Supporting Information€¦ · 1 Supporting Information Modeling gas/particle partitioning of...

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Supporting Information

Modeling gas/particle partitioning of polybrominated diphenyl

ethers (PBDEs) in atmosphere: A review

Li-Na Qiao1,2,3, Peng-Tuan Hu1,2,3, Robie Macdonald4, Kurunthachalam Kannan5, Anatoly

Nikolaev6, Yi-Fan Li1,2,3,7*

1 International Joint Research Center for Persistent Toxic Substances (IJRC-PTS), State Key

Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology, Harbin

150090, China

2 International Joint Research Center for Arctic Environment and Ecosystem (IJRC-AEE),

Polar Academy, Harbin Institute of Technology, Harbin 150090, China

3 School of Environment, Harbin Institute of Technology, Harbin 150090, China

4 Institute of Ocean Sciences, Department of Fisheries and Oceans, P.O. Box 6000, Sidney,

BC, V8L 4B2, Canada

5 Department of Pediatrics and Department of Environmental Medicine, New York University

School of Medicine, New York, NY 10016, USA

6 Institute of Natural Sciences, North-Eastern Federal University, Russia

7 IJRC-PTS-NA, Toronto, Ontario, M2N 6X9, Canada

*Corresponding author:

E-mail address: [email protected] (Yi-Fan Li)

IJRC-PTS

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Text

S1. Equilibrium models

S1.1 Junge-Pankow model

The Junge-Pankow (J-P) model was originally suggested by Junge and later critically

reviewed by Pankow, assuming the SVOCs are entirely adsorbed onto the surface of particle

matters. The particulate phase fraction (ϕP) in the J-P model could be calculates by

𝜙P =𝐶J𝜃

𝐶J𝜃+𝑃L (S1)

where Ɵ (cm2surfacecm-3

air) is the particle surface area concentration, which was assumed to be

1.1×10−5 for urban air (Bidleman, 1988) , 1.5×10−6 for rural air (Bidleman, 1988). CJ (Pa cm)

is based on the heat of desorption from the particle surface, the heat of vaporization of the

compound, and the moles of adsorption sites on the aerosol and typically used as 17.2 Pa cm.

The PL (Pa) is the sub-cooled liquid vapor pressure, which is a function of temperature T (K).

S1.2 Harner-Bidleman model

Pankow et al. (Pankow, 1994) derived the equations to describe the G/P partitioning of

SVOCs based adsorption mechanism,

𝐾P = 𝑁𝑠𝐴𝑡𝑠𝑝𝑇𝑒(𝑄1−𝑄𝑣) 𝑅𝑇⁄

1600𝑃𝐿0 (𝑃𝐿

0 in torr) (S2)

And based on both adsorption and absorption mechanism,

𝐾P = 1

𝑃𝐿0 [

𝑁𝑠𝐴𝑡𝑠𝑝𝑇𝑒(𝑄1−𝑄𝑣) 𝑅𝑇⁄

1600+

760𝑓𝑂𝑀𝑅𝑇

𝑀𝑊𝑜𝑚𝜁𝑜𝑚106] (𝑃𝐿0 in torr) (S3)

Then, an absorption mechanism for gas-particle partitioning of SVOCs was described in

relation to the chemical octanol-air partition coefficient, KOA (unitless), by Finizio et al.(Finizio

et al., 1997),

log𝐾P = log𝐾𝑂𝐴 + log1.22×10−12𝑓𝑂𝑀𝑀𝑜𝑐𝑡𝜁𝑜𝑐𝑡

𝑀𝑊𝑜𝑚𝜁𝑜𝑚 (S4)

Later, Pankow modified the absorption equation(Pankow, 1998),

log𝐾P = log𝐾𝑂𝐴 + log𝜁𝑜𝑐𝑡

𝜁𝑜𝑚+ log

𝑀𝑜𝑐𝑡𝑓𝑂𝑀

1012𝑀𝑊𝑜𝑚𝜌𝑜𝑐𝑡 (S5)

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With assuming absorption is the main processes between gas- and particle- phases, Harner

and Bidleman derived an absorption equation under equilibrium condition to calculate KP,

designed as KP-HB, given by (Harner and Bidleman, 1998)

log KP-HB = log KOA + log fOM -11.91 (S6)

where fOM is the fraction of the particle mass.

S1.3 Dachs-Eisenreich model

Dachs-Eisenreich (D-E) model was developed considering both absorption and adsorption

mechanisms(Dachs and Eisenreich, 2000). Assuming that EC is a surrogate for the soot phase,

in this study, the D-E model can be formulated as

KP-DE = KP-HB + KP-EC (S7)

where KP-HB represents the absorption term of D-E model, whereas KP-EC is the adsorption term

of D-E model, which is given by

KP-EC = 10-12fECKSA (S8)

where KSA is the soot-air partition coefficient (L kg-1), fEC (unitless) is the fraction of elemental

carbon (EC) in particle matters(Zhen et al., 2014).

Then, van Noort(van Noort, 2003) introduced the equation by a thermodynamic

estimation model to estimate the value of KSA for different PBDE congeners:

log𝐾𝑆𝐴 = −0.85log𝑃𝐿 + 8.94 − log (998

𝑎𝐸𝐶) (S9)

The value of 18.21 m2g-1 was used for αEC in the present study.

