Introduction

Low molecular weight methylamines (MAs), namely monomethylamine (MMA), dimethylamine (DMA), and trimethylamine (TMA), are emitted from various natural and anthropogenic sources, and can influence key atmospheric aerosol processes1,2,3,4,5. Numerous laboratory and field studies underline their role in new particle formation (NPF), formation of secondary organic aerosol (SOA) mass2,5, and impact on the atmospheric acidity6. MAs are bases characterised by a higher nucleation capability with sulfuric acid than ammonia (NH3)7. At typical gas-phase mixing ratios of about 3 ppt in the planetary boundary layer (BL), the nucleation capability of DMA is about a 1000 times higher than that of ammonia8. Furthermore, uptake of MMA, DMA and TMA or their oxidation products on existing aerosol particles increases SOA mass. Thus, chemical processing of MAs in the atmosphere can significantly affect global climate, as SOA is able to absorb and scatter solar radiation, influences the concentration of CCNs and cloud droplets9.

Significant contributions of MAs to SOA are suggested by a field study where amines were measured in Antarctica10. This study proposed that photochemical processes convert aliphatic amines into oxidised compounds detected in aerosol particles. Recent laboratory studies involving our laboratory revealed that an internal H-atom shift dominates the gas-phase oxidation of DMA and TMA11,12. This process rapidly leads to oxidation products characterised by an increase of the molar mass from 45 and 59 up to 91 and 137 g mol-1 for DMA or TMA, respectively. Because of the high O/C ratio, the formed products HOOCH2NHCHO and HOOCH2N(CHO)CH2OOH could efficiently condense onto existing aerosol particles.

Uptake of MMA, DMA and TMA on aerosol particles affect their acidity and thus influences key atmospheric chemistry processes, e.g. sulfuric acid formation, and the partitioning of acidic compounds6,13. However, the oxidation of amines can result into amides and, because of the carbonyl group, the basic character is lost3. Thus, amides contribute to SOA mass, but do not contribute to NPF. This reveals that reactions in the atmospheric system are essential in understanding the multiphase concentrations and processing of these MAs and are crucial to determine their (i) aerosol particle concentration and distribution, (ii) contribution to radiative forcing of SOA and (iii) effect on cloud droplet number concentration.

Over the continents, high MMA, DMA, and TMA concentrations can be measured and related to near agricultural and other anthropogenic sources3,4. Source assignment in the marine boundary layer (MBL) is complicated. High DMA concentrations are measured within the MBL, but field studies suggest that oceans are generally sinks for DMA14,15,16. No conclusive view exists on what the source of DMA in the MBL is. It is suggested that MAs evaporating from freshly emitted sea spray aerosol (SSA) into the gas phase establish higher concentrations than could be calculated solely by emission fluxes from the ocean into the atmosphere, taking into account sea water concentrations10. However, mechanisms and dependencies of the phase partitioning of amines remained unclear and further studies are needed. Additionally, in environments with high OH concentrations or low concentration of volatile organic compounds (VOCs), atmospheric oxidations of MAs can play an important role. Thus, complex interactions between atmospheric gas and aqueous phase are key to understand the observed higher than expected DMA concentration. In conclusion, multiphase chemical processes need to be considered in models to gain a comprehensive view on amine abundance, sources and chemical processing14.

Currently, no detailed multiphase chemistry mechanism for MMA, DMA and TMA exists that can be applied in atmospheric models. Thus, it is a challenge to investigate the (i) processes responsible for the unexpectedly high concentrations of DMA in the MBL, (ii) the effect of multiphase oxidation on MMA, DMA, and TMA concentrations in pristine environments, and (iii) importance of the recently discovered autoxidation of DMA and TMA on SOA formation. In the present study, a multiphase chemistry mechanism is developed, examining the oxidation of MMA, DMA, and TMA, to close these knowledge gaps. Process simulations are performed for a pristine marine scenario, and mechanistic chemical rate studies are presented.

Results

Performed model simulations

For the numerical simulations, the model framework SPectral Aerosol Cloud Chemistry Interaction Model (SPACCIM)17 is used to investigate the importance of amine-related multiphase chemistry under pristine cloudy MBL conditions. Simulations are performed for a monodisperse marine aerosol population and a polydisperse marine aerosol particle population under different irradiation conditions. A detailed overview on the performed simulations is provided in Table 1.

Table 1 List of simulation runs and their specification
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The developed amine mechanism CAPRAM–AAM2.0 takes into consideration the tropospheric degradation of MMA, DMA, and TMA and their corresponding oxidation products, as well as the degradation for NH3. For the development, literature values from laboratory and theoretical works are implemented and appropriate estimations methods are applied (see section Materials and Methods and the SI). All in all, the developed CAPRAM–AAM2.0 mechanism module contains 235 gas-phase reactions, 51 phase transfers, and 256 aqueous-phase reactions.

Modelled gas-phase concentrations of MMA, DMA and TMA

First, the predicted concentrations and related chemical pathways were investigated for the simulations Amine and Amine-DU05 considering a monodisperse aerosol particle population. Figure 1 shows the modelled gas-phase concentrations. To avoid any influence from the model spin-up and to provide better distinguishability, only the second and third model day are depicted. Interestingly, DMA concentrations with similar concentration levels as MMA and TMA are simulated even without DMA emissions considered. All three MAs have distinctly modelled diel concentration profiles. Modelled concentrations of MMA and TMA are about 1 ng m-3, which is in-line with measurements representing pristine open-ocean conditions14,15,16.

Fig. 1: Modelled gas-phase concentration of methylamines.
figure 1

Modelled gas-phase concentrations of a) MMA, b) DMA, c) TMA for the simulations Amine and Amine-DU05, and d) DMA for the simulations Amine and Amine-DU05 as well as simulations with 50% irradiation attenuation and additional simulations with included particle-phase initialisation of DMA and TMA (simulation runs Amine DMA + TMA in particles and Amine–DU05 DMA + TMA in particles) at the second and third model day. Cloud periods are marked with light blue bars. The night is represented by grey shaded bars.

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Gas-phase MMA concentrations increase linearly during the night and flatten with sunrise, because of increased oxidation. During cloud periods, the concentration drops to nearly zero, due to effective phase transfer. Modelled gas-phase DMA concentrations depict a different pattern. During night periods without cloud occurrence, the concentrations are roughly constant and decrease with sunrise. During the cloud periods, DMA concentrations are negligible and increase strongly after the daytime cloud passage. At night, there is almost no effect modelled during cloud periods pointing towards an effective photochemical DMA formation. Gas-phase TMA concentrations increase almost linearly from late afternoon to late morning, decrease with sunrise, and drop to nearly zero during cloud periods. After the daytime clouds, the concentrations have decreased by about half compared to the time before cloud processing. At night, this effect is not modelled. Different to MMA and DMA, the concentration pattern of TMA is similar at the second and third model day. Thus, its steady-state concentration is modelled.

Modelled chemical gas-phase rates of MMA, DMA and TMA

Detailed chemical rate analyses are performed for the simulation Amine to understand the modelled concentration-time profiles, especially the DMA increase after daytime cloud processing. The focus is on the time after the first simulation day to avoid impacts from model spin-up. The overall multiphase chemical rates of MMA, DMA and TMA are provided in Supplementary Figs. 1 to 3 for the third model day.

