A new empirical equation for the gas/particle partitioning of OPFRs in ambient atmosphere

Abstract

Gas/particle (G/P) partitioning is a core process governing the atmospheric transport of organophosphate flame retardants (OPFRs). However, accurately predicting the G/P partition performance of OPFRs remains a challenge. In this study, four independent models were employed to estimate the characteristics of OPFR G/P partitioning within the octanol–air partition coefficient range of 4.7 (TMP) to 14.2 (TMPP). The results showed that in the maximum partition domain, the Li–Ma–Yang steady-state model fitted the best, with 85.2% of the predicted G/P partition quotient (log K_P) values within an acceptable deviation range of ±1 log units for OPFRs. Accordingly, no significant deviations were observed between the predicted (0.56 ± 0.32) and monitored (0.52 ± 0.11) values of the average particle-bound fraction (φ_P) for the Li–Ma–Yang model in the maximum partition domain. Large deviations were observed between the monitored values and predicted log K_P values by these four models in the equilibrium domain. Several factors responsible for the significant deviations observed in G/P partitioning values of OPFRs were discussed. These identified factors were used to develop a new empirical equation, which substantially improved log K_P predictions for OPFRs to 75.8% in the equilibrium domain.

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Environmental significance

The gas/particle partitioning behavior of emerging chemicals such as organophosphate flame retardants determines their long-range transport, wet and dry deposition and atmospheric fate. Currently, the accurate prediction of the gas/particle partition quotient of OPFRs remains a challenge. Understanding the characteristics and influencing factors of gas particle partition of OPFRs is the key to addressing this challenge. In this study, the characteristics of gas/particle partition of OPFRs and the determining factors were comprehensively investigated in the octanol–air partition coefficient (K_OA) range of 4.7 (TMP) to 14.2 (TMPP). Large deviations were observed between the measured and predicted log K_P values in the EQ domain (log K_OA < 11.4). A new empirical equation for the EQ domain was developed with a better agreement between the predicted and measured data, and the percentage of data points that fall within the ADR increased from 23.1% to 75.8%.

1. Introduction

Organophosphate flame retardants (OPFRs) have been widely used as alternatives to brominated flame retardants in household appliances, building materials, textiles, wires, cables, and other products due to their excellent flame-retarding performance, and some of the OPFRs are evaluated to have the potential for long-range transport via air and water.^1–3 Unlike polybrominated diphenyl ethers (PBDEs), OPFRs are not chemically bonded to the material, which makes them more prone to leaching from the material, leading to significantly higher concentration of OPFRs in environment than other flame retardants.⁴ In recent years, OPFRs have been detected in the atmosphere,^5,6 waters,⁷ sediments,⁸ aquatic organisms⁹ and even in areas, such as the Antarctic Peninsula and the Arctic,^10,11 posing potential hazards to the environment and human health.

After OPFRs are released into the atmosphere, they are adsorbed or absorbed onto/into particulate matter, and their distribution between gas and particle phases determines their global long-range atmospheric transport, wet and dry deposition, degradation and the pathways to human exposure.¹² Generally, gaseous OPFRs are more easily transported through the atmosphere. Higher gaseous concentrations of OPFRs are observed in summer, while higher particulate concentrations of OPFRs are found in winter.¹³ Additionally, both gaseous and particulate OPFRs can enter organisms through different pathways and pose potential hazards. Hence, more attention has to be paid to the gas/particle partitioning (GPP) behavior of OPFRs in the environment that affects their long-range transport and human exposure pathways. Particulate OPFRs might be more persistent in the air due to their low vapor pressure.^14–16 The G/P partition of OPFRs could affect their long-range transport via both air and seawater, even from the European continent and seas to the polar regions.¹¹ Thus, the knowledge of GPP of OPFRs is of great significance for understanding their environmental behavior and fate.