S1.4 pp-LFER model

The poly-parameter liner free energy relationship (pp-LFER) model considers the G/P

partitioning of SVOCs at molecular level. This pp-LFER approach was developed by

Abraham(Abraham, 1993), and modified by Goss(Goss, 2005) to form a single pp-LFER

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equation (Eq.S10)

log 𝐾𝑃‐L = 𝑠𝑆 + 𝑎𝐴 + 𝑏𝐵 + 𝑣𝑉 + 𝑙𝐿 + 𝑐 (S10)

where the capital letter V is the molar volume, L is the hexadecane/air partition coefficient, S

characterizes the dipolarity/polarizability of the substance, A describes the H-bond donor

properties, B the H-bond acceptor properties. The descriptors S, A, and B characterize the

specific interactions. The two descriptors L, V are used to describe non-specific interactions

like cavity formation energy and the energy that comes from dispersive van der Waals

interaction(Endo and Goss, 2014). The corresponding small letters are known as system

parameters and reflect the matrix-specific solute-independent energetic contribution to the KP.

The system parameters are given in Table S3.

Before making the use of the pp-LFER model to predict the G/P partitioning behavior, the

chemical descriptors need to be known for each target compounds. However, the descriptors

are not available for most of the chemicals, such as BDE-209. For BDE-209, the parameters of

pp-LFER model are calculated by present study.

The molecular formula of BDE-209 is C12Br10O. The V value is calculated by the

following equation:

𝑉 = ∑ (𝑉𝑋𝑖×𝑁𝑖)−(∑ 𝑁𝑖𝑖 +1)×6.56𝑖

100 (S11)

where the i represents the atom in the chemical, such as C, Br and O. Ni is the number of the i

atom in the chemical. When estimating the value of V, it should be noted that in the calculation

of molecular characteristic volumes, 6.56 cm3mol-1 is subtracted for each bond, no matter

whether single, double or triple. The list of atomic Vx values (cm3mol-1) needed for the

calculation of capital letter V of BDE-209 are as follows: C, 16.35; Br, 26.21; O,

12.43(Abraham and Mcgowan, 1987).

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A is zero for all the PBDE congeners. The S, B, L values reported by Stenzel(Stenzel et

al., 2013) for PBDEs congeners have linear relationship with the molecular weight,

respectively. The linear relationship of the S=0.0007MW + 1.0788 (R2 = 0.8772), B =

0.001MW - 0.145 (R2 = 0.9791), L = 0.0125MW + 4.5865 (R2 = 0.9969). Then the parameters

of BDE-209 needed for the LFER model could be gained.

S1.5 mp-pp-LFER model

Later, GÖtz developed the pp-LFER sorption model to predict the G/P partitioning of

SVOCs, considering the multiphase of particles(GÖtz et al., 2007).

𝐾P∗

= ∑ 𝐶𝑖𝐾𝑖,

𝑏𝑢𝑙𝑘

𝑎𝑖𝑟

𝑖⋯𝑛𝑖 + ∑ 𝐶𝑗𝐾

𝑗,𝑠𝑢𝑟𝑓

𝑎𝑖𝑟

𝑗⋯𝑛𝑗 (S12)

With considering the element carbon, (NH4)2SO4, NH4Cl as the adsorbent in adsorption process,

and the organic matter and organic polymers as the absorbent in the absorption process. The

G/P partitioning quotient, 𝐾𝑃‐𝑚𝐿 , in unit of μg/m3, could be calculated by the following

equation (Shahpoury et al., 2016),

𝐾𝑃‐𝑚𝐿 = (𝐾𝐸𝐶 × 𝑎𝐸𝐶 × 𝑓𝐸𝐶 + 𝐾(𝑁𝐻4)2𝑆𝑂4× 𝑎(𝑁𝐻4)2𝑆𝑂4

× 𝑓(𝑁𝐻4)2𝑆𝑂4+ 𝐾𝑁𝐻4𝐶𝑙 × 𝑎𝑁𝐻4𝐶𝑙 ×

𝑓𝑁𝐻4𝐶𝑙 + 𝐾𝐷𝑀𝑆𝑂/𝜌𝐷𝑀𝑆𝑂 × 𝑓𝑂𝑀,1 + 𝐾𝑃𝑈 × 𝑓𝑂𝑀,2) × 10−6 (S13)

The parameters in Eq. (S13) are shown in SI Table S4, respectively.

The log KP values calculated by Eqs (S10), and (S13) should be corrected by temperature

using the following equation:

𝑙og𝐾P = 𝑙og𝐾𝑃0 + (∆𝐻𝑣𝑎𝑝/2.303R)(1/T − 1/T0) (S14)

where the ∆Hvap (KJ/mol) of PBDEs are shown in SI Table S3.

S2 QSPR model

QSPR model is an empirical model considering the molecular mechanism and the effect

of temperature into the G/P partitioning behavior of PBDEs. Quantum chemical computations

were implemented at B3LYP/6-31G (d,p) level of theory based on the neutral electronic ground

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state of PBDE congeners by Gaussian 09 software package. The logKP value at the ambient

temperature range from 10 to 30 oC could be calculated by

𝑙og𝐾𝑃 = (0.026 ± 0.001)𝑉′ + (−0.030 ± 0.005)𝑇 + (−0.858 ± 0.272)𝑞𝐶− + (3.864 ±

1.342)𝑞𝐻+ + (0.002 ± 1.394) (S15)

In above equation, the V’ is the molecular volume, T is the ambient temperature (K), qC-

is the most negative charge on a carbon atom, qH+ is the most positive charge on a hydrogen

atom. The values of these parameters are shown in SI Table S5.

