Synergistic enhancement and competitive mechanisms of multiple amide molecules on atmospheric sulfuric acid nucleation

Summary

Amides, especially multiple amide molecules, play a critical yet under-resolved role in new particle formation (NPF), which in turn affects aerosol formation. This study systematically evaluates the potential and mechanisms of multiple amide molecules on promoting SA-NH₃ nucleation, including methylacetamide (MAA) and methylpropionamide (MPA). Results demonstrate that clusters (SA)₁·(MPA)₁ and (SA)₁·(MAA)₁ display excellent thermodynamic and kinetic stability compared with (SA)₁·(NH₃)₁, even (SA)₁·(DMA)₁, suggesting the nucleation potential of MPA and MAA. Crucially, a profound synergistic enhancement of MPA and MAA was identified in ternary SA-NH₃-MPA/MAA and quaternary SA-NH₃-MPA-MAA nucleation systems, where the synergistic enhancement strength exceeds individual enhancement by an order of magnitude, especially at lower SA concentrations and temperatures. Moreover, a competitive mechanism was identified where MPA replaces NH₃ and MAA replaces MPA. The study highlights the synergistic enhancement of multiple alkaline precursors on NPF, offering theoretical data and mechanism support for the improvement of global nucleation models.

Graphical abstract

Highlights

• •Amides can form stable clusters with SA possessing excellent stability
• •MAA and MPA could promote SA nucleation either individually or synergistically
• •Synergistic enhancement strength are pronounced at lower SA and temperatures
• •Synergistic and competitive mechanisms of multi-amide in SA nucleation were traced

Materials science; Materials structure; Materials mechanics

Introduction

Aerosols have a significant impact on atmospheric systems, particularly in atmospheric visibility,¹ cloud condensation nucleus (CCN) formation,² global climate,³ photochemical reactions,⁴ and human health.^5,6 Aerosols can be divided into primary and secondary aerosols based on the formation process. New particle formation (NPF), a gas-to-particle conversion process, contributes significantly to secondary aerosols in the presence of strong oxidation and high concentrations of gaseous pollutants.⁷ NPF encompasses the nucleation and growth steps.⁸ Nucleation precursors in the gas phase gradually form critical clusters via sticky collisions, which will grow further into aerosol particles. Hence, critical clusters serve as a bridge between nucleation precursors and macroscopic particles, and it is essential to investigate the potentially uncovered nucleation precursors and nucleation mechanisms to comprehensively understand the NPF.

Sulfuric acid (SA) is the main crucial atmospheric nucleation precursor with gaseous concentrations up to 10⁶–10⁷ molecules cm⁻³.^9,10 Field observations, experiments, and theoretical studies have successively proposed a variety of SA-contained nucleation¹¹ in which water molecule (H₂O), base molecules such as ammonia (NH₃),^12,13 methylamine (MA),^14,15 dimethylamine (DMA),¹⁶ guanidine,¹⁷ and piperazine,¹⁸ organic acids such as acetic acid,¹⁹ propanoic acid,²⁰ malonic acid,²¹ and highly oxidized multifunctional (HOM) organics,^22,23 inorganic acids such as iodine oxides (I₂O₅, HIO₃, and HIO₂)^24,25,26,27 potentially improve the stability of atmospheric clusters by preventing monomer evaporation. Alkaline molecules potentially form acid-base pairs with SA molecules via proton transfer process, which results in the conversion of weak hydrogen bond interactions into electrostatic attraction and improves cluster stability more effectively. Therefore, the potency of SA-base clusters formation is associated with the basicity of alkaline molecules. DMA exhibits a thousand-fold higher enhancement effect on nucleation rates than NH₃,²⁸ even at concentrations 10–1,000 times lower than NH₃. Moreover, DMA could replace NH₃ in molecular clusters for its higher basicity.

