Enhanced Sulfate Formation from Gas-Phase SO 2 Oxidation in Non– •OH–Radical Environments

: Recent research on atmospheric particle formation has shown substantial discrepancies between observed and modeled atmospheric sulfate levels. This is because models mostly consider sulfate originating from SO 2 oxidation by • OH radicals in mechanisms catalyzed by solar radiation while ignoring other pathways of non-radical SO 2 oxidation that would substantially alter atmospheric sulfate levels. Herein, we use high-level quantum chemical calculations based on density functional theory and coupled cluster theory to show that monoethanolamine (MEA), a typical alka-nolamine pollutant released from CO 2 capture technology, can facilitate the conversion of atmospheric SO 2 to sulfate in a non– • OH–radical oxidation mechanism. The initial process is the MEA-induced SO 2 hydrolysis leading to the formation of HOSO − 2 • MEAH + . The latter entity is thereafter oxidized by ozone (O 3 ) and nitrogen dioxide (NO 2 ) to form HSO − 4 • MEAH + , which is an identiﬁed stabilizing entity in sulfate-based aerosol formation. Results show that the HOSO − 2 • MEAH + reaction with O 3 is kinetically and thermodynamically more feasible than the reaction with NO 2 . The presence of an additional water molecule further promotes the HOSO − 2 • MEAH + reaction with O 3 , which occurs in a barrierless process, while it instead favors HONO formation in the reaction with NO 2 . The investigated pathway highlights the potential role alkanolamines may play in SO 2 oxidation to sulfate, especially under conditions that are not favorable for • OH production, thereby providing an alternative sulfate source for aerosol modeling. The studied mechanism is not only relevant to sulfate formation and may effectively compete with reactions with sulfur dioxide and hydroxyl radicals under heavily polluted and highly humid conditions such as haze events, but also an important pathway in MEA removal processes.


