A parsimonious model for the release of volatile organic compounds (VOCs) encapsulated in products

Atmospheric Environment 127 (2016) 223e235

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Atmospheric Environment journal homepage: www.elsevier.com/locate/atmosenv

A parsimonious model for the release of volatile organic compounds (VOCs) encapsulated in products Lei Huang*, Olivier Jolliet Environmental Health Sciences, School of Public Health, University of Michigan, Ann Arbor, MI 48109-2029, United States

h i g h l i g h t s
A parsimonious model is developed for emission of VOCs encapsulated in products.
Mass fraction emitted over 15 years can be modeled by two exponential terms.
Concentrations in air and on product surface can be derived from the mass emitted.
Parameters can be predicted from physiochemical properties by explicit equations.
The model performs well for a wide range of compounds and material thicknesses.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 June 2015 Received in revised form 28 November 2015 Accepted 1 December 2015 Available online 12 December 2015

Studies have demonstrated that near-field chemical intakes may exceed environmentally mediated exposures and are therefore essential to be considered when assessing chemical emissions across a product's life cycle. VOCs encapsulated in materials/products can be a major emission source in the use phase. Previous models describing such emissions require complex analytical or numerical solutions, which poses a great computational burden and lack transparency for use in high-throughput screening of chemicals. In the present study, we adapted a model which describes VOC emissions from building materials and subsequent removal by ventilation, and decoupled the material and air governing equations by assuming a pseudo-steady-state between emission and loss. Results of this decoupled model show good agreement with the original more complex model and the experimental data. The solution of this decoupled model for mass fraction emitted, which still consists of an infinite sum of exponential terms, is further reduced to a sum of only two exponentials with parameters which can be predicted from physiochemical properties using explicit equations. Results of this simple two-exponential model agree well with the original full model over a 15-year time period with R-square greater than 0.99 for a wide range of compounds and material thicknesses. Moreover, the chemical concentration at the material surface can be simply calculated from the derivative of this two-exponential model, which also agrees well with the surface concentration calculated using the original full model. The present parsimonious approach greatly reduces the computational burden, and can be easily implemented for highthroughput screening. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Consumer products Exposure models Encapsulated chemicals Volatile organic compounds Indoor environment

1. Introduction Exposure assessments over product life cycles have often focused on the human health impacts of outdoor emissions without considering near-field releases and exposures during product use. However, studies have demonstrated that near-field chemical

* Corresponding author. E-mail address: [email protected] (L. Huang). http://dx.doi.org/10.1016/j.atmosenv.2015.12.001 1352-2310/© 2015 Elsevier Ltd. All rights reserved.

intakes may exceed environmentally mediated exposures (Crinnion, 2010; Lorber, 2007). Thus, it is necessary to extend the LCA practices with an improved focus on near-field chemical emissions and exposures during the use stage. Besides LCA, high-throughput exposure analysis for screening the risk of chemicals in consumer products is also gaining increasing attention since there are thousands of existing and new chemicals being manufactured and used in a large variety of products. Wambaugh et al. (Wambaugh et al., 2013) have shown that considering exposure during product use is a key when

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screening chemicals. Useful model and approaches have been proposed (Delmaar et al., 2005; Isaacs et al., 2014), but they tend to only consider very simple indicators to assess direct exposure during consumer product use for dermal impact pathways or for exposure to chemicals encapsulated in articles. As a result, more detailed high-throughput models for chemical emissions and exposures during consumer use are needed to improve the exposure predictions and the subsequent prioritization. Volatile organic compounds (VOCs) encapsulated in materials and products can be a major emission source in the indoor environment and in the use phase, including, for example adhesives, solvents and paints in various building materials and furniture. Three main chemical descriptors are necessary to provide the required data for LCA or high-throughput exposure assessment for VOCs encapsulated in products: the evolution over product life time of the chemical concentration at the product surface, the corresponding indoor chemical releases from products over the life time of these products and the resulting air concentrations and intakes by inhabitants. Earlier modeling efforts have focused on chemical releases and the resulting air concentrations. Various empirical models have been constructed to predict the VOC emission rate from building materials and other indoor sources, such as constant emission, first-order decay, dual 1st-order decay, secondorder decay, and so on (Guo, 2002a). However, although simple in structure, these empirical models rely on parameters that are derived using statistical analysis of emission chamber test data. Such parameters generally lack a physical basis, and are difficult to predict for other conditions and chemical-product combinations. These models are therefore not suitable for LCA or high-throughput analysis, where large variations in chemical properties, products and environmental conditions would be expected. In contrast to the empirical models, a series of physically-based models, first presented by Little et al. (Little et al., 1994), have been developed based on the diffusion of chemicals inside the material to predict the aforementioned three descriptors. It is assumed that the chemicals encapsulated in products diffuse out of a single uniform layer of material, and the governing equation describing the transient diffusion through the material is given by the Fick's Second Law (Little et al., 1994). This governing equation needs to be coupled with various boundary and initial conditions, which describe the properties of the material, the material base, the air and the room, to get a solution. Numerous models have been developed for VOCs employing different boundary and initial conditions. For example, the base (bottom) of the material can be assumed as impervious (Deng and Kim, 2004; Huang and Haghighat, 2002; Little et al., 1994) or pervious (Wang et al., 2006); the material can be either homogeneous (Deng and Kim, 2004; Huang and Haghighat, 2002; Little et al., 1994) or heterogeneous (Kumar and Little, 2003; Xu and Zhang, 2004); the convective mass transfer resistance between the material and the air may be included (Deng and Kim, 2004; Huang and Haghighat, 2002; Yang et al., 2001b) or neglected (Kumar and Little, 2003; Little et al., 1994); the room air can be well-mixed (Deng and Kim, 2004; Huang and Haghighat, 2002; Little et al., 1994) or non-uniform (Yang et al., 2001a, 2001b); the sink/sorption effect of indoor surfaces can be considered (Deng et al., 2007, 2008; Yang et al., 2001a) or ignored (Deng and Kim, 2004; Huang and Haghighat, 2002; Little et al., 1994); and the internal chemical reactions may also be considered (Wang and Zhang, 2011). Among the various boundary and initial conditions, a simple but common scenario assumes that the material has an impervious base, the initial concentration inside the material is uniformly distributed, and the room air is well-mixed. Also, commonly resistance to convective mass transfer is included but the sink/ sorption effect for VOCs can be considered negligible (Deng and