As the representative alkaline molecules in the atmosphere alongside NH₃ and amines, amides exhibit both primary emission sources and secondary formation sources.²⁹ The main anthropogenic sources of gaseous amides include wastewater and waste treatment,^30,31 vehicle exhaust,^32,33 industrial processes,^34,35 biomass combustion in the food service industry,^36,37,38 and tobacco combustion.³⁹ Secondary sources of gaseous amides include the photooxidation of organic amines, the reaction products of amines or NH₃ with anthropogenically emitted mono- or dicarboxylic acids.^32,40,41 Gaseous amides are widely detected in urban and natural atmospheric environments, with their distribution characteristics being greatly impacted by both geographical location and anthropogenic emission sources.²⁹ Its concentrations in natural environments such as forests and marine areas remain relatively lower, generally falling within the range of 1–10 pptv.^42,43,44 Amides exhibit higher concentrations in urban regions affected by anthropogenic emissions, usually within the range of pptv to ppbv levels.^{30,33,38,45,46} In areas near landfills and wastewater treatment facilities, amide concentrations may experience a significant increase, potentially reaching ppbv levels. In 2016, Yao et al. found that the atmospheric amide concentrations in Shanghai ranged from pptv to ppbv, and the volume concentration of C₃ amide was the highest, up to 8.7 ppbv.⁴⁵ In Beijing urban area, Zhu et al. found that the volume concentration of C_1-3 amides was 101.1 ± 94.5 pptv. In the early morning, the volume concentration of amides was at its lowest, but it gradually increased throughout the day and was consistently greater than that of amine possessing the same number of C atoms.³³ Atmospheric amides could participate in NPF processes via collision with SA molecules to establish stable clusters. Glasoe et al. showed that atmospheric nucleation was improved by urea and acetamide (AA), despite the significantly weaker effects compared with amines.⁴⁷ Chen et al. measured the adsorption coefficients of alkyl amides (C₁–C₃) on SA particles, indicating that amides can compete with amine molecules to form ammonium salt on acidic particles in regions with higher amide concentrations, facilitating NPF.⁴⁸ Ma et al. conducted density functional theory (DFT) calculations at the M06-2X/6-311++G(3df,3pd) level of theory, finding that the incorporation of amides enhances SA-driven nucleation, with SA-amide binding strengths surpassing those of NH₃ but remaining weaker than MA.⁴⁹ Zuo et al. compared the interaction strengths between amides and SA versus organic acids. As a result, amides could stabilize SA less effectively than amines but more strongly than NH₃, with SA-amide systems exhibiting greater nucleation potential than organic acid-amide systems.²⁰ Zhao et al. investigated the role of propionamide (PA) in SA-mediated NPF, revealing that PA-containing clusters were thermodynamically favorable. Clusters with more PA than SA molecules exhibited a reduction in formation Gibbs free energy changes as a result of the hydrogen bonding of the C=O group in PA, which improved the thermodynamic stability of the clusters.⁵⁰ And the formation rate of SA-PA clusters could reach 10⁻⁹ cm⁻³ s⁻¹ at PA concentrations of ppbv level. Janardanan and co-workers further reported an unexpectedly high enhancement potential of aminopropanamide (APA) compared with that of PA in SA-mediated NPF.⁵¹ Ni et al. employed CCSD(T)/6-311++G(d,p)//B3LYP/6-311G(d,p) calculations to investigate the catalytic mechanisms of amides and their clusters in the hydrolysis of NO₂.⁵² The results demonstrated that amide dimers are more catalytically efficient than monomers and monohydrates, thus promoting nitrate hydrate NPF and acid dissociation while enhancing the extinction characteristics of clusters. Moreover, amides could greatly increase NPF at low temperatures, high pressure, and high-altitude conditions.

Previous studies predominantly focused on investigating the promoting effect of specific individual alkaline molecules on SA nucleation. In the case that the atmosphere is a complex mixture of different gas precursors, especially under the complex polluted background of China, the effect of multiple amide molecules on SA-nucleation, as well as the influence of atmospheric conditions on the amide-participated nucleation mechanisms still remain unclear, necessitating a thorough analysis. This study comprehensively investigated and compared the potential role of nine typical amides, particularly the multiple amide molecules, in SA-nucleation process and the nucleation mechanism via a combination of quantum chemical calculations and atmospheric cluster dynamics code (ACDC) simulations.

Results

Monomer structure analysis

This study selected nine typical amide molecules (Figure S1) relevant to atmospheric studies, including formamide (FA), N-methylformamide (MFA), N, N-dimethylformamide (DMFA), AA, N-methylacetamide (MAA), N, N-dimethylacetamide (DMAA), PA, N-methylpropionamide (MPA), and N, N-dimethylpropionamide (DMPA). They cover primary and secondary amides with varied alkyl chain lengths (C₁–C₃), different degrees of N-substitution, cis- and trans-isomers, encompassing a broader class of amides. The electronic structures of these amides are characterized by p-π conjugation between the soliton pairs in the p-orbital of the amino group (–NHR) and the π-electrons of the carbonyl group (–CO), resulting in equalized electron cloud density and bond lengths, limiting the rotation around the C–N bond. For MFA and MAA, the spatial orientation of the C=O and N–H bonds results in cis- and trans-isomers with the C–N bond as the rotational axis. According to the M06-2X/6-311++G(3df,3pd) calculations, cis-isomers demonstrate lower Gibbs free energy (G), suggesting higher thermodynamic stability compared to trans-isomers. For example, cis-MFA and cis-MAA possess lower G values of 1.29 and 2.80 kcal/mol relative to their trans-isomers, respectively, consistent with a previous study by Ma et al.⁴⁹

Dimer clusters analysis

Basic molecules such as amides, DMA, MA, and NH₃ play a critical role in the stabilization of SA clusters by forming acid-base pairs with SA, reducing the evaporation of SA monomers. This process involves proton transfer process from acidic molecules to basic molecules, shifting hydrogen bonding interactions to electrostatic interactions, hence improving the stability of clusters. To investigate the nucleation potential of amides, thermodynamic and kinetic stability of binary clusters formed between nine different amides and SA were initially assessed and compared with (SA)₁·(DMA)₁, (SA)₁·(MA)₁, and (SA)₁·(NH₃)₁ at the M06-2X/6-311++G(3df,3pd) level of theory. As a result, (SA)₁·(amide)₁ clusters mainly comprise two types of hydrogen bonds (Figure 1): (1) an –O–H---O hydrogen bond, where the O atom from amide’s C=O group bonds with the –OH group of SA, and (2) an –N–H---O hydrogen bond, involving the H atom from amide’s –N–H group and the O atom of SA.

Figure 1.

The most stable configurations of (SA)₁·(Amide)₁, (SA)₁·(DMA)₁, (SA)₁·(MA)₁, and (SA)₁·(NH₃)₁ at the M06-2X/6-311++G(3df,3pd) level of theory

The hydrogen bonds are shown as dashed lines and given in Å. The gray, red, yellow, and white spheres represent C, O, S, and H atoms, respectively.