Introduction
Secondary atmospheric aerosol particles, formed from gas-to-particle conversion, are primarily composed of sulfate, which is one of the major water-soluble inorganic species in the atmosphere [1,2].These particles are of great concern for their ability to affect human health, reduce visibility, acidify rainwater, and to alter the radiation balance of the atmosphere [3][4][5].The main source of atmospheric sulfate is from the photooxidation of sulfur dioxide (SO 2 ) [6] and although a large number of studies have connected the formation rate of secondary atmospheric aerosol particles to atmospheric sulfate concentration [7][8][9][10], numerical models still fail to reproduce observed atmospheric sulfate concentrations [11].This has led to considerable debate regarding the mechanisms responsible for sulfate formation, especially during winter haze events where sunlight radiation is weakened [3,12,13].The incomplete understanding of the sulfate formation mechanism substantially hinders the efficient prediction of haze events, climate change, air quality monitoring, and the development and implementation of measures to mitigate air pollution [14].
Recently, numerous researchers have focused on atmospheric sulfate formation mechanisms and, most importantly, on how they alter aerosol formation rates under severe pollution conditions.Sulfate is formed from the oxidation of sulfur dioxide (SO 2 ), primarily by hydroxyl radicals (•OH) in the gas phase and ozone (O 3 ), nitrogen oxides (NO x ), hydrogen peroxide (H 2 O 2 ), and O 2 ¯catalyzed by transition metal ions in aqueous-phase and cloud droplets [15][16][17].Multiphase oxidation of SO 2 on solid or aqueous particles is considered a potentially important source of sulfate in the atmosphere as well [18].Although various SO 2 oxidation pathways have been identified, the sources of sulfate and the relative importance of the various SO 2 oxidation pathways for sulfate formation in the atmosphere are yet to be clarified.For example, significant increases in sulfate concentrations were observed during haze events, but their sources remain elusive [19].
The primary gas-phase oxidant, •OH radical, is produced from excited oxygen and water under solar ultraviolet radiation.Despite the fast oxidation of SO 2 by •OH that initially forms sulfur trioxide (SO 3 ), which is further hydrolyzed to form sulfate, many observations have indicated that there is insufficient •OH in the atmosphere to account for the generally observed increasing sulfate formation in polluted environments [12,20].Such low solar ultraviolet radiation conditions are particularly pronounced during haze events.Although the abundance of other oxidants (O 3 , H 2 O 2 , NO x ) is relatively high, their reactions with SO 2 are generally hindered by high energy barriers.This suggests that important alternative pathways for atmospheric sulfate formation do exist, yet they have not been extensively investigated.
Atmospheric bases, including ammonia and amines, are other important components of secondary aerosols.Besides alkylamines such as methylamine and dimethylamine that have been identified as key species in sulfate aerosol formation [21], monoethanolamine (MEA, H 2 NCH 2 CH 2 OH), a typical alkanolamine, has been found to enhance new particle formation as well and to stabilize acidic particles [22,23].MEA is the most widely used baseline solvent in amine-based post-combustion CO 2 capture (PCC) technology [24,25].Considering the potential large-scale implementation of amine-based PCC, relatively large amounts of MEA and possibly other alkanolamines may be emitted into the atmosphere from PCC units due to their relatively high vapor pressure [26,27].It is estimated that nearly 80 tons of MEA may be released into the atmosphere from a CO 2 capture unit that removes 1 million tons of CO 2 per year [21,28] thereby increasing the environmental risk that MEA may potentially pose.Many studies have shown that atmospheric SO 2 conversion can be facilitated by the degradation of amines despite the lack of proper mechanism and kinetics of the driving process [29,30].Xie et al. showed that MEA can effectively cluster with sulfuric acid and significantly enhance new particle formation [23].They showed that the removal rate of MEA due to this process was comparable to the rate of MEA oxidation by •OH at 217 K. Nevertheless, the complete role of MEA in environmental chemistry and aerosol chemistry remains unclear.
This study investigates the importance of direct SO 2 reactions in sulfate aerosol formation in the absence of •OH radicals.Long-term measurements have continually revealed the presence of abundant ammonia and amines in ambient air, including in the marine environment [31,32], and their role has mainly been limited to stabilizing sulfate clusters.Herein, we have investigated sulfate formation from SO 2 oxidation assisted by MEA using density functional theory calculations and kinetic modeling.The investigated SO 2 oxidation assisted by MEA is not only a potential source for atmospheric sulfate, but also a removal pathway for MEA.The kinetics of the studied reaction were evaluated and its implication in sulfate aerosol modeling was assessed.

Quantum Chemical Calculations
Geometric optimizations of all stationary states of the studied reactions were conducted in Gaussian 09 using the ωB97X-D functional [33] in conjunction with the 6-311++G (3df,3pd) basis set.Vibrational frequency analysis and zero-point energies of ωB97XD/6-311++G (3df,3pd) structures were performed at the same level of theory under the harmonic oscillator-rigid rotor approximation at 298.15 K and 1 atm.This level of theory has been shown in previous studies to be sufficient for calculating the geometries and thermochemistry of atmospherically relevant systems [25,[34][35][36][37][38].Transition state configurations were determined using the synchronous transit quasi-Newton method [39] at the same level of theory, while single-point energy corrections on ωB97XD/6-311++G (3df,3pd) structures were performed at the DLPNO-CCSD(T)/aug-cc-pVTZ level of theory [40,41] using the ORCA 4.2.1 program package [42].

