Gas–particle (G–P) partitioning is a crucial atmospheric process for semi-volatile organic compounds (SVOCs), particularly polycyclic aromatic hydrocarbons (PAHs). However, accurately predicting the G–P partitioning of
PAHs has remained a challenge. In this study, we established a new
steady-state G–P partitioning model based on the level-III multimedia
fugacity model, with a particular focus on the particulate proportion
(ϕ0) of PAHs in emissions. Similar to previous steady-state
models, our new model divided the G–P partitioning behavior into three domains based on the threshold values of logKOA (octanol–air partitioning coefficient), with slopes of 1, from 1 to 0, and 0 for the three domains. However, our model differed significantly from previous models in different domains. We found that deviations from the equilibrium-state G–P partitioning models were caused by both gaseous interference and
particulate interference, with ϕ0 determining the influence of
this interference. Different forms of the new steady-state model were
observed under different values of ϕ0, highlighting its
significant impact on the G–P partitioning of PAHs. Comparison of the G–P partitioning of PAHs between the prediction results of our new steady-state model and monitored results from 11 cities in China suggested varying prediction performances under different values of ϕ0, with the lowest root mean square error observed when ϕ0 was set to 0.9 or 0.99. The results indicated that the ϕ0 was a crucial factor for
the G–P partitioning of PAHs. Furthermore, our new steady-state model also demonstrated excellent performance in predicting the G–P partitioning of
PAHs with entirely gaseous emission and polybrominated diphenyl ethers with
entirely particulate emission. Therefore, we concluded that the ϕ0 should be considered in the study of G–P partitioning of PAHs, which
also provided a new insight into other SVOCs.
National Natural Science Foundation of China4167147042077341State Key Laboratory of Urban Water Resource and Environment2023TS18Introduction
The phenomenon of long-range atmospheric transport is capable of
transporting semi-volatile organic compounds (SVOCs) from their sources to
remote regions, such as the Arctic and the Tibetan Plateau, where they are
neither produced nor utilized (Hung et al., 2005, 2010; C. Wang
et al., 2018). The gas–particle (G–P) partitioning of SVOCs is an important
atmospheric process that governs their fate and long-range transport
(Zhao et al., 2020; Li et al., 2015). Furthermore, the distribution
between the gas and particle phases plays a pivotal role in controlling the
wet and dry depositions of SVOCs, thereby impacting the efficiency and
extent of their long-range transport from sources to remote regions
(Bidleman, 1988). Furthermore, the G–P partitioning of SVOCs is a
significant issue for human exposure assessment, as gaseous and particulate
SVOCs enter the human body through different routes (Weschler et al.,
2015; Hu et al., 2021).
The G–P partitioning of SVOCs has been the subject of extensive research for several decades. Various models have been developed to predict the G–P partitioning coefficient (KP) of SVOCs (Zhu et al., 2022; Qiao et al., 2020). Qiao et al. (2020) recently categorized eight G–P partitioning models into three groups: (1) models based on equilibrium-state theory (Pankow, 1987; Harner and Bidleman, 1998; Dachs and Eisenreich, 2000; Goss, 2005), (2) empirical models based on monitoring data (Li and Jia, 2014; Wei et al., 2017; Shahpoury et al., 2016), and (3) models based on steady-state theory (Li et al., 2015). Additionally, a new
empirical model (equation) for polycyclic aromatic hydrocarbons (PAHs)
(Zhu et al., 2022) and a new steady-state mass balance model for
polybrominated diphenyl ethers (PBDEs) (Zhao et al., 2020)
have recently been established. These models have been evaluated using field
monitoring programs (Vuong et al., 2020; Qiao et al., 2019) and are
frequently used to predict the G–P partitioning behavior of SVOCs
(Qiao et al., 2020).