The Gibbs free energy of formation (ΔG, kcal/mol) is a crucial indicator of the thermodynamic stability of molecular clusters, with a larger absolute value corresponding to greater stability. ΔG values (Table S1) for (SA)₁·(amide)₁ clusters range from −4.70 to −10.68 kcal/mol, proposing that all amide molecules can establish stable clusters with SA through intermolecular interactions. The (trans-SA)₁·(amide)₁ clusters showed higher thermodynamic stability by comparison analysis, with greater absolute ΔG values than their (cis-SA)₁·(amide)₁ counterparts. For instance, (trans-SA)₁·(PA)₁ has a ΔG value of −9.51 kcal/mol, which is smaller than −5.56 kcal/mol for (cis-SA)₁·(PA)₁. The ΔG values of (SA)₁·(amide)₁, (SA)₁·(DMA)₁, (SA)₁·(MA)₁, and (SA)₁·(NH₃)₁ are compared more intuitively (Figure 2). Most of the (cis-SA)₁·(amide)₁ clusters have smaller absolute ΔG values than (SA)₁·(NH₃)₁, except for a specific cluster (cis-SA)₁·(trans-MFA)₁, (cis-SA)₁·(AA)₁, (cis-SA)₁·(trans-MAA)₁, and (cis-SA)₁·(MPA)₁ whose ΔG values are between (SA)₁·(MA)₁ and (SA)₁·(NH₃)₁, suggesting that cis-SA-containing clusters have relatively lower thermodynamic stability. Most of the (trans-SA)₁·(amide)₁ clusters demonstrate larger absolute ΔG values than (SA)₁·(NH₃)₁, except for (trans-SA)₁·(cis-MFA)₁ and (trans-SA)₁·(cis-MAA)₁, further confirming the higher thermodynamic stability of trans-SA clusters. The (trans-SA)₁·(trans-MAA)₁ and (trans-SA)₁·(MPA)₁ clusters particularly exhibit the absolute ΔG values of −10.46 and −10.68 kcal/mol, respectively, considerably greater than (SA)₁·(DMA)₁ (−10.38 kcal/mol), indicating that trans-MAA and MPA have a greater nucleation potential than NH₃ and DMA. Hence, more investigation is needed into the nucleation mechanisms and how MPA and trans-MAA (hereafter referred to as MAA) contribute to SA-driven nucleation.

Figure 2.

Gibbs free energy of formation (ΔG, kcal/mol) for (SA)₁·(Amide)₁, (SA)₁·(DMA)₁, (SA)₁·(MA)₁, and (SA)₁·(NH₃)₁ at the M06-2X/6-311++G(3df,3pd) level of theory

SA-MPA and SA-MAA binary nucleation systems

The thermodynamic characteristics and most stable cluster configurations across three distinct binary nucleation systems (SA)_x·(Base)_y (where 0 ≤ y ≤ x ≤ 3, with “Base” indicating MPA, MAA, and NH₃) were further analyzed at the M06-2X/6-311++G(3df,3pd) level of theory over a temperature range of 258.15–298.15 K to explore the nucleation potential of MAA and MPA. The maximum cluster in the system contains 3 SA molecules and 3 base molecules. Boundary clusters fluxing out of the nucleation system were set as (SA)₄·(Base)₃. All the clusters in SA-MPA, SA-MAA, and SA-NH₃ systems demonstrate negative ΔG values (Figure 3), emphasizing that SA can form stable clusters with MPA, MAA, and NH₃ through intermolecular interactions under atmospheric conditions. Most SA-MPA clusters possess comparable ΔG values with those of corresponding SA-MAA clusters, with differences ranging from −0.07 to 0.78 kcal/mol, demonstrating similar nucleation abilities of MPA and MAA. SA-NH₃ clusters with 2–3 molecules have smaller absolute ΔG values than their comparable SA-MPA and SA-MAA clusters, whereas larger clusters (4–6 molecules) exhibit larger absolute ΔG values, implying that MPA and MAA are more effective in stabilizing smaller SA clusters, whereas NH₃ is more effective in forming larger SA clusters.

Figure 3.

Gibbs free energy of formation (ΔG, kcal/mol) for three distinct binary nucleation systems (SA)_x·(Base)_y at the M06-2X/6-311++G(3df,3pd) level of theory under 298.15 K

(A) (SA)_x·(NH₃)_y system.

(B) (SA)_x·(MAA)_y system.

(C) (SA)_x·(MPA)_y system.

Cluster formation rate (J) is an essential parameter for evaluating the nucleation potential of precursors in facilitating SA-driven nucleation. A series of ACDC simulations for SA-MPA and SA-MAA binary nucleation systems was performed using the cluster thermodynamic data at the M06-2X/6-311++G(3df,3pd) level of theory. J_SA-MAA (Table S2) and J_SA-MPA (Table S3) were systematically compared with J_SA-NH3 (Table S4) to identify the atmospheric significance of SA-MPA and SA-MAA nucleation. The J_SA-MPA and J_SA-MAA demonstrate similar levels and exceed J_SA-NH3 by around two orders of magnitude at 298.15 K, with the concentrations of SA and base molecules (MPA/MAA/NH₃) ranging from 10⁴–10⁸ molecules cm⁻³ to 10⁴–10¹¹ molecules cm⁻³, respectively, indicating that MPA and MAA have a greater nucleation potential than NH₃ under similar conditions.

A comparative analysis of the logarithmic values (lg) of J_SA-MPA and J_SA-NH3 related to monomer concentrations ([SA] and [Base]) was performed to accurately depict the differences in nucleation rates among various binary nucleation systems. Both J_SA-MPA and J_SA-NH3 increased with increasing [SA] from 10⁴ to 10⁸ molecules cm⁻³ and [MPA or NH₃] from 10⁴ to 10¹¹ molecules cm⁻³, respectively, demonstrating a positive correlation between J (J_SA-MPA or J_SA-NH3) and monomer concentrations (Figure 4A). The differences in J (ΔJ = J_SA-MPA − J_SA-NH3) were further calculated to assess the advantage of MPA or MAA over NH₃ in terms of nucleation potential (Figure 4B). The logarithm of ΔJ exhibits a positive correlation with the increasing [SA] and [Base], indicating a widening gap between J_SA-MPA and J_SA-NH3, verifying the stronger nucleation potential of MPA and MAA compared with NH₃.