During the non-cloud periods, gas-phase oxidation dominates MMA and DMA concentration evolution, whereas for TMA phase transfer into the particle phase dominates. The averaged gas-phase oxidation rates during the non-cloud periods are 153, 74, and 214 molecules cm-3 s-1 for MMA, DMA, and TMA, respectively. With cloud formation, MAs are effectively taken up into cloud droplets, where oxidation through aqueous-phase OH radicals occur.

Formation of DMA through daytime cloud processing

The analyses reveal that the simultaneous decrease of TMA concentrations and increase of DMA concentrations after daytime cloud evaporation relates to photochemistry within cloud droplets. The aqueous-phase oxidation of protonated TMA ((CH3)3NH+) initiates a rapid reaction sequence (Eq. (1) to Eq. (5), including Schiff base reactions) that forms DMA.

$${({{\rm{CH}}}_{3})}_{3}{{\rm{NH}}}^{+}+{\rm{OH}}\to {({{\rm{CH}}}_{3})}_{2}{{\rm{NH}}}^{+}{\dot{{\rm{C}}}{\rm{H}}}_{2}+{{\rm{H}}}_{2}{\rm{O}}$$
(1)
$${({{\rm{CH}}}_{3})}_{2}{{\rm{NH}}}^{+}{\dot{{\rm{C}}}{\rm{H}}}_{2}\rightleftharpoons {({{\rm{CH}}}_{3})}_{2}{{\rm{N}}\dot{{\rm{C}}}{\rm{H}}}_{2}+{{\rm{H}}}^{+}$$
(2)
$${({{\rm{CH}}}_{3})}_{2}{{\rm{N}}\dot{{\rm{C}}}{\rm{H}}}_{2}+{{\rm{O}}}_{2}\to {({{\rm{CH}}}_{3})}_{2}{{\rm{N}}}^{+}={{\rm{CH}}}_{2}+{{\rm{O}}}_{2}^{-}$$
(3)
$${({{\rm{CH}}}_{3})}_{2}{{\rm{N}}}^{+}={{\rm{CH}}}_{2}+{{\rm{OH}}}^{-}\rightleftharpoons {({{\rm{CH}}}_{3})}_{2}{{\rm{NCH}}}_{2}{\rm{OH}}$$
(4)
$${({{\rm{CH}}}_{3})}_{2}{{\rm{NCH}}}_{2}{\rm{OH}}\rightleftharpoons {({{\rm{CH}}}_{3})}_{2}{\rm{NH}}+{\rm{HCHO}}$$
(5)

TMA is oxidised by the OH radical (Eq. (1), average rate during daytime clouds of 928 molecules cm-3 s-1) and quickly converted into a dimethylaminomethylene cation, with a yield of 84% (Eq. (2) and Eq. (3)). The dimethylaminomethylene cation reacts with OH- to yield dimethylaminomethanol (Eq. (4)) that subsequently undergoes hydrolysis leading to DMA and formaldehyde (Eq. (5))18. On average, the DMA formation rate by this pathway is 810 molecules cm-3 s-1 during daytime clouds, which is about five and three times higher than the included MMA and TMA emission rate, respectively. The equilibrium of Eq. (5) is strongly shifted towards DMA, due to its rapid protonation as well as the hydration of formaldehyde under atmospheric aqueous-phase conditions. During the cloud evaporation, the liquid water content decreases and accordingly aqueous-phase DMA concentration increases by about three orders of magnitude. Thus, the ratio between gas- and particulate phase concentrations is much lower than calculated by the effective Henry’s Law constant and a rapid transfer into the gas phase is modelled.

Formation of DMA through daytime aerosol processing

The modelled aqueous-phase oxidation rate of TMA within aerosol particles during daytime is about two orders of magnitude lower than in daytime cloud droplets. This is an effect of the on average about a factor of 32 and 25 lower particle-phase OH radical concentration in the simulation Amine and Amine-DU05, respectively. Except for the first model day, the average modelled OH-radical concentration is 6.2 × 10-13 mol l-1 and 2.6 × 10-13 mol l-1 (maxima of 1.0 × 10-12 mol l-1 and 3.9 × 10-13 mol l-1) within daytime cloud droplets, whereas under daytime aerosol particle (non-cloud) conditions, the average is 2.0 × 10-14 mol l-1 and 1.1 × 10-14 mol l-1 (maxima of 7.2 × 10-14 mol l-1 and 3.5 × 10-14 mol l-1) for the simulation Amine and Amine-DU05, respectively (see Supplementary Fig. 4). For protonated TMA, the reaction with the OH radical is the only included oxidation pathway. Another possible oxidant is the Cl2- radical that is higher concentrated in particulate solution for MBL conditions19. The modelled Cl2- radical concentration is on average 4.4 × 10-16 mol l-1 and 2.9 × 10-16 mol l-1 (maxima of 4.9 × 10-15 mol l-1 and 3.8 × 10-15 mol l-1) in daytime cloud droplets, but 3.4×10-13 mol l-1 and 1.2 × 10-13 mol l-1 (maxima of 3.5 × 10-12 mol l-1 and 8.8 × 10-13 mol l-1) during daytime particle conditions for the simulation Amine and Amine-DU05, respectively (see Supplementary Fig. 4). Hence, the TMA-to-DMA conversion in aerosol particles could be higher if this reaction rate coefficient would be available.

Formation of MMA through daytime cloud processing

During the day, DMA oxidation in cloud droplets induces a similar formation mechanism for MMA, but besides hydrolysis of the methylaminomethylene cation another important formation rate is modelled to be the oxidation of HOOCH2NH2CH3+ by the OH radical. During daytime cloud conditions, this oxidation pathway dominates the modelled chemical formation pathways for MMA with on average 8 molecules cm-3 s-1. Due to the emission of MMA and very small formation rate of CH3NHCH2OH through DMA oxidation (3 molecules cm-3 s-1 under daytime cloud conditions), the equilibrium CH3NH2 + HCHO ⇌ CH3NHCH2OH is shifted towards the righthand side. During non-cloud periods, the equilibrium shifts towards the lefthand side and contributes to an average MMA formation rate of 47 molecules cm-3 s-1 (Supplementary Fig. 1). The overall averaged formation rate (during cloud and non-cloud conditions) is 39 molecules cm-3 s-1 representing about 26% of the MMA emission rate, whereas the MMA oxidation rate is 143 molecules cm-3 s-1, which is nearly the emission rate. Thus, aqueous-phase production explains the modelled steadily increased MMA gas-phase concentration.

Sensitivity simulation on TMA-to-DMA conversion with multiple short cloud periods

In order to investigate how rapidly TMA is converted into DMA during cloud processing, two sensitivity studies were performed with a different meteorological scenario including 12 cloud passages of about ten minutes each at the second model day. Figure 2 depicts the modelled concentrations of DMA. The DMA production by cloud chemistry is slightly enhanced compared to the single daytime cloud case (see Fig. 1). A strong linear increase is modelled until noon and weakening after that point. This result indicates that not in-cloud duration is the limiting factor for the fast TMA to DMA conversion. On the third model day, no cloud interaction occurs resulting into an effective DMA oxidation. Altogether, the results of the two sensitivity simulations imply that a convective MBL situation with more frequent cloud interactions and strong vertical mixing favours higher conversions of TMA to DMA.