There are many factors that affect the G/P partition of OPFRs in ambient atmosphere. Previous studies have shown that high temperature can promote the mass transfer of OPFRs from particles to the gas phase, which will lead to OPFRs distributing in the gas phase.¹⁷ A negative correlation between temperature and particle-bound fraction (φ_p) has been observed, suggesting the temperature might affect the GPP of OPFRs (except for triphenyl phosphate (TPHP)).¹⁸ High particle matter (PM) mass and low temperature will facilitate the condensation effect of OPFR, contributing to the migration of gaseous OPFRs into solid particulate matter.¹⁹ Therefore, it is generally acknowledged that temperature and TSP are the driving forces of OPFR sorption on particulate matter.²⁰ Recent studies show that relative humidity and wind speed positively correlate with the φ_P of OPFRs.²¹ The octanol-air partition coefficient (K_OA), organic matter fraction (f_OM), liquid vapor pressure, volatility, mass of the target compound, and aerosol surface area also are essential parameters relevant to the GPP of OPFRs.^17,19 The potential point sources and sampling measurements also have strong influence on the GPP of semi-volatile organic compounds (SVOCs), such as OPFRs.²² The contribution of these GPP-influencing factors to predicting the K_P values of OPFRs is still unclear and not quantified.¹⁷

Many gas/particle partition models have been developed to quantify the factors that influence and determine the G/P partitioning of SVOCs, such as OPFRs. The Harner–Bidleman (H–B) model (equilibrium model) might be more reliable for predicting the K_P values of OPFRs in typical urban cities and rural sites.¹³ Both Junge–Pankow (J–P) and H–B models tend to underestimate the φ_P of low-molecular-weight OPFRs and overestimate those of high-molecular-weight OPFRs.²³ By comparing the results of J–P model and H–B model in the island in the South China Sea, it is suggested that the GPP of OPFRs might be in a non-equilibrium state.²⁴ Due to the small temperature range, both the temperature-related models did not fit the monitored log K_P data well. The pp-LFER model, H–B model, D–E model and steady-state model, which are used to evaluate the phase distribution of OPFRs in urban areas, suggest that all these models underestimate the log K_P values in winter and summer conditions, especially for relatively volatile OPFRs that are mainly distributed in the equilibrium (EQ) domain.¹⁷ It has been shown previously that a glass fiber filter can change the observed particle-bound fraction of compounds with higher volatility but has little impact on relatively non-volatile components.²² The relative humidity, temperature, and TSP might affect the ability of the glass fiber filter to capture OPFRs, and further research is needed to quantify the impact of these factors.²² Therefore, the questions of how to consider these factors into the G/P partition model and predict the G/P partitioning of OPFRs more accurately are desired to be answered.

In this study, the characteristics and new empirical prediction equation of the G/P partitioning of OPFRs are investigated. Here, we intended (1) to identify the characteristics of G/P partitioning of OPFRs in three aspects: monitoring data, model prediction, and substituent groups in the three partition domains; (2) to develop a new empirical equation for the G/P partitioning of OPFRs in the EQ domain. The findings of this study will provide more knowledge on the dominating mechanisms underlying the partition of various OPFR compounds in the atmosphere.

2. Models and data source

2.1 G/P partitioning quotient and particle-bound fraction

The G/P partition quotient (K_P, m³ μg⁻¹) is calculated by monitoring the concentrations of selected OPFRs in the gaseous and particulate phases, and the total suspended particle concentration (TSP, μg m⁻³):where C_P and C_G represent the concentrations (in pg m⁻³) of the OPFRs in the particulate and gas phases, respectively.

The particle-bound fraction (φ_p) is another commonly used dimensionless parameter to describe the G/P partitioning behavior of OPFRs:

2.2 G/P partitioning models

In this study, four models, including the steady state model (L–M–Y model) and three equilibrium models, namely Junge–Pankow (J–P) model, Harner–Bidleman (H–B) model, Dachs–Eisenreich (D–E) model, were evaluated. To ensure consistency in model comparison and evaluation, the pp-LFER model is not discussed in this study due to the absence of parameters needed for pp-LFER. Considering both wet and dry particle deposition and absorption are dominant in the G/P partitioning process, the L–M–Y model could be represented as:²⁵

log K_P-LMY = log K_PE + log α (3)

where the log K_P-LMY is the value of log K_P predicted by the L–M–Y model, and log K_PE is the equilibrium term calculated by the Harner–Bidleman model. The equilibrium is a special case of the steady state when log α = 0. The log α is the non-equilibrium term, corresponding to the wet and dry deposition on particles:²⁵which is a function of f_OM and K_OA.

