the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 29 Oct 2025
Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and agricultural regions
Abstract. Organosulfates (OSs) are key components of atmospheric aerosols and serve as tracers for secondary organic aerosol (SOA) formation. Among these, lactic acid sulfate (LAS) has been increasingly detected in the atmosphere. However, its molecular formation pathways and its role in new particle formation (NPF) remain poorly understood. In this work, we investigate the gas-phase formation mechanism of LAS via the reaction between lactic acid (LA) and SO3, and assess its impact on sulfuric acid-ammonia (SA-A) driven NPF using quantum chemical calculations and Atmospheric Cluster Dynamics Code (ACDC) kinetic modeling. Our results show that SA and H2O significantly catalyze the LA-SO3 reaction, enhancing the effective rate coefficient by 7–10 orders of magnitude within the temperature range of 280–320 K. Further molecular-level analysis using the ACDC reveals that LAS not only significantly enhances the clustering stability of SA and A up to 108-fold, but also plays a significant and direct role in SA-A nucleation under conditions typical of forested and agricultural regions. Notably, LAS-SA-A clusters contribute to 97 % of the overall cluster formation pathways in regions with high LAS concentrations like Centreville, Alabama. Additionally, our findings show that the nucleation potential of LAS-SA-A clusters is stronger than that of LA-SA-A clusters, aligning with field observations, even though LAS concentrations are typically three orders of magnitude lower than LA. These findings imply that OSs formed through SO3 consumption may significantly contribute to the enhanced NPF rates observed in continental regions.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-4894', Anonymous Referee #1, 26 Nov 2025
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AC1: 'Reply on RC1Responses to Referee #1’s comments We are grateful to the reviewers for their valuable and helpful comments on our manuscript “Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and ', Tianlei Zhang, 15 Jan 2026
Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and agricultural regions
Rui Wang, Shuqin Wei‡, Zeyao Li‡, Kaiyu Xue, Rui Bai, Tianlei Zhang*
Shaanxi Key Laboratory of Catalysis, School of Chemical & Environment Science, Shaanxi University of Technology, Hanzhong, Shaanxi 723001, P. R. China
Abstract
Organosulfates (OSs) are key components of atmospheric aerosols and serve as tracers for secondary organic aerosol (SOA) formation. Among these, lactic acid sulfate (LAS) has been increasingly detected in the atmosphere. However, its molecular formation pathways and its role in new particle formation (NPF) remain poorly understood. In this work, we investigate the gas-phase formation mechanism of LAS via the reaction between lactic acid (LA) and SO3, and assess its impact on sulfuric acid-ammonia (SA-A) driven NPF using quantum chemical calculations and Atmospheric Cluster Dynamics Code (ACDC) kinetic modeling. Our results show that SA and H2O significantly catalyze the LA-SO3 reaction, enhancing the effective rate coefficient by 7-10 orders of magnitude within the temperature range of 280-320 K. Further molecular-level analysis using the ACDC reveals that LAS not only significantly enhances the clustering stability of SA and A up to 108-fold, but also plays a significant and direct role in SA-A nucleation under conditions typical of forested and agricultural regions. Notably, LAS-SA-A clusters contribute to 97% of the overall cluster formation pathways in regions with high LAS concentrations like Centreville, Alabama. Additionally, our findings show that the nucleation potential of LAS-SA-A clusters is stronger than that of LA-SA-A clusters, aligning with field observations, even though LAS concentrations are typically three orders of magnitude lower than LA. These findings imply that OSs formed through SO3 consumption may significantly contribute to the enhanced NPF rates observed in continental regions.
- Introduction
Atmospheric aerosol particles pose significant risks to public health, adversely affecting both the respiratory and cardiovascular systems (Anderson et al., 2012; Xing et al., 2016; Zhang et al., 2023b). Beyond health implications, these particles contribute to global warming by reducing visibility and disrupting the Earth’s radiative balance (Lund et al., 2019; Zheng et al., 2018). As a major source of atmospheric aerosols, new particle formation (NPF), accounts for over 50% of the total particle number concentration and is strongly associated with severe haze events in megacities across China (Kulmala et al., 2004; Brean et al., 2020). Despite its significance, accurately characterizing the NPF process remains a considerable challenge, primarily due to limitations in current measurement techniques and an incomplete comprehension of the underlying mechanisms. While field observations and CLOUD chamber experiments (Kulmala et al., 2004; Dai et al., 2023; Lee et al., 2019; Hirsikko et al., 2011; Zhang et al., 2015) have provided valuable insights, they are insufficient to fully elucidate these processes. To address these gaps, a molecular-level approach is essential, as it allows for a more precise understanding of nucleation mechanisms (Yang et al., 2021; Li et al., 2017). This approach enables the detailed determination of molecular cluster geometries, the strengths of intermolecular interactions, and the pathways of cluster formation (Long et al., 2013; Zu et al., 2024b; Rong et al., 2020b). Such molecular insights are critical to evaluating the impacts of aerosols on the atmosphere and for devising effective strategies to mitigate haze formation.
Gaseous sulfuric acid (SA), derived from the oxidation of SO2, has long been recognized as a key NPF precursor (Kirkby et al., 2011; Zhao et al., 2024). Molecular-level studies have shown that various nucleation precursors, including water (H2O) (Zhang et al., 2012b), ammonia (A) (Kirkby et al., 2011; Zhang et al., 2015), methylamine (MA) (Shen et al., 2020), dimethylamine (DMA) (Cai et al., 2021; Kurtén et al., 2008), monoethanolamine (MEA) (Shen et al., 2019), piperazine (PZ) (Ma et al., 2019) and iodic acid (Sipilä et al., 2016), are involved in SA-driven binary nucleation, which serves as a primary initiator of NPF. However, binary nucleation mechanisms alone cannot fully account for the discrepancies observed between measured and modeled global NPF rates (Hodshire et al., 2019; Kirkby et al., 2016), suggesting the involvement of additional gaseous species. Then plenty of low weight molecular organic acids such as glycolic acid (Zhang et al., 2017), malonic acid (Zhang et al., 2018) and pyruvic acid (Tsona Tchinda et al., 2022) also exhibit enhancement effects on ternary nucleation driven by SA-A nucleation system through catalytic mechanisms. Despite recognizing the enhancement provided by SA-A-driven ternary nucleation, the nucleation rates predicted by these mechanisms still fall short when compared to field observations (Kirkby et al., 2016; Hodshire et al., 2019; Yin et al., 2021). The persistent underestimation underscores the need for further investigation into the role of additional gaseous species to better understand the complex mechanisms driving NPF.
Organosulfates (OSs), formed through the chemical transformation of organic acids, constitute a major portion of organosulfur species in atmospheric aerosols, contributing 5-30% to the organic mass in PM10 (Sun et al., 2025; Brüggemann et al., 2017). These compounds are prevalent in atmospheric particles and are commonly employed as markers to track the formation of secondary organic aerosols (SOAs) in environmental research (Tan et al., 2022; Zhang et al., 2012a; Froyd et al., 2010a; Brüggemann et al., 2017; Mutzel et al., 2015; Glasius et al., 2017). Recent research has led to the identification and characterization of various OSs in fine particulate matter samples from regions including the United States, China, Mexico City and Pakistan (Hettiyadura et al., 2017; Wang et al., 2018; Olson et al., 2011). Meanwhile, studies suggest that the cycloaddition of SO3 to organic acids could be a key mechanism for OSs formation resulting in compounds with lower vapor pressures than their parent carboxylic acids and increased inter-molecular interaction sites (Smith et al., 2020; Tan et al., 2020; Yao et al., 2020; Zhang et al., 2023a). Notably, lactic acid sulfate (LAS) has been identified as the dominant OSs species across all these field observations (Darer et al., 2011; Riva et al., 2015; Kundu et al., 2013). However, the specific formation mechanism of LAS from the reaction of lactic acid (LA) with SO3 remains largely unexplored. Additionally, SA and water (H2O) (Tan et al., 2022; Zhang et al., 2025; Li et al., 2018b), both prevalent in the atmosphere, act as strong hydrogen atom donors/acceptors, facilitating proton transfer reactions and potentially catalyzing the LA-SO3 reaction.
The reaction products of SO3 with major atmospheric trace species have been shown proven to significantly influence the formation of NPF. For instance, compounds such as sulfamic acid (Li et al., 2018a), oxalic sulfuric anhydride (Yang et al., 2021), methyl hydrogen sulfate (Liu et al., 2019), glyoxylic sulfuric anhydride (Rong et al., 2020a) and formic acid sulfate (Wang et al., 2025), generated through reactions of SO3 with A, oxalic acid, methanol, glyoxylic acid and formic acid, all exhibit catalytic effects on NPF in aerosols. Structurally, LAS, the product of the SO3 + LA reaction, contains both -COOH and -SO3H functional groups, which facilitate additional hydrogen bonding with atmospheric particle precursors (Yao et al., 2020). However, the role of LAS in enhancing SA-A nucleation remains underexplored, limiting our ability to comprehensively evaluate its impact on NPF processes. Furthermore, LA, a highly oxidized α-hydroxy acid with both -OH and -COOH groups (Mochizuki et al., 2019), can enhance the stability of SA-A clusters and facilitate NPF (Li et al., 2017). Given its relatively larger atmospheric concentrations, particularly in regions with elevated organic acid pollution, LA may also significantly influence NPF. So, understanding the distinct contributions of LAS and LA to SA-A nucleation is crucial, as this will advance our understanding of NPF events, particularly in agricultural and forested regions.
In this work, we utilized quantum chemical calculations together with master equation analysis to investigate the gas-phase reaction of SO3 with LA that forms LAS, with H2O and SA serving as catalysts. The role of LAS in enhancing SA-A nucleation was then explored by examining the formation mechanisms of the (LAS)x(SA)y(A)z (0 ≤ z ≤ x + y ≤ 3) system using the Atmospheric Clusters Dynamic Code (ACDC) kinetic model. Additionally, the potential influence of LAS on atmospheric new particle formation (NPF) was assessed across diverse global regions. Finally, a comparative study of LA and LAS was also conducted to elucidate the respective roles of organic acids and OSs in enhancing SA-A nucleation, focusing on the formation mechanisms of both LA-SA-A and LAS-SA-A systems.
- Methodology
2.1 Quantum chemical calculations
The gas-phase reaction of SO3 with LA to form LAS, both in the absence and presence of H2O and SA as catalysts, was systematically optimized and calculated using the Gaussian 09 program (Faloona et al., 2009) at the M06-2X/6-311++G(2df,2pd) level (Stewart, 2007; Walker et al., 2013). Intrinsic reaction coordinate analyses (Hratchian and Schlegel, 2005) were carried out at the same computational level to verify the connection between transition states and their respective pre-reactive complexes and products. Furthermore, single-point energy calculations were refined at the CCSD(T)-F12/cc-pVDZ-F12 level with the ORCA program (Neese, 2012), employing the optimized geometries as input.
To identify the global minimum energy configurations of (SA)x(A)y(LAS)z clusters ( where 0 ≤ y ≤ x + z ≤ 3), we utilized the ABCluster program (Zhang and Dolg, 2016) to systematically generate initial structures for various clusters combinations. Specifically, using the ABCluster procedure and the CHARMM force field, a diverse set of initial structures n × 1000 (1 ≤ n ≤ 3) were randomly produced. Initially, the primary structures were optimized and their energies were ranked using the PM6 method in MOPAC 2016 (Partanen et al., 2016; Stewart, 2007). After the initial sampling, considering the excellent performance of the M06-2X method in accurately characterizing the geometries of atmospheric clusters (Walker et al., 2013; Lu et al., 2020), up to 1000 favorable configurations were selected for rigorous re-optimization at the M06-2X/3-21G* level of theory. Subsequently, the 100 lowest-energy configurations were further optimized using the M06-2X/6-31G(d, p) level of theory, from which the 10 configurations with the lowest energies were identified. Finally, to accurately determine the global minimum, the M06-2X/6-311++G(2df, 2pd) method was applied to refine these 10 lowest-energy configurations.
2.2 Rate coefficients calculations
Rate constants for the SO3 + LA reaction, both without and with H2O and H2SO4 as catalysts, were determined via Rice-Ramsperger-Kassel-Marcus (RRKM) theory (Glowacki et al., 2012; Wardlaw and Marcus, 1984) within the Master Equation (ME/RRKM) framework in MESMER (Master Equation Solver for Multi-Energy Well Reactions) code (Glowacki et al., 2012; Klippenstein and Marcus, 1988). Specifically, in the MESMER calculations, the rate constants for the barrierless formation of pre-reactive complexes from reactants were determined using the Inverse Laplace Transform (ILT) method (Horváth et al., 2020), whereas the subsequent conversion of these complexes to products via transition states was evaluated using RRKM theory (Mai et al., 2018). The ILT method and RRKM theory can be represented in Eqs. (1) and (2), respectively:
(1)
(2)
Here, h represents Planck’s constant, ρ(E) indicates the density of accessible states for the reactant at energy E, E0 is the reaction threshold energy and W(E-E0) refers to the rovibrational states of the transition state, excluding motion along the reaction coordinate. Geometries, vibrational frequencies, and rotational constants were obtained at the M06-2X/6-311++G(2df,2pd) level, with single-point energies refined at the method of CCSD(T)-F12/cc-pVDZ-F12.
2.3 ACDC kinetics simulation
The ACDC was utilized to investigate the molecular-level collision coefficient (β, cm3 s-1), evaporation coefficient (g, s-1) and cluster formation rates (J, cm-3 s-1). Thermodynamic parameters and structural information for cluster formation, obtained from quantum chemical calculations performed by M06-2X/6-311++G(2df,2pd), served as input parameters for the ACDC model. The MATLAB-R2014a platform, leveraging its odel5s solver (Shampine and Reichelt, 1997), performed numerical integration of the birth-death equation for the ACDC model, thereby elucidating the kinetics of cluster growth over time. The general form of the birth-death equation for the concentration ci of cluster i given by,
(3)
In this formulation, βi,j corresponds to the collision frequency factor between clusters of sizes i and j, γ(i+j)→i quantifies the fragmentation rate of composite clusters into their constituent monomers i and j. The system’s open nature is accounted for through Qi, representing the external flux of cluster i, and Si, characterizing its removal rate. Sensitivity tests were conducted by varying the condensation sink (Cs) from 6 × 10-4 ~ 6 × 10-2 s-1, indicating that the Cs exerted minimal influence on the main conclusions (Fig. S11). Therefore, the Cs was set to a representative value of 2.6 × 10-3 for all subsequent calculations (Liu et al., 2021). Additionally, (LAS)4(A)3, (LAS)4(A)4, (LAS)2(SA)2(A)3, (LAS)2(SA)2(A)4, (LAS)(SA)3(A)3, (LAS)(SA)3(A)4, (SA)4(A)3 and (SA)4(A)4 clusters are acting as boundary clusters for LAS-SA-A system. Also, the details of the contribution of LAS to SA-A nucleation was estimated in the first part of the Supplement.