Figure 4.

The logarithmic values (lg) of formation rates at 298.15 K, [SA] = 10⁴–10⁸ molecules cm⁻³, and [MPA or NH₃] = 10⁴–10¹¹ molecules cm⁻³

(A) J_SA-MPA and J_SA-NH3.

(B) ΔJ = J_SA-MPA − J_SA-NH3.

ACDC simulations were performed to elucidate the cluster formation mechanisms of SA-MPA and SA-MAA binary nucleation systems at the atmospheric condition of T = 298.15 K; [SA] = 10⁴, 10⁶, and 10⁸ molecules cm⁻³; and [MPA or MAA or NH₃] = 10⁴, 10⁷, and 10¹¹ molecules cm⁻³. The SA-MPA binary nucleation system demonstrates a single continuous collision-growth pathway at lower monomer concentrations (Figure 5A, 10⁴ molecules cm⁻³): SA + MPA→(SA)₁·(MPA)₁+SA→(SA)₂·(MPA)₁+(SA)₁·(MPA)₁→(SA)₃·(MPA)₂. As [MPA] increased to 10⁷ molecules cm⁻³ (Figure 5B), formation pathways of (SA)₂·(MPA)₁ from (SA)₁·(MPA)₁ diversify, with the initial pathway remaining the original monomer collision, (SA)₁·(MPA)₁+SA→(SA)₂·(MPA)₁, contributing only 6%. A bimolecular collision followed by MPA monomer evaporation predominates (up to 93%), (SA)₁·(MPA)₁+(SA)₁·(MPA)₁→(SA)₂·(MPA)₂–MPA→(SA)₂·(MPA)₁. Increasing [MPA] to 10¹¹ molecules cm⁻³ causes the increased (SA)₁·(MPA)₁ cluster concentration to initiate the exclusive bimolecular collision pathway for the formation of (SA)₂·(MPA)₁ (Figure 5C). Overall, the SA-MPA binary nucleation at [SA] = 10⁴ molecules cm⁻³ is mostly accomplished by collisions with (SA)₁·(MPA)₁. When [SA] increased to 10⁶ molecules cm⁻³ while [MPA] were 10⁴, 10⁷, and 10¹¹ molecules cm⁻³ (Figures 5D–5F), cluster growth pathways are comparable with those at [SA] = 10⁴ molecules cm⁻³. When [SA] further increased to 10⁸ molecules cm⁻³ with [MPA] at 10⁴ molecules cm⁻³ (Figure 5G), a mass of (SA)₁·(MPA)₁ and (SA)₂ dimer via monomer collision generated, resulting in the formation of (SA)₂·(MPA)₁ through two different pathways: (1) sequential collision growth pathway SA + MPA→(SA)₁·(MPA)₁+SA→(SA)₂·(MPA)₁, which accounts for 64% of the contribution, and (2) a bimolecular collision-SA monomer evaporation pathway SA + SA→(SA)₂+(SA)₁·(MPA)₁→(SA)₃·(MPA)₁–SA→(SA)₂·(MPA)₁, accounting for 34% of the contribution. As [MPA] increased to 10⁷ molecules cm⁻³ (Figure 5H), the primary pathway shifts to bimolecular collision-MPA monomer evaporation: (SA)₁·(MPA)₁+(SA)₁·(MPA)₁→(SA)₂·(MPA)₂–MPA→(SA)₂·(MPA)₁ due to the increased concentration of (SA)₁·(MPA)₁, representing 73% contribution. Contribution of (SA)₂ in another bimolecular collision-SA monomer evaporation pathway decreases from 34% to 27%. As [MPA] increased to 10¹¹ molecules cm⁻³, the (SA)₂·(MPA)₁ forms only through the bimolecular collision-MPA monomer evaporation pathway (Figure 5I). Furthermore, ΔG values for most clusters in SA-MAA binary nucleation system are similar to those of SA-MPA system, resulting in similar cluster formation pathways with differences mostly in percentage contributions of the specific pathways (Figure S2).

Figure 5.

Cluster formation pathways in SA-MPA binary nucleation system under varying monomer concentrations at T = 298.15 K

(A) [SA] = 10⁴ molecules cm⁻³ and [MPA] = 10⁴ molecules cm⁻³.

(B) [SA] = 10⁴ molecules cm⁻³ and [MPA] = 10⁷ molecules cm⁻³.

(C) [SA] = 10⁴ molecules cm⁻³ and [MPA] = 10¹¹ molecules cm⁻³.

(D) [SA] = 10⁶ molecules cm⁻³ and [MPA] = 10⁴ molecules cm⁻³.

(E) [SA] = 10⁶ molecules cm⁻³ and [MPA] = 10⁷ molecules cm⁻³.

(F) [SA] = 10⁶ molecules cm⁻³ and [MPA] = 10¹¹ molecules cm⁻³.

(G) [SA] = 10⁸ molecules cm⁻³ and [MPA] = 10⁴ molecules cm⁻³.

(H) [SA] = 10⁸ molecules cm⁻³ and [MPA] = 10⁷ molecules cm⁻³.

(I) [SA] = 10⁸ molecules cm⁻³ and [MPA] = 10¹¹ molecules cm⁻³.