K _OA is a necessary parameter to predict log K_P and is the function of temperature:²⁶

The log K_OA could be calculated from the relationship between the log K_OA and log P_L by the following equation:²⁷

log K_OA = −log P_L + 6.46 (6)

The A_o and B_o values of the OPFRs are listed in Table S1.†

C in eqn (4) is a weighting factor for the mass transfer coefficient, with a value of 5 for OPFRs in this study. C = 5 has been successfully used for several SVOCs, such as PBDEs,^28,29 non-PBDE brominated flame retardants,³⁰ halogenated flame retardants,³¹ polychlorinated dibenzo-p-dioxins/furans,³² organochlorine pesticides,³³ short- and medium-chain chlorinated paraffins,³⁴ and polychlorinated biphenyls.³⁵

The Junge–Pankow model assumes that particle surface adsorption dominates the GPP process as a function of subcooled liquid vapor pressure (P_L, Pa) and the surface area concentration of particulate matter in the air (θ, cm_surface² cm_air⁻³). The formula for φ_P is given below :³⁶

where θ is assumed to be 1.1 × 10⁻⁵ for urban air, 1.5 × 10⁻⁶ for rural air³⁷ and marine area; the C_J value is 17.2 Pa cm; P⁰_L is the subcooled liquid vapor pressure (Pa).

The Harner–Bidleman model assumes that the absorption of SVOCs by the particles is equivalent to that in octanol, which acts as a surrogate to the sorbing organic matter in the particles.³⁸ The Harner–Bidleman formula is a function of K_OA and f_OM:

log K_P-HB = log K_OA + log f_OM − 11.91 (8)

By considering the adsorption and absorption processes as two equally important parts, the soot–air partition coefficient (K_SA, L kg⁻¹) and the fraction of elemental carbon (f_EC) as the core factors of the adsorption process, the equation of the Dachs–Eisenreich model is derived as follows:

K_P−DE = 10⁻¹²f_OMK_OA + 10⁻¹²f_ECK_SA (9)

log K_SA is given by the following equation:

where the value of α_EC used is 18.21 m² kg⁻¹ in this study.²⁸

2.3 Data sources of OPFRs

The measured data of OPFRs were collated from published articles by retrieving from the “Web of Science” using “OPFRs” and “air”, “organophosphate flame retardants” and “air”, “OPFRs” and “gas particle partitioning”, “organophosphate flame retardants” and “gas particle partitioning” as the topics; the sampling sites (Table S2†) included Beijing, Tianjin, Shanghai, Wuhan, Guiyang, Shijiazhuang, Lanzhou, Jinan, Chengdu, Zhengzhou, Guangzhou in China;^39–41 Woody Island in the South China Sea;⁴² West Antarctic Peninsula;⁴³ New York state;⁴⁴ and German part of the North Sea.⁴⁵ Thirteen OPFRs with a wide range of chlorination, namely Tris (2-butoxyethyl) phosphate (TBOEP), tri (2-chloroethyl) phosphate (TCEP), tri (chloropropyl) phosphate (TCPP), Tris (1,3-dichloro-2-propyl) phosphate (TDCIPP), Tris (2-ethyl hexyl) phosphate (TEHP), tri-ethyl phosphate (TEP), trihexyl phosphate (THP), tri-isobutyl phosphate (TIBP), trimethyl phosphate (TMP), Tris(methylphenyl)phosphate (TMPP), tri-n-butyl phosphate (TNBP), tripentyl phosphate (TPEP), and triphenyl phosphate (TPHP), were selected in the present study (Table S3†). A total of 2058 data points measured from all the sampling sites were used to compare the log K_P predictions of OPFRs based on the four models. More detail information on the sampling method, quality assurance and quality control can be found in Table S2†. The measured data used for modeling are displayed in Table S4†.

