Modeling and analysis of sampling artifacts in measurements of gas-particle partitioning of semivolatile organic contaminants using filter-sorbent samplers

Atmospheric Environment 117 (2015) 99e109

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Modeling and analysis of sampling artifacts in measurements of gas-particle partitioning of semivolatile organic contaminants using filter-sorbent samplers Xinke Wang a, b, Chenyang Bi b, Ying Xu b, * a b

School of Human Settlements and Civil Engineering, Xi'an Jiaotong University, Xi'an 710049, Shaanxi, China Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, TX, USA

h i g h l i g h t s
A mechanistic model to characterize air sampling process was developed and validated.
Positive sampling bias were observed for almost all the target SVOCs.
Correlations and plots provided can be used to estimate sampling bias for various SVOCs.
Particle penetration may result in underestimation of the gas/particle partition coefficient.
The option of backup filters must be considered carefully in field measurements.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 April 2015 Received in revised form 27 June 2015 Accepted 29 June 2015 Available online 6 July 2015

Measurements of gas/particle partition coefficients for semivolatile organic compounds (SVOCs) using filtersorbent samplers can be biased if a fraction of gas-phase mass is measured erroneously as particle-phase due to sorption of SVOC gases to the filter, or, if a fraction of particle-phase mass is measured erroneously as gasphase due to penetration of particles into the sorbent. A fundamental mechanistic model to characterize the air sampling process with filter-sorbent samplers for SVOCs was developed and partially validated. The potential sampling artifacts associated with measurements of gas-particle partitioning were examined for 19 SVOCs. Positive sampling bias (i.e., overestimation of gas/particle partition coefficients) was observed for almost all the SVOCs. For certain compounds, the measured partition coefficient was several orders of magnitude greater than the presumed value. It was found that the sampling artifacts can be ignored when the value of log½Kf =ðKp ,Cp;a Þ is less than 7. By normalizing the model, general factors that influence the sampling artifacts were investigated. Correlations were obtained between the dimensionless time required * Þ and the chemical V values, which can be for the gas-phase SVOCs within the filter to reach steady state ðTs;s p used to estimate appropriate sampling time. The potential errors between measured and actual gas/particle partition coefficients of SVOCs as a function of sampling velocity and time were calculated and plotted for a range of SVOCs (vapor pressures: 108 ~ 103 Pa). These plots were useful in identifying bias from the sampling in previously-completed field measurements. Penetration of particles into the sorbent may result in significant underestimation of the partition coefficient for particles in the size range between 10 nm and 2 mm. For most of the selected compounds, backup filters can be used to correct artifacts effectively. However, for some compounds with very low vapor pressure, the artifacts remained or became even larger than they were without the backup filter. Thus, the option of backup filters must be considered carefully in field measurements of the gas/particle partitioning of SVOCs. The results of this work will allow researchers to predict potential artifacts associated with SVOC gas/particle partitioning as functions of compounds, the concentration of particles, the distribution of particle sizes, sampling velocity, and sampling time. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Air sampling Sampling artifacts Gas/particle partitioning Semivolatile organic compounds (SVOCs) Modeling

* Corresponding author. Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, 301 E Dean Keeton St. Stop C1752 ECJ Hall 5.436, Austin, TX 78712-1094, USA. E-mail address: [email protected] (Y. Xu). http://dx.doi.org/10.1016/j.atmosenv.2015.06.053 1352-2310/© 2015 Elsevier Ltd. All rights reserved.