Fig. 2: Modelled gas-phase concentration of DMA for sensitivity simulations.
figure 2

Modelled gas-phase concentrations of DMA during the second and third model day for the model run with 12 cloud passages of ten minutes during the second model day. The cloud periods are marked with the small light blue bars. The night is represented by grey-shaded bars. The black line indicates the simulation with full irradiation and the red line with 50% irradiation attenuation.

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Sensitivity study with particulate DMA and TMA initialised in SSA

In the previous simulations, no DMA or TMA are initialised within aerosol particles. However, DMA can be strongly enhanced in the SML14 and the same might be true for TMA. Thus, both can be part of freshly emitted SSA. To investigate if primary particulate DMA and TMA may evaporate in high amounts from freshly emitted SSA into the gas phase, two additional sensitivity simulations were performed. For the first sensitivity simulation, the maximum DMA concentration (196 nmol l-1) in the SML measured by van Pinxteren et al.14 is initialised. The second sensitivity simulation includes particulate DMA initialised the same as in the first sensitivity simulation and particulate TMA initialised with assumed SML concentrations of 100 nmol l-1. The results are presented in Fig. 1d for the simulation Amine-DU05. No apparent effect on the gas-phase DMA concentration is modelled. The degassing of the initialised amines results5 into concentrations below pg m-3 range. Therefore, the sensitivity simulations indicate that direct injection of gas-phase DMA from freshly emitted SSA does not seem to be important for the gas-phase DMA level. Still, the process model does not permanently inject or deplete SSA and, thus, a possible underestimation of this source is likely. It has to be analysed in the future by combined model and field studies with advanced emission flux measurements.

Comparison of modelled DMA concentrations with available field measurement data

Comparison with gas-phase and total aerosol DMA measurements

Modelled gas-phase DMA concentrations were compared with measurements at marine observational sites with low interference of anthropogenic pollutants to determine whether (i) the discovered cloud chemistry-related formation mechanism can explain the observed unexpected phenomena of enhanced gas-phase DMA concentration in the MBL and (ii) the model adequately represents the concentrations in the gas and particle phase. To be closer to reality, results from four simulations with a typical polydisperse marine particle spectrum20 are used.

The polydisperse particle spectrum is characterised by having different microphysical properties compared to the monodisperse case. This induces different surface areas that result into stronger uptake of MAs. As a consequence, the modelled gas-phase MA concentrations are lower than for the monodisperse case (Supplementary Fig. 5). For gas-phase DMA, the comparison between marine field measurements14,15,16,21,22 and model is done for the modelled average concentration after the last cloud period and is provided in Table 2. With modelled concentrations of 0.71 and 1.16 ng m-3, the simulations Amine-TMA-AP and Amine-TMA-AP-DU05 predict values in the lower range of the measurements within pristine marine environments CVAO14 and the Arabian Sea15. This indicates cloud chemistry processing as one, but not necessarily dominant process to explain the higher-than-expected measured gas-phase DMA concentrations.

Table 2 Simulated average of the gas-phase and total particulate DMA concentration after the last cloud of the four simulations with a polydisperse aerosol distribution as well as measured average concentrations
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The model results fit better for the measured particulate DMA. The average modelled particulate concentrations after the last cloud are about 1.6, 14.8, 1.8, and 16.1 ng m-3 in the simulations Amine-AP, Amine-TMA-AP, Amine-AP-DU05, and Amine-TMA-AP-DU05, respectively. The modelled total particulate MA concentrations are provided in Supplementary Fig. 6. Total measured particulate DMA concentrations in pristine marine environments range between 2 and 10.9 ng m-314,15,23,24, (see Table 2).

Comparison with size-resolved DMA aerosol particle measurements

In addition to the total modelled particulate DMA, the modelled concentrations at the end of the simulation were separated into the five size-ranges of the Berner impactor stages (ISs) for further comparison. The data is provided in Table 3. The highest concentrations are predicted by the model in the first (0.05–0.14 µm, IS1) and second (0.14–0.42 µm, IS2) IS with the maximum in IS1. Interestingly, the model does not show significant concentrations in the third IS. This is an effect of the prescribed fixed aerosol particle spectrum. There, the highest surface area is provided for the second IS, followed by the first and then the third IS. Thus, the partitioning of MAs occurs mainly into the first and second IS.

Table 3 Simulated impactor stages concentrations of DMA at the end of the simulations with a polydisperse aerosol distribution
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The modelled values for the IS2 in the simulations Amine-AP (0.6 ng m-3) and Amine-AP-DU05 (0.5 ng m-3) are in line with measurements of Müller et al.25, who measured on average 0.22, 0.20 and 0.57 ng m-3 in May, June and December 2007 at CVAO. The simulations with higher MMA and TMA emission largely overpredict these. Nevertheless, the modelled concentrations in the simulations Amine-TMA-AP (4.6 ng m-3) and Amine-TMA-AP-DU05 (3.6 ng m-3) could be representative for marine regions with higher biological activity. Facchini et al.24 found that, in regions with a higher biological activity, particulate DMA concentrations are enhanced by up to 8 – 10 ng m-3 within the covered size range of IS2 and IS3. In regions with lower biological activity, the measured values were only about 0.8 ng m-3.

Gas-aerosol partitioning of DMA and the role of particle pH

The modelled high partitioning of DMA into IS1 is not in line with observations. In air masses originating from the open North Atlantic Ocean, Müller et al.25 measured the highest contribution in IS2 followed by the fifth IS (IS5), whereas the IS1, third (IS3) and fourth IS (IS4) contributed around 10%. However, the high contribution of the IS5 is proposed to be biased26.

Possible reasons for the discrepancy between measured and modelled DMA concentrations in IS1 is the modelled pH of the impactor stages. In IS1, the modelled pH is <0 with slightly decreasing tendency, whereas in IS2 it is decreasing from three to around one during the simulation time. For the IS3, IS4 and IS5, the modelled pH ranges between three to four without clear tendency. MAs tend to partition into the most acidic regime, because of their higher pKa value in comparison to NH3. Thus, the very low pH in IS1 induces the strongest partitioning of MAs.

The modelled high acidity in IS1 results from cloud chemistry-related production of acids, e.g., sulfate and methane sulfonate. In the model, CCN activation under the pristine conditions occurs for particles with a diameter >55 nm and particles in the size range of IS1 dominate the particle number concentrations, because of the initialised particle spectrum. Therefore, cloud processing is dominated by particles in the size range of IS1 affecting the partitioning of the MAs. If the modelled acidity in IS1 would be lower a much higher gas-phase DMA concentration would be simulated even for the simulations Amine-AP and Amine-AP-DU05 (see Discussion section for further details).

Importance of the autoxidation

Recent investigations in our laboratory at TROPOS reported autoxidation as key reaction pathway of DMA and TMA11. To investigate the chemical processing under atmospheric conditions, gas-phase oxidations of DMA and TMA were analysed in more detail for the simulation ‘Amine’. The chemical sink and source rates were analysed from the second model day on. Only chemical pathways contributing more than 5% to the total sink and source rates are further discussed. In Fig. 3, a scheme of the multiphase oxidation of TMA, DMA, and MMA is provided focusing on gas-phase oxidation processes as well as TMA-to-DMA, DMA-to-MMA, and MMA-to-NH3 conversion.

