the type C₁₀C₁₀C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$. Thus, the trimer is likely the combination of a monomer and a covalently bound dimer (C₂₀C₁₀ ⋅ NH${}_{\mathrm{4}}^{+}$). According to our calculations (Table 3) the preferred evaporation path for this cluster is the loss of C₁₀ rather than the evaporation of C₂₀. Therefore, we have chosen to represent only this path in Fig. 8. The ΔG of this cluster crosses the evaporation–condensation equilibrium around 5 and 14 ^∘C for a HOM mixing ratio of 0.3 and 1 pptv, respectively, in good agreement with the observed signal increase of the trimer at −25 ^∘C (Fig. 3a–c). It is important to note that, due to the uncertainty in the calculations, estimated to be ≤ 2 kcal mol⁻¹, we do not consider the crossing as an exact reference.

The ΔG of the negative ion clusters, which are also presented in Table 3, decrease similarly to the positive ion clusters by around 2 kcal mol⁻¹ between 25 and −25 ^∘C. The cluster formation energies of the monomer and the dimer with NO${}_{\mathrm{3}}^{-}$ are in agreement with the observed comparable signal intensity in the spectrum (Fig. 2) in a similar way as the positive ion clusters. The covalently bonded dimer ion C₂₀ ⋅ NO${}_{\mathrm{3}}^{-}$ is also more stable compared to the dimer cluster C₁₀C₁₀ ⋅ NO${}_{\mathrm{3}}^{-}$, suggesting that the observed composition results from covalently bonded dimers clustering with NO${}_{\mathrm{3}}^{-}$ rather than two individual C₁₀ clustering to form a dimer.

The formation of a covalently bonded trimer seems unlikely, so the formation of highly oxygenated molecules is restricted to the monomer and dimer region. The trimer could result from the clustering of C₁₀ and C₂₀ species. Similarly, and based on the C₂₀ pattern observed in Fig. 1b, we believe that the formation of the tetramer corresponds to the collision of two dimers. No calculations were done for this case due to the complexity related to the sizes of the molecules, which prevents feasible high-level quantum chemical calculations.

Finally, a comparison of the ΔG values as presented in Table 3 confirms the expected higher stability of charged clusters compared to neutral clusters, decreasing the evaporation rate of the nucleating clusters and enhancing new particle formation.