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1. Introduction Semivolatile organic compounds (SVOCs) are a class of chemical compounds that typically have vapor pressure (Vp) values between 109 and 10 Pa (Weschler and Nazaroff, 2008). Many SVOCs, such as polycyclic aromatic hydrocarbons (PAHs), polybrominated diphenylethers (PBDEs), polychlorinated biphenyls (PCBs), and phthalates, are persistent organic pollutants that are ubiquitous in ambient and indoor environments. Exposure to some of the SVOCs may result in adverse health effects, including allergic reactions (Bornehag et al., 2004, Jaakkola and Knight, 2008), irreversible changes in the development of the human reproductive tract
gou, 2014; Latini et al., 2006; Saillenfait et al., 2013; Su (Albert and Je et al., 2014 and Wolff et al., 2014), neurodevelopmental and behavioral disorders (Le Cann et al., 2011 and Wang et al., 2015), immunotoxicity (Birnbaum, 1994 and Van den Berg et al., 2006), € m et al., 2002; Denissenko et al., 1996 and and even cancer (Bostro Lewtas, 2007). Inhalation, dermal absorption, and nondietary ingestion of settled dust have been identified as the major exposure pathways to SVOCs (Allen et al., 2007; Frederiksen et al., 2009; Harrad et al., 2006; Meeker et al., 2009; Weschler and Nazaroff, 2010, 2014; Wilson et al., 2009; Xu et al., 2009 and Xu et al., 2010). A number of field campaigns have been conducted to measure air concentrations of SVOCs in indoor (Blanchard et al., 2014; Kolarik et al., 2008; Trabue et al., 2008; Wang et al., 2014 and Xu et al., 2014) and outdoor environments (Albinet et al., 2007; Chao et al., 2003; He and Balasubramanian, 2010; MacLeod et al., 2007 and Xie et al., 2014b). The fate and transport of SVOCs, as well as human exposures to them, can be influenced significantly by gas/particle partitioning. Particle-phase SVOCs are expected to account for a great fraction of the air concentrations due to their low Vp, particularly for compounds with high molecular weight (Wang et al., 2014; Weschler and Nazaroff, 2008 and Weschler et al., 2008). Recent studies have shown that inhalation of particle-phase phthalates is significant because such exposure is capable of creating high local concentrations in airways at the particle deposition site and potentially causing bronchial obstruction (Jaakkola and Knight, 2008; Oie et al., 1997 and Pankow, 2001). Both the location and the efficiency of the deposition of SVOCs in the respiratory tract are dependent strongly on gas/particle partitioning. Furthermore, because the kinetics of gas-particle sorption/ desorption are sufficiently rapid (Benning et al., 2013; Odum et al., 1994 and Weschler and Nazaroff, 2008 and Liu et al., 2013), in indoor environments, airborne particles might be important carriers that accelerate the transport of SVOCs from their original sources to other indoor locations through deposition, resuspension and air advection, although particle-phase SVOCs typically have lower characteristic transport distances than the gas-phase in outdoor environments. Therefore, to understand the fate and transport of SVOCs, accurate estimations of the partition coefficients between SVOC gases and particles are necessary (Hung et al., 2013, Melymuk et al., 2014). Several field measurements were conducted to determine the gas/particle partitioning for SVOCs (Cincinelli et al., 2014; Saral et al., 2015; Wang et al., 2014 and Xie et al., 2014a,b). In those studies, filter-sorbent samplers were used extensively, in which air was pulled through a filter to collect the particle-phase SVOCs and then followed by a sorbent to collect the gas fraction. This technique has been one of the most popular methods of sampling SVOCs over the past 40 years because of its simplicity and its ability to sample large volumes of air (Galarneau and Bidleman, 2006, Melymuk et al., 2014). Although measurements of the total airborne concentrations of SVOCs usually were acceptable, sampling artifacts were identified in the determination of gas/particle

partitioning (Ahrens et al., 2011, Melymuk et al., 2014). When gasphase molecules not being fully trapped by the sorbent, breakthrough happens and results in overestimation of the particle/gas partition coefficient. This positive bias may occur due to saturated sorbents or desorption of compounds from sorbents and is affected by the type and geometry of sampling medium, target compound properties and concentrations, and sampling volume, flow rate, temperature, and humidity (Melymuk et al., 2014). Breakthrough has been investigated extensively in previous studies (Harper, 1993; Peter et al., 2000; Martin et al., 2002 and Galarneau and Harner et al., 2006). In contrast, gas-phase SVOCs may sorb strongly to the filter, thereby increasing the mass of SVOCs on the filter. Mader and Pankow (2000) conducted systematic experiments and found that artifacts could be orders of magnitude for certain SVOC compounds due to their adsorption on the filter (Mader and Pankow, 2000, 2001a). Arp et al. (2007) studied the equilibrium sorption of SVOCs on fiber filters and derived linear free energy relationships for predicting the sorption isotherms. Corrections for the gas/filter adsorption artifacts were made by using a backup filter and subtracting the mass of SVOCs found on the backup filter from the total amount found on the front filter. However, the assumption that the sorption of the SVOCs on the front and backup filters is equal is not valid if the gas/filter sorption equilibrium has not been reached on either of the filters (Mader and Pankow, 2001b). In addition, particles may pass through the filter and subsequently be captured by the gas-phase sorbent material. However, there is limited information on how particles are distributed within the sampler and how the penetration contributes to uncertainty in the gas/particle partitioning of SVOCs. Theoretical analyses have been conducted to estimate the sampling artifacts associated with various sampling parameters. McDow (1999) presented a basic mass balance model to analyze the adsorption artifacts with various sampling volumes and types of filters. Galarneau and Bidleman (2006) used a simple mathematic model to study the bias due to temperature variations over the sampling period. Mader and Pankow (2001b) examined the partitioning of SVOCs to two types of filters and predicted the magnitude of the compound-dependent gas adsorption artifacts. However, the process of air samples passing through filter-sorbent samplers has not been fully characterized. Typically, some important processes, such as the diffusion of gas-phase SVOCs within the filter, the distribution of particles and particle-phase SVOCs in the filter, and the extent of penetration of particles, have been ignored even though they may have significant impacts on the estimation of sampling artifacts. The aim of this study was to analyze the sampling artifacts associated with measurements of gas-particle partitioning of SVOCs using filter-sorbent samplers. The specific objectives were to: 1) develop and validate a fundamental mechanistic model to characterize the air sampling process with filter-sorbent samplers for SVOCs; 2) examine the potential sampling artifacts of gas/particle partitioning for a range of SVOC contaminants; and 3) normalize the model and investigate the general factors that influence sampling artifacts and the effectiveness of backup filters. The results of this work can be used by researchers to predict the sampling artifacts in measurements of SVOC gas/particle partitioning as a function of compounds, sampling velocity, sampling duration, and the concentration and size distribution of particles. 2. Development of the model Fig. 1 shows a schematic representation of the air sampling process with filter-sorbent samplers. The air is passed through the filter in which the particle-phase SVOCs are expected to be trapped; in addition, gas-phase SVOCs can be captured via adsorption and

