Inverse Problem Optimization Method to Design Passive Samplers for

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Inverse problem optimization method to design passive samplers for volatile organic compounds: principle and application Jianping Cao, Zhengjian Du, Jinhan Mo, Xinxiao Li, Qiujian Xu, and Yinping Zhang Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b04872 • Publication Date (Web): 18 Nov 2016 Downloaded from http://pubs.acs.org on November 22, 2016

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Environmental Science & Technology

1

Inverse problem optimization method to design passive samplers for

2

volatile organic compounds: principle and application

3 4

Jianping Cao1,2,#, Zhengjian Du1,2,#, Jinhan Mo1,2, Xinxiao Li1,2, Qiujian Xu1,2, and

5

Yinping Zhang1,2,*

6 7

1

8

2

9

100084, China

Department of Building Science, Tsinghua University, Beijing 100084, China Beijing Key Laboratory of Indoor Air Quality Evaluation and Control, Beijing

10 11

#

These authors contributed equally.

12

*

Corresponding e-mail: [email protected]

13 14

Abstract

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Passive sampling is an alternative to active sampling for measuring concentrations

16

of gas-phase volatile organic compounds (VOCs). However, the uncertainty or

17

relative error of the measurements, have not been minimized due to the limitations of

18

existing design methods. In this paper we have developed a novel method, the inverse

19

problem optimization method, to address the problems associated with designing

20

accurate passive samplers. The principle is to determine the most appropriate physical

21

properties of the materials, and the optimal geometry of a passive sampler, by

22

minimizing the relative sampling error based on the mass transfer model of VOCs for

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a passive sampler. As an example application, we used our proposed method to

24

optimize radial passive samplers for the sampling of benzene and formaldehyde in a

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normal indoor environment. A new passive sampler, that we have called the Tsinghua

26

Passive Diffusive Sampler (THPDS), for indoor benzene measurement was developed

27

according to the optimized results. Silica zeolite was selected as the sorbent for the

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THPDS. The measured overall uncertainty of THPDS (22% for benzene) is lower

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than most commercially available passive samplers; but is quite a bit larger than the

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modeled uncertainty (4.8% for benzene, optimized result), suggesting that further

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research is required.

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ACS Paragon Plus Environment


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1. Introduction

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Man-made chemicals are abundant in a variety of indoor environments.1 Exposure

35

to some of these chemicals, especially certain volatile organic compounds (VOCs), is

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related to sick building syndrome (SBS, e.g., mucous membrane irritation, headache

37

and fatigue)

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concentrations of VOCs in various environments is essential to determine exposure

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levels and evaluate the associated health risks. Generally speaking, enrichment is a

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very important step for the quantitative determination of these compounds.7 Two

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sorbent enrichment technologies are most commonly used: active sampling and

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passive sampling.7 A passive sampler is a device which is capable of preconcentrating

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the analyte by no forced flow. Due to its simplicity and low cost (both for

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manufacture and sample analysis), passive sampling is considered to be a more

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promising method for multi-point sampling, remote-area sampling, long-term

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sampling and personal sampling, compared to active sampling.7, 8 Besides, evidence

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has shown that certain passive samplers have similar accuracy to active sampling (e.g,

48

sampling of benzene, toluene and xylenes (BTX)) 7; while the accuracy of some

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passive samplers is lower than active sampling (e.g, sampling of semi-volatile organic

50

compounds) 9, implying that the accuracy of passive samplers needs to be improved.

2-4

, adverse health effects 5, and even cancer 6. Therefore, monitoring

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With the growing demand for environmental monitoring and exposure evaluation

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over the past few decades, the design and application of passive samplers has been

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greatly improved and expanded.10-13 In most cases, passive samplers are made up of

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two main parts: the sorbent, and the barrier covering the sorbent. The barrier helps to

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ensure a relatively steady sampling rate, which is crucial for quantitative analysis, by

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eliminating or minimizing the effects of environmental factors. In general, three types

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of passive samplers can be identified based on their geometry: tube-type samplers,

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badge-type samplers, and radial samplers, as shown in Figure 1 (a). Furthermore,

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passive samplers can be classified into two types based on their barrier material:

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diffusion samplers and permeation samplers.14 Samplers shown in Figure 1 are all

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diffusion samplers. Representative passive samplers are summarized in Table S1 of

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the Supporting Information (SI), which shows that diffusion samplers are more

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frequently employed.

