Sulfate aerosols constitute a critical fraction of atmospheric particulate matter, with their formation mechanisms representing a pivotal yet unresolved aspect of air pollution control (He et al., 2012; Wang et al., 2018; Dao et al., 2019; Tao et al., 2016; Chen et al., 2023; Yu et al., 2026). The oxidation processes of sulfur dioxide (SO₂) exhibit remarkable mechanistic complexity stemming from its dual physicochemical nature (Kang et al., 2016; Mukai et al., 2001; Ma et al., 2026). The exceptionally high hydration equilibrium constant drives near-instantaneous formation of S(IV) species (HSO3-/SO32-) (Zhang et al., 2026), while the thermodynamically favorable oxidation potential creates a multidimensional reaction pathways including both homogeneous radical processes and heterogeneous interfacial reactions (He et al., 2018; Harris et al., 2013b; Tanaka et al., 1994; Zhang and Chan, 2023). These intrinsic reaction dynamics, when coupled with the extreme spatiotemporal variability of atmospheric conditions, create substantial obstacles for mechanistic elucidation under ambient environments. Current investigative approaches, including controlled laboratory simulations, field measurement, and computational modeling, each face inherent limitations when applied in isolation. Laboratory studies inevitably simplify the unbounded nature of atmospheric systems, while field observations struggle to isolate specific chemical processes amid complex real-world interactions. Modeling studies (Yang et al., 2025; Zheng et al., 2024; Lin et al., 2022, 2025), though valuable for hypothesis testing, remain constrained by incomplete mechanistic understanding and parameterization challenges. This methodological trilemma has resulted in persistent knowledge gaps regarding the dominant pathways and quantitative contributions of various sulfate formation mechanisms in different atmospheric regimes.

The application of stable isotope techniques in sulfate source attribution has emerged as a powerful analytical approach, leveraging the distinct isotopic fingerprints characteristic of different pollution sources and their remarkable stability during atmospheric transport (Yang et al., 2025; Lin et al., 2022; Harris et al., 2012b; Guo et al., 2024). This methodology capitalizes on the system-specific fractionation patterns inherent to various sulfate formation pathways, which serve as critical tracers for reconstructing oxidation mechanisms. Contemporary research has quantitatively established the sulfur isotopic signatures (δ34S) (Han et al., 2022; Yang et al., 2025) associated with major atmospheric oxidation routes, including transition metal ion-catalyzed (TMI), ozone-mediated (O₃), nitrogen oxide-driven (NO_x), and hydrogen peroxide-initiated (H₂O₂) pathways, through systematic analysis of particulate matter samples (Yang et al., 2025; Fan et al., 2020a; Harris et al., 2013a; Guo et al., 2019; Ruan et al., 2025; Wang et al., 2016, 2020). Advanced analytical tools, particularly Bayesian isotopic mixing and Rayleigh fractionation models, have demonstrated substantial utility in deconvoluting complex sulfate formation mechanisms. Yet, their diagnostic potential is often overshadowed by a fundamental theoretical flaw: the reliance on complete SO₂ oxidation paradigms. Because genuine atmospheric regimes rarely achieve such idealized conversion, this oversimplification severely penalizes the accuracy of sulfur transformation kinetics. Ultimately, conventional Rayleigh approaches introduce systematic uncertainties into source apportionment by neglecting the vital kinetic isotope effects and partial intermediates generated during incomplete SO₂ processing.

Building upon these insights, the present study establishes a comprehensive multi-model analytical framework that synergistically couples ambient field observations with a suite of diagnostic tools, ranging from backward trajectory analysis to Bayesian isotope mixing and process-specific Rayleigh fractionation modeling. This integrated approach achieves precision in quantifying sulfate formation pathways while systematically addressing the critical but often neglected kinetic limitations inherent to incomplete SO₂ oxidation under real atmospheric conditions. By applying sulfur and oxygen isotope analyses to seasonally resolved aerosol samples from Nanjing, we demonstrate significant divergence between conventional complete-oxidation Rayleigh models and our kinetic fractionation-corrected framework. Our systematic model intercomparison highlights the essential calibration requirements for stable isotope fractionation, successfully resolving the systematic biases that have long plagued sulfate source attribution. This methodological leap provides a refined method for tracking urban sulfate pollution, particularly within complex environments characterized by incomplete oxidation. Ultimately, the seasonally partitioned data from Nanjing serves as a quantitative benchmark, explicitly detailing how traditional complete-oxidation frameworks misrepresent source contributions during both summer photochemical and winter coal-combustion episodes.