3. Results and discussion

3.1 Monitoring log K_Pvs. log K_OA in ambient atmosphere

The relationship between log K_P and log K_OA is an important descriptor of the G/P partitioning of SVOCs. According to the two log K_OA thresholds (log K_OA1 = 11.4 and log K_OA2 = 12.5), the partitioning span could be divided into three domains: equilibrium (EQ) domain (log K_OA ≤ 11.4), non-equilibrium (NE) domain (11.4 < log K_OA < 12.5), and the maximum partition (MP) domain (log K_OA ≥ 12.5).²⁵ Fig. S1† displays the partition domains of the 13 OPFRs compounds in the sampling temperature range (0–30 °C) and simulated temperature range (−50–50 °C) according to their temperature-adjusted log K_OA and the two log K_OA thresholds. About 70.2% of the observed OPFR data were in the EQ domain, including those of TMP, TEP, TCEP, TIBP, TNBP, TCIPP, and TPEP at the sampling temperature. All the recorded TMPP data points were found to be distributed in the MP domain under the monitoring conditions. According to the steady state model, the log K_P of TMPP will be a constant value in the MP domain. TDCIPP, TPHP, TBOEP were the EQ-NE domain compounds in the sampling temperature range. The log K_P values of OPFRs ranged from −4.86 to 1.10 m³ μg⁻¹, with a mean value ± standard deviation of −1.58 ± 1.17 m³ μg⁻¹ and a median value of −1.58 m³ μg⁻¹. The relationship regression equation between the log K_P of the monitored OPFRs and their log K_OA is shown in Fig. 1, with log K_OA ranging from 4.7 for TMP to 14.2 for TMPP. After entering the MP domain, the log K_P value should approach a constant according to the steady state theory. As shown in Fig. 1, the constant value of log K_P (−1.21) observed for the OPFRs in the MP domain is close to the predicted log K_P-LMY value of −1.53. The slope (m_o) and intercept (b_o) values from the log–log relationship between K_P and K_OA of the OPFRs were 0.09 and −2.58, respectively, revealing a much smoother curve than those of other SVOCs. For example, the slope and intercept of the log K_Pversus log K_OA plot were 0.53 and −7.60 for PBDEs sampled in the Arctic,⁴⁶ 0.24 and −4.21 for organochlorine compounds sampled in west Antarctica,⁴⁷ and 0.62 and −7.81 for PAHs sampled in China,⁴⁸ respectively. Based on our previous study,⁴⁹ the value of m_o should lie between 0 and 1 depending on the values of log K_OA under the steady state. The relationship between b_o and m_o when C equals 5 can be presented as b_o = −11.38 × m_o − 1.53. The b_o value was calculated as −2.55 using the above equation, which is very close to the monitored b_o value of −2.45, along with a measured m_o of 0.09. The normality results of the Kolmogorov–Smirnov test revealed that the monitored log K_P and log K_OA data points did not follow a normal distribution. Log K_P of the OPFRs positive correlated with log K_OA (p < 0.05), with a Spearman correlation coefficient of 0.21. This suggests a non-linear relationship between the observed log K_P and log K_OA of the OPFRs.

Fig. 1 Monitoring of log K_Pvs. log K_OA.

3.2 Characteristics of log K_P and φ_P obtained using the models and measured data

The prediction performance of these models (equilibrium models: H–B model, D–E model, J–P model; steady state model: L–M–Y model) were compared in terms of log K_P and φ_P, respectively. As shown in Fig. 2, the absolute errors between the data predicted by the four models and the observed data (Δlog K_P = predicted log K_P − measured log K_P) were compared, respectively, for the 13 target OPFR compounds. The percentage of data points falling within the acceptable deviation range (ADR) was used to evaluate the prediction capability of these gas-particle distribution models. The ADR is defined as the region bounded by a deviation of ±1 (ADR: −1 ≤ Δlog K_P ≤ 1).^28,29 As shown in Fig. 2, in the MP domain, the L–M–Y model showed a better performance, with 85.2% (with root mean square error (RMSE) = 0.68) of the monitored data points of the MP domain compounds (TMPP, THP, and TEHP) within the ADR. The other models (H–B model, D–E model and J–P model) tended to overestimate the log K_P values of the OPFRs, with less than 33% of data points in the ADR. These results indicate that the log K_P predicted using the L–M–Y model that considers log K_OA and particle deposition agree well with the measured log K_P values of TMPP, THP, and TEHP in the MP domain. In the NE domain, 78.6% (with RMSE = 0.82) of log K_P-LMY data points belonging to 5 OPFRs compounds (THP, TEHP, TBOEP, TPHP, and TDCIPP) were within the ADR in comparison with 70.7% (with RMSE = 1.00) for log K_P-HB, 68.7% (with RMSE = 1.03) for log K_P-DE, and 19.4% (with RMSE = 1.83) for log K_P-JP.