The G–P partitioning process of PAHs is more complex than that of other
SVOCs due to concurrent particle formation (Dachs and Eisenreich, 2000;
Shahpoury et al., 2016; Zhu et al., 2022). For instance, when the
octanol–air partitioning coefficient (logKOA) exceeds 12, the monitored values of KP-M (monitoring data of G–P partitioning) of PAHs deviate
from the predictions of both equilibrium-state and steady-state G–P
partitioning models (Ma et al., 2020; Zhu et al., 2022). Recent studies
have found that the particulate proportion (ϕ0) of SVOCs in the
emissions could affect the G–P partitioning of SVOCs (Qin et al., 2021;
Zhao et al., 2020). As ϕ0 increases, the predictions can diverge
from the steady-state G–P partitioning model to the equilibrium-state G–P
partitioning model (Qin et al., 2021; Zhao et al., 2020). Moreover, the
emission sources of PAHs in the atmosphere are complex, including stationary
sources (residential combustion, industrial production, and agricultural
burning) and mobile sources (motor vehicles, railways, and shipping)
(Zhang et al., 2020; Tang et al., 2020), in which both gaseous and
particulate PAHs exist (Zimmerman et al., 2019; R. Wang et al., 2018; Shen
et al., 2011; Cai et al., 2018b). Therefore, the detailed influence of
ϕ0 on the G–P partitioning of PAHs could be considered to explain the deviation of the measured KP-M from both the equilibrium-state and the steady-state G–P partitioning model predictions.
In this study, we establish a new steady-state G–P partitioning model
(hereafter referred to as the new steady-state model) based on the level-III
multimedia fugacity model for PAHs and comprehensively discuss the
influence of ϕ0. Specifically, we (1) establish and deeply study
the new steady-state model under different threshold values of logKOA, (2) comprehensively discuss the influence of ϕ0 on the G–P partitioning of PAHs, and (3) study the performance of the new
steady-state model for prediction of KP of PAHs.
Establishment of the new steady-state G–P partitioning modelEstablishment method of the new steady-state model
In the current study, a steady-state six-compartment six-fugacity model was
employed. The intricacies of this model can be found in Text S1 of the
Supplement. The input and output fluxes of PAHs in both the
gaseous and the particulate phases were graphically depicted in Fig. 1. The
comprehensive computational techniques utilized to determine these fluxes
are elaborated upon in Text S2.
The fluxes related to the gas and particle phase in the
six-compartment model. FGR: degradation flux of gas-phase PAHs, FPR: degradation flux of particle-phase PAHs, FGP: migration flux from the gas phase to the particle phase, FPG: migration flux from the particle phase to the gas phase, FGWS_diff: diffusion fluxes from the gas phase to water and/or soil phases, FGW: wet deposition flux of gas-phase PAHs to water and/or soil phases, FWSG_diff: diffusion fluxes from soil and/or water phases to the gas phase, FPD: dry deposition flux of particle-phase PAHs to suspended particle matter (SPM) in water phase and/or soil phase, FPW: wet deposition flux of
particle-phase PAHs to SPM and/or soil phases, (1-ϕ0)E: emission
flux of gas-phase PAHs, and ϕ0E: emission flux of particle-phase
PAHs.
Four groups were compared in terms of gas-phase and particle-phase input and
output fluxes, namely input fluxes of the gas phase, output fluxes of the gas phase,
input fluxes of the particle phase, and output fluxes of the particle phase. The
results for PAHs were illustrated in Fig. S1. In order to establish a
universal and concise model, the four fluxes (FGWS_diff,
FWSG_diff, FPR, and FGW) were excluded from the system as their contributions were less than 10 % of the total fluxes. Furthermore, the special situation was not taken into account. For instance, even if the contribution of the flux of FGW for dibenzo[a,h]anthracene (DahA) exceeded 10 %, it was still removed. After simplifying the function in Text S1, the two linear equations describing the input and output fluxes of the gas phase and the particle phase were established as follows:
1-ϕ0E+DGPfP=DGR+DGPfGϕ0E+DGPfG=DGP+DPD+DPWfP,
where fP is the fugacity for particle-phase PAHs; fG is the fugacity for gas-phase PAHs; DGP is the intermedia D value between the gas phase and the particle phase; DGR is the D value for the degradation of gas-phase PAHs; and DPD and DPW are the D values of the dry and wet
depositions of particle-phase PAHs, respectively.