- Results and discussions
3.1 Formation of LAS via the reaction of SO3 with LA
In the direct cycloaddition pathway (Channel LAS) illustrated in Fig. 1, the hydroxyl (-OH) group of LA reacts with the sulfur atom of SO3, leading to the formation of LAS via proton transfer from LA to SO3. However, the resulting SO3LA complex (denoted as IM) is thermodynamically unstable, primarily due to the significant ring strain in the four-membered structure, exhibiting a relative Gibbs free energy of 5.6 kcal·mol-1. The Gibbs free energy barrier for this reaction is calculated to be 22.3 kcal·mol-1. As indicated in Table S5, the rate coefficients for Channel LAS are extremely low, spanning from 1.35 × 10-26 to 6.21 × 10-25 cm3·molecule-1·s-1 across the temperature range of 230-320 K. These values suggest that this pathway is both slow and thermodynamically unfavorable for LAS formation under typical atmospheric conditions.
H2O, highly abundant in the atmosphere with concentration around 1017 molecules·cm-3 (Huang et al., 2015), serves as both a donor and acceptor of hydrogen bonds, and is widely recognized for its ability to catalyze a wide range of proton transfer reactions. To assess its catalytic effect on the formation of LAS, we examined the SO3 + LA reaction in the presence of H2O (Channel WM), as illustrated in Fig. 1. This reaction can proceed via three possible sequential bimolecular pathways: (i) SO3LA + H2O, (ii) SO3H2O + LA and (iii) LAH2O + SO3. Considering typical atmospheric concentrations of SO3 (105molecules·cm-3) (Zhang et al., 2024), LA (1012 molecules·cm-3) (Li et al., 2017) and H2O (1017 molecules·cm-3) (Huang et al., 2015), the calculated concentrations of SO3LA, SO3H2O and LAH2O complexes at 298 K are 4.18 × 10-2, 5.80 × 103 and 2.32 × 108 molecules·cm-3, respectively (see Table S2 in the Supplement). These results suggest that Channel WM predominantly proceeds via the collision of LAH2O with SO3.
The free energy barrier for Channel WM is 7.8 kcal×mol-1, which is 14.5 kcal×mol-1 lower than the barrier for the uncatalyzed cycloaddition pathway. At the experimental concentration of H2O ([H2O] = 1017 molecules·cm-3) (Huang et al., 2015), the effective rate coefficient for the H2O-catalyzed reaction is 2.00 × 10-16 cm3 molecule-1 s-1, which is nine orders of magnitude greater than the rate for the direct cycloaddition pathway (2.22 × 10-25 cm3 molecule-1 s-1). These results clearly demonstrate that the H2O-catalyzed LA + SO3 reactionrepresents a significantly more favorable route for LAS formation. Detailed effective rate coefficients for the H2O-catalyzed reaction are provided in Fig. 2(a).
SA is another abundant atmospheric species that efficiently donates and accepts hydrogen bond, facilitating proton transfer (Yao et al., 2018; Tan et al., 2018) and potentially catalyzing the LA + SO3 reaction. As shown in Fig. 1, SA is significantly more effective than H2O in promoting LAS formation via cycloaddition. Specifically, SA increases the stabilization energy of the SO3LA complex by 7.1 kcal×mol-1, 5.0 kcal×mol-1 greater than the stabilization provided by H2O and reduces the distance between the oxygen atom of the -OH group in LA and the sulfur atom in SO3 by 0.09 Å in the SO3LASA complex. As compared with six-membered ring transition state TSWM, the transition state TSSA shows eight-membered ring structure, which reduces the ring tension greatly. So, from an energetic point of view, SA lowers the Gibbs free energy barrier to 3.5 kcal×mol-1, 4.3 kcal×mol-1 lower than the barrier observed for the H2O-catalyzed pathway. The effective rate coefficients for the SA ([SA] = 107molecules·cm-3)-catalyzed reaction (k′SA) is 4-5 orders of magnitude higher than that for the H2O-catalyzed pathway (k′WM) at 100 % relative humidity, indicating that SA is kinetically more favorable, particularly at altitudes of 5-10 km. Thus, SA predominantly catalyzes the SO3 + LA reaction, significantly contributing to the gas-phase loss of SO3 in LA-rich atmospheric regions.
Previous theoretical studies have indicated that atmospheric acids can catalyze the hydrolysis of SO3 to form SA (Hazra and Sinha, 2011; Cheng et al., 2022; Long et al., 2013; Lv et al., 2019). In this context, the potential catalytic role of LA in SO3 hydrolysis was also explored. The potential energy surface (PES) for this reaction is presented in Fig. S2, with the effective rate coefficients compared to those for SO3 hydrolysis catalyzed by SA, HNO3, HCOOH, and OA. As shown in Fig. 2(b), LA predominantly catalyzes SO3 hydrolysis within the temperature range of 280-320 K at a concentration of 1.0 × 1012 molecules·cm-3. Besides, given the current lack of atmospheric field data on gas-phase LAS and lactic acid sulfuric anhydride (LASA, the product from the reaction between SO3 and the carboxyl group of LA, Fig. S1), thermodynamic equilibrium calculations were used to estimate their concentrations and assess their potential impacts on atmospheric NPF. Modeling results suggest LAS concentrations of 103-105 molecules·cm-3, which is nine orders of magnitude higher than that of LASA (ranging from 10-6-10-4 molecules·cm-3). This suggests that LAS has significantly more atmospheric relevance than LASA, with a correspondingly higher potential to influence NPF. Detailed calculations and further insights are provided in Table S4.
3.2 Enhancing effect of LAS on SA-A-driven NPF
The role of LAS in promoting SA-A-driven NPF process was thoroughly examined. Initially, potential interaction sites between LAS and SA-A clusters were identified through molecular analyses. Next, the stable structures and thermodynamic stabilities of various (LAS)x(SA)y(A)z (y ≤ x + z ≤ 3) clusters were characterized, providing insight into their structural integrity. Building on these findings, the nucleation mechanism of the SA-A-LAS system was investigated, with a particular focus on the impact of temperature and precursor concentrations on LAS-mediated NPF processes. Finally, the atmospheric implications of LAS-enhanced SA-A nucleation were evaluated, especially in forested and agricultural-developed regions.
3.2.1 Cluster stability analysis
Stable cluster formation is primarily driven by strong interactions between nucleation precursors (Lu and Chen, 2012). To assess the binding potential of LAS with the SA-A cluster, the electrostatic potential (ESP)-mapped molecular van der Waals surface was calculated to identify key interaction sites. As shown in Fig. 3, the hydrogen atom of the -SO3H moiety in LAS exhibits a positive ESP of +78.73 kcal·mol-1, suggesting its role as a hydrogen bond donor that can interact with the double-bonded oxygen atom of SA or the nitrogen atom of A, both of which act as hydrogen bond acceptors. Additionally, the double-bonded oxygen in LAS, with a negative ESP of -32.51 kcal·mol-1, can act as a hydrogen-bond acceptor, interacting with the hydroxyl hydrogen of SA (-OH) or the hydrogen of A. These intermolecular interactions imply that LAS enhances nucleation efficiency between SA and A during aerosol nucleation, thereby stabilizing the resulting molecular clusters. Based on the ESP analysis, the most stable configurations of (LAS)x(SA)y(A)z (z ≤ x + y ≤ 3) clusters were identified (Fig. S3), with the observed interaction sites in the ternary clusters corresponding well to the ESP predictions.
To quantitatively evaluate the binding strength of LAS within binary SA-A-based clusters, the Gibbs free energies (ΔG, kcalmol-1, Table S7) for the (LAS)x(SA)y(A)z (z ≤ x + y ≤ 3) clusters were calculated at temperatures of 238.15 K, 258.15 K, 278.15 K and 298.15 K. All clusters exhibited negative ∆G values, confirming thermodynamic favorability. Importantly, ternary SA-A-LAS clusters consistently demonstrated lower ΔG values compared to their binary counterparts, suggesting that the presence of LAS reinforces the stability of SA-A clusters. Further analysis of stability at 278.15 K was carried out by examining total evaporation rates (åg), derived from cluster ΔG values (Table S7) and collision rates (β, Table S8), as summarized in Fig. 4. Previous research indicates that lower åg are indicative of greater cluster stability (Li et al., 2024; Zu et al., 2024a). At 278.15 K, clusters incorporating LAS exhibit a lower åg compared to those composed solely of SA and A molecules. For example, the åg values for the (A)1·(LAS)1 (1.19 × 104 s-1) and (A)3·(LAS)3 (8.64 × 10-8 s-1) clusters were 3.1-108 times lower than those for the (SA)1·(A)1 (3.73 × 104 s-1) and (SA)3·(A)3 (3.28 × 101 s-1) clusters. Similarly, the åg values of the (SA)1·(A)3·(LAS)2 (1.99 × 100 s-1) and (SA)2·(A)3·(LAS)1 (2.29 × 10-4 s-1) clusters at 278.15 K were found to be 101-105 times lower than the most stable binary cluster, (SA)3·(A)3 (3.28 × 101 s-1). Moreover, these clusters exhibited βC/åg ratios greater than 1 (Table S11), suggesting a favorable balance between cluster growth and evaporation. Similar trends in ΔG and åg were observed across the other temperatures studied, including 238.15 K, 258.15 K and 298.15 K. Taken together, the ΔG and åg analyses provide strong evidence that LAS incorporation enhances SA-A cluster stability, thereby increasing their likelihood of participating in nucleation events.
3.2.2 Cluster formation pathways
To investigate the detailed nucleation pathways of LAS in the formation of SA-A clusters, ACDC simulation were conducted at 278.15 K, with the concentrations of [SA] (106 molecules·cm-3), [A] (109 molecules·cm-3) and [LAS] (105 molecules·cm-3). The results are presented in Fig. 5(a), illustrating two distinct mechanisms for cluster growth. The first pathway (depicted by black arrows) corresponds to pure SA-A clustering, starting from the (SA)1·(A)1 dimer. Subsequent stepwise addition of SA or A monomers drives the assembly of progressively larger and more stable clusters such as (SA)3·(A)3, which eventually exit the system. The second pathway (depicted by blue arrows) includes clusters containing LAS, in which LAS performs two distinct roles: one as a “catalyst” and the other as a “participant”. When LAS acts as a “catalyst”, the (SA)1·(A)2·(LAS)1 trimer collides with the SA monomer, forming the (SA)2·(A)2·(LAS)1 cluster. Subsequently, LAS evaporates from the cluster, leaving behind the (SA)2·(A)2 cluster. Meanwhile, when LAS acts as a “participant”, collisions between the (SA)1·(A)1 dimer and LAS monomers lead to the assembly of the (SA)1·(A)1·(LAS)1 cluster. This trimer then undergoes further collisions with either an SA or A monomer, producing the (SA)2·(A)3·(LAS)1 cluster, which ultimately grows out of the system. These dual roles of LAS in SA-A clusters are observed across other temperatures of 298.15 K, 238.15 K and 258.15 K; however, at lower temperatures, such as 238.15 K, the LAS-involved pathway simplifies (as shown in Figs. S8, S9 and S10).
As shown in Fig. 5(b), the contributions of LAS to the SA-A nucleation process were examined across a range of temperatures, with a focus on the nucleation mechanism that involves LAS participation. As temperature increases, the influence of LAS-involved pathways becomes progressively more dominant, due to the elevated vapor pressure of LAS raises its gas-phase concentration, thereby promoting further cluster formation. At lower temperatures (238.15 and 258.15 K), SA-A clustering remains the dominant process, accounting for 73% of nucleation events, while LAS-involved pathways contribute a modest 21%, because of the reduced collision frequency of LAS. However, as the temperature rises to 278.15 K, LAS participation increases to 33%, signaling a more prominent role in cluster growth. At 298.15 K, this contribution further rises to 49%, nearly double that observed at the lower temperatures. These results highlight the crucial role of elevated temperatures in enhancing LAS’s contribution to SA-A nucleation, emphasizing the temperature-dependent amplification of LAS-driven cluster formation.
3.2.3 Atmospheric implications of LAS
In addition to temperature, the concentrations of precursors play a pivotal role in SA-A aerosol nucleation. Atmospheric LAS concentrations exhibit considerable variability across different global environments (Tan et al., 2022; Mochizuki et al., 2017; Ristovski et al., 2010; Hettiyadura et al., 2017; Kanellopoulos et al., 2022). For example, lower LAS concentrations, ranging from 1.00 × 104 to 8.34 × 105 molecules·cm-3, are found in regions such as eucalypt forest (Ristovski et al., 2010), Mt. Tai (China) (Mochizuki et al., 2017) and Athens (Kanellopoulos et al., 2022). In contrast, higher LAS concentrations have been recorded in Centreville, Alabama (1.77 × 106 molecules·cm-3) (Hettiyadura et al., 2017), with peak levels in Patra (Kanellopoulos et al., 2022) , reaching up to 1.70 × 107 molecules·cm-3. Similarly, the concentrations of SA and A vary, with SA ranging from 104-107 molecules∙cm-3 (Zhang et al., 2024; Ding et al., 2019), and A ranging from 107-1011 molecules∙cm-3 (Wu et al., 2017; Luo et al., 2014). Elevated concentrations of these species are particularly prominent in regions such as northern China, the Midwestern United States, and agricultural areas in Europe. Based on field observations of LAS, SA and A concentrations, the contribution of LAS to SA-A nucleation was systematically assessed. As illustrated in Fig. S18, the impact of LAS on the SA-A system is primarily governed by the concentrations of LAS and SA, with minimal dependence on [A]. Consequently, Fig. 6 illustrates how the contribution ratio of LAS varies with different concentrations of SA and LAS, under the previously identified favorable high-temperature condition of 278.15 K.