Kim, 2004; Huang and Haghighat, 2002; Liu et al., 2013). Huang and Haghighat (Huang and Haghighat, 2002) first derived an approximate analytical solution by assuming that the concentration in the bulk air (y) is much smaller than the concentration in the air adjacent to the material surface (y0), which completely decoupled the material and its boundary air from the bulk room air. However, in the case of an enclosed room/chamber with little or no ventilation, y would increase and finally get close to or reach y0, making this solution invalid. Deng and Kim (Deng and Kim, 2004) later obtained a fully analytical solution using Laplace transforms, but the complexity of the solution is also increased. More importantly, both solutions need to find the roots of x$tan(x) ¼ C (C is one or more terms with or without x), which is a transcendental equation that can only be solved numerically. As a result of the transcendental equation, the solutions for concentration in air, concentration in material, and mass emitted all require the calculation of the sum of infinite terms, which in certain cases need more than 5000 terms to achieve convergence. These solutions thus pose a great computational burden for certain products and chemicals and are hard to interpret, which make them difficult to implement and not well-suited for the high-throughput analysis of a wide range of chemical-product combinations. The present study aims to seek out an alternative between the simple empirical models and the complex diffusion models for the modeling of indoor emissions of VOCs encapsulated in products as well as the material surface concentrations. Our overall objective is to develop a parsimonious approach which (1) is simple in structure but can reasonably approximate the complex models, and (2) contains parameters that are physically meaningful and are predictable from chemical, product and environmental properties. First, we will use a more accurate approach to decouple the emission process from the indoor air system. We will then approximate the complex solutions for the mass emitted and the concentration at material surface using two exponentials and will predict the parameters using simple explicit equations, which eliminates the need to solve transcendental equations or to calculate the sum of infinite terms. We finally provide a short example illustrating how the developed approach can be applied to a given chemical. Although previous studies have also proposed a dual-exponential equation to describe the emission rate, their parameters were obtained using regressions of experimental data (Chang and Guo, 1992; Dunn, 1987) and thus cannot be generalized to other situations. The major advantage of our approach is that all the parameters can be predicted without experimental data. Therefore, this parsimonious approach is expected to greatly reduce the computational burden and to provide a method that can be generalized across various environmental conditions and chemical-product combinations. Such approach is important since it is currently lacking for LCA and high-throughput analysis of chemicals encapsulated in products. The model predictions of VOC emissions and material surface concentrations can also be used to estimate human exposure potentials. For example, the predicted mass emitted can be fed into an indoor air model to calculate the occupants’ inhalation exposure and dermal absorption and the predicted surface concentration can be used to calculate human exposures through skin contact and hand-to-mouth activities. 2. Model development 2.1. Decoupling of the emission process from indoor air We employ the scenario used by Huang et al. and Deng et al. (Deng and Kim, 2004; Huang and Haghighat, 2002), which assumes that the material has an impervious base, the initial concentration inside the material is uniformly distributed, the room air is well-

L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

mixed, and the convective mass transfer resistance is included but the sink/sorption effect of indoor surfaces is neglected. This scenario can be described by the following equations:

vCðx; tÞ v2 Cðx; tÞ ¼ D, vt vx2

(1)

vCðx; tÞ ðx ¼ 0Þ ¼ 0 vx

(2)


vCðx; tÞ CðL; tÞ ðx ¼ LÞ ¼ hm ðy0 ðtÞ  yðtÞÞ ¼ hm  yðtÞ D, vx K (3)

V

dy ¼ A,hm ðy0 ðtÞ  yðtÞÞ  Q ,yðtÞ dt

(4)

where C(x, t) (mg/m3) is the concentration of the chemical in the material, t (s) is time, x (m) is the linear distance from the bottom of the material, D (m2/s) is the diffusion coefficient of the chemical in the material, L (m) is the material thickness, hm (m/s) is the convective mass transfer coefficient at the material surface, y(t) (mg/ m3) is the gas-phase chemical concentration in the bulk room air, y0(t) (mg/m3) is the gas-phase chemical concentration in the air adjacent to material surface, K (dimensionless) is the chemical's partition coefficient between material and air, V (m3) is the room volume, A (m2) is the surface area of the material, and Q (m3/s) is the room's ventilation rate. Eqn. (1) is the governing equation describing the transient diffusion through the material. Eqn. (2) assumes no mass flux at the base of the material (i.e., impervious). Eqn. (3) assumes that the diffusion flux at the material surface is driven by the concentration gradient between the boundary-layer air and the bulk air, and is controlled by convective mass transfer. It also assumes that equilibrium exists at the materialeair interface. Eqn. (4) describes the mass balance in the room air, assuming the inflow concentration is zero, and the VOC is only lost by ventilation. Huang and Haghighat (Huang and Haghighat, 2002) assumed that the concentration in the bulk air is much smaller than the concentration in the boundary-layer air, i.e., replacing y0(t)-y(t) with y0(t) in Eqn. (3):

vCðx; tÞ CðL; tÞ ðx ¼ LÞ ¼ hm, y0 ðtÞ ¼ hm, D, vx K

(5)

Using Eqns. (1), (2), (4) and (5), they derived an approximate analytical solution for the concentration in the material, concentration in air, and the cumulative emitted mass at time t as:

Cðx; tÞ ¼ C0 ,

∞ X

fðx; qn ; L; DÞ,eqn Dt 2

(6)

n¼1

yðtÞ ¼ C0 ,

∞ X

  Q 2 gðqn ; L; D; Q ; A; VÞ, eqn Dt  eV t

(7)

qn ,tanðqn LÞ ¼

hm DK

(9)

and where f(x, qn, L, D), g(qn, L, D, Q, A, V) and h(L, qn, D) are relatively complicated functions of these variables [Eqn. (5)], as given in SI Section S1. However, this solution is not applicable to the case of restricted ventilation, where y could be not negligible compared to y0, leading to violation of the assumption and thus invalid model predictions (Liu et al., 2013). Therefore, Deng et al. (Deng and Kim, 2004) proposed a more exact but increasingly complex solution that fully coupled both compartments, as given in SI Section S2. In contrast to those two approaches, we propose an intermediary alternative, which uses a hypothesis that is different from Huang and Haghighat's while preserving their format and solution. We consider that the room dynamic is much faster than the dynamic of material release and therefore assume that the indoor air concentration is at quasi-steady-state between the emission from the material and the loss by ventilation, that is V dy/dt << Q$y(t). It should be noted that this assumption is valid only after a short period of time from the beginning; the larger the air exchange rate (Q) is, the shorter this period will be. This period would not exceed 10 h even for a minimum air exchange rate under real conditions, which will be further discussed in Section 3.1. With this assumption, Eqn. (4) is changed to:


A,hm

 CðL; tÞ  yðtÞ yQ ,yðtÞ K

yðtÞ ¼

CðL; tÞ 1  ,
K Q 1 þ Ah

0

Substituting Eqn. (11) into Eqn. (3) yields:

D,

vCðx; tÞ 0 CðL; tÞ ðx ¼ LÞ ¼ hm , vx K

(12)

with 0

hm ¼ hm ,


1



(13)

m 1 þ Ah Q

SI Section S3 shows how the term hm’ can be generalized to also account for indoor degradation and sorption on airborne particles using the approach developed by Wenger et al. (Wenger et al., 2012). The substitution of hm by hm’ accounts for the feedback effect and influence of the indoor concentration on the material surface concentration and releases, while keeping the same format and solution as Huang and Haghighat (Huang and Haghighat, 2002). Therefore, the solutions for concentration in material, air concentration and mass emitted are still given by Eqns. (6)e(8), with qns as the positive roots of: 0

∞   X 2 CðL; tÞ dt ¼ M0 , A,hm , hðL; qn ; DÞ, 1  eqn Dt K n¼1

(8) where qns are the positive roots of

(11)

m

qn L,tanðqn LÞ ¼ g; where g ¼ Zt

(10)

Solving Eqn. (10) for y(t) yields:

n¼1

MðtÞ ¼

225

hm L DK

(14)

This is essentially Eqn. (9) with hm replaced by hm’ and with both sides multiplied by L. We will test the quality of the quasi-steady state assumption by comparison to the exact but more complex solution from Deng et al. (Deng and Kim, 2004) and the experimental data from Yang et al. (Yang et al., 2001b).

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2.2. Understanding the long-term dynamic e q1 approximation Similar to Huang and Haghighat's solution, the new decoupled solution relies on the solution of Eqn. (14), a transcendental equation. Eqn. (14) has an infinite number of positive roots (qns), and the solutions (Eqns. (6)e(8)) are thus the sums of infinite terms. According to the properties of Eqn. (14), qns is a monotonically increasing series, and the first positive root q1 is thus the 2 smallest. Since Eqns. (6)e(8) are dependent on eqn Dt , the contribution of the smallest root q1 dominates the dynamic for large t. Thus, q1 is the most important determinant for the long-term dynamic, and our next step is to approximate q1 using explicit equations. Fig. 1 shows in a contour plot how q1 changes with L and DK using Eqn. (14), for a given value of h0m (2.15$104 m/s). We can distinguish three different patterns: a) for log DK > 4, q1 becomes largely independent of L; b) For log DK < 6, q1 is mainly determined by L; and c) for log DK between 4 and 6, there is an intermediary zone in which q1 is influenced by both L and DK. In correspondence to these three patterns, q1 may be approximated by a piecewise function of 3 segments. a) For g ¼ hm’L/DK that is very small (e.g., g < 0.0001), the left side of Eqn. (14) can be approximated by the Taylor expansion of tan(x) (SI Section S4). This corresponds to the area to the right of the white dotted line in Fig. 1.

q1 L,tanðq1 LÞy q1 L,q1 L ¼ ðq1 LÞ2 ¼ g pffiffiffi q1 L ¼ g

(15)

b) For g that is relatively large (e.g., g > 5), q1L can be approximated by a modified arctangent function (SI Section S4), which corresponds to the area to the left of the white solid line in Fig. 1.

 .p q1 Lyarctan g k

(16)

According to the properties of the tangent function, the parameter k will be tending to 2 if g is very large (e.g., g > 1000), but larger deviation for smaller g values will be generated with k ¼ 2. Therefore, we will use a k value slightly different from 2 to ensure a better fit for smaller g values (e.g., 5
highest value corresponds to D·K ¼ 1$1012 (m2/s), hm’ ¼ 2.15$104 (m/s), and L ¼ 0.2 (m), which would be a high-end plausible value of g for real situations. These calculations used Matlab R2014a (MathWorks Inc., Natick, MA) and the function fminsearch (NelderMead simplex direct search) and yielded an optimal value of k ¼ 2.21. Thus, q1 can be approximated as a product of 1/L and a weighted sum of Eqns. (15) and (16) using a factor l:

q1

proxy y

 . p  pffiffiffi 1  , ð1  lÞ, g þ l,arctan g L 2:21

(17)

where l is predicted using a generalized logistic function:

1 l¼ d 1 þ a,ebðgcÞ

(18)

The parameters l, a, b, c, and d were again estimated by minimizing the sum of squared differences between the predicted q1L (Eqn. (17)) and real q1L (Eqn. (14)) using randomly created g values between 0.0001 and 5, which were selected as cut-off points since the difference between the real q1 (Eqn. (14)) and the high/low-end approximations (Eqns. (15) and (16)) is small enough at these two points - lower than 2%. These calculations used Matlab R2014a and the function fminsearch. The resulting values of the parameters in Eqn. (18) are presented in Eqn. (19):

1 l¼ 433 1:34ðgþ6:12Þ 1 þ 38:7$e

(19)

A sensitivity analysis of the four parameters a, b, c and d is given in SI Section S4.3. Fig. 2 shows the final q1L approximation (Eqn. (17)) along with the low-end and high-end approximations (Eqns. (15) and (16)). The final approximation, which uses a logistic function to link the low-end and high-end approximations, can replicate the real q1L nearly perfectly. We tested 2200 random values of g ¼ hm’L/DK ranging from 2$105 to 5$107. The difference between the real and approximate q1L does not exceed 3.5% for g less than 5. At the high end (g > 5) the error decreases as g increases. When g is larger than 900, the error is less than 0.01%. These results indicate that q1 can be accurately calculated using the explicit function of Eqn. (17) instead of solving the transcendental Eqn. (14) numerically.

3.5 Numerical Low-end proxy

3

High-end proxy 2.5

Final proxy

q1L

2 1.5 1 0.5 0 0

1

2

3

4

5

6

7

8

9

10

hm'L/DK Fig. 1. Values of q1 as a function of L and D·K, with a fixed value of h0m (2.15$104 m/s). The white solid line indicates where h0m L/DK ¼ 5, while the white dotted line indicates where h0m L/DK ¼ 0.0001.