64 Figure 1. (a) Three types of representative passive samplers; (b) schematic of mass 2


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transfer of VOCs from ambient air to the sorbent in a radial sampler. 65 66

Passive samplers have been successfully used for monitoring concentrations of

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pollutants in indoor and outdoor air, and other matrices (e.g., soil and water), as

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reviewed by Partyka

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passive samplers for monitoring VOC concentrations still varies between different

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sampling environments. Significant uncertainties were observed by researchers when

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employing OVM badge samplers to measure concentrations of BTX.7,

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sampling rates of Perkin-Elmer tube samplers deviated by up to 300% (for benzene)

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in some studies.17 By testing various samplers, Plaisance et al.18 concluded that

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sampling rate is the main factor influencing the performance (accuracy) of passive

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samplers, e.g., variation in the sampling rate contributes to more than 80% of the

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sampling uncertainty (benzene measured with a Radiello sampler, lower uncertainty

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corresponding to higher accuracy). In general, the traditional method for improving

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passive samplers is by “trial-and-error”, i.e., testing the performance of passive

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samplers using different combinations of sorbent and barrier materials as well as

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different sizes, and selecting the optimal one with minimum testing error. Using this

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method, numerous tests are required, which may result in a long testing period and

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high cost, making it difficult to find an optimized passive sampler that meets the

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requirements of a particular field test (especially for a wide range of target pollutants).

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In 1973, Palmes and Gunnison 19 developed a steady-state model describing VOC

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mass transfer in passive samplers by assuming the sorbent to be an ideal sink for

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VOCs (VOC concentration in the sorbent is zero, i.e., sampling rate of the passive

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sampler is a constant over the whole sampling period), and ignoring the effect of

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convective mass transfer at the barrier surface. This kind of model is still frequently

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used to design and evaluate passive samplers.20-23 However, the assumption of this

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model (that the sorbent is an ideal sink) is only applicable for the uptake of chemicals

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in strong sorbents. Sampling rates of passive samplers were observed to decrease as

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sampling time increased (VOC concentrations in the sorbent increased) in both

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laboratory and field experiments.17, 24-27 In addition, convective mass transfer at the

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barrier surface proved to significantly affect sampling rates.28-31 Figure 1 (b) shows

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the schematic of mass transfer of VOCs from ambient air to the sorbent of passive

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samplers (radial type), which includes three processes: transportation through the

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convective concentration boundary layer around the barrier surface; diffusion through

15

and Kot-Wasik 8. Nevertheless, the performance of existing

3


16

The


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the barrier; and sorption and diffusion within the sorbent. As summarized in Table S2

99

of SI, several mass transfer models were modified to describe VOC uptake by passive

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samplers.17, 32-34 However, none of the existing models fully considered these three

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processes.

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Recently, Zhang et al.35 proposed an inverse-problem-based approach for solving

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building energy and environment problems. As they have noted, “the objective of an

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inverse problem is to find the most suitable model parameters to obtain model results

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that are the most expected (those that tend to be maximal or minimal)”.35 Therefore,

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an optimized passive sampler can be determined by combining the mass transfer

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model of VOCs in passive samplers with the goal of minimum sampling error. In this

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way, the traditional “trial-and-error” method can be avoided. The objective of this

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study is to propose an inverse problem optimization method to guide the improvement

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of passive samplers, to clarify its principle and to demonstrate its advantages through

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an illustrative example (i.e., a novel radial diffusive sampler developed by Du et al.7

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based on optimized results obtained in this study).

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2. Inverse Problem Optimization Method

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2.1 Method principle

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In this study, the parameters to be determined are the sorption properties of the

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materials of the passive sampler (both barrier and sorbent materials) and the geometry

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of the passive sampler. Since the objective of a passive sampler is to determine gas-

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phase VOC concentrations based on the measured mass of VOCs collected by the

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sampler (M, i.e., sorption mass of VOCs in the sorbent), the relative error of M should

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be minimized. According to existing studies, error in the value of M originates

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primarily from these three factors: the fluctuation of VOC concentration in the

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measured environment, the variation in air flow velocity in the measured

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environment, and the error introduced by chemical analysis.18, 21 It should be noted

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that several other factors can also introduce error to M, such as temperature variation,

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humidity, storage time of samplers, and desorption efficiency of the sorbent.