Fig. 2 Δlog K_P predicted by the four models versus log K_OA of the OPFRs: (a) H–B model; (b) L–M–Y model; (c) D–E model; (d) J–P model; (e) percentage of predicted data points within the ADR; (f) RMSE of the G/P partition models of OPFRs. The points in blue denote data points within the ADR. The points in pink and brown indicate that the predicted results overestimate and underestimate the measured data, respectively.

As shown in Fig. 2, large deviations between the measured and predicted log K_P of OPFRs were observed in the EQ domain. Furthermore, in the NE and MP domains, the L–M–Y model, which considers both log K_OA and particle deposition in the GPP process (or temperature, A_o and B_o), showed acceptable performance in predicting log K_P. Thus, log K_OA (or temperature) and particle deposition might be the core factors that promote the mass transfer of OPFRs (TMPP, THP, TEHP, TBOEP, TPHP, and TDCIPP) between the gas and particle phases in the NE and MP domains.

The particle-bound fraction (φ_P) is a crucial parameter for characterizing the G/P partitioning of OPFRs. Fig. S2† presents the predicted φ_P values of OPFRs and measured values across the three partition domains. In the EQ domain, all four models tended to underestimate the φ_P values of OPFRs. In the NE domain, predictions from the steady state (L–M–Y) model aligned more closely with the measured results. The average φ_P value ± standard deviation (SD) for the monitored data was 0.52 ± 0.11, while that predicted by the steady state model was 0.56 ± 0.32 for THP, TEHP, TBOEP, TPHP, and TDCIPP. Within the MP domain, there was clear consistency between the measured data and φ_P predicted by the L–M–Y model for TMPP, THP, and TEHP, with monitored values at 0.72 ± 0.21 and predicted φ_P at 0.61 ± 0.07. Consequently, these results clearly demonstrate that the L–M–Y model provides better agreement with the monitored φ_P values of OPFRs, particularly within the NE and MP domains.

3.3 Effects of functional groups on the G/P partitioning of OPFRs

OPFRs are phosphoric-acid derivatives composed of phosphate radicals and three different groups, which can generally be divided into halogenated phosphate esters, aromatic phosphate esters and alkyl phosphate esters.⁵ Among the 13 organophosphorus flame retardants, there are 2 aryl-OPFRs (TMPP and TPHP), 3 chlorine-OPFRs (TCEP, TCIPP, and TDCIPP), and 8 alkyl-OPFRs (TMP, TEP, TIBP, TNBP, TPEP, THP, TEHP, and TBOEP). As shown in Fig. S3,† the measured particle-bound fractions of these 13 OPFR compounds are listed from left to right according to the molecular weight (from light to heavy), with the aryl-OPFRs in orange, chlorine-OPFRs in green and alkyl-OPFRs in blue. The mean particle-bound fractions of alkyl-OPFRs (TEP, TIBP, TNBP, TPEP, THP, TEHP) ranged from 0.30 for TIBP to 0.39 for TNBP, indicating that these six OPFR compounds were dominant in the gas phase, though the molecular weight increased from 182.2 for TEP to 434.6 for TEHP. This is consistent with the observed annual average φ_P value of 0.35 reported in a previous study.²⁴ The distribution ratio of chlorine-OPFRs (TCEP, TCIPP, and TDCIPP) in both gaseous and particulate phases was equivalent, with the mean particulate-bound fraction approaching 0.50. TCEP and TCIPP were usually observed in remote areas, suggesting a potential long-range transport behavior. The average φ_P value of aryl-OPFRs (TMPP and TPHP) was 0.62, and the high-molecular-weight aryl-OPFR component TMPP had a larger proportion in the particle phase due to low vapor pressure and high octanol–air partition coefficients. These results indicate that the functional groups might affect the G/P partitioning process of OPFRs. For OPFR compounds with more branched chains and fewer functional groups, the monitoring φ_P values were generally low, such as those of TEHP, THP and TIBP. Interestingly, both TMP (alkyl-OPFR with low molecular weight) and TBOEP (alkyl-OPFR with high molecular weight) exhibited higher average φ_P values over 0.70. This discrepancy can be partially attributed to the probable sorption of gas-phase OPFRs to the filters during active air sampling.²² Another possible explanation is that OPFRs have better persistence and longer half-lives in the particle phase than in the gaseous phase, resulting in a higher proportion in the particle phase.³

