Transient Method for Determining Indoor Chemical Concentrations

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A transient method for determining indoor chemical concentrations based on SPME: model development and calibration Jianping Cao, Jianyin Xiong, Lixin Wang, Ying Xu, and Yinping Zhang Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b01328 • Publication Date (Web): 01 Aug 2016 Downloaded from http://pubs.acs.org on August 1, 2016

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Environmental Science & Technology

1

A transient method for determining indoor chemical concentrations

2

based on SPME: model development and calibration

3 4

Jianping Cao1, 2, Jianyin Xiong3, *, Lixin Wang4, Ying Xu5, Yinping Zhang1, 2

5 6

1

Department of Building Science, Tsinghua University, Beijing 100084, China

7

2

Beijing Key Laboratory of Indoor Air Quality Evaluation and Control, Beijing

8

100084, China

9

3

School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081,

10

China

11

4

12

Engineering and Architecture, Beijing 100044, China

13

5

14

of Texas at Austin, Texas 78712-1094, United States

School of Environment and Energy Engineering, Beijing University of Civil

Department of Civil, Architectural and Environmental Engineering, The University

15 16

Abstract

17

Solid-phase micro-extraction (SPME) is regarded as a non-exhaustive sampling

18

technique with a smaller extraction volume and a shorter extraction time than

19

traditional sampling techniques, and is hence widely used. The SPME sampling

20

process is affected by the convection or diffusion effect along the coating surface, but

21

this factor has seldom been studied. This paper derives an analytical model to

22

characterize SPME sampling for semi-volatile organic compounds (SVOCs) as well

23

as for volatile organic compounds (VOCs) by considering the surface mass transfer

24

process. Using this model, the chemical concentrations in a sample matrix can be

25

conveniently calculated. In addition, the model can be used to determine the

26

characteristic parameters (partition coefficient and diffusion coefficient) for typical

27

SPME-chemical samplings (SPME calibration). Experiments using SPME samplings 1

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of two typical SVOCs, dibutyl phthalate (DBP) in sealed chamber and di

29

(2-ethylhexyl) phthalate (DEHP) in ventilated chamber, were performed to measure

30

the two characteristic parameters. The experimental results demonstrated the

31

effectiveness of the model and calibration method. Experimental data from the

32

literature (VOCs sampled by SPME) were used to further validate the model. This

33

study should prove useful for relatively rapid quantification of concentrations of

34

different chemicals in various circumstances with SPME.

35 36

Introduction

37

Emissions of volatile organic compounds (VOCs) and semi-volatile organic

38

compounds (SVOCs) from building materials and consumer products contribute to

39

poor indoor air quality, adversely affecting people’s comfort, health and

40

productivity.1-3 Exposure to certain VOCs and SVOCs can result in serious health

41

problems (e.g., external malformations, reproductive disorders), sick building

42

syndrome (SBS), and elevated risks of asthma, allergies and cancer.4-7 For these

43

reasons, a method to rapidly quantify these chemical pollutants in the indoor

44

environment is required, so that exposure levels and associated health risks can be

45

evaluated. Knowledge of techniques to monitor levels of chemical pollutants in

46

various environments is currently an important area of interest.8

47

The development of highly specific and sensitive instruments, e.g., gas

48

chromatography/mass

spectrometry

(GC/MS)

and

high

49

chromatography (HPLC), has greatly improved the reliability and accuracy of

50

chemical quantifications. These days the main obstacles faced by analytical chemists

51

include the operational complexity of sample preparation and the inconvenience of

52

introducing extracted components to analytical instruments.9 Typical techniques of

53

sample preparation include the Tenax-TA sorbent technique, the polyurethane foam

54

(PUF) sorption technique, the 2,4-dinitrophenylhydrazine (DNPH) technique, and the

55

solid-phase micro-extraction (SPME) technique.10-14 Only the SPME method is 2


performance

liquid

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defined as a non-exhaustive sampling technique where a very small sample volume is

57

used in the extraction phase relative to the sample volume. This feature allows for

58

convenient monitoring of the investigated system since sampling causes minimal

59

perturbation to the sample.15 The extraction time of the SPME technique is much less

60

than that of Tenax-TA sorbent, PUF or DNPH techniques due to the small extraction

61

volume, and this merit becomes significant for sampling SVOCs. In addition, SPME

62

is quite applicable for sealed chamber tests (it can simplify the experimental system

63

and improve the rapidity of measuring the characteristic parameter of SVOC

64

emissions16-18) because of the features of SPME mentioned above.16 The SPME

65

sampling technique has therefore gained in popularity since its invention.12, 19

66 Figure 1. Schematic of SPME for chemical sampling. (a) SPME sampling in liquid or gas phase; (b) flow across a flat plate (simplified SPME sampling). 67 68

The structure of an SPME system is optimized to facilitate speed, convenience of

69

use, and sensitivity. The system comprises a thin stainless steel (SS) needle and a