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Considering the feasibility of modeling (a lack of quantitative descriptions of their

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effects on the error of M) and the primary objective of this study (guide the selection

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of the material and size of passive samplers), they were not involved in this study,

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however they should be taken into account in practice. 4


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The relative error attributed to the fluctuation of VOC concentration in the

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measured environment, ε(C), is defined as:

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ε (C ) =

M − MC

(1)

MC

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where M is the mass of VOC collected by the sampler in time ts during which the

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concentration of VOC varies (in a real environment the VOC concentration is Ca,

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µg/m3), MC is the mass of VOC collected by the sampler in time ts during which the

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concentration of VOC remains constant (in a controlled chamber, the VOC

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concentration is Cc, µg/m3). Taking this into account,

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∫

140 141

ts

0

∫

ts

0

C c dt should be equal to

Ca dt , where ts is the sampling period.

The relative error caused by the variation in air flow speed in the measured environment, ε(v), is defined as:

M  M v,max  − 1, 1 − v ,min  MC   MC

ε ( v ) = max 

142

(2)

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where Mv,max is the mass of VOC collected by the sampler at the maximum air flow

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speed, Mv,min is the mass of VOC collected by the sampler at the minimum air flow

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speed.

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The relative error of M introduced by chemical analysis is supposed to be related to the method detection limit (MDL), i.e.,

ε ( MDL) = MDL MC

148 149 150

(3)

Taking these three factors into consideration, the function of relative error of M, ε, is defined as:

ε = ε (C ) 2 + ε ( v ) + ε ( MDL ) 2

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2

(4)

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The principle behind the method is to obtain the sorption properties of the sorbent

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and of the barrier materials, as well as the geometry of the passive sampler by

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minimizing ε. This can be done based on the mass transfer model of VOCs in passive

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samplers. Since existing models always make assumptions that lead to inaccurate

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estimates, a model that can avoid this problem is required. We develop and evaluate

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this model below.

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5



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2.2 Modified mass transfer model of passive sampling

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Due to a higher surface area which leads to a high uptake rate and consequently

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provides good sensitivity in cases of shorter sampling duration or lower

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concentrations, the radial-tube type passive sampler is frequently used (e.g., Radiello

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7

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(b), when a passive sampler is exposed to the measured matrix, VOCs will initially

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transfer through the concentration boundary layer around the barrier surface, then

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diffuse through the barrier, and finally be adsorbed by the sorbent and diffuse in the

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sorbent. The barrier and sorbent are both made of porous media. Several assumptions

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are made here: 1) VOC mass transfer in a passive sampler is one-dimensional, i.e.,

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only in the radial direction; 2) VOCs in the air-filled pores within the sorbent are

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assumed to be in equilibrium with the sorbent at each point, and the sorption isotherm

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is linear over the concentration range of interest 34, 36; 3) transport within the barrier is

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treated as a pseudo-steady state process (due to the rate of mass transfer within the

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barrier being much greater than the rate of mass transfer within the sorbent, e.g.,

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barrier diffusivity is about 105 times higher than sorbent diffusivity, as we estimate in

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the following sections)

176

assumption is validated for BTX in this study).

177 178

, Figure 1(a)), which is the focus of the following model. As illustrated in Figure 1

34

; 4) sorption of VOCs onto the barrier is ignored (this

Mass transport within the sorbent can be treated as the sorption of chemicals by permeable porous media 36, the governing equation is expressed as:

 ∂ 2C 1 ∂C  ∂C = D 2 +  ∂t r ∂r   ∂r

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( 0 < r < R0 )

(5)

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where C is the VOC concentration in the sorbent, µg/m3; D is the “equivalent”

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diffusivity of VOC in the sorbent 37, m2/s; r is the distance to the cylinder axis of the

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sorbent, mm; t is the time, s; and R0 is the radius of the sorbent cylinder (also the inner

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radius of the barrier), mm. Here, the surface diffusion (diffusion of VOCs on the

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surface of a solid skeleton of porous media

185

coefficient is several orders of magnitude lower than the diffusion coefficient in the

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porous media.38, 39

187 188 189

38

) is negligible as the surface diffusion

At the cylinder axis of the sorbent (there is no mass flux here), the boundary condition is: ∂C ∂r

=0 r =0

6


(6)

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190 191

At the interface between the sorbent and the barrier, the boundary condition is expressed as:

D

192

∂C ∂r

r = R0

C  = hm,e  Ca ( t ) −  K 

(7)

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where Ca(t) is the VOC concentration in the bulk air (measured matrix), µg/m3; K is