S3 The characteristic condensation temperature of PBDEs

A parameter, the characteristic temperature of condensation (TC), was developed (Wania

and Mackay, 1996) at which the chemical is equally partitioned between the gaseous and

particulate phases. Equation to calculate the values of TC was not given in the paper (Wania

and Mackay, 1996), however, we found out that the characteristic condensation temperature

was calculated by assuming the chemical’s logPL(TC) equals -4. As shown in Table S9, using

the values of TC given by (Wania and Mackay, 1996), and the published Clausius-Clapeyron

coefficients AL and BL values, we can calculate the values of logPL(TC) (= AL + BL / TC) which

is equal to -4 for all chemicals listed in the Table. Taking -HCH for example, as shown in the

Table S9 from the paper (see following table), the values of TC for -HCH is -40oC, and the

parameters AL is 11.34 and BL is -3575, then logPL(TC) = 11.34 - 3575/(273.15-40) = -4. Thus,

we calculated the characteristic condensation temperature of PBDEs in that method, with the

AL and BL shown in Table S1. The Tc of PBDEs is shown in Fig. 6. By using equation logKOA

= 6.46 - logPL (Yang et al, 2019), we have logKOA(TC) = 10.46.

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Figures

Fig. S1. logKOA for selected SVOCs (PBDEs, PCBs, PAHs, PCNs, OCPs, PCDD/Fs) at the

temperature of 25oC. Two vertical dashed lines represent two threshold values of logKOA

(logKOA1 and logKOA2). It is notice that PBDEs have highest values of logKOA from 9.5 for

BDE-28 to 15.1 for BDE-209.

BD

E-2

8

BD

E-4

7

BD

E-9

9

BD

E-1

00

BD

E-1

53

BD

E-1

54

BD

E-1

83

BD

E-2

09

4

6

8

10

12

14

16

log K

OA

logKOA1

logKOA2

PBDEs

PC

B-1

8

PC

B-4

4

PC

B-9

5

PC

B-1

26

PC

B-1

53

PC

B-1

55

PC

B-1

80

PC

B-1

87

PCBs

Acy

Flu

Ph

e

Pyr

BaA

Ch

r

Bap

Db

ah

A

SVOCs

PAHs

CN

-13

CN

-27

CN

-46

CN

-52

CN

-53

CN

-69

CN

-72

CN

-73

PCNs

α-H

CH

β-H

CH

EN

d I

EN

d I

I

CC

CN

TN

p,p

'-D

DE

OCPs

TC

DD

PeC

DD

Hx

CD

D

OC

DD

TC

DF

PeC

DF

Hx

CD

F

OC

DF

PCDD/Fs

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Fig. S2. The G/P partition coefficients of PBDEs as functions of logKOA calculated by two

equations. First one is G/P partition equation logKP-HB at equilibrium (Eq. (7)), presented by

the dark blue straight line, and the second one is our newly developed G/P partition equation

at steady state logKP-LMY (Eq. (13)), presented by the red curve in the figure. Two threshold

values of logKOA (logKOA1 and logKOA2, represented by two vertical purple dashed lines) divide

the range of logKOA into three domains: the equilibrium (EQ) domain, the nonequilibrium (NE)

domain, and the maximum partition (MP) domain (Li et al., 2015).

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Fig. S3. The first and second threshold temperatures, tTH1 and tTH2 for 8 PBDE congeners,

which divide the temperature space into the same three domains (EQ, NE, and MP).

-30

-20

-10

0

10

20

30

40

50

60

70

80

28 47 99 100 153 154 183 209

Th

resh

old

Tem

pera

ture o

C

PBDEs

tTH1 tTH2

EQ Domain

NE Domain

MP Domain

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Fig. S4. The ranges of logKOA of selected 5 PBDEs for the three different temperature spans

(50 − -50oC, 38 − -22oC, and 30 − 10oC). The ranges of logKOA for the QSPR and L-J models

are shorter since these two models are empirical ones with monitoring temperature being 30

− 10oC for the former and 38 − -22oC for the latter.

BDE-28

BDE-47

BDE-99

BDE-100

BDE-153

BDE-154

BDE-183

BDE-209

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

logKOA

PB

DE

s

EQ NE MP

logKOA1 logKOA2

-50oC — 50oC

-22oC — 38oC

10oC — 30oC

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Fig. S5. The predicted logKP (m3μg-1) versus logKOA for eight selected PBDE congeners (BDE-

28, -47, -99, -100, -153, -154, -183, -209) by H-B model, D-E model, pp-LFER model, mp-pp-

LFER model, J-P model, QSPR model, L-J empirical model, and L-M-Y model.

-6

-4

-2

0

2

4

6

8

10

12

14

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

log

KP

m

3μ

g-1

log KOA

pp-LFER-28 pp-LFER-47 pp-LFER-99 pp-LFER-100

pp-LFER-153 pp-LFER-154 pp-LFER-183 pp-LFER-209

mp-pp-LFER-28 mp-pp-LFER-47 mp-pp-LFER-99 mp-pp-LFER-100

mp-pp-LFER-153 mp-pp-LFER-154 mp-pp-LFER-183 mp-pp-LFER-209

L-J-28 L-J-47 L-J-99 L-J-100

L-J-153 L-J-154 L-J-183 QSPR-28

QSPR-47 QSPR-99 QSPR-100 QSPR-153

QSPR-154 QSPR-183 QSPR-209 D-E

J-P H-B L-M-Y

log KOA2

10 - 30 oC

-22 - 38 oC

-50 - 50 oC

-1.53

MP

log KOA1

EQ NE

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Fig. S6. The logKP of 8 PBDEs congeners predicted by H-B model and D-E model vs logKOA.

(a): fOM=0.1, fEC=0.02; (b): fOM=0.1, fEC=0.05; (c): fOM=0.1, fEC=0.1; (d): fOM=0.1 and fEC=0.2.

The two dashed blue lines give the ±1 log unit boundary for logKP-HB. The two dashed gray

lines represent the two logKOA threshold values (logKOA1 and logKOA2).