70

sampling fiber attached to the SS.20 The sampling fiber consists of a cylindrical fused

71

silica fiber with a coating surrounding it. The schematic of the SPME sampling fiber

72

for chemical (or analyte) sampling is shown in Figure 1 (a).20 During the sampling

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process, the sampling fiber is exposed to the sample matrix and the chemical (or

74

analyte) is sorbed (or extracted) by the coating surrounding the fiber. The fused silica

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is generally assumed to be impenetrable to chemicals.21 The SPME needs to be

76

calibrated to facilitate its application. The calibration method involves two procedures:

77

the first is to establish a model for characterizing the SPME samplings; the second is

78

to determine the parameters involved in the model. Equilibrium and kinetic

79

calibration methods are the two most commonly used methods for SPME

80

calibration.22 In the equilibrium calibration method, measurements are made after

81

partition equilibrium has been reached between the coating and the target chemical. 3



82

This method establishes a linear relationship between the amount of chemical in the

83

SPME coating and the constant chemical concentration in the sample matrix, with an

84

equilibrium partition coefficient that needs to be determined.22, 23 In some situations it

85

may not be feasible to reach extraction equilibrium, and this has led to the

86

development of the kinetic calibration method. This method considers the

87

diffusion-controlled process inside the coating, and a kinetic model relating the

88

amount of chemical extracted to the extraction time is derived, with two model

89

parameters (the coating/sample partition coefficient, K; and the diffusion coefficient

90

of the chemical inside the coating, Dm) that need to be measured.22, 24, 25 It should be

91

pointed out that the existing kinetic calibration method seldom considers the

92

convection effect on the SPME coating surface when there is relative movement

93

between SPME and the sample matrix. In some cases, a convective boundary layer

94

thickness is introduced, but a linear concentration distribution inside the layer is

95

assumed.24 This assumption results in significant deviations since the real

96

concentration distributions are ignored. Prior studies have shown that for chemical

97

emissions from building materials and consumer products, the convective mass

98

transfer process played a significant role on the emission characteristics, especially for

99

SVOCs.26-28 Given that SPME sampling (i.e., sorption process) is the inverse process

100

of chemical emissions, the convective mass transfer process will also significantly

101

affect the SPME sampling. For some scenarios, SPME is used to measure the

102

concentration of target analyte in static mode (both the sample matrix and SPME are

103

static). Under these conditions, the concentration gradient of target analyte between

104

the sample matrix and SPME coating surface also needs to be considered. Therefore,

105

ignoring the effect of mass transfer between the sample matrix and SPME coating

106

surfaceduring sampling may lead to model prediction error and error in the

107

measurement of parameters in the kinetic model. Moreover, in SVOC sampling, the

108

SPME mainly focuses on quantification of liquid samples, and it has seldom been

109

reported to quantify gaseous samples due to the difficulties associated with low gas 4


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phase SVOC concentrations, as well as the ubiquitous SVOC contamination in

111

laboratories.

112

Taking the above observations into consideration, the objectives of this paper are

113

to: (1) establish an analytical model to characterize the SPME sampling by taking into

114

account the mass transfer process between the sample matrix and SPME coating

115

surface; (2) determine the characteristic parameters (partition and diffusion

116

coefficients) for typical SPME-chemical samplings, particularly for gas phase

117

SVOCs.

118 119

Analytical model and calibration method

120

If in the SPME, the thickness of the coating (e.g., 7 µm, designated as L) is much

121

smaller than the radius of the fused silica (e.g., 55 µm, designated as R), the

122

cylindrical coating can be unfolded into a flat plate, as shown in Figure 1(b).29

123

Detailed discussion about the error introduced by unfolding the cylindrical coating

124

into a flat plate is presented in Section S1 of the supporting information (SI), showing

125

that this error is less than 5% when L is less than 7 µm (for R = 55 µm). It is assumed

126

that the coating is uniform, and that the chemical diffusion process inside the coating

127

is one-dimensional. According to the mass transfer mechanism, the controlling

128

equation can be written as:

129

∂C m ∂ 2Cm = Dm ∂t ∂x 2

130

where Cm is the concentration of chemicals in the coating, µg/m3; Dm is the diffusion

131

coefficient of the chemicals in the coating, m2/s; t is the time, s; and x is the distance

132

to the coating/silica interface, m.