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the equilibrium partition coefficient of the VOC between the sorbent and the air,

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dimensionless; and hm,e is the “equivalent” convective mass transfer coefficient of the

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VOC from the bulk air to the sorbent-barrier interface, m/s. According to assumption

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(3), hm,e can be calculated according to the superposition theorem of mass transfer

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resistance for a series composite system: 40 1 1 1 1 = + = + hm , e hm hm′ hm

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ln  

Rs

R R0  s

Ds

(8)

200

where Rs is the outer radius of the barrier, m; Ds is the equivalent diffusion coefficient

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of VOC in the barrier, m2/s; and hmʹ (=Ds/Rs/ln(Rs/R0)) is the equivalent mass transfer

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coefficient for VOC diffusion through the barrier, m/s, which is obtained by the mass

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transfer resistance for diffusion through a cylindrical system (one-dimensional steady-

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state diffusion)

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external surface of the barrier, m/s, which can be calculated using the empirical

206

formula 40:

207

40

; hm is the convective mass transfer coefficient of the VOC at the

Sh =

hm ⋅ 2 Rs = m Re n Sc1 3 , for Re = 0.4 − 4 × 105 DA

(9)

208

where Sh is the Sherwood number, DA is the diffusivity of the VOC in bulk air, m2/s;

209

Re is the Reynolds number, Re = vRs/υ; Sc is the Schmidt number, Sc = υ/DA; v is the

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air flow speed, m/s; υ is the kinematic viscosity of the air, m2/s, and m and n are

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parameters related to the Reynolds number range, which are 0.911 and 0.385 for Re =

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4 ~ 40 or 0.683 and 0.465 for Re = 40 ~ 4000, respectively.40 Equation (9) indicates

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that hm is a function of the air flow speed, v, and hm increases as v increases. If the

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value of Re is out of the range in equation (9), another appropriate formula should be

215

employed, which can be found in Bergman et al.40

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Before sampling, VOCs remaining in the passive sampler should be eliminated. Therefore, the initial condition is:

t = 0: C = 0

( 0 < r < R0 )

7


(10)


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219

Equations (5)-(10) form the complete model that describes the mass transfer of

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VOCs from the bulk air to the sorbent of a radial-tube diffusion passive sampler. For

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tube-type diffusion samplers, a similar model can be obtained by transforming the

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current cylindrical system into rectangular system (make small modifications to

223

equations (5), (8) and (9), see details in SI Section S2).

224 225

2.3 Method implementation

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To numerically solve the model, the sorbent and the barrier were divided into 30

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and 100 slices (which were found to be sufficient to provide for stable results

228

insensitive to the size of slices), respectively. Then the partial differential equations

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were discretized into a system of ordinary differential equations that were solved

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using Matlab R2009a. The ranges of D, K and hmʹ were selected to be 1×10-15 - 1×10-7

231

m2/s, 1×102 - 1×108 and 2×10-5 - 1×10-2 m/s, respectively, to encompass as many

232

cases as possible.

233

Equations (4)-(10) indicate that the relative error of M, ε, is of the following form:

(

ε = f D, K , hm′ , R0 , Ca ( t ) , ε ( v ) , MDL, ts

234

)

(11)

235

Sampling of a VOC concentration in a normal indoor environment is used as an

236

illustrative case in the following analysis. For the calculation, the combined standard

237

conditions were set to be: temperature of 20 oC, air flow speed of 0.2 m/s, VOC

238

concentration of 0.05 mg/m3 (a common indoor average level of benzene or toluene 2,

239

40-43

240

Radiello

241

measured environment was developed using a sinusoidal function:

242

), R0 = 2.4 mm (commonly used for radial-tube type passive samplers, e.g., 13

), and sampling time (ts) of 24 h. The fluctuant VOC concentration in the

Ca (t ) = C AVE + 0.5 ⋅ C AVE ⋅ sin(

2π t + 160°) tT

(12)

243

where tT is the period of concentration change, 24 h; CAVE is the time-weighted

244

average concentration, = 0.05 mg/m3. Values in equation (12) were determined by

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fitting results from a field test in a residential bedroom (more than three months after

246

decoration, measured by ourselves), thus equation (12) is expected to reflect the real

247

characteristics of indoor concentration fluctuation.