-6

-4

-2

0

2

4

6

8

8.5 10.5 12.5 14.5 16.5 18.5

log

KP

m3

μg

-1

log KOA

D-E model H-B model

fOM=0.1 fEC=0.02

(a)

20

EQ NE MP

log KOA2log KOA1 -6

-4

-2

0

2

4

6

8

8.5 10.5 12.5 14.5 16.5 18.5

log

KP

m3

μg

-1

log KOA

D-E model H-B model

fOM=0.1 fEC=0.05

(b)

20

EQ NE MP

log KOA2log KOA1

-6

-4

-2

0

2

4

6

8

8.5 10.5 12.5 14.5 16.5 18.5

log

KP

m3

μg

-1

log KOA

D-E model H-B model

fOM=0.1 fEC=0.1

(c)

20

EQ NE MP

log KOA2log KOA1 -6

-4

-2

0

2

4

6

8

8.5 10.5 12.5 14.5 16.5 18.5

log

KP

m3

μg

-1

log KOA

D-E model H-B model

fOM=0.1 fEC=0.2

(d)

20

EQ NE MP

log KOA2log KOA1

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Fig. S7. Variation of logKP-LMY (the thick red line) and logKP-LJ (the thin lines) versus logKOA

for the seven PBDE congeners (BDE-28, -47, -99, -100, -153, 154, and -183). The line of

logKP-HB (the thick blue line) is also included for comparison.

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Tables

Table S1. Parameters AO, BO, AL, and BL for all 209 PBDE congeners (Yang et al., 2018).

PBDEs Ao Bo AL BL PBDEs Ao Bo AL BL

BDE-1 -4.14 3415 10.60 -3415 BDE-37 -4.61 4286 11.07 -4286

BDE-2 -3.90 3415 10.36 -3415 BDE-38 -4.84 4286 11.3 -4286

BDE-3 -3.70 3415 10.16 -3415 BDE-39 -4.84 4286 11.3 -4286

BDE-4 -4.93 3851 11.39 -3851 BDE-40 -6.08 4722 12.54 -4722

BDE-5 -4.71 3851 11.17 -3851 BDE-41 -5.86 4722 12.32 -4722

BDE-6 -4.71 3851 11.17 -3851 BDE-42 -5.86 4722 12.32 -4722

BDE-7 -4.49 3851 10.95 -3851 BDE-43 -6.08 4722 12.54 -4722

BDE-8 -4.49 3851 10.95 -3851 BDE-44 -6.08 4722 12.54 -4722

BDE-9 -4.71 3851 11.17 -3851 BDE-45 -6.30 4722 12.76 -4722

BDE-10 -4.95 3851 11.41 -3851 BDE-46 -6.30 4722 12.76 -4722

BDE-11 -4.49 3851 10.95 -3851 BDE-47 -5.64 4722 12.1 -4722

BDE-12 -4.26 3851 10.72 -3851 BDE-48 -5.86 4722 12.32 -4722

BDE-13 -4.26 3851 10.72 -3851 BDE-49 -5.86 4722 12.32 -4722

BDE-14 -4.49 3851 10.95 -3851 BDE-50 -6.08 4722 12.54 -4722

BDE-15 -4.03 3851 10.49 -3851 BDE-51 -6.08 4722 12.54 -4722

BDE-16 -5.51 4286 11.97 -4286 BDE-52 -6.08 4722 12.54 -4722

BDE-17 -5.29 4286 11.75 -4286 BDE-53 -6.30 4722 12.76 -4722

BDE-18 -5.51 4286 11.97 -4286 BDE-54 -6.52 4722 12.98 -4722

BDE-19 -5.73 4286 12.19 -4286 BDE-55 -5.64 4722 12.1 -4722

BDE-20 -5.29 4286 11.75 -4286 BDE-56 -5.64 4722 12.1 -4722

BDE-21 -5.07 4286 11.53 -4286 BDE-57 -5.86 4722 12.32 -4722

BDE-22 -5.06 4286 11.52 -4286 BDE-58 -5.86 4722 12.32 -4722

BDE-23 -5.29 4286 11.75 -4286 BDE-59 -6.08 4722 12.54 -4722

BDE-24 -5.51 4286 11.97 -4286 BDE-60 -5.41 4722 11.87 -4722

BDE-25 -5.06 4286 11.52 -4286 BDE-61 -5.64 4722 12.1 -4722

BDE-26 -5.29 4286 11.75 -4286 BDE-62 -5.86 4722 12.32 -4722

BDE-27 -5.51 4286 11.97 -4286 BDE-63 -5.64 4722 12.1 -4722

BDE-28 -4.84 4286 11.30 -4286 BDE-64 -5.86 4722 12.32 -4722

BDE-29 -5.06 4286 11.52 -4286 BDE-65 -6.08 4722 12.54 -4722

BDE-30 -5.28 4286 11.74 -4286 BDE-66 -5.42 4722 11.88 -4722

BDE-31 -5.06 4286 11.52 -4286 BDE-67 -5.64 4722 12.1 -4722

BDE-32 -5.29 4286 11.75 -4286 BDE-68 -5.64 4722 12.1 -4722

BDE-33 -5.06 4286 11.52 -4286 BDE-69 -5.86 4722 12.32 -4722

BDE-34 -5.29 4286 11.75 -4286 BDE-70 -5.64 4722 12.1 -4722

BDE-35 -4.84 4286 11.3 -4286 BDE-71 -5.86 4722 12.32 -4722

BDE-36 -5.06 4286 11.52 -4286 BDE-72 -5.86 4722 12.32 -4722

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BDE-73 -6.08 4722 12.54 -4722 BDE-110 -6.43 5157 12.89 -5157