(1)

133

Since the fused silica is generally assumed to be impenetrable to the chemicals21,

134

there is no mass flux at the coating/silica interface. The boundary condition at the

135

fused silica surface can then be written as:

136

∂C m = 0, x = 0 ∂x 5


(2)


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137

At the coating surface exposed to the sample matrix (gas or liquid phase) of

138

chemicals, there is a concentration gradient between the coating surface and the

139

sample matrix. It should be noted that this concentration gradient (it will cause

140

convective or diffusive mass transfer effect) is seldom considered in the traditional

141

models, but it does in fact significantly affect the coating extraction characteristics. In

142

the SPME sampling process, the amount extracted by the coating is generally very

143

small, and will thus not influence the concentration of chemicals in the sample

144

matrix.22, 30 If the measured media moves around SPME or SPME shakes during

145

sampling (e.g., SPME sampling in ventilated chamber), the boundary condition at the

146

coating surface can be expressed as:

147

Dm

∂C m C = hm (Cin − m ), x = L ∂x K

(3)

148

where Cin is the concentration of chemicals in the sample matrix (liquid or gas phase),

149

µg/m3; K is the coating/sample partition coefficient (or distribution coefficient),

150

dimensionless; L is the thickness of the coating, m; hm is the convective mass transfer

151

coefficient across the coating surface, m/s, which can be calculated by the following

152

empirical correlation (for cross flow over a cylinder) 29, 31:

153

Sh = C ⋅ Ren Sc1/3

154

where Sh (=hmd/Da) is the Sherwood number; Re (=ud/v) is the Reynolds number; Sc

155

(=v/Da) is the Schmidt number; u is the velocity over the coating surface, m/s; v is the

156

kinematic viscosity of the sample matrix, m2/s; d is the diameter of the coating, m (d

157

= 2R+2L); Da is the diffusion coefficient of chemicals in the sample matrix, m2/s; C

158

and n are parameters related to the Reynolds number, which are given the values of

159

0.989 and 0.33, respectively. These values are appropriate for cross flow over a

160

cylinder with Re in the range of 0.4-4 and Sc over 0.7.29, 31 Da can be estimated using

161

empirical correlations 32 or obtained from measurement results in the literature 33.

(4)

162

As mentioned previously, SPME is sometimes used to measure the concentration

163

of target analyte in static mode (e.g., SPME sampling in sealed chamber). In these

164

scenarios, equation (4) is no longer applicable since Re approaches zero, and the mass 6


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transfer of target analyte from the measured media to SPME is controlled by

166

molecular diffusion. The boundary condition at x = L, i.e., equation (3), should be

167

represented as: 29, 34

168

Dm A

∂Cm C = Da S (Cin − m ) ∂x K

(5)

169

where A is the exposed area of the coating, m2, A = 2π(R+L)·H; H is the length of

170

SPME coating.

171 172

Comparing this equation with equation (3), it is easy to find that hm can be expressed as (here, hm is treated as an “equivalent” mass transfer coefficient):

173

hm = Da S A

174

where S is the shape factor (commonly used in the field of two dimensional mass or

175

heat transfer) for a finite cylinder in an infinite medium with uniform concentration,

176

m 29; A is the surface area of SPME coating, A = 2π(R+L)·H. In this way, equation (5)

177

can be rewritten in the same form of equation (3). In the case of cylindrical SPME

178

coating in a uniform SVOC concentration, S can be estimated by:29, 34 S = 4π L 1 − γ 2

179 180

1 + 1 − γ 2 ln  1 − 1 − γ 2

(6)

  with γ = d H 

(7)

Initially there are no chemicals in the coating, or: Cm ( x, t ) = 0, t = 0, 0 ≤ x ≤ L

181 182

(8)

The amount of chemicals extracted onto the coating can be expressed as: t

M (t ) = ∫ Dm A

183

0

∂Cm ∂x

dt

(9)

x= L

184

where M(t) is the amount of chemicals extracted onto the coating in extraction time t,

185

µg.

186 187

For equations (1)-(9), the amount of chemicals extracted onto the coating can be derived using a Laplace transform, or: ∞

188

−2 2 sin qn e− Dm L qn t n =1 q sin qn + qn cos qn

M (t ) = M equ − 2M equ ∑

2 n

7


(10)


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where Mequ (=KCinVm) is the equilibrium amount of chemicals extracted onto the

190

coating, µg; Vm is the volume of the coating, m3, Vm = A·L; qn are the positive roots of

191

the following equations:

qn tan qn =

192 193

hm L Dm K

( n = 1, 2,...)

(11)

The terms in the infinite exponential series of equation (10) decay very fast as

194

time increases. Thus if the sampling time is sufficiently long, only the first term (n = 1)

195

is significant. This means:

196 197

−2 2   sin q1 M (t ) = M equ 1 − 2 2 e− Dm L q1 t  = M equ (1 − α e − β t ) q1 sin q1 + q1 cos q1  

where α = 2 sin q1

(q

2 1

(12)

−2 2 sin q1 + q1 cos q1 ) ; β = Dm L q1 .

198

Detailed calculation (See SI Section S2) indicates that when t ≥ 0.12L2/Dm, the

199

relative deviation is less than 5% when applying equation (12) as an substitute for

200

equation (10). Thus, the condition for simplifying equation (7) into equation (12) is t

201

≥ 0.12L2/Dm (0.12L2/Dm is referred to as tmin).