Reaction Kinetics Computation
The reaction rate constants were evaluated using the transition-state theory with the Wigner tunneling correction [43][44][45].Previous studies have shown that the formation of a ternary complex from three separate reactants first proceeds through formation of a binary complex that interacts with the third species thereafter [46,47].Given the high atmospheric concentration of water relative to those of other reactants, it is most likely that initial collisions between the three separate reactants (SO 2 , H 2 O and MEA) will preferably form the hydrates of SO 2 and MEA prior to the formation of the ternary complex, MEA•H 2 O•SO 2 .Based on these considerations, SO 2 •H 2 O and MEA•H 2 O will be determinant in computing the total rate constant of the MEA-assisted SO 2 hydrolysis.According to our calculations (see Table 1), MEA•H 2 O is the most abundant binary complex among possible binary complexes and its interaction with SO 2 is likely to lead the process of MEA-mediated SO 2 hydrolysis according to the following equation: Assuming equilibrium between MEA•H 2 O•SO 2 and reactants MEA•H 2 O and SO 2 based on the pseudo steady-state approximation, the overall rate of reaction (R1) can be written as: where k MEA•H2O•SO2 is the reaction rate constant written as •SO 2 back to initial reactants, K eq is the equilibrium constant of formation of the reactant complex, k uni is the unimolecular rate constant of the reaction of the reactant complex to the product.The equilibrium constant is expressed as: where ∆G eq is the Gibbs free energy change for the formation of the reactant complex, R is the gas constant, and T is the absolute temperature.k uni is expressed as with ∆G ‡ being the activation Gibbs free energy change separating the reactant complex from the product state.Γ is the tunnelling effect factor, given by Wigner tunnelling correction: where h is the Planck constant, ν ± the imaginary frequency of the transition state, k B is the Boltzmann constant, T is the absolute temperature.

MEA-Assisted SO 2 Hydrolysis
As explained above, the formation of the ternary complex would proceed through the prior formation of the binary complex, followed by interaction with the third species [46,47].According to our calculations, the formation of MEA  1.
Table 1.Electronic energy change (∆E in kcal mol −1 ) and Gibbs free energy change (∆G in kcal mol −1 ), equilibrium constants (K eq , cm 3 molecule −1 ) of relevant reactions and equilibrium concentration (in molecule cm −3 ) for some binary complexes in the MEA-assisted SO 2 hydrolysis, all calculated at 298.15 K and 1 atm.These electronic energy changes are plotted in Figures 1 and 3-6.This complex rearranges through a transition state configuration located at −6.21 kcal mol −1 below separate reactants, to form HOSO − 2 •MEAH + .As expected from the average local ionization energy mapped van der Waals surface shown in Figure 2, the nitrogen atom is the reactive site of MEA in this process.This is the site with the most deficient potential, which is hence the most susceptible to undergo an electrophilic addition.The electronic energy barrier height in HOSO − 2 • MEAH + formation is 6.83 kcal mol −1 , much lower than the 33.9 kcal mol −1 energy barrier in the SO 2 +H 2 O → H 2 SO 3 reaction, as reported in a much earlier study [48].A previous quantum chemical study showed that ammonia can lower the barrier height of SO 2 hydrolysis to ~12.0 kcal mol −1 [49]; however, it is still higher than that reported for the MEA-assisted SO 2 hydrolysis in the current study.Much lower barriers were determined in SO 2 hydrolysis assisted by methylamine (5.80 kcal mol −1 ) and dimethylamine (3.17 kcal mol −1 ) [50].Despite little differences that may arise as the result of different theoretical methods, the decreasing effect of ammonia, MEA, methylamine, and dimethylamine on the energy barrier in SO 2 hydrolysis is in line with the order of their basicity [51].This further confirms the stronger ability of amines, compared to ammonia, to promote SO 2 hydrolysis.

HSO MEAH •NO
Our calculations indicate that although a second water molecule did not explicitly participate in the reaction, it contributed to further reducing the energy barrier height for HOSO − 2 • MEAH + formation down to 4.18 kcal mol −1 , rendering the SO 2 hydrolysis more favorable, as shown in the energy profile of Figure 3. Similar effects of water in decreasing energy barrier heights in chemical processes have been observed in several previous studies [49,[52][53][54].