Fig. 2. Relationship between q1L and h0m L/DK. “Numerical” represents the q1L calculated by solving Eqn. (14) numerically using Matlab; “Low-end proxy” represents Eqn. (15); “High-end proxy” represents Eqn. (16); and “Final proxy” represents Eqn. (17).

L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

2.3. Parsimonious prediction and cross-validation of mass fraction emitted Section 2.2 has determined an approximate q1, designated as q1_proxy, as an explicit function of h0m , L, D and K. The next step is to further reduce the mass fraction emitted into a parsimonious equation. As given by Eqn. (8), the mass fraction emitted M(t)/M0, is a sum of infinite exponential terms, so it may be possible to reduce it into a finite number of exponentials. As observed by Chang et al. (Chang and Guo, 1992), the emission rate of VOCs from newly applied wood stain can be described by a dual first-order decay model with two ekt terms, where the first exponential describes the relatively fast emission when the wood stain is still wet, and the second exponential describes the much lower emission after the wood stain dries. The total mass of VOC emitted, which is the integration of the emission rate, will then take the form of (1ekt), similar to the exponential terms in Eqn. (8). Thus, we propose to reduce Eqn. (8) into a sum of two exponentials while keeping a similar format for each exponential term:

f ¼

    2 2 MðtÞ ¼ a1 , 1  eb1 Dt þ ð1  a1 Þ, 1  eb2 Dt M0

(20)

where a1, b1, and b2 are parameters which will be predicted as explicit functions of D, K, L and q1_proxy. Eqn. (20) guarantees that M(t)/M0 is equal to zero when t ¼ 0. The coefficients for the two exponential terms are set as a1 and 1  a1 to ensure that M(t)/M0 is equal to 1 when t is large enough, meaning that all of the chemical inside the material will be finally emitted. b1 and b2 are positive, and b1 is set to be smaller than b2. Therefore, the second exponential term with b2 describes the relatively fast, short-term process during which the chemicals at or near the material surface are readily released, while the first exponential term with b1 describes the relatively slow, long-term process during which the chemicals near surface are depleted and the chemicals deep inside need to diffuse through the material and be released. To obtain the predictions for a1, b1, and b2, we first selected a set of test chemicals, which included 36 real chemicals with D and K values from the literature and 30 hypothetical chemicals with manually created D and K which are random numbers within the literature-reported maximum and minimum values (SI Table S3). The hypothetical compounds and 6 real SVOCs are included in order to cover a wider range of D and K combinations, especially for those that might not exist in real compounds such as a high D and high K. Each chemical was tested with two values of L (1.5 cm and 15 cm), thus a total of 132 test cases. Room volume (V), ventilation rate (Q), and material surface area (A) were assumed to be the same for all test chemicals, and we used the experimental data given by Yang et al. (Yang et al., 2001b). Since the convective mass transfer coefficients (hm) for different chemicals do not change considerably under similar conditions (Holmgren et al., 2012; Huang and Haghighat, 2002; Liu et al., 2013), for simplicity a fixed value of hm (7.10$104 m/s) was used for all test chemicals. Although fixed values of V, Q, A and hm resulted in a fixed value of h0m , the large variations in L, D and K still led to a wide range of h0m L/DK values. Since q1_proxy is determined by h0m L/DK, and the parameters a1, b1 and b2 are determined by q1_proxy (discussed below), our predictions of a1, b1 and b2 (discussed below) are valid for a wide range of h0m L/ DK values spanning several orders of magnitude. If a different set of V, Q, A and hm is to be used, it will only result in a change of h0m L/DK, which can certainly be handled by our predictions. For each test case, we first fit the three parameters (a1_fitted, b1_fitted, and b2_fitted) by minimizing the sum of squared differences between the simplified mass fraction emitted (Eqn. (20)) and the reference (i.e., the full analytical solution developed by Deng

227

et al. (Deng and Kim, 2004) with 5000 terms) across more than 10,000 time points over 15 years. These calculations were performed with Matlab R2014a using the fmincon function. Each test case yielded a very good fit, with an R2 larger than 0.99. We then analyzed how the three fitted parameters can be predicted across all test cases as an explicit function of q1_proxy, D, K, and L to establish the prediction factors and rules. Finally, these prediction rules were applied back to 47 test chemicals which meet the criteria of VOCs (discussed below) and extending the set to four values of L (15 cm, 1.5 cm, 0.15 cm and 0.015 cm), constituting 188 prediction cases. a1, b1, and b2 were predicted from D, K, L and q1_proxy for each of the 188 cases. The predicted mass fractions emitted for 15 years were then calculated and were evaluated against the reference values calculated with the complex model for each chemical and across all prediction cases for 10 days, 100 days, 3 years and 15 years in order to characterize the final predictability. The quality of the correspondence with the detailed model was measured using R2, standard errors on the log, standard errors and coefficient of variations, focusing on the 1 day to 15 years interval since the present model is not intended to be used at very early stage before the product is in effective use. 2.4. Parsimonious prediction of concentration at the material surface Once M(t) is determined, the chemical concentration at the material surface can be calculated from the predicted M(t) by taking the derivative of the left part of Eqn. (8):

CðL; tÞ ¼

dMðtÞ K , 0 dt Ahm

(21)

Substitution of Eqn. (20) into Eqn. (21) yields:

i 2 2 LK h CðL; tÞ ¼ C0 , 0 , a1 b21 D,eb1 Dt þ ð1  a1 Þb22 D,eb2 Dt hm

(22)

We will test the accuracy of this equation from time zero up to the 15 years considered in this study. 2.5. Evaluation against experimental data Our results are also evaluated against the experimental data from Yang et al. (Yang et al., 2001b), who measured the VOC emissions from new particleboards in a small test chamber of 0.5  0.4  0.25 m3. The experimental conditions are given in SI Table S4. They investigated the emissions of TVOC (total VOCs), hexanal and a-Pinene from two different particleboards (PB1 and PB2) with the same dimensions, and the VOC concentrations in air were measured for 96 h. These experimental data were also employed by Huang et al. (Huang and Haghighat, 2002) and Deng et al. (Deng and Kim, 2004) to validate their models. The diffusion coefficients in the material, materialeair partition coefficients and initial VOC concentrations in the material were provided by Yang et al. (Yang et al., 2001b), and the convective mass-transfer coefficient hm were calculated using an empirical relationship which is presented in SI Section S5. The values of these parameters can be found in SI Table S5. 3. Results and discussions 3.1. Validation of the decoupled model with h0m The decoupled model with h0m (Eqns. (6)e(8) and (14)) was applied to VOC emissions from building materials using the experimental parameters obtained by Yang et al. (Yang et al.,

