C-Depth Method to Determine Diffusion Coefficient and Partition

Sep 8, 2015 - ACS eBooks; C&EN Global Enterprise .... Polychlorinated biphenyls (PCBs) have been found to be persistent in ... Sensitivity analysis in...
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C‑Depth Method to Determine Diffusion Coefficient and Partition Coefficient of PCB in Building Materials Cong Liu,† Barbara Kolarik,*,‡ Lars Gunnarsen,‡ and Yinping Zhang† †

Department of Building Science, Tsinghua University, Beijing 100084, China Aalborg University, Danish Building Research Institute, Department of Construction and Health, 2450 Copenhagen, Denmark

‡

S Supporting Information *

ABSTRACT: Polychlorinated biphenyls (PCBs) have been found to be persistent in the environment and possibly harmful. Many buildings are characterized with high PCB concentrations. Knowledge about partitioning between primary sources and building materials is critical for exposure assessment and practical remediation of PCB contamination. This study develops a C-depth method to determine diffusion coefficient (D) and partition coefficient (K), two key parameters governing the partitioning process. For concrete, a primary material studied here, relative standard deviations of results among five data sets are 5%−22% for K and 42−66% for D. Compared with existing methods, C-depth method overcomes the inability to obtain unique estimation for nonlinear regression and does not require assumed correlations for D and K among congeners. Comparison with a more sophisticated two-term approach implies significant uncertainty for D, and smaller uncertainty for K. However, considering uncertainties associated with sampling and chemical analysis, and impact of environmental factors, the results are acceptable for engineering applications. This was supported by good agreement between model prediction and measurement. Sensitivity analysis indicated that effective diffusion distance, contacting time of materials with primary sources, and depth of measured concentrations are critical for determining D, and PCB concentration in primary sources is critical for K.

1. INTRODUCTION Polychlorinated biphenyls (PCBs) are classified as persistent organic pollutants (POPs) due to their resistance to degradation, toxicity, and bioaccumulation. Before they were banned in the 1970s, the worldwide production of these compounds was estimated to be 1.5 million metric tons between 1930 and 1971.1 Recently, PCBs were classified as carcinogens in humans.2 This and other adverse effects of this class of pollutants on the nervous,3−6 endocrine,7−9 and reproductive10,11 systems greatly threaten the health of people exposed to them. Primary sources, which are products originally containing PCBs, include electrical transformers and capacitors as well as soft and flexible construction products. Due to their chemical properties and low volatility, PCBs migrating from the primary sources can readily partition to many building materials, such as concrete12,13 and paint.13,14 The partitioning to building materials can proceed in two ways: diffusion via direct contact with primary sources and adsorption from indoor air contaminated by PCBs emitted from primary sources. The materials contaminated by diffusion (direct contact) are called secondary sources, while materials contaminated by adsorption from contaminated air are called tertiary sources.15 These slowly developed secondary and tertiary sources are in reality reservoirs of PCB which in a dynamic indoor climate sometimes act as sources and sometimes as sinks. In this paper, they are always referred to as sources. The partitioning to materials is critical because it can directly influence PCB concentration in the air, which leads to exposure through © 2015 American Chemical Society

inhalation as well as via oral intake and dermal contact (due to partitioning to dust and adsorption on surfaces including food and clothing). For exposure assessment based on model prediction, the partitioning is required to be included; for practical intervention, a clear understanding of the partitioning can help to determine how much secondary and tertiary PCBcontaminated material should be removed to meet the requirements concerning indoor air quality. Figure 1 illustrates two key parameters identified to describe the partitioning process for building materials as secondary sources by diffusion: (1) the diffusion coefficient of PCB in building materials, D; (2) the partition coefficient between the primary source and the adjacent material, K. For a primary PCB source−building material combination, D is the same independently of whether the material acts as a secondary or a tertiary source. K, however, is different: for a secondary source, K indicates the ratio of PCB concentration in the primary source to the concentration in the layer of adjacent building material in contact with the primary source, while for a tertiary source, K indicates the ratio of PCB concentration in air close to the material surface to the concentration in the surface of the material. Guo et al.16 and Liu et al.17 estimated these two parameters for a series of PCB congeners in building materials which act as tertiary sources. They used a nonlinear regression Received: Revised: Accepted: Published: 12112

February 26, 2015 September 1, 2015 September 8, 2015 September 8, 2015 DOI: 10.1021/acs.est.5b03352 Environ. Sci. Technol. 2015, 49, 12112−12119

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Environmental Science & Technology

where C (mg/kg) is the PCB concentration in building materials such as concrete, D (m2/s) is the diffusion coefficient of PCB in the material, Cm0 (mg/kg) is the PCB concentration in a primary source, K is the partition coefficient in the primary and secondary source, L (m) is effective diffusion distance within which diffusion from the primary source dominates over absorption from the polluted air. D and K are assumed to be constant in terms of space and time here. In fact, these two parameters are subject to influence of environmental factors such as temperature and humidity. The boundary condition at x = 0 implies assumption of constant concentration of PCBs in primary sources. The analytical solution to eqs 1−3 is derived,27

Figure 1. Schematic diagram of the PCB migration in secondary sources. Two key parameters are identified: the diffusion coefficient, D, and the partition coefficient, K. Cm0 is the PCB concentration in a primary source, and C is the PCB concentration in secondary contaminated building materials.

2 2 2 ⎛ ∞ e−(Dt / L )(m − 0.5) π sin (m − 0.5)π x Cm0 ⎜ L C(x , t ) = 1−2∑ K ⎜⎜ ( m 0.5) − π m=1 ⎝

(

2. METHODOLOGY 2.1. Method Development. First, a mass balance model was developed to describe the migration process, as illustrated in Figure 1: PCBs from a primary source such as PCBcontaining sealant migrate to a building material which had direct contact with it. The mass transfer equation of the PCB in the building material is in accordance with Fick’s second law of diffusion, as follows:

C(x , t ) =

⎛ C(x , t ) x⎞ = SL ·sin⎜0.5π ⎟ + INT ⎝ Cm0 L⎠

(6)

SL = −

4 −Dt / L2(0.5π )2 e Kπ

(7)

INT =

1 K

(8)

(1)

(2)

eq 6 shows a linear relationship between C(x,t)/Cm0 and sin(0.5πx/L), meaning that a nonlinear correlation has been simplified into a linear one. If the input parameters required to conduct such linear fitting (L, t, x and C(x,t)/Cm0) are all known, then one can linearly fit C(x,t)/Cm0 as a function of sin(0.5πx/L). The intercept of the obtained linear correlation

The boundary conditions are as follows: C(x = 0) = Cm0/K =0 x=L

(5)

where,

The initial concentration is as follows:

∂C ∂x

2 2 Cm0 ⎛ ⎛ 4 x ⎞⎞ ⎜1 − e−Dt / L (0.5π ) sin⎜0.5π ⎟⎟ ⎝ π K ⎝ L ⎠⎠

Dividing both sides of eq 5 by Cm0 yields the following:

2

C(x , t = 0) = 0

⎟⎟ ⎠ (4)

In eq 4, the diffusion coefficient (D) and the partition coefficient (K) are two key parameters. To obtain these two parameters, a usual step is to fit experimentally obtained concentration (C(x,t)) to the model described as eq 4, but as stated before, the nonlinearity of eq 4 would lead to unstable and nonunique results. In an analogous case of heat transfer, Grigull and Sander28 stated in Section 6.7 that it is possible to use the one-term approximation when Fo is higher than a critical value, where Fo, the Fourier number, is a dimensionless parameter of time. When examining the emission of gas pollutants from building materials, Xiong et al.29 obtained an analytical solution in the form of infinite exponential series similar to eq 4. They stated that when the duration of the emission process (t) is sufficiently long, only the first term in the series becomes significant. The other terms can therefore be neglected, and the original nonlinear problem can be transformed into a linear problem.30 We use the same idea to transform the nonlinear problem in eq 4 to a linear one as shown in eqs 5 and 6. When t is long enough, like in this case where materials had been in contact with PCB sources for over 40 years, only the first term of the infinite exponential series in eq 4 becomes significant for part of or the whole material, i.e., the terms from m = 2 to m = ∞ are negligible.

method in their studies fitting observed data to a model developed for the mass transfer scenario. As stated by Guo et al., the main limitation of the nonlinear regression is that it is not possible to obtain unique parameter estimation. Furthermore, to avoid unstable results from the data fitting, exponential correlations for D and K among PCB congeners should be assumed, and the value of one of the exponential power parameters needs to be known as input. As far as the authors know, the papers by Guo et al. and Liu et al. are the only work to examine these two key parameters of PCBs in building materials, while most previous efforts focus on diffusion and/or partition in sediment,18−21 soil,22,23 and airborne particles.24−26 The objectives of this study were therefore (1) to develop a new linear-regression based method (named as C-depth method) that would overcome the aforementioned limitations to determine the diffusion coefficient and partition coefficient of PCBs in building materials acting as secondary sources; (2) to examine the sensitivity of the obtained parameters D and K on the following input parameters for the C-depth method: effective diffusion distance in building materials, contact time with primary sources, depth of measured concentration, and measured PCB concentrations.

∂C ∂C =D 2 ∂t ∂x

) ⎞⎟

(3) 12113

DOI: 10.1021/acs.est.5b03352 Environ. Sci. Technol. 2015, 49, 12112−12119

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the critical depth increases as Fom increases. When Fom is higher than 0.12, the critical relative depth is one, which means that measurement at any depth can be used in the C-depth method. The criteria used, i.e., limit of tolerable error, affects the consequent condition under which C-depth method is suitable. For example, in the analogous case of heat transfer,28 when the absolute error resulting from one-term approximation is required to be less than 0.01, Fo needs to be higher than 0.24. While in the present study, as stated above, when the difference between one-term approximation and complete solution is required to be less than a factor of 2 for the whole material, Fom (subscript m denotes mass transfer, instead of heat transfer) needs to be higher than 0.12. Whether a sampling depth is in the shadowed area or not can be known only after diffusion coefficient is determined, as it is needed to calculate Fom. Therefore, at this stage, we cannot perform such evaluation. The horizontal solid bars for concrete, Masonite, and Wooden frame are already plotted in Figure 2 to avoid repeated plotting. It will be further discussed in Section 4.1, after diffusion coefficients are obtained. 2.4. Measurement of PCB Concentration in Concrete, Masonite, and Wooden Door Frame. On a housing estate constructed in stages between 1970 and 1974 in Farum, Denmark, PCB-containing sealants were used in one section (approximately 300 of 1645 apartments) around indoor door frames and between some of the concrete panels in the inner walls. As a part of a large remediation process, concentrations of PCB in sealants, air, and different building materials like concrete, Masonite and wooden door frames were measured. The measurements included six PCB congeners: PCB-28, PCB52, PCB-101, PCB-118, PCB-128 and PCB-153, whose selected properties are listed in Table 1. PCB concentrations (C(x,t))

(INT) can be used to determine K, and the slope (SL) can be used to determine D by combining it with the obtained K: K=

1 INT

D=−

⎛ −SL ·Kπ ⎞ 1 ⎟ ln⎜ 2 ⎠ 4 (0.5π /L) t ⎝

(9)

(10)

2.2. Error Analysis. The standard error of K (σK) and D (σD) can be calculated from the standard error of INT (σINT) and SL (σSL), according to the error-propagating theory. The relative standard error of K (RSEK) and D (RSED) can also be obtained. If there are multiple determinations of K and D, then the relative standard deviation (RSD) can be determined. The equations to calculate σK, σD, RSEK, RSED, and RSD are included in the Supporting Information (SI). 2.3. Dimensionless Condition under Which the CDepth Method Applies. A prerequisite for the application of the C-depth method using eq 4 is that only the first term of the infinite exponential series in eq 4 is significant, i.e., the terms from m = 2 to m = ∞ may be assumed negligible. If the prerequisite is satisfied, then C(x,t)/(Cm0/K) predicted by eq 5 can be expected to be close to that found by eq 4. It can be seen that C(x,t)/(Cm0/K) is a function of two grouped parameters: x/L and Fom = Dt/L2 (the Fourier number). In the present study, we suggest that the terms from m = 2 to m = ∞ in eq 4 are negligible when C(x,t)/(Cm0/K) predicted by eq 5 differs from that of eq 4 by less than a factor of 2. For a given Fom, concentration profile is calculated using both eq 4 and eq 5. An critical x/L, designated as (x/L)0, exists so that the difference between the two calculated profiles is less than a factor of 2 within the range of 0 < x/L < (x/L)0, and the difference beyond the range is larger than a factor of 2. Then (x/L)0 is plotted against Fom, as Figure 2 of the condition under which the Cdepth method applies. If the relative depth (x/L) at which the measurement is conducted falls into the shadowed area in Figure 2, then the corresponding prediction by eq 5 differs from that of eq 4 by less than a factor of 2. It can be seen that

Table 1. Properties of Six PCB Congeners Identified in Sealants at 25 °C congeners

MW g/mol

log(KOA)a

log Vpb (Pa)

PCB-28 PCB-52 PCB-101 PCB-118 PCB-138 PCB-153

257.5 292.0 326.4 326.4 360.9 360.9

8.09 8.62 9.51 10.0 10.5 10.4

−1.5 −1.7 −2.4 −3.0 −3.3 −3.1

a Octanol/air partition coefficient (KOA) from Weschler and Nazaroff, 201031 bVapor pressures (Vp) are the results of method B in the study by Fischer et al. 199232

were measured at various depths (x) in these three materials. Results of these measurements are presented in Table S1. These data were used for the model development, and are referred to in this article as concrete NO.1, Masonite, and wooden door frame. More measurements of PCB in concrete and adjacent sealant taken at later time from the same housing estate were used for model validation. For these measurements, sampling of concrete was conducted in two ways, by drilling and chiselling, with two repetitions for each. These data are therefore referred as NO.2 with A or B corresponding to first and second repetition and method of sampling given after dash (e.g., NO.2A−chisel). Details about samplings are provided in the SI. For concrete NO.1, the measurement closest to the sealant/ concrete interface was made at a depth of 0.32 cm, and the maximum depth was 4.47 cm. As the concentration at the

Figure 2. Condition under which the C-depth method applies (the shadowed area). The horizontal solid bars indicate the relative depth at which PCB measurements were conducted for concrete NO.1 (5 points), Masonite (3 points) and wooden door frame (2 points) in the present study. The length of the horizontal solid bars indicates the range of Fom calculated for the PCB congeners in each material. 12114

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Environmental Science & Technology Table 2. Fitted Diffusion Coefficients (D) and Partition Coefficients (K, Sealant/Material) of PCB in Concrete

a The numbers on the first line for PCB congeners are for concrete NO.1. The other four numbers on the second line are for concrete NO.2. From left: NO.2A−chisel, NO.2B−chisel, NO.2A−drill and NO.2B−drill. bResults obtained by Guo et al.16 cResults obtained by Liu et al.17 dThe value of D was directly given for PCB-52 in Table 6.5 of Guo et al. D for the other PCB congeners are calculated by the correlation in Guo et al.: D_PCB-52/ D = (MW/MW_PCB-52)6.5. eThe values are not given. fThe value is the average of D obtained by the two methods in Table 5 of Liu et al. gThe fitted values are negative, therefore not shown. hNot determined due to data scarcity.

All the regression coefficients (R2) are bigger than 0.7. The values of SL, INT, σINT and σSL are listed in the Table S2. For concrete, the relative standard error of K (σK/fitted value, RSE) is smaller than 45% for all the five data sets. Since concrete NO.1 contacts with a sealant different from that NO.2 contacts with, it makes no sense to compare K between these two cases, and we discuss them therefore separately. Taking concrete NO.2 first, the results of K from the four data sets are reasonably consistent, giving a relative standard deviation (RSD) of the four fitted values of 5%−22% for PCB-28, 52, 101, and 118. The averaged K of the four data sets varies by less 20% among these four congeners, indicating similar affinity of these congeners with concrete. Results for concrete NO.1 exhibit a similar feature. Diffusion coefficient, D, is sealant-independent, which justifies pooling of results for the two concrete samples. Despite large relative standard error, the fitted values of D agree well between the five data sets for each of the congeners. The relative standard deviation of the fitted values is in a range of 42%−66% for PCB-28, 52, 101, 118, and 138. The large relative standard error of D is further discussed in Section 4.1. To further validate the results obtained by the linear fitting, a two-term approach is developed by adding the term of m = 2 in eq 6 into eq 7. The model development is detailed in the SI. Keeping one more term in the infinite series in eq 6, the twoterm approach could provide a reference to evaluate the results by the linear fitting, i.e., C-depth method. The results by the two-term approach are provided in the Table S3. As for concrete NO.1, both K and D obtained by the two-term approach were smaller than these obtained by C-depth method, with up to 30% of mean fractional error (MFE, see SI for definition) for K and up to 40% for D, the difference varying slightly between congeners. The differences were higher for concrete NO.2, where K and D obtained by the two-term approach were respectively up to 50% and 70% lower than those obtained by C-depth method, except for D in NO.2B− drill. For D in NO.2B−drill, the MFE between the two approaches was however up to 120%. When comparing average of the four fitting values of the four data sets for concrete NO.2 between these two approaches, the MFE of K and D are smaller than 40% and 60%, respectively.

maximum depth was about 2 orders of magnitude lower than that of the minimum depth, in our calculations L (effective diffusion distance) was set to 5 cm for concrete. For a similar reason, L is set to 4 cm for concrete NO.2, 5 cm for Masonite, and 3 cm for wooden door frame. PCB concentrations in the sealants determined Cm0 and the time from erection of the buildings to sample taking (approximately 40 years) is used as input for t in eq 8. The PCB concentrations in sealants and building materials are shown in Table S1. Environmental factors such as temperature and humidity impact D and K. Since these factors have not been monitored since the installation of PCB-containing materials, accurate capture of their influence is difficult. Therefore, the results obtained here are interpreted as averages within ranges of relevant environmental factors.

3. RESULTS 3.1. Determination of K and D of PCBs in Concrete, Masonite, and Wooden Door Frame. Table 2 and Table 3 show the results of D and K for six PCB congeners in concrete, Masonite, and wooden door frame obtained by linear regression between C(x,t)/Cm0 and sin(0.5πx/L) (eqs 8−12). Table 3. Fitted Diffusion Coefficients (D) and Partition Coefficients (K, Sealant/Material) of PCB in Masonite and Wooden Door Frame wooden door framea

Masonite

−3

PCB PCB-28 PCB-52 PCB-101 PCB-118 PCB-138 PCB-153

K (fitted value ± σK) 19 34 59 77 118 139

± ± ± ± ± ±

4.8 12 23 35 62 68

D × 1014(m2/s) (fitted value ± σD) 13 10 9.7 8.0 6.6 7.2

± ± ± ± ± ±

37 50 53 63 71 67

K × 10 (fitted value) 1.4 1.6 1.5 1.7 1.4 1.4

D× 1014 (m2/s) (fitted value) 6.5 6.4 6.4 6.3 7.3 6.8

a

As there are only two data points available for the linear regression, the standard deviations of slope and intercept are zero. 12115

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Figure 3. Comparison of predicted PCB concentration in concrete NO.1, Masonite, and wooden door frame with the measurement. t = 40 yrs for the three materials, L = 5 cm for concrete and Masonite, and L = 3 cm for wooden door frame. (a): PCB-28 (3 chlorines); (b): PCB-52 (4 chlorines); (c): PCB-101 (5 chlorines); and (d): PCB-138 (6 chlorines).

the obtained D, K and the other known parameters (L, t, Cm0, and x), we can predict PCB concentrations at various depths in concrete NO.1, Masonite, and wooden door frame with the analytical solution expressed as eq 4. Figure 3 shows the comparison of the predicted with the measured concentrations for PCB-28 (three chlorines), PCB-52 (4 chlorines), PCB-101 (5 chlorines), and PCB-138 (6 chlorines), which can serve as an evaluation of D and K determined by linear regression. The predicted PCB concentrations in concrete, Masonite, and wooden door frame agree reasonably well with the measurement results. The comparison for the other PCB congeners, included in Figure S1, also exhibits reasonable agreement. This indicates that the method introduced in the present study determines D and K satisfyingly, especially with regard to engineering applications. In addition, the present method can give unique parameter estimates from a single data set, and do not need the assumed correlations for D and K among PCB congeners as input, which is required in the previous methods.16,17 A fair amount of sampling and chemical analysis work, however, is required to obtain enough data for the proposed method.

For comparison, diffusion coefficients estimated by Guo et al.16 and Liu et al.17 are also included in Table 2. The results of the present study for concrete differ from those of the two studies by about 1 order of magnitude. The difference could be attributed to both methods, such as assumed correlation of K and D among congeners in their studies and uncertainty of results of the current method. In addition, the properties of concrete, such as composition, porosity, and heterogeneity, might be different between the present study and the two other studies. Further investigation, e.g., model development, measurement accuracy, and material characterization, is needed to narrow down this gap. As shown in Table 3, for Masonite, K increases as the vapor pressure of PCBs decreases, indicating the stronger affinity of less volatile congeners for Masonite. In a wooden door frame, K changes only slightly among congeners, similar to that for concrete. It should be noted that the sealants (the primary PCB sources) with which the three investigated materials had contact have different PCB concentration profiles, which makes a direct comparison between these materials impossible. As mentioned above, the properties of the material have a significant influence on the estimated values of K; this issue is however beyond the scope of the present study. 3.2. Comparison of the Predicted with the Measured PCB Concentrations in Specific Building Materials. Using

4. DISCUSSION 4.1. Whether the C-Depth Method and Fickian Diffusion Apply. Since diffusion coefficients have been 12116

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frame is less than 10%, results not shown here. It means that the effective diffusion distance has significant impact on the obtained diffusion coefficient (D). The changes of K in concrete NO.1, Masonite, and wooden frame are less than 5%, when L varies by 10%. In fact the L for concrete could be considered infinitethe walls in reality are much longer than the effective diffusion distance used in the paper. At some distance from the primary source (beyond the effective diffusion distance), the tertiary polluting processes become more dominant than the secondary mechanism of diffusion from primary source. At some distance from the primary source (beyond the effective diffusion distance), the tertiary polluting processes (adsorption from contaminated air) become more dominant than the secondary polluting mechanism of diffusion from primary source. The tertiary polluted surfaces act more or less equally at all distances from primary sources, and are also developing with time. One interpretation of L could be the distance from primary source where tertiary polluting processes becomes more dominant than secondary diffusion process. This distance in fact may be close to the chosen 5 cm. It could also be somewhat longer. As an illustration, Table S4 shows that when L increases by 10% for concrete (5.5 cm), the estimated D becomes closer to findings by Guo et al. and Liu et al. listed in Table 2. On the basis of eqs 9 and 10, the contacting duration (t) only impacts D, not K. Figure S2 shows that when it varies by 50%, the change of D is 33%−100%. The impact of PCB concentration in primary sources (Cm0) on K shows a linear pattern. When Cm0 varies by 50%, the change of K is 50%. The influence of Cm0 on D is smaller than 10% when Cm0 varies by 50%. The middle point of a depth range for sampling is used as a representative depth as reported in Table S1. As described in the SI, for NO.2 concrete by drilling, drill dust was collected after approximately 1 cm of drilling. To test the impact of choice of depth on results, the depths for NO.2-drill reported in Table S1 is increased by 0.5 cm, which could be upper limits of depth for each sampling. A newly obtained set of D and K were compared to those for the original choice of depth. The results, not shown here, indicate that K varies by less than 30%, and D by more than 100%. It means that choice of depth has significant influence on D. Due to the lack of necessary information on sampling, such an analysis was not performed for the other data set. Therefore, an accurate determination of L, t, and depth of measured concentrations is critical for obtaining an accurate D, and an accurate determination of Cm0 is critical for K. In addition, having more data in the shadowed area of Figure 2 (the domain in which the C-depth method applies) can also reduce the error of D and K. As shown in Figure 2, since the area close to the source−sink interface tends to be in the application domain, rather than that far away from the interface, samplings for as many layers as possible are recommended to be conducted near the interface, in order to get as much data at various depths close to the interface as possible. 4.3. Practical Application of the Results. The buildings with PCB in sealants, double glazed windows, and flooring systems remained in use, despite the fact that many countries and intergovernmental organizations have now banned or severely restricted the use, transport, handling, and disposal of PCBs.37,38 It is therefore of great importance to ensure proper waste handling during renovation and demolition of the buildings built or renovated in the period when PCBs were used. As shown in the present study and other investiga-

obtained in Section 3.1, whether a sampling depth is in the shadowed area of Figure 2 or not can be evaluated now. As illustrated by horizontal solid bars in Figure 2, only one data point is in the shadowed area for concrete NO.1, whereas there are two for Masonite. This might be the reason that the standard error of D (σD) is much higher than the fitted value of D for these two materials. When the two data points in the shadowed area of Figure 2 were used only in the C-depth method for Masonite, negative values of D were obtained. It might be because of the measurement error of these two data points. Moreover, the present method assumes constant D and K across each secondary material for each PCB congener. It is acknowledged that some materials might be heterogeneous and that the present method might not be suited to predict PCB concentrations inside heterogeneous materials in the centimeter scale. Furthermore, it should be noted that eq 1 implies justification of Fickian diffusion. Previous studies have indicated Fickian diffusion could be suitable for diffusion of chlorine ion33−35 and some volatile organic compounds in concrete. While in the case of transport of water in concrete, a term describing chemical reaction needs to be added to Fick’s equation if hydration occurs.36 PCBs, however, are generally nonreactive, which is partially why they are classified as persistent organic pollutants. Therefore, Fickian diffusion might be adequate for transport of PCBs in concrete. Further study is required to better address this issue. 4.2. Sensitivity Analysis. A sensitivity analysis of input parameters for the regression results (D and K) can help identify critical parameters and thus guide experimental design. Figure 4 shows the sensitivity of the obtained D and K of PCB

Figure 4. Sensitivity of D to 10% change in effective diffusion distance of concrete NO.1 (L). As D of PCB-153 is negative from the regression for concrete, the sensitivity analysis of D was only conducted for the other five congeners for concrete.

to the effective diffusion distance (L). The sensitivity of D and K to contacting duration with the sealant (t) and PCB concentration in the sealant (Cm0) is included in Figure S2. In addition, the influence of depth of measured concentrations, reported as the distance from the sealant in Table S1, is also examined. Figure 4 shows that when the distance (L) varies by 10%, the change of the obtained D can be up to 85% for D in concrete NO.1 and 20% in Masonite. The change of D in wooden door 12117

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Environmental Science & Technology tions,39,40 concentrations of PCB in the adjacent materials can exceed the limit for dangerous waste. It is therefore not only the primary sources, but also the secondary and tertiary contaminated surfaces that must be considered as such. Furthermore, exposure via contaminated air has been a growing issue in recent years41−44 and some countries, like Denmark, have introduced requirements for acceptable PCB air concentrations in PCB contaminated buildings.45 This has led to remediation processes with the aim to decrease PCB indoor air concentrations. However, in several buildings, removal of the primary sources as the only taken action has been shown to be insufficient for decreasing the indoor concentrations, due to the high impact of secondary and tertiary sources.46,47 As the secondary and tertiary sources are particularly expensive and cumbersome to get rid of, the accurate estimate of the polluted area is therefore essential for optimal planning of the renovation works and success of the remediation process. For both of these applications, namely identification of the strong secondary sources having a large impact on the indoor air concentrations and identification of material depth needed to be disposed as hazardous waste, C-depth method can be a simple and inexpensive tool substituting a number of otherwise needed expensive chemical measurements.

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two research groups to each another, and for making valuable suggestions for the present study. We thank Solveig Nissen from SBi/Aalborg University for language correction. C.L. and Y.Z. were supported by the Natural Science Foundation of China (Grant No. 51136002) and Tsinghua University Initiative Scientific Research Program (20121088010). B.K. and L.G. were supported by RealDania.

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(1) Pereira, M. D. Polychlorinated dibenzo-p-dioxins (pcdd), dibenzofurans (pcdf) and polychlorinated biphenyls (pcb): Main sources, environmental behaviour and risk to man and biota. Quim. Nova 2004, 27 (6), 934−943. (2) Lauby-Secretan, B.; Loomis, D.; Grosse, Y.; El Ghissassi, F.; Bouvard, V.; Benbrahim-Tallaa, L.; Guha, N.; Baan, R.; Mattock, H.; Straif, K. Carcinogenicity of polychlorinated biphenyls and polybrominated biphenyls. Lancet Oncol. 2013, 14 (4), 287−8. (3) Boix, J.; Cauli, O. Alteration of serotonin system by polychlorinated biphenyls exposure. Neurochem. Int. 2012, 60 (8), 809−816. (4) Miller-Perez, C.; Sanchez-Islas, E.; Mucio-Ramirez, S.; MendozaSotelo, J.; Leon-Olea, M. The polychlorinated biphenyls (pcbs) environmental pollutants and their effects on the nervous system and health. Salud Mental 2009, 32 (4), 335−346. (5) Polanska, K.; Jurewicz, J.; Hanke, W. Review of current evidence on the impact of pesticides, polychlorinated biphenyls and selected metals on attention deficit/hyperactivity disorder in children. International Journal of Occupational Medicine and Environmental Health 2013, 26 (1), 16−38. (6) Winneke, G. Developmental aspects of environmental neurotoxicology: Lessons from lead and polychlorinated biphenyls. J. Neurol. Sci. 2011, 308 (1−2), 9−15. (7) Masuda, Y. Health effect of polychlorinated biphenyls and related compounds. J. Health Sci. 2003, 49 (5), 333−336. (8) Rudel, R. A.; Perovich, L. J. Endocrine disrupting chemicals in indoor and outdoor air. Atmos. Environ. 2009, 43 (1), 170−181. (9) Zhou, J. M.; Qin, Z. F.; Cong, L.; Xu, X. B. Research progress of the endocrine disrupting activities of polychlorinated biphenyls. Chin. Sci. Bull. 2004, 49 (3), 215−219. (10) Govarts, E.; Nieuwenhuijsen, M.; Schoeters, G.; Ballester, F.; Bloemen, K.; de Boer, M.; Chevrier, C.; Eggesbo, M.; Guxens, M.; Kramer, U.; Legler, J.; Martinez, D.; Palkovicova, L.; Patelarou, E.; Ranft, U.; Rautio, A.; Petersen, M. S.; Slama, R.; Stigum, H.; Toft, G.; Trnovec, T.; Vandentorren, S.; Weihe, P.; Kuperus, N. W.; Wilhelm, M.; Wittsiepe, J.; Bonde, J. P.; Obelix, E. Birth weight and prenatal exposure to polychlorinated biphenyls (pcbs) and dichlorodiphenyldichloroethylene (dde): A meta-analysis within 12 european birth cohorts. Environ. Health Perspect. 2011, 120 (2), 162−170. (11) Meeker, J. D.; Hauser, R. Exposure to polychlorinated biphenyls (pcbs) and male reproduction. Syst. Biol. Reprod. Med. 2010, 56 (2), 122−131. (12) Pizarro, G. E. L.; Dzombak, D. A.; Smith, J. R. Evaluation of cleaning and coating techniques for pcb-contaminated concrete. Environ. Prog. 2002, 21 (1), 47−56. (13) Jartun, M.; Ottesen, R. T.; Steinnes, E.; Volden, T. Painted surfaces - important sources of polychlorinated biphenyls (pcbs) contamination to the urban and marine environment. Environ. Pollut. 2009, 157 (1), 295−302. (14) Andersson, M.; Ottesen, R. T.; Volden, T. Building materials as a source of pcb pollution in bergen, norway. Sci. Total Environ. 2004, 325 (1−3), 139−144. (15) Kolarik, B.; Frederiksen, M.; Meyer, H. W.; Ebbehøj, N. E.; Gunnarsen, L. B. Investigation of the importance of tertiary contamination, temperature and human behaviour on pcb concentrations in indoor air. Indoor Built Environ. 2014, DOI: 10.1177/ 1420326X14543505. (16) Guo, Z. S.; Liu, X. Y.; Krebs, K. A.; Greenwell, D. J.; Roache, N. F.; Stinson, R. A.; Nardin, J. A.; R.H, P. Laboratory Study of

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.5b03352. (1) Definition of parameters for error analysis (2) Table S1. PCB concentrations measured in concrete, Masonite, and wooden door frames together with adjacent sealant. (3) Table S2.Values of SL, INT, σINT and σSL from the linear regression. (4) Development of two-term approach. (5) Table S3. Results of D and K for concrete by the twoterm approach. (6) Figure S1. Comparison of predicted PCB concentration in concrete, Masonite and wooden door frame with the measurement. (7) Figure S2. Sensitivity of D and/or K to contacting duration with the sealant (t) and PCB concentration in the sealant (Cm0). (8) Sampling procedure and chemical analyses. (9) Table S4. Influence of L on estimated D for concrete (PDF).

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Phone: +4529100334; e-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Scandinavian Bio-Medical Institute (SBMI, Hørsholm, Denmark) and KAB, the owner of the Farum Midtpunkt housing estate (http://www.kab-bolig.dk/) for their consent to use of their data from PCB measurements in building materials. Furthermore, we thank Thomas Witterseh, and Kathrine Birkemark Olesen from the Danish Technological Institute for consent to use data from PCB measurements in concrete. We thank Dr. Charles Weschler for introducing the 12118

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