The three pie charts in the upper map illustrate the changing contribution of LAS to SA-A aerosol nucleation as SA concentration increases from 3.00 × 104 to 6.00 × 104 molecules⸱cm-3, with a corresponding decrease in LAS contribution as [SA] rises. In regions characterized by low SA concentrations (3.00 × 104 molecules⸱cm-3), such as Hyytiälä, nucleation is predominantly driven by the LAS-SA-A pathway, contributing approximately 93%. However, at higher SA concentrations (up to 2.00 × 106 molecules⸱cm-3), such as on the west coast of Ireland (O'dowd et al., 2002), the LAS contribution drops from 93% to 33%. At even higher SA levels (up to 1.00 × 107 molecules⸱cm-3), LAS-involved pathways account for only 18% of the total nucleation flux, as observed in Beijing, China (Wang et al., 2011). In contrast, environments with typically high SA concentrations, such as urban and industrial areas, promote SA-A self-aggregation nucleation, thereby diminishing the relative contribution of LAS (Fig. S10). These findings highlight that lower [SA] levels substantially amplify the contribution of LAS contribution to SA-A aerosol nucleation.
The contribution of LAS to SA-A aerosol nucleation increases with LAS concentration, ranging from 1.00 × 104 to 1.77 × 106 molecules⸱cm-3, as shown in the pie chart below the map. This pattern indicates a positive correlation between LAS concentration and its contribution to nucleation. In regions with low LAS concentrations (1.00 × 104 molecules⸱cm-3), such as eucalypt forests (Ristovski et al., 2010), LAS-mediated pathways account for only 15% of the total nucleation flux. While LAS contributes to the initial stages of cluster formation, it subsequently evaporates from the pre-nucleation cluster, ultimately functioning in a catalyst-like capacity (Fig. S16). In areas with moderate LAS concentrations, such as Athens (8.34 × 105 molecules⸱cm-3) (Kanellopoulos et al., 2022) and Mt. Tai (1.00 × 105 molecules⸱cm-3) (Mochizuki et al., 2017), LAS contribution increases substantially, rising from 15% to 73%. At high [LAS], as observed in the Centreville, Alabama (1.77 × 106 molecules·cm-3) (Hettiyadura et al., 2017), LAS-driven nucleation becomes dominant, resulting in a ‘participant’ synergistic nucleation mechanism that works like ‘hand in hand’ (Fig. S17), contributing up to 97 % of the total nucleation rate. These findings underscore that elevated LAS concentrations significantly enhance SA-A nucleation. Thus, in regions characterized by high T, low [SA], high [A] and high [LAS], especially in agricultural-developed areas and forested areas, the LAS contribution to SA-A aerosol nucleation can be substantial.
3.3 The comparison of enhancement effect between LAS and LA
To evaluate the relative enhancing effects of LA versus LAS in the typical SA-A-driven nucleation. The ΔG (pink histograms) and åg (red points) of the (LAS)x(SA)y(A)3 and (LA)x(SA)y(A)3 (x = 0 - 3, x + y = 3) clusters at 278.15 K are presented in Fig. 7(a) as a comparison. The (SA)3(A)3 cluster, the thermodynamic minimum of the SA-A system (Chen et al., 2025; Li et al., 2020), was chosen as a reference for comparison. Relative to this baseline, (LA)1-3(SA)0-2(A)3 clusters consistently exhibited higher ΔG values, elevated by roughly 18.36-41.94 kcal·mol-1. In contrast, (LAS)1-3(SA)0-2(A)3 clusters were slightly more stable, differing from the reference by only 0.09-5.80 kcal·mol-1. This suggests that LAS incorporation leads to a slight stabilization of the cluster relative to LA.
Moreover, the evaporation rate (åg) of the (Org)x(SA)y(A)3 (Org = LA and LAS; x =1-3，x + y =3) clusters do not exhibit a simple relationship with the proportion of organic components within the clusters. The highest åg was observed for the (Org)2·(SA)1·(A)3 (Org = LA and LAS) clusters, regardless of whether LA or LAS was used. For the (LAS)1·(SA)2·(A)3 and (LAS)3·(A)3 clusters, the åg ranged from 10-4 to 10-1 s-1, lower than that of the (SA)3·(A)3 cluster, indicating that replacing one or three SA molecules with LAS enhances the thermodynamic stability of the clusters. In contrast, the åg of the LA-SA-A clusters were found to be higher than those of the corresponding LAS-SA-A and (SA)3·(A)3 clusters, as displayed in Fig. 7(a). The LAS-SA-A clusters exhibit more negative ΔG values and lower åg, suggesting that their formation is thermodynamically more favorable than that of the LA-SA-A system. This enhanced stability can be attributed to stronger interactions between LAS and SA-A systems relative to those between LA and SA-A. Based on these results, we can conclude that LAS, produced through the LA + SO3 reaction, more effectively stabilizes the SA-A system than LA itself.
Fig. 7(b) illustrates the variation in the cluster formation rate (J) and enhancement strength (R) as a function of [LAS] and [LA] at 278.15 K, under the condition of [SA] = 106 molecules·cm-3 and [A]=109 molecules·cm-3. In the LAS-SA-A system, J increases sharply with rising [LAS], particularly when [LAS] exceeds 105 molecules·cm-3. As [LAS] grows from 105 to 106 molecules·cm-3, J for the LAS-SA-A system rises by three orders of magnitude, whereas in the LA-SA-A system, J exhibits only a modest increase from 3.36 × 10-9 to 1.12 × 10-8 cm-3 s-1, consistent with the corresponding increase in [LA] (Fig. 7b). Although LAS concentrations are typically three orders of magnitude lower than LA (Tan et al., 2022), LAS exerts a substantially stronger enhancement effect in SA-A-driven nucleation. These contrasting trends are primarily due to the combined influence of cluster thermodynamic properties ΔG and åg, and the concentrations of organic species within the respective systems. The sharp increase in J for the LAS-SA-A system stems from the favorable ΔG and low åg of the (LAS)x(SA)y(A)z clusters, along with the relatively high non-equilibrium concentration of LAS. In contrast, the less favorable ΔG and higher åg of the (LA)x(SA)y(A)z clusters limit the kinetic efficiency of the LA-SA-A system, even at elevated [LA].
This study reveals that the reaction of LA and SO3 generates LAS which acts as an effective atmospheric nucleation precursor and significantly accelerates SA-A nucleation. Consequently, atmospheric LA can react with part of SO3, potentially accounting for the relatively low observed low SA concentration, while the generated LAS markedly promotes SA-A-driven NPF under such conditions. To date, the effects of hydroxy acids and their derivatives on atmospheric NPF have not been comprehensively investigated. The mechanism proposed here offers a general approach to evaluate the roles of these acids, like 2-Methylglyceric acid, aromatic acids and their derivates, influence atmospheric nucleation processes. Incorporating this novel OSs pathways into contemporary atmospheric models will advance the quantitative understanding of OSs’ contributions to aerosol formation. Furthermore, OSs originating from secondary processes, such as gas-phase chemical reactions, deserve further observation and evaluation.
- Conclusions
In this study, quantum chemical calculations, master equation analysis, and the ACDC kinetic model were employed to investigate the cycloaddition reaction between SO3 and LA, the role of LAS in SA-A nucleation, and its impact on NPF.
Quantum chemical results in the gas phase indicate that SA and H2O effectively lower the reaction barriers for LAS formation from the LA-SO3 reaction, functioning as catalysts and even enabling a barrierless reaction. The effective rate coefficient for the SO3-LA reaction catalyzed by SA (107 molecules·cm-3) is 4-5 times higher than the pathway catalyzed by H2O (1017 molecules·cm-3), making it more effective, particularly at altitudes of 5-10 km. Additionally, the effective rate coefficients for LA (1012 molecules·cm-3) catalyzing the SO3 + H2O → SA reaction is about 101-104 times larger than the corresponding values for SO3 hydrolysis catalyzed by H2SO4 (107 molecules·cm-3), HNO3 (109 molecules·cm-3), HCOOH (1011 molecules·cm-3), and OA (109 molecules·cm-3), indicating that LA primarily catalyzes SO3 hydrolysis within the temperature range of 280-320 K.
LAS, functioning as both a hydrogen-bond donor and acceptor, participates in SA-A-driven ternary nucleation, directly interacting with SA and A. Gibbs free energy analysis demonstrates that ternary SA-A-LAS clusters consistently exhibit lower ΔG values than their binary counterparts, suggesting that LAS incorporation stabilizes the SA-A clusters. ACDC kinetic simulations further demonstrate that LAS significantly enhances NPF, especially at low temperatures, low SA concentration, and high A and LAS concentrations. In regions with elevated LAS concentrations, such as Centreville, Alabama, particle formation rates can increase by up to 108-fold, with SA-A-LAS clusters contributing up to 97% of the overall cluster formation pathways. It is noteworthy that LAS not only acts as a catalyst in enhancing SA-A cluster stability but also directly participates in nucleation. Moreover, LAS exerts a stronger enhancement effect than LA, making it a more effective stabilizing agent for atmospheric NPF. These findings suggest that LAS plays a critical role in enhancing SA-A-driven NPF in forested and agriculturally developed regions, providing insights into previously unaccounted NPF sources and refining nucleation models.
This study deepens the understanding of OSs formation in organic acid-polluted regions and underscores the potential contribution of other OSs to NPF. Neglecting the contribution of OSs in the SA-A aerosol nucleation, particularly in forested and agricultural regions, may lead to an underestimation of organic aerosol nucleation risks.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No: 22203052; 22073059) and the Funds of Graduate Innovation of Shaanxi University of Technology (No: SLGYCX2506).
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Map source: ©Google Maps (https://www.google.com/maps)
Graphic abstract
Fig. 1 Potential energy profiles and corresponding molecular structures for the LA + SO3 → LAS reaction in the absence and presence of H2O and H2SO4 investigated at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311++G(2df,2pd) level
Fig. 2 (a) Effective rate constants for the LA + SO3 → LAS reaction in the presence of H2O (k'WM, cm3·molecule-1·s-1) and H2SO4 (k'SA, cm3·molecule-1·s-1) calculated using the master equation over the temperature range of 230-320 K; (b) Effective rate constants (k', s-1) for the hydrolysis of SO3 with various species X (X = LA, SA, NA, FA and OA) within the temperature range of 230-320 K, where SA, NA, FA and OA are denoted as H2SO4, HNO3, HCOOH and H2C2O4, respectively.
Fig. 3 Electrostatic potential (ESP)-mapped van der Waals surfaces of A, LAS and SA molecules. ESP minima and maxima for different functional groups are shown as blue and yellow spheres, respectively, with their corresponding values (kcalmol-1) indicated in parentheses. Red arrows denote preferred directions for hydrogen bond formation, while blue arrows illustrate likely pathways for proton transfer.
Fig. 4 The total evaporation rates (∑γ) (s-1) of (SA)x(A)y(LAS)z (y ≤ x + z ≤ 3) clusters at 278.15 K and 1 atm calculated at the M06-2X/6-311++G(2df, 2pd) level of theory. (a) without LAS monomer, (b) containing 1 LAS monomer, (c) containing 2 LAS monomers, and (d) containing 3 LAS monomers
Fig. 5 Nucleation mechanism of the LAS-SA-A system. (a) Cluster formation pathway at 278.15 K, with concentrations of [SA] = 106, [A] = 109 and [LAS] = 105 molecules·cm-3; (b) the branch ratio of outward flux at different temperatures. Only net fluxes contributing more than 5% to cluster growth are depicted.
Fig. 6 Branching ratios of SA-A-LAS (red) and SA-A (blue) cluster growth pathways in regions with varying [LAS] concentrations. Black data points indicate field observations, while blue points represent the median values used in this study. Ammonia concentration is fixed at 109 molecules·cm-3. Map source: ©Google Maps (https://www.google.com/maps)
Fig. 7 (a) Gibbs free energies ΔG (kcalmol-1) and total evaporation rates ∑γ (s−1) for (LA)x(SA)y(A)3 and (LAS)x(SA)y(A)3 (x = 0-3, x + y = 3) clusters calculated at the M06-2X/6-311++G(2df, 2pd) level of theory and 278.15 K; (b) Cluster formation rate (J) and enhancement strength (R) for LAS as a function of monomer concentrations ([LA] and [LAS]) at 278.15 K, with [SA] fixed at 105 molecules·cm-3 and [A] at 109 molecules·cm-3.
* Corresponding authors Tel: +86-0916-2641083, Fax: +86-0916-2641083.
E-mail addresses: ztianlei88@l63.com (T. L Zhang)
‡ Shuqin Wei and Zeyao Li contributed equally to this work.
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AC3: 'Reply on AC1', Tianlei Zhang, 15 Jan 2026
Responses to Referee #1’s comments
We are grateful to the reviewers for their valuable and helpful comments on our manuscript “Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and agricultural regions” (Manuscript ID: egusphere-2025-4894). We have revised the manuscript carefully according to reviewers’ comments. The point-to-point responses to the Referee #1’s comments are summarized below:
Referee Comments:
The manuscript by Wang et al. presents a comprehensive theoretical investigation into the formation mechanism of lactic acid sulfate (LAS) and its unexpected role in enhancing sulfuric acid-ammonia (SA-A) driven new particle formation (NPF). The combination of quantum chemical calculations and ACDC kinetic modeling provides molecular-level insights into the catalytic effects of SA and H2O on LAS formation and the role of LAS in enhancing SA-A nucleation. This study advances our molecular-level mechanistic understanding of how organosulfates influence nucleation events. The manuscript is well-structured and clearly written. Therefore, I recommend publication of this manuscript after consideration of the following comments.
Response: We would like to thank the reviewer for the positive and valuable comments, and we have revised our manuscript accordingly.
Specific Comments:
Comment 1:
In the Introduction (Lines 52-53), the rationale for specifically investigating the enhancement of the SA-A system is introduced somewhat abruptly. The transition to this focus would be strengthened by briefly outlining the existing evidence or theoretical basis that suggests such an enhancement is plausible and significant.