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The air flow speed is in the range of 0.1~3 m/s, covering the common indoor air

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flow speeds and the normal speed at which people walk.44-46 MDLs of benzene,

250

toluene and ethylbenzene analyzed using gas chromatograph-thermal desorption 8


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251

regulated by GB 11737-89 (in Chinese), are 50 ng/sample, 100 ng/sample and 200

252

ng/sample, respectively.47 However, the MDL of toluene (VOCs) for the same method

253

is 5 ng/sample according to MDHS 80.48 For the present study, we selected 50

254

ng/sample as a conservative estimate of the MDL for the analysis of VOCs.

255

Considering the above conditions, D, K and hmʹ are therefore the parameters that

256

need to be optimized. Once this is done we can determine the sorbent material, barrier

257

material and the size of the passive sampler.

258 259

3. Results and discussion

260

3.1 Model evaluation

261

In order to investigate the performance of passive samplers, the sampling rate (SR)

262

was measured in several studies.7,

16-18, 30

263

compared to the measured SRs from the literature to evaluate our proposed model.

264

The expression for SR is: SR =

265

Thus, in this section, the modeled SR is

M C AVE ⋅ t s

(13)

266

where M is the amount of target VOC in the sampler at the end of the sampling

267

period, µg; and CAVE is the average concentration of target VOC during the sampling

268

period, µg/m3.

269

Figure 2. The measured sampling rates (SRs) from the literature, and the model predictions for the same experimental conditions: (a) benzene using a Radiello, (b) toluene using a Radiello, (c) toluene using a Perkin-Elmer. 270 271

The comparison between the measured SRs of benzene and toluene sampled by

272

the Radiello sampler (obtained from Table II of Oury et al.49), and the modeled results

273

for the same experimental conditions is shown in Figures 2 (a) and (b). As can be

274

seen, there is good agreement between modeled SRs and measured SRs both for

275

benzene and toluene, implying high accuracy of the proposed model. The maximum

276

deviation between them is calculated to be less than 15%. Since several model

277

parameters were not measured by Oury et al.49, they were determined according to the

278

processes given in SI Section S1. However, it should be noted that the model

279

parameters, D, Ds, and K, were not directly determined in the same experiment of 9



280

Oury et al.49 Further study will be needed to know, in the event of more accurate

281

model parameters being obtained, whether the consistency between Oury et al.’s

282

results and the predictions of our model can be improved.

283

In addition, Brown et al.50 measured the SRs of toluene with a Perkin-Elmer

284

sampler (tube type) over a period of four weeks in an experimental chamber.

285

Parameters used for modeling the Perkin Elmer sampler are described in SI Section

286

S2. Figure 2 (c) shows the comparison between the measured SRs and the modeled

287

results. Similarly, the modeled SRs agree well with the measured SRs, and the mean

288

deviation between them is less than 10% (5%-22%), further giving confidence in the

289

proposed model (under rectangular coordinate system).

290 291

3.2 Sensitivity analysis

292

The impact of some model parameters (D, K, and hmʹ) on the relative error of M

293

was analyzed by performing sensitivity analysis with the derived mass transfer model.

294

The standard model parameters are D = 9.0 × 10-12, K = 2.0 × 106, and hmʹ = 3.6 × 10-

295

4

296

bound to the upper bound of its range mentioned in the Method implementation

297

section, and investigated the variation trend of ε. The results of the sensitivity analysis

298

of D, K, and hmʹ are shown in Figure 3.

. We increased the targeted parameter (D, K, and hmʹ, respectively) from the lower

299

Figure 3. Sensitivity analysis of model parameters for the relative error of M (ε). (a) D; (b) K; and (c) hmʹ. 300 301

Figure 3 (a) shows the variation of the relative errors of M attributed to the

302

fluctuation of VOC concentration (ε(C)), the variation of air flow speed (ε(v)) and

303

chemical analysis (ε(MDL)), as well as the composite error of M (ε) for various D.

304

The figure shows that as D increases: 1) ε(C) is decreasing, i.e., the effect of the

305

fluctuation of concentration is weakening; 2) ε(v) will increase, since the effect of

306

external mass transfer resistance (associated with air flow speed) will be more

307

significant for larger D (reducing the internal mass transfer resistance); 3) ε(MDL)

308

will decrease, since the sorption amount of VOC in the sorbent with the same

309

sampling time will increase for larger D (which reduces the mass transfer resistance of

310

the whole process). This figure also indicates that the composite error, ε, will decrease 10


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311

to a constant value as D increases; and that, ε is insensitive to the variation of D

312

(specifically, when D is larger than 10-13 m2/s).