BDE-74 -5.41 4722 11.87 -4722 BDE-111 -6.43 5157 12.89 -5157

BDE-75 -5.63 4722 12.09 -4722 BDE-112 -6.65 5157 13.11 -5157

BDE-76 -5.64 4722 12.1 -4722 BDE-113 -6.65 5157 13.11 -5157

BDE-77 -5.19 4722 11.65 -4722 BDE-114 -5.99 5157 12.45 -5157

BDE-78 -5.41 4722 11.87 -4722 BDE-115 -6.21 5157 12.67 -5157

BDE-79 -5.41 4722 11.87 -4722 BDE-116 -6.43 5157 12.89 -5157

BDE-80 -5.64 4722 12.1 -4722 BDE-117 -6.43 5157 12.89 -5157

BDE-81 -5.19 4722 11.65 -4722 BDE-118 -5.99 5157 12.45 -5157

BDE-82 -6.43 5157 12.89 -5157 BDE-119 -6.21 5157 12.67 -5157

BDE-83 -6.65 5157 13.11 -5157 BDE-120 -6.21 5157 12.67 -5157

BDE-84 -6.87 5157 13.33 -5157 BDE-121 -6.43 5157 12.89 -5157

BDE-85 -6.24 5157 12.7 -5157 BDE-122 -6.21 5157 12.67 -5157

BDE-86 -6.43 5157 12.89 -5157 BDE-123 -5.99 5157 12.45 -5157

BDE-87 -6.43 5157 12.89 -5157 BDE-124 -6.21 5157 12.67 -5157

BDE-88 -6.65 5157 13.11 -5157 BDE-125 -6.43 5157 12.89 -5157

BDE-89 -6.65 5157 13.11 -5157 BDE-126 -5.80 5157 12.26 -5157

BDE-90 -6.43 5157 12.89 -5157 BDE-127 -5.99 5157 12.45 -5157

BDE-91 -6.65 5157 13.11 -5157 BDE-128 -6.78 5592 13.24 -5592

BDE-92 -6.65 5157 13.11 -5157 BDE-129 -7.00 5592 13.46 -5592

BDE-93 -6.87 5157 13.33 -5157 BDE-130 -7.00 5592 13.46 -5592

BDE-94 -6.87 5157 13.33 -5157 BDE-131 -7.22 5592 13.68 -5592

BDE-95 -6.87 5157 13.33 -5157 BDE-132 -7.22 5592 13.68 -5592

BDE-96 -7.10 5157 13.56 -5157 BDE-133 -7.22 5592 13.68 -5592

BDE-97 -6.43 5157 12.89 -5157 BDE-134 -7.45 5592 13.91 -5592

BDE-98 -6.65 5157 13.11 -5157 BDE-135 -7.45 5592 13.91 -5592

BDE-99 -6.21 5157 12.67 -5157 BDE-136 -7.67 5592 14.13 -5592

BDE-100 -6.44 5157 12.9 -5157 BDE-137 -6.78 5592 13.24 -5592

BDE-101 -6.43 5157 12.89 -5157 BDE-138 -6.78 5592 13.24 -5592

BDE-102 -6.65 5157 13.11 -5157 BDE-139 -7.00 5592 13.46 -5592

BDE-103 -6.65 5157 13.11 -5157 BDE-140 -7.00 5592 13.46 -5592

BDE-104 -6.87 5157 13.33 -5157 BDE-141 -7.00 5592 13.46 -5592

BDE-105 -5.99 5157 12.45 -5157 BDE-142 -7.22 5592 13.68 -5592

BDE-106 -6.21 5157 12.67 -5157 BDE-143 -7.22 5592 13.68 -5592

BDE-107 -6.21 5157 12.67 -5157 BDE-144 -7.22 5592 13.68 -5592

BDE-108 -6.21 5157 12.67 -5157 BDE-145 -7.45 5592 13.91 -5592

BDE-109 -6.43 5157 12.89 -5157 BDE-146 -7.00 5592 13.46 -5592

15

16



BDE-147 -7.22 5592 13.68 -5592 BDE-179 -8.24 6027 14.7 -6027

BDE-148 -7.22 5592 13.68 -5592 BDE-180 -7.35 6027 13.81 -6027

BDE-149 -7.22 5592 13.68 -5592 BDE-181 -7.57 6027 14.03 -6027

BDE-150 -7.45 5592 13.91 -5592 BDE-182 -7.57 6027 14.03 -6027

BDE-151 -7.45 5592 13.91 -5592 BDE-183 -7.44 6027 13.9 -6027

BDE-152 -7.67 5592 14.13 -5592 BDE-184 -7.80 6027 14.26 -6027

BDE-153 -6.76 5592 13.22 -5592 BDE-185 -7.80 6027 14.26 -6027

BDE-154 -7.02 5592 13.48 -5592 BDE-186 -8.02 6027 14.48 -6027

BDE-155 -7.22 5592 13.68 -5592 BDE-187 -7.80 6027 14.26 -6027

BDE-156 -6.53 5592 12.99 -5592 BDE-188 -8.02 6027 14.48 -6027

BDE-157 -6.56 5592 13.02 -5592 BDE-189 -7.13 6027 13.59 -6027

BDE-158 -6.78 5592 13.24 -5592 BDE-190 -7.35 6027 13.81 -6027

BDE-159 -6.78 5592 13.24 -5592 BDE-191 -7.35 6027 13.81 -6027