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2001b), which are presented in SI Tables S4 and S5. Fig. 3 compares the chamber air concentrations of TVOC, hexanal and a-Pinene emitted from particleboard 1 (PB1) predicted by the decoupled model with Deng et al.’s fully analytical solution (Deng and Kim, 2004), Huang et al.’s approximate analytical solution (Huang and Haghighat, 2002), and the measured data (Yang et al., 2001b). The corresponding data can be found in SI Table S6. Results of the decoupled model approximate well Deng's full solution, the only observable differences occurring for the first 3 h (quasi-steady state hypothesis only valid after a couple of hours). Both the present model and Deng's model agree well with the experimental results, but underestimate the concentrations of a-Pinene at the early stage, probably due to errors in its physical properties such as the diffusion coefficient (Deng and Kim, 2004) (Yang et al., 2001b). In contrast, Huang's model greatly overestimates the air concentrations at the initial stage, especially for the peak air concentration, since it neglects any feedback from indoor air to material surface thus overestimates the initial emission rate (Huang and Haghighat, 2002).

As mentioned above, our quasi-steady state assumption is only valid after a short period of time, and this period is longer for smaller air exchange rates. For strictly sealed room/chamber where Q ¼ 0, our decoupled model with h0m is invalid since h0m will be equal to zero which means no chemical emissions from material according to Eqn. (12). However, in reality, Q is never equal to zero even in tight rooms and buildings. The American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) Standard 62e1999 (ASHRAE, 1999) recommends an air exchange rate (ACH) of 0.35 h1 to ensure indoor air quality. The lowest basic air exchange rate in Japan dwellings with doors and windows closed was 0.7 h1 (Iwashita and Akasaka, 1997). The air exchange rate ensuring an acceptable indoor formaldehyde concentration in Canadian homes is 0.26e0.37 h1 (Gilbert et al., 2008). Therefore, it is reasonable to assume that in reality ACH  0.3 h1. Using the lowest ACH of 0.3 h1 and real room characteristics, the model predictions of air concentrations of the above three VOCs are presented in Fig. 4. Even with this low air exchange rate, the present model converges with Deng's model after the first 6e8 h, while Huang's

Fig. 3. Chamber air concentration of (A) TVOC, (B) hexanal and (C) a-Pinene emitted from particleboard 1 (PB1), with time.

L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

model still greatly overestimates the peak concentration and remains overestimated after 40 h. Additional comparisons can be found in SI Section S6. Therefore, the present model with h0m can accurately predict the air concentration of VOCs under realistic ventilation conditions, except for the first couple hours. Since the present model is intended to estimate the emissions during consumer use, which usually happens at least 10 days after manufacturing, inaccuracy of the model at the initial hours can be neglected. In short, with the same solutions as Huang's model (Eqns. (6)e(8)) but with h0 m accounting for ventilation rate Q (the feedback), we are able to “decouple” the material from the room air without losing much accuracy at the early stage, while enabling us to use a solution that is simpler than the full solution and can then be further simplified as presented below.

229

3.2. Prediction of mass fraction emitted As described in the methods, we used two exponentials to fit the mass fraction emitted in 15 years for 132 test cases, which included 30 real VOCs, 6 real SVOCs and 30 hypothetical chemicals. The fitting results revealed that there were two types of behaviors, one of which included all the real VOCs, while the other included all the real SVOCs. The classification of these two types is determined by the value of D$K. Therefore, in the context of our model, we define “VOCs” as compounds with D$K < 2$106 m2/s, and “SVOCs” as compounds with D$K  2$106 m2/s. Since the governing equations of our model (Eqns. (1)e(4)) do not consider any sorption effects on indoor surfaces which is crucial for SVOCs, our model is only valid for the VOCs. Thus, the following results and discussions will only focus on chemicals that meet the VOC criterion, that is, compounds with D$K < 2$106 m2/s.

Fig. 4. Gas-phase concentration of (A) TVOC, (B) hexanal and (C) a-Pinene emitted from a 0.0159 m-thick particleboard, with A ¼ 113.6 m2, V ¼ 277 m3, hm ¼ 8.8 m/h ¼ 0.0024 m/s, and ACH ¼ 0.3 h1 (i.e., Q ¼ 0.0231 m3/s).

230

L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

a) Example chemicals The newly defined “VOCs” include 30 real VOCs and 17 hypothetical compounds. This group corresponds to the left region of Fig. 1 where q1 is primarily determined by L. As an example of a typical VOC, a-Pinene has a relatively low D$K value, equal to 6.72$107 m2/s. As shown in Fig. 5A and B, its mass fraction emitted behaves like a piecewise function consisting of several straight lines with different slopes (on a logelog scale). Therefore, at least two exponentials are needed to predict its emission kinetic: The first exponential controls the long-term dynamic, while the second controls the short-term. Comparing the format of Eqns. (8) and (20) suggests that b1 should be related to q21$D. Fig. 6 presents how the values of a1, b1, and b2 are directly related to the value of q21_proxy$D. Both a1 and b1/q1_proxy decrease as q21_proxy$D increases, and they reach a constant value of 0.85 and 1, respectively, for q21_proxy$D larger than 109 s1. The ratio of b2/b1 also decreases as q1_proxy 2$D increases, but it does not reach a constant value when q1_proxy 2$D becomes large. For certain VOCs, the two exponentials described above are only able to represent the emission kinetic after 100 days. For example, the prediction for n-pentadecane is inaccurate before 100 days (Fig. 5C and D). To be more accurate for day 10 to day 100, a separate short-term model is needed for VOCs with relatively small q21_proxy·D values which are smaller than 108 s1, indicative of a relatively slow emission kinetic. The short-term model will take the same format as the long-term (15-yr) model, but with different values of a1, b1, and b2. Thus, similar as the 15-yr model, two exponentials were used to fit the mass fraction emitted in the first 100 days, and the fitting results were used to derive the prediction rules of a1, b1, b2. As shown in Fig. 5D, the short-term model gives better predictions than the long-term model for the early stage. The time scale of the emission process is dependent on q21_proxy$D, which is a function of D, K, the material thickness L and the adjusted convective mass-transfer coefficient h0 m . Therefore, for a given type of material, the time scale of the emission of a chemical will vary depending on the convection, ventilation, thickness of the material and the material's loading factor (A/V). Table 1 summarizes the correlations that enable us to predict the three coefficients a1, b1, and b2 as a function of q1_proxy 2$D. Using these correlations, the mass fraction emitted over 15 years can be