The fugacity ratio of the particle phase to the gas phase can be obtained by
solving Eq. (1) as follows:
fPfG=DGP+ϕ0DGRDGP+1-ϕ0DPD+DPW.
According to the fugacity method (Li et al., 2015) (see details in
Text S3), the new steady-state model can be expressed as follows:
logKP-NS=logKP-HB+logDGP+ϕ0DGRDGP+1-ϕ0DPD+DPW.
In Eq. (3), logKP-HB is the equilibrium-state G–P partitioning model (named the H–B model in this study, logKP-HB=logKOA+logfOM-11.91; fOM is the fraction of organic matter in particles, and KOA is the octanol–air partitioning coefficient)
(Harner and Bidleman, 1998). DGR, caused by the degradation
of PAHs in the gas phase, is defined as the gaseous interference, and
DPD+DPW, caused by the deposition of PAHs in the particle phase, is defined as the particulate interference. The magnitude of this
interference is determined by the value of ϕ0.
By applying the calculation method of the D values in the multimedia fugacity model (Table S1) and the values of the related parameters in Tables S2, S3, S4, S5, and S6, Eq. (2) can be simplified as follows:
fPfG=1+13.2ϕ0×kdeg1+10-10.31(1-ϕ0)fOMKOA,
where kdeg is the degradation rate of PAHs in the gas phase (h-1).
Therefore, Eq. (3) can also be expressed as follows:
logKP-NS=logKP-HB+log1+13.2ϕ0×kdeg1+10-10.31(1-ϕ0)fOMKOA.
Thus, it can be found that the new steady-state model (logKP-NS) is a function of ϕ0, kdeg, fOM, and KOA.
Different domains of the new steady-state model
Three domains have been delineated based on the threshold values of logKOA. For example, if 10-10.31(1-ϕ0)fOMKOA≪1, the initial threshold of logKOA (logKOA1) can be derived. Subsequently, Eq. (5) can be expressed as follows:
logKP-NS=logKP-HB+log1+13.2ϕ0×kdeg.
In this domain, the value of logKOA was less than logKOA1, and logKP-NS was a function of KOA, fOM, ϕ0, and
kdeg. As depicted in Fig. 2, the domain was illustrated with vertical lines serving as the backdrop. Notably, the prediction line of the new steady-state model was parallel to that of the H–B model within this
domain.
The three domains of the new steady-state G–P partitioning model divided by the two threshold values of logKOA.
In addition, if 10-10.31(1-ϕ0)fOMKOA≫1, the secondary threshold of logKOA (logKOA2) can be determined. Eq. (5) can be expressed as follows:
logKP-NS=logKP-HB+log1+13.2ϕ0×kdeg10-10.31(1-ϕ0)fOMKOA.
Through substitution of logKP-HB using the equation logKP-HB=logKOA+logfOM-11.91 as proposed by Harner and Bidleman (1998), Eq. (7) can be simplified as follows:
logKP-NS=log1+13.2ϕ0×kdeg1-ϕ0-1.6.
Within this domain, the value of logKOA was higher than logKOA2; logKP-NS was solely dependent on ϕ0 and kdeg; and logKP-NS reached a maximum constant value (logKP-NSmax), as depicted by the section with horizontal lines in Fig. 2.
Within this domain, the prediction line of the new steady-state model was
parallel to that of the L–M–Y model.
Moreover, in the range where logKOA1<logKOA<logKOA2, logKP-NS exhibited a positive correlation with logKOA, with a decreasing slope from 1 to 0 (Eq. 5). Within this domain, logKP-NS was influenced by several factors, including KOA, fOM, ϕ0, and kdeg. This particular range is depicted in
Fig. 2 with a background of diagonal lines. Notably, within this domain, the
prediction line of the new steady-state model closely resembled that of the
L–M–Y model.
Difference between the new steady-state model and previous models
The dissimilarity between the new steady-state model and the H–B
(Text S4) and L–M–Y models (the steady-state model) (Li et
al., 2015) (Text S4) can be computed using Eq. (5) in different domains.