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Fig. 1. (a) Schematic representation of a filter-sorbent sampler collecting air samples; (b) gas- and particle-phase SVOCs within the filter.

particle penetration may occur. To simplify the model, we assumed that the air flow through the filter and the mass transfer of SVOC molecules within the filter were one-dimensional. Because breakthrough (i.e., loss of compounds downstream of the sampling medium) is typically examined in sampling set-ups or checked using a framework based on early breakthrough studies (Melymuk et al., 2014), it is not included within the scope of the current study. Therefore, we assumed that gas-phase SVOCs and the particles that penetrated the filter and entered the downstream air were fully captured by the sorbent. In addition, re-suspension of particles from the filter and the drift effect of the particles in the air flow were ignored. Finally, we assumed an equilibrium relationship between gas- and particle-phase SVOCs and ignored the internal mass transfer resistance inside particles (Liu et al., 2013). With reference to Fig. 1, the concentration of particles in the filter is governed by the following mass balance equation in Eulerian form:

ε

vCp;f vCp;p v2 Cp;p vCp;p ¼ Dp  ð1  εÞ v vt vx vt vx2

(1)

where Cp,p (mg/m3) is the concentration of particles in the pores of the filter, ε is the porosity of the filter, t (s) is the time, Dp (m2/s) is the effective diffusion coefficient of the particles in the filter, x (m) is the distance from the front of the filter, v (m/s) is the face velocity across the filter, Cp,f (mg/m3) is the concentration of particles trapped by the fibers of the filter. The initial and inlet boundary conditions are expressed in Equations (2) and (3):

Cp;p ¼ 0; for 0  x  L; t ¼ 0

(2)

Cp;p ¼ Cp;a ; for x ¼ 0; t > 0

(3)

where L (m) is the thickness of the filter, and Cp, a (mg/m3) is the concentration of particles in the sampling air. Assuming that the outlet boundary condition of the filter obeys the zero gradient condition (Brenner, 1962):

vCp;p ¼ 0; for x ¼ L; t > 0 vx

(4)

In addition, the capture rate of particles was assumed to be proportional to the concentration of particles in the pore (Song and Elimelech, 1993):

vCp;f ¼ kdep Cp;p vt

(5)

where kdep (s1) is the deposition constant of particles in the filter. The governing equation that describes the transient mass transfer of SVOCs in the filter is:

ε

vCs;f vCs;g vCs;p v2 Cs;g v2 Cs;p;p vCs;g þ þ ð1  εÞ ¼ Ds þ Dp v 2 vt vt vt vx vx vx2 vCs;p;p v vx (6)

where Cs;g (mg/m3) is the concentration of gas-phase SVOCs in the pores of the filter, Cs;p (mg/m3) is the total concentration of SVOCs in the particle phase in the filter, Cs;f (mg/m3) is the concentration of SVOCs adsorbed on the fibers of the filter, Ds (m2/s) is the effective diffusion coefficient of the gas-phase SVOCs in the filter, and Cs;p;p (mg/m3) is the concentration of particle-phase SVOCs in the pores of the filter. The related initial and boundary conditions are expressed in Equations (7)e(9):

Cs;g ¼ Cs;p ¼ Cs;f ¼ 0; for 0  x  L; t ¼ 0

(7)

Cs;g ¼ Cs;g;a ; for x ¼ 0; t > 0

(8)

vCs;g ¼ 0; for x ¼ L; t > 0 vx

(9)

where Cs;g;a (mg/m3) is the gas-phase concentrations of SVOCs in the sampling air. A linear, instantaneously reversible, equilibrium relationship was assumed to exist between the particles and the gas-phase SVOCs in the sampling air as well as between the filter's fibers and the gas-phase SVOCs, or

h i Cs;p ¼ Kp εCp;p þ ð1  εÞCp;f Cs;g ; Cs;p;p ¼ Kp Cp;p Cs;g ; Cs;f ¼ Kf Cs;g (10) where Kp (m3/mg) is the gas/particle partition coefficient of SVOCs, Kf (dimensionless) is the gas/filter partition coefficient of SVOCs. The fundamental mechanistic model that characterizes the air sampling process for SVOCs using filter-sorbent samplers is obtained by combining Equations 1e10. The model can be used to analyze the sampling artifacts in measurements of gas-particle

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partitioning of SVOCs and to predict temporal and spatial variations of SVOCs in the filter.

mea ), gas-phase concentration (C mea ) and particle mass concen(Cs;p;a s;g;a mea ): tration (Cp;a