Further Reaction with NO 2
The sulfite ion in HOSO − 2 • MEAH + is susceptible to react with relevant atmospheric oxidants.For example, it can be oxidized by NO 2 to form the HSO − 4 (reaction (R4)).The different steps in this process are the formation of an intermediate complex, HOSO − 2 MEAH + •NO 2 lying at −2.76 kcal mol −1 , and overcoming a relatively high energy barrier prior to HSO − 4 • MEAH + •NO formation (see Figure 4).The energy barrier in this process is 25.58 kcal mol −1 , which drastically increases to 46.09 kcal mol −1 in the presence of an additional water molecule (reaction (R5), Figure 5).This substantial increase in the energy barrier height is the result of a strong stability of the reactant complex due to additional water that facilitates the formation of a tighter ring structure than without water.Even though this process is highly exergonic (with −23.42 kcal mol −1 free energy change at 298.15 K and 1 atm), the high energy barrier would prevent this reaction at standard conditions.Moreover, the formation of nitrous oxide (HONO) in the HONO•SO − 3 • MEAH + product complex was observed to be a potential product in HOSO − 2 • MEAH + •NO 2 decomposition in the presence of an additional water molecule (reaction (R6)).Color coding is yellow for sulfur atoms, red for oxygen atoms, white for hydrogen atoms, and blue for nitrogen atoms.Electronic energy values of all stationary states are indicated, and corresponding Gibbs-free energy values are presented in Table 1.

Further Reaction with O 3
The reaction of HOSO Color coding is yellow for sulfur atoms, red for oxygen atoms, white for hydrogen atoms, and blue for nitrogen atoms.Electronic energy values of all stationary states are indicated, and corresponding Gibbs-free energy values are presented in Table 1.
Atmosphere 2024, 15, 64 10 of 15 Contrary to the effect of water in the HOSO − 2 • MEAH + + NO 2 , the presence of additional water molecules significantly promotes the conversion of HOSO − 2 • MEAH + to HSO − 4 • MEAH + by reaction with O 3 , which becomes barrierless (see Figure 6).This effect of additional water is contrary to that observed in the reaction with NO 2 .The effect of water in promoting O 3 ¯oxidation reactions was also observed in our previous studies [52].It is speculated that different reactive behaviors of MEA-assisted SO 2 hydrolysis towards NO 2 and O 3 compared to methylamine-assisted and dimethylamine-assisted SO 2 hydrolysis [51] can be attributed to the electronic effect of the •OH group in MEA.