accurately predicted for all the real VOCs and most hypothetical VOCs for thick (L ¼ 1.5 cm and 15 cm) and thin (L ¼ 0.15 cm and 0.015 cm) materials: the coefficient of variation (CV, root mean standard error normalized by the mean reference value) for the period of 10 de15 yr fall between 1.72$1011 and 0.711, with a median of 0.0131. The cases with CV larger than 0.1 are several hypothetical compounds, which belong to the “special group” for which the prediction is less accurate (discussed below). The detailed prediction results can be found in SI Table S7. b) Overall evaluation As a final evaluation, the mass fraction emitted predicted by the present model (long-term model only) are plotted against those predicted by Deng's fully analytical model for the 188 test cases (47 chemicals, 4 thicknesses) at four different time points: day 10, day 100, year 3, and year 15 (Fig. 7). For normal VOCs (solid circles in Fig. 7), the present model predictions are very accurate after 100 days but show slight deviations around 10 days. The overall R2 to the 1:1 line of the log mass fraction emitted is 0.943, 0.995, 0.999 and 0.999 with standard error (SE) of 0.216, 0.048, 0.013 and 0.009 for day 10, day 100, year 3 and year 15, respectively. For several hypothetical chemicals with intermediate D$K and relatively large K values which correspond to the middle region of Fig. 1, error is larger when using the prediction rules presented in Table 1, as presented in Fig. 7 by the crossing symbols. These chemicals are defined as “Special”, whose criteria are D·K < 2$105 m2/s and K > 1$106. Note that the “Special” group can include VOCs or SVOCs, but our results will only focus on the special VOCs which are designated as “VOC-Special”. The overall R2 to the 1:1 line including the “VOC-Special” chemicals is 0.917, 0.935, 0.961 and 0.976 with a higher standard error (SE) of 0.320, 0.218, 0.120 and 0.069 for day 10, day 100, year 3 and year 15, respectively. Their prediction could be further improved if needed, by introducing additional correction rules, which are explained in SI Section S7. Incorporating the additional correction rules, the accuracy of the overall prediction is improved: the overall R2 to the 1:1 line of the log mass fraction emitted becomes 0.968, 0.996, 0.997 and 0.994 with SE of 0.199, 0.051, 0.034 and 0.035 for day 10, day 100, year 3 and year 15, respectively; it is comparable to the initial accuracy prior to considering these special chemicals.

Fig. 5. Mass fraction emitted over 15 years of (A) (B) a-Pinene (D ¼ 1.20$1010 m2/s, K ¼ 5602), and (C) (D) n-Pentadecane (D ¼ 6.70$1014 m2/s, K ¼ 4.20$105) from a 15 cm-thick material. (A) (C) are shown in normal scales, while (B) (D) are shown in log scales.

L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

1-α

A

q _proxy ·D (s )

β / q _proxy

B

231

(R2 ¼ 0.968, SE ¼ 0.199) is the lowest among the four time points. Applying the short-term model for these chemicals can greatly improve the accuracy of the model predictions at day 10 (SI Fig. S4), increasing the R2 to 0.993 (SE ¼ 0.094). It should be noted that the prediction of the present model, even with the incorporation of the short-term model, is inaccurate for the initial stage of the emission process, which is generally from time zero to 10 days (Fig. 5) that would require a specific fit. This is because the fitting algorithm (which was used to derive the prediction rules) minimized the sum of squares of absolute values over 15 years. The points at the early stage have very small absolute values, so even with the same absolute errors, the relative errors between predicted and reference values would be larger compared to the points at the later stage. However, this parsimonious model is intended to estimate the emissions during consumer use, which usually happens at least 10 days after manufacturing. Thus, the inaccuracy of the model before 10 days has little importance for most consumer products.

3.3. Prediction of surface concentration

q _proxy ·D (s )

ln (β / β )

C

As described in the methods, the chemical concentration at the material surface can be easily calculated from the derivative of mass emitted (Eqn. (22)). Fig. 8A presents the resulting concentrations for hexanal and shows that the prediction is accurate for the long term kinetic, but that the predicted surface concentration may be severely under-predicted for the short term. This is directly related to the high inaccuracies in the predicted mass fraction emitted that was observed for the early stage of the emission process and was discussed in Section 3.2. Unlike the mass fraction emitted which must be equal to zero at time zero as given by Eqn. (20), the surface concentration given by Eqn. (22) cannot guarantee C0 at the beginning. To correct this, we therefore propose a simple adjustment applied between time zero and a certain time (tcutoff) to improve the accuracy of the predicted surface concentration (Cs) for this time period, while Eqn. (22) is only used after this period:


a ; C0 ; 0  t  tcutoff Cs ¼ CðL; tÞ ¼ min C0 ,pffiffi tþa

ln (q _proxy ·D) (s ) Fig. 6. Prediction of (A) a1, (B) b1, and (C) b2 based on q1_proxy2·D for the long-term model of mass fraction emitted.