Chemical profiling of fine particulate matter in Nanjing reveals that sulfate dictates the water-soluble inorganic fraction, accounting for 27.9 % to 42.3 % of the total ionic mass. This pronounced dominance explicitly underscores the region's persistent susceptibility to sulfate-driven aerosol pollution. This pattern aligns with observations from other Chinese urban centers including Hangzhou (33.7 %) (Lin et al., 2022), Guangzhou (40.2 %–61.0 %) (Tao et al., 2014b), and Beijing (33.0 %) (Wei et al., 2018), collectively highlighting the prevalence of sulfate-rich PM_2.5 across China. Pollution episodes were categorized by PM_2.5 concentrations into clean (≤35 µgm-3), moderate (35–75 µgm-3), heavy (75–150 µgm-3), and haze (>150 µgm-3) periods, with haze frequency (20 %, Fig. 1) doubling that of clean periods (10 %). Sulfate concentrations exhibited pronounced pollution-dependence, peaking at (27.55±14.36 µgm-3) during haze events 3.2 times higher than clean-phase levels (8.56±3.19 µgm-3).

NH4+ and NO3- jointly accounted for 50.1 %–57.9 % of water-soluble ions (Fig. 2a), while their strong covariation with SO42- (Fig. 2a, b) substantiates secondary sulfate formation as the principal PM_2.5 component and implicates combustion-derived emissions as its dominant source. The significant positive correlation between SO42- and PM_2.5 concentrations (Fig. S2) further establishes sulfate's direct mechanistic role in particulate pollution escalation. The atmospheric source apportionment can be quantitatively assessed through the [NO3-]/[SO42-] mass ratio, where elevated values reflect increasing dominance of mobile versus stationary emission sources (Xiao et al., 2014; Arimoto et al., 1996). Our measurements yielded ratios spanning 0.15–1.95 (mean 0.98±0.42), exceeding Shanghai's 2002 baseline (0.43) (Yao et al., 2002) yet remaining below Jiaozuo's 2017 levels (1.36) (Zheng et al., 2024), collectively demonstrating Nanjing's intermediate position in mobile-source contribution among Chinese cities. These secondary aerosols originate through atmospheric oxidation of precursor gases, with SO₂ and NO_x principally derived from coal combustion and vehicular emissions respectively, while NH₃ predominantly stems from agricultural and livestock activities (Tao et al., 2014a). The strong inter-species correlations (Fig. S3a, b) confirm the co-formation of (NH4)2SO₄ and NH₄NO₃ through gas-to-particle conversion processes. Revealed across distinct pollution episodes, the unique sulfur and oxygen isotopic signatures (Fig. 2b) provide unequivocal evidence of temporal shifts in sulfate formation pathways. To accurately deconvolute the relative contributions of these specific reaction routes, rigorous mechanistic modeling becomes indispensable. Crucially, the persistent incomplete oxidation of sulfur dioxide to sulfate under all pollution conditions (Fig. 2c) underscores the imperative for oxidation-process-constrained model optimization to elucidate the authentic atmospheric sulfate formation mechanisms.