Kinetics of MEA-Assisted SO 2 Hydrolysis and Implications for Atmospheric Sulfate Formation
As introduced in Section 2.2, the rate constant of MEA-assisted SO 2 hydrolysis is determined by considering the formation of the pre-reactive complex from MEA•H 2 O + SO 2 and SO 2 •H 2 O + MEA interactions, given the high atmospheric concentration of water relative to those of other reactants.This is further justified by the values of equilibrium constants and equilibrium concentrations (presented in Table 1) of the three possible binary complexes susceptible to form from the interactions between MEA, SO 2 and H 2 O. Assuming [SO 2 ] ~10 12 molecule cm −3 , [MEA] ~2.43 × 10 15 molecule cm −3 and [H 2 O] ~7.77 × 10 17 molecule cm −3 corresponding to highly polluted conditions [29,[55][56][57], MEA•H 2 O has the highest equilibrium concentration among all the binary complexes.Hence, we determined the bimolecular rate constant of the MEA-assisted SO 2 hydrolysis based on the MEA•H 2 O + SO 2 interaction to be 1.90 × 10 −14 cm 3 molecule −1 s −1 at 298.15 K.All reaction rate constants at this temperature are presented in Table 2, while the positive temperature-dependency of the rate constant is plotted in Figure 7. Taking into account the equilibrium concentration of MEA•H 2 O, which is equal to 3.63 × 10 9 cm 3 molecule −1 as provided in Table 1, and the SO 2 concentration given above, we obtain a reaction rate (calculated according to Equation (1) of 6.89 × 10 7 molecule cm −3 s −1 for the SO 2 hydrolysis assisted by MEA at 300 K.This rate is one order of magnitude higher than the estimated rate of SO 2 oxidation by •OH determined to be 1.50 × 10 6 molecule cm −3 s −1 at the same temperature [57], considering an average •OH concentration of ~10 6 molecule cm −3 during daytime and 1.30 × 10 −12 cm 3 molecule −1 s −1 rate constant of SO 2 oxidation by •OH.
Although the presence of additional water molecules increases the unimolecular rate constant of hydrated HOSO − 2 •MEAH + formation by two orders of magnitude relative to the reaction with one water molecule less, the overall effect on the bimolecular rate constant is reduced by the weaker binding between MEA•(H 2 O) 2 and SO 2 to form the reactant complex, MEA•(H 2 O) 2 •SO 2 .For this reaction, we obtain a rate constant of 1.93 × 10 −14 cm 3 molecule −1 s −1 at 298.15 K. Similar to the reaction without additional water, the rate constant of the reaction in the presence of additional water exhibits a positive temperature-dependent variation in the range 200-400 K, though the effect is significantly weak.Considering [(H 2 O) 2 ] ~4.35 × 10 12 molecule cm −3 according to our calculations, the reaction rate of SO 2 hydrolysis assisted by MEA with additional water was estimated to be 3.88 × 10 3 molecule cm −3 s −1 , three order of magnitude lower than the estimated rate of SO 2 oxidation by •OH reported previously [57].
- Given the high rate of MEA-assisted SO 2 hydrolysis, it is evident that under extremely polluted conditions such as during haze events where there is insufficient •OH production due to low ultraviolet solar radiation, the investigated pathway might be a highly competitive process in atmospheric SO 2 oxidation.
Further exploration of the chemistry of HOSO − 2 •MEAH + shows that oxidation by NO 2 •MEAH + oxidation leading to sulfate formation in the gas phase.Besides its fate in sulfate formation, the studied mechanism could also be an efficient removal pathway for MEA, which is believed to potentially represent an environmental risk [56,58].So far, the reported sink processes for MEA include gas-phase oxidation by •OH and •Cl, and reactive uptake by sulfuric acid molecules [22,59,60].Rate constants of 7.10 × 10 −11 cm 3 molecule −1 s −1 and ~10 −10 cm 3 molecule −1 s −1 were reported for MEA oxidation by •OH and •Cl, respectively [59,60].With average •OH concentrations of ~10 6 molecule cm −3 during daytime and •Cl concentration of ~10 5 molecule cm −3 , the estimated rates of MEA+•OH (1.73 × 10 11 molecule cm −3 s −1 ) and MEA + •Cl (2.43 × 10 10 molecule cm −3 s −1 ) are respectively 5 × 10 3 and 7 × 10 2 times higher than the rate of MEA•H 2 O + SO 2 reaction.Under highly polluted conditions with elevated concen-trations of MEA and low •OH concentration induced by low solar radiation, the mechanism reported in this study may also be a competitive pathway in MEA removal processes.

Conclusions
Sulfate formation was investigated from MEA-assisted SO 2 oxidation using firstprinciples simulations.Results indicate that decomposition of the direct SO 2 hydrolysis product, HOSO − 2 •MEAH + , by O 3 is more favored than by NO 2 .The presence of additional water was found to play a varied role in the further oxidation process of HOSO − 2 •MEAH + , significantly facilitating the decomposition by O 3 while substantially preventing the reaction with NO 2 .Besides sulfate formation mechanisms including ion-mediated and acid-catalyzed mechanisms that have already been elucidated in some previous studies, the current mechanism is an alternative pathway for sulfate formation and can be used to explain elevated sulfate formation observed under severe haze events where there is insufficient •OH production for SO 2 oxidation.Moreover, the presence of water introduces an additional feature, i.e., the HONO formation, in the reaction with NO 2 , though at a relatively lower rate.This latter mechanism might be a potential source for •OH under low ultraviolet solar radiation.We found that the title reaction can significantly outperform SO 2 + •OH reaction under low •OH conditions, providing new pathways for sulfate formation that would prevail under conditions of heavy pollution, high humidity, and low solar radiation, such as during haze events.The MEA-assisted SO 2 oxidation would also potentially compete with the •OH oxidation pathway in MEA removal processes under such conditions.This study highlights the role of alkanolamines in SO 2 oxidation, with implication in sulfate aerosol formation.