Response: Thank you for your valuable comments. To better transition to the focus on the ternary nucleation process driven by SA-A, relevant existing studies and theoretical foundations have been added in the introduction, emphasizing the plausibility and significance of this enhancement effect, thereby providing a clearer rationale for investigating the enhancement of the SA-A system. According to the reviewer’s suggestion, in Lines 52-55 Page 2 of the revised manuscript, the sentence of “In response to this, several studies have explored the role of ternary nucleation driven by SA-A, which involves a broader array of atmospheric species, including ammonia (NH3) (Li et al., 2020b; Yin et al., 2021a), organic amines (Li et al., 2017; Li et al., 2018a), organic and inorganic acids (Wang et al., 2011; Liu et al., 2018), and highly oxidized multifunctional compounds (HOMs) (Liu et al., 2021a; Liu et al., 2019a; Ning and Zhang, 2022; Yin et al., 2021b; Zhang et al., 2018).” has been changed as “Then plenty of low weight molecular organic acids such as glycolic acid (Zhang et al., 2017), malonic acid (Zhang et al., 2018) and pyruvic acid (Tsona Tchinda et al., 2022) also exhibit enhancement effects on ternary nucleation driven by SA-A nucleation system through catalytic mechanisms.”.
Comment 2:
The acronym “SA-A” (where “A” stands for ammonia) is inconsistent with the use of “NH₃” throughout the text. This can be confusing for readers. For improved readability, please adopt a single, consistent acronym.
Response: Thanks for the suggestion of the reviewer. We apologize for the misunderstanding about ammonia. As the suggestion of the reviewer, the name of ammonia have been corrected. Specifically, ammonia has been labeled as “ammonia (A)” when they are first used. Besides, when they are used again, ammonia has been labeled as “A”. The specific revisions are as follows:
(a) In Line 45 Page 2 of the revised manuscript, the “ammonia (NH3)” has been changed as “ammonia (A)”.
(b) In Line 82 Page 3 of the revised manuscript, the “ammonia” has been changed as “A”.
Comment 3:
In Section 2.1, regarding the search for the global minimum configuration of the (SA)x(A)y(LAS)z clusters (when y = 3, x + z = 3), it is unclear whether the sampling of 4000 initial configurations is sufficient to adequately explore the complex conformational space.
Response: Thanks for your valuable comments. Indeed, a multi-path searching approach is utilized to explore the stable structures of (LAS)x(SA)y(A)z ( where 0 ≤ y ≤ x + z ≤ 3). For each global minimum cluster of (LAS)x(SA)y(A)z ( where 0 ≤ y ≤ x + z ≤ 3), n different searching pathways were considered to ensure a thorough exploration of the complex conformational space. Specifically, a single monomer is incorporated to form a larger cluster on top of the existing smaller ones. For instance, in the process of searching for the stable structure of (SA)2·(A) clusters, two search pathways exist: (SA)·(A) + SA and (SA)2 + A. Similarly, in the search for the stable structure of (LAS)·(SA)·(A) clusters, three pathways are considered: (SA)·(A) + LAS, (SA)·(LAS) + A and (LAS)·(A) + SA. Additionally, we apologize for the incorrect range of n values previously used. Upon reviewing all the search pathways, we confirm that the correct range for n is 1 ≤ n ≤ 3, rather than n = 2 to 4. Consequently, the sentence of “a diverse set of initial structures n × 1000 (1 < n ≤ 4) were randomly produced.” has been changed as “a diverse set of initial structures n × 1000 (1 ≤ n ≤ 3) were randomly produced.” in Line 115 on Page 5 of the revised manuscript.
Comment 4:
The computational details, such as the definition of boundary clusters and the coagulation sink in the ACDC simulations, should be more thoroughly described in the main text or supplementary information to ensure reproducibility.
Response: Thank you for your valuable comments. According to your suggestion, boundary conditions and the coagulation sink in the ACDC simulations have been added in Lines 155-160 Page 6 of the revised manuscript, which has been organized as “Sensitivity tests were conducted by varying the condensation sink (Cs) from 6 × 10-4 ~ 6 × 10-2 s-1, indicating that the Cs exerted minimal influence on the main conclusions (Fig. S11). Therefore, the Cs was set to a representative value of 2.6 × 10-3 for all subsequent calculations(Liu et al., 2021). Additionally, (LAS)4(A)3, (LAS)4(A)4, (LAS)2(SA)2(A)3, (LAS)2(SA)2(A)4, (LAS)(SA)3(A)3, (LAS)(SA)3(A)4, (SA)4(A)3 and (SA)4(A)4 clusters are acting as boundary clusters for LAS-SA-A system.”.
Comment 5:
Line 210, please explain the reason for introducing lactic acid sulfuric anhydride (LASA). A clarification on its chemical relationship and distinction to LAS would be helpful for readers to follow the viewpoint.
Response: Thank you for your valuable comments. Following your suggestion, the distinctions between lactic acid sulfate (LAS) and lactic acid sulfuric anhydride (LASA) have been clarified. Both LAS and LASA are products of the reaction between SO3 and lactic acid (LA). LAS is generated via esterification of the hydroxyl group of LA with SO3, whereas LASA is formed through cycloaddition of the carboxyl group of LA, as illustrated by the potential energy surfaces in Fig. S1. Based on this, the detailed introduction of LASA has been clarified and added in Lines 215-216 Page 8 of the revised manuscript, which has been organized as“LASA, the product from the reaction between SO3 and the carboxyl group of LA, Fig. S1”.
Comment 6:
In Section 3.2.3, please clarify how “LAS contribution” is quantitatively calculated. Specifically, is it determined by the fraction of outgrowing clusters that contain at least one LAS molecule? A brief description of the calculation methodology is needed.
Response: Thank you for your valuable comments. According to your suggestion, regarding the calculation of the final outgoing fluxes of LAS in the ACDC simulations have been added in Lines 160-161 Page 6 of the revised manuscript, which has been organized as “Also, the details of the contribution of LAS to SA-A nucleation was estimated in the first part of the Supplement”.
To further elaborate on the computational procedures, we have included the specific outgoing fluxes of LAS in the ACDC simulations in the supplementary material, organized as follows: “To quantify the contribution of LAS to SA-A nucleation, we analyzed the steady-state cluster formation fluxes (J) output by ACDC. The LAS-related nucleation fraction at a given temperature was defined as the ratio of the total formation flux of all nucleated clusters containing at least one LAS molecule to the total nucleation flux from all pathways. Specifically,
(S1)
where Jout(Ci) denotes the outgoing flux of cluster Ci that meets the nucleation criterion (size/composition threshold), and CLAS represents the set of all nucleated clusters containing one or more LAS molecules. This metric directly reflects the proportion of new particles formed through LAS-involved pathways under steady-state conditions.”.
Comment 7:
In Section 3.2.3, the authors state that LAS contributions are more pronounced in forested and agricultural regions. It would be helpful to clarify why these regions exhibit higher LAS relevance compared to urban or industrial areas.
Response: Thank you for your valuable comments. The influence of LAS on sulfuric acid-ammonia (SA-A)-driven new particle formation (NPF) show that, under elevated SA concentrations, such as those commonly observed in urban or industrial environments, the dominant effect of SA suppresses the nucleation-promoting role of LAS, thereby substantially diminishing its contribution to nucleation. In contrast, in forested and agricultural regions characterized by relatively low SA concentrations and more abundant sources of LAS, LAS exhibits a markedly stronger nucleation-promoting effect within the sulfuric SA-A system. Accordingly, we infer that in forested and agricultural regions, which are typically characterized by low SA concentrations, LAS plays a pronounced role in promoting SA-A nucleation. The corresponding explanations can be mainly attributed to two aspects.
(a) The enhancement factor R in the SA-A-based system is strongly influenced by the concentrations of both SA and LAS. To illustrate this dependence, Fig. S10 shows R as functions of [SA] and [LAS] under the conditions of [A] = 109 molecules∙cm-3 and T = 278.15 K. As depicted in Fig. S10, the R increases as the [SA] decreases. At low [SA] (105 molecules·cm-3), the R value reaches its maximum of 1.32 × 107 fold at [LAS] = 106 molecules∙cm-3. In contrast, at high [SA] (107 molecules·cm-3), the influence of [LAS] on R is markedly reduced, resulting in a 1.54 fold increase in R at [LAS] = 106 molecules∙cm-3. Based on the above analysis, in Lines 322-324 Page 12 of the revised manuscript, the discussion of why agricultural-developed and forested areas exhibit higher LAS relevance compared to urban or industrial areas, which has been added and organized as “In contrast, environments with typically high SA concentrations, such as urban and industrial areas, promote SA-A self-aggregation nucleation, thereby diminishing the relative contribution of LAS (Fig. S10).”
Fig. S10 Enhancement factor R as functions of [SA] and [LAS] at [A] = 109 molecules·cm-3 and 278.15 K.
(b) During formation of LAS via the reaction of SO3 with LA strongly competes with SA formation. To further evaluate the competitive interactions between LAS and SA molecules, another set of ACDC simulations was conducted, considering different ratios of the concentrations of LAS and SA ([LAS]/[SA]) and varying the total concentration of LAS and SA. Fig. S12 shows particle formation rates (J, cm-3·s-1) with varying ratios of [LAS]:[SA] at 278.15 K under different concentrations ((a)107 molecules∙cm-3, (b)109 molecules∙cm-3 and (c)1011 molecules∙cm-3). The specific revisions are as follows:
Fig. S12 Particle formation rates (J, cm-3·s-1) with varying ratios of [LAS]:[SA] at 278.15 K under different concentrations ((a)107 molecules∙cm-3, (b)109 molecules∙cm-3, (c)1011 molecules∙cm-3). [LAS] + [SA] = 104-108 molecules∙cm-3
The corresponding revision has been added and organized as “The observed concentration dependence indicates that the LAS-driven nucleation process becomes particularly significant in environments with moderate to high LAS concentrations and relatively low SA levels. Therefore, in the LAS-SA-A ternary nucleation system, LAS is likely to function as an “acid” molecule, exhibiting a competitive effect. To evaluate the competitive interactions between LAS and SA molecules, another set of ACDC simulations was conducted, considering different ratios of the concentrations of LAS and SA ([LAS]/[SA]) and varying the total concentration of LAS and SA. Fig. S12 shows the variation of JLAS/SA with the total concentrations of SA and LAS at A concentrations of 107, 109, and 1011 molecules∙cm-3.
As shown in Fig. S12(a), at lower atmospheric concentration of A (107 molecules∙cm-3), the formation rate JLAS/SA increases with the substitution percentage. At a 50% substitution rate ([LAS]:[SA] = 1:1), JLAS/SA sharply increases to 1.46 × 10-9 cm-3·s-1, which is larger by 1-2 orders of magnitude than the value at unsubstituted condition. At a 99% substitution rate ([LAS]:[SA] = 99:1), JLAS/SA reaches its maximum value of 6.99 × 10-9 cm-3·s-1, which is 1-3 orders of magnitude greater than the value under non-substituted conditions. These results indicate that, at lower atmospheric concentrations of A, the enhancing effect of LAS on the SA-A group particle formation rate increases with the substitution percentage. At intermediate (109 molecules∙cm-3) and higher concentrations (1011 molecules∙cm-3) of atmospheric A, the JLAS/SA at a 99% substitution rate ([LAS]:[SA] = 99:1) reaches its maximum value (Fig. S12(b) and Fig. S12(c)). Compared to the JLAS/SA under non-substituted conditions, the value at a 99% substitution rate is increased by one order of magnitude. In contrast, urban and industrial environments, which typically have high SA concentrations, favor SA-A self-aggregation nucleation, thereby reducing the relative contribution of LAS. Thus, in regions characterized by high T, low [SA], high [A] and high [LAS], especially in agricultural-developed areas and forested areas, the LAS contribution to SA-A aerosol nucleation can be substantial.” in the supplementary material.
Comment 8:
Line 398 and Line 17: “particle formation rates can increase by up to 108-fold”, if this value is provided in the SI, please indicate where it can be found.
Response: Thanks for your valuable comments. We apologize for not clearly citing the source of this data in the previous version of the manuscript. According to the reviewer’s suggestion, the specific data indicating that particle formation rates can increase by up to 108-fold has been clarified in the revised manuscript. The supporting data can be directly viewed in Fig. S5(b).
Comment 9:
Some minor mistakes are shown in the manuscript, e.g., Line 64: “PM10”; Line 100: “nucleation and particle formation (NPF)”; Line 267: “exits the system”; Line 348: “negative negative ΔG values”; Line 64: “whereas in the LAS-SA-A system” and so on. Please totally and carefully recheck the whole manuscript and correct all the mistakes.
Response: Thanks to the reviewer’s insightful comment, we are sorry for the trouble we have caused by oversight. In order to improve the accuracy of the expression, the corresponding main revision has been made as follows:
(a) In Line 62 Page 3 of the revised manuscript, “PM10” has been changed as “PM10”.
(b) In Line 98 Page 4 of the revised manuscript, “nucleation and particle formation (NPF)” has been changed as “new particle formation (NPF)”.
(c) In Line 272 Page 10 of the revised manuscript, “exits the system” has been changed as “exit the system”.
(d) In Line 360 Page 13 of the revised manuscript, “negative negative ΔG values” has been changed as “negative ΔG values”.
(f) In Line 369 Page 13 of the revised manuscript, “whereas in the LAS-SA-A system” has been changed as “whereas in the LA-SA-A system”.
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AC1: 'Reply on RC1Responses to Referee #1’s comments We are grateful to the reviewers for their valuable and helpful comments on our manuscript “Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and ', Tianlei Zhang, 15 Jan 2026
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RC2: 'Comment on egusphere-2025-4894', Anonymous Referee #2, 28 Nov 2025
Wang et al. utilized quantum chemical calculations, master equation analysis, and Atmospheric Clusters Dynamic Code kinetic model to systematically investigate the formation mechanism of lactic acid sulfate (LAS) and its enhancing effect on sulfuric acid (SA)–NH3(A) nucleation. Particular attention is given to the reaction between lactic acid and SO3, the catalytic effects of H2O/SA, and the dual role played by LAS in the SA–A–LAS ternary system (both as a participant and as a catalyst). The topic is novel, the methodology is sound, and the work provides an important—yet previously underappreciated—mechanistic explanation for the unusually high NPF rates observed in forested and agricultural regions. Most of this manuscript is well written and will be of broad interest to the readers of Atmospheric Chemistry and Physics. I recommend its publication in the journal, provided that the following comments are addressed.
Specific Comments:
- The results indicate that the barriers to the reaction between lactic acid and SO3 are substantially reduced with the addition of SA. However, the underlying mechanism driving SA’s pronounced catalytic effect has not been adequately addressed. Providing one or two specific structural characteristics, such as the lengths of critical hydrogen bonds or specific geometric changes in transition states, would clarify why SA exhibits higher catalytic efficiency than H2O, thereby allowing readers to fully comprehend the mechanism driving the “barrier reduction”.