Fig. 3: Scheme of modelled multiphase chemistry of methylamines.
figure 3

Schematic depiction of the modelled multiphase chemical rates (in molecules cm-3 s-1) of MMA, DMA and TMA (yellow box) oxidation for the simulation Amine. Bold compound names represent stable species and aqueous species are blue coloured. Oxidation processes of MMA, DMA and TMA in the gas phase are tracked until the uptake is most important. For simplicity, the aqueous-phase oxidation of MMA, DMA and TMA is tracked until the first stable oxidation product is reached (except for fluxes of TMA-to-DMA, DMA-to-MMA and MMA-to-NH3 conversion). Moreover, NH3, MMA, DMA and TMA represent both protonated and non-protonated form. Given numbers represent the averaged rates of all timesteps (including cloud periods) from the second model day on. Note that only oxidation rates contributing more than 5% to the total averaged flux and exceeding 5 molecules cm-3 s-1 are included. The width of arrows indicates the amount of the mass rates. Red arrows represent emission rates, brown arrows gas-phase oxidation rates, blue arrows aqueous-phase reaction rates, and green arrows represent the corresponding phase transfer fluxes. For equilibrium reactions, the larger arrowhead indicates the net direction. Phase transfer rates can be higher than the total production rates due to large peaks at cloud edges, which distort the averaging.

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Autoxidation of DMA

The averaged gas-phase DMA oxidation rate (day and night) is modelled to be 62 molecules cm-3 s-1, and DMA is predominantly oxidised by the OH radical and the Cl atom with contributions of 91% and 7%, respectively. Thereby, 61% of the gas-phase DMA oxidation occurs via H-atom abstraction from the methyl group. The further reaction pathways of the CH3NHCH2O2-radical formed are determined to be 65% internal H-shift and 34% decomposition to form the HOOCH2NHCH2O2-radical or CH2 = NCH3, respectively. The HOOCH2NHCH2O2-radical proceeds by an internal H-shift with a contribution of about 53% to yield HOOCH2NHCHO. Decomposition of the HOOCH2NHCH2O2-radical contributes about 9% and the reaction with HO2 about 34%, respectively. Overall, 21% of the total oxidised gas-phase DMA reacts directly to HOOCH2NHCHO. The further degradation of HOOCH2NHCHO is determined by gas-phase oxidation through the OH-radical. On average, about 68% (20 molecules cm-3 s-1) are oxidised by the OH radical, predominantly during non-cloud periods. The modelled average uptake into the aqueous phase is 8 molecules cm-3 s-1. During cloud periods, the dominant sink for HOOCH2NHCHO is uptake into the cloud droplets. However, over the whole model time gas-phase oxidation is simulated to be the dominant sink even the HOOCH2NHCHO has a very high HA value. This might be related to the missing DMA emission and cloud chemistry acting as sole DMA source. Accordingly, HOOCH2NHCHO formation is only related to TMA-to-DMA conversion. Hence, the gas phase is likely undervalued in HOOCH2NHCHO concentration, too, establishing a smaller flux from the gas to the aqueous phase. Under continental conditions, at which DMA is also emitted, much more HOOCH2NHCHO will be formed and thus uptake on aerosol particles might be a more potent sink for gas-phase HOOCH2NHCHO.

Autoxidation of TMA

The total averaged gas-phase TMA oxidation rate is modelled to be 178 molecules cm-3 s-1 dominated by oxidation of the OH-radical followed by O3 and the Cl atom with contributions of 78%, 15% and 7%, respectively. The formed CH3N(CH3)CH2O2 radical fully undergoes autoxidation. About 81% of the secondly formed HOOCH2N(CH3)CH2O2 radical reacts away by internal H-shift yielding the HOOCH2N(CH2O2)CH2OOH radical, but 18% by yielding HOOCH2N(CH3)CHO. About 85% of the HOOCH2N(CH2O2)CH2OOH radical undergoes an internal H-shift and the reaction with HO2 accounts for approximately 12%. Overall, 69% of the TMA oxidised in the gas phase reacts directly to HOOCH2N(CHO)CH2OOH. Overall, about 73% on average of the HOOCH2N(CHO)CH2OOH is taken up into the aqueous phase, where it is rapidly oxidised (see Fig. 4).

Fig. 4: Chemical sink and source rates of HOOCH2N(CHO)CH2OOH.
figure 4

Modelled time-resolved multiphase chemical sink and source rates of HOOCH2N(CHO)CH2OOH at the third model day for the simulation Amine. Positive rates describe production and negative rates relates to the chemical oxidation in both gas phase and aqueous phase. Blue bars indicate in-cloud periods of the air parcel and grey shaded areas represent night periods.

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Effects on the gas-phase OH radical concentration are modelled to be minor, because of the small TMA emission. The average OH radical reproduction rate through autoxidation of both DMA and TMA is small (137 molecules cm-3 s-1) in comparison to the overall average OH production rate of 1.0 × 106 molecules cm-3 s-1.

Impact on aerosol particle mass

A comparison between the simulations Amine-AP and Amine-AP-DU05 and two simulations with the same setup, but without integrated CAPRAM–AMM2.0, revealed an increase of the total dry particle mass of about 10 and 8 ng m-3, respectively. MMA, DMA and TMA and their oxidation products contribute about 5 and 6 ng m-3, respectively. The residual, non-amine related, increase in total dry particle mass results from production and/or uptake of acids. For example, the increase for methane sulfonic acid is modelled to be about 3 and 1 ng m-3 for the simulations Amine-AP and Amine-AP-DU05, respectively. In the following, the contribution of MMA, DMA and TMA and their oxidation products for the simulations Amine-AP and Amine-AP-DU05 is outlined (Table 4).

Table 4 Absolute concentration of amines and their oxidation products in ng m-3 at the end of the simulations Amine-AP and Amine-AP-DU05
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MMA, DMA, and TMA are the most important contributor to the organic mass. Within the group of these three methylamines, even its emission strength is the highest, the TMA has the lowest contribution, because it is much faster oxidised. However, the simulations indicate DMA as an oxidation product of TMA. Thus, even the concentration of MMA is higher, TMA is an equal contributor to amine-related organic mass increase.

Contribution of autoxidation products to particle mass

HOOCH2N(CHO)CH2OOH, the autoxidation product of TMA, contributes minorly to the organic particle mass. Figure 4 reveals that cloud droplets are a very active oxidation media for HOOCH2N(CHO)CH2OOH, preventing it from being a strong SOA compound.

The autoxidation product of DMA, HOOCH2NHCHO, does not contribute to the organic mass. The HA constants of HOOCH2NHCHO is <1 × 108 mol l-1 atm-1, and a protonation is not included. Thus, the partitioning into aerosol particles is below 1%. Due to the low DMA concentration, negligible aerosol particle concentrations of HOOCH2NHCHO are modelled.