In essence, as shown in Fig. 2, when logKOA<logKOA1, the
contrast between the new steady-state model and the H–B model or the L–M–Y
model can be denoted as δ1=log(1+13.2ϕ0×kdeg). The value of δ1 increased along with the
increase in ϕ0 and reached the maximum value of log(1+13.2kdeg) when ϕ0=1 (Fig. S2a). When logKOA>logKOA2, the difference between the new steady-state model
and the L–M–Y model can be expressed as δ2=log[(1+13.2ϕ0×kdeg)/(1-ϕ0)]. The value
of δ2 also increased along with the increase in ϕ0
and approached infinity when ϕ0 is infinitely close to 1 (Fig. S2b). When logKOA1<logKOA<logKOA2, the
difference between the new steady-state model and the L–M–Y model was the
function of ϕ0 and KOA, which increased along with the
increase in ϕ0 and KOA. Further information can be found in the subsequent section.
Influence of <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> on <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> of PAHs
In general, varying values of ϕ0 correspond to distinct
configurations of the new steady-state model (Eq. 3). Specifically, three
different forms can be obtained depending on the values of ϕ0: 0<ϕ0<1, ϕ0=0, and ϕ0=1.
When 0<ϕ0<1, both the particulate and the gaseous
PAHs are present in the emission, and the new steady-state model is
expressed as Eq. (3). In this form, it is necessary to consider both gaseous interference
and particulate interference for the G–P partitioning of PAHs in the
atmosphere. The deviation of the new steady-state model from the H–B model
depends on the ratio of ϕ0DGR to (1-ϕ0)(DPD+DPW). When the ratio exceeds 1, logKP-NS deviates upwards from the prediction of the H–B model, whereas logKP-NS deviates downwards when the ratio is lower than 1.
When ϕ0=0, the PAHs in the emission are entirely in the form
of gaseous PAHs, and Eq. (3) can be expressed as follows:
logKP-NS=logKP-HB+logDGPDGP+DPD+DPW.
Indeed, this equation is identical to that of the L–M–Y
model, wherein α is defined as DGP/(DGP+DPD+DPW) (Li et al., 2015).
When ϕ0=1, the PAHs in the emission are entirely in the form
of particulate PAHs, and Eq. (3) can be expressed as follows:
logKP-NS=logKP-HB+logDGP+DGRDGP.
The disparity of the new steady-state model from the H–B model can
primarily be attributed to the degradation of PAHs in the gas phase. In cases where
kdeg is negligible, the new steady-state model is equivalent to the H–B model.
The comparison between the new steady-state model and the H–B model
and the L–M–Y model. (a) The prediction lines of the three models; (b) the difference between the new steady-state model and the L–M–Y model with different values of ϕ0.
The impact of ϕ0 on KP-NS of PAHs was investigated by
analyzing different values of ϕ0, and the results are presented
in Fig. 3. As depicted in Fig. 3a, the prediction line of the new
steady-state model diverged from the L–M–Y model towards the H–B model as ϕ0 increased, which was consistent with previous studies (Zhao et
al., 2020; Qin et al., 2021). In addition, obvious differences were observed
between the prediction lines for the three models. Notably, when ϕ0=1, the line of logKP-NS was parallel to the line of logKP-HB. When ϕ0=0, the prediction line of logKP-NS was identical to that of logKP-LMY. When 0<ϕ0<1, the trend of the prediction lines of logKP-NS was similar to that of logKP-LMY. The deviation between the prediction lines of logKP-NS and logKP-LMY is illustrated in Fig. 3b. Generally, the
deviations between the prediction lines varied with the values of ϕ0 and logKOA. Additionally, the deviation increased with the
increase in ϕ0 and exhibited three distinct trends with the
increase in logKOA, separated by the two threshold values of logKOA (logKOA1 and logKOA2).
