Environ. Sci. Technol. 2010, 44, 6789–6794
An Improved Method for Estimating in Situ Sampling Rates of Nonpolar Passive Samplers
In the original PRC method (2, 4), sampling rates (Rs) are estimated from
K E E S B O O I J * ,† A N D F O P P E S M E D E S ‡ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Texel, The Netherlands, and Deltares, P.O. Box 85467, 3508 AL Utrecht, The Netherlands
where N and N0 are the PRC amounts at the end and at the beginning of the exposure, Ksw is the sampler-water partition coefficient (L L-1), Vs is the sampler volume (L), and t is the exposure time. In cases where Ksw is given in volume per mass units (e.g., L kg-1), Vs should be replaced by the sampler mass. The original PRC method suffers from the difficulty that some PRC-based Rs estimates must be rejected due to the fact that the retained amounts are either too close to the detection limit (low logKow range), or too close to the initial amounts (high logKow range). To exclude the contribution of inaccurate Rs estimates, some authors recommended that the amount of retained PRCs should be larger than 20% of the initial amount (to prevent quantification problems near the detection limit) and smaller than 80% (to avoid quantifying insignificant dissipation) (12, 13, 18, 19). In the remainder we will refer to this approach as the 80/20 method. Huckins et al. (18) postulated that f ) N/N0 should conform to
Received April 23, 2010. Revised manuscript received July 15, 2010. Accepted July 16, 2010.
The quality of passive sampling methods for measuring concentrations of dissolved hydrophobic contaminants relies on accurate knowledge of in situ sampling rates. In currently used methods for estimating these sampling rates from the dissipation rates of performance reference compounds (PRCs), the PRCs that show either insignificant or complete dissipation are ignored. We explored the merits of nonlinear leastsquares (NLS) methods for estimating sampling rates, aiming to retain the information stored in PRC data that is neglected in the traditional methods. To this end, we examined the error structure of weighted NLS, unweighted NLS, and the traditional methods, using model simulations. The results show that sampling rates are best estimated using unweighted NLS. Uncertainties in the sampler-water partition coefficients may result in biased estimates that only weakly depend on the number of PRCs being used. The major advantage of unweighted NLS over the traditional method is that sampling rate estimates and uncertainties are available where the traditional method fails, and that the variability of sampling rate estimates is smaller.
Introduction Knowledge of in situ water sampling rates is essential for estimating concentrations of dissolved contaminants from the amounts that are absorbed by passive samplers. These sampling rates depend on the water flow velocities and temperatures prevailing at the exposure sites, and on the amount of biofouling on the sampler surface (1-3). Sampling rates can be estimated from the dissipation rates of performance reference compounds (PRCs), compounds that do not occur in the environment and that are spiked into the passive samplers prior to deployment (2-5). The PRC method relies on the assumption that both the uptake and the release process follow first order kinetics with the same rate constants (isotropic exchange). This assumption appears to be valid for the sampling of hydrophobic contaminants by nonpolar samplers, such as triolein-filled semipermeable membrane devices (SPMDs), Chemcatchers, and low-density polyethylene (LDPE) and silicone strip samplers (1-3, 6-10). The PRC method also has been successfully used for passive sampling of semivolatile contaminants in air (11-14). Diverse evidence exists on isotropic exchange for polar samplers (15-17), and these samplers are therefore not considered in the present study. * Corresponding author tel: +31 222 369 463; fax: +31 222 319 674; e-mail:
[email protected]. † Royal Netherlands Institute for Sea Research. ‡ Deltares. 10.1021/es101321v
2010 American Chemical Society
Published on Web 08/11/2010
Rs ) -
ln(N/N0) t
KswVs
(1)
3CV < f < 1 - 3CV
(2)
where CV is the coefficient of variation of the chemical analysis (expressed as a fraction rather than as a percentage). Smedes (10) suggested that the final concentration should be larger than 10 times the detection limit, and that the retained fraction should be smaller than 1 - 7CV. The above criteria for accepting or rejecting particular PRC-based sampling rate estimates are somewhat arbitrary, and thereby allow investigators to widen or narrow the acceptance window of f, depending on whether they like or dislike the Rs estimates based on particular PRCs. Retention data that fall outside the acceptance window can then only be used to set upper and lower limits to the sampling rates (19). Sampling rates can be estimated using nonlinear leastsquares (NLS) methods, by considering f as a continuous function of Ksw, with Rs as an adjustable parameter
(
f ) exp -
Rst KswVs
)
(3)
In this approach, all PRC retention data can be used to estimate Rs, including the fractions that are close to 0 or 1. Several issues require further study, however. First, the assumption that the independent variable is error free is invalid, because errors in Ksw typically amount to 0.1-0.3 log units. Although methods exist to take errors in both the dependent and the independent variable into account, these methods are complex and require additional assumptions regarding the relative magnitude of these errors (20). Second, it should be decided whether weighted or unweighted NLS should be used. Errors in instrumental analysis typically are expressed as a percentage of the measured amount, which would call for weighted regression. However, the assumption of constant relative errors fails when the measured amounts are close to the detection limit, as is often the case for PRCs with low log Kow values. Third, both Rs and Ksw may be complex functions of the properties of the PRCs (e.g., hydrophobicity, molar volume, molar mass, compound class), particularly when some PRCs follow membrane-controlled uptake and other PRCs are under boundary layer-controlled uptake. VOL. 44, NO. 17, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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The aims of this study were (1) to assess the merits and limitations of NLS for estimating sampling rates compared with the 80/20 method, (2) to quantify the expected uncertainties in the final Rs estimate, and (3) to develop practical guidelines for an improved Rs estimation method.