313

Figure 3 (b) shows sensitivity analysis results for K. Similar to the results for D,

314

ε(v) will increase as K increases, while ε(C) and ε(MDL) will decrease. The composite

315

error, ε, will decrease to a constant as K increases, and the effect of K on ε is quite

316

significant for K with small values (i.e., K less than 3 × 105). Figure 3(c) shows that ε

317

is very sensitive to changes in hmʹ, the value of ε will decrease initially and then

318

increase as hmʹ increases. The sensitivity analysis results have guiding significance for

319

determining the optimized parameters of a passive sampler with a minimum ε. The

320

analysis suggests that when searching for the optimized parameters, we can increase

321

the values of D, K and hmʹ from certain values (i.e., the lower bound of the range of

322

each parameter determined in the “Method implementation” section), and then stop

323

calculation when ε approaches the minimum value (constant for D and K, while

324

beginning to increase for hmʹ).

325 326

3.3 Optimized results

327

In this study, an optimization of radial passive samplers for benzene and

328

formaldehyde in a normal indoor environment (the indoor conditions are described in

329

the “Method implementation” section) was performed based on the above method.

330

The optimized parameters and minimum values of ε are listed in Table 1. It can be

331

seen that the minimum ε are just 4.5% and 3.7% for sampling of benzene and

332

formaldehyde, respectively. Figure 4 shows the calculated results of ε for various D

333

and K when hmʹ is equal to the value listed in Table 1, which indicates that the value of

334

ε is decreasing as K and D increases (consistent with the sensitivity analysis results).

335

Table 1. Optimized parameters of radial passive samplers for benzene and formaldehyde in a normal indoor environment. 336

Figure 4. Variation of ε for various D and K when: (a) hmʹ = 3.6 × 10-4 m/s for benzene, (b) hmʹ = 4.4 × 10-4 m/s for formaldehyde. 337 338

Due to the limitations of existing sorbents (i.e., it is unlikely that we will be able

339

to find a sorbent meeting the optimized values of D and K), Figure 4 is useful for 11



340

selecting the appropriate sorbent by plotting ε of existing sorbents in the figure. Figure

341

4 compares the calculated ε of six commonly used sorbents, i.e., Carbograph 4 (used

342

by the Radiello sampler), activated alumina, activated carbon, activated manganese

343

oxide, silica gel, and silica zeolite. From this figure we can see that for passive

344

sampling of benzene, activated alumina, activated carbon, Carbograph 4, and silica

345

zeolite are the appropriate sorbents with minimum ε (calculated); while for

346

formaldehyde, activated alumina and activated manganese oxide are the most suitable

347

(Carbograph 4, silica gel, and silica zeolite are also acceptable). Although the

348

calculated ε should not be interpreted as the measurement uncertainty in a field test,

349

the modeled results are expected to reflect the uncertainty and the performance of

350

passive samplers to some extent. In addition, assumption (2) of the proposed model

351

may not be suitable for sorption of formaldehyde (because a chemical reaction may

352

occur). The applicability of this assumption, or the error introduced by it for modeling

353

of formaldehyde in passive samplers requires further research.

354

It should be noted that, in the practical selection of a sorbent, the physical and

355

chemical properties of the sorbent must be considered. Since active manganese oxide

356

may react with VOCs when the temperature is sufficiently high, it is not a suitable

357

sorbent if we analyze the samples by thermal desorption-GC-MS. Due to abundant

358

pores in activated carbon, thermal desorption of VOCs from this sorbent takes a long

359

time and the desorption efficiency is relatively low7, so solvent extraction must be

360

used instead. In addition, water vapor is easily adsorbed by silica gel and activated

361

carbon, which may result in uncertainty of sampling of VOCs (e.g., formaldehyde).

362

Furthermore, when optimizing passive samplers, cost should also be considered, and

363

Carbograph 4 is much more expensive than silica zeolite.7 Therefore, silica zeolite,

364

which is quite cheap, hydrophobic and has good desorption efficiency7, is suggested

365

to be the most appropriate sorbent among the aforementioned sorbents for sampling of

366

benzene (the modeled ε < 5%) and formaldehyde (the modeled ε < 15%).