Validation of the new steady-state G–P partitioning modelValidation
As is widely acknowledged, the sources of atmospheric PAH emission are
multifaceted, encompassing both stationary sources and mobile sources
(Zhang et al., 2020). Moreover, varying proportions of particulate
PAHs have been reported across different emission sources (Zimmerman et
al., 2019; R. Wang et al., 2018; Shen et al., 2011; Cai et al., 2018b). As a
result, determining precise values of ϕ0 is no easy feat. In this
section, we consider different values of ϕ0 (0, 0.1, 0.5, 0.9,
0.99, and 1) in conjunction with the new steady-state model for predicting
KP-M of PAHs, in order to obtain representative results.
To assess the performance of the new steady-state model, the monitored logKP-M values of PAHs from 11 cities across China were utilized (Ma et al.,
2018, 2019, 2020). As depicted in Fig. 4, the
prediction line of the new steady-state model exhibited a remarkable
concurrence with the monitoring data of logKP-M. Notably, for the
monitoring data with high logKOA, the data were predominantly distributed
between the prediction lines of the steady-state model with the values of
ϕ0 from 0 to 1. Furthermore, for different cities (Fig. S3), the values of ϕ0 for the best-matched prediction lines of
the new steady-state model varied, which was anticipated, since the sources
of PAHs also differed among the 11 cities. The degree of concurrence of the
new steady-state model was also evaluated using the root mean square error
(RMSE) method (Text S5). Generally, for PAHs with high values of logKOA (such as the high-molecular-weight PAHs), when ϕ0 was set to 0.9 or 0.99, the value of RMSE for each city was the lowest (Fig. S4),
indicating the best degree of concurrence between the prediction results and
the monitoring results. In fact, previous studies have shown that high-molecular-weight PAHs were dominant in the particle phase in emissions with
higher ϕ0 (Shen et al., 2011; Mastral et al., 1996; Lu et
al., 2009), which lends credence to our findings.
The comparison between the monitored data of logKP-M of PAHs from 11 cities in China and the prediction lines of the new steady-state
model with different values of ϕ0.
Moreover, the performance of the new steady-state model in predicting logKP-M of PAHs in a special scenario was also examined. Notably, in the prototype coking plant, the dust removal efficiency was an impressive 96 % (Liu et al., 2019). In this scenario, the gaseous PAHs were
the primary source of emissions, and the values of ϕ0 were
approximately 0. As illustrated in Fig. S5, the monitored data of logKP-M from the coking plant aligned most closely with the prediction line of the new steady-state model with ϕ0=0, exhibiting the
lowest RMSE. Based on this comparison, the optimal ϕ0 in the
steady-state model was consistent with that in the emission profile. This
finding underscored the exceptional performance of the new steady-state
model in this unique scenario.
It is possible to extend the steady-state model to other SVOCs by taking
into account their comparable partitioning characteristics, while the model
was originally developed based on the parameters of PAHs. To validate the
performance of the new steady-state model for other SVOCs, a special
scenario involving the recycling of electrical and electronic waste
(e-waste) sites was considered. In this case, PBDEs were predominantly found
in the particle phase of emissions, and the value of ϕ0 was
estimated to be approximately 1 (Cai et al., 2018a). Fig. S6
depicts the comparison between the monitored data of logKP-M from
several e-waste sites (Tian et al., 2011; Han et al., 2009; Chen et al.,
2011) and the prediction lines of the new steady-state model with varying
values of ϕ0 (0, 0.1, 0.5, 0.9, 0.99, and 1). The corresponding
results for RMSE are presented in Fig. S7. Notably, the monitored data of logKP-M exhibited the best agreement with the prediction line of the new steady-state model with ϕ0=1, which also had the lowest values of RMSE. Thus, it can be inferred that the new steady-state model can be expanded to predict the KP-M of PBDEs in e-waste sites.
Implication
The present study has introduced a new steady-state G–P partitioning model, which incorporates the particulate proportion of SVOCs in emissions. In
essence, the study has shed new light on the field of G–P partitioning and other related disciplines involving SVOCs. Firstly, in cases where SVOCs in the atmosphere originate from diverse emission sources with varying ϕ0, the new steady-state model is more appropriate for the G–P
partitioning study and other related assessments, such as those pertaining
to health risks. Secondly, when examining the pollution characteristics and
regional transport of SVOCs from a single point source, such as the
transport of PBDEs around an e-waste site or the transport of SVOCs around
chemical factories, the G–P partitioning of SVOCs must account for the
particulate fraction of SVOCs in emissions. Thirdly, for long-range
atmospheric transport studies, if there are multiple sources of SVOCs along
the transport way, the continuous impact of the particulate fraction of
SVOCs in emissions on the transport and fate of SVOCs needs careful
consideration, such as the development of an atmospheric transport model.