BDE-160 -7.00 5592 13.46 -5592 BDE-192 -7.57 6027 14.03 -6027

BDE-161 -7.00 5592 13.46 -5592 BDE-193 -7.57 6027 14.03 -6027

BDE-162 -6.78 5592 13.24 -5592 BDE-194 -7.93 6463 14.39 -6463

BDE-163 -7.00 5592 13.46 -5592 BDE-195 -8.15 6463 14.61 -6463

BDE-164 -7.00 5592 13.46 -5592 BDE-196 -8.15 6463 14.61 -6463

BDE-165 -7.22 5592 13.68 -5592 BDE-197 -8.37 6463 14.83 -6463

BDE-166 -6.78 5592 13.24 -5592 BDE-198 -8.37 6463 14.83 -6463

BDE-167 -6.56 5592 13.02 -5592 BDE-199 -8.37 6463 14.83 -6463

BDE-168 -6.78 5592 13.24 -5592 BDE-200 -8.59 6463 15.05 -6463

BDE-169 -6.34 5592 12.8 -5592 BDE-201 -8.59 6463 15.05 -6463

BDE-170 -7.35 6027 13.81 -6027 BDE-202 -8.81 6463 15.27 -6463

BDE-171 -7.57 6027 14.03 -6027 BDE-203 -8.15 6463 14.61 -6463

BDE-172 -7.57 6027 14.03 -6027 BDE-204 -8.37 6463 14.83 -6463

BDE-173 -7.80 6027 14.26 -6027 BDE-205 -7.93 6463 14.39 -6463

BDE-174 -7.80 6027 14.26 -6027 BDE-206 -8.72 6898 15.18 -6898

BDE-175 -7.80 6027 14.26 -6027 BDE-207 -8.94 6898 15.4 -6898

BDE-176 -8.02 6027 14.48 -6027 BDE-208 -9.16 6898 15.62 -6898

BDE-177 -7.80 6027 14.26 -6027 BDE-209 -9.50 7333 15.96 -7333

BDE-178 -8.02 6027 14.48 -6027

16

17

Table S2. Comparisons for different modes

No. Model Absorption Adsorption State

condition

Linear or not

vs logKOA Equation Ref.

1 Junge-Pankow

model N Y Equilibrium Y ϕ =

𝐶𝐽𝜃

𝐶𝐽𝜃 + 𝑃𝐿0 (Pankow, 1987)

2 Harner-Bidleman

model Y N Equilibrium Y log𝐾𝑃−𝐻𝐵 = log𝐾𝑂𝐴 + log𝑓𝑂𝑀 − 11.91 (Harner and

Bidleman, 1998)

3 Dachs-Eisenreich

model Y Y Equilibrium Y 𝐾P−DE = 𝐾𝑃−HB + 10−12𝑓

𝐸𝐶𝐾𝑆𝐴 (Dachs and

Eisenreich, 2000)

4 pp-LFER model Y Y Equilibrium Y log𝐾P−L = 𝑠𝑆 + 𝑎𝐴 + 𝑏𝐵 + 𝑣𝑉 + 𝑙𝐿 + 𝑐 (Goss, 2005)

5 Li-Jia Empirical

model NA NA Empirical

model

N log𝐾P−LJ =0.011𝐵𝑜(log𝐾𝑂𝐴 − 12.27)

𝑙𝑜𝑔𝐾𝑂𝐴 − 𝐴𝑜− 2.74log𝐾𝑂𝐴 + 31.85

(Li and Jia, 2014)

6 Li-Ma-Yang

model Y N Steady State N log𝐾P−LMY = log𝐾𝑃−𝐸𝑞 + log 𝛼 (Li et al., 2015)

7 mp-pp-LFER

model Y Y Equilibrium Y 𝐾P−mL = (𝐾𝐸𝐶 × 𝑎𝐸𝐶 × 𝑓𝐸𝐶 + 𝐾(𝑁𝐻4)2𝑆𝑂4

× 𝑎(𝑁𝐻4)2𝑆𝑂4× 𝑓(𝑁𝐻4)2𝑆𝑂4

+ 𝐾𝑁𝐻4𝐶𝑙 × 𝑎𝑁𝐻4𝐶𝑙 × 𝑓𝑁𝐻4𝐶𝑙

+ 𝐾𝐷𝑀𝑆𝑂/𝜌𝐷𝑀𝑆𝑂 × 𝑓𝑂𝑀,1 + 𝐾𝑃𝑈 × 𝑓𝑂𝑀,2) × 10−6

(Shahpoury et al.,

2016)

8 QSPR model Y Y Empirical

model

N log𝐾P−QSPR = 0.026𝑉′ − 0.030𝑇 − 0.858𝑞𝐶− + 3.864𝑞𝐻+

+ 0.002

(Wei et al., 2017)

17

18

Table S3. the Abraham solvation parameters of PBDEs and the system parameters used

in pp-LFER model and mp-pp-LFER model, and the values of ∆Hvap for 8 PBDEs.

PBDEs Abraham solvation parameters

Ref. ∆Hvap

KJ/mol Ref.

S A B V L

BDE-28 1.38 0 0.27 1.908 9.68 (Stenzel et al., 2013) 94 (Tittlemier and

Tomy, 2001)


Tomy, 2001)


Tomy, 2001)

BDE-100 1.48 0 0.41 2.258 11.48 (Stenzel et al., 2013) 102 (Tittlemier et al.,

2002)

BDE-153 1.54 0 0.52 2.433 12.65 (Stenzel et al., 2013) 108 (Wong et al.,

2001)


2002)


2002)

BDE-209 1.75 0 0.81 3.133 16.58 Calculated in

present study 133 Present study

system parameters

s a b v l c T(K) Ref

1.19 3.37 0.03 0.73 0.66 -7.08 288 (Arp et al., 2008)

18

19

Table S4. The parameters for mp-pp-LFER model 1

Parameters System Unit e s a b v l c T(K) Ref.