202

The analytical model, equation (10) or (12), establishes the relationship between

203

the quantity of chemicals extracted onto the coating, and the extraction time when

204

using SPME for chemical sampling. When determining chemical concentrations in

205

the sample matrix (i.e, Cin) based on SPME, we can measure the quantity of chemicals

206

adsorbed by SPME fiber coatings (M), Cin can then be determined using equation (12),

207

if the characteristic parameters (Dm and K) are known. Therefore, in routine

208

application, we need to first determine Dm and K for the target chemical (calibration

209

of SPME). Equation (12) can also be applied to address the calibration problem

210

(determine Dm and K) if the time-dependent SPME adsorbed chemical amounts are

211

measured. The calibration method provides a basis for quantifying the concentration

212

of chemicals in various circumstances with SPME. Therefore, this paper mainly

213

focuses on the determination of the characteristic parameters (Dm and K ) for different

214

SPME-chemical combinations, which is closely related to the adsorption/desorption

215

properties of chemicals on the SPME fiber. 8


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Once the extraction amount (M) of a target chemical is measured at a series of

217

intervals (> tmin), Mequ, α, and β can be obtained by fitting equation (12) to these

218

measured points. Then K and Dm can be determined by following these steps:

219

(1) Solve the following equation (13) for q1 (positive root):

sin 2 q1 α = 2 q1 + q1 sin q1 cos q1 2

220

(13)

221

(2) Calculate Dm: Dm = β L2 q12 ;

222

(3) Calculate hm using equations (4) or (6), and then determine K according to

223

equation (11), or: K=

224

hm L Dm q1 tan q1

(14)

225

(4) Calculate tmin (= 0.12L2/Dm) with the obtained Dm. If the shortest sampling

226

time is less than tmin, eliminate the sampling data before tmin and then repeat

227

steps (1)-(4) with the remaining data; otherwise output Dm and K.

228

Although the error introduced by unfolding the cylindrical coating into a flat

229

plate can be large when L is larger than 7 µm (as shown in SI Figure S2), the analysis

230

in SI Section S4 demonstrates that the model (i.e., equation (12)) is also effective

231

when the coating thickness is comparable to the radius of the fused silica (55 µm for

232

commonly used SPME35).

233 234

Experimental section

235

Dibutyl phthalate (DBP) and di (2-ethylhexyl) phthalate (DEHP) are widely used

236

as plasticizers and are the main SVOCs emitted from polyvinylchloride (PVC)

237

products.36-38 In addition, the gas phase concentrations of DBP and DEHP have

238

seldom been sampled by SPME. For these reasons we chose DBP and DEHP as the

239

target pollutants for the SPME calibration experiments. The experiments for DBP and

240

DEHP were conducted in sealed and ventilated chambers, respectively. It should be

241

noted that a sealed chamber is not very common for SVOC emission tests in prior 9



242

studies. The reason is that the traditional sampling methods (e.g., Tenax TA tube and

243

PUF sampling methods) are not suitable for a sealed chamber since they need to

244

extract significant amounts of pollutants from the chamber (especially for multiple

245

samplings) but the quantity of pollutants in sealed chamber is limited. However, the

246

SPME is a non-exhaustive sampling technique with a smaller extraction volume and a

247

shorter extraction time, and thus is quite applicable for sealed chamber as mentioned

248

in the “Introduction” section. Using two kinds of chambers aims to examining the

249

adaptation of SPME calibration in different test conditions, thereby extending the

250

application range of SPME in routine analysis.

251

The schematic of the experimental system for SPME calibration is shown in

252

Figure 2. Figure 2 (a) is the experimental system designed for DBP. Pure DBP

253

(purchased from Sigma-Aldrich Co. LLC, purity 99%, product ID. 524980-500 mL)

254

in a petri dish (without cover) was put inside a 30 L chamber designed for VOC

255

emission tests

256

0.5 °C). During the experiment, the 30 L chamber was sealed. Once the concentration

257

of DBP in the chamber reached equilibrium (about two days according to our

258

observations), the gas phase DBP was sampled by SPME. Several SPMEs were

259

inserted into the chamber, and adsorbed the DBP for different lengths of time, so as to

260

get the time-dependent SPME extraction curve for calibration. After sampling, the

261

surfaces of the stainless steel rod of SPME, which would also adsorb DBP (and other

262

chemicals), were wiped using medical cotton wool soaked with dichloromethane

263

(CH2Cl2). The SPME was finally analyzed using gas chromatography-flame

264

ionization detection (GC-FID, Agilent Technologies 7890A GC system equipped with

265

a flame ionization detector) as follows: inserted SPME (the whole sampling fiber and

266

part of stainless steel rod) into the injection port (280 ºC) of the GC; allowed the

267

coating of sampling fiber to desorb for 15 min; cooled to room temperature.