Ternary SA-NH₃-MPA/MAA and quaternary SA-NH₃-MPA-MAA nucleation systems

MPA, MAA, and NH₃ could significantly improve SA nucleation in the atmosphere. Given the coexistence of multiple basic molecules in the atmosphere, understanding their synergistic effects on SA nucleation is essential. The subsequent section focused on the examination of ternary SA-NH₃-MAA and SA-NH₃-MPA and quaternary SA-NH₃-MPA-MAA nucleation systems.

ACDC simulations were performed to determine nucleation rates J of SA-NH₃-MAA (J_SA-NH3-MAA, Table S5) and SA-NH₃-MPA (J_SA-NH3-MPA, Table S6) ternary systems at 298.15 K, [SA] = 10⁴–10⁸ molecules cm⁻³, and [MPA/MAA/NH₃] = 10⁴–10¹¹ molecules cm⁻³. For comparison, the dots represent J values of binary systems, while the surfaces depict J for ternary systems (Figure 6). As the monomer concentrations increase, both J_SA-NH3-MAA and J_SA-NH3-MPA significantly increase, continuously surpassing the J of corresponding binary nucleation system, suggesting that MPA and MAA have an enhanced effect on SA-NH₃ nucleation, respectively.

Figure 6.

Cluster formation rates J of SA-NH₃-MAA and SA-NH₃-MPA ternary nucleation systems under varying monomer concentrations at 298.15 K. The dots and planes represent J values for binary and ternary systems, respectively. The color intensity (increasing toward red) corresponds to higher J

(A) [SA] = 10⁴ molecules cm⁻³ and [NH₃ and MAA] = 10⁴–10¹¹ molecules cm⁻³.

(B) [SA] = 10⁶ molecules cm⁻³ and [NH₃ and MAA] = 10⁴–10¹¹ molecules cm⁻³.

(C) [SA] = 10⁸ molecules cm⁻³ and [NH₃ and MAA] = 10⁴–10¹¹ molecules cm⁻³.

(D) [SA] = 10⁴ molecules cm⁻³ and [NH₃ and MPA] = 10⁴–10¹¹ molecules cm⁻³.

(E) [SA] = 10⁶ molecules cm⁻³ and [NH₃ and MPA] = 10⁴–10¹¹ molecules cm⁻³.

(F) [SA] = 10⁸ molecules cm⁻³ and [NH₃ and MPA] = 10⁴–10¹¹ molecules cm⁻³.

To quantify the enhancement effect, enhancement strength R for MPA and MAA on SA-NH₃ nucleation system was defined with Equation 1,

$$R=\frac{J\left(\left[\text{SA}\right]=\mathrm{x},\left[\mathrm{N}{\mathrm{H}}_3\right]=\mathrm{y},\left[\mathrm{M}\right]=\mathrm{z}\right)}{J\left(\left[\text{SA}\right]=\mathrm{x},\left[\mathrm{N}{\mathrm{H}}_3\right]=\mathrm{y}\right)}$$ (Equation 1)

where J represents the cluster formation rate of nucleation system, [SA] and [NH₃] denote the concentrations of SA and NH₃, [M] indicates the concentrations of MPA, MAA, or MPA+MAA, in molecules cm⁻³. Specifically, when [M] = 10⁸ molecules cm⁻³, the concentration of MPA or MAA is 10⁸ molecules cm⁻³ in the ternary systems, whereas in the quaternary system, the concentrations of both MPA and MAA are 10⁸ molecules cm⁻³. R quantifies the enhancement on J from the incorporation of M, where R > 1.0 signifies an enhancement effect of M. The formation rates of SA-NH₃-MPA-MAA nucleation system were further calculated at 298.15, 278.15, and 258.15 K (Table S7).

The logarithmic variation of R for MPA and MAA with fixed SA and NH₃ concentrations at 10⁶ and 10⁷ molecules cm⁻³, respectively, was illustrated. The enhancement strength follows the order R_MAA+MPA ≥ R_MPA ≥ R_MAA across most of the concentration ranges, demonstrating the synergistic enhancement of MPA and MAA on SA-NH₃ nucleation (Figure 7). R_MAA+MPA is approximately an order of magnitude greater than R_MAA and R_MPA, and increases considerably with the concentration of monomers (Tables S8, S9, and S10). Meanwhile, R_MAA+MPA, R_MAA, and R_MPA gradually decreased to 1.0 when NH₃ concentration increased to 10¹¹ molecules cm⁻³, indicating that there is no synergistic enhancement or individual enhancement at higher NH₃ concentration. To investigate the impact of temperature on the synergistic enhancement of MPA and MAA, ΔG for both ternary and quaternary nucleation systems at 258.15 and 278.15 K were calculated to further perform ACDC simulations. The decrease of temperature from 298.15 to 258.15 K promotes an increase of R_MAA+MPA, R_MAA, and R_MPA by up to approximately 2–3 orders of magnitude (Figure 7). Under different monomer concentrations, a consistent exponential increase was also found (Figures S3 and S4). This is mostly because clusters are more thermodynamically and kinetically stable at lower temperatures, which in turn leads to higher cluster formation rates. In conclusion, at atmospheric temperatures between 258.15 and 298.15 K, MAA and MPA can significantly enhance SA-NH₃ nucleation, either individually or synergistically, with the synergistic effect exceeding individual contributions by a remarkable order of magnitude. Furthermore, the enhancement effects positively correlate with monomer concentrations while negatively correlate with temperatures.

Figure 7.