As indicated above, a significant portion of the VOCs need a separate short-term model, as they are under-predicted by the long-term model at day 10 (Fig. 7A). Thus, the overall R2 for day 10

Cs ¼ CðL; tÞ ¼ C0 ,

(23a)

i 2 2 LK h a b2 D,eb1 Dt þ ð1  a1 Þb22 D,eb2 Dt ; 0 hm 1 1

t  tcutoff (23b) where tcutoff is determined by b2 and D:

Table 1 Prediction of parameters for mass fraction emitted (Eqn. (20)). Chemical groupa

Propertiesb,c

a1

1. SVOCs 2. VOCs with q12 D  1e-8eoverall (10 de15 yr) 3.1 VOCs with q12 D < 1e-8elong-term (100 de15 yr) 3.2 VOCs with q12 D < 1e-8eshort-term (10d-100d)

D$K  2$106 D$K < 2$106 and q12$D  1$108

N/A (the present model is invalid for SVOCs due to neglecting the sorption effects) max (1e1483$(q12$D)0.450; max (0.0137$(q12$D)0.209$q1; exp(0.0091*(ln(q12$D))2 0.85) q1) þ 0.2115*ln(q12$D) þ 2.5910)*b1

b1

b2

D$K < 2$106 and q12$D < 1$108

max (1e1483$(q12$D)0.450; 0.85)

max (0.0137$(q12$D)0.209$q1; q1)

exp(0.0091*(ln(q12$D))2 þ 0.2115*ln(q12$D) þ 2.5910)*b2

D$K < 2$106 and q12$D < 1$108

1e708$(q12$D)0.50

0.0158$(q12$D)0.240$q1

0.0820*(q12$D)0.2497*b1

A special treatment is proposed as a more accurate alternative for hypothetical special chemicals with D$K < 2$105 and K > 1$106 (SI Section S7). The unit for D$K is m2/s, and the unit for q21$D is s1. c To determine the critical value of D$K to distinguish “VOCs” and “SVOCs”, the prediction rules 1 & 2 were applied to all 132 test cases separately. After careful examination of the results, 2$106 was selected as the critical value to avoid any large divergence between our simplified solution and Deng's complex solution for all 132 test cases. a

b

232

L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

Fig. 7. Comparison of mass fraction emitted of 264 test cases between the present model and the original full model at day 10, day 100, year 3 and year 15.

Fig. 8. Surface concentration over 15 years of (A) hexanal (D ¼ 7.65$1011 m2/s, K ¼ 3289) and (B) benzaldehyde (D ¼ 8.16$1014 m2/s, K ¼ 10565) in a 15 cm-thick material.

tcutoff ¼

0:5 b22 ,D

(24)

And the parameter a satisfies the following relationship:

  a ¼ C L; tcutoff C0 ,pffiffiffiffiffiffiffiffiffiffiffiffi tcutoff þ a

(25)

where C(L,tcutoff) is the surface concentration at tcutoff calculated using Eqn. (23b). Here only the long-term model (Table 1, 2nd and

3rd rows) was used to calculate the parameters a1, b1, b2 for all chemicals using Eqn. (23b), and the introduced correction of Eqn. (23a) ensures a good fit at times lower than 100 days in all cases. Fig. 8A illustrates the surface concentrations of hexanal in a 15 cm-thick material predicted using Eqns. (23)e(25) and Eqn. (22), respectively. It shows that the prediction using only Eqn. (22) reaches saturation at about 19 days, i.e., the predicted Cs/C0 is almost constant in the first 19 days, leading to significant underestimation for this period. This results from the underestimate of the mass emitted in the early stage, which is due to a lack of exponentials representing the very early kinetics. In contrast, the

L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

233

Fig. 9. Comparison of the fractional surface concentration (Cs/C0) of 188 test cases between the present model and the original full model at day 10, day 100, year 3 and year 15. Values below 1$1015 are not shown.

adjustment using Eqn. (23a) can perfectly replicate the surface concentration for the early stage, which greatly improves the accuracy of the overall prediction. Moreover, compared to the fully analytical model, the present model has an advantage that it can guarantee Cs ¼ C0 at time zero. The fully analytical model, in certain cases, requires a very large number of terms to obtain an accurate Cs at the beginning. For example, as shown in Fig. 8B, the surface concentration of benzaldehyde predicted by the fully analytical model using 5000 terms is wrong by an order of magnitude at time zero. In this case, the present model is even better than the fully analytical model, in terms of both accuracy and simplicity. Using Eqns. (23)e(25), we predicted the surface concentrations over 15 years for the 188 test cases and compared them to the reference concentrations calculated by the fully analytical solution (Deng and Kim, 2004). Detailed comparison for each test case can be found in SI Table S8, and Fig. 9 summarizes the comparison at four different time points: day 10, day 100, year 3 and year 15. It shows that the present model's predictions perfectly match the fully analytical model predictions, except for several chemicals at day 10, whose deviations are within one order of magnitude. In fact, the predicted and reference surface concentrations for these chemicals at day 10 are already so low that they can both be viewed as negligible. In conclusion, the results demonstrate that the present parsimonious model can accurately predict the surface concentration for VOCs with a wide range of physiochemical properties and for a wide range of material thicknesses.

key parameters. The key chemical- and material-specific parameters include the material-phase diffusion coefficient D, the material/air partition coefficient K, and the initial concentration in the material C0. Several methods are available to estimate these parameters. Both D and K can be measured experimentally, and the various methods for VOCs have been reviewed extensively by Liu et al. (Liu et al., 2013). Besides experimental methods, empirical correlation methods are also available to estimate D and K, which have been reviewed by Guo (Guo, 2002b) and Holmgren et al. (Holmgren et al., 2012). The empirical correlation methods mainly predict the values of D and K as functions of vapor pressure, molecular weight, molar volume or Abraham solvation parameters. However, these empirical correlations generally require fitting coefficients that are only available for certain types of materials and compound groups, which limit their application to less studied materials or compound groups. The initial concentration C0 can be simply estimated from the composition data reported by the manufacturer of the material (Xu and Little, 2006), or it can be directly measured by extracting the target compounds from the material by solvent or heat, which has been reviewed by Liu et al. (Liu et al., 2013). Alternatively, C0 can also be estimated by fitting the experimentally measured air concentration data to model predictions by numerical methods (Little et al., 1994; Yang et al., 2001b).