39

, where the air temperature was controlled using a water bath (25 ±

268

Since DEHP can be very easily adsorbed by the chamber surface (e.g., chamber

269

surface/air partition coefficient (Ks) = 1500 m for DEHP while Ks = 60 m for DBP 38) 10


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270

and the sorption area of the 30 L chamber surface is much larger than the emission

271

area of the pure SVOC, the time required for the DEHP concentration in the 30 L

272

chamber to reach equilibrium would be relatively long.17, 40 For example, the DEHP

273

concentration reached equilibrium after more than 150 days in a CLIMPAQ (with a

274

volume of 51 L).17,

275

system for DEHP, as shown in Figure 2 (b). The small chamber is made of stainless

276

steel, with a volume of 1.8 L and interior surface area of 0.13 m2. Pure liquid DEHP

277

(purchased from Sigma-Aldrich Co. LLC, purity ≥ 99%, product ID. D201154-500

278

mL) was put inside the small chamber. The temperature of the chamber was

279

controlled by a water bath, fixed at 25.0 ± 0.5 ºC. During the experiment, clean air

280

with controlled relative humidity (50 ± 5%) was introduced into the chamber. The air

281

flow was 90 mL/min, and the diameters of the inlet and outlet tubes were both 6.0 mm.

282

To reduce the effect of DEHP sorption on the chamber and tube, the surfaces of the

283

chamber and tube were wiped with pure DEHP at the beginning of the experiment.

284

After two days (the time required for DEHP concentration to reach equilibrium

285

according to our observations), gas phase DEHP was sampled by SPME at the

286

chamber outlet. The procedure for analyzing the SPME sample is the same as

287

described above for DBP.

40

To obviate this problem, we designed a new experimental

288

Figure 2. Experimental system for SPME calibration. (a) for DBP, (b) for DEHP. 289 290

A six-point calibration curve for DBP (similarly for DEHP) was obtained by

291

following these steps. Pure DBP (DEHP) was diluted to 1, 10, 60, 200, 500, and 1000

292

µg/mL (the solvent is CH2Cl2), and 1.0 µL of each dilution was injected into a GC. All

293

samples, SPME samples and dilutions, were analyzed by GC-FID. The

294

chromatographic column was an HP-5MS SemiVol (30 m × 0.25 mm × 0.50 µm). The

295

carrier gas was He, with a flow rate of 50 mL/min, split, 10:1. The column

296

temperature program was: 120 ºC for 2 min; increased to 300 ºC at a rate of 15 ºC/min; 11



Page 12 of 28

297

and held for 10 min (24 min in total). The temperature of the injection port and FID

298

were both 280 ºC. The calibration curve is demonstrated to be valid since R2 of the

299

curve is greater than 0.99.

300

SPMEs were purchased from Sigma-Aldrich Co. LLC. (Supelco Analytical, Cat.

301

NO. 57302). The coating was made of polydimethylsiloxane (PDMS, feasible for

302

sampling of nonpolar SVOCs) with a thickness of 7.0 µm and a length of 1.0 cm. The

303

diameter of the fused silica fiber was 110.0 µm. Before the experiment, each SPME

304

was conditioned by heating it in a GC injection port at 280 ºC for 5 min. The carrier

305

gas was He, with a flow rate of 10 mL/min. After conditioning, the remained mass of

306

DBP and DEHP in the coating should be below the limit of quantitation (LOQ, i.e., 1

307

ng) of the relevant GC-FID method.

308 309

Results and discussion

310

Sensitivity analysis

311

For SPME samplings, it is necessary to perform sensitivity analysis with the

312

derived analytical model, so as to know the impact of some model parameters (hm, K,

313

and Dm) especially hm on the extraction of chemicals from the sample into the coating.

314

The SPME introduced in the experimental section is used for this analysis. For

315

common material-SVOC combinations, K is in the range of 105-1011.13,

316

estimated to be in the range of 10-14-10-10 m2/h according to equation (S3) in Cao et

317

al.’s study.18 Based on these data and the analytical model, we can obtain the SPME

318

extraction amount for different model parameters. Figure S5 (a) of the SI shows the

319

results of sensitivity analysis of hm under a typical condition (the baseline parameters

320

are set as: K = 1×108, Dm = 1×10-11 m2/h, hm = 0.01 m/s, and Cin = 1 µg/m3). This

321

figure reveals that hm has a substantial impact on the extraction rate of SPME, and the

322

smaller the value of hm, the greater the impact. For SPME in these experiments, hm is

323

calculated to be 3.36 × 10-2 m/s for the DEHP experimental system (ventilated

324

chamber) by virtue of equation (4) (with Re = 0.414, Da = 3.37 mm2/s 12


33

28

Dm is

and Sc =

Page 13 of 28


325

4.72). While for the DBP system (sealed chamber), since there is no bulk air

326

movement around the SPME during the whole experiment, hm (the “equivalent” mass

327

transfer coefficient) should be calculated with equations (5) and (6). In this way, hm is