Discussion

The simulations demonstrate that multiphase chemistry related to clouds effectively converts TMA into DMA and DMA into MMA through oxidation and Schiff base reactions. Thereby, sensitivity studies revealed that TMA-to-DMA conversion is able to explain up to 10% of observed gas-phase DMA concentrations, and roughly the measured particulate DMA concentrations in the MBL. However, the comparison of the simulated gas- and particle-phase DMA concentrations with measurements does not provide an exact picture.

On the one hand, high biological activity under medium light intensity is able to reproduce the lower end of measured gas-phase DMA concentrations, but on the other hand, these simulations highly overestimate the particulate DMA concentrations. For particulate DMA concentrations, the simulation with normal TMA emission and medium light intensity is better suited for size-resolved measurements.

The simulation scenarios without solar attenuation model higher aqueous-phase radical concentrations, which are important for (i) conversion of TMA into DMA and (ii) gas- and particulate phase concentrations of MMA, DMA and TMA. Both DMA and TMA oxidation rates are increased under high solar intensity indicating that such conditions suppress the NPF potential of amines and affect the particulate mass in the MBL. Perspectively, estimations methods describing NPF from conversion of TMA into DMA in higher-scale chemical transport models have to consider the effect of solar irradiation.

Also, the simulations still undervalue the measured gas-phase DMA and tend to strongly partition MAs into the smaller particles of the first impactor stage (IS1, 0.05 – 0.14 µm in diameter). In the simulation Amine-AP and Amine-AP-DU05, 1.0 and 1.3 ng m-3 particulate DMA are modelled in IS1 and 0.6 and 0.5 ng m-3 in the second impactor stage (IS2, 0.14–0.42 µm in diameter). The concentrations in IS2 match the measured concentration ranges, but the concentrations in IS1 are too high, as field experiments reveal that most of particulate DMA is in IS2. The partitioning into the IS1 relates to its very high modelled acidity. It can be expected that with a lower acidity in IS1, a high amount of the DMA can partition almost exclusively into the gas-phase, without a repartitioning. This could then add up to 1 ng m-3 to the DMA gas-phase concentration significantly increasing the model capability to match observed gas-phase DMA concentrations.

In addition to the effect on DMA production, detailed chemical rate analyses revealed that the autoxidation of TMA determines the atmospheric processing of its gas-phase peroxyl radical. The autoxidation product is rapidly oxidised in cloud droplets and thus does not contribute importantly to the organic mass in marine aerosol particles. The cloud droplet chemistry related TMA-to-DMA conversion has a much stronger effect on SOA mass, because of the higher stability of dissolved protonated DMA against oxidation.

In conclusion, the mechanism development in conjunction with the performed model simulations indicate that there are still many uncertainties regarding the multiphase chemistry of amines. The simulations suggest that there are important processes influencing the phase partitioning and further sources of DMA in the marine atmosphere such as cloud processing, entrainment from fresh SSA and particle aging in relation to acidity. Uncertainties remain in the chemical reactivity of autoxidation products in both gas and aqueous phase, as well as their phase partitioning. Moreover, there is still a lack of measured reaction rate coefficients for the important TMA-to-DMA conversion. Secondary radicals that are higher concentrated in particles, such as Cl2-, might increase the effectiveness of particle chemistry-related TMA-to-DMA conversion. To uncover these processes, laboratory and field studies are needed from which more advanced estimation methods could be derived in the future. Thereby, field measurements have to measure simultaneously (i) concentrations of MAs in seawater, gas phase and particulate phase as well as the fluxes between the atmosphere and ocean (ii) acidity of particles and (iii) MA concentrations in a size-resolved manner.

Methods

In this section, the development of the so-called CAPRAM amine module 2.0 (CAPRAM–AAM2.0) is explained, and a brief discussion of the kinetic and mechanistic uncertainties is provided. This module is an advanced follow-up module of the CAPRAM amine module 1.027. Finally, a description of the simulation setup is also provided.

Gas-phase oxidation mechanism development

NH3 oxidation

The oxidation of NH3 is described by the provided gas-phase mechanism of Kohlmann and Poppe28. The reaction rate coefficients and products have been updated by IUPAC recommendations and recent literature data29,30. The updated NH3 reaction scheme is given in Supplementary Table 1.

Oxidation of MMA, DMA and TMA

The oxidation of MMA, DMA, and TMA is implemented for the OH- and NO3-radical as well as the Cl atom. Oxidation by ozone is included for DMA and TMA, only. Temperature-dependent measurements are available for the Cl atom31, but not for the NO3 radical1. For the OH radical, an Arrhenius expression was obtained from three measured points at temperatures ranging between 298-426 K, revealing a low temperature dependency32,33. However, the temperature dependence has a high standard deviation and in case of MMA and TMA the values at 299 K differ from single measurements at 295 K and 298 K34,35. Within the present study, a combination of these values were used to derive a Arrhenius expression for MMA, DMA and TMA using the Python function curve_fit() (see Supplementary Fig. 7). However, for TMA, both the old and fitted Arrhenius expression do not reproduce measured data at 295 K well. Thus, more detailed temperature-dependent measurements under tropospheric conditions have to be performed.

The oxidation of methylamines is dominated by H-atom abstraction. For MMA and DMA, H-atom abstraction can occur either at the CH3- or the NHx-group (x = 1 or 2). The implementation of the reaction mechanisms for MMA and DMA mainly follows the description in Nielsen et al.36 and Nielsen et al.1. When oxidations occur at the NHx group, further reaction with O2 results in a formation of an imine, while reactions with NO or NO2 lead to the formation of nitrosamines and nitrosoamines, respectively. The reaction of the RO2-radicals is included for HO2-, NO-, and other RO2-radicals. Besides these classical reaction pathways, recent laboratory and theoretical work highlighted the importance of the internal H-atom shift for RO2-radicals from DMA and TMA oxidation that potentially dominate the first order oxidation products of these species11,12. The reaction rate coefficients provided in the cited studies are implemented in the mechanistic scheme developed here. The further oxidation of the formed stable species is not investigated through laboratory studies which constitutes a certain limitation. The same is true for reaction rate coefficients and products from the reaction of the corresponding RO2-radicals with HO2-, NO- and other RO2-radicals.

To solve issues in mechanism development regarding unknown reaction rate coefficients and products, specific estimation methods have been developed. The reaction rate coefficient for the OH radical can be calculated with the structure−activity relationship (SAR) method introduced by Atkinson37. For amines, SAR group rate constants and substituent factors were developed1,38. Here, the more detailed and more recent SAR group rate constants and substituent factors by Borduas et al.38 are applied. Borduas et al.38 neither provides temperature dependencies for the group rate constants nor substituent factors. This is most likely related to the fact that there are not many temperature-dependent experimental studies for amines and their oxidation products and when available a low-temperature dependency, e.g. MMA, DMA and TMA, is obtained. In case of missing measured reaction rate coefficients for the derive RO2 radicals, the calculation methods provided by Jenkin et al.39 are applied. It is to note that the method by Jenkin et al.39 was developed by using values determined for RO2 radicals from VOC, but not from MA oxidation.