Limitation
In light of the foregoing discussion, it can be inferred that the new
steady-state model exhibited commendable performance in predicting
KP-M of PAHs in diverse real-world atmospheres, thereby providing a
fresh avenue for investigating the G–P partitioning of PAHs and other SVOCs. Nonetheless, certain limitations of the new steady-state model persisted in the present study. Firstly, the values of ϕ0 varied across different compounds and different emission sources (Zimmerman et al.,
2019; R. Wang et al., 2018; Shen et al., 2011; Cai et al., 2018b). In the
present study, constant values of ϕ0 were employed for the new
steady-state model, which were merely considered to be special examples. The
precise values of ϕ0 should be utilized for the application of
the new steady-state model in the future. Secondly, for kdeg and
fOM, only one constant and common value was employed for the new
steady-state model. Generally, these two parameters were also complex in the
real atmosphere. For example, kdeg was related not only to the
physicochemical properties of chemicals, but also to the environmental
parameters, such as temperature and concentration (Wilson et
al., 2021). Moreover, even though the fOM can be directly measured, the actual values of fOM also fluctuated with various factors, such as emission sources (Gaga and Ari, 2019; Lohmann and Lammel, 2004) and particle sizes (Hu et al., 2020). To evaluate the impact of
the three parameters on KP-NS in the new steady-state model, the sensitivity analysis was conducted via a Monte Carlo analysis with 100 000 trials employing the commercial software package Oracle Crystal Ball. To obtain comprehensive results, the sensitivity analysis was conducted for different values of logKOA from 6 to 16. As presented in Fig. S8, it is noteworthy that three different ranges of logKOA were observed based on different characteristics. For the range of logKOA from 6 to 10, the influence of ϕ0 dominated followed by kdeg and fOM. Furthermore, for each parameter, the influence remained stable for different logKOA values in this range. For the range of
logKOA from 10 to 12, the influence of ϕ0 dominated followed by kdeg and fOM. Additionally, the influence of ϕ0 increased, while for the other two parameters the influence decreased. In the third range of logKOA (12 to 16), the influences of the three parameters remained stable. Moreover, the influence of ϕ0 dominated, and the influence of fOM can be disregarded. In fact, the three ranges of logKOA were consistent with the three domains. It can be concluded that the different influences of the three parameters on KP-NS for different logKOA values should be considered
for the new model. Therefore, the precise values of ϕ0,
kdeg, and fOM for the real atmosphere should be employed for the application of the new steady-state model in the future.
Furthermore, the new steady-state model was established based on a single
multimedia environment, in which the advections of air and water were not
considered. Additionally, some fluxes were removed to simplify the
parameters of the model. Therefore, the influence of all fluxes and
parameters related to gas and particle compartments should
comprehensively be evaluated in the future. Furthermore, the validation and
implication of the new steady-state G–P partitioning model should also be conducted for other SVOCs in a real multimedia environment.
Code availability
Code is available upon request to the corresponding author.
Data availability
Data are available upon request to the corresponding author.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-23-8583-2023-supplement.
Author contributions
FJZ: methodology, investigation, writing (original draft preparation). PTH: writing (review and editing). WLM:
conceptualization, methodology, writing (review and editing).
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
This research has been supported by the Heilongjiang Touyan Innovation Team Program, China.
Financial support
This research has been supported by the National Natural Science Foundation of China (grant nos. 41671470 and 42077341). This research has been partially supported by the State Key Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology (grant no. 2023TS18), and the Heilongjiang Provincial Natural Science Foundation of China (grant no. YQ2020D004).
Review statement
This paper was edited by Leiming Zhang and reviewed by two anonymous referees.
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