328

calculated to be 1.33 × 10-2 m/s (with Da = 4.21 mm2/s 33) for the DBP system. These

329

values (3.36 × 10-2 m/s and 1.33 × 10-2 m/s) lie within the simulated range of hm

330

shown in Figure S5 (a), implying that it is very necessary to take hm into account in

331

the models for characterizing SPME samplings. Therefore, the analytical model

332

derived in this study can be regarded as a significant improvement on previous model

333

studies that generally ignore the impact of hm. Results of sensitivity analysis of Dm

334

and K are shown in SI Figures S5 (b) and (c), respectively. It indicates that K has a

335

significant impact on the extraction amount of SPME. With the increase of K, the

336

equilibrium extraction amount (Mequ) increases and the time required to reach

337

equilibrium increases as well. The influence of Dm on the extraction process is not as

338

significant as that of K. Dm mainly takes effects in the initial extraction period (the

339

extraction rate increases with the increase of Dm) and doesn’t influence the

340

equilibrium extraction amount of SPME.

341 342

Determination of the characteristic parameters

343

The SPME experiment for DBP lasts for 26 h, while for DEHP experiment takes

344

141 h. Using the measured time-dependent extraction amount, the simplified

345

analytical model (equation (12)) is used to perform nonlinear curve fitting. The

346

characteristic parameters (Dm and K) can be obtained using the procedure described at

347

the end of the Section “Analytical model and calibration method”. OriginPro 8

348

(OriginLab Corporation) was employed for curve fitting. The fitted curves for the two

349

SVOCs as well as the R2 for regression are shown in Figure 3, and the determined

350

parameters are listed in Table 1. According to the ASTM Standard D5157-97

351

correlation coefficient (R) of 0.9 or greater can be regarded as generally indicative of

352

adequate model performance. In this case, all R2 are greater than 0.95, implying high 13


41

, a


353

regression precision.

354

Figure 3. Fitted curves and comparison of SPME extraction amount for the simulated results based on the determined characteristic parameters and the experimental data. (a) DBP; (b) DEHP. 355

Table 1. Determined characteristic parameters by virtue of the model, and comparison of the saturated gas phase concentrations of pure chemicals measured in this study with that measured in the literature. 356 357

The two characteristic parameters (Dm and K) determined by the simplified

358

model (equation (9)) can be substituted into the complete analytical model (equation

359

(10)) to calculate the extraction amount of the SPME. We can then compare the

360

simulated results with the experimental data, as shown in Figure 3. The comparison

361

can be regarded as a preliminary validation of the calibration method. Figure 3

362

indicates that the simulated results agree well with the measured data. In addition, the

363

simulated results from the complete analytical model (equation (10)) and from the

364

simplified model (equation (12)) are almost the same when the time is longer than the

365

application condition (tmin) of equation (12). The accord between the results from the

366

two models and the experimental data demonstrates that the measured characteristic

367

parameters are reliable. From the simulated results shown in Figure 3, we can see that

368

the extraction amount approaches equilibrium after 26 h for DBP, while for DEHP the

369

equilibrium is still not reached. These results imply that the calibration process can be

370

terminated before the sorption of SVOC on to the SPME coating reaches equilibrium.

371

This is a salient feature of the present method because it can save time, particularly

372

for the calibration of chemicals with large vaules of K (e.g., DEHP).

373

14


Page 14 of 28

Page 15 of 28


374

Measured saturated gas phase SVOC concentration and comparison with

375

literature

376

In the calibration method, the equilibrium extraction amount of chemicals onto

377

the SPME coating (Mequ) can be obtained by virtue of nonlinear curve fitting,

378

following which the steady state concentration of SVOCs in the gas phase

379

(Cin=Mequ/KVm) can be determined. The determined gas phase concentrations for DBP

380

and DEHP are 488 µg/m3 and 5.58 µg/m3, respectively. In the experimental section,

381

pure SVOC liquids are used. So for the sealed chamber, the Cin determined from the

382

experiment should be the same as the saturated gas phase concentration (designated as

383

ysat) of pure chemicals, i.e., ysat = Cin. While for the ventilated chamber, ysat is a

384

function of Cin, i.e., ysat = Cin·(1+Q/(hm,eA)) (equation (5) of Liang et al.38), where Q is

385

the air flow rate of the chamber; hm,e is the convective mass transfer coefficient at the

386

source surface; A is the emission area of the SVOC source. In this study, for DBP, ysat

387

is equal to Cin because sealed chamber is used, i.e., ysat = 488 µg/m3; while for DEHP,

388

ysat = 1.09Cin (Q/(hm,eA) = 0.09 with Q = 90 mL/min, hm,e = 0.26 m/h 42, A = 0.13 m2),

389

i.e., ysat = 6.08 µg/m3, as listed in Table 1.