3. Estimation of parameters and validation of model

Kpmea ¼

The effective diffusion coefficient of particles in the filter's pores (Dp) was estimated based on the filter's porosity (ε) (Ho and Webb, 2006) and the diffusion coefficient of particles in air (Dp,a). Similarly, the effective diffusion coefficient of gas-phase SVOCs in the filter's pores (Ds) was calculated based on ε and the diffusion coefficient of SVOCs in air (Da). Dp,a is related to particle size and can be determined by using the StockseEinstein Equation (Kulkarni et al., 2011). Da was estimated by OnSite (EPA, 2014) and other SVOC chemical properties were obtained by using EPI Suite TM. The deposition constant (kdep) was determined based on the collection efficiency of a single fiber (Sun et al., 2001). Detailed information on the estimation of these parameters is presented in the Supporting Information (SI). Quartz fiber filters (QFFs) and Teflon membrane filters (TMFs) are the two most commonly used filters in filter/sorbent air samplers. Mader and Pankow (2000, 2001a and 2001b) measured gas adsorption onto QFFs and TMFs for various SVOCs, including polycyclic aromatic hydrocarbons (PAHs), polychlorinated dibenzofurans (PCDFs), and polychlorinated dibenzodioxins (PCDDs). In this study, we corrected their data using the filter's porosity and density and then used the data to obtain the gas/filter partition coefficient (Kf) for SVOCs. Simple loglinear relationships were established between Kf and chemical Vp, as shown in Figure S1 (Table and Figure numbers preceded by an “S” are in the SI), and then the correlations were used to obtain Kf for other SVOCs that were not included in their measurements. The partition coefficients between gas- and particlephase SVOCs (Kp) were calculated using four different methods, as described in detail in the SI, and the median values were used in this study. Mader (2000) conducted experiments to examine the adsorption of SVOCs by TMFs at a temperature of 25  C. Air flow with constant SVOC concentrations was produced and drawn through two clean TMF filters, and the outlet concentrations were measured periodically. Unfortunately, airborne particles were not included in the study, and the measured gas/filter partition coefficient (Kf) was not reported. Therefore, we fitted their experimental data to obtain Kf and compared the fitted Kf with those in the literature, partially validating the model. Three SVOC compounds were selected, i.e., chrysene, 1,3,7,8-tetrachlorodibenzofuran (1,3,7,8-TetraCDF), and 1,2,4,7,8-pentachlorodibenzo-p-dioxin (1,2,4,7,8-PeCDD), and Table 1 summarizes the parameters used in the model. Since the face velocity was not provided by Mader (2000), it was estimated based on the given general range of sampling volume flow rates. (No information of sampling flow rate for each specific measurement could be found.) As shown in Fig. 2, Kf was obtained by fitting the model to the experimental data of concentration ratio between the outlet and inlet SVOCs (Cout/Cin) vs. sampling volume. The two solid lines represent model fitting at the minimum and maximum sampling face velocities, respectively, and the shadow area indicates the possible zone into which the model's prediction may fall. Then, the fitted Kf values were compared with those reported in the literature, as shown in Table 1. The small relative deviations partially validated the accuracy of the model. 4. Results According the definition of gas/particle partition coefficient for SVOCs (Pankow, 1994), the measured partition coefficient (Kpmea ) can be expressed by the measured particle-phase concentration

mea Cs;p;a mea mea Cs;g;a Cp;a

(11)

mea can be determined based on mass balance: Cp;a

Z Lh mea Cp;a ¼

0

i εCp;p þ ð1  εÞCp;f dx (12)

vts

where ts is the sampling time. Because a certain amount of gasphase mass could be measured improperly as being in the particle-phase due to adsorption onto the filters, the actual mea ) can be calcumeasured particle-phase SVOC concentration (Cs;p;a lated using the following equation:

Z L mea Cs;p;a ¼

0

 εCs;g þ Cs;p þ ð1  εÞCs;f dx vts

(13)

Similarly, particle penetration may result in erroneous measurements of gas-phase concentration, or

Z mea Cs;g;a ¼

0

ts

  Cs;g x¼L þ Cs;p x¼L dt ts

(14)

Therefore, the measured gas/particle partition coefficient (Kpmea ) can be calculated and compared with the actual partition coefficient (Kp) in the model. Nineteen SVOC compounds, including PAHs, PCDFs, PCDDs, and phthalates, were investigated in this study. Their physical and chemical properties are listed in Tables S1 through S3. The calculated median values of Kpmea were compared with those of the presumed Kp in the model at a sampling velocity of 0.1 m/s and sampling time of 24 h. As shown in Fig. 3, positive bias was observed for almost all target SVOCs. For certain compounds, such as chrysene and 1,2,4,7,8-PeCDD, the measured partition coefficient could be several orders of magnitude greater than the presumed value. The uncertainties associated with the data in the figure were due to the different methods used to determine Kp for each SVOC compound (Table S3). It was also found that the sampling artifact was smaller with TMFs than QFFs, and this was because of their smaller gas/filter partition coefficient (Table S2). Theoretically, gas/ filter sorption artifacts will be small when the amount of SVOCs adsorbed on the filters is small compared to that adsorbed on the collected particles. To further investigate the relationship, we plotted the potential sampling artifact (Kpmea =Kp ) with the mass ratio of SVOCs adsorbed on the filter to that on the particles [Kf =ðKp ,Cp;a Þ], as shown in Fig. 4. We found that the sampling artifacts can be ignored when the value of log½Kf =ðKp ,Cp;a Þ is less than 7, and small sampling artifacts will be achieved when the gas/ filter partition coefficients (Kf) are low, the particle loading on the filter (Cp,a) is high, and/or the sampling time is long. 5. Normalization of the model and discussion 5.1. Normalization of the model In order to investigate the general factors that influence the sampling artifacts, it is helpful to nondimensionalize the model. First, dimensionless variables and parameters were defined, including dimensionless linear distance (X * ; X * ¼ x=L), time (T * ; * ; T * ¼ t=L=v), concentration of particles in the filter's pores (Cp;p