The logarithmic values (lg) of enhancement strength R_MPA+MAA, R_MPA, and R_MAA as a function of monomer concentration at T = 258.15, 278.15, and 298.15 K; [SA] = 10⁶ molecules cm⁻³; [NH₃] = 10⁷ molecules cm⁻³; and [MPA and MAA] = 10⁴–10¹¹ molecules cm⁻³

To get a deeper insight into how MAA and MPA improve SA-NH₃ nucleation individually or synergistically, ACDC simulations were performed to trace the cluster formation pathways in ternary SA-NH₃-MAA, SA-NH₃-MPA, and quaternary SA-NH₃-MPA-MAA systems.

Cluster formation pathways of ternary SA-NH₃-MAA/MPA nucleation

At relatively lower concentrations (10⁴ molecules cm⁻³) of SA, NH₃, and MAA, only one continuous (SA)₁·(MAA)₁ collision growth pathway was observed in ternary SA-NH₃-MAA nucleation system (Figure 8A): SA + MAA→(SA)₁·(MAA)₁+SA→(SA)₂·(MAA)₁+(SA)₁·(MAA)₁→(SA)₃·(MAA)₂+(SA)₁·(MAA)₁→Flux Out. Notably, NH₃ remains uninvolved in the pathway due to the low concentrations. The lower thermodynamic as well as kinetic stability of small clusters formed by SA and NH₃ render NH₃-participated pathway uncompetitive. As a result, cluster growth is primarily facilitated by collisions with SA, MAA, and (SA)₁·(MAA)₁ clusters.

Figure 8.

Cluster formation pathways of SA-NH₃-MAA ternary system under varying monomer concentrations at 298.15 K

(A) [SA] = [NH₃] = [MAA] = 10⁴ molecules cm⁻³.

(B) [SA] = 10⁶ molecules cm⁻³ and [NH₃] = [MAA] = 10⁷ molecules cm⁻³.

(C) [SA] = 10⁸ molecules cm⁻³ and [NH₃] = [MAA] = 10¹¹ molecules cm⁻³.

When the concentrations of SA, NH₃, and MAA increase to 10⁶, 10⁷, and 10⁷ molecules cm⁻³, respectively, the formation of cluster (SA)₂·(MAA)₁ occurs through two distinct pathways (Figure 8B). In addition to the bimolecular collision-MAA monomer evaporation pathway SA + MAA→(SA)₁·(MAA)₁+(SA)₁·(MAA)₁→(SA)₂·(MAA)₂-MAA→(SA)₂·(MAA)₁ which accounts for 39% contribution, a competitive substitution pathway (SA)₂·(NH₃)₁+MAA-NH₃→(SA)₂·(MAA)₁ contributes 60% where NH₃ is replaced by MAA. Within this pathway, cluster (SA)₂·(NH₃)₁ is formed through two different monomer collision routes: (1) SA + NH₃→(SA)₁·(NH₃)₁+SA→(SA)₂·(NH₃)₁ (8% contribution) and (2) SA + SA→(SA)₂+NH₃→(SA)₂·(NH₃)₁ (92% contribution). Subsequently, the (SA)₂·(MAA)₁ cluster grows larger through the continued collisions with (SA)₁·(MAA)₁.

Upon further increasing SA concentration to 10⁸ molecules cm⁻³, NH₃ and MAA to 10¹¹ molecules cm⁻³ (Figure 8C), the contribution of bimolecular collision-monomer evaporation pathway to (SA)₂·(MAA)₁ increases from 39% to 77%, whereas the competitive substitution pathway (SA)₂·(NH₃)₁+MAA-NH₃→(SA)₂·(MAA)₁ decreases from 60% to 22%.

In summary, for SA-NH₃-MAA nucleation system, when SA, NH₃, and MAA concentrations are lower, NH₃ molecules do not participate in cluster formation, and monomer or bimolecular collisions dominate the cluster growth pathways. As monomer concentrations increase, NH₃ begins to be involved in cluster growth pathways. Notably, a substitution mechanism was identified where MAA competitively replaces NH₃ in (SA)₁·(NH₃)₁ to form (SA)₁·(MAA)₁ or replaces NH₃ in (SA)₂·(NH₃)₁ to generate (SA)₂·(MAA)₁ due to the superior thermodynamic and kinetic stability of small MAA-containing clusters compared with SA-NH₃ clusters. The SA-NH₃-MPA system exhibits growth pathways analogous to the SA-NH₃-MAA system, differing only in the contribution percentages of specific pathways to cluster formation (Figure S5).

Cluster formation pathways in quaternary SA-NH₃-MPA-MAA nucleation system

Two distinct growth pathways were observed for the quaternary SA-NH₃-MPA-MAA system under conditions at SA, NH₃, MPA, and MAA concentrations of 10⁴ molecules cm⁻³ (Figure 9A). (1) The SA-MAA dominant pathway following SA + MAA→(SA)₁·(MAA)₁+SA → (SA)₂·(MAA)₁+(SA)₁·(MAA)₁→ (SA)₃·(MAA)₂+(SA)₁·(MPA)₁ (37% contribution to the flux out) or (SA)₃·(MAA)₂+(SA)₁·(MAA)₁ (24% contribution to the flux out). (2) the SA-MPA dominant pathway following SA + MPA→(SA)₁·(MPA)₁+SA→(SA)₂·(MPA)₁+(SA)₁·(MPA)₁→(SA)₃·(MPA)₂+(SA)₁·(MPA)₁ (contributing 22% to the flux out) or (SA)₃·(MPA)₂+(SA)₁·(MAA)₁ (contributing 15% to the flux out). At lower monomer concentrations, NH₃ was not involved in cluster growth pathways due to the lower thermodynamic and kinetic stability of small SA-NH₃ clusters in comparison to those generated by MPA and MAA, rendering NH₃ uncompetitive in nucleation.

Figure 9.