390

Recently, Liang et al.38 designed a special chamber to measure phthalate

391

emissions from building materials, in which the gas phase concentrations were

392

measured by Tenax TA tube sampling followed by thermal desorption (TD)-GC/MS.

393

In their study, ysat of DBP and DEHP were measured by coating the interior chamber

394

surfaces with pure DBP and DEHP liquids. According to Liang et al.’s results38, ysat

395

are 464 µg/m3 and 5.64 µg/m3 for DBP and DEHP, respectively. The ysat values in the

396

literature are very similar to the measured values in this study, with relative deviations

397

(RD) of no more than 7.8%, as indicated in Table 1. Although there is no direct

398

comparison with traditional analytics (e.g., Tenax TA tube sampling followed by

399

TD-GC/MS) in our experiments, the consistency between our results of ysat and that in

400

literature for the same compounds also provides convincing evidence that the

401

application of SPME for SVOC samplings is appropriate and effective. 15



402 403

Impact of test time on the determined parameters

404

As mentioned above, a major benefit of this method is that the process can be

405

terminated before the sorption process of the SPME coating reaches equilibrium. It is

406

therefore necessary to investigate the impact of test time on the determined

407

characteristic parameters (Dm and K), so as to determine whether the test time can be

408

further reduced. To this end, the values of Dm and K are obtained again by fitting

409

equation (12) to the experimental data while excluding the longest test times (i.e., 26

410

h for DBP and 141 h for DEHP). For DBP, when the test time is shortened from 26 h

411

to 11.7 h, the obtained Dm decreases from 2.81 × 10-15 m2/s to 1.37 × 10-15 m2/s, and K

412

decreases from 3.20 × 107 to 2.93 × 107. For DEHP, when the test time is shortened

413

from 141 h to 97.5 h, the obtained Dm value decreases from 2.13 × 10-16 m2/s to 1.31

414

× 10-16 m2/s, while K increases from 6.49× 108 to 6.83 × 108. These results show that

415

the deviation of K is very small (relative deviation is less than 10%) as a result of

416

shortening the test time, while that of Dm is fairly large (the relative deviations are 38%

417

and 51% for DEHP and DBP, respectively). By substituting the values of Dm and K

418

obtained using the reduced sampling data into equation (9), the value of M at 26 h for

419

DBP and 141 h for DEHP can be estimated. The relative deviations between the

420

estimated M and measured M are quite small, i.e., 7.7% for DBP and 5.8% for DEHP.

421

Such small deviations indicate that the results for the characteristic parameters

422

obtained by shortening the test time are acceptable, despite the relative deviation of

423

Dm being as large as 51%. This analysis indicates that the SPME extraction amount is

424

not very sensitive to Dm especially for SVOC samples (consistent with the result of

425

sensitivity analysis of Dm), implying that the extraction process is externally

426

controlled for SVOCs. This result is consistent with a prior study28 where the

427

emission process of DEHP from vinyl flooring was found to be controlled by the

428

external convection process. In this study, we found that no meaningful results could

429

be obtained through nonlinear curve fitting by further shortening the test time. The 16


Page 16 of 28

Page 17 of 28


430

primary reason for this is that there are not enough samplings. The relationship

431

between the shortest test time, the characteristic parameters, the number of samplings

432

and the time interval between contiguous measurements needs further investigation.

433

In addition, systematic studies focusing on the impact of shortening test time on the

434

accuracy of the determined parameters are also required.

435

The previous sections demonstrate the effectiveness of the calibration method for

436

DBP and DEHP (SVOCs) tests. There are many experimental data reported in the

437

literature for other SPME-chemical combinations. To further validate the applicability

438

of the calibration method for VOCs, we analyze data from two references43, 44 as

439

examples. Detailed analysis and results are described in SI Section S4 (Using the

440

calibration method to analyze data from the literature). The fitted curves of equation

441

(12) together with the model predictions all agree well with the experimental data,

442

implying that the proposed calibration method can be regarded as a general method

443

both for SVOCs and VOCs (for the compounds studied).

444 445

Limitations and further study

446

For the cases from the literature, the good results (SI Section S4) illustrate the

447

feasibility of unfolding the cylindrical coating into a flat surface, even when the

448

coating thickness and the silica radius are comparable. Such treatment reduces the

449

complexity in the model development while still maintaining high precision (see

450

detail in SI Section S3, the solution of the model of an unfolded cylindrical coating is

451

quite complicated). Nonetheless, the results of Dm should be interpreted with caution

452

when the coating thickness is not much smaller than the radius of the fused silica,

453

since under this condition the Dm obtained with the present method is an equivalent

454

value (i.e., the diffusion pathway is in fact along the cylindrical wall rather than along

455

the flat wall). The deviation between the determined Dm and the actual Dm may be

456

dependent on R (radius of the fused silica), L (thickness of the coating) and K.