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103

Table 1 Model parameters for SVOC adsorption to TMFs. Compounds

Chrysene

1,3,7,8-TetraCDF

1,2,4,7,8-PeCDD

Ds (106 m2/s)a L (mm)b Sampling flow rate (L/min)c Filter cross-sectional area (cm2)c Porosity (ε)d Log (Kp,face) (at 20  C) (m3/cm2) Log(Kf) (at 25 ºC)g Fitted log(Kf) (at 25 ºC)h

1.85 0.152  2 11e77 77 0.50 0.61e 7.70 7.85 ~ 7.90

1.98

1.84

0.53f 7.69 7.90 ~ 7.95

0.04e 8.25 8.00 ~ 8.11

a

See Table S2. There were two TMFs in the experiments (Mader, 2000). Mader, 2000. d See Table S4. e See Tables 2 and 3 in Mader and Pankow, 2001a. f Obtained by the equation listed in Table 1 in Mader and Pankow, 2000. g Kp,face in Mader and Pankow 92001a) was converted to Kf, using Kf ¼ Kp,face/L/(1-ε). The values of Kf at 20  C were then corrected to a temperature of 25  C using the equation listed in Table 1 in Mader and Pankow, 2000. h The minimum and maximum values correspond to the sampling flow rates of 11 and 77 L/min, respectively. b c

* ¼C Cp;p p;p =Cp;a ), concentration of particles captured by the filter's * ; C * ¼ C =C ), gas-phase SVOC concentration (C * ; fibers (Cp;f p;a p;f s;g p;f * ¼ C =C Cs;g particle-phase SVOC concentration s;g s;g;a ), * ;C * ¼ C =C * * (Cs;p s;p s;g;a Cs;p;p ; Cs;p;p ¼ Cs;p;p =Cs;g;a ), effective diffusion s;p coefficient for particles in filter pores (D*p ; D*p ¼ Dp =Lv ), deposition constant (k* ; k* ¼ kdep L=v), effective diffusion coefficient of SVOCs in the filter's pores (D*s ; D*s ¼ Ds =Lv), and gas/particle partition coefficient (Kp* ¼ Kp Cp;a ). Then, these variables and parameters were substituted into Equations 1e10 to obtain the following dimensionless equations:

ε

* vCp;p

vT *

¼ D*p

* v2 Cp;p

vX *2



* vCp;p

vX *

 ð1  εÞ

* vCp;f

vT *

(16)

* Cp;p ¼ 1; for X * ¼ 0; T * > 0

(17)

vX *

¼ 0 for X * ¼ 1; T * > 0

vT *

* ¼ k* Cp;p

(19)

(15)

* Cp;p ¼ 0; for 0  X *  1; T * ¼ 0

* vCp;p

* vCp;f

(18)

Fig. 2. Comparison of fitted SVOC concentration ratio between outlet and inlet (Cout/ Cin) with data measured by Mader (2000).

Fig. 3. Comparison of the measured gas/particle partition coefficient Kpmea and the presumed value (Kp): (a) QFFs; (b) TMFs.

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X. Wang et al. / Atmospheric Environment 117 (2015) 99e109

Z

1

h i * * * εCp;p dX * Cs;g þð1εÞCp;f

f2 ¼ 0Z 1 h 0

Z f3 ¼

0

* * εCp;p þð1εÞCp;f

i

dX

*

Z z

0

1

h i * * * εCp;p dX * Cs;g þð1εÞCp;f hf Ts* (27)

Ts*



*  Cs;g dT * X * ¼1

Ts*

(28)

These scales are in the range between 0 and 1, and the smaller the value, the more non-uniform the distribution is in the filter; and when the value is equal to 1, a uniform distribution of the gas-phase SVOCs in the filter's pores will be achieved. The normalized model suggests that several factors may have strong impacts on Kp*mea and the air sampling artifacts, and these factors are discussed in the following sections. Fig. 4. Logarithmic relationship between potential sampling artifact (Kpmea =Kp ) and the mass ratio of SVOCs adsorbed on the filter to that on the particles [Kf =ðKp ,Cp;a Þ].