367

Noting that we assumed the radius of the sorbent, R0, to be 2.4 mm in the above

368

analysis, it can be optimized after selecting the suitable sorbent, in this case, silica

369

zeolite. According to equation (11), if D and K of silica zeolite are measured, hmʹ and

370

R0 are the remaining two parameters needing to be optimized for sampling of a VOC

371

concentration in a normal indoor environment. By referencing the method and

372

experimental system developed by Xu et al.51, D and K of silica zeolite are measured

373

to be 7.5 × 10-11 m2/s and 3.1 × 105 respectively for benzene. Similarly to the method 12


Page 12 of 29

Page 13 of 29


374

(just mentioned above) for determining D, K and hmʹ, the optimized hmʹ and R0 are

375

determined to be 2.45 × 10-4 m/s and 2.15 mm, respectively, for sampling of benzene

376

in a normal indoor environment with the minimum ε to be 4.8%. The value of ε for a

377

commonly used sampler (i.e., Radiello

378

be 28%, which is significantly larger than our optimized passive sampler, implying

379

that our optimization method is very effective.

13

) under the same conditions is calculated to

380 381

4. Application, limitations and further study

382

Benzene has been identified as the predominant indoor-air risk compound

383

compared with other VOCs (e.g., formaldehyde).52 We therefore developed a novel

384

radial diffusive sampler, the Tsinghua Passive Diffusive Sampler (THPDS), for indoor

385

benzene measurement, according to the above optimization results.7 Specifically,

386

silica zeolite (FX-2021, Shanghai Fuxu Molecular Sieve Ltd.) was selected as the

387

sorbent with a radius of 2.15 mm (the mass is about 60 mg), the effective mass

388

transfer coefficient (hmʹ) was set to be 2.45 × 10-4 m/s (which is determined by the size

389

and material of the barrier). A stainless-steel power sintered porous cylinder (which is

390

low cost and exhibits weak benzene sorption capacity 7) was selected as the barrier

391

with a length of 30 mm, inner diameter of 4.3 mm (i.e., 2R0), external diameter of

392

10.3 mm (i.e., 2Rs), and porosity of 37-38%. Other components and the structure of

393

the THPDS are illustrated in Figure 5. As assumed in Section 2.2 that sorption of

394

VOCs to the barrier should be ignored, the adsorptivity of porous stainless-steel for

395

benzene was tested by exposing the THPDS without sorbent (i.e., just the porous

396

stainless-steel) to 10 µg/m3 gas-phase benzene for 30 days. After this exposure, the

397

amount of benzene sorbed in the barrier was lower than the detection limit of our

398

chemical analysis method (which is the same method for analyzing THPDS by ATD-

399

GC-MS, see detail in Du et al.7), implying that it is reasonable to ignore the sorption

400

of benzene to the barrier. Similar results were obtained for benzene series compounds,

401

i.e., toluene and xylene.

402

Figure 5. Tsinghua Passive Diffusive Sampler (THPDS): (a) structure illustration; (b) photo. 403 404

The performance of the newly designed THPDS was evaluated through 13



405

experimental measurement (in seven real indoor environment tests) by Du et al.7 Their

406

evaluation showed that the THPDS sampler was also suitable for sampling of gas-

407

phase toluene and xylene. The mean relative standard deviations (MRSD, or

408

coefficient of variation

409

than 11%, 11% and 7%, respectively. The overall uncertainties (calculated by

410

equation (3) of Du et al.7) of the THPDS, which combines bias between active

411

samplers and passive samplers (accuracy) and MRSD of passive samplers (precision),

412

for benzene, toluene, and xylene were 22%, 23%, and 17%, respectively. Compared

413

with several commercial passive samplers, the uncertainty of the THPDS is lower

414

than most of the other samplers (see Figure 10 in Du et al.7). In addition, no

415

significant difference between BTX concentrations obtained by THPDS samplers and

416

active samplers (Tenax TA samplers) was observed (relative bias is below 5%).7

14

) of the THPDS for benzene, toluene, and xylene were less

417

However, it should be noted that the overall uncertainty of benzene (22%) is quite

418

a bit higher than the modeled value of ε (4.8%), which may be due to limitations of

419

the present study. The definition of ε is different from the overall uncertainty, ε is a

420

subset of the overall uncertainty of passive samplers. As we mentioned in the Method

421

principle section, errors introduced by several factors (e.g., temperature variation,

422

humidity, storage time, desorption efficiency, and the bias between passive and active

423

samplers) were not considered when modeling the composite error. Efforts addressing

424

this challenge are worthy of further research. In addition, this study did not consider

425

the effect of the height of the sorbent (and the barrier) on the accuracy of passive

426

samplers. As the height increases, the amount of VOCs collected by the sorbent will

427

increase and the error introduced by chemical analysis (ε (MDL)) will consequently

428

decrease.