457

Determination of the actual Dm of chemicals in the fiber coating requires a complete 17



458

model, i.e., a model expressed in cylindrical coordinates (the structure of SPME is

459

cylindrical) rather than in rectangular coordinates. The complete model is described in

460

SI Section S1, and the analytical solution of this model is provided in SI Section S3

461

(equations (S9)-(S18)). Applying equation (S18), the actual Dm of chemicals in the

462

cylindrical coating can be obtained with a similar procedure provided at the end of the

463

Section “Analytical model and calibration method”. However, the solving process

464

may require multifarious mathematical methods due to the complexity of the

465

analytical solution, which is out of the scope of the present study. In some scenarios,

466

we need to optimize the structure of the SPME for target chemical sampling to

467

minimize the measurement error (e.g., optimize the thickness of SPME coating and

468

select the optimum coating material). Under this condition, the actual Dm is requisite.

469

Therefore, further study is necessary to solve the mathematical challenges for

470

determining the actual Dm with the complete model. In addition, the present method

471

requires to estimate the mass transfer coefficient (hm) with an empirical correlation,

472

which may introduce some uncertainties to the determined characteristic parameters.45,

473

46

474

influence the precision of SPME in real field samplings. Development of novel

475

methods that can eliminate the effect of hm on the determination of Dm and K warrants

476

further investigation. It should be noted that whether the analytical model is

477

applicable for the calibration of other extraction scenarios when using SPME for

478

sampling is still unknown, thus more experimental validation is needed.

Moreover, as discussed in “Sensitivity analysis”, uncertainty in hm may also

479 480

Associated content

481

Supporting Information

482

Additional detail on discussion about the error introduced by simplifying the

483

cylindrical coating into a flat plate (Section S1); determination of the applied

484

condition for equation (12) (Section S2); analytical solution of the model of an

485

unfolded cylindrical coating (Section S3); using the calibration method to analyze 18


Page 18 of 28

Page 19 of 28


486

data from the literature (Section S4); determined characteristic parameters for

487

different SPME-chemical combinations in the literature (Table S1); maximum

488

deviation between M calculated by equation (S5) and that by equation (9) (Figure S1);

489

comparison of M between the results of equation (S5) and that of equation (9) for

490

different Fom (Figure S2); the determined Fom,c for Bim/K in the range of 10-3 to 105

491

(Figure S3); comparison of the model predictions with the experimental data from the

492

literature (Figure S4); and results of sensitivity analysis of hm, K and Dm (Figure S5).

493

This material is available free of charge via the Internet at http://pubs.acs.org.

494 495

Author information

496

Corresponding Author *

497

E-mail: [email protected]; Phone: +86 10 68914304; Fax: +86 10 68412865;

498

Address: School of Mechanical Engineering, Beijing Institute of Technology, Beijing

499

100081, China

500

Note

501

The authors declare no competing financial interest.

502 503

Acknowledgements

504

This research was supported by the National Natural Science Foundation of

505

China (grant Nos. 51476013 and 51136002). We thank Dr. Cong Liu of Tsinghua

506

University for helpful discussions.

507 508

References

509

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44. Bartelt, R. J.; Zilkowski, B. W. Nonequilbrium quantitation of volatiles in air

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45. Holman, J. P. Heat Transfer, 9th Edition; McGraw-Hill: New York, 2002.

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46. Xiong, J. Y.; Cao, J. P.; Zhang, Y. P. Early stage C-history method: Rapid and

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623

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624 23



625

TOC Art

626 627

24


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Page 25 of 28


628

Figures

629

Figure 1. Schematic of SPME for chemical sampling. (a) SPME sampling in liquid or

630

gas phase, (b) flow across a flat plate (simplified SPME sampling).

631

632 633

(a)

634

635 636

(b)

637 638

25



639

Figure 2. Experimental system for SPME calibration. (a) for DBP, (b) for DEHP.

640 641

(a)

642 643

(b)

644

26


Page 26 of 28

Page 27 of 28


645

Figure 3. Fitted curves and comparison of SPME extraction amount for the simulated

646

results based on the determined characteristic parameters and the experimental data. (a)

647

DBP; (b) DEHP.

648 649

(a)

650 651

(b)

652 27



Page 28 of 28

653

Tables

654

Table 1. Determined characteristic parameters by virtue of the model, and comparison

655

of the saturated gas phase concentrations of pure chemicals measured in this study with

656

that measured in the literature. Chemicals

Dm (m2/s)

ysat_measured K (-)

3 a

ysat_literature 3 b

(µg/m )

(µg/m )

RD (%)c

DBP

2.81 × 10-15

3.20 × 107

488

464

5.2

DEHP

2.13 × 10-16

6.49 × 108

6.08

5.64

7.8

657

a

Measured in this study.

658

b

Measured results of Liang et al.38

659

c

RD is calculated by ǀysat,measured-ysat,literatureǀ/ysat,literature × 100%.

660

28


Transient Method for Determining Indoor Chemical Concentrations

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