ε

* vCs;g

vT *

þ

* vCs;p

vT *

þ ð1  εÞ

* vCs;f

vT *

¼ D*s

* v2 Cs;g

vX *2

þ D*p

* v2 Cs;p;p

vX *2



* vCs;g

vX *



* vCs;p;p

vX * (20)

* * * ¼ Cs;p ¼ Cs;f ¼ 0; for 0  X *  1; T * ¼ 0 Cs;g

(21)

* Cs;g ¼ 1; for X * ¼ 0; T * > 0

(22)

* vCs;g

vX *

¼ 0; for X * ¼ 1; T * > 0

(23)

h i * * * * * * * * Cs;g ¼ Kp* εCp;p þ ð1  εÞCp;f ; Cs;p;p ¼ Kp* Cp;p Cs;g ; Cs;f Cs;p * ¼ Kf Cs;g

5.2. Sampling time and velocity When sampling SVOCs with filter/sorbent samplers, the mass * ) reaches steady concentration of particles in the filter's pores (Cp;p state quickly and distributes non-uniformly within the filter (Figures S2 and S3). However, the concentration of particles on the * ) increases continuously as more particles are filter's fibers (Cp;f captured during air sampling. Meanwhile, gas-phase SVOCs diffuse within the filter and sorb strongly to the filter's fibers. As a result, the adsorptive partition relationship of SVOCs between the gas, particle, and filter phases was re-established. Similar to particles, * ) have a non-uniform distrigas-phase SVOC concentrations (Cs;g bution within the filter, which decreases along the filter depth and changes with time. Fig. 5 shows an example of the distribution of the gas-phase concentration of 1,2,4,7,8-PeCDD along the filter as a function of time. Thus, the gas-phase SVOC concentrations measured by the downstream sorbent are typically lower than the actual concentrations in the upstream air until the filter is saturated * distributes uniformly with SVOCs. After the filter is saturated, Cs;g within the filter and does not change with time, i.e., it reaches steady state. Therefore, the longer the non-steady state lasts in comparison to sampling time, the greater the difference will be between the measured and actual gas-phase SVOC concentrations. Assume the criterion to identify steady state for the gas phase is

(24) The dimensionless forms of measured gas- and particle-phase SVOC concentrations, as well as the mass concentrations of particles, can be expressed as shown in Equations (S7) e (S9) in the SI. Therefore, the measured dimensionless gas/particle partition coefficient can be obtained:

Kp*mea ¼

εf1 þ Kp* f2 hf Ts* þ ð1  εÞKf f1 h   i f3 1 þ 1  hf Kp* Ts* hf

(25)

where hf is the filter's collection efficiency, and f1 , f2 , and f3 are the defined non-uniform scales that were expressed in Equation 26e28, respectively:

Z1 f1 ¼ 0

* Cs;g dX *

(26) * ) Fig. 5. Distribution of dimensionless gas-phase concentration of 1,2,4,7,8-PeCDD (Cs;g within QFF at different dimensionless sampling time (Ts* ).

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that the concentration of the gas-phase SVOC downstream of the filter is no less than 99.9% of the incoming air flow. We calculated the time for the gas-phase concentration of selected compounds to reach steady state. Fig. 6 shows that correlations were obtained * to reach steady state (T * ) between the dimensionless time for Cs;g s;s * may also and chemical Vp for both QFFs and TMFs. In addition, Ts;s be influenced by the sampling velocity (v), but we found that this impact was small when v is was greater than 0.1 m/s (Figure S4), which is typical for high-volume air sampling (EPA, 1999). The main reason is that the diffusion terms in Equation (6) become negligible in comparison to the advection terms when v is large, resulting in a shorter time to reach steady state (t); the increase of v counters the * relatively constant. Therefore, the decrease of t and makes Ts;s correlations identified in Fig. 6 can be used to estimate the appropriate sampling time in measurements of gas-particle partitioning of SVOCs. For example, at a sampling velocity of 0.1 m/s, for an SVOC compound with a Vp of approximately less than 104 Pa using a QFF or with a Vp less than 106 with a TMF, steady state may not be reached (i.e., sampling bias may be developed) if the sampling time is less than 24 h. Sampling volume (or sampling volume flow rate) has been the focus when investigating the sampling bias in the gas/particle partitioning of SVOCs (Mader and Pankow, 2001b). However, we found that sampling velocity may be more important, because it is the parameter that determines the dimensionless diffusivities of particles and SVOCs, particle deposition velocity, and dimensionless sampling time. Therefore, we calculated the potential error between the measured and actual gas/particle partition coefficients of SVOCs (relative bias ¼ ðKp*mea  Kp* Þ=Kp* , %) as a function of sampling velocity and time, as shown in Fig. 7. For example, for one SVOC compound with a particular Vp, sampling time, and sampling velocity, the relative bias in measuring gas/particle partitioning can be determined from Fig. 7. The results can be used to identify sampling artifacts for a range of combinations of sampling times, velocities, and filter thicknesses used in field measurements and to develop appropriate protocols in measurements of gas-particle partitioning of SVOCs using filter-sorbent samplers. 5.3. Particle penetration Particles may pass through the filter and subsequently be trapped by the gas-phase sorbent material, which would result in

Fig. 7. Relative bias between measured and actual gas/particle partition coefficients for compounds with different chemical vapor pressures and with a range of combinations of sampling times, velocities, and filter thicknesses: (a) QFFs and (b) TMFs.