429

Application of the method presented here to other VOCs, e.g., aldehydes and

430

hydrochloric ethers, warrants further investigation. Furthermore, the optimized results

431

are focused on one specific compound (e.g., benzene or formaldehyde) in this study.

432

Optimization of passive samplers that can simultaneously monitor the concentrations

433

of different VOCs is very challenging. As mentioned above, it is unlikely that we will

434

identify a sorbent that meets the optimized values of D and K. Development of new

435

sorbents would be helpful for the optimization of passive samplers. Further studies

436

comparing different sorbents (conducted under the same experimental conditions) are

437

also expected. In addition, the proposed model is applicable to diffusion samplers,

438

further study is required to determine how to extend the proposed optimization 14


Page 14 of 29

Page 15 of 29


439

method to permeation samplers. Finally, further study focusing on the optimization of

440

passive samplers for semi-volatile organic compounds (SVOCs) would be valuable.53

441

These samplers may require elimination of the barrier layer due to the low volatility

442

of SVOCs.54 Recently, several studies have demonstrated that solid-phase micro-

443

extraction (SPME) can be used for passive sampling of SVOCs in laboratory

444

experiments31, 55. Further tests are needed to evaluate whether it is also applicable in

445

the field.

446 447

Associated content

448

Supporting Information

449 450

The supporting information as noted in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

451

Additional details on summary of representative passive samplers (Table S1),

452

summary of mass transfer model of passive samplers (Table S2), determination of

453

parameters used for model evaluation (Section S1), mass transfer model of tube-type

454

diffusion sampler and model parameters of Perkin-Elmer sampler (Section S2 and

455

Figure S1).

456 457

Author information

458

Corresponding Author *

459

E-mail: [email protected]; Phone: +86 10 62772518; Fax: +86 10

460

62773461; Address: Department of Building Science, Tsinghua University, 100084,

461

Beijing, China

462

Note

463

The authors declare no competing financial interest.

464 465

Acknowledgements

466 467

The research is supported by National Natural Science Foundation of China (Grant NO. 51521005).

468 469

References

470

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DOI:

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10.1111/ina.12312.

Page 21 of 29


628 629

TOC art

630 631 632

21



Page 22 of 29

633 634

Figures

635

Figure 1. (a) Three types of representative passive samplers; (b) schematic of mass transfer of VOCs

636

from ambient air to the sorbent in a radial sampler.

Tube-type sampler10 (Perkin-Elmer)

637

Badge-type sampler11 (OVM 3500)

(a)

638

639 640

(b)

641 642

22


Radial sampler12 (Radiello)

Page 23 of 29


643 644

Figure 2. The measured sampling rates (SRs) from the literature, and the model predictions for the

645

same experimental conditions: (a) benzene using a Radiello, (b) toluene using a Radiello, (c) toluene

646

using a Perkin-Elmer.

647 648

(a)

649 650

(b) 23



651 652 653

(c)

24


Page 24 of 29

Page 25 of 29


654

Figure 3. Sensitivity analysis of model parameters for the relative error of M (ε). (a) D; (b) K; and

655

(c) hmʹ.

656 657

(a)

658

659 660

(b) 25



661

662 663

(c)

26


Page 26 of 29

Page 27 of 29


664 665

Figure 4. Variation of ε for various D and K when: (a) hmʹ = 3.6 × 10-4 m/s for benzene, (b) hmʹ = 4.4

666

× 10-4 m/s for formaldehyde.

667 668

(a)

669 670

(b)

671 672

27



673 674

Figure 5. Tsinghua Passive Diffusive Sampler (THPDS): (a) structure illustration; (b) photo.

675 676

(a)

677 678

(b)

679 680

28


Page 28 of 29

Page 29 of 29


681

Tables

682

Table 1. Optimized parameters of radial passive samplers for benzene and formaldehyde in a normal

683

indoor environment Chemicals

D (×10-12 m2/s)

K (×107)

hmʹ (×10-4 m/s)

ε (%)

Benzene

0.70

0.60

3.6

4.5

Formaldehyde

6.0

3.0

4.4

3.7

684 685 686

29


Inverse Problem Optimization Method to Design Passive Samplers for

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