A comparison of log K_P as a function of log K_OA values predicted by the four models for the three OPFRs groups (2 aryl-OPFRs, 3 chlorine-OPFRs, and 8 alkyl-OPFRs) is presented along with the measured data in Fig. 3 and S4.† OPFR compounds with high molecular weights and high log K_OA values were mainly distributed in the MP domain, such as the aryl-OPFR compound TMPP. The monitoring constant, log K_P, values of TMPP, TEHP and THP were observed in the MP domain (Fig. 3(f), (e) and S4(g)†). The L–M–Y model presented better consistency with the measured log K_P values of OPFRs in the ADR in the MP domain: 97.2% for the alkyl-OPFR compound TEHP, 76% for the aryl-OPFR molecule TMPP, and 100% for the alkyl-OPFR compound THP. In contrast, the other equilibrium models tended to overestimate the log K_P values of TEHP, TMPP, and THP. Especially in the MP domain, the observed constant log K_P values of OPFRs, including −1.51 ± 0.36 for TEHP, −1.16 ± 0.62 for TMPP, −1.45 ± 0.35 for THP, were close to the constant value (−1.53 ± 1) predicted by the L–M–Y model. In the NE domain, the L–M–Y model also demonstrated superior performance in predicting the G/P partition quotients for OPFRs, with 79.8% of the TEHP data points in the ADR (with RMSE = 0.81) in comparison with 60.1% (with RMSE = 1.14) for log K_P-HB, 58.3% (with RMSE = 1.18) for log K_P-DE, and 8.72% (with RMSE = 2.18) for log K_P-JP. Comparing the prediction theories and results of these four models, the wet and dry deposition might be an important factor for better prediction performance of the L–M–Y model in NE and MP domain.

Fig. 3 Log K_P predicted by the four models vs. log K_OA for 6 OPFR compounds: (a) TCEP; (b) TNBP; (c) TPHP; (d) TBOEP; (e) TEHP; (f) TMPP. (1) Chlorine-OPFR (TCEP), (2) aryl-OPFRs (TPHP and TMPP), and (3) alkyl-OPFRs (TNBP, TEHP, and TBOEP).

3.4 Driving factors for deviations in GPP predictions of OPFRs

As mentioned above, large deviations were observed between the measured log K_P and φ_P values of the OPFRs in the EQ domain and those predicted by the GPP models. These significant discrepancies may be attributed to sampling artifacts and some key influential factors that impact the GPP process of OPFRs, particularly the low-molecular-weight alkyl-OPFR compounds.⁵⁰ However, the deviation may also be caused by atmospheric processes that are overlooked or not described by these models, such as photodegradation and photocatalysis. These atmospheric processes are influenced by meteorological parameters, including temperature, relative humidity, wind speed, atmospheric pressure, solar radiation, UV index, and OH radicals.⁵¹ In a previous study, temperature (R = 0.789, p < 0.01), humidity (R = 0.525, p < 0.01), solar radiation (R = 0.429, p < 0.01), wind speed (R = −0.456, p < 0.01), and atmospheric pressure (R = −0.634, p < 0.01) have been correlated with the gas-phase OPFR concentration.⁵⁰ In previous research, the concentration of gaseous OPFRs has been found to have a significantly positive correlation with temperature and relative humidity.¹³ Higher relative humidity will cause the formation of liquid film covering the surface of the particle, which may disturb the interactions between the OPFRs and particle components via H-bonding or π–π bonding interactions.⁵² Greater wind speed is conducive to the diffusion, dilution and partition behavior of OPFRs.⁵³ Hence, we analyzed the correlation between the influencing factors (log K_OA, temperature, wind speed, and relative humidity) and the deviation of the results predicted by each model. The results show that the deviation of values predicted by these models has a significant correlation with log K_OA (Table S5†). The deviations of the L–M–Y, H–B, and D–E models exhibit significant correlation with log K_OA, temperature, and relative humidity, suggesting that these parameters might be the main factors influencing the deviation. Therefore, log K_OA, temperature, and relative humidity are considered to be the main drivers of OPFR distribution in the particulate phase in the EQ domain.