Cluster formation pathways of quaternary SA-NH₃-MPA-MAA system under varying monomer concentrations at 298.15 K

(A) [SA] = [NH₃] = [MPA] = [MAA] = 10⁴ molecules cm⁻³.

(B) [SA] = 10⁶ molecules cm⁻³ and [NH₃] = [MPA] = [MAA] = 10⁷ molecules cm⁻³.

(C) [SA] = 10⁸ molecules cm⁻³ and [NH₃] = [MPA] = [MAA] = 10¹¹ molecules cm⁻³.

When SA concentration increases to 10⁶ molecules cm⁻³ with NH₃, MPA, and MAA concentrations elevates to 10⁷ molecules cm⁻³ (Figure 9B), there are still two distinct growth pathways flux out the nucleation system, the SA-MAA dominant pathway and the SA-MPA dominant pathway. In the SA-MAA dominant pathway, two distinct routes exist for the formation of (SA)₂·(MAA)₁, both involving competitive substitution between MAA and MPA: (1) (SA)₁·(MPA)₁+(SA)₁·(MAA)₁-MPA→(SA)₂·(MAA)₁ (10% contribution), (2) (SA)₂·(MPA)₁+MAA-MPA→(SA)₂·(MAA)₁ (83% contribution). Concurrently, the SA-MPA dominant pathway contains two routes for generating (SA)₂·(MPA)₁, the direct monomer collision pathway (SA)₁·(MPA)₁+SA→(SA)₂·(MPA)₁ (83% contribution), and a collision-evaporation pathway (SA)₁·(MPA)₁+(SA)₁·(MPA)₁→(SA)₂·(MPA)₂-MPA→(SA)₂·(MPA)₁ (8% contribution). While, NH₃ further participates in cluster growth through two pathways: SA + NH₃→(SA)₁·(NH₃)₁+SA→(SA)₂·(NH₃)₁ and SA + SA→(SA)₂+NH₃→(SA)₂·(NH₃)₁. The resulting (SA)₂·(NH₃)₁ contribute 6% to (SA)₂·(MPA)₁ formation via competitive substitution pathway (SA)₂·(NH₃)₁+MPA-NH₃→(SA)₂·(MPA)₁.

As the SA concentration reached 10⁸ molecules cm⁻³ and NH₃, MPA, and MAA reached 10¹¹ molecules cm⁻³ (Figure 9C), the SA-MAA pathway dominates the clusters flux out of the system where three distinct pathways for generating (SA)₂·(MAA)₁ from (SA)₁·(MPA)₁ exist: (1) the competitive substitution pathway (SA)₁·(MPA)₁+MAA-MPA→(SA)₁·(MAA)₁+(SA)₁·(MAA)₁→(SA)₂·(MAA)₂-MAA→(SA)₂·(MAA)₁ (contributing 15%); (2) another competitive substitution pathway (SA)₂·(MPA)₁+MAA-MPA→(SA)₂·(MAA)₁ (contributing 58%); and (3) a collision-evaporation pathway (SA)₁·(MPA)₁+(SA)₁·(MAA)₁-MPA→(SA)₂·(MAA)₁ (accounting for 25% contribution). Simultaneously, (SA)₂·(MPA)₁ in pathway (2) is generated via two pathways: the direct collision pathway (SA)₁·(MPA)₁+SA→(SA)₂·(MPA)₁ (contributing 77%) and the collision-evaporation pathway (SA)₁·(MPA)₁+(SA)₁·(MPA)₁→(SA)₂·(MPA)₂-MPA→(SA)₂·(MPA)₁ (contributing 17%). The resulting (SA)₂·(MAA)₁ subsequently collides with (SA)₁·(MAA)₁ to form (SA)₃·(MAA)₂ which then evolves through further collisions with (SA)₁·(MAA)₁ (contributing 54% to the flux out) or (SA)₁·(MPA)₁ (contributing 43% to the flux out).

In summary, for the quaternary SA-NH₃-MPA-MAA nucleation system, when SA, NH₃, MPA, and MAA concentrations are relatively lower, NH₃ molecules do not participate in cluster formation, and the system exhibits two dominant cluster growth pathways: SA-MAA and SA-MPA. As nucleation monomer concentrations increase, NH₃ begins to participate in cluster growth, with the three basic molecules (NH₃, MPA, and MAA) synergistically promoting SA nucleation. Furthermore, competitive substitution pathways exist where MPA substitutes NH₃ in clusters, and MAA substitutes MPA in clusters. Overall, the cluster growth and competitive substitution process is complex. It is jointly affected by monomer concentrations, cluster evaporation coefficients (Table S11), collision frequency and probability.

Discussion

This study systematically investigated the enhancement mechanism of amide molecules in SA nucleation by combining quantum chemical calculations with ACDC simulations. All amides could form stable molecular clusters with SA, where MPA and MAA demonstrate the maximum thermodynamic stability, surpassing that of DMA. ACDC simulations on the binary nucleation (SA-MPA, SA-MAA, and SA-NH₃), ternary (SA-NH₃-MPA and SA-NH₃-MAA), and quaternary (SA-NH₃-MPA-MAA) systems demonstrate that MPA and MAA are almost equally effective at promoting SA nucleation, outperforming NH₃ in forming small clusters. Their nucleation rates are higher than that of NH₃ and exhibit a positive correlation with the monomer concentration. Furthermore, MPA and MAA synergistically facilitate SA-NH₃ nucleation, with the strength of synergistic promotion being one order of magnitude higher than that of the individual promotion strength. According to ACDC simulations on cluster formation mechanisms, small clusters are mainly formed through collisions with single molecule, whereas large clusters are primarily formed via collisions with molecular clusters. Due to differences in the Gibbs free energy of clusters, competitive substitution processes are observed where MAA competitively substitutes MPA and MPA competitively substitutes NH₃ in the clusters. The present study highlights the synergistic promotion of multiple amides on SA nucleation, which could explain the missing sources of NPF, offer theoretical data support for the improvement of nucleation models and help to understand deeply the organic nitrogen chemistry under the complex air pollution background.