- The authors’ calculations reveal that the dominant nucleation pathways shift with temperature, however, the manuscript does not adequately explain why the contribution of LAS-related pathways increases with increasing temperature. Further clarification of the underlying mechanism is required, such as whether this behavior is associated with variations in collision frequency or the fact that LAS exhibits a relatively weak temperature dependence in its evaporation rate. Incorporating such an explanation would greatly enhance the interpretability of the trend presented in Fig. 5 of the manuscript.
- The manuscript proposes that LAS may function either as a “participant” or as a “catalyst-like promoter,” which is an interesting and meaningful finding. At present, the distinction between these two roles is mainly inferred from the ACDC pathways in Fig. 5 (i.e., whether LAS ultimately remains in the cluster), whereas Fig. 6 and Fig. 7 primarily illustrate how the contribution of LAS varies with temperature and precursor concentrations. Their connection to the role distinction is not explicitly established. To make the origin of this “dual role” clearer, a brief clarification in the discussion section would help enhance the manuscript’s logical coherence assist readers in better understanding how LAS behaves under different conditions.
- I suggest the authors explicitly outline how boundary conditions were set in their ACDC simulations, along with justifying the maximum cluster size they selected. Nucleation rates are often sensitive to the choice of boundary conditions. Accordingly, it is essential to clarify why setting the maximum cluster size at x + y + z ≤ 3 was adequate for their simulations, or alternatively, to discuss the implications of extending this boundary to larger clusters. Even a short, targeted explanation would greatly enhance the clarity and reproducibility of the methodology.
- A single value of 2.6 × 10-3 s-1 was adopted for the condensation sink in the ACDC kinetics simulation under different atmospheric conditions of agricultural and forested regions (Figure 6), without addressing whether this parameter is representative of such diverse conditions. In practice, condensation sinks can vary by orders of magnitude depending on aerosol loading. Hence, the manuscript ought to explain the rationale for using a single CS value across all cases, or discuss the uncertainties associated with this choice for the cluster formation rates or pathways. Including such justification would greatly enhance the credibility of the modeled nucleation rates.
Technical corrections:
Page 6 line 161: “In the direct cycloaddition pathway (Channel LAS) illsutrated in Fig. 1”
The word “illsutrated” should be corrected to “illustrated”. In addition, there is a spelling error in the caption of Fig. 4, where “nunber” should be corrected to “number.”
Page 5 line 114: “To identity the global minimum energy configurations of …”
The word “identity” should be corrected to “identify”.
Page 10 line 278: “… the contributions of LAS to the SA-A nucleation process was examined, …”
The word “was” should be corrected to “were”.
Page 12 lines 325-326: “LAS-driven nucleation becomes dominate, …”
The word “dominate” should be corrected to “dominant”.
Page 21 lines 665-672: In the reference list, Yin et al., 2021a and Yin et al., 2021b share the same title and page numbers (Acid-base clusters during atmospheric new particle formation in urban Beijing” Environ. Sci. Technol., 55, 10994–11005). Please remove the duplicate references and update the citation numbers in the main text.
Citation: https://doi.org/10.5194/egusphere-2025-4894-RC2 -
AC2: 'Reply on RC2Responses to Referee #2’s comments We are grateful to the reviewers for their valuable and helpful comments on our manuscript “Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and ', Tianlei Zhang, 15 Jan 2026
Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and agricultural regions
Rui Wang, Shuqin Wei‡, Zeyao Li‡, Kaiyu Xue, Rui Bai, Tianlei Zhang*
Shaanxi Key Laboratory of Catalysis, School of Chemical & Environment Science, Shaanxi University of Technology, Hanzhong, Shaanxi 723001, P. R. China
Abstract
Organosulfates (OSs) are key components of atmospheric aerosols and serve as tracers for secondary organic aerosol (SOA) formation. Among these, lactic acid sulfate (LAS) has been increasingly detected in the atmosphere. However, its molecular formation pathways and its role in new particle formation (NPF) remain poorly understood. In this work, we investigate the gas-phase formation mechanism of LAS via the reaction between lactic acid (LA) and SO3, and assess its impact on sulfuric acid-ammonia (SA-A) driven NPF using quantum chemical calculations and Atmospheric Cluster Dynamics Code (ACDC) kinetic modeling. Our results show that SA and H2O significantly catalyze the LA-SO3 reaction, enhancing the effective rate coefficient by 7-10 orders of magnitude within the temperature range of 280-320 K. Further molecular-level analysis using the ACDC reveals that LAS not only significantly enhances the clustering stability of SA and A up to 108-fold, but also plays a significant and direct role in SA-A nucleation under conditions typical of forested and agricultural regions. Notably, LAS-SA-A clusters contribute to 97% of the overall cluster formation pathways in regions with high LAS concentrations like Centreville, Alabama. Additionally, our findings show that the nucleation potential of LAS-SA-A clusters is stronger than that of LA-SA-A clusters, aligning with field observations, even though LAS concentrations are typically three orders of magnitude lower than LA. These findings imply that OSs formed through SO3 consumption may significantly contribute to the enhanced NPF rates observed in continental regions.
- Introduction
Atmospheric aerosol particles pose significant risks to public health, adversely affecting both the respiratory and cardiovascular systems (Anderson et al., 2012; Xing et al., 2016; Zhang et al., 2023b). Beyond health implications, these particles contribute to global warming by reducing visibility and disrupting the Earth’s radiative balance (Lund et al., 2019; Zheng et al., 2018). As a major source of atmospheric aerosols, new particle formation (NPF), accounts for over 50% of the total particle number concentration and is strongly associated with severe haze events in megacities across China (Kulmala et al., 2004; Brean et al., 2020). Despite its significance, accurately characterizing the NPF process remains a considerable challenge, primarily due to limitations in current measurement techniques and an incomplete comprehension of the underlying mechanisms. While field observations and CLOUD chamber experiments (Kulmala et al., 2004; Dai et al., 2023; Lee et al., 2019; Hirsikko et al., 2011; Zhang et al., 2015) have provided valuable insights, they are insufficient to fully elucidate these processes. To address these gaps, a molecular-level approach is essential, as it allows for a more precise understanding of nucleation mechanisms (Yang et al., 2021; Li et al., 2017). This approach enables the detailed determination of molecular cluster geometries, the strengths of intermolecular interactions, and the pathways of cluster formation (Long et al., 2013; Zu et al., 2024b; Rong et al., 2020b). Such molecular insights are critical to evaluating the impacts of aerosols on the atmosphere and for devising effective strategies to mitigate haze formation.
Gaseous sulfuric acid (SA), derived from the oxidation of SO2, has long been recognized as a key NPF precursor (Kirkby et al., 2011; Zhao et al., 2024). Molecular-level studies have shown that various nucleation precursors, including water (H2O) (Zhang et al., 2012b), ammonia (A) (Kirkby et al., 2011; Zhang et al., 2015), methylamine (MA) (Shen et al., 2020), dimethylamine (DMA) (Cai et al., 2021; Kurtén et al., 2008), monoethanolamine (MEA) (Shen et al., 2019), piperazine (PZ) (Ma et al., 2019) and iodic acid (Sipilä et al., 2016), are involved in SA-driven binary nucleation, which serves as a primary initiator of NPF. However, binary nucleation mechanisms alone cannot fully account for the discrepancies observed between measured and modeled global NPF rates (Hodshire et al., 2019; Kirkby et al., 2016), suggesting the involvement of additional gaseous species. Then plenty of low weight molecular organic acids such as glycolic acid (Zhang et al., 2017), malonic acid (Zhang et al., 2018) and pyruvic acid (Tsona Tchinda et al., 2022) also exhibit enhancement effects on ternary nucleation driven by SA-A nucleation system through catalytic mechanisms. Despite recognizing the enhancement provided by SA-A-driven ternary nucleation, the nucleation rates predicted by these mechanisms still fall short when compared to field observations (Kirkby et al., 2016; Hodshire et al., 2019; Yin et al., 2021). The persistent underestimation underscores the need for further investigation into the role of additional gaseous species to better understand the complex mechanisms driving NPF.
Organosulfates (OSs), formed through the chemical transformation of organic acids, constitute a major portion of organosulfur species in atmospheric aerosols, contributing 5-30% to the organic mass in PM10 (Sun et al., 2025; Brüggemann et al., 2017). These compounds are prevalent in atmospheric particles and are commonly employed as markers to track the formation of secondary organic aerosols (SOAs) in environmental research (Tan et al., 2022; Zhang et al., 2012a; Froyd et al., 2010a; Brüggemann et al., 2017; Mutzel et al., 2015; Glasius et al., 2017). Recent research has led to the identification and characterization of various OSs in fine particulate matter samples from regions including the United States, China, Mexico City and Pakistan (Hettiyadura et al., 2017; Wang et al., 2018; Olson et al., 2011). Meanwhile, studies suggest that the cycloaddition of SO3 to organic acids could be a key mechanism for OSs formation resulting in compounds with lower vapor pressures than their parent carboxylic acids and increased inter-molecular interaction sites (Smith et al., 2020; Tan et al., 2020; Yao et al., 2020; Zhang et al., 2023a). Notably, lactic acid sulfate (LAS) has been identified as the dominant OSs species across all these field observations (Darer et al., 2011; Riva et al., 2015; Kundu et al., 2013). However, the specific formation mechanism of LAS from the reaction of lactic acid (LA) with SO3 remains largely unexplored. Additionally, SA and water (H2O) (Tan et al., 2022; Zhang et al., 2025; Li et al., 2018b), both prevalent in the atmosphere, act as strong hydrogen atom donors/acceptors, facilitating proton transfer reactions and potentially catalyzing the LA-SO3 reaction.
The reaction products of SO3 with major atmospheric trace species have been shown proven to significantly influence the formation of NPF. For instance, compounds such as sulfamic acid (Li et al., 2018a), oxalic sulfuric anhydride (Yang et al., 2021), methyl hydrogen sulfate (Liu et al., 2019), glyoxylic sulfuric anhydride (Rong et al., 2020a) and formic acid sulfate (Wang et al., 2025), generated through reactions of SO3 with A, oxalic acid, methanol, glyoxylic acid and formic acid, all exhibit catalytic effects on NPF in aerosols. Structurally, LAS, the product of the SO3 + LA reaction, contains both -COOH and -SO3H functional groups, which facilitate additional hydrogen bonding with atmospheric particle precursors (Yao et al., 2020). However, the role of LAS in enhancing SA-A nucleation remains underexplored, limiting our ability to comprehensively evaluate its impact on NPF processes. Furthermore, LA, a highly oxidized α-hydroxy acid with both -OH and -COOH groups (Mochizuki et al., 2019), can enhance the stability of SA-A clusters and facilitate NPF (Li et al., 2017). Given its relatively larger atmospheric concentrations, particularly in regions with elevated organic acid pollution, LA may also significantly influence NPF. So, understanding the distinct contributions of LAS and LA to SA-A nucleation is crucial, as this will advance our understanding of NPF events, particularly in agricultural and forested regions.
In this work, we utilized quantum chemical calculations together with master equation analysis to investigate the gas-phase reaction of SO3 with LA that forms LAS, with H2O and SA serving as catalysts. The role of LAS in enhancing SA-A nucleation was then explored by examining the formation mechanisms of the (LAS)x(SA)y(A)z (0 ≤ z ≤ x + y ≤ 3) system using the Atmospheric Clusters Dynamic Code (ACDC) kinetic model. Additionally, the potential influence of LAS on atmospheric new particle formation (NPF) was assessed across diverse global regions. Finally, a comparative study of LA and LAS was also conducted to elucidate the respective roles of organic acids and OSs in enhancing SA-A nucleation, focusing on the formation mechanisms of both LA-SA-A and LAS-SA-A systems.
- Methodology
2.1 Quantum chemical calculations
The gas-phase reaction of SO3 with LA to form LAS, both in the absence and presence of H2O and SA as catalysts, was systematically optimized and calculated using the Gaussian 09 program (Faloona et al., 2009) at the M06-2X/6-311++G(2df,2pd) level (Stewart, 2007; Walker et al., 2013). Intrinsic reaction coordinate analyses (Hratchian and Schlegel, 2005) were carried out at the same computational level to verify the connection between transition states and their respective pre-reactive complexes and products. Furthermore, single-point energy calculations were refined at the CCSD(T)-F12/cc-pVDZ-F12 level with the ORCA program (Neese, 2012), employing the optimized geometries as input.
To identify the global minimum energy configurations of (SA)x(A)y(LAS)z clusters ( where 0 ≤ y ≤ x + z ≤ 3), we utilized the ABCluster program (Zhang and Dolg, 2016) to systematically generate initial structures for various clusters combinations. Specifically, using the ABCluster procedure and the CHARMM force field, a diverse set of initial structures n × 1000 (1 ≤ n ≤ 3) were randomly produced. Initially, the primary structures were optimized and their energies were ranked using the PM6 method in MOPAC 2016 (Partanen et al., 2016; Stewart, 2007). After the initial sampling, considering the excellent performance of the M06-2X method in accurately characterizing the geometries of atmospheric clusters (Walker et al., 2013; Lu et al., 2020), up to 1000 favorable configurations were selected for rigorous re-optimization at the M06-2X/3-21G* level of theory. Subsequently, the 100 lowest-energy configurations were further optimized using the M06-2X/6-31G(d, p) level of theory, from which the 10 configurations with the lowest energies were identified. Finally, to accurately determine the global minimum, the M06-2X/6-311++G(2df, 2pd) method was applied to refine these 10 lowest-energy configurations.
2.2 Rate coefficients calculations
Rate constants for the SO3 + LA reaction, both without and with H2O and H2SO4 as catalysts, were determined via Rice-Ramsperger-Kassel-Marcus (RRKM) theory (Glowacki et al., 2012; Wardlaw and Marcus, 1984) within the Master Equation (ME/RRKM) framework in MESMER (Master Equation Solver for Multi-Energy Well Reactions) code (Glowacki et al., 2012; Klippenstein and Marcus, 1988). Specifically, in the MESMER calculations, the rate constants for the barrierless formation of pre-reactive complexes from reactants were determined using the Inverse Laplace Transform (ILT) method (Horváth et al., 2020), whereas the subsequent conversion of these complexes to products via transition states was evaluated using RRKM theory (Mai et al., 2018). The ILT method and RRKM theory can be represented in Eqs. (1) and (2), respectively:
(1)
(2)
Here, h represents Planck’s constant, ρ(E) indicates the density of accessible states for the reactant at energy E, E0 is the reaction threshold energy and W(E-E0) refers to the rovibrational states of the transition state, excluding motion along the reaction coordinate. Geometries, vibrational frequencies, and rotational constants were obtained at the M06-2X/6-311++G(2df,2pd) level, with single-point energies refined at the method of CCSD(T)-F12/cc-pVDZ-F12.