As mentioned above, the L–M–Y model shows better consistency with the measured data in the NE and MP domains. Thus, the L–M–Y model was chosen as the basic model to develop an empirical steady state model. In the EQ domain, similar to the other models, the L–M–Y model also demonstrates a large deviation from the measured data of the OPFR compounds with strong volatility and low lipophilicity.

3.5 An empirical equation for G/P partitioning of OPFRs

To reduce the deviation, an empirical equation was developed in the EQ domain based on the steady state theory. Firstly, considering the significant correlation between the deviation and log K_OA (R² = 0.87, p < 0.05), a relationship between the L–M–Y model-predicted deviations and log K_OA in the EQ domain was obtained as a linear regression:

Δlog K_P = 0.961 log K_OA − 10.68 (EQ domain) (11)

Secondly, by combining eqn (3) and (11), the empirical equation in the EQ domain could be written as

log K_P = 0.039 log K_OA + log f_OM + log α − 1.23 (12)

The percentage of measured data within the ADR of prediction increased from 23.1% in the original steady state model to 65.0% using the new empirical equation (eqn (12)), decreasing the impact coefficient of log K_OA from 1 to 0.039.

Furthermore, the Pearson correlation statistical method was applied for variable selection. Thus, log K_OA, relative humidity, and temperature might also be the reasons for data deviation in the EQ domain. A five-fold cross validation was adopted in modeling and validation to ensure the reliability and generalization ability of the model. The monitored data set used for modeling was randomly divided into five equally sized subsets, followed by 5 modeling and validation processes. Four subsets were selected as the modeling sets, and one subset was selected as the validation set each time. Considering these three parameters, a multilinear regression method was employed to establish the deviation equation for the OPFRs in the EQ domain using SPSS.22.0. In the established equations, the P-values of relative humidity were higher than 0.05. Therefore, log K_OA and temperature were considered as the main factors to reconstruct the equations using the above method. Five equations were derived to describe Δlog K_P based on log K_OA and temperature. The R² values of the five equations were 0.750, 0.747, 0.755, 0.762, and 0.754, respectively. The P values were lower than 0.01. Finally, deviation of the data predicted by the L–M–Y model in the EQ domain improved:

Δlog K_P = (0.966 ± 0.007)log K_OA + (0.011 ± 0.001)T − (10.961 ± 0.062) (13)

Then, the empirical prediction equation was improved:

log K_P = 0.034 log K_OA + log f_OM + log α − 0.011T − 0.949 (14)

where T denotes temperature (°C) in the range of 0–30 °C.

As mentioned above, overestimation of the contribution of log K_OA and temperature is the main reason for the large deviation observed in the values predicted in the EQ domain. As shown in eqn (14), wet and dry deposition, organic matter, and temperature could affect the G/P partition of OPFRs. Based on the characteristics of individual OPFRs, chlorinated OPFRs are more resistant to degradation than non-chlorinated compounds. Low-molecular-weight OPFRs (TEP and TPP) are expected to evaporate more readily than polymeric compounds and be less-associated with airborne particulate matter.⁵⁴ Some high-molecular-weight OPFRs containing benzene rings, such as TMPP, usually have good thermal and hydrolytic stability and high log K_OA values, and they are usually distributed in the particular phase at higher concentrations.^24,42

In addition to the factors mentioned above, the gas particle partitioning behavior of OPFRs can be influenced by other environmental factors, such as solar radiation, UV index, and OH radicals.⁵¹ OPFRs can be preferentially removed from the atmosphere by photooxidation. If the reactivity of OPFRs is related to their molecular weight, photooxidation may explain the observed OPFR partition behavior.⁵⁵

Then, the ADR of the improved empirical equation (eqn (14)) contained 75.8 ± 3.4% of the measured data points, as shown in Fig. 4, which represents a 10.8% increase compared with eqn (12) and a 52.7% increase compared with the original steady state model. The RMSE was 2.84 ± 0.04 for the improved empirical equation, in contrast to 4.52 ± 0.94 for the original steady state model. Therefore, eqn (14) can be considered the empirical equation for the G/P partitioning of OPFRs in the EQ domain.

