Henry's Constants of Persistent Organic Pollutants by a Group

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Henry’s Constants of Persistent Organic Pollutants by a Group-Contribution Method Based on Scaled-Particle Theory Neil K. Razdan, David M. Koshy, and John M Prausnitz Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b03023 • Publication Date (Web): 09 Oct 2017 Downloaded from http://pubs.acs.org on October 13, 2017

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Environmental Science & Technology

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Henry’s Constants of Persistent Organic Pollutants

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by a Group-Contribution Method Based on Scaled-

3

Particle Theory

4

Neil K. Razdan⸹,†,*,‡, David M. Koshy⸹,†, John M. Prausnitz⸹

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⸹Chemical and Biomolecular Engineering Department, University of California, Berkeley, CA,

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94720-1462, USA

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KEYWORDS: Henry’s constant; persistent organic pollutants; polychlorinated biphenyls; van’t

8

Hoff equation; group-contribution; scaled-particle theory

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ABSTRACT: A group-contribution method based on scaled-particle theory was developed to

10

predict Henry’s constants for six families of persistent organic pollutants: polychlorinated

11

benzenes,

12

dibenzofurans, polychlorinated naphthalenes, and polybrominated diphenyl ethers. The group-

13

contribution model uses limited experimental data to obtain group-interaction parameters for an

14

easy-to-use method to predict Henry’s constants for systems where reliable experimental data are

15

scarce. By using group-interaction parameters obtained from data reduction, scaled-particle theory

16

gives the partial molar Gibbs energy of dissolution, Δ𝑔̅2, allowing calculation of Henry’s constant,

17

H2, for more than 700 organic pollutants. The average deviation between predicted values of log

polychlorinated

biphenyls,

polychlorinated

dibenzodioxins,

polychlorinated

ACS Paragon Plus Environment

1


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H2 and experiment is 4%. Application of an approximate van’t Hoff equation gives the temperature

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dependence of Henry’s constants for polychlorinated biphenyls, polychlorinated naphthalenes, and

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polybrominated diphenyl ethers in the environmentally relevant range 0 to 40oC.

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1. INTRODUCTION

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Persistent organic pollutants (POPs) are chemicals that have long environmental lifetimes and

23

provide serious health threats to humans and wildlife.1-10 POPs travel through sediments, bodies

24

of water, and air for decades. They are often lipophilic and accumulate in fatty tissue, thereby

25

persisting in food chains before re-entering a cycle of dissolution and slow evaporation.1-3,6,8-10 In

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2001, the Stockholm Convention on Persistent Organic Pollutants, an international treaty with 128

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signatories, was formed to limit the environmental impact of these toxic chemicals.1-3

28

Thermodynamic, chemical and transport properties of POPs are of much interest to track and

29

minimize POPs within the environment.1-10

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Of primary significance is the Henry’s constant that governs the air-water partition of POPs. In

31

recent years, there has been much work measuring, tabulating, and correlating Henry’s

32

constants.11-29 Shen et al (2005) and Mackay et al (2006) have published large databases for

33

Henry’s constants and other key properties for hundreds of chemicals, including POPs.17,30

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Bamford et al (2000, 2002), Cetin et al (2005) and Odabasi et al (2016) have measured and

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correlated temperature-dependent Henry’s constants for some polychlorinated biphenyls,

36

polybrominated diphenyl ethers, and polychlorinated naphthalenes; these pollutants are

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representative of the most studied families of POPs.11,13,16,20 However, data are not available for

38

many POPs that are of interest for environmental protection.

39

This work concerns Henry’s constants of polychlorinated benzenes (CBs), polychlorinated

40

biphenyls (PCBs), polychlorinated dibenzodioxins (PCDDs), polychlorinated dibenzofurans


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(PCDFs), polychlorinated naphthalenes (PCNs), and polybrominated diphenyl ethers (PBDEs).

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These six families of POPs contain a total of 706 congeners that provide a major environmental

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threat.1-3,6-10,31A congener is a variant, or configuration, of a common chemical structure. For

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example, each of the 209 PCB congeners is a unique configuration of chlorine atoms substituted

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on a biphenyl backbone. Reliable data for these pollutants are limited, in part, due to experimental

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difficulty in measuring very small solubilities.

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UNIFAC has been used extensively to estimate activity coefficients for liquid-mixture

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components.32 However, for highly dilute aqueous solutions, UNIFAC predictions of Henry’s

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constant are often in serious error.33-35

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Several studies have presented models that predict Henry’s constants for solutes in water.18-23

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Group-contribution models and quantitative structure-property relationships (QSPR) have

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provided a basis for correlating molecular structure to Henry’s constant for numerous aqueous

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solutes.24-29 While often reliable, these models are computationally demanding and require specific

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software packages for implementation. The model we present is arithmetic and uses only

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rudimentary matrix algebra in the calculation of group-interaction parameters. Further, many

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published models are applicable only to one family of POPs.

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In this work, we propose a simple group-contribution model for predicting temperature-

58

dependent Henry’s constants based on molecular structure. We use an additive method to

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determine solute-solvent interaction energies for constituent functional groups. Using interaction

60

energies, scaled-particle theory (SPT) provides the partial molar Gibbs energy of inserting and

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solvating a solute molecule in a given solvent.36,37 This Gibbs energy can then be converted to a

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Henry’s constant.


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To our knowledge, applying the group-contribution method toward the calculation of energetic

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interaction parameters for Henry’s constant predictions has not been reported in the literature.

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When pertinent data are available, our novel method can be easily extended by future investigators

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because it requires only arithmetic operations to arrive at Henry’s constant predictions; the

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energetic contributions of new functional groups can be determined by basic matrix algebra. Thus,

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this physically based group-contribution method, applied to several families of POPs, provides a

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useful advance in group-contribution techniques.

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2. MATERIALS AND METHODS

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2.1 Thermodynamic Framework. For a solute 2 in solvent 1, Henry’s constant for the solute,

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H2, [Pa] is defined as the ratio of the solute’s liquid-phase fugacity, 𝑓2L , to its liquid-phase mole

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fraction, x2, at high dilution

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H2 =

𝑓2L for 𝑥2 → 0 𝑥2

(1a)

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At vapor-liquid equilibrium (e.g. air-water partition), 𝑓2L = 𝑓2V , where 𝑓2V is the solute’s vapor-

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phase fugacity. At modest pressure, fugacity is replaced by partial pressure. Henry’s constant then

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relates the solute’s equilibrium partial pressure, y2P, to the liquid-phase mole fraction

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H2 =

𝑦2 P for 𝑥2 → 0 𝑥2

(1b)

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where y2 is the vapor-phase mole fraction of the solute and P is pressure. At high dilution, there

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are very few solute-solute interactions; solute-solvent interactions determine the energetics of

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solvation, required for SPT.

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SPT provides a framework to determine H2. In SPT, the partial molar Gibbs energy of

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dissolution, Δ𝑔̅2, is the sum of two contributions. The first contribution, 𝑔̅c , is the work required

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to create a cavity in the solvent for inserting one molecule of solute. The second contribution, 𝑔̅i ,


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is the partial molar Gibbs energy of interaction between one molecule of solute and its surrounding

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solvent molecules. SPT assumes that the dominant entropic contributions to Δ𝑔̅2 are included in

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𝑔̅c . Strictly, this is not correct; 𝑠̅i is a small negative value because favorable interactions between

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the solute and solvent restrict motion of the solute. However, the entropic gain from cavity

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formation, 𝑠̅c, is significantly larger than 𝑠̅i . Neglecting 𝑠̅i greatly simplifies calculation of 𝑔̅i while

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only negligibly affecting the accuracy of 𝑠̅2 = 𝑠̅i + 𝑠̅c .36,37

91 92

Henry’s constant is given by ln

H2 𝜈1 Δ𝑔̅2 𝑔̅c + 𝑔̅i = = 𝑅𝑇 𝑅𝑇 𝑅𝑇

(2)

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where 𝜈1 is the liquid-phase molar volume of the solvent, R is the gas constant and T is absolute

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temperature. Δ𝑔̅2 is the partial molar Gibbs energy change of the solute going from a pure vapor

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phase to a dissolved solute in aqueous solution.

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In scaled-particle theory36-39, 𝑔̅c is a function of solvent molecular diameter, 𝜎1 , solute molecular

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diameter, 𝜎2 , and solvent molecular density, 𝜌1 . From SPT, 𝑔̅c is

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3 2 𝑔̅c = 𝐾 (0) + 𝐾 (1) σ12 + 𝐾 (2) 𝜎12 + 𝐾 (3) 𝜎12

(3)

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where 𝜎12 = (𝜎1 + 𝜎2 )/2. 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) are theoretically-derived functions given in

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the Supporting Information (SI).36,37 For water at 25oC, 𝜎1 = 0.275 nm, and 𝜌1 = 3.34 ∙ 1028

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molecules/m3.23

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𝐾 (0) = 4.767 ∙ 103

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𝐾 (1) = −8.396 ∙ 1013

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𝐾 (2) = 4.177 ∙ 1023

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𝐾 (3) = 2.52 ∙ 1029

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J mol J m ∙ mol

m2

J ∙ mol

J . m3 ∙ mol

Partial molar Gibbs energy of interaction, 𝑔̅i , is


5


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𝑔̅i 32 𝜖12 3 = (− ) ( ) (𝜋𝜌1 𝜎12 ) 𝑅𝑇 9 𝑘B 𝑇

(4)

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where subscript 1 refers to water and subscript 2 refers to solute. Here, 𝜖12 = √𝜖1 𝜖2 is the solute-

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solvent interaction parameter [J], kB is Boltzmann’s constant [J/K], 𝜌1 is the molecular density of

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the solvent [molecules/m3]. For dispersion forces in water23, 𝜖1 /𝑘B = 85.3 [K]; for the solutes

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considered in this work, 𝜖2 is rarely tabulated.

112 113

Bondi (1964) presents a group-contribution method for diameter 𝜎2 based on molecular structure.40

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We use a group-contribution method for 𝜖2 = ∑j 𝑛j 𝜖j where nj is the number of times group j

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appears in a solute molecule and 𝜖j represents the energetic contribution of functional group j

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interacting with water.

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As shown in Table 1, we consider 15 functional groups contained in six major classes of POPs.

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Fig 1 shows the 15 functional groups amongst the six families of POPs. Group contributions

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for 𝜖2 were determined from Henry’s-constant data for 51 POPs. Using group-contributions for 𝜎2

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reported by Bondi (1964), and group-contributions for 𝜖2 reported in this work, we calculate

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Henry’s constant for the solute using Eqs (1)-(4).

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Table 1: Group-contribution 𝜖j and Bondi volume, Vj, for 15 groups Group j

Group Identification

𝝐𝒋 /𝐤 [K]

𝐕𝐣 [cm3/mol]

Aromatic C-H (ACH)

1

88.65

8.06

Aro-Chlorine (Cl)

2

93.82

12

Ortho-Chlorine (ClOrtho)

3

91.18

12

Aro-Bromine (Br)

4

131.78

15.12

Ortho Bromine (BrOrtho)

5

128.16

15.12


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Group Identification

𝝐𝒋 /𝐤 [K]

𝐕𝐣 [cm3/mol]

Biphenyl

6

-372.9

9.48

𝛼-PCB-Chlorine

7

72.06

12

Ether

8

-435.1

6.4

𝛼-PBDE-Bromine

9

114.82

15.12

Condensed C-H

10

-219.3

4.74

𝛼-PCN-Chlorine

11

124.75

12

Dioxin

12

-83

12.8

𝛼-PCDD-Chlorine

13

94.18

12

Furan

14

-71.83

11.14

𝛼-PCDF Chlorine

15

77.14

12

Group j Polychlorinated Biphenyls (PCBs)

Polybrominated Diphenyl ethers (PBDEs)

Polychlorinated Naphthalenes (PCNs)

Polychlorinated Dibenzodioxins (PCDDs)

Polychlorinated Dibenzofurans (PCDFs)

123 124 125 126 127 128 129

𝛼-halogens are those next to the linkage between two aromatic groups (i.e. biphenyl, ether, condensed C-H, dioxin, and furan). The family-specific aromatic linkages (biphenyl, ether, condensed C-H, dioxin, and furan) are a single group regardless of number of bonds and atoms. Ortho-halogens are substituted halogens that are directly next to another halogen. Ortho-halogens are lower priority than 𝛼-halogens. For example, 2,3 dichlorobiphenyl has one α-Chlorine and one ortho-Chlorine atoms instead of 2 ortho-Chlorine atoms. Examples in Appendix A demonstrate conversion of volume, V2, to σ2 .


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Fig 1: 15 functional groups in six families of POPs with group IDs from Table 1.

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For the temperature range 0 to 40oC, the temperature-dependence of Henry’s constant was

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determined by application of a simplified van’t Hoff equation using approximate values for partial

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molar entropy of dissolution, Δ𝑠̅2, shown in Table A-1, in the Appendix.11,13,16

135

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An approximate form of the van’t Hoff equation (Eq. 5) is H2 𝜈1 d ln ( 𝑅𝑇 ) Δℎ̅2 Δ𝑔̅2 (298K) + 298K ∙ Δ𝑠̅2 = = d(1/𝑇) 𝑅 𝑅

(5a)

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where T = 298 K is the reference state, Δℎ̅2 and Δ𝑠̅2 are the partial molar enthalpy and partial

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molar entropy change due to dissolution of the solute from a pure vapor phase to a dissolved solute

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in aqueous solution. We assume 𝜈1 , Δ𝑠̅2, and Δℎ̅2 are constant in the small temperature range

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considered here.11,13 The partial molar Gibbs energy change is given by Δ𝑔̅2 = 𝑔̅i + 𝑔̅c , as

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calculated by Eq’s (1)-(4). Because Δ𝑠̅2, and Δℎ̅2 are constant, Δ𝑔̅2 is linear with respect to

142

temperature, with slope −Δ𝑠̅2.

143

Integrating Eq. 5a,


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ln

H2 (𝑇) 𝑇 Δ𝑔̅2 (298K) + 298K ∙ Δ𝑠̅2 1 1 = ln ( )∙[ ( − )] H2 (298K) 298K 𝑅 𝑇 298K

(5b)

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Table A-1 gives approximate Δ𝑠̅2 determined by correlating published experimental data to the

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number of chlorine or bromine substitutions, that is, to the halogenation number.11,13,16 Table SI-1

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gives Δ𝑔̅2 at 298K for all solutes considered in this work.

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2.2 Data Reduction. Literature reports on POP Henry’s-constant data often show large

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disagreement. To ensure the consistency of the data used for data reduction, Henry’s-constant data

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for each POP family were obtained from a single literature source.11-17 Sources for H2 data were

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chosen based on the number of solutes studied and on the range of halogenation number. Henry’s

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constants were obtained from published sources for CBs, PCBs, PCNs, and PBDEs that calculated

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values using measurements of y2 and x2 and application of Eq. 1a.11,12,16,17 For the remaining

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solutes, Henry’s constants were calculated from literature data for gas-chromatogram retention

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index (GC-RI) correlations for solute subcooled liquid vapor pressure and experimentally

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measured solid-phase solute solubility.14,15 Supplemental information (SI) gives the compiled

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experimental data used in this study. Data were collected for 72 POPs, where data for 51 were

158

used to determine group-interaction parameters and data for 21 POPs were used to test the model.

159

Data for these 21 solutes were not used to determine group contributions for 𝜖2 .

160

We identified 15 functional groups contained in the six families of POPs investigated; these

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groups are listed in Table 1 are shown in Fig 1. To account for the large variation in Henry’s

162

constant as a function of halogen location, we distinguish groups for 𝛼-halides (substitutions

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adjacent to aromatic linkages), adjacent (ortho) halide groups, and isolated halide groups (Aro-

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halide). All 15 functional groups are represented at least three times in the fitting set and at least

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once in the validation set. Molecules for the fitting set were also chosen such that the full range of

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halogenation number is represented within each POP family. We constructed a 51 x 15 matrix to


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represent the linear combination of constituent functional groups for each molecule in the fitting

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set, reproduced in Fig SI-4, and performed a least-squares regression analysis to determine the

169

energy parameter, 𝜖j , for each functional group.

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In the fitting set, data for all solutes were used to determine aromatic carbon-hydrogen (ACH),

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non-ortho chlorine (Cl), ortho chlorine (Clortho), non-ortho bromine (Br), and ortho bromine

172

(Brortho) group-interaction parameters. The remaining functional groups are unique to a family of

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POPs; they were fitted using only experimental data for that family.

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Each group’s unique 𝜖j and molecular volume, Vj , are compiled in Table 1. Appendix A

175

demonstrates conversion of Vj to 𝜎2 and provides sample calculations for Henry’s constant, H2.

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Table SI-2 lists 𝜎2 and 𝜖2 for all solutes considered in this work.

177

3. RESULTS AND DISCUSSION

178

For both fitting and validation sets, Fig 2 and Table SI-1 compare experimental and predicted

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room-temperature log H2. Both fitting and validation sets show strong agreement with

180

experimental log H2. The average deviation between predicted results for log H2 and experimental

181

results is 4%. The average deviations and root-mean-square-error (RSME) varied slightly for

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different POP families. Average deviations and RSME amongst CBs, PCBs, PCDDs, PCDFs,

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PCNs, and PBDEs are 2%, 3%, 5%, 5%, 3%, and 5% and 0.26, 0.26, 0.33, 0.27, 0.19, and 0.29,

184

respectively. The average deviation, RMSE, squared coefficient of determination (r2), and squared

185

Pearson coefficient (p2), between our predicted log H2 and experiment in the fitting set and

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validation set are 4%, 0.22, 0.89, and 0.91 and 4%, 0.27, 0.88, and 0.91, respectively. Considering

187

experimental uncertainty, these metrics show an excellent fit indicating very good predictive

188

accuracy of our model. It is important to note that errors in H2 are larger than those in log H2.


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For comparison, we calculated log H2 for the validation set of POPs using the EPISuiteTM

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computational software developed by the US Environmental Protection Agency (US EPA). We

191

obtained an average deviation, RMSE, r2, and p2 of 7%, 0.46, 0.38, and 0.71, respectively. Results

192

from our model are better than those from the EPISuiteTM software provided by the US EPA. The

193

EPISuiteTM software was chosen because it is freely available and is one of the few QSPR models

194

able to calculate H2 for all six families of POPs.

195

Most of the functional groups in Table 1 yield a positive 𝜖j indicating that addition of that

196

functional group parameter increases the energetic term toward higher solubility in water,

197

indicating increased solvation. However, some functional groups (biphenyl, ether, furan, dioxin,

198

and condensed C-H) give a negative 𝜖j , indicating that these linker groups decrease solubility. The

199

negative 𝜖j may arise from a steric effect that limits water-solute interaction.

200

201 202

Fig 2: Experimental and predicted logarithm of Henry’s constants at 25oC in units of Pa. Solid line

203

corresponds to perfect fit. Filled squares are the fitting set. Empty triangles are the validation set.


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There are only four studied POPs with deviation in log H2 greater than 10%: 1, 2, 3, 4, 7-CDD;

205

2, 3, 4, 7, 8-CDF; PBDE-100; and 1, 2, 3, 4, 7-CDD. In each of these four molecules, there is a

206

sequence of at least four consecutively adjacent functional groups that are not Group ACH. The

207

relatively high error in H2 of these POPs suggests that higher-order effects are needed to account

208

for the effect of four or more consecutively adjacent halogen substitutions and benzene linkages

209

(e.g biphenyl).

210

Using suggested values for Δ𝑠̅2, given in Table A-1, and an approximate van’t Hoff equation,

211

we extended the model to the environmentally relevant temperature range 0 to 40oC and compared

212

results to experimental data for 39 solutes.

213

214 215

Fig 3: Logarithm of Henry’s constants in units of Pa versus temperature for a selection of PCBs,

216

PBDEs, and PCNs. Squares are experimental data.11,13,16 Lines are predicted using SPT and the

217

approximate van’t Hoff equation.


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Fig 3 compares temperature-dependent experimental and predicted log H2 for 9 of the 39 solutes

219

studied. Figs SI-1, SI-2, and SI-3 compare temperature-dependent log H2 for all PCBs, PCNs, and

220

PBDEs, respectively, for those solutes where data are available. The average deviation of predicted

221

results for log H2 over the temperature range 0 to 40oC is within 5% for PCBs, PCNs, and PBDEs

222

and the RMSE for each family is 0.32, 0.29, and 0.26, respectively. No meaningful correlation was

223

found between temperature and any of the reported evaluation metrics.

224

The slopes of the curves in Fig. 3 are primarily determined by Δ𝑠̅2, since, at constant pressure,

225

dΔ𝑔̅2/dT = −Δ𝑠̅2. The ordinate intercepts of the curves in Fig. 3 are primarily determined by the

226

predicted H2 at 298K, as shown in Eq. 5b. Thus, any systematic overestimation or underestimation

227

of H2, such as in PCB-195, result from inaccuracy in predicted H2 at 298K. In cases, such as PCB-

228

170, where there is both overestimation and underestimation, prediction of H2 at 25oC is accurate

229

but the suggested Δ𝑠̅2 deviates from the experimental entropy change.

230

The proposed group-contribution method is accurate for calculation of Henry’s constants and

231

validates the use of scaled-particle theory to calculate energetic-interaction parameters for

232

prediction of Henry’s constant. As a predictive tool, this method addresses the lack of reliable

233

experimental data for many congeners of POPs. Environmental scientists and engineers can

234

implement this model to calculate Henry’s constants that will aid in assessment of air-water

235

partitioning of POPs in the environment. In addition, because this SPT method is general, future

236

work can apply the method to additional classes of molecules with repeating functional groups.

237

For example, Henry’s constants for highly toxic bromo/chloro-POPs could be correlated by the

238

methods of our work.41,42 We anticipate that our SPT model will be a useful advance in group-

239

contribution models for Henry’s constant predictions.

240


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241

APPENDIX A

242

We present some examples for calculating Henry’s constants.

Page 14 of 23

243

Example 1. To illustrate the use of our model, we show a sample calculation for Henry’s

244

constant for 1-chlorodibenzo-p-dioxin. This molecule contains 7 aromatic CH groups, one dioxin

245

linkage, and one 𝛼 − PCDD chlorine group.

246

Using the 𝜖j values in Table 1 and Eq’s (1)-(4) we find:

247

𝜖2 = 𝑘B ∙ (7 ∙ [88.65] + [−83.00] + [94.18]) = 630.9 ∙ 𝑘B 𝜖12

248

𝑘B

𝜖 𝜖2

= √ 𝑘1

B

𝜖

= 232.0K , with 𝑘1 = 85.3K. B

249

We use Bondi’s method for estimation of van der Waals diameter to calculate 𝜎2 . A molecule

250

of 1-chlorodibenzo-p-dioxin contains 7 aromatic CH (ACH groups), one dioxin linkage, and one

251

aromatic Cl (AroC-Cl) group. 1

252

3 107 nm 6 ∙ [7 ∙ V ACH + VDioxin + VCl ] 1 mol 𝜎2 = ( ∙ ) ∙ = 0.636 nm 𝜋 6.02 ∙ 1023 molecules 1 cm

253 254

𝜎12 =

𝜎1 +𝜎2 2

= 0.456 nm, with 𝜎1 = 0.275 nm.

At 298K, we calculate 𝑔̅c using values for 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) and Eq. 3, found in the body

255

of the paper

256

3 2 𝑔̅c = 𝐾 (0) + 𝐾 (1) σ12 + 𝐾 (2) 𝜎12 + 𝐾 (3) 𝜎12 = 53.2

257 258

261

(3)

Using 𝜎12 and 𝜖12 and substituting into Eq. 4, found in the body of the paper 𝑔̅i = 𝑅𝑇 (−

32 𝜖12 kJ 3 )( ) (𝜋𝜌1 𝜎12 ) = −68.0 9 𝑘B T mol

259 260

kJ mol

Δ𝑔̅2 = 𝑔̅i + 𝑔̅c = −14.8

(4) kJ mol

Finally, rearranging Eq. 2 from the body of the paper, H2 (298K) =

𝑅𝑇 Δ𝑔̅2 ∙ exp ( ) = 3.5 ∙ 105 Pa 𝜈1 𝑅𝑇


14

Page 15 of 23


262

This calculated result matches the experimental value 3.5 ∙ 105 Pa.15

263

Example 2. We also show a sample calculation for Henry’s constant for PCB-87. This molecule

264

contains 5 aromatic CH groups, one biphenyl linkage, 2 𝛼 − PCB chlorine groups, one non-ortho

265

chlorine, and 2 ortho chlorines.

266 267

Using the 𝜖j in Table 1 and Eq’s (1)-(4) we find: 𝜖2 = 𝑘B ∙ (5 ∙ [88.648] + [−372.9] + 2 ∙ [72.05] + [93.82] + 2 ∙ [91.18]) = 490.3 ∙ 𝑘B 𝜖12

268

𝑘B

𝜖 𝜖2

= √ 𝑘1

B

ϵ

= 204.6K, with k1 = 85.3K B

269

We use Bondi’s method for estimation of van der Waals diameter to calculate 𝜎2 . A molecule

270

of PCB-87 contains 5 aromatic CH (ACH groups), 1 biphenyl linkage, and 5 aromatic Cl (AroC-

271

Cl) groups. 1

272

3 6 ∙ [5 ∙ V ACH + VBiphenyl + 5 ∙ VCl ] 1 mol 107 nm 𝜎2 = ( ∙ ) ∙ = 0.704 nm 𝜋 6.02 ∙ 1023 molecules 1 cm

273 274

𝜎12 =

𝜎1 +𝜎2 2

= 0.439 nm, with 𝜎1 = 0.275 nm.

At 298K, we calculate 𝑔̅c using values for 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) and Eq. 3, found in the body

275

of the paper

276

3 2 𝑔̅c = 𝐾 (0) + 𝐾 (1) σ12 + 𝐾 (2) 𝜎12 + 𝐾 (3) 𝜎12 = 63.8

277 278

(3)

Using 𝜎12 and 𝜖12 and substituting into Eq. 4, found in the body of the paper 𝑔̅i = 𝑅𝑇 (−

32 𝜖12 kJ 3 )( ) (𝜋𝜌1 𝜎12 ) = −74.4 9 𝑘B T mol

279 280

kJ mol

Δ𝑔̅2 = 𝑔̅i + 𝑔̅c = −10.6

(4) kJ mol

Finally, rearranging Eq. 2 from the body of the paper, 𝑅𝑇 Δ𝑔̅2 ∙ exp ( ) = 1.90 ∙ 106 Pa 𝜈1 𝑅𝑇

281

H2 (298K) =

282

This calculated result compares favorably to experiment 2.11 ∙ 106 Pa.11


15


Page 16 of 23

283

To illustrate the temperature dependence of Henry’s constant, we use an approximate van’t Hoff

284

equation (Eq. 5b). PCB 87 has 5 chlorine substituents, so an averaged entropy of −156 K∙mol is

285

chosen (Table A-1).

286 287 288 289

J

For T = 304K, rearrangement of Eq. 5b yields: H2 (𝑇) = H2 (298K) ∙ (

[Δ𝑔̅2 (298K) + 298K ∙ Δ𝑠̅2 ] 1 𝑇 1 ) ∙ exp ( ∙( − )) = 2.99 ∙ 106 Pa 298K 𝑅 𝑇 298K

This calculated result is comparable to the experimental value 2.77 ∙ 106 Pa.11 Table A-1: Suggested Δs̅ 2 for PCBs, PBDEs, and PCNs Halogenation number

Suggested 𝚫𝐬̅𝟐 [J/mol/K] PCBs11

1

-104

2

-110

3

-78

4

-67

5

-156

6

-234

7

-358

8

-488

9

--

10

-PBDEs13

1

--

2

--

3

-150

4

-130


16

Page 17 of 23


Halogenation number

Suggested 𝚫𝐬̅𝟐 [J/mol/K]

5

-140

6

-115

7

--

8

--

9

--

10

-120 PCNs16

1

--

2

--

3

-175

4

-175

5

-262

6

-334

7

-280

8

-210

290 291 292 293

Suggested partial molar entropies, Δs̅ 2 , for PCBs, PBDEs, and PCNs are determined from averaging experimental results for a given number of chlorines or bromines on the hydrocarbon molecule.

294

ASSOCIATED CONTENT

295

Supporting Information. The following files are available free of charge.

296

Full expressions for constants 𝐾 (0) , 𝐾 (1) , 𝐾 (2) , and 𝐾 (3) , two tables of H2, Δ𝑔̅2, 𝜎2 , and 𝜖2 at

297

25oC for 72 solutes, three figures of temperature-dependent H2 for 39 solutes, and SMILES tags

298

for all 72 solutes. (PDF) 51 x 15 matrix describing constituent functional groups for each

299

molecule in the fitting set. (XLSX)


17


300

AUTHOR INFORMATION

301

Corresponding Author

302

*Phone (408) 772-6293; e-mail [email protected].

303

Present Address

304

‡Department of Chemical Engineering and Materials Science, University of Minnesota,

305

Minneapolis, MN 55455, USA: effective September 1, 2017.

306

Author Contributions

307

†These authors contributed equally.

308

Notes

309

The authors declare no competing financial interest.

310

REFERENCES

311 312

Page 18 of 23

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FOR TABLE OF CONTENTS ONLY:

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23

Henry's Constants of Persistent Organic Pollutants by a Group

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