Theory
models at log Kow > 5 is artificial, and is caused by contaminant sorption to dissolved organic matter present in the calibration setup (4, 7), but this requires further study. Theoretical Rs models take the mass transfer resistance posed by the membrane and by the water boundary layer (WBL) into account. These models take the form
(
) ( )
Error Structure of PRC Data. The variance in Rs (σ2Rs) follows from applying error propagation to eq 1, neglecting the errors in sampler volume and exposure time
1 1 1 ) + Rs AkmKmw Akw
( ) ( ) ( )
where A is the sampler surface area, Kmw is the membranewater partition coefficient, and km and kw are the mass transfer coefficients of the membrane and WBL, respectively. Since km and kw depend on the diffusion coefficient in the respective phases, the sampling rate is a function of both Ksw and molecular size (molar volume or molar mass). Therefore, (at least) two independent variables are needed if eq 9 is used in NLS estimation methods. Booij et al. (21) fitted kw and kmKsw as a function of Kow in an attempt to model Rs as a function of Kow as the only compound property. This semiempirical model was given as
2
σRs Rs
σf ) f ln f
2
+
σKsw
2
(4)
Ksw
where σ2f and σ2Ksw are the variances of the retained PRC fraction and the sampler-water partition coefficient, respectively. The errors in f originate from the errors in the background amounts (σb) and from the analytical repeatability (r). 2 σN ) σb2 + (Nr)2
(5)
(
The variance in f can be expressed as
(( ) ( ) ) (( ) ( ) )
σf2 ) f 2
σN N
2
+
σN0 N0
2
) f2
σb N σb N0
2
+
σb N0
2
+ 2r2 )
( ) (( ) 2
) (
1 1 1 ) + 0.682 -0.044 Rs ABmKow ABwKow
2 σN ) σb2 + (N0r)2 0
+ f2
σb N0
2
)
+ 2r2
(6)
In weighted NLS, the squared residual errors are ideally weighted by 1/σ2f , prior to minimizing their sum. Although the errors in Ksw, N, and N0 all contribute to the errors in Rs, the level at which these errors come into play is different. Laboratories typically use a fixed set of Ksw values (including an adopted temperature dependence) for prolonged time periods. If these values deviate from the true values, then the use of such a Ksw set results in biased Rs estimates. This bias is unique for a given Ksw set. By contrast, the errors in N and N0 are random, and average out over a large number of measurements. The total error in a single Rs determination originates therefore from a constant error due to uncertainties in the Ksw values that are used (the bias), and a random error that is due to uncertainties in the measured values of N and N0 (the variability). Rs Models. A suitable model for Rs and Ksw should be selected before eq 3 can be used to estimate sampling rates by NLS. A number of models exist for the dependency of sampling rates on compound properties. With empirical models, the experimental sampling rates are given as a polynomial in log Kow. For SPMDs, this relationship is given for the range 3 < log Kow < 8.3 as (4)
(9)
)
(10)
where Bm and Bw are empirical parameters, obtained by modeling experimental sampling rates as a function of Kow. The right-hand terms in eq 10 reflect the mass transfer resistances of the membrane and the WBL, respectively (c.f., eq 9). For SPMDs with a 70-µm-thick LDPE membrane, the value of Bm was about 34 nm s-1 (∼ 135 cm d-1) at 25 °C, which leaves Bw as the only parameter to be estimated from the dissipation of PRCs. Rusina et al. (22) showed that silicone-water mass transfer rates are controlled by the WBL at water flow velocities of 0.14 and 9 cm s-1, for compounds with log Kow > 3, and that Rs can be modeled by -0.08 Rs ) βsilKsw
(11)
where Ksw is expressed in L kg-1 units, and Rs is in units of L d-1. The value of the proportionality constant βsil can be determined from PRC dissipation data. Based on theoretical considerations, Booij et al. (21) and Huckins et al. (4) argued that the Rs of SPMDs are simple functions of molecular size, for compounds with log Kow > 4.5 Rs ) βMWMW -0.35
(12)
-0.39 Rs ) βVV LeBas
(13)
For the Chemcatcher, a similar equation has been reported for the range 3.8 < log Kow < 7 (7)
where MW is the analyte molecular weight, VLeBas is the LeBas molar volume, and βMW and βV are proportionality constants. The value of the constants β in eqs 11-13 can be estimated from PRC dissipation data. Ksw Models. Models for estimating log Ksw values for some commonly used samplers are summarized in Table 1. Most log Ksw data are given as a function of log Kow, but Smedes et al. (23) showed that the molecular weight of PAHs and PCBs is a better descriptor for five silicone rubbers and for LDPE.
log Rs ) a0,CC + 22.755 log Kow - 4.061(log Kow)2 +
Experimental Section
log Rs ) a0,SPMD + 2.244 log Kow - 0.3173(log Kow)2 + 0.013(log Kow)3 (7)
0.2318(log Kow)
3
(8)
The constants a0 represent the exposure-specific effect, and the other terms reflect the compound-specific effect. The value of a0 may be estimated from PRC dissipation data by substituting eq 7 or 8 in eq 3. It has been speculated that the large drop in Rs that is predicted by these empirical Rs 6790
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To examine the errors involved in Rs estimation by NLS compared with the 80/20 method, a number of model simulations were carried out. PRC retention data were generated for SPMDs using Ksw values from eq 20 and Rs values from the semiempirical eq 10, adopting a value of Bm ) 34 nm s-1 (21), a sampler surface area of 460 cm2, a volume of 0.00495 L, and an exposure time of 30 d, for PRCs with true
TABLE 1. Models to Predict Sampler-Water Partition Coefficients (Ksw) of Some Commonly Used Passive Samplers sampler
R2
Ksw model
s
n
range
eq
LDPE (24)
log Ksw ) 1.05 log Kow - 0.59
0.92
-
89
3 < log Kow < 7
14
LDPE (23)
PCBs: log Ksw ) 0.0153MW + 1.23 a PAHs: log Ksw ) 0.0307MW - 1.19
0.94 0.99
0.20 0.13
41 26
223 < MW < 464 128 < MW < 300
15
PDMS (5)
log Ksw ) 1.060log Kow - 1.39
0.92
0.36
74
3 < log Kow < 7
16
silicone, Altec translucent (23)
PCBs: log Ksw ) 0.0128MW + 2.09 a
0.95
0.15
41
223 < MW < 464
17
PAHs: log Ksw ) 0.0205MW + 0.47
0.99
0.13
26
128 < MW < 300
Chemcatcher (6)
log Ksw ) 1.382 log Kow - 1.77
0.97
0.13
31
4< log Kow < 5
18
SPMDs (4)
log Ksw ) -0.1618 (log Kow)2 +
0.94
0.25
45
2 < log Kow < 7
19
0.99
0.16
8
4 < log Kow < 8
20
2.321 log Kow - 2.61 SPMDs (Booij, unpublished data) a
log Ksw ) 0.988log Kow + 0.33
More precise models that account for differences in chlorine substitution patterns in PCBs are available from the same reference.
log Kow values between 3 and 7. Sampling rates spanned a range of 1 to 20 L d-1 (evaluated at an arbitrarily chosen log Kow value of 5). After choosing a specific Rs, the true value of ABw was calculated from eq 10. Subsequently, the Rs and Ksw values were calculated for all PRCs and the true values of the retained PRC amounts were calculated from eq 3. For each sampling rate, nk log Kow sets were generated by adding random errors (δlog Kow) to the true log Kow values δlog Kow ) [rnormal]σlog Kow
(21)
where [rnormal] is a random normal number with zero mean and unit variance, and σlogKow is the standard error in log Kow. For each logKow set, nN repetitive experiments were simulated by adding errors δN to the true PRC amounts δN ) [rnormal]1σb + [rnormal]2rN
(22)
Errors in the initial amounts were added similarly. Throughout, we adopted average background levels equal to zero, which is equivalent to applying perfect background subtraction for all PRCs. For each experiment, log ABw was estimated by weighted and unweighted NLS (using all PRC data), and by the 80/20 method. The reciprocal variance in f (eq 6) was used as a weight factor, where applicable. The errors in the log ABw estimates were calculated by subtracting the true value of log ABw. The bias and the variability associated with each log Kow set were calculated as the average and the standard deviation of the errors in log ABw, taken over the nN repetitive experiments. Finally, the median bias was evaluated from the distribution of bias estimates (taken over all log Kow sets and all sampling rates). The 95% confidence range was evaluated from the 2.5% and 97.5% percentiles of the distribution. Median variability and 95% confidence range
of the variability estimates were calculated similarly. The errors in log Rs are essentially equal to those in log ABw, because the sampling rates are controlled by the WBL for all sampling rates that were investigated (>99% WBL control at Rs ) 2 L d-1 and >88% at Rs ) 20 L d-1 for PRCs with log Kow > 4.5). This also means that the term ABm and its associated errors are of minor importance. All model simulations were run using the statistical package R version 2.8.0 (25). The model code is listed in the Supporting Information (section S4). A typical example of PRC retention data generated in the model simulations is shown in Figure 1.
Results and Discussion Weighted versus Unweighted NLS. An important feature of weighted NLS is that the probability of a large bias is higher than for unweighted NLS (Figure 2). We recall that that the bias originates from the use of erroneous log Kow values. If the adopted log Kow value for a particular PRC is higher than its true value, then this causes log ABw to be overestimated (i.e., the curve of f versus log Kow in Figure 1 is shifted to the right). The errors in the log Kow values for multiple PRCs average out to some extent, because the probability that some adopted log Kow values are too high and others are too low is larger than the probability that all adopted log Kow values are too high or too low. In weighted NLS this averaging out is less efficient than in unweighted NLS, because PRCs with low f values have a higher weight. This is further illustrated in Figure 3. With 5 PRCs (log Kow spacing between successive PRCs ) 1), the widths of the bias distributions are comparable for weighted and unweighted NLS. Increasing the number of PRCs reduces the width of the bias distributions, but this effect is only minor for weighted NLS. The median variability for weighted NLS is somewhat smaller (0.01 log units) than for unweighted NLS, and the width of the VOL. 44, NO. 17, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Example of PRC retention data generated in the model simulations. The drawn line represents the error-free retained PRC fractions for Rs ) 15 L d-1. Data points show the PRC data for ten simulations with three log Kow sets (different symbol for each set). Other model parameters: σlogKow ) 0.2, σb ) 0.005 × N0, r ) 0.05. The data shown yields three estimates of bias and variability, where each estimate is based on ten observations. variability distribution is similar for both methods (0.02 log units difference for the upper confidence interval, Figure 3). We recommend the use of unweighted NLS rather than weighted NLS, because the former method minimizes the risk of a high bias. An additional problem with weighted NLS is that it may be difficult to obtain the correct weight factors for PRCs that are almost completely dissipated. The amounts of these PRCs are low, but the chemical background at the end of the exposure may be high. As a result, both the average background levels and the standard deviations of these levels may be site specific, and can only be obtained by exposing multiple samplers without PRCs at the exposure sites. The cost of this extra effort may well be prohibitive. Evidently, the chemical background should always be carefully examined, because the
results with unweighted NLS may also be affected by matrix interferences in the PRC quantitation. The occurrence of substantial interferences may result in large residual errors in the NLS analysis. For example, f values of 1.14 may be perfectly acceptable for very hydrophobic PRCs, when the analytical precision is 5%, but f estimates >1.3 clearly are problematic. Similarly, f values of 0.2 at the low log Kow end may be indicative of matrix interferences if neighboring PRCs have retained fractions around zero. Unweighted NLS versus the 80/20 Method. The bias distributions for unweighted NLS are up to 0.4 log units narrower than for the 80/20 method (Figures 2 and 3). The median variability is smaller for unweighted NLS by 0.03 log units. The most important advantage of unweighted NLS over the 80/20 method, however, lies in the availability of log ABw estimates and their uncertainties. Using 5 PRCs with log Kow values in the range 3-7, the 80/20 method gave no results at all in 5% of the cases (clustered at Rs values between 3 and 6 L d-1), because all retained fractions fell outside the 20-80% interval. For another 92% of the cases, the log ABw estimate was based on only one PRC. Uncertainty estimates for individual exposure simulations were only available for 3% of the cases. By contrast, NLS always yielded both an estimate of log ABw and an uncertainty in this estimate. For the case of 9 PRCs, all methods yielded an estimate of log ABw, but an uncertainty estimate was not available for the 80/20 method in 26% of the cases. Another relevant question is to what extent the uncertainty estimate from a single simulation is representative of the true variability that is estimated from repetitive simulations within a particular log Kow set. To address this question, we evaluated the ratio of standard deviations (estimate of the standard error from an individual simulation divided by the standard deviation of log ABw estimates within the corresponding log Kow set). Median s-ratios increase from 1 at σlogKow ) 0 to about 3 at σlogKow ) 0.4 (Figure 3), indicating that the variability estimates for individual experiments typically are higher than the true variability. Summarizing, unweighted NLS is preferred over the 80/ 20 method, because (1) unweighted NLS always yields log ABw estimates as well as the uncertainties in these estimates,
FIGURE 2. Bias and variability of log ABw estimates (∼ log Rs estimates) from simulated PRC data, using three estimation methods. Model parameters: σlogKow ) 0.2, σb ) 0.005 × N0, r ) 0.05, 30 log Kow sets per sampling rate, 30 simulations per log Kow set, 9 PRCs (log Kow spacing 0.5). 6792
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FIGURE 3. Bias, variability, and ratio of standard deviations (see text) for the log ABw estimates (∼ log Rs estimates) obtained for the 80/20 method, unweighted NLS, and weighted NLS, as a function of the uncertainty in the log Kow values for the case of 5 (circles), 9 (squares), and 17 (crosses) PRCs (∼log Kow increments between successive PRCs of 1, 0.5, and 0.25). Model parameters: r ) 0.05, σb ) 0.005 × N0, 20 sampling rates in the range 1-20 L d-1, 30 log Kow sets, 30 simulations per log Kow set. Data points are slightly shifted in the x-direction to make the error bars better visible. Error bars span the 2.5-97.5% percentiles.
and (2) because the variability of results from unweighted NLS is smaller. Application to Other Rs and Ksw Models. Although the errors in Rs estimation using the PRC approach were evaluated using eq 10 as a Rs model and eq 20 as a Ksw model, the same principles apply when other models are used. It can be argued that the model Rs ) constant would perform equally well, because the sampling rate is relatively constant over the range where the retained PRC fractions drop from 1 to 0. However, the estimated sampling rate is later used to calculate aqueous concentrations of compounds that are taken up by the sampler. If compound-dependent sampling rates are used in these calculations, then the exposure specific effect (i.e., ABw in eq 10, or βsil in eq 11) first has to be calculated from the PRC-based Rs estimate. It is therefore more straightforward to estimate the exposure-specific effect immediately from the PRC data. Thus, the model Rs ) constant only has an advantage when the compound-specific effect on the sampling rates can be neglected throughout. The sampling rate models eqs 7-13 all have one adjustable parameter that can be used for modeling PRC dissipation data and for calculating sampling rates of other compounds. Because these adjustable parameters are difficult to interpret, we recommend that the sampling rate at log Kow ) 5 or log Ksw ) 5 be reported for each exposure, to help readers appreciate the approximate value of the sampling rates. It is appealing to use Rs models and Ksw models that are based on the same compound property (e.g., both are given as a function of log Kow, or both as a function of MW), because this allows to present experimental and estimated PRC fractions in a 2D scatter plot. However, NLS methods have no difficulty in handling multiple independent variables, e.g., compound-dependent log Ksw-MW correlations (eqs 15 and 17) as a Ksw model, and Rs ) βV VLeBas-0.39 as a sampling rate model. With multiple independent variables, the quality of the fit can then be graphically inspected by plotting the residual errors versus one of the independent variables. Implementation of NLS can be done with statistics software, or with spreadsheet operations using the solver function (26). Examples of the implementation of NLS for estimating sampling rates in R are given in the Supporting Information (Sections S2, S3), and an implementation using spreadsheet operations is available from the authors. Three examples of applying NLS to PRC data are shown in Figure 4. The example for SPMDs (Figure 4, left panel) was taken from a previous study (1). The 80/20 method yields a log ABw estimate of 0.97, which corresponds to an Rs of 5.4 L d-1 at log Kow )5. Because there is only one acceptable data point (at f ) 0.4), there is no uncertainty estimate available. Unweighted NLS gives log ABw ) 0.95 ( 0.03, corresponding to Rs ) 5.1 ( 0.3 L d-1 at log Kow ) 5. The use of the quadratic
FIGURE 4. Example of retained PRC fractions and model fit for water sampling by SPMDs (left) and Altesil silicone rubber (middle), and for air sampling by PUF disks (right). The drawn lines represent the best NLS fit. VOL. 44, NO. 17, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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log Ksw - log Kow correlation (eq 19) gave a poor description of these data (Supporting Information, S1). The second example was taken from a passive sampling trial survey for silicone sheets (Figure 4, middle panel). The PRC data were modeled using eq 11 as an Rs model and experimental values of Ksw (23). The 80/20 method yielded log βsil ) 1.51 ( 0.04 (Rs ) 12.9 ( 1.1 L d-1 at log Ksw ) 5). Unweighted NLS yielded log βsil ) 1.46 ( 0.03 (Rs ) 11.6 ( 0.7 L d-1 at log Ksw ) 5). The third example (Figure 4 right panel) was taken from a study on passive air sampling with polyurethane (PUF) disks (13), using the model Rs ) constant (27). The 80/20 method gave Rs ) 4.2 m3 d-1 (no uncertainty estimate), based on the retention of γ-HCH-d6 (f ) 0.404). Unweighted NLS gave Rs ) 5.0 ( 0.6 m3 d-1. The improved Rs estimation method guarantees that sampling rates and their associated uncertainties can always be estimated from PRC dissipation data. Efforts to reduce the bias and variability in these estimates should primarily focus on reducing the uncertainties in the Ksw values of the PRCs. Increasing the number of PRCs that are used has a smaller effect (Figure 3). An additional contribution to the bias may originate from the use of inappropriate Rs models. Because Rs models all contain parameters that account for compound-specific and exposure-specific effects, we expect that improved Rs models can easily be implemented in the proposed NLS method.
Acknowledgments This work was supported by the Royal Netherlands Institute for Sea Research and Deltares. We thank three anonymous reviewers for making valuable suggestions for improvement of the original manuscript.
Supporting Information Available Poor results obtained with the quadratic log Ksw-log Kow correlation for SPMDs, R code for Rs estimation with NLS for SPMDs and silicone sheets, R code for the model simulations. This information is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Booij, K.; van Bommel, R.; Mets, A.; Dekker, R. Little effect of excessive biofouling on the uptake of organic contaminants by semipermeable membrane devices. Chemosphere 2006, 65, 2485–2492. (2) Huckins, J. N.; Petty, J. D.; Lebo, J. A.; Almeida, F. V.; Booij, K.; Alvarez, D. A.; Cranor, W. L.; Clark, R. C.; Mogensen, B. B. Development of the permeability/performance reference compound approach for in situ calibration of semipermeable membrane devices. Environ. Sci. Technol. 2002, 36, 85–91. (3) Booij, K.; Sleiderink, H. M.; Smedes, F. Calibrating the uptake kinetics of semipermeable membrane devices using exposure standards. Environ. Toxicol. Chem. 1998, 17, 1236–1245. (4) Huckins, J. N.; Petty, J. D.; Booij, K. Monitors of Organic Chemicals in the Environment: Semipermeable Membrane Devices; Springer: New York, 2006. (5) Booij, K.; Vrana, B.; Huckins, J. N. Theory, modelling and calibration of passive samplers used in water monitoring. In Passive Sampling Techniques in Environmental Monitoring; Greenwood, R., Mills, G. A., Vrana, B., Eds.; Elsevier: Amsterdam, 2007; pp 141-169. (6) Vrana, B.; Mills, G. A.; Dominiak, E.; Greenwood, R. Calibration of the Chemcatcher passive sampler for the monitoring of priority organic pollutants in water. Environ. Pollut. 2006, 142, 333–343. (7) Vrana, B.; Mills, G. A.; Kotterman, M.; Leonards, P.; Booij, K.; Greenwood, R. Modelling and field application of the Chemcatcher passive sampler calibration data for the monitoring of hydrophobic organic pollutants in water. Environ. Pollut. 2007, 145, 895–904.
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