𝐾EC NIST diesel soot-air m3airm

2surface - - 2.7 2.45 - 1.09 -8.47 288 (Roth et al., 2005)

K(NH4)2SO4 (NH4)2SO4 (60% RH) m3

air m-

2surface

- - 2.13 5.34 - 0.88 -8.47 288 (Goss et al., 2003)

KNH4Cl NH4Cl (60% RH) m3

air m-

2surface

- - 2.28 4.72 - 0.92 -8.47 288 (Goss et al., 2003)

KDSMO Dry dimethyl sulfoxide-

air Lair L

-1solvent -0.22 2.9 5.04 0 - 0.72 -0.56 298

(Abraham et al.,

2010)

KPU Polyurethane ether (PU)-

air Lair kg-1

PU - 1.69 3.66 0 0.36 0.71 -0.15 288 (Kamprad and Goss,

2007)

Parameters Value

m2 g-1 Parameters

Value

m2 g-1 Parameters

Value

m2 g-1 Parameters

Value

kg m-3 Ref.

aEC 18.21 a(NH4)2SO4 0.13 aNH4Cl 0.083 𝜌DMSO 1100 (Shahpoury et al.,

2016)

Parameters Value Parameters Value Parameters Value Parameters Value Ref.

fEC 0.02 f(NH4)2SO4 0.15 fNH4Cl 0.002 𝑓OM,1/ 𝑓OM,2 3/2 (Shahpoury et al.,

2016)

2

19

20

Table S5. the parameters of PBDEs used in QSPR model (10 ~ 30 oC)

PBDEs V’ (cm3/mol) qC- qH+ Ref.

BDE-28 174.081 -0.109 0.133 (Wei et al., 2017; Zhang et al.,

2009)


2009)


2009)


2009)


2009)


2009)


2009)

BDE-209 289.937 0 0 (Wei et al., 2017; Zhang et al.,

2009)

20

21

Table S6. Sources of the data used in the paper

Sampling

sites

Sampling

period

Sample

number PBDEs*

Temperature

(oC) Ref.

Palmer station,

Antarctic

2010.10.19-

2010.11.11 7

BDE-28、-47、-99、-

100 -1.5 ~ 2

(Khairy et

al., 2016)

Arctic Alaska 2013.07.06-

2013.09.04 30

BDE-17, -28, -47, -66,

-71, -85, -99, -100, -

138, -153, -154,

-183, and -209

-2.5 ~ 16.8

(Davie-

Martin et

al., 2016)

northern

Greece

2013.01.16-

2013.06.02 16

BDE-15, -17, -28, -

49+71, -47, -66, -99, -

100, -153, -154,

-183

10 ~26 (Besis et

al., 2016)

Florence, Italy 2009.06.08-

2009.12.17 12

BDE-28, -47, -99, -

100, -153, -154,

-183, and -209

7 ~ 23

(Cincinell

i et al.,

2014)

Kyoto, Japan

2000.08.17-

2001.02.05;

2001.09.04-07

5

BDE-28, -47, -49, -66, -

77, -99, -100, -153, -

154, -183

3 ~ 29

(Hayakaw

a et al.,

2004)

China 2008.09-

2009.08 >700

BDE-17, -28, -47, -66,

-85, -99, -100, -138, -

153, -154,

-183, and -209

-22 ~ 38

(Li et al.,

2017;

Yang et

al., 2013)

Harbin, China 2008.08.05-

2013.07.02 223

BDE-17, -28, -47, -66,

-85, -99, -100, -138, -

153, -154,

-183, and -209

-27 ~ 29 (Li et al.,

2016)

Izmir Bay,

Turkey

2005.07.06-13

2005.11.20-26 15

BDE-28, -47, -99, -

100, -153, -154,

and -209a

5 ~ 32

(Cetin

and

Odabasi,

2007)

Zurich,

Switzerland

2010.08.20-24

2011.01.29-

2011.02.06

31

BDE -28, -47, -99, -

100, -138, -153, -183,

and -209

-2.5 ~21b

(Bogdal

et al.,

2014)

Pairs, France 2008.05.26-

2009.05.25 27

BDE -28, -47, -99, -

100, -138, -153, -154, -

183, and -209 a

1.3 ~ 22.5 (Tlili et

al., 2012)

Tengchong,

China

2005.10.22-

2006.12.27 60

BDE -28, -47, -99, -

100, and -209 a ----

(Xu et al.,

2011)

Alert, Canada 2007.01.01 54 BDE-47, -99, -100, -

153, and -209 -32.43 ~ 5.3

(Xiao et

al., 2012)

*BDE-28, -47, -99, -100, -153, -154, -183, -209 are considered in present study. aBDE-209 is included in present study b the temperature range is based on the weather given in weather channel.com

21

22

Table S7. The percentage (%) of data point predicted within one order of magnitude accuracy for PBDEs dataset.