2.3 ACDC kinetics simulation
The ACDC was utilized to investigate the molecular-level collision coefficient (β, cm3 s-1), evaporation coefficient (g, s-1) and cluster formation rates (J, cm-3 s-1). Thermodynamic parameters and structural information for cluster formation, obtained from quantum chemical calculations performed by M06-2X/6-311++G(2df,2pd), served as input parameters for the ACDC model. The MATLAB-R2014a platform, leveraging its odel5s solver (Shampine and Reichelt, 1997), performed numerical integration of the birth-death equation for the ACDC model, thereby elucidating the kinetics of cluster growth over time. The general form of the birth-death equation for the concentration ci of cluster i given by,
(3)
In this formulation, βi,j corresponds to the collision frequency factor between clusters of sizes i and j, γ(i+j)→i quantifies the fragmentation rate of composite clusters into their constituent monomers i and j. The system’s open nature is accounted for through Qi, representing the external flux of cluster i, and Si, characterizing its removal rate. Sensitivity tests were conducted by varying the condensation sink (Cs) from 6 × 10-4 ~ 6 × 10-2 s-1, indicating that the Cs exerted minimal influence on the main conclusions (Fig. S11). Therefore, the Cs was set to a representative value of 2.6 × 10-3 for all subsequent calculations (Liu et al., 2021). Additionally, (LAS)4(A)3, (LAS)4(A)4, (LAS)2(SA)2(A)3, (LAS)2(SA)2(A)4, (LAS)(SA)3(A)3, (LAS)(SA)3(A)4, (SA)4(A)3 and (SA)4(A)4 clusters are acting as boundary clusters for LAS-SA-A system. Also, the details of the contribution of LAS to SA-A nucleation was estimated in the first part of the Supplement.
- Results and discussions
3.1 Formation of LAS via the reaction of SO3 with LA
In the direct cycloaddition pathway (Channel LAS) illustrated in Fig. 1, the hydroxyl (-OH) group of LA reacts with the sulfur atom of SO3, leading to the formation of LAS via proton transfer from LA to SO3. However, the resulting SO3LA complex (denoted as IM) is thermodynamically unstable, primarily due to the significant ring strain in the four-membered structure, exhibiting a relative Gibbs free energy of 5.6 kcal·mol-1. The Gibbs free energy barrier for this reaction is calculated to be 22.3 kcal·mol-1. As indicated in Table S5, the rate coefficients for Channel LAS are extremely low, spanning from 1.35 × 10-26 to 6.21 × 10-25 cm3·molecule-1·s-1 across the temperature range of 230-320 K. These values suggest that this pathway is both slow and thermodynamically unfavorable for LAS formation under typical atmospheric conditions.
H2O, highly abundant in the atmosphere with concentration around 1017 molecules·cm-3 (Huang et al., 2015), serves as both a donor and acceptor of hydrogen bonds, and is widely recognized for its ability to catalyze a wide range of proton transfer reactions. To assess its catalytic effect on the formation of LAS, we examined the SO3 + LA reaction in the presence of H2O (Channel WM), as illustrated in Fig. 1. This reaction can proceed via three possible sequential bimolecular pathways: (i) SO3LA + H2O, (ii) SO3H2O + LA and (iii) LAH2O + SO3. Considering typical atmospheric concentrations of SO3 (105molecules·cm-3) (Zhang et al., 2024), LA (1012 molecules·cm-3) (Li et al., 2017) and H2O (1017 molecules·cm-3) (Huang et al., 2015), the calculated concentrations of SO3LA, SO3H2O and LAH2O complexes at 298 K are 4.18 × 10-2, 5.80 × 103 and 2.32 × 108 molecules·cm-3, respectively (see Table S2 in the Supplement). These results suggest that Channel WM predominantly proceeds via the collision of LAH2O with SO3.
The free energy barrier for Channel WM is 7.8 kcal×mol-1, which is 14.5 kcal×mol-1 lower than the barrier for the uncatalyzed cycloaddition pathway. At the experimental concentration of H2O ([H2O] = 1017 molecules·cm-3) (Huang et al., 2015), the effective rate coefficient for the H2O-catalyzed reaction is 2.00 × 10-16 cm3 molecule-1 s-1, which is nine orders of magnitude greater than the rate for the direct cycloaddition pathway (2.22 × 10-25 cm3 molecule-1 s-1). These results clearly demonstrate that the H2O-catalyzed LA + SO3 reactionrepresents a significantly more favorable route for LAS formation. Detailed effective rate coefficients for the H2O-catalyzed reaction are provided in Fig. 2(a).
SA is another abundant atmospheric species that efficiently donates and accepts hydrogen bond, facilitating proton transfer (Yao et al., 2018; Tan et al., 2018) and potentially catalyzing the LA + SO3 reaction. As shown in Fig. 1, SA is significantly more effective than H2O in promoting LAS formation via cycloaddition. Specifically, SA increases the stabilization energy of the SO3LA complex by 7.1 kcal×mol-1, 5.0 kcal×mol-1 greater than the stabilization provided by H2O and reduces the distance between the oxygen atom of the -OH group in LA and the sulfur atom in SO3 by 0.09 Å in the SO3LASA complex. As compared with six-membered ring transition state TSWM, the transition state TSSA shows eight-membered ring structure, which reduces the ring tension greatly. So, from an energetic point of view, SA lowers the Gibbs free energy barrier to 3.5 kcal×mol-1, 4.3 kcal×mol-1 lower than the barrier observed for the H2O-catalyzed pathway. The effective rate coefficients for the SA ([SA] = 107molecules·cm-3)-catalyzed reaction (k′SA) is 4-5 orders of magnitude higher than that for the H2O-catalyzed pathway (k′WM) at 100 % relative humidity, indicating that SA is kinetically more favorable, particularly at altitudes of 5-10 km. Thus, SA predominantly catalyzes the SO3 + LA reaction, significantly contributing to the gas-phase loss of SO3 in LA-rich atmospheric regions.
Previous theoretical studies have indicated that atmospheric acids can catalyze the hydrolysis of SO3 to form SA (Hazra and Sinha, 2011; Cheng et al., 2022; Long et al., 2013; Lv et al., 2019). In this context, the potential catalytic role of LA in SO3 hydrolysis was also explored. The potential energy surface (PES) for this reaction is presented in Fig. S2, with the effective rate coefficients compared to those for SO3 hydrolysis catalyzed by SA, HNO3, HCOOH, and OA. As shown in Fig. 2(b), LA predominantly catalyzes SO3 hydrolysis within the temperature range of 280-320 K at a concentration of 1.0 × 1012 molecules·cm-3. Besides, given the current lack of atmospheric field data on gas-phase LAS and lactic acid sulfuric anhydride (LASA, the product from the reaction between SO3 and the carboxyl group of LA, Fig. S1), thermodynamic equilibrium calculations were used to estimate their concentrations and assess their potential impacts on atmospheric NPF. Modeling results suggest LAS concentrations of 103-105 molecules·cm-3, which is nine orders of magnitude higher than that of LASA (ranging from 10-6-10-4 molecules·cm-3). This suggests that LAS has significantly more atmospheric relevance than LASA, with a correspondingly higher potential to influence NPF. Detailed calculations and further insights are provided in Table S4.
3.2 Enhancing effect of LAS on SA-A-driven NPF
The role of LAS in promoting SA-A-driven NPF process was thoroughly examined. Initially, potential interaction sites between LAS and SA-A clusters were identified through molecular analyses. Next, the stable structures and thermodynamic stabilities of various (LAS)x(SA)y(A)z (y ≤ x + z ≤ 3) clusters were characterized, providing insight into their structural integrity. Building on these findings, the nucleation mechanism of the SA-A-LAS system was investigated, with a particular focus on the impact of temperature and precursor concentrations on LAS-mediated NPF processes. Finally, the atmospheric implications of LAS-enhanced SA-A nucleation were evaluated, especially in forested and agricultural-developed regions.
3.2.1 Cluster stability analysis
Stable cluster formation is primarily driven by strong interactions between nucleation precursors (Lu and Chen, 2012). To assess the binding potential of LAS with the SA-A cluster, the electrostatic potential (ESP)-mapped molecular van der Waals surface was calculated to identify key interaction sites. As shown in Fig. 3, the hydrogen atom of the -SO3H moiety in LAS exhibits a positive ESP of +78.73 kcal·mol-1, suggesting its role as a hydrogen bond donor that can interact with the double-bonded oxygen atom of SA or the nitrogen atom of A, both of which act as hydrogen bond acceptors. Additionally, the double-bonded oxygen in LAS, with a negative ESP of -32.51 kcal·mol-1, can act as a hydrogen-bond acceptor, interacting with the hydroxyl hydrogen of SA (-OH) or the hydrogen of A. These intermolecular interactions imply that LAS enhances nucleation efficiency between SA and A during aerosol nucleation, thereby stabilizing the resulting molecular clusters. Based on the ESP analysis, the most stable configurations of (LAS)x(SA)y(A)z (z ≤ x + y ≤ 3) clusters were identified (Fig. S3), with the observed interaction sites in the ternary clusters corresponding well to the ESP predictions.
To quantitatively evaluate the binding strength of LAS within binary SA-A-based clusters, the Gibbs free energies (ΔG, kcalmol-1, Table S7) for the (LAS)x(SA)y(A)z (z ≤ x + y ≤ 3) clusters were calculated at temperatures of 238.15 K, 258.15 K, 278.15 K and 298.15 K. All clusters exhibited negative ∆G values, confirming thermodynamic favorability. Importantly, ternary SA-A-LAS clusters consistently demonstrated lower ΔG values compared to their binary counterparts, suggesting that the presence of LAS reinforces the stability of SA-A clusters. Further analysis of stability at 278.15 K was carried out by examining total evaporation rates (åg), derived from cluster ΔG values (Table S7) and collision rates (β, Table S8), as summarized in Fig. 4. Previous research indicates that lower åg are indicative of greater cluster stability (Li et al., 2024; Zu et al., 2024a). At 278.15 K, clusters incorporating LAS exhibit a lower åg compared to those composed solely of SA and A molecules. For example, the åg values for the (A)1·(LAS)1 (1.19 × 104 s-1) and (A)3·(LAS)3 (8.64 × 10-8 s-1) clusters were 3.1-108 times lower than those for the (SA)1·(A)1 (3.73 × 104 s-1) and (SA)3·(A)3 (3.28 × 101 s-1) clusters. Similarly, the åg values of the (SA)1·(A)3·(LAS)2 (1.99 × 100 s-1) and (SA)2·(A)3·(LAS)1 (2.29 × 10-4 s-1) clusters at 278.15 K were found to be 101-105 times lower than the most stable binary cluster, (SA)3·(A)3 (3.28 × 101 s-1). Moreover, these clusters exhibited βC/åg ratios greater than 1 (Table S11), suggesting a favorable balance between cluster growth and evaporation. Similar trends in ΔG and åg were observed across the other temperatures studied, including 238.15 K, 258.15 K and 298.15 K. Taken together, the ΔG and åg analyses provide strong evidence that LAS incorporation enhances SA-A cluster stability, thereby increasing their likelihood of participating in nucleation events.
3.2.2 Cluster formation pathways
To investigate the detailed nucleation pathways of LAS in the formation of SA-A clusters, ACDC simulation were conducted at 278.15 K, with the concentrations of [SA] (106 molecules·cm-3), [A] (109 molecules·cm-3) and [LAS] (105 molecules·cm-3). The results are presented in Fig. 5(a), illustrating two distinct mechanisms for cluster growth. The first pathway (depicted by black arrows) corresponds to pure SA-A clustering, starting from the (SA)1·(A)1 dimer. Subsequent stepwise addition of SA or A monomers drives the assembly of progressively larger and more stable clusters such as (SA)3·(A)3, which eventually exit the system. The second pathway (depicted by blue arrows) includes clusters containing LAS, in which LAS performs two distinct roles: one as a “catalyst” and the other as a “participant”. When LAS acts as a “catalyst”, the (SA)1·(A)2·(LAS)1 trimer collides with the SA monomer, forming the (SA)2·(A)2·(LAS)1 cluster. Subsequently, LAS evaporates from the cluster, leaving behind the (SA)2·(A)2 cluster. Meanwhile, when LAS acts as a “participant”, collisions between the (SA)1·(A)1 dimer and LAS monomers lead to the assembly of the (SA)1·(A)1·(LAS)1 cluster. This trimer then undergoes further collisions with either an SA or A monomer, producing the (SA)2·(A)3·(LAS)1 cluster, which ultimately grows out of the system. These dual roles of LAS in SA-A clusters are observed across other temperatures of 298.15 K, 238.15 K and 258.15 K; however, at lower temperatures, such as 238.15 K, the LAS-involved pathway simplifies (as shown in Figs. S8, S9 and S10).
As shown in Fig. 5(b), the contributions of LAS to the SA-A nucleation process were examined across a range of temperatures, with a focus on the nucleation mechanism that involves LAS participation. As temperature increases, the influence of LAS-involved pathways becomes progressively more dominant, due to the elevated vapor pressure of LAS raises its gas-phase concentration, thereby promoting further cluster formation. At lower temperatures (238.15 and 258.15 K), SA-A clustering remains the dominant process, accounting for 73% of nucleation events, while LAS-involved pathways contribute a modest 21%, because of the reduced collision frequency of LAS. However, as the temperature rises to 278.15 K, LAS participation increases to 33%, signaling a more prominent role in cluster growth. At 298.15 K, this contribution further rises to 49%, nearly double that observed at the lower temperatures. These results highlight the crucial role of elevated temperatures in enhancing LAS’s contribution to SA-A nucleation, emphasizing the temperature-dependent amplification of LAS-driven cluster formation.