4. Application example 3.4. Estimation of key parameters To apply the present parsimonious model to other chemicalmaterial combinations, it is important to accurately estimate the

To illustrate how the approach can be easily applied, we present a short example for a VOC with both short-term (10e100 days) and longer-term kinetics (100 days-15 years). The chemical chosen is nPentadecane, and Table 2 shows how the release rate and surface

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L. Huang, O. Jolliet / Atmospheric Environment 127 (2016) 223e235

Table 2 Determination of the released mass fraction of n-Pentadecane in vinyl flooring, with D ¼ 6.7$1014 m2/s and K ¼ 4.20$105 (Cox et al., 2002). Volume (V), ventilation rate (Q), material surface area (A) and convective mass-transfer coefficient (hm) used the data for a typical North American home: V ¼ 277 m3, Q ¼ 0.79 h1 ¼ 0.0608 m3/s, and A ¼ 113.6 m2, hm ¼ 8.8 m/h ¼ 0.0024 m/s (Rosenbaum et al., 2015; Wenger et al., 2012). Material thickness L is assumed to be 1.5 cm which is 0.015 m. Calculation steps: (1) (2) (3) (4) (5)

Determine h0m using Eqn. (13): h0m ¼ 4.39$104 m/s Calculate q1_proxy using Eqn. (17): q1_proxy ¼ 104 m1 D$K ¼ 2.81$108 < 2$106 m/s, so it meets the VOC criterion. q21_proxy$D ¼ 7.29$1010 < 108 s1, so it needs a long-term (100 de15 yr) model and a short-term (10e100 d) model. Determine the long-term model: using Table 1 Row 3, a1 ¼ 0.886, b1 ¼ 116, b2 ¼ 1010, b21$D MðtÞ M0

10

¼ 0:89,ð1  e9:0,10

(6) Determine MðtÞ M0

the

,t Þ

þ 0:11,ð1  e6:8,10

short-term 9

¼ 0:98,ð1  e4:4,10

,t Þ

model:

8

using 6

þ 0:02,ð1  e1:1,10

¼

9.0$1010,

b22$D ¼ 6.8$108

,t Þ; 100d < t < 15yr

Table

1

,t Þ; 10d

 t  100d

Row

a1 ¼ 0.981, b1 ¼ 255, b2 ¼ 4000, b21$D ¼ 4.4$109, b22$D ¼ 1.1$106

4,

(7) To calculate surface concentration,first determine tcutoff using Eqn. (24) and parameters obtained in step (5): tcutoff ¼ 0.5/(6.8$108) ¼ 7.30$106 (s) 0

(8) Determine the long-term Cs using Eqn. (23b) with LK=hm ¼ 1:44,107 (9) Calculate the parameter a using Eqn. (25): a ¼ 233. (10) Determine the short-term Cs using Eqn. (23a):

Cs ðtÞ C0


¼ min

pffi233 ; 1 t þ233

Cs ðtÞ C0

10

¼ 0:011,ð1  e9:0,10

,t Þ

þ 0:11,ð1  e6:8,10

8

,t Þ; t

 7:30$106 s

 ; 0  t  7:30  106 s


(11) The air concentration y(t) can also be calculated using Eqn. (11), with : K,

1

 ¼ 1:95$106 y(t) ¼ 1.95$106 Cs(t), with Cs(t) given above in steps (8) or (10).

1þAhQm

concentration are easily determined from chemical properties. Steps one to four enable us to determine the long term rate constant of q1_proxy 2$D ¼7.29$1010, which means that the long term release kinetic is happening on more than 1/q1_proxy 2$D ¼ 43 years for this compounds. Steps five and six provide the long-term and short-term equations expressed as a sum of only two exponentials. Steps seven to ten yield the surface concentrations, whereas the final step eleven provides the air concentration. However, due to our quasi-steady-state assumption, the air concentration predicted by step eleven cannot capture the concentration trend at the very beginning of the emission (i.e., the first 10 h), where the air concentration rises from zero to the peak concentration. Table 2 illustrates how releases, surface concentrations and indoor air concentrations can be easily characterized by the different sets of two exponentials. The explicit functions of exposure duration can be used to perform sensitivity studies with respect to model parameters, and also can be used as inputs for LCA of flooring materials or near-field exposure estimates in a high-throughput context. 5. Future research needs for SVOCs As mentioned above, the present parsimonious model is only valid for VOCs. However, SVOCs in the indoor environment, such as plasticizers, flame retardants and biocides, are gaining increasing attention due to their relatively high concentrations in building materials and consumer products and their potential health effects (Liang and Xu, 2015; Little et al., 2012; Xu and Little, 2006; Xu et al., 2012). Therefore, a parsimonious model for SVOCs will also be needed. In contrast to the VOCs, the SVOCs present at much higher concentrations in the source materials and are released very slowly, so their concentrations in the source materials can be considered constant over time (Liang and Xu, 2015; Little et al., 2012; Xu et al., 2012). In addition, the SVOCs present in the indoor air can adsorb to various interior surfaces such as furniture, ceiling and walls, and subsequently diffuse into the materials. This process is likely to be also controlled by convective mass transfer and Fickian diffusion (Liang and Xu, 2015), as a reverse process of the VOC emissions. This complex SVOC system can be solved by numerical methods (Liang and Xu, 2015). However, it may be simplified by similar approaches as the VOC model, as shown in the present paper, since the SVOC model basically includes a constant source (SVOC emission) and a reverse process of the VOC emission (surface

adsorption). We are currently testing the feasibility of such approaches. 6. Conclusions In conclusion, the results demonstrate that the complex full model for mass fraction emitted and surface concentration can be approximated by the present parsimonious model with reasonable accuracy, especially for the long term (typically after 10 days). The main advantage of the present model is that it eliminates the need to solve transcendental equations or summing infinite series, which greatly reduces the computational burden and thus can facilitate high-throughput screening of chemical emissions or exposure potentials. These models can now be coupled with recently available chemical-product databases such as the Chemical-Product Categories Database (Dionisio et al., 2015) to calculate potential emissions for identified chemical-product combinations and to determine Product Intake Fractions - the fraction of a chemical encapsulated in the articles that is taken in by the exposed population (Jolliet et al., 2015). One limitation of the present model is that it is only valid for a specific time scale, which is up to 15 years. If any information beyond 15 years is needed, a new set of prediction rules for a1, b1, and b2 can be easily determined for longer time scales by only changing the prediction coefficients without changing the model structure. Several other developments will be needed in the future to complement the present work and make it more broadly applicable: a) The approach needs to be generalized to objects with multiple layers, b) the determined releases and surface concentrations will need to be related to inhalation and dermal exposure models, c) the input chemical properties, in particular the diffusivity and the materialeair partition coefficient need to be made available for a broader set of compounds using existing or newly developed QSARs, and d) a parsimonious model considering surface adsorption needs to be developed for SVOCs. Acknowledgments We thank Alexi Ernstoff (Technical University of Denmark) for her comments and English correction. Funding was provided by US EPA contract EP-14-C-000115 on Development of Modular Risk Pathway Descriptions for Life Cycle Assessment, the University of Michigan Risk Science Center, and the Long Range Research

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