The oxygen isotopic composition of atmospheric sulfate serves as a reliable indicator of oxidation pathways, with sulfate in PM_2.5 predominantly originating from SO₂ oxidation, consistent with established atmospheric chemistry. The δ34S-SO42- values (+1.7 ‰ to +6.3 ‰) of Nanjing sulfate aerosols, indicating coal combustion (+4.6 ‰ to +6.6 ‰) as the dominant source, thereby reflecting a greater coal-derived contribution relative to other Chinese regions. Cluster analysis of air mass trajectories reveals distinct seasonal patterns. During summer (Fig. 3b), trajectories originating locally (54.55 %), southwest China (13.64 %), southeast China (18.18 %), and the eastern Yellow Sea (13.64 %) exhibit higher SO42- concentrations locally (19.81±5.61 µgm-3) versus southwest (7.34±2.35 µgm-3), southeast (15.6±4.31 µgm-3), and Yellow Sea (16.98±5.29 µgm-3) sources, while δ34S-SO42- values show an inverse trend with lower values locally (2.88±0.73 ‰) and in the southwest (2.70±0.93 ‰) compared to southeast (3.33±0.9 ‰) and Yellow Sea regions (4.55±0.25 ‰), suggesting heterogeneous sources and formation mechanisms. Winter measurements (Fig. 3a) display significant sulfate concentration disparities across back trajectories of air mass (e.g., cluster 1: 23.84±15.28 µgm-3; cluster 3: 7.34 µgm-3), but statistically invariant δ34S-SO42- values (cluster 1: 4.77±0.99 ‰; cluster 3: 5.04±0.46 ‰); northeastern province (5.48±0.29 ‰), with both concentration and δ34S elevated versus summer, attributable to long-range transport of primary sulfates and coal-combustion emissions enriched in heavy isotopes. The significant negative correlation (Fig. 2b, d) between δ34S and temperature arises as higher temperatures promote OH-mediated uniform oxidation, facilitating isotopic equilibrium fractionation during HSO3-/SO42- exchange, which favors light-sulfur-isotope incorporation into sulfate and lowers summer δ34S (Han et al., 2016; Novák et al., 2001). Thus, secondary sulfate formation pathways and source variations primarily drive the observed winter-high/summer-low δ34S pattern in PM_2.5, underscoring the mechanistic study's critical role in sulfate pollution control.

Besides, by synergistically combining AMBTs (Fig. S4), CWT (Fig. S5) analysis, and FLEXPART footprint modeling (Fig. 4a, b), our integrated framework now successfully bridges the gap between empirical trajectory data and actual emission source strengths. This robust spatial validation explicitly supports our overarching objective to resolve long-standing discrepancies in atmospheric sulfate source attribution.

The atmospheric sulfate formation pathways exhibit distinct sulfur isotope fractionation signatures, as demonstrated by theoretical calculations of δ34S-SO42- evolution under different oxidation mechanisms. Complete oxidation of SO₂ via H2O2/O3 pathways would drive δ34S-SO42- depletion from 15.3 ‰ to 2.6 ‰ (Fig. 5a), while OH-mediated oxidation would produce isotopic depletion from 11.8 ‰ to 3.4 ‰ (Fig. 5a), both scenarios reflecting progressive sulfur oxidation (SOR 0 to 1). Conversely, exclusive S(IV) + O₂ (TMI) pathway participation would generate δ34S-SO42- enrichment from -6.4 ‰ to -1.0 ‰ (Fig. 5a). These differential fractionation patterns confirm the coexistence of multiple sulfate production routes in the atmosphere, with all observed δ34S-SO42- values falling within the predicted theoretical ranges. However, our field measurements demonstrate that total particulate sulfate concentrations peak at 27.55±14.36 µgm-3 during severe haze events, which predominantly occur in winter. Consequently, when translating these relative fractions into absolute mass concentrations, the NO₂ pathway produces a substantially higher burden of particulate sulfate in winter compared to summer.

The isotopic fractionation factor α for sulfur isotopes was derived via Rayleigh fractionation models applied to δ34S-SO_2−emission calculations based on atmospheric δ34S-SO42- and SOR, with synchronous field measurements (InCO Process) of δ34S-SO₂ averaging 1.7±1.2 ‰ (range: -1.80 ‰ to +4.05 ‰), yielding α=2.0±1.8 ‰ (range: -1.2 ‰ to +6.7 ‰) (Fig. 6b) per designated formula. Under complete oxidation (CO Process) (SOR = 1), δ34S-SO42- demonstrated a significant negative correlation with SOR (δ34S-SO42-=-3.16×SOR+5.03=5.03; r=-0.36, p≤0.05) (Fig. S6), resulting in δ34S-SO_2−emission of 1.8 ‰ at full conversion, which exceeds values from Shanghai (1.3 ‰) (Li et al., 2020), Hangzhou (1.5 ‰) (Lin et al., 2022), and Jiaozuo (1.7 ‰) (Zheng et al., 2024) and represents the pre-transformation source signature. An alternative α calculation (formula 9) generated a mean of 2.8±1.7 ‰ (range: -0.2 ‰ to +6.1 ‰), higher than Guangzhou (<1.5 ‰) (Fan et al., 2020b) but lower than Beijing (4.2±1.2 ‰) (Lin et al., 2018) with elevated α in eastern China attributable to temperature-dependent fractionation increases (Fig. S7). The discrepancies arose from oxidation-rate variations under full-oxidation assumptions that alter pathway quantification.