Fig. 4 Percentage of data points in the ADRs of the steady state model and the new empirical equation.

As shown in a previous article, wet and dry deposition are non-ignorable determining processes in the G/P partitioning of SVOCs, such as PBDEs,²⁸ OCPs,³³ and PCBs.³⁵ In this work, an empirical equation without considering particle deposition was also derived, and the percentage of measured data points in the ADR was obviously lower than that obtained using eqn (14). Therefore, wet and dry deposition could also be an important factor for the G/P partitioning of OPFRs in the EQ domain.

Organic matter constitutes an important part of atmospheric particulate matter. According to eqn (14), the variation curves of log K_P with log K_OA at different organic matter concentrations are presented in Fig. S5.† As shown in Fig. S5,† the log K_P values of the OPFRs increased with an increase in f_om in the whole EQ domain. When log K_OA < 10, the log K_P of OPFRs increased nearly by 1 log unit as f_om increased from 0.1 to 0.9. When 10 < log K_OA < 11.4, the log K_P values of OPFRs increased slightly about 0.25, with the increase of f_om from 0.1 to 0.9. Thus, organic matter is also a crucial factor that influenced the G/P partitioning of OPFRs in the equilibrium domain.

In the EQ domain, inflection points of log K_Pvs. log K_OA of the OPFRs were observed in Fig. S5.† These inflection points mainly occurred at log K_OA values between 9.5 and 11.4. When log K_OA was below the inflection point, log K_P exhibited an increasing trend with respect to an increase in log K_OA. Conversely, log K_P decreased as log K_OA increased. Furthermore, the value of f_om also affected the occurrence of these inflection points. The larger the f_om, the smaller the log K_OA value at the inflection point. That is, the larger the f_om, the higher the temperature at which the inflection point appeared. This is an interesting discovery. The underlying reasons also warrant further investigations in the future to provide comprehensive answers.

4. Conclusions

The G/P partitioning of OPFRs in the atmosphere controls their atmospheric behaviors, such as long-range transport, as well as wet and dry deposition. In order to identify the key influencing factors and describe the OPFR gas/particle partition process more accurately, the characteristics of G/P partitioning of OPFRs were investigated by comparing the measured data and values predicted using four G/P partitioning models. Large deviations were observed between the measured log K_P and values predicted by these models in the EQ domain. The results indicated that in the MP domain, a constant value of log K_P (−1.21) was observed for the OPFRs, which is close to the predicted log K_P-LMY value of −1.53. The steady state model shows some advantages on predicting the log K_P of OPFRs with 85.2% of data points in ADR and φ_P close to the measured data in the MP domain. The deviation between the steady state model and measured data could be a function of log K_OA and temperature. A new empirical equation was derived to achieve better consistency between the predicted and monitored data, and the percentage of data points in the ADR increased from 23.1% to 75.8% in the EQ domain. These results demonstrate that wet and dry deposition could also be an important process for the GPP of OPFRs in the EQ domain. The higher f_OM value will lead to a higher log K_P value for OPFRs in the EQ domain, provided that all other conditions remain constant. Inflection points of log K_P with respect to log K_OA of the OPFRs have also been predicted in the EQ domain. Further research is required to discover the reasons behind the appearance of these inflection points.

Data availability

Data are available from the authors upon request.

Author contributions

Man Li collected data and wrote the manuscript. Wenhao Hou collected and checked data, analysed and revised the manuscript. Lina Qiao designed, wrote and revised the manuscript. Hong Zhang revised the manuscript. Mengdan Wang analysed data. Yonghui Wen analysed data. Zejiang Jia analysed data.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.42307472), the Natural Science Foundation of Shandong Province (No. ZR2021QD149). We also thank Prof. Yi-Fan Li and Prof. Wan-Li Ma for their valuable suggestions.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4em00531g

‡ Contributed equally as the first author.

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