sampling bias. Typical QFFs and TMFs have a collection efficiency of 99%, but they do not often have a specified cutoff for fine particles (Melymuk et al., 2014). Researchers have found that ultrafine particles (typically < 100 nm) can penetrate the filter (Kim et al., 2007; Lee and Nicholson, 1994 and Melymuk et al., 2014). There is very limited information on how particles are distributed within the sampler, and this may contribute to uncertainty in the measurements of gas/particle partitioning. With particle penetration, the concentration of particles in the filter's pores (C*p,p) normally can reach steady state within a short period of time (Figures S2 and S3). Therefore, the distribution of C*p,p within the filter and the filter's collection efficiency (hf) are relatively stable during the sampling process. Since the dimensionless diffusion coefficient for particles (D*p) is much smaller than 1, the distribution of the steady state concentration of C*p,p in the filter can be obtained by solving Equations 15e19 with ignorance of the diffusion and unsteady terms, or: * to reach steady state (T * ) Fig. 6. Correlations between the dimensionless time for Cs;g s;s and chemical vapor pressure (Vp).

    Cp* X * ¼ exp  ð1  εÞk* X *

(29)

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We assumed that the criterion used to identify particle penetration was that more than 1% of the incoming particles pass through the filter and reach the sorbent. Thus, penetration occurs when k* is smaller than 4.6/(1-ε). Both k* and filter collection efficiency (hf) depend strongly on particle sizes and can be calculated (Kulkarni et al., 2011), as listed in Table S1 in the SI. To investigate the influence of particle penetration on the sampling artifacts, we ignored the adsorption of SVOCs onto the filter's fibers as well as the non-uniform distribution of gas-phase SVOCs in the filter. Therefore, the measured gas/particle partition coefficient can be expressed as:

Kp*mea ¼

þ Kp* K*  z  p  1 þ 1  hf Kp* 1 þ 1  hf Kp* 1 hf Ts



(30)

The ratio between Kp*mea and Kp* were plotted as a function of particle size in Fig. 8. As expected, penetration may result in negative sampling bias on the gas/particle partition coefficient, because the particle-phase SVOCs are captured by the downstream gas-phase sorbent. Particles with different sizes can cause different degrees of sampling artifacts. For instance, there is no obvious sampling bias for particles with sizes larger than 2 mm or smaller than 10 nm because particles in this size range are collected very efficiently by the filter. In contrast, significant underestimation of the partition coefficient could occur for particles in the size range between 10 nm and 2 mm. For some SVOC compounds with low vapor pressure (i.e., high Kp) and/or high particle concentration (i.e., Cp,a), the underestimation can reach as much as two orders of magnitude. Particles <2.5 mm in size (PM2.5) represent more than 75% of the total suspended particles by mass, and they are most relevant for human health and risk assessment estimates (Englert, 2004, Melymuk et al., 2014). Considering that the majority of SVOCs (80%) are typically found in particles at this size fraction (Degrendele et al., 2014, Okonski et al., 2014), sampling artifacts due to particle penetration in measurements of gas-particle partitioning for certain SVOCs cannot be ignored. 5.4. The effect of backup filters Air sampling with filter/sorbent samplers is sometimes

conducted using a backup filter to correct the adsorption of SVOCs to the front filter (Mader and Pankow, 2001). Assume that the amount of SVOCs sorbed on the front and backup filters have reached equilibrium with the SVOCs in the incoming sampling air. Corrections for the gas/filter adsorption artifact can be made by subtracting the mass of SVOCs on the backup filter from the total mass of SVOCs found on the front filter (particle phase þ sorbed on filter). However, this method will be appropriate only if both filters have reached equilibrium with the gas-phase SVOCs in the incoming sampling air. A backup filter was added in the dimensionless model, with the concentrations of SVOCs and particles at the inlet of the backup filter being equal to those of the outlet of the front filter. The governing equation and the initial and other boundary conditions were set the same for both filters. Then, in Fig. 9, we plotted the potential sampling artifact Kp*mea =Kp* with and without backup filter corrections for the selected SVOC compounds for sampling times of 10 and 72 h, respectively. As expected, the sampling artifacts with QFFs were mostly larger than those with TMFs due to their larger gas/filter partition coefficient; and an increase in the sampling time reduced the artifacts because the gas-phase concentration gradient decreased within the filter. For most of the selected compounds, backup filters can be used to correct artifacts efficiently (sampling time < 10 h) and effectively (log (Kp*mea =Kp* ) ¼ 0). However, for some compounds with very low vapor pressures, such as chrysene (compound number ¼ 4) and 1,2,4,7,8-PeCDD (compound number ¼ 13), the artifacts remained or became even larger than they were without the backup filter. The main reason for this occurrence was that the gas/particle partition coefficient (Kp) is related to both particle-phase concentration of SVOCs (Cs,p) and the concentration of the gas phase (Cs,g). When the filters were not saturated (i.e., non-steady state), subtracting the mass amount of SVOCs on the backup filter from the mass on the front filter helped to reduce the bias in the measured particle-phase concentration (Cs,p) to some extent. However, the great concentration gradients within the two filters made the gas-phase concentration (Cs,g) measured by the downstream sorbent significantly lower than reality. When the effect on Cs,g was stronger than the correction of Cs,p, the artifact was increased by using backup filters, as shown in the case of 1,2,4,7,8-PeCDD in Fig. 9. Therefore, the option of backup

Fig. 8. Potential sampling artifacts (Kp*mea =Kp* ) caused by particle penetration as a function of particle size: (a) QFFs; (b) TMFs.