Figure 3 .
Figure 3. Energy surface for the MEA-catalyzed SO 2 hydrolysis with the presence of an additional water molecule.Color coding is yellow for sulfur atoms, red for oxygen atoms, white for hydrogen atoms, and blue for nitrogen atoms.Electronic energy values of all stationary states are indicated, and corresponding Gibbs-free energy values are presented in Table 1.The energy barrier in this decomposition is 26.97 kcal mol −1 , being 19.11 kcal mol −1 lower than the barrier in HSO − 4 formation.Despite the somewhat more favorable formation of HONO than HSO − 4 from HOSO − 2 • MEAH + oxidation by NO 2 in the presence of water, the overall rate of HONO formation would be limited given the relatively high energy barrier to its formation.A similar conclusion was observed by Wang et al. while studying the SO 2 hydrolysis assisted by methylamine and dimethylamine [50].The fate of HOSO − 2 • MEAH + would then depends on other oxidants, such as O 3 .

Figure 4 .
Figure 4. Potential energy profile for the oxidation reaction of HOSO − 2 •MEAH + and NO 2 .Color coding is yellow for sulfur atoms, red for oxygen atoms, white for hydrogen atoms, and blue for nitrogen atoms.Electronic energy values of all stationary states are indicated, and corresponding Gibbs-free energy values are presented in Table1.

− 2 •Figure 5 .Figure 6 .
Figure 5. Potential energy profiles for the oxidation reaction for HOSO − 2 •MEAH + and NO 2 , with additional H 2 O.Color coding is yellow for sulfur atoms, red for oxygen atoms, white for hydrogen atoms, and blue for nitrogen atoms.Electronic energy values of all stationary states are indicated, and corresponding Gibbs-free energy values are presented in Table1.
2 and O 3 to form HSO − 4 •MEAH + occurs with unimolecular rate constants of 1.29 × 10 −6 s −1 and 1.35 × 10 −2 s −1 , respectively.With the presence of additional water molecules, HOSO − 2 •MEAH + decomposition by O 3 to form HSO − 4 •MEAH + is essen- tially barrierless, whereas decomposition by NO 2 is further prevented by a high energy barrier.For the reaction with NO 2 in the presence of water, instead, the decomposition of HOSO − 2 •MEAH + to HONO•SO − 3 •MEAH + is slightly preferred.The relevance of HONO•SO − 3 •MEAH + can be found both in •OH production through HONO and in sulfate formation through SO − 3 .HONO•SO − 3 •MEAH + is formed at a unimolecular rate constant of 2.41 × 10 −7 s −1 ; however, this is still much lower than the rate constant of the reaction with O 3 .This indicates that the reaction with O 3 is the most likely process for HOSO − •H 2 O and H 2 O•SO 2 is more favorable than that of MEA•H 2 O as can be seen from the equilibrium constants of their formation presented in Table 1.The two pathways of MEA•H 2 O•SO 2 formation from MEA•H 2 O + SO 2 and H 2 O•SO 2 + MEA interactions were readily assessed (see Figure 1).While the formation of MEA•H 2 O is energetically more favorable (electronic energy change of −5.49 kcal mol −1 relative to precursor reactants) than H 2 O•SO 2 (electronic energy change of −3.12 kcal mol −1 relative to precursor reactants) due to higher ability to form hydrogen bonds, MEA•H 2 O•SO 2 is formed from both MEA•H 2 O + SO 2 and H 2 O•SO 2 + MEA interactions with nearly identical electronic energy changes, −13.04 kcal mol −1 and −13.10 kcal mol −1 , respectively.The formation Gibbs free energies of these MEA•H 2 O•SO 2 isomers at 298.15 K and 1 atm are similar within 1.70 kcal mol −1 , with the formation from MEA•H 2 O + SO 2 interaction being more favorable.Though both interactions will cumulatively form MEA•H 2 O•SO 2 at standard atmospheric conditions, for simplicity, only the numerical results from MEA•H 2 O + SO 2 interaction are reported in Table