3.2.3 Atmospheric implications of LAS
In addition to temperature, the concentrations of precursors play a pivotal role in SA-A aerosol nucleation. Atmospheric LAS concentrations exhibit considerable variability across different global environments (Tan et al., 2022; Mochizuki et al., 2017; Ristovski et al., 2010; Hettiyadura et al., 2017; Kanellopoulos et al., 2022). For example, lower LAS concentrations, ranging from 1.00 × 104 to 8.34 × 105 molecules·cm-3, are found in regions such as eucalypt forest (Ristovski et al., 2010), Mt. Tai (China) (Mochizuki et al., 2017) and Athens (Kanellopoulos et al., 2022). In contrast, higher LAS concentrations have been recorded in Centreville, Alabama (1.77 × 106 molecules·cm-3) (Hettiyadura et al., 2017), with peak levels in Patra (Kanellopoulos et al., 2022) , reaching up to 1.70 × 107 molecules·cm-3. Similarly, the concentrations of SA and A vary, with SA ranging from 104-107 molecules∙cm-3 (Zhang et al., 2024; Ding et al., 2019), and A ranging from 107-1011 molecules∙cm-3 (Wu et al., 2017; Luo et al., 2014). Elevated concentrations of these species are particularly prominent in regions such as northern China, the Midwestern United States, and agricultural areas in Europe. Based on field observations of LAS, SA and A concentrations, the contribution of LAS to SA-A nucleation was systematically assessed. As illustrated in Fig. S18, the impact of LAS on the SA-A system is primarily governed by the concentrations of LAS and SA, with minimal dependence on [A]. Consequently, Fig. 6 illustrates how the contribution ratio of LAS varies with different concentrations of SA and LAS, under the previously identified favorable high-temperature condition of 278.15 K.
The three pie charts in the upper map illustrate the changing contribution of LAS to SA-A aerosol nucleation as SA concentration increases from 3.00 × 104 to 6.00 × 104 molecules⸱cm-3, with a corresponding decrease in LAS contribution as [SA] rises. In regions characterized by low SA concentrations (3.00 × 104 molecules⸱cm-3), such as Hyytiälä, nucleation is predominantly driven by the LAS-SA-A pathway, contributing approximately 93%. However, at higher SA concentrations (up to 2.00 × 106 molecules⸱cm-3), such as on the west coast of Ireland (O'dowd et al., 2002), the LAS contribution drops from 93% to 33%. At even higher SA levels (up to 1.00 × 107 molecules⸱cm-3), LAS-involved pathways account for only 18% of the total nucleation flux, as observed in Beijing, China (Wang et al., 2011). In contrast, environments with typically high SA concentrations, such as urban and industrial areas, promote SA-A self-aggregation nucleation, thereby diminishing the relative contribution of LAS (Fig. S10). These findings highlight that lower [SA] levels substantially amplify the contribution of LAS contribution to SA-A aerosol nucleation.
The contribution of LAS to SA-A aerosol nucleation increases with LAS concentration, ranging from 1.00 × 104 to 1.77 × 106 molecules⸱cm-3, as shown in the pie chart below the map. This pattern indicates a positive correlation between LAS concentration and its contribution to nucleation. In regions with low LAS concentrations (1.00 × 104 molecules⸱cm-3), such as eucalypt forests (Ristovski et al., 2010), LAS-mediated pathways account for only 15% of the total nucleation flux. While LAS contributes to the initial stages of cluster formation, it subsequently evaporates from the pre-nucleation cluster, ultimately functioning in a catalyst-like capacity (Fig. S16). In areas with moderate LAS concentrations, such as Athens (8.34 × 105 molecules⸱cm-3) (Kanellopoulos et al., 2022) and Mt. Tai (1.00 × 105 molecules⸱cm-3) (Mochizuki et al., 2017), LAS contribution increases substantially, rising from 15% to 73%. At high [LAS], as observed in the Centreville, Alabama (1.77 × 106 molecules·cm-3) (Hettiyadura et al., 2017), LAS-driven nucleation becomes dominant, resulting in a ‘participant’ synergistic nucleation mechanism that works like ‘hand in hand’ (Fig. S17), contributing up to 97 % of the total nucleation rate. These findings underscore that elevated LAS concentrations significantly enhance SA-A nucleation. Thus, in regions characterized by high T, low [SA], high [A] and high [LAS], especially in agricultural-developed areas and forested areas, the LAS contribution to SA-A aerosol nucleation can be substantial.
3.3 The comparison of enhancement effect between LAS and LA
To evaluate the relative enhancing effects of LA versus LAS in the typical SA-A-driven nucleation. The ΔG (pink histograms) and åg (red points) of the (LAS)x(SA)y(A)3 and (LA)x(SA)y(A)3 (x = 0 - 3, x + y = 3) clusters at 278.15 K are presented in Fig. 7(a) as a comparison. The (SA)3(A)3 cluster, the thermodynamic minimum of the SA-A system (Chen et al., 2025; Li et al., 2020), was chosen as a reference for comparison. Relative to this baseline, (LA)1-3(SA)0-2(A)3 clusters consistently exhibited higher ΔG values, elevated by roughly 18.36-41.94 kcal·mol-1. In contrast, (LAS)1-3(SA)0-2(A)3 clusters were slightly more stable, differing from the reference by only 0.09-5.80 kcal·mol-1. This suggests that LAS incorporation leads to a slight stabilization of the cluster relative to LA.
Moreover, the evaporation rate (åg) of the (Org)x(SA)y(A)3 (Org = LA and LAS; x =1-3，x + y =3) clusters do not exhibit a simple relationship with the proportion of organic components within the clusters. The highest åg was observed for the (Org)2·(SA)1·(A)3 (Org = LA and LAS) clusters, regardless of whether LA or LAS was used. For the (LAS)1·(SA)2·(A)3 and (LAS)3·(A)3 clusters, the åg ranged from 10-4 to 10-1 s-1, lower than that of the (SA)3·(A)3 cluster, indicating that replacing one or three SA molecules with LAS enhances the thermodynamic stability of the clusters. In contrast, the åg of the LA-SA-A clusters were found to be higher than those of the corresponding LAS-SA-A and (SA)3·(A)3 clusters, as displayed in Fig. 7(a). The LAS-SA-A clusters exhibit more negative ΔG values and lower åg, suggesting that their formation is thermodynamically more favorable than that of the LA-SA-A system. This enhanced stability can be attributed to stronger interactions between LAS and SA-A systems relative to those between LA and SA-A. Based on these results, we can conclude that LAS, produced through the LA + SO3 reaction, more effectively stabilizes the SA-A system than LA itself.
Fig. 7(b) illustrates the variation in the cluster formation rate (J) and enhancement strength (R) as a function of [LAS] and [LA] at 278.15 K, under the condition of [SA] = 106 molecules·cm-3 and [A]=109 molecules·cm-3. In the LAS-SA-A system, J increases sharply with rising [LAS], particularly when [LAS] exceeds 105 molecules·cm-3. As [LAS] grows from 105 to 106 molecules·cm-3, J for the LAS-SA-A system rises by three orders of magnitude, whereas in the LA-SA-A system, J exhibits only a modest increase from 3.36 × 10-9 to 1.12 × 10-8 cm-3 s-1, consistent with the corresponding increase in [LA] (Fig. 7b). Although LAS concentrations are typically three orders of magnitude lower than LA (Tan et al., 2022), LAS exerts a substantially stronger enhancement effect in SA-A-driven nucleation. These contrasting trends are primarily due to the combined influence of cluster thermodynamic properties ΔG and åg, and the concentrations of organic species within the respective systems. The sharp increase in J for the LAS-SA-A system stems from the favorable ΔG and low åg of the (LAS)x(SA)y(A)z clusters, along with the relatively high non-equilibrium concentration of LAS. In contrast, the less favorable ΔG and higher åg of the (LA)x(SA)y(A)z clusters limit the kinetic efficiency of the LA-SA-A system, even at elevated [LA].
This study reveals that the reaction of LA and SO3 generates LAS which acts as an effective atmospheric nucleation precursor and significantly accelerates SA-A nucleation. Consequently, atmospheric LA can react with part of SO3, potentially accounting for the relatively low observed low SA concentration, while the generated LAS markedly promotes SA-A-driven NPF under such conditions. To date, the effects of hydroxy acids and their derivatives on atmospheric NPF have not been comprehensively investigated. The mechanism proposed here offers a general approach to evaluate the roles of these acids, like 2-Methylglyceric acid, aromatic acids and their derivates, influence atmospheric nucleation processes. Incorporating this novel OSs pathways into contemporary atmospheric models will advance the quantitative understanding of OSs’ contributions to aerosol formation. Furthermore, OSs originating from secondary processes, such as gas-phase chemical reactions, deserve further observation and evaluation.
- Conclusions
In this study, quantum chemical calculations, master equation analysis, and the ACDC kinetic model were employed to investigate the cycloaddition reaction between SO3 and LA, the role of LAS in SA-A nucleation, and its impact on NPF.
Quantum chemical results in the gas phase indicate that SA and H2O effectively lower the reaction barriers for LAS formation from the LA-SO3 reaction, functioning as catalysts and even enabling a barrierless reaction. The effective rate coefficient for the SO3-LA reaction catalyzed by SA (107 molecules·cm-3) is 4-5 times higher than the pathway catalyzed by H2O (1017 molecules·cm-3), making it more effective, particularly at altitudes of 5-10 km. Additionally, the effective rate coefficients for LA (1012 molecules·cm-3) catalyzing the SO3 + H2O → SA reaction is about 101-104 times larger than the corresponding values for SO3 hydrolysis catalyzed by H2SO4 (107 molecules·cm-3), HNO3 (109 molecules·cm-3), HCOOH (1011 molecules·cm-3), and OA (109 molecules·cm-3), indicating that LA primarily catalyzes SO3 hydrolysis within the temperature range of 280-320 K.
LAS, functioning as both a hydrogen-bond donor and acceptor, participates in SA-A-driven ternary nucleation, directly interacting with SA and A. Gibbs free energy analysis demonstrates that ternary SA-A-LAS clusters consistently exhibit lower ΔG values than their binary counterparts, suggesting that LAS incorporation stabilizes the SA-A clusters. ACDC kinetic simulations further demonstrate that LAS significantly enhances NPF, especially at low temperatures, low SA concentration, and high A and LAS concentrations. In regions with elevated LAS concentrations, such as Centreville, Alabama, particle formation rates can increase by up to 108-fold, with SA-A-LAS clusters contributing up to 97% of the overall cluster formation pathways. It is noteworthy that LAS not only acts as a catalyst in enhancing SA-A cluster stability but also directly participates in nucleation. Moreover, LAS exerts a stronger enhancement effect than LA, making it a more effective stabilizing agent for atmospheric NPF. These findings suggest that LAS plays a critical role in enhancing SA-A-driven NPF in forested and agriculturally developed regions, providing insights into previously unaccounted NPF sources and refining nucleation models.
This study deepens the understanding of OSs formation in organic acid-polluted regions and underscores the potential contribution of other OSs to NPF. Neglecting the contribution of OSs in the SA-A aerosol nucleation, particularly in forested and agricultural regions, may lead to an underestimation of organic aerosol nucleation risks.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (No: 22203052; 22073059) and the Funds of Graduate Innovation of Shaanxi University of Technology (No: SLGYCX2506).
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Map source: ©Google Maps (https://www.google.com/maps)
Graphic abstract
Fig. 1 Potential energy profiles and corresponding molecular structures for the LA + SO3 → LAS reaction in the absence and presence of H2O and H2SO4 investigated at the CCSD(T)-F12/cc-pVDZ-F12//M06-2X/6-311++G(2df,2pd) level
Fig. 2 (a) Effective rate constants for the LA + SO3 → LAS reaction in the presence of H2O (k'WM, cm3·molecule-1·s-1) and H2SO4 (k'SA, cm3·molecule-1·s-1) calculated using the master equation over the temperature range of 230-320 K; (b) Effective rate constants (k', s-1) for the hydrolysis of SO3 with various species X (X = LA, SA, NA, FA and OA) within the temperature range of 230-320 K, where SA, NA, FA and OA are denoted as H2SO4, HNO3, HCOOH and H2C2O4, respectively.
Fig. 3 Electrostatic potential (ESP)-mapped van der Waals surfaces of A, LAS and SA molecules. ESP minima and maxima for different functional groups are shown as blue and yellow spheres, respectively, with their corresponding values (kcalmol-1) indicated in parentheses. Red arrows denote preferred directions for hydrogen bond formation, while blue arrows illustrate likely pathways for proton transfer.
Fig. 4 The total evaporation rates (∑γ) (s-1) of (SA)x(A)y(LAS)z (y ≤ x + z ≤ 3) clusters at 278.15 K and 1 atm calculated at the M06-2X/6-311++G(2df, 2pd) level of theory. (a) without LAS monomer, (b) containing 1 LAS monomer, (c) containing 2 LAS monomers, and (d) containing 3 LAS monomers
Fig. 5 Nucleation mechanism of the LAS-SA-A system. (a) Cluster formation pathway at 278.15 K, with concentrations of [SA] = 106, [A] = 109 and [LAS] = 105 molecules·cm-3; (b) the branch ratio of outward flux at different temperatures. Only net fluxes contributing more than 5% to cluster growth are depicted.
Fig. 6 Branching ratios of SA-A-LAS (red) and SA-A (blue) cluster growth pathways in regions with varying [LAS] concentrations. Black data points indicate field observations, while blue points represent the median values used in this study. Ammonia concentration is fixed at 109 molecules·cm-3. Map source: ©Google Maps (https://www.google.com/maps)
Fig. 7 (a) Gibbs free energies ΔG (kcalmol-1) and total evaporation rates ∑γ (s−1) for (LA)x(SA)y(A)3 and (LAS)x(SA)y(A)3 (x = 0-3, x + y = 3) clusters calculated at the M06-2X/6-311++G(2df, 2pd) level of theory and 278.15 K; (b) Cluster formation rate (J) and enhancement strength (R) for LAS as a function of monomer concentrations ([LA] and [LAS]) at 278.15 K, with [SA] fixed at 105 molecules·cm-3 and [A] at 109 molecules·cm-3.
* Corresponding authors Tel: +86-0916-2641083, Fax: +86-0916-2641083.
E-mail addresses: ztianlei88@l63.com (T. L Zhang)
‡ Shuqin Wei and Zeyao Li contributed equally to this work.