Limitations of the study

This study provides molecular-level evidence for the enhancement effects of amides on SA nucleation, however, several limitations remain. The present simulations focused on a limited number of amides and simplified SA-NH₃-amide nucleation systems, while the influences of water, ions, oxidants, and more complex organic mixtures were not fully considered. In addition, the predicted nucleation enhancement is mainly based on quantum chemical calculations and ACDC simulations, and thus requires further validation through laboratory chamber experiments and field observations. Hence, further studies are in great need to evaluate the broader contribution of organic nitrogen to atmospheric nucleation under the complex air pollution background.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Haijie Zhang (zhanghaijie@craes.org.cn).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •All cluster formation rates, cluster formation pathways, promotion strength, evaporation coefficients, and the optimized Cartesian coordinates of all structures reported in this study are available within the article and the supplemental information file.
• •This study does not report original code.
• •Any additional information required to reanalyze the data reported in this study is available from the lead contact upon request.

Acknowledgments

The authors thank the National Natural Science Foundation of China (nos. 22306179, 42307139, and 42405104), the National Key Research and Development Program of China (no. 2024YFC3713400) for supporting this study.

Author contributions

Conceptualization, H.Z.; data curation, L.F., X.Z., J.L., and Y.R.; data analysis, L.F.; investigation, L.F., Y.S., and R.T.; project administration, H.Z. and C.C.; supervision, R.G., H.L., and Y.X.; validation, Y.S.; visualization, X.Z.; writing – original draft, L.F., Y.S., and X.Z.; writing – review and editing, H.Z.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Software and algorithms
ABCluster	Jun Zhang	https://zhjun-sci.com/abcluster.html
Mopac	Computer program	https://openmopac.net/
Gaussian 09	Gaussian, Inc.	https://gaussian.com/glossary/g09/
ACDC	McGrath et al.	https://doi.org/10.5194/acp-12-2345-2012

Method details

Quantum chemical calculations at the M06-2X/6–311++G(3df,3pd) level of theory were performed with the Gaussian 09 program.⁵³ The M06-2X/6–311++G(3df,3pd) level of theory was selected for its reliable performance in describing the structures and energies of atmospheric nucleation clusters and reactions through benchmark calculations, with a good balance between accuracy and computational cost.^54,55 An artificial bee colony algorithm software, ABCluster, was employed to determine the global minimum structure of a cluster.⁵⁶ Initially, 1000 structures with lower energies were automatically produced using ABCluster and subsequently pre-optimized using the PM7 semi-empirical method with Mopac software.⁵⁷ Up to 100 structures with relatively lower energies were refined at the level of M06-2X/6-31+G∗, and M06-2X/6–311++G(3df,3pd) was used to further optimize the 30 best-guessed structures to obtain the global minimum structure.

ACDC simulations were conducted using the MATLAB-R2013a program to determine the molecular cluster concentration, evaporation coefficient, and cluster formation mechanism by solving the birth-death equations.^58,59

$$\frac{d{c}_i}{dt}=\frac{1}{2}\sum _{j<i}{\beta }_{j,\left(i-j\right)}{c}_j{c}_{\left(i-j\right)}+\sum _j{\gamma }_{\left(i+j\right)\to i}{c}_{i+j}-\sum _i{\beta }_{i,j}{c}_i{c}_j-\frac{1}{2}\sum _{j<i}{\gamma }_{i\to j}{c}_i+Q_i-S_i$$ (Equation 2)

$${\gamma }_{\left(i+j\right)\to i}={\beta }_{ij}{c}_{ref}\exp \left(\frac{\Delta G_{i+j}-\Delta G_i-\Delta G_j}{k_{b}T}\right)$$ (Equation 3)

$${\beta }_{ij}={\left(\frac{3}{4\mathrm{\pi }}\right)}^{\frac{1}{6}}{\left(\frac{6k_{b}T}{m_i}+\frac{6k_{b}T}{m_j}\right)}^{\frac{1}{2}}{\left(V_i^{\frac{1}{3}}+V_j^{\frac{1}{3}}\right)}^2$$ (Equation 4)

where γ_(i+j)→i is evaporation coefficient and β_ij is the collision coefficient between cluster i and j. The c_ref is the monomer concentration of reference vapor, ΔG_i is the Gibbs free energy of formation of cluster i, V_i and m_i are the volume and mass of cluster i, respectively, T is the temperature, and k_b is the Boltzmann constant.

In this work, the simulation was treated as a “3 × 3” box system in which the total count of acid and base molecules are both in the range of 0–3. Besides, the number of base molecules kept less than the total number of SA molecules. The mobility diameter of the largest cluster is up to 1.67 nm. Furthermore, the present ACDC model mainly performed at 298.15 K, 278.15 K, and 258.15 K (a troposphere temperature range) to probe the temperature effect on formation rates and growth paths. And the boundary clusters were set as (SA)₄·(Base)₃ with “Base” indicating MPA, MAA, and NH₃. Meanwhile, a constant coagulation sink coefficient 1 × 10⁻³ s⁻¹ was used to take into account external losses.

Quantification and statistical analysis

Gaussian 09 program⁵³ was used for geometry optimization. ACDC^58,59 was used to quantify the cluster formation rates, evaporation coefficient, and cluster formation pathways.