Oxidation of functionalised aliphatic amines using SAR methods

For non NHx groups, the temperature-dependent group rate constants and substituent factors from Jenkin et al.40 are applied. The group rate constant and the substituent factors for NHx are not temperature dependent, because of restricted number of kinetic temperature-dependent measurements inhibiting temperature-dependent group rate constants and substituent factors for MMA, DMA and TMA oxidation products. However, the combination with the SAR factors for amine-related species has specific issues related to MMA, DMA and TMA oxidation products. With regard to these issues, specific adjustments and assumptions were done, which are outlined in more detail in the following.

One issue is related with α-aminoalcohols. Jenkin et al.40 provided a group substituent factor f(–CH2OH). When applying this factor for aminoethanol (a β-aminoalcohol), a reaction rate coefficient of 4.74 × 10-11 cm3 molecules-1 s-1 at 298 K is calculated. This rate constant is about a factor of 2 smaller than the measured ones, but higher than the one calculated by Nielsen et al.1. However, applying this group substituent factor for smaller α-aminoalcohols a reaction rate coefficients of > 1 × 10-10 cm3 molecules-1 s-1 is calculated. For α-aminoalcohols of TMA, it can be even > 1 × 10-9 cm3 molecules-1 s-1. These are too fast and, thus, the substituent factor f(–CH2OH) seems not applicable for further calculations of reaction rate coefficients for α-aminoalcohols and instead the group substituent factor f(–CH2–) is applied, as done by Nielsen et al.1.

A second issue is the treatment of temperature dependences for gas-phase oxidation of amides. One laboratory study is available that measured a temperature-dependent reaction rate coefficient for CH3NHCHO (MF) and (CH3)2NCHO (DMF)41. In this study, a negative temperature dependency was determined. The reaction rate coefficients were measured as absolute values and are lower than the ones determined by relative as well as absolute measurements from other studies (Fig. 5)41,42,43,44,45, possibly because of different measurement techniques used. Still, the temperature dependency should be unaffected and, thus, is assumed to be reasonable. However, applying the SAR method, a positive temperature dependency is calculated (Fig. 5). Accordingly, the SAR method has been adjusted to represent the negative temperature dependency for amides. By comparing measured values for formamide with (4.4 ± 0.46) × 10-12 at 298 K42 and (4.5 ± 0.4) × 10-12 at 309 K46, it is concluded that the H-atom abstraction from the NCHO group is, most certainly, almost independent of temperature. As a consequence, the measured temperature dependency should be mainly caused by the H-atom abstraction from the CH3-group. The available provided group rate constant of CH3 is positive temperature dependent40 and, thus, the substituent factor of NCHO is assumed to be negative temperature dependent. From comparing the measured reaction rate coefficient of formamide at 298 K with the reaction rate coefficients of MF and DMF from Bunkan et al.41, a temperature-dependent substituent factor f(–NRCHO) was calculated and used to derive the reaction rate coefficient for all amides. The following fit function (deviation: 0.1% ± 0.8%) is derived:

$${\rm{f}}(-{\rm{NRCHO}})=2.794\times {10}^{-3}\exp \left(\frac{2480}{{\rm{T}}}\right)$$
Fig. 5: Reaction rate coefficients for oxidation of MF and DMF.
figure 5

Comparison of measured and theoretical reaction rate coefficients for oxidation of a) MF left41,43,44, and b) DMF right41,42,44,45, by the OH radical calculated using the SAR method of Borduas et al.38 combined with the values given in Jenkin et al.40 (brown dashed line) and calculated using the adjusted substituent factor f(–NRCHO) (blue dashed line). The temperature dependency measured by Bunkan et al.41 is displayed as red line.

Full size image

It is to note that the developed temperature-dependent substituent factor is only valid for amides related to MMA, DMA and TMA. In Fig. 5, the calculated values for MF and DMF are compared with available measurements and theoretical work. It can be seen that the substituent factor f(–NRCHO) is capable to reproduce the observed temperature dependency. The calculated reaction rate coefficients at 298 K are about a factor of two lower than the measurements of Speak et al.45 or Borduas et al.42, but reproduce those observed by Bunkan et al.41. Photolysis of the NRCHO group is not implemented, because it is unimportant under atmospheric conditions47.

The group rate constant and the substituent factors for NHx are not adjusted because no measured temperature dependence of amines with a CH2OH- or CH2OOH-group are obtained from literature. More work on developing an adequate SAR method for amines and their oxidation products is needed45.

Chemical pathway of formed RO2 radicals

Reaction rate coefficients of the formed RO2-radicals are implemented using the estimation method of Jenkin et al.39. The focus in the mechanism development is on reaction with HO2-, NO- and other RO2-radicals. The reaction with NO is implemented to solely yield a RO-radical that instantly reacts with O2 forming an amide. For the RO2-radical cross-reaction, the products and ratios provided for an RO2- and an acyl peroxyl radical (ACO3) are used. The reaction of RO2-radicals with HO2 yields a ROOH. This is further oxidised using a SAR-derived OH radical oxidation and photolysis, with a photolysis rate approximately equal to that for CH3OOH in accordance with the MCM. For the reaction of ACO3-type radicals with HO2, the product yields are adjusted. In Jenkin et al.39, a yield of 0.37, 0.13 and 0.5 for peroxy acids, acids and RO-radicals are suggested, respectively. However, in case of MMA, DMA and TMA, the formation of an acid group would result into the formation of carbamic acid derivates. Carbamic acid (NH2COOH) is unstable under atmospheric conditions and decomposes rapidly into NH3 and CO248. This is true for the carbamic acid derivates, as well. A formation of a peroxy acid type might therefore be also unlikely and the formation of RO-radicals is assumed (Eq. (6)). However, it should be noted that the ratios change when a group, other than an alkyl group, is next to the acyl peroxyl group. Thus, the NHx-group might affect the ratio, which is currently not described in the literature.

$${{\rm{R}}}_{2}{\rm{N}{\rm{C}}}\left(={\rm{O}}\right){{\rm{O}}}_{2}+{\rm{H}}{{\rm{O}}}_{2}\to 0.13{\rm{R}}-{\rm{NR}}+0.13{{\rm{O}}}_{3}+0.87\,{{\rm{R}}}_{2}\dot{{\rm{N}}}+0.87\,{\rm{O}{\rm{H}}}+{\rm{C}}{{\rm{O}}}_{2}$$
(6)
$$\left({\rm{with}}\,{\rm{R}}={\rm{H}}\,{\rm{o}}{\rm{r}}\,{\rm{C}}{\rm{H}}_{3}\,{\rm{o}}{\rm{r}}\;{\rm{C}}{\rm{H}}{\rm{O}}\; {\rm{o}}{\rm{r}}\;{\rm{C}}{\rm{H}}_{2}{\rm{O}}{\rm{O}}{\rm{H}}\;{\rm{o}}{\rm{r}}\;{\rm{C}}{\rm{H}}_{2}{\rm{O}}{\rm{H}}\right)$$

For ACO3 type radicals, also the formation of PAN-equivalents through the reaction with NO2 occurs. The reaction rate coefficient is estimated to be the same as for the reaction between ACO3 with NO2. The thermal decomposition of the formed PAN-equivalents is measured for (CH3)2NC(O)OONO249 and assumed to be equal to the other possible PAN-equivalents.

In total, the resulting gas phase amine oxidation mechanism contains 235 reactions, including 20 photolysis processes. The mechanism and kinetic data are summarised in Supplementary Table 1.