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Fig. 9. Comparison of potential sampling artifact with and without backup filter corrections: (a) QFFs; (b) TMFs.

filters must be considered carefully when conducting field measurements of the gas/particle partitioning of SVOCs. 6. Conclusions A fundamental mechanistic model to characterize the air sampling process with filter-sorbent samplers for SVOCs was developed and partially validated. The potential sampling artifacts associated with measurements of gas-particle partitioning were examined for 19 SVOC compounds. Positive sampling bias (i.e., overestimation of gas/particle partition coefficients) was observed for almost all the SVOCs. For certain compounds, the measured partition coefficient was several orders of magnitude greater than the presumed value. It was found that the sampling artifacts can be ignored when the value of log½Kf =ðKp ,Cp;a Þ is less than 7, and small sampling artifacts will be achieved when the gas/filter partition coefficients (Kf) are low, the particle loading on the filter (Cp,a) is high, and/or the sampling time is long. We normalized the model and investigated the general factors that influence the sampling artifacts. Correlations were obtained between the dimensionless time required for the gas-phase SVOCs * ) and the chemical V within the filter to reach steady state (Ts;s p values, which can be used to estimate appropriate sampling time. The potential errors between measured and actual gas/particle partition coefficients of SVOCs as a function of sampling velocity and time were calculated and plotted for a range of SVOCs (vapor pressures: 108 ~ 103 Pa). These plots were useful in identifying sampling bias in previously-completed field measurements. Particle penetration may result in underestimation of the partition coefficient for particles in the size range between 10 nm and 2 mm; this underestimation can be about two orders of magnitude, especially for some SVOCs compounds with low vapor pressure (i.e., high Kp) and/or high particle concentration (i.e., Cp,a). For most of the selected compounds, backup filters can be used to correct

artifacts efficiently and effectively; however, for some compounds with very low vapor pressures, such as chrysene and 1,2,4,7,8PeCDD, the artifacts remained or became even larger than they were without the backup filter. Therefore, the option of backup filters must be considered carefully in field measurements of the gas/particle partitioning of SVOCs. The results of this work will allow researchers to predict the potential artifacts associated with SVOC gas/particle as functions of the compounds involved, the concentrations of particles, the distribution of particle sizes, sampling velocity, and sampling time. It will also help researchers develop appropriate protocols for the measurement of gas-particle partitioning of SVOCs using filtersorbent samplers. Acknowledgments Financial support was provided by the National Science Foundation (NSF) of United States (CBET-1150713 and CBET- 1066642), American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE) (Grant-In-Aid and NIA Awards), the National Natural Science Foundation of China (No. 51206134), and the Fundamental Research Funds for the Central Universities of China (2015GIHZ14). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.atmosenv.2015.06.053. Nomenclature Cp,a Cp,f

concentration of particles in the sampling air (mg/m3) concentration of particles trapped by the fiber of the filter (mg/m3)

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Concentration of particles in the pore of the filter (mg/m3) concentration of SVOCs adsorbed on the fibers of the filter (mg/m3) Cs;g concentration of gas-phase SVOCs in the pore of the filter (mg/m3) Cs;g;a gas-phase concentration of SVOCs in the sampling air (mg/ m3 ) Cs;p total concentration of SVOCs in the particle phase in the filter (mg/m3) Cs;p;a particle-phase concentration of SVOCs in the sampling air (mg/m3) Cs;p;p concentration of particle-phase SVOCs in the pore of the filter (mg/m3) Da diffusion coefficient of SVOCs in air (m2/s) Dp effective diffusion coefficient of the particles in the filter (m2/s) Dp,a diffusion coefficient of particles in air (m2/s) Ds effective diffusion coefficient of the gas-phase SVOCs in the filter (m2/s) k* dimensionless particle deposition constant kdep deposition constant of particle in the filter (s1) Kp gas/particle partition coefficient of SVOCs (m3/mg) Kf gas/filter partition coefficient of SVOCs (dimensionless) Kp,face gas/filter partition coefficient of SVOCs in the literature (m3/mg) L The thickness of the filter (m) t time (s) T* Dimensionless time v the face velocity across the filter (m/s) Vapor pressure (Pa) Vp x distance from the front of the filter (m) X* Dimensionless distance f1 , f2 , f3 the defined non-uniform scales Cp,p Cs;f

Greek ε

hf

porosity (dimensionless) filter collection efficiency

Superscript * dimensionless parameter mea measured value Subscript a s s,s p

the value in the sampling air SVOCs or sampling steady state particle or pore

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