By systematically evaluating the reaction-specific fractionation factors intrinsic to distinct SO₂ oxidation mechanisms, we successfully apportioned the diverse pathways governing sulfate formation. This evaluation reveals that TMI-catalyzed and NO₂-mediated reactions collectively dictate atmospheric sulfate production across all considered scenarios. Crucially, as corroborated by isotopic mass balance calculations, imposing idealized complete-oxidation assumptions systematically suppresses the calculated contribution of the TMI pathway, a bias successfully resolved through the application of kinetic partial-oxidation models. This systematic bias originates from neglecting kinetic fractionation effects during intermediate oxidation stages, particularly under high aerosol acidity conditions where TMI chemistry prevails. The persistent dominance of these two pathways persists despite varying meteorological conditions and emission profiles, suggesting their fundamental role in sulfur cycling.

Quantitative source apportionment of atmospheric sulfate was achieved through coupled δ34S-SO42- measurements and Bayesian isotopic mixing models, requiring emission source-specific δ34S signatures as critical input parameters. Correction for sulfur isotopic fractionation during SO₂– to –SO42- conversion is essential, as this process enriches δ34S values by 1.2 ‰–7.2 ‰ (Lin et al., 2022), necessitating subtraction of pathway-specific fractionation coefficients prior to source quantification. Neglecting fractionation effects distorts source contributions, yielding winter estimates of 19 % (anthropogenic primary sulfate), 4 % (terrestrial sulfate and sea salt), 32 % (coal), 4 % (oil), 15 % (biomass), and 26 % (vehicle), alongside summer values of 8 %, 2 %, 62 %, 3 %, 9 %, and 16 % (Fig. 7a) respectively–results that inaccurately emphasize traffic emissions contrary to regional emission inventories and chemical transport modeling. Incorporating fractionation factors resolves this discrepancy, aligning sulfate sources with inventory data where coal combustion dominates annually, while idealized complete-oxidation models underestimate summer vehicle contributions by 8 % and overestimate coal combustion proportions (about 10 %) by comparable margins despite minimal winter deviations (Fig. 7b). This systematic validation underscores the requirement for fractionation correction in isotope-based atmospheric sulfate sourcing.

This study advances atmospheric sulfate source apportionment by transcending the idealized complete SO₂ oxidation assumptions that constrain conventional isotopic models. By integrating ambient sulfur and oxygen isotope field observations with Rayleigh fractionation models, we successfully derived kinetic partial-oxidation fractionation factors that reflect genuine atmospheric conditions. Our integrated framework reveals the predominance of TMI-catalyzed and NO₂-mediated pathways in atmospheric sulfate production across varying seasonal extremes. By comparing our kinetic fractionation-corrected framework against traditional complete-oxidation models, we demonstrate that idealized frameworks systematically obscure chemical realities. Neglecting kinetic fractionation effects during intermediate oxidation stages disproportionately diminishes the calculated contributions of the TMI pathway, particularly under high aerosol acidity conditions where TMI chemistry prevails. By applying our corrected framework, we align our source apportionment more accurately with regional emission inventories, successfully resolving calculation discrepancies that have long plagued isotopic and transport-modeling approaches. While our multi-model analytical framework corrects systematic biases in pathway quantification, certain caveats remain. The empirical validation in this study is currently constrained to seasonal extremes, specifically January and July observations, at a single monitoring site in Nanjing. Future work is needed to expand this kinetic fractionation-corrected framework across diverse geographical regions and continuous temporal scales to further validate oxidation-process-constrained model optimizations. Correcting these systematic isotopic biases carries profound implications for our understanding of atmospheric pollution states and climate regulation. Our findings expose a significant seasonal misalignment in current evaluations, demonstrating that traditional approaches overestimate summer coal combustion contributions by 10 % while underestimating summer traffic emissions by 8 %. Consequently, effective sulfate mitigation cannot rely solely on blanket SO₂ reductions. Regulatory frameworks must pivot toward multi-pollutant, seasonally differentiated strategies that dynamically target summer vehicular dynamics and the co-emitted transition metals driving catalytic sulfate formation.