Domains PBDEs J-P H-B D-E L-J* L-M-Y pp-LFER mp-pp-LFER QSPR*

EQ Domain

BDE-28 66.74 94.28 94.7 94.28 94.49 59.32 4.02 45.55

BDE-47 45.74 94.26 94.26 91.31 93.93 81.84 88.52 72.95

BDE-99 52.43 94.59 92.43 89.73 96.22 79.46 82.16 71.89

BDE-100 37.63 93.30 92.27 92.78 96.39 89.18 73.20 85.57

BDE-153 ---- ---- ---- ---- ---- ---- ---- ----

BDE-154 14.29 71.43 71.43 100 85.71 100 28.57 ----

BDE-183 ---- ---- ---- ---- ---- ---- ---- ----

BDE-209 ---- ---- ---- ---- ---- ---- ---- ----

NE Domain

BDE-28 38 90 90 94 98 96 62 ----

BDE-47 11.56 75.38 73.87 94.97 94.97 90.45 40.2 ----

BDE-99 12.04 81.48 81.48 87.04 95.37 96.30 47.22 66.67

BDE-100 69.48 90.82 90.07 98.26 98.76 97.52 79.90 81.39

BDE-153 7.19 65.27 58.68 95.81 97.01 94.61 21.56 86.23

BDE-154 7.25 62.32 59.42 95.65 95.65 59.42 13.04 90.34

BDE-183 0 40 40 100 100 100 0 40

BDE-209 ---- ---- ---- ---- ---- ---- ---- ----

MP Domain

BDE-28 ---- ---- ---- ---- ---- ---- ---- ----

BDE-47 0 10.34 5.17 77.59 96.55 37.93 0 ----

BDE-99 0 7.55 7.55 87.74 95.28 36.79 2.83 ----

BDE-100 0 8.47 6.78 83.05 94.92 30.51 1.69 ----

BDE-153 0 6.45 5.65 95.16 94.76 38.31 0.40 37.10

BDE-154 0 18.94 18.18 92.42 92.42 37.88 0 31.82

BDE-183 0 3.66 3.38 84.51 92.39 27.61 0 54.93

BDE-209 0 0 0 ---- 91.86 0 0 53.61

*: The monitoring data point out of the application of L-J empirical model and QSPR model are taken as out of one order of magnitude accuracy.

22

23

Table S8. The root mean square errors (RMSE) of eight models for PBDEs dataset.

Domains PBDEs J-P H-B D-E L-J* L-M-Y pp-LFER mp-pp-LFER QSPR*

EQ Domain

BDE-28 0.96 0.52 0.51 0.51 0.53 1.03 0.53 0.91

BDE-47 1.16 0.52 0.53 0.55 0.51 0.78 0.67 0.56

BDE-99 1.16 0.49 0.51 0.66 0.46 0.76 0.77 0.71

BDE-100 1.26 0.55 0.58 0.56 0.49 0.64 0.85 0.53

BDE-153 ---- ---- ---- ---- ---- ---- ---- ----

BDE-154 1.69 0.85 0.90 0.54 0.65 0.54 1.47 ----

BDE-183 ---- ---- ---- ---- ---- ---- ---- ----

BDE-209 ---- ---- ---- ---- ---- ---- ---- ----

NE Domain

BDE-28 1.3 0.65 0.68 0.53 0.45 0.48 0.98 -----

BDE-47 1.8 0.85 0.89 0.51 0.49 0.58 1.31 ----

BDE-99 1.73 0.78 0.82 0.61 0.49 0.55 1.23 0.69

BDE-100 1.10 0.52 0.54 0.33 0.28 0.35 0.77 0.27

BDE-153 1.84 0.99 1.03 0.54 0.48 0.52 1.51 0.63

BDE-154 1.86 0.99 1.03 0.47 0.48 0.53 1.67 0.53

BDE-183 2.03 1.12 1.16 0.44 0.42 0.48 1.95 0.65

BDE-209 ---- ---- ---- ---- ---- ---- ---- ----

MP Domain

BDE-28 ---- ---- ---- ---- ---- ---- ---- ----

BDE-47 2.63 1.65 1.68 0.43 0.4 1.36 2.32 ----

BDE-99 2.93 1.98 2.00 0.47 0.46 1.47 2.57 ----

BDE-100 3.10 2.02 2.05 0.48 0.47 1.50 2.53 ----

BDE-153 3.30 2.40 2.42 0.53 0.51 1.65 2.95 0.51

BDE-154 2.96 2.10 2.13 0.56 0.54 1.57 2.86 0.59

BDE-183 3.74 2.96 2.98 0.68 0.57 2.30 3.80 0.65

BDE-209 5.98 5.13 5.13 ---- 0.57 4.33 7.15 0.59

*: The monitoring data point in the application of L-J empirical model and QSPR model are considered for the RMSE

23

24

Table S9. Temperature of condensation Tc for POPs (From Table 1, Wania and Mackay,

1996), Clausius-Clapeyron coefficients AL and BL, and calculated values of logPL (All

equal to -4).

Group POPs TC/°C AL BL log(PL/Pa)

PAHs Naphthalene

Anthracene -33 11.18 -3642 -4

Pyrene -15 11.92 -4104 -4

Flouranthene -10 11.35 -4040 -4

Benz[a]anthracene 12 12.63 -4742 -4

Benzolalpyrene 47 11.59 -4989 -4

PCBs 2,4,4'-C3B (#28) -22 12.2 -4075 -4

2,2',5,5'-C4B (#52) -15 12.36 -4220 -4

2,2',4,5,5'-C5B(#101) -2 12.67 -4514 -4

2,2',4,4',5,5'-C6B (#153) 10 12.85 -4775 -4

2,2',3,3',4,4',6-C7B(#171) 20 13.07 -5008 -4

2,2',3,3',4,4',5,5'-C8B (#194) 37 13.43 -5402 -4

CBzs HC6Bz -36 11.11 -3582 -4

Pesticides -HCH -40 11.34 -3575 -4

-HCH -30 11.15 -3680 -4

p,p'-DDT 13 13.02 -4865 -4

p,p'-DDE -2 12.79 -4554 -4

p,p'-DDD 7 12.49 -4622 -4

cis-Chlordane -6 12.04 -4284 -4

trans-Chlordane -9 11.96 -4216 -4

Dieldrin -11 12.46 -4310 -4

Note: The values of AL and BL for PCBs are from Falconer et al., 1994, all others are from Hinckley et

al, 1990.

Hinckley, D.A., Bidleman, T.F., Foreman, W.T., Determination of vapor pressures for nonpolar and

semipolar organic compounds from gas chromatographic retention data. Journal of Chemical &

Engineering Data 1990, 35, 232-237.

Falconer, Renee L.，Bidleman, Terry F，Vapor pressures and predicted particle/gas distributions of

polychlorinated biphenyl congeners as functions of temperature and ortho-chlorine substitution，

Atmospheric Environment，1994，28，547-554

24

25

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