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AC4: 'Reply on AC2', Tianlei Zhang, 15 Jan 2026
Responses to Referee #2’s comments
We are grateful to the reviewers for their valuable and helpful comments on our manuscript “Unexpected enhancement of new particle formation by lactic acid sulfate resulting from SO3 loss in forested and agricultural regions” (Manuscript ID: egusphere-2025-4894). We have revised the manuscript carefully according to reviewers’ comments. The point-to-point responses to the Referee #2’s comments are summarized below:
Referee Comments:
Wang et al. utilized quantum chemical calculations, master equation analysis, and Atmospheric Clusters Dynamic Code kinetic model to systematically investigate the formation mechanism of lactic acid sulfate (LAS) and its enhancing effect on sulfuric acid (SA)-NH3(A) nucleation. Particular attention is given to the reaction between lactic acid and SO3, the catalytic effects of H2O/SA, and the dual role played by LAS in the SA-A-LAS ternary system (both as a participant and as a catalyst). The topic is novel, the methodology is sound, and the work provides an important-yet previously underappreciated-mechanistic explanation for the unusually high NPF rates observed in forested and agricultural regions. Most of this manuscript is well written and will be of broad interest to the readers of Atmospheric Chemistry and Physics. I recommend its publication in the journal, provided that the following comments are addressed.
Response: We would like to thank the reviewer for the positive and valuable comments, and we have revised our manuscript accordingly.
Specific Comments:
Comment 1:
The results indicate that the barriers to the reaction between lactic acid and SO3 are substantially reduced with the addition of SA. However, the underlying mechanism driving SA’s pronounced catalytic effect has not been adequately addressed. Providing one or two specific structural characteristics, such as the lengths of critical hydrogen bonds or specific geometric changes in transition states, would clarify why SA exhibits higher catalytic efficiency than H2O, thereby allowing readers to fully comprehend the mechanism driving the “barrier reduction”.
Response: Thank you for your valuable comments. According to your suggestion, the geometrical structure of the eight-membered ring transition state TSSA has been compared with that of the six-membered ring transition state TSWM. In Lines 199-202 Page 8 of the revised manuscript, this comparison is presented as follows: “As compared with six-membered ring transition state TSWM, the transition state TSSA shows eight-membered ring structure, which reduces the ring tension greatly. So, from an energetic point of view, SA lowers the Gibbs free energy barrier to 3.5 kcal×mol-1, 4.3 kcal×mol-1 lower than the barrier observed for the H2O-catalyzed pathway.”.
Comment 2:
The authors’ calculations reveal that the dominant nucleation pathways shift with temperature, however, the manuscript does not adequately explain why the contribution of LAS-related pathways increases with increasing temperature. Further clarification of the underlying mechanism is required, such as whether this behavior is associated with variations in collision frequency or the fact that LAS exhibits a relatively weak temperature dependence in its evaporation rate. Incorporating such an explanation would greatly enhance the interpretability of the trend presented in Fig. 5 of the manuscript.
Response: Thanks for your valuable comments. According to the reviewer’s suggestion, the reason for the variation of LAS-related pathways with temperature has been added. The corresponding changes are as follows.
(a) In Lines 285-287 Page 10 of the revised manuscript, the reason for the increasing influence of LAS-involved pathways with rising temperature is added and organized as “ As temperature increases, the influence of LAS-involved pathways becomes progressively more dominant, due to the elevated vapor pressure of LAS raises its gas-phase concentration, thereby promoting further cluster formation.”.
(b) In Lines 288-290 Page 11 of the revised manuscript, at lower temperatures, the reason for the modest contribution of LAS-involved pathways is presented and organized as “ At lower temperatures (238.15 and 258.15 K), SA-A clustering remains the dominant process, accounting for 73% of nucleation events, while LAS-involved pathways contribute a modest 21%, because of the reduced collision frequency of LAS.”.
Comment 3:
The manuscript proposes that LAS may function either as a “participant” or as a “catalyst-like promoter,” which is an interesting and meaningful finding. At present, the distinction between these two roles is mainly inferred from the ACDC pathways in Fig. 5 (i.e., whether LAS ultimately remains in the cluster), whereas Fig. 6 and Fig. 7 primarily illustrate how the contribution of LAS varies with temperature and precursor concentrations. Their connection to the role distinction is not explicitly established. To make the origin of this “dual role” clearer, a brief clarification in the discussion section would help enhance the manuscript’s logical coherence assist readers in better understanding how LAS behaves under different conditions.
Response: Thanks for your valuable comments. Specifically, we highlight that the dual role of LAS is determined by its behavior in the cluster formation pathway, as illustrated in Fig. 5. When LAS functions as a ‘catalyst’, it temporarily participates in the cluster formation but evaporates after facilitating the growth process. In contrast, when LAS acts as a ‘participant’, it remains within the cluster throughout the entire nucleation process. To make the origin of this ‘dual role’ clearer, the corresponding changes are as follows.
(a) In Lines 331-332 Page 12 of the revised manuscript, an example illustrating the role of LAS as a catalyst has been added and organized as “While LAS contributes to the initial stages of cluster formation, it subsequently evaporates from the pre-nucleation cluster, ultimately functioning in a catalyst-like capacity (Fig. S16).”.
(b) In Lines 335-338 Page 12 of the revised manuscript, an example illustrating the role of LAS as a participant has been added and organized as “At high [LAS], as observed in the Centreville, Alabama (1.77 × 106 molecules·cm-3) (Hettiyadura et al., 2017), LAS-driven nucleation becomes dominant, resulting in a ‘participant’ synergistic nucleation mechanism that works like ‘hand in hand’ (Fig. S17), contributing up to 97 % of the total nucleation rate.”.
Comment 4:
I suggest the authors explicitly outline how boundary conditions were set in their ACDC simulations, along with justifying the maximum cluster size they selected. Nucleation rates are often sensitive to the choice of boundary conditions. Accordingly, it is essential to clarify why setting the maximum cluster size at x + y + z ≤ 3 was adequate for their simulations, or alternatively, to discuss the implications of extending this boundary to larger clusters. Even a short, targeted explanation would greatly enhance the clarity and reproducibility of the methodology.
Response: Thanks for your valuable comments. For reviewers' comments, the corresponding revision has been made as follows.
(a) In ACDC simulations, boundary clusters are those allowed to flux out of the simulation box for further growth. Consequently, the smallest clusters outside the simulated system must be sufficiently stable to prevent immediate evaporation back into the system. In addition, considering the formation Gibbs free energy (Table S7) and evaporation rates (Table S9), the clusters (LAS)4(A)3, (LAS)4(A)4, (LAS)2(SA)2(A)3, (LAS)2(SA)2(A)4, (LAS)(SA)3(A)3, (LAS)(SA)3(A)4, (SA)4(A)3 and (SA)4(A)4 clusters are selected as the boundary clusters for LAS-SA-A system. Based on the above analysis, in Lines 158-160 Page 6 of the revised manuscript, the relevant information about boundary clusters have been added and organized as “Additionally, (LAS)4(A)3, (LAS)4(A)4, (LAS)2(SA)2(A)3, (LAS)2(SA)2(A)4, (LAS)(SA)3(A)3, (LAS)(SA)3(A)4, (SA)4(A)3 and (SA)4(A)4 clusters are acting as boundary clusters for LAS-SA-A system.”.
(b) As reported by Besel et al. (J. Phys. Chem. A, 2020, 124(28), 5931-5943), the explicitly simulated set of clusters should always include the “critical cluster”. Usually, the highest barrier on the lowest-energy path connecting the monomers to the outgrowing clusters (a saddle point on the actual ΔG surface) represents the “critical cluster”. So, at 278.15 K (Fig. S4), the actual ΔG of (A)y(LAS)z (0 ≤ y ≤ z ≤ 4), (SA)x(A)y (0 ≤ y ≤ x ≤ 3), (SA)x(A)y(LAS)1 (0 ≤ y ≤ 4, 0 ≤ x ≤ 3), and (SA)x(A)y(LAS)2 (0 ≤ y ≤4, 0 ≤ x ≤ 2) clusters were calculated to verify that the 3 × 3 systems adequately capture the influence of LAS on SA-A nucleation. As seen in Fig. S4, the actual ΔG surface represented that the simulated set of clusters always included the critical cluster. So, we conclude that, in atmospherically relevant conditions, a 3 × 3 cluster set is adequate for predicting the particle formation in the SA-A system.
Fig. S4 A typical actual ΔG surface at 278.15 K. [SA] is the concentration of sulfuric acid monomers, [A] the concentration of ammonia monomers and [LAS] is lactic acid sulfate
Comment 5:
A single value of 2.6 × 10-3 s-1 was adopted for the condensation sink in the ACDC kinetics simulation under different atmospheric conditions of agricultural and forested regions (Figure 6), without addressing whether this parameter is representative of such diverse conditions. In practice, condensation sinks can vary by orders of magnitude depending on aerosol loading. Hence, the manuscript ought to explain the rationale for using a single Cs value across all cases, or discuss the uncertainties associated with this choice for the cluster formation rates or pathways. Including such justification would greatly enhance the credibility of the modeled nucleation rates.
Response: We sincerely appreciate the reviewer's careful reading of our manuscript. As the reviewer pointed out, the condensation sink (Cs) coefficients vary significantly across regions. According to previous reports (Jayaratne et al., 2017; Qi et al., 2015; Shen et al., 2020), the effect of Cs on results was examined, by additional runs with various values covering cases of clean and haze days (6 × 10-4 to 6 × 10-2 s-1). To further evaluate the influence of Cs values on cluster formation rates, two additional sets of ACDC simulations were performed using different Cs values (Fig. S11). The results indicate that varying Cs value settings (6 × 10-4 ~ 6 × 10-2 s-1) does not affect the main conclusions of this study (Fig. S11). Thus, a representative Cs value of 2.6 × 10-3 s-1, was adopted as the sink term in the ACDC simulations. Following the reviewer’s suggestion, in Lines 155-158 Page 6 of the revised manuscript, the sentence of “Here, the condensation sink coefficient was assigned 2.6 × 10-3.” has been changed as “Sensitivity tests were conducted by varying the condensation sink (Cs) from 6 × 10-4 ~ 6 × 10-2 s-1, indicating that the Cs exerted minimal influence on the main conclusions (Fig. S11). Therefore, the Cs was set to a representative value of 2.6 × 10-3 for all subsequent calculations (Liu et al., 2021).”.
Fig. S11 The formation rate J (cm-3 s-1) of LAS at varying consentrations of A and different condensation sink (Cs) values in the SA-A-LAS-based system where T = 278.15 K, [SA] = 105 molecules cm-3, [LAS] = 103 ~ 106 molecules cm-3. Cs = 6×10-4 s-1(dotted lines), 2.6×10-3 s-1 (solid lines) and 6×10-2 s-1 (dash-dotted lines)
References
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Qi, X. M., Ding, A. J., Nie, W., Petäjä, T., Kerminen, V. M., Herrmann, E., Xie, Y. N., Zheng, L. F., Manninen, H., Aalto, P., Sun, J. N., Xu, Z. N., Chi, X. G., Huang, X., Boy, M., Virkkula, A., Yang, X. Q., Fu, C. B., and Kulmala, M.: Aerosol size distribution and new particle formation in the western Yangtze River Delta of China: 2 years of measurements at the SORPES station, Atmos. Chem. Phys., 15, 12445-12464, 2015.
Shen, J., Elm, J., Xie, H. B., Chen, J., Niu, J., and Vehkamäki, H.: Structural effects of amines in enhancing methanesulfonic acid-driven new particle formation, Environ. Sci. Technol., 54, 13498-13508, 2020.
Comment 6:
Technical corrections:
Page 6 line 161: “In the direct cycloaddition pathway (Channel LAS) illsutrated in Fig. 1”
The word “illsutrated” should be corrected to “illustrated”. In addition, there is a spelling error in the caption of Fig. 4, where “nunber” should be corrected to “number.”
Page 5 line 114: “To identity the global minimum energy configurations of …”
The word “identity” should be corrected to “identify”.
Page 10 line 278: “… the contributions of LAS to the SA-A nucleation process was examined, …”
The word “was” should be corrected to “were”.
Page 12 lines 325-326: “LAS-driven nucleation becomes dominate, …”
The word “dominate” should be corrected to “dominant”.
Page 21 lines 665-672: In the reference list, Yin et al., 2021a and Yin et al., 2021b share the same title and page numbers (Acid-base clusters during atmospheric new particle formation in urban Beijing” Environ. Sci. Technol., 55, 10994-11005). Please remove the duplicate references and update the citation numbers in the main text.
Response: Thanks to the reviewer’s insightful comment, we are sorry for the trouble we have caused by oversight. In order to improve the accuracy of the expression, the corresponding main revision has been made as follows:
(a) In Line 164 Page 6 of the revised manuscript, “illsutrated” has been corrected to “illustrated”.
(b) In Fig. 4, the “nunber” has been corrected to “number”. The newly revised Fig. 4 is shown below.
Fig. 4 The total evaporation rates (∑γ) (s-1) of (SA)x(A)y(LAS)z (y ≤ x + z ≤ 3) clusters at 278.15 K and 1 atm calculated at the M06-2X/6-311++G(2df, 2pd) level of theory. (a) without LAS monomer, (b) containing 1 LAS monomer, (c) containing 2 LAS monomers, and (d) containing 3 LAS monomers
(c) In Line 112 Page 4 of the revised manuscript, “identity” has been corrected to “identify”.
(d) In Line 283 Page 10 of the revised manuscript, “was” has been corrected to “were”.
(e) In Line 337 Page 12 of the revised manuscript, “dominate” has been corrected to “dominant”.
(f) In Line 57 Page 3 of the revised manuscript, we have removed the duplicate reference and updated all corresponding citation numbers throughout the manuscript accordingly.
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The manuscript by Wang et al. presents a comprehensive theoretical investigation into the formation mechanism of lactic acid sulfate (LAS) and its unexpected role in enhancing sulfuric acid-ammonia (SA-A) driven new particle formation (NPF). The combination of quantum chemical calculations and ACDC kinetic modeling provides molecular-level insights into the catalytic effects of SA and H2O on LAS formation and the role of LAS in enhancing SA-A nucleation. This study advances our molecular-level mechanistic understanding of how organosulfates influence nucleation events. The manuscript is well-structured and clearly written. Therefore, I recommend publication of this manuscript after consideration of the following comments:
Comments: