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A simple method to measure the vapor pressure of phthalates and their alternatives Yaoxing Wu, Clara M. A. Eichler, Shengyang Chen, and John C. Little Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b02643 • Publication Date (Web): 29 Aug 2016 Downloaded from http://pubs.acs.org on August 31, 2016

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Environmental Science & Technology

1

A simple method to measure the vapor pressure of phthalates and their alternatives

2

Yaoxing Wu,1 Clara M. A. Eichler,1 Shengyang Chen,2 and John C. Little1*

3 4

1

5

USA

6

2

Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA 24061,

School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia

7 8 9 10 11 12

*

Corresponding author Address: 401 Durham Hall, Virginia Tech, Blacksburg, VA, 24061; Phone: (540) 231 0836; Email: [email protected]

1 ACS Paragon Plus Environment


13

Abstract. Phthalates and alternative plasticizers are semi-volatile organic compounds (SVOCs),

14

an important class of indoor pollutants that may have significant adverse effects on human health.

15

Unfortunately, models that predict emissions of and the resulting exposure to SVOCs have

16

substantial uncertainties. One reason is that the characteristics governing emissions, transport

17

and exposure are usually strongly dependent on vapor pressure. Furthermore, available data for

18

phthalates exhibit significant variability and vapor pressures for the various alternatives are

19

usually unavailable. For these reasons, a new approach based on modelling of the evaporation

20

process was developed to determine vapor pressures of phthalates and alternate plasticizers. A

21

laminar flow forced convection model was used in the design of a partial saturator (PS) tube.

22

The mass transfer mechanisms in the PS tube are accurately modeled and enable the

23

determination of vapor pressure even when the carrier gas is not completely saturated, avoiding

24

the complicated procedure to establish vapor saturation. The measured vapor pressures ranged

25

from about 10-2 to 10-7 Pa. Compared to the traditional gas saturation method, the model-based

26

approach is advantageous in terms of both predictability and simplicity. The knowledge

27

provides new insight into experimental design and a sound basis for further method development.

28 29

Keywords. Phthalates; SVOCs; Vapor pressure; Plasticizers.

30


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TOC/Abstract art

32



33

INTRODUCTION

34

Phthalates and alternative plasticizers are used to enhance the flexibility of polyvinyl chloride

35

(PVC) products. They have been produced in large quantities since the 1930s.1 These semi-

36

volatile organic compounds (SVOCs) are found in a wide range of building materials and

37

consumer products including floor and wall coverings, toys, carpets, furniture, and food

38

packaging.2, 3 Because phthalates are not chemically bound to the polymer matrix, they can

39

migrate from the original source to air and other media, and have become ubiquitous in the

40

indoor environment. Human exposure to phthalates occurs through inhalation, ingestion and

41

dermal sorption.4 The potential adverse health effects associated with certain phthalates include

42

endocrine disruption, asthma, and allergies.5-7 Despite these possible health impacts, phthalates

43

still dominate the plasticizer market.8

44 45

Following restrictions on using certain phthalates in toys and child-care products in the

46

Consumer Product Safety Improvement Act (CPSIA),9 there has been a trend towards using

47

plasticizers of higher molecular weight and lower volatility.8, 10 For example, the market share of

48

some alternate plasticizers such as diisononyl cyclohexane-1,2-dicarboxylate (DINCH) and di(2-

49

ethylhexyl) adipate (DEHA) has been growing continuously.11 However, there is a lack of

50

physical/chemical information for many plasticizers. As alternate plasticizers share similar

51

chemical structures and physicochemical properties with phthalates, similar emission

52

characteristics and environmental behavior may be expected.

53 54

Although there is mounting interest in human exposure to SVOCs in the indoor environment, the

55

substantial analytical challenges and extensive surface sorption have impeded progress.8, 12 The


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use of indoor emission and exposure assessment models has become increasingly relevant.8

57

However, there is still substantial uncertainty associated with the characteristics governing

58

emissions, transport and exposure in these models. For example, compound-specific

59

physicochemical properties such as vapor pressure are typical model inputs to predict SVOC

60

emission rates from indoor sources. A recent overview of exposure assessment models

61

suggested that knowledge of key physicochemical properties including vapor pressure is critical

62

in decreasing the uncertainty and variability in model predictions.8, 13 Unfortunately, the

63

availability of reliable measurements of these parameters is limited for many phthalates and

64

alternate plasticizers. Even though some vapor pressure data for certain well-researched

65

phthalates are available in the literature, they are mutually inconsistent and subject to large

66

uncertainties.14, 15 To better understand the environmental behavior of phthalates and their

67

alternatives, more reliable vapor pressure measurements are clearly needed.

68 69

Vapor pressure is a key physicochemical parameter that influences the environmental fate and

70

behavior of organic compounds. To date, both direct and indirect techniques have been

71

developed for measuring vapor pressure. The direct techniques, which directly measure the

72

vapor pressure, are generally considered unsuitable for measurements of low-volatility

73

compounds.16-18 Among the considerable efforts made to measure the vapor pressure of low-

74

volatility organic compounds, the gas saturation method is an indirect technique that has been

75

accepted as being sufficiently accurate to measure vapor pressures lower than ~1 Pa.17, 19-21 It is

76

based on the saturation of a carrier gas stream with the vapor of a condensed phase of the

77

compound of interest. The most common approach to produce a saturated vapor phase is to pass

78

an inert gas stream through a saturator column packed with powdered compound or with a



79

liquid-coated inert support such as glass beads.22, 23 Although several studies have focused on

80

the development of different analytical techniques, inert support materials, and column sizes for

81

the gas saturation method, little effort has been devoted to the understanding of mass transfer

82

mechanisms in the vapor saturator column.17 A noticeable feature of the available literature on

83

the gas saturation method is the lack of a physically-based model that can guide experimentation.

84

As a result, the extent to which the system achieves a state of saturation is based on experience

85

regarding residence time of the carrier gas in the saturator. Preliminary tests of different flow

86

rates or column lengths have to be carried out to ensure complete saturation of the carrier gas.20,

87

24, 25

88 89

This study uses the basic principles of the gas saturation method to determine vapor pressures of

90

SVOCs including phthalates and their alternatives at ambient temperatures. For most of the

91

target compounds, reliable experimental vapor pressures are not available. A cylindrical tube

92

with laminar flow regime was selected as the partial saturator (referred to as a PS tube), with the

93

inner wall coated with pure liquid compound (no inert support materials were used). The

94

development of the concentration profile of SVOCs in the PS tube due to the evaporation process

95

was accurately predicted using a fully developed laminar forced convection mass transfer model,

96

avoiding the tedious experimental procedure to establish vapor saturation. The vapor pressure

97

was calculated based on the model and experimentally determined effluent concentration. The

98

fundamental knowledge provides new insight into the design of experiments to measure vapor

99

pressure and a sound basis for further method development.

100 101

MODELING


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Development of velocity profile

103

First, the velocity field in the cylindrical tube (PS tube) with laminar flow regime is modeled.

104

The entire experimental system is in a thermally-controlled environment to minimize thermal

105

gradients inside the tube, and internal mixing imposed by small thermal gradients is highly

106

unlikely. The air flow in the tube is considered laminar as long as the Reynolds number (Re =

107

DU/ υ ) is lower than 2300, where D (m) is the diameter of the tube, U (m/s) is the air flow

108

velocity, and υ (m2/s) is the kinematic viscosity of air. In the case of air flow through a straight

109

0.017 m I.D. tube at 50-100 mL/min, the value of Re is less than 10. At this condition,

110

hydrodynamically fully developed laminar flow persists beyond the hydrodynamic entrance

111

length Lhy, which is given by:

112

Lhy = 0.05Re D

113

The calculated values of Lhy are 0.4 and 0.7 cm at 50 and 100 mL/min, respectively.

(1)

114 115

Development of concentration profile

116

The inner wall of the PS tube is coated with a thin layer of pure SVOC liquid, serving as a

117

constant emission source. The coating layer as emission source is characterized by the vapor

118

pressure of the SVOC, which drives diffusion of SVOC from the emission surface into the air

119

passing through the tube. When the clean air enters the PS tube, the velocity and mass transfer

120

boundary layers both develop from the entrance, and their thickness grows along the flow path

121

(Figure 1). As the flow passes along the tube, the mass transfer boundary layers merge at

122

distance x = Lma. The region 0 < x < Lma is the mass transfer entrance region, with Lma defined as:



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Lma = 0.05 Re⋅ D ⋅υ / Da

124

where Da (m2/s) is the gas-phase mass diffusion coefficient of the specific SVOC, which

125

generally falls into a relatively narrow range (10-6 to 10-5 m2/s) for SVOCs at standard conditions.

126

Taking di-2-ethylhexyl phthalate (DEHP) at 25 °C as an example, the calculated entrance length

127

Lma is less than 5 cm at a flow rate of 100 mL/min. In the region x > (Lhy, Lma), which is 5 cm

128

maximum in this case, the flow field is fully developed with respect to both hydrodynamics and

129

mass transfer.26

(2)

Constant wall concentration r C=0

x

C(x,r)

U(r) y0

130 131

Figure 1. Laminar forced convection mass transfer of SVOC in the flow region with fully

132

developed velocity and concentration profiles

133 134

Modelling of fully developed concentration profile

135

In a next step, the forced convection mass transfer of SVOCs after emission from the surface of

136

the cylindrical PS tube wall in the flow region with fully developed velocity and mass transfer is

137

modeled (Figure 1). It is assumed that axial advection dominates and that axial diffusion is

138

negligible. Considering the constant and uniform wall concentration as a boundary condition,

139

the governing equation is:


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 r 2  C − y0 dCm 1 ∂  ∂C  2   r U = 1 −   m r ∂r  ∂r  Da  R02  Cm − y0 dx

141

where r is the radial coordinate, x is the axial coordinate, R0 (m) is the radius of the PS tube, Um

142

(m/s) is the mean flow velocity in the cross section, and C (µg/m3) is the gas-phase concentration.

143

Cm (µg/m3) is the mean gas-phase concentration in the cross section of the tube, and y0 (µg/m3) is

144

the gas-phase SVOC concentration immediately adjacent to the wall of the tube, which is equal

145

to the vapor pressure of the SVOC liquid in this case. The analytical solution to equation 3 is

146

obtained from an analogous heat transfer problem, which is transformed into mass transfer

147

terms.26, 27 When the dimensionless axial position at x* = xDa/DRe υ > 0.0335, the

148

concentration profile asymptotically approaches

149

Cm ( x) − y0 2 = 0.81905 exp (−2λ0 x*) Cin − y0

150

where λ0 =2.7043644 and Cin is the gas-phase concentration entering the tube, which is zero in

151

this study. Cm(x) is the mean gas-phase concentration in the cross section of the tube at axial

152

position x. Since remarkably few measured values are available for diffusion coefficients of

153

phthalates, the value of the mass diffusion coefficient Da of SVOCs in air was estimated using

154

the SPARC Perform Automated Reasoning in Chemistry online calculator

155

(http://archemcalc.com/sparc-web/calc#).28 Based on equation 4, the vapor pressure (y0) of the

156

analytes can be calculated using the concentration measured at the outlet of the PS tube

157

Cm(outlet).

(3)

(4)

158



159

Computational fluid dynamics (CFD) was used to confirm the analytical solution. In the CFD

160

model, flow motion is controlled by the usual two-dimensional Navier-Stokes equation. Pressure

161

inlet and pressure outlet boundary conditions were used for the inlet and outlet of the tube,

162

respectively. For the surface of the tube in contact with the fluid, a rigid wall boundary

163

condition was used. The model domain was initially filled with air at zero velocity. The

164

governing equations along with the boundary and initial conditions were solved using the

165

commercial CFD package FLUENT 16.1, which is a finite volume based solver. The SIMPLE

166

scheme was adopted for the pressure-velocity coupling. The discretization of the convective

167

terms (dividing the continuous convective terms into a finite number of discrete elements) used a

168

second-order upwind scheme, while that of the diffusion terms used a second-order central-

169

differenced scheme. A non-uniform grid was constructed with finer grids distributed in the

170

vicinity of the wall boundaries and close to the inlet. All results were obtained using a double

171

precision solver. Figure 2 shows the CFD simulation for the velocity field within the PS tube,

172

which agrees with the predictions based on equation 1.

173

174

175


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Figure 2. The steady-state air flow velocity contour (m/s) at 50 and 100 mL/min in the partial

177

saturator (PS) tube.

178 179

EXPERIMENTAL

180

Chemicals

181

All standards and solvents used in this study were of high quality and purity. Details on

182

suppliers and purity are shown in Table 1. All analytes are liquids at ambient temperature.

183

Optima grade acetone and methanol used for cleaning and as solvents were obtained from Fisher

184

Scientific, Waltham, MA, USA.

185 186

Table 1. Analytes, acronyms, purity, CAS, molecular weight (MW), and vendor information. Compound

Acronym

Purity

CAS

MW

Supplier

Diisobutyl phthalate

DiBP

99%

84-69-5

278.3

Sigma Aldrich

Di-n-butyl phthalate

DnBP

99%

84-74-2

278.3

Sigma Aldrich

Tributyl O-acetylcitrate

ATBC

98%

77-90-7

402.5

Sigma Aldrich

Bis (2-ethylhexyl) adipate

DEHA

99%

103-23-1

370.6

Sigma Aldrich

Di-2-ethylhexyl phthalate

DEHP

≥ 99.5 %

117-81-7

390.6

Sigma Aldrich

1,2-Cyclohexane

DINCH

≥ 99%

166412-78-8

424.7

Just In Time

dicarboxylic acid

Chemical Sales,

diisononyl ester

NJ

Dioctyl terephthalate

DEHT

≥ 96%

6422-86-2

390.6

Sigma Aldrich

Di-n-octyl phthalate

DnOP

≥ 98%

117-84-0

390.6

Sigma Aldrich

Diisononyl phthalate

DiNP

≥ 99%

28553-12-0

418.6

Sigma Aldrich

Diisodecyl phthalate

DiDP

≥ 99%

24761-40-0

446.7

Sigma Aldrich



187 188

Partial saturator tube

189

Important experimental parameters including dimension of the tube and air flow rate were

190

chosen based on model prediction and sampling technique. A 0.3 m long stainless steel tube

191

(0.017 m I.D., 8989K818, McMASTER, Elmhurst, Illinois, USA) was used as the PS tube

192

(Figure 3). A thin layer of pure target SVOC liquid serving as the emission source was carefully

193

coated on the inner wall of the tube using a cotton cloth saturated with the target analyte,

194

resulting in a film thickness in the range of tens to hundreds of micrometers (a few grams).

195

Based on the model prediction (equation 4), the vapor pressure y0 can be precisely calculated

196

from the effluent concentration Cm(0.3).

197 198

Vapor pressure measurements at different temperatures

199

The experimental setup is shown schematically in Figure 3. Breathing grade air (0% relative

200

humidity, Airgas, Pennsylvania, USA) was used as the gas supply. Two identical PS tubes were

201

placed in a temperature-controlled cabinet for duplicate measurements with a thermometer

202

alongside (Figure 4). Industry-standard sorbent tubes (89 mm long, 6.35 mm O.D., Supelco, St.

203

Louis, Missouri, USA) packed with 200 mg Tenax TA (40-60 mesh, MARKES International,

204

Llantrisant, Wales, UK) were used to collect effluent air samples. The Tenax tube was attached

205

to the outlet of each PS tube using modified Swagelok fittings so that the sorbent tube could be

206

completely inserted through the fitting, minimizing the sorption area along the sampling path.29

207

Backup tubes were connected to the primary sample tube to check for breakthrough. Column

208

gas flow rates were precisely controlled by mass flow controllers (MFCs) coupled with a vacuum

209

pump. As shown in Figure 3, the sampling flow rate is equal to the air flow rate through the PS 12 ACS Paragon Plus Environment

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tube. Based on the model prediction and the specification of the sorbent tubes, sampling rates of

211

20-100 mL/min were chosen for all analytes except DEHP. The sampling periods last between

212

0.2-72 h, depending on the vapor pressure of the target plasticizers. Rough calculations show

213

that complete evaporation of the coating (a few grams) at the designated emission rates (< 3 µg/h)

214

is unlikely for the duration of the test due to the low vapor pressure of targeted SVOCs, thus y0

215

could be considered a constant. The measurement of vapor pressure was carried out at ambient

216

temperatures (283 to 303 K for DiBP and DnBP, and 288 to 308 K for the remainder of the

217

compounds). The measured effluent plasticizer concentration Cm(0.3) was used to calculate the

218

vapor pressure y0 based on equation 4.

219

220 221

Figure 3. Schematic representation of the experimental setup.

222

223 13 ACS Paragon Plus Environment


224

Figure 4. Photo of partial saturator (PS) tubes.

225 226

Chemical analysis

227

All samples were analyzed by thermal desorption (TurboMatrix TD, Perkin-Elmer) coupled with

228

gas chromatography/flame ionization detector (Agilent 6890 GC/FID). Details regarding the

229

analysis protocol can be found in the Supporting Information. The reliability of the analytical

230

method has been verified through a pilot inter-laboratory study with an analytical detection limit

231

at 10 ng/tube.29

232 233

RESULTS AND DISCUSSION

234

Model validation

235

Accurate modelling is an essential prerequisite for the successful experimental design of the new

236

PS tube. The results of CFD modelling for the concentration contour, using DEHP at 25 °C as

237

an example, indicated that the effluent concentration of DEHP is approximately equivalent to its

238

vapor pressure at low flow rates around 50 mL/min (Figure 5). This is consistent with model

239

prediction using equation 4. The gas-phase DEHP concentrations in the effluent air stream of the

240

0.3 m long PS tube (Cm(0.3)) at sampling flow rates between 30 and 500 mL/min were thus

241

measured for model validation. The value of Cm(0.3) measured at 30 mL/min was used as vapor

242

pressure of DEHP (y0) in modelling.

243


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The sampling data and model prediction of Cm(0.3) using equation 4 are shown in Figure 6. The

245

standard deviations of the duplicate sampling data sets are between 2-15%, proving the reliability

246

of the coating method for the PS tube. Good agreement between the experimental measurements

247

and model predications are achieved, as indicated in Figure 6. Because the flow within the PS

248

tube is laminar, mass diffusion of DEHP determines the mass transfer rate of DEHP from the

249

emission surface into the air in the radial direction of the tube. Based on equation 4 and CFD

250

modelling, the vapor pressure of DEHP can be approximated by Cm(0.3) with flow rates below

251

100 mL/min. The experimental data clearly proves that the effluent concentration Cm(0.3)

252

maintains approximately the same level at lower flow rates, and it starts to decrease as the flow

253

rate increases. The DEHP vapor pressure y0 calculated from these measurements of Cm(0.3) at

254

different flow rates using equation 4 shows a low level of variation (2.5 ± 0.1 µg/m3). Overall,

255

the results confirm the applicability of the laminar flow model to the vapor pressure

256

measurements of SVOCs, and success in the design of the PS tube.

257

258 259

a)

260



261

b)

262

Figure 5. CFD modelling of concentration contour of DEHP in the PS tube (25 ◦C) at a) 50

263

mL/min; b) 100 mL/min.

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264

265 266

Figure 6. Effluent concentration of DEHP from the PS tube at different flow rates (25°C).

267 268

Due to the lack of reliable data for diffusion coefficients of phthalates and alternative plasticizers,

269

the variability of Da estimated from SPARC is a source of uncertainty in model prediction. The

270

variability of the model predictions about the true value of Da was thus estimated through a

271

Monte Carlo method using DEHP as example.30 Since the molecular diffusivities fall within a

272

narrow range for SVOCs, Da of DEHP (2.6×10-6 m2/s) was assumed to follow a normal

273

distribution with standard deviation at 1×10-6 m2/s. A total of 1,000,000 repeated model

274

predictions were performed to evaluate the uncertainty, with Da randomly sampled from the

275

distribution and other parameters fixed. The results of all predictions were then pooled to assess

276

the expected variation in effluent gas-phase concentration Cm(0.3) as a function of flow rate.

277


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278

As shown in Figure S1 (Supporting Information), the average predicted Cm(0.3) obtained from

279

the Monte Carlo simulation is close to the measured concentration. However, it is also clear that

280

the uncertainty of Cm(0.3) increases with increasing flow rate. For the flow rate range used in

281

this study (20-100 mL/min), the uncertainty of model prediction is expected to be relatively

282

insignificant.

283 284

Because the SVOC mass transfer mechanisms in the new PS tube are well understood and

285

characterized, the vapor pressure of target SVOCs can be calculated using the mass transfer

286

model even when the carrier gas is not completely saturated in the tube. The complicated

287

procedure to ensure the saturation of the carrier gas, which is a key component of all previous

288

experimental procedures,24, 25, 31 is therefore not required in this new method. All the values of

289

vapor pressure of phthalates and their alternatives were back-calculated using measured Cm(0.3)

290

and equation 4. Furthermore, the method is relatively simple compared to the experimental setup

291

used in other gas saturation methods such as concatenated gas saturation method,31 thus some

292

potential problems related to a complicated experimental setup (e.g., leaks) can be minimized or

293

prevented.

294 295

Results of vapor pressure measurements

296

Although experimental measurements of vapor pressure are limited for phthalates and for other

297

SVOCs, the vapor pressure of DEHP has been measured over many years using a variety of

298

methods.29, 32 Thus the quality of data was examined using both n-hexadecane and DEHP as

299

reference compounds. The vapor pressure of n-hexadecane at temperature of 298 K is

300

determined as 0.16 Pa, which is in good agreement with literature value (0.19 Pa).33 The



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301

reference values of vapor pressure for DEHP in the literature are shown in Table 2 together with

302

the value of DEHP obtained from this study. It is clear that the vapor pressure of DEHP

303

determined in this work falls within the range of previous experimental studies, and appears to be

304

close to most of the reference values. The agreement provides strong support that the new PS

305

tube is functioning correctly.

306 307

Table 2. Values of vapor pressure VP of phthalates and alternate plasticizers at 298 K (25 °C).

308

VP is reported for the isomeric mixture of DINCH, DiNP, and DiDP due to the unresolved peaks

309

by GCFID.

310 Chemical VP (µg/m3) DiBP

9,600±400 a 510 b

DnBP

751±23

6,700±200

ATBC

13.2±0.9

81±5 a

DEHA

10.4±0.03

a

340

70±0.2

a a

8.4

DINCH

1.6±0.01

9.2±0.1 a

0.13 b

0.4±0.05

2.7±0.3

a

b

2.3±0.1

a

2.3±0.1

a

0.6±0.1

a

DiNP DiDP

0.4±0.02 0.4±0.02 0.1±0.01

3.9×10 9.1×10

-3 b

8.8×10

-4 b

1,900 17

25

-2 b

c

-

-

-

-

d

4,100 -

d

5.3

-

d

36

c

-

e

-

4,700 g

-

4,700

g

-

-

e

-

-

-

-

-

b

16±0.3

0.37

c

-

b

0.14

-

4,300

57 b

2.5±0.04

DnOP

-

b

DEHP DEHT

311 312 313 314 315 316 317 318 319 320

1076±49

VP × 106 (Pa) at 298 K

20

3.1 -

-

-

-

-

-

-

a. Measured in this study b. Estimated using SPARC v4.5 c. Reported in EPA Product Properties Test Guidelines (OPPTS 830.7950)23 d. Schossler, Schripp et al. 20118 e. Liang and Xu, 201415 f. Clausen, Liu et al. 201232 g. Weschler, Salthammer et al. 200814 h. Staples, Peterson et al. 199734 i. Gobble, Chickos et al. 201435


13

-

13

h

4,300 i -

g

e

25

3,600 -

f

77,000 h

h

5.6 i -

h

-

< 67

h

-

< 67

h

-

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321

Table 2 also shows the values of the other target analytes determined in this study and vapor

322

pressures reported in the literature. Duplicate measurements of vapor pressure were made for

323

each compound at each temperature, and the relative standard deviation of the replicate samples

324

in terms of mass concentration (µg/m3) ranged from 0.1% to 20%. Most of the values are higher

325

than the SPARC estimations, which is consistent with the report by Liang and Xu.15 Similar to

326

DEHP, most vapor pressure values of other analytes determined in this study and available data

327

in previous studies are on the same order of magnitude, although there are some significant

328

discrepancies. DiBP has the highest values of vapor pressure in the temperature range, about

329

four orders of magnitude higher than DiDP, which has the lowest values.

330 331

Figure 7 shows Clausius-Clapeyron plots for target phthalates and alternative plasticizers over

332

the temperature range studied. As shown in Figure 7, vapor pressure increases significantly with

333

increasing temperature. The enthalpy of vaporization, ∆H, was derived from linear regressions

334

of the Clausius-Clapeyron plots with values shown in Table 3. The R2 values for the linear

335

regression analysis of all target compounds ranged from 0.9891 to 0.9998, suggesting that ∆H

336

was invariant over the investigated temperature range.

337

338



339

Figure 7. Clausius-Clapeyron plots for phthalates and alternate plasticizers over ambient

340

temperatures (283 – 303 K for DiBP and DnBP, and 288 – 308K for the remainder of the

341

compounds).

342 343

Table 3. Parameters of Clausius-Clapeyron equation (ln(VP) = - ∆H/R (1/T) + C). ∆H

C

R2

(kJ·mol-1)

∆H (kJ·mol-1) in literature

DiBP

92±10

32.601

0.996

-

DnBP

90±2

31.435

0.9998

89 a, 95.0±1.1 b

ATBC

119±8

38.589

0.9987

-

DEHA

115±5

36.647

0.9995

-

DEHT

122±9

36.258

0.9983

123.3±1.1 b

DINCH

120±5

36.952

0.9995

-

DEHP

122±4

37.982

0.9996

96 a, 116 c

DnOP

136±20

41.652

0.9938

122.6±1.4 b

DiNP

129±4

39.027

0.9997

-

DiDP

144±28

44.189

0.9891

-

344 345 346 347 348

a. Reported in EPA Product Properties Test Guidelines (OPPTS 830.7950)23 b. Gobble, Chickos et al. 201435 c. Clausen, Liu et al. 201232

349 350

Vapor pressure is a critical physicochemical property, as it is important for the calculation or

351

prediction of several derived properties such as gas/particle partition coefficient and air/water

352

partition coefficient. As no single method is applicable for the entire vapor pressure range of

353

environmentally significant compounds, the gas saturation method is generally used for the


Page 20 of 26

Page 21 of 26


354

vapor pressure measurement of low-volatility compounds. However, existing gas saturation

355

methods require complicated experimental tests to ensure complete saturation of the carrier gas.

356

In contrast, the introduction of mathematic modelling of the evaporation process of SVOCs in

357

the PS tube provides fundamental understanding of the mass transfer mechanisms, avoids the

358

tedious procedure to establish vapor saturation, and proves to be successful in the measurements

359

of compounds with vapor pressure as low as 10-7 Pa. This method can also be applied to

360

measure SVOC emission rates from liquid consumer products. One of the disadvantages of this

361

method is that it requires sample masses of at least a few grams. For many compounds, a large

362

amount of pure material can be difficult to obtain. In addition, the uncertainty of the diffusion

363

coefficient due to the lack of reliable experimental data could result in uncertainty in model

364

prediction, especially at high flow rates. The accurate determination of diffusion coefficients of

365

SVOCs requires further research. Nevertheless, the fundamental mathematical model and the

366

simple experimental approach provide a sound basis for the further development of the method.

367 368

ASSOCIATED CONTENT

369

Supporting Information

370

Supporting Information Available: Table S1: Thermal desorption and GC parameters; Figure S1:

371

Probability distributions of the model predictions based on Monte Carlo analysis of the diffusion

372

coefficient using DEHP as an example. This material is available free of charge via the Internet

373

at http://pubs.acs.org.

374 375

ACKNOWLEDGEMENT 21 ACS Paragon Plus Environment


376

Financial support was provided by the United States Environmental Protection Agency (Grant

377

Number RD – 83560601 – 0).

Page 22 of 26

378 379

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