Phase transfer implementation

Amines and their oxidation products undergo phase transfer from the gas into the aqueous phase, that is because of their basic character and low acidity of ambient aerosol particles and cloud droplets. Moreover, the high oxidation state of the autoxidation products from DMA and TMA can be characterised by high Henry’s Law constants (HA). Thus, their phase transfer is effectively increased. In the mechanism, phase transfer processes are implemented for MMA, DMA and TMA and all of their formed stable oxidation products according to the approach by Schwartz50, except for PAN-equivalents. This approach considers the gas-phase diffusion coefficient (Dg), the mass accommodation coefficient (α), and the HA solubility. The HA values implemented are based on the literature given in the review of Sander51 or more recent values e.g., Leng et al.52. For MMA, DMA and TMA, values with temperature dependence are preferred. Only for a small number of oxidation products of MMA, DMA and TMA measured HA values are available. No HA values exist for oxidation products derived from auto-oxidation processes and are thus estimated. For the estimation, the EPISUITE program53 was used. The Dg values were calculated using the Fuller-Schettler-Gidings (FSG) method54. The α values are estimated to have a lower limit of 0.1, in line with measured values of NH3 at 288 K55. In total, 51 uptake processes are included in the mechanism (see Supplementary Table 2 in the Supporting Information).

Aqueous-phase oxidation mechanism development

NH3 oxidation

Pai et al.29 stated gas-phase NH3 oxidation to be important for the formation of NOx and N2O under specific atmospheric conditions. As gas-phase NH3 effectively undergoes phase transfer into the atmospheric aqueous phase, it is worth to represent its oxidation there. NH3 oxidation in the aqueous phase has been incorporated into the mechanism based on the available measured values of the rate coefficients for OH and SO4- radicals with NH3/NH4+ in aqueous solution56,57. The further oxidation of the NH2/NH3+-radicals formed as products is implemented to occur with O256,58, OH, and H2O259 leading either to NO or hydroxylamine (NH2OH)59,60. Included oxidations of NH2OH/NH3OH+ via the OH radical result into the NHOH/NH2OH+ radicals61 that can react with O2- leading to HONO62 or further react with O2 yielding either to N2O, N2 or NO61.

MMA, DMA and TMA oxidation

Temperature-dependent pKa values of MMA, DMA, and TMA are included and taken from the review of Ge et al.63 with pKa values for MMA, DMA and TMA of 10.66, 10.73, and 9.8 at 298 K, respectively. Thus, under the acidic conditions of the atmospheric aqueous phase (pH values < 813), only the oxidation of their protonated forms is favoured and included into the mechanism. In the current literature, oxidation by the OH radical is suggested to be only important under atmospheric conditions1. However, reactions with other aqueous-phase radicals are undervalued, including their possible effect. Investigations of the reaction rate coefficient of the unprotonated and protonated amines by the OH radical reveal that protonation seems to inhibit H-atom abstraction from nitrogen atom64. Accordingly, oxidation is assumed to be solely at the CH3 group with instantaneous addition of oxygen to form an RO2-radical with a positive charged amine group (RyN\({\text{H}}_{\text{x}}^{+}\)CH2O2, with y = 0, 1 or 2, and x = 0, 1 or 2).

$${{\rm{R}}}_{{\rm{y}}}{\rm{N}}{{\rm{H}}}_{{\rm{x}}}^{+}{\rm{C}}{{\rm{H}}}_{3}+{\rm{OH}}\mathop{\to }\limits^{+{{\rm{O}}}_{2}}{{\rm{R}}}_{{\rm{y}}}{\rm{N}}{{\rm{H}}}_{{\rm{x}}}^{+}{\rm{C}}{{\rm{H}}}_{2}{{\rm{O}}}_{2}+{{\rm{H}}}_{2}{\rm{O}}$$
(7)

The further reactions of the RyN\({\text{H}}_{\text{x}}^{+}\)CH2O2-radical are implemented to be with another RyN\({\text{H}}_{\text{x}}^{+}\)CH2O2-radical, following the CAPRAM protocol65, or with the HO2-radical to form a RyN\({\text{H}}_{\text{x}}^{+}\)CH2OOH. The reaction rate coefficient of the RyN\({\text{H}}_{\text{x}}^{+}\)CH2O2-radical with the HO2-radical is estimated to be 1.0 × 107 l mol-1 s-166.

Chemical pathways of RyN\({\text{H}}_{\text{x}}^{+}\)CH2OOH

The RyN\({\text{H}}_{\text{x}}^{+}\)CH2OOH formed by the reaction of RyN\({\text{H}}_{\text{x}}^{+}\)CH2O2 with HO2 is further oxidised by either photolysis of the OOH-group or by the OH radical reacting with the CH2OOH-group in analogy to the oxidation of methylhydroperoxide (CH3OOH)67. The reaction rate coefficient is estimated to be equal to CH3OOH for simple RyN\({\text{H}}_{\text{x}}^{+}\)CH2OOH and calculated using the group contribution method of Minakata et al.68 for higher functionalised RyN\({\text{H}}_{\text{x}}^{+}\)CH2OOH (see text below). Product yields are assumed to be 80% the RyN\({\text{H}}_{\text{x}}^{+}\)CH2O2-radical and 20% the smaller amine, because of the predicted formation of a carbamic acid derivate. Furthermore, a Fenton-like reaction has been included, with reaction rate coefficients assumed to be similar as for CH3OOH and CH3CH2OOH69.

$${{\rm{R}}}_{{\rm{y}}}{\rm{N}}{{\rm{H}}}_{{\rm{x}}}^{+}{\rm{C}}{{\rm{H}}}_{2}{\rm{OOH}}+{\rm{OH}}\mathop{\to }\limits^{-{{\rm{H}}}_{2}{\rm{O}}}0.8{{\rm{R}}}_{{\rm{y}}}{\rm{N}}{{\rm{H}}}_{{\rm{x}}}{\rm{C}}{{\rm{H}}}_{2}{{\rm{O}}}_{2}+0.2\,{{\rm{R}}}_{{\rm{y}}}{\rm{N}}{{\rm{H}}}_{{\rm{x}}}+0.2{\rm{H}}{{\rm{O}}}_{2}+0.2{\rm{C}}{{\rm{O}}}_{2}$$
(8)
$${{\rm{R}}}_{{\rm{y}}}{\rm{N}}{{\rm{H}}}_{{\rm{x}}}^{+}{\rm{C}}{{\rm{H}}}_{2}{\rm{OOH}}+{\rm{F}}{{\rm{e}}}^{2+}\to {{\rm{R}}}_{{\rm{y}}}{\rm{N}}{{\rm{H}}}_{{\rm{x}}}^{+}{\rm{C}}{{\rm{H}}}_{2}{\rm{O}}+{\rm{F}}{{\rm{e}}}^{3+}+{\rm{O}}{{\rm{H}}}^{-}$$
(9)

Formation and oxidation of amides

The processing of the RyN\({\text{H}}_{\text{x}}^{+}\)CH2O2-radical results mainly into formation of an amide group. For formamide, the oxidation is well described leading to isocyanic acid70. Isocyanic acid is very stable against oxidation by OH radicals and only hydrolysis is realised in the mechanism71,72.

For MF and DMF oxidation, the OH radical attacks predominantly the CH3 group73,74. The further chemical processing of the RO2-radicals will result into formation of higher functionalised amides. As for the gas phase, photolysis of the amide group is assumed to be negligible and is thus not included for amides. However, the acid-catalysed hydrolysis of amides is considered with a reaction rate coefficient estimated to be equal to the one measured for formamide75.

$${\rm{RNRCHO}}+{{\rm{H}}}^{+}\mathop{\to }\limits^{{{\rm{H}}}_{2}{\rm{O}}}{\rm{RNR}}+{\rm{HCOOH}}+{{\rm{H}}}^{+}$$
(10)

Oxidation of functionalised amines and amides

For higher oxidised amines and amides from autoxidation, no reaction rate coefficients from laboratory studies are published in literature, because of their novelty. Different to the gas-phase SAR method, the group contribution method of Minakata et al.68 allows to calculate reasonable reaction rate coefficients for MF (kcalc = 1.8 × 109 l mol-1 s-1 compared to kexp = 1.2 × 109 l mol-1 s-173,) and DMF (kcalc = 5.9 × 109 l mol-1 s-1 compared to kexp = 1.7 × 109 l mol-1 s-173,) with the OH radical. Following this reasonable agreement, the method by Minakata et al.68 was applied to calculate the reaction rate coefficients for OH radical reactions. The chemical processing of the formed RO2- and RN\({\text{H}}_{\text{x}}^{+}\)CH2O2-radicals follow the outlined description for MMA, DMA, and TMA oxidation. The final stable products of functionalised DMA and TMA oxidation products are methyl isocyanate and its oxidation products. The further chemical processing of methyl isocyanate and its oxidation products is included to be hydrolysis, only76.

Besides oxidation, also protonation of oxidised amines can occur. Protonation equilibrium constants were calculated for T = 298 K using the MARVIN sketch program77 as experimental values are lacking. However, the more oxidised the amines, the more they lose their basic character and, thus, only small or even no pKa values are calculated for them. Besides, protonation is not included for NH2CH2OH and CH3NHCH2OH as these α-aminoalcohols are intermediates in imine formation.

Formation and oxidation of imines

The reaction cycle of Schiff bases is represented in the mechanism by the species CH2 = NH, CH2 = NH2+, CH3N = CH2, CH3NH+ = CH2 and (CH3)2N+ = CH2.

$${\rm{C}}{{\rm{H}}}_{2}={\rm{NR}}{{\rm{H}}}^{+}+{{\rm{H}}}_{2}{\rm{O}}\rightleftharpoons {\rm{HOC}}{{\rm{H}}}_{2}{\rm{NRR}}+{{\rm{H}}}^{+}({\rm{R}}={\rm{C}}{{\rm{H}}}_{3}\,{\rm{or}}\; {\rm{H}})$$
(11)
$${\rm{C}}{{\rm{H}}}_{2}={\rm{NR}}{{\rm{H}}}^{+}+{\rm{O}}{{\rm{H}}}^{-}\rightleftharpoons {\rm{HOC}}{{\rm{H}}}_{2}{\rm{NRR}}\,({\rm{R}}={\rm{C}}{{\rm{H}}}_{3}\,{\rm{or}}\; {\rm{H}})$$
(12)
$${\rm{HOC}}{{\rm{H}}}_{2}{\rm{NRR}}\rightleftharpoons {\rm{RNR}}+{\rm{HCHO}}\,({\rm{R}}={\rm{C}}{{\rm{H}}}_{3}\,{\rm{{or}\,{H}}})$$
(13)

Unfortunately, equilibrium constants of this cycle are not well determined for small imines as well as α-aminoalcohols and, thus, are estimated for treated imines to be the same as for species-specific values given in literature18,78,79,80,81. Likewise, the reaction of MMA with glyoxal to form oligomers has been suggested to be important during cloud evaporation82 and is assumed to occur also for DMA2 as well as for reaction of methylglyoxal with MMA and DMA83,84. However, in the studies a forward reaction rate for a stabilised product is provided, but no equilibrium constant. Hence, these are pseudo-steady-state reaction rate coefficients and a detailed description as needed for explicit models is missing. Additionally, the provided reaction rate coefficients for glyoxal are 1.882 to 7083 M-1 s-1 and hence five to six orders of magnitude lower than the ones for the reaction between HCHO and amines. HCHO is in excess to glyoxal and methylglyoxal under atmospheric conditions. Therefore, the reactions with glyoxal and methylglyoxal might be unimportant and are not considered. Still, because of their possible importance for SOA formation, a sensitivity simulation has been performed to investigate its potential in the pristine marine air (see Supplementary Notes).

Overall, the mechanism consists of 256 aqueous-phase processes, thereof 41 equilibrium reactions and 18 photolysis processes; all provided in Supplementary Table 3.

Simulation setup

The developed CAPRAM–AAM2.0 was coupled to the existing CAPRAM system, which has been applied in a previous study dealing with polluted coastlines85. This multiphase chemistry system contains the chemistry of reactive halogen species and dimethyl sulfide important in the MBL in a detailed manner. Besides the coupled amine chemistry, the reactions between HOCl and HOBr with HSO3- are updated following recent experimental findings86. The reaction between HOI with HSO3- is assumed to be as fast as the one of HOBr.

To investigate the importance of amine-related multiphase chemistry under pristine MBL conditions the CAPRAM pristine marine scenario87 is used and has been updated to treat now emission of methylamines. Field studies suggested that oceans are both source and sink for methyl amines acting as a source for MMA and TMA, but as a sink for DMA4. Thus, only MMA (151 molecules cm-3 s-1) and TMA (252 molecules cm-3 s-1) emissions are included. The calculated flux is based on the values in the review of Ge et al.4. Moreover, the emissions of other trace gases have also been updated. A complete overview on the emissions used is provided in Supplementary Table 4. The simulations were carried out using a monodisperse aerosol population to investigate important processes and a fixed polydisperse particle spectrum typical for pristine marine regions20 (Supplementary Fig. 8) to investigate the accuracy of the model to partition the MAs. The simulations covered a model time of 108 hours and represent summer conditions at 288 K and 70% relative humidity at 45° latitude. Eight cloud passages, four beginning at 11 a.m. and at 11 p.m. with an in-cloud residence time of about two hours are included. The cloud formation is initialised by an adiabatic cooling of the air parcel through uplifting of 15 minutes until supersaturation is reached before 11 a.m. and p.m., respectively. Then, activation of CCN is modelled and the cloud is formed. The cloud evaporation occurs when the air parcel is adiabatically heated within 15 minutes reaching 70% relative humidity after 1 p.m. and a.m., respectively. The condensation and evaporation of water vapour on the particles as well as droplet activation is included to follow the Köhler theory88. The in-cloud residence time is consistent with calculated turnover rates89. For sensitivity studies, the simulations were carried out varying the amount of incoming solar radiation (no irradiation attenuation and irradiation attenuation by 50%) to investigate the effect of stronger and lower photochemistry on MA oxidation. Additional sensitivity simulations for the polydisperse particle spectrum were performed in which MMA and TMA emissions are increased by a factor of ten